Properties

Label 252.4.t.a.89.1
Level $252$
Weight $4$
Character 252.89
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + 14344616 x^{9} - 18123280 x^{8} - 273588032 x^{7} + 1239640536 x^{6} - 1407381792 x^{5} - 1961185792 x^{4} + 4297169408 x^{3} + 2991779296 x^{2} - 11217342336 x + 7375227456\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.1
Root \(4.65022 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.89
Dual form 252.4.t.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-10.1259 + 17.5386i) q^{5} +(12.0269 + 14.0838i) q^{7} +O(q^{10})\) \(q+(-10.1259 + 17.5386i) q^{5} +(12.0269 + 14.0838i) q^{7} +(-15.4532 + 8.92191i) q^{11} -33.1829i q^{13} +(-22.9077 - 39.6772i) q^{17} +(-35.0091 - 20.2125i) q^{19} +(-69.7804 - 40.2877i) q^{23} +(-142.568 - 246.935i) q^{25} +233.844i q^{29} +(-195.398 + 112.813i) q^{31} +(-368.793 + 68.3228i) q^{35} +(135.456 - 234.617i) q^{37} -154.432 q^{41} +367.102 q^{43} +(-263.852 + 457.006i) q^{47} +(-53.7086 + 338.769i) q^{49} +(78.8892 - 45.5467i) q^{53} -361.370i q^{55} +(-312.768 - 541.729i) q^{59} +(-78.8343 - 45.5150i) q^{61} +(581.982 + 336.007i) q^{65} +(-431.509 - 747.395i) q^{67} -303.596i q^{71} +(-999.127 + 576.846i) q^{73} +(-311.508 - 110.338i) q^{77} +(3.48120 - 6.02961i) q^{79} +815.694 q^{83} +927.844 q^{85} +(155.494 - 269.323i) q^{89} +(467.343 - 399.087i) q^{91} +(708.998 - 409.340i) q^{95} +1832.92i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{7} + O(q^{10}) \) \( 16q - 4q^{7} - 72q^{19} - 212q^{25} - 708q^{31} + 76q^{37} + 1408q^{43} + 400q^{49} - 1632q^{61} - 1528q^{67} - 2700q^{73} - 364q^{79} + 7392q^{85} + 2472q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) −10.1259 + 17.5386i −0.905689 + 1.56870i −0.0856984 + 0.996321i \(0.527312\pi\)
−0.819990 + 0.572378i \(0.806021\pi\)
\(6\) 0 0
\(7\) 12.0269 + 14.0838i 0.649390 + 0.760455i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −15.4532 + 8.92191i −0.423574 + 0.244551i −0.696605 0.717455i \(-0.745307\pi\)
0.273031 + 0.962005i \(0.411974\pi\)
\(12\) 0 0
\(13\) 33.1829i 0.707945i −0.935256 0.353973i \(-0.884831\pi\)
0.935256 0.353973i \(-0.115169\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −22.9077 39.6772i −0.326819 0.566067i 0.655060 0.755577i \(-0.272643\pi\)
−0.981879 + 0.189510i \(0.939310\pi\)
\(18\) 0 0
\(19\) −35.0091 20.2125i −0.422718 0.244056i 0.273522 0.961866i \(-0.411811\pi\)
−0.696239 + 0.717810i \(0.745145\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −69.7804 40.2877i −0.632618 0.365242i 0.149147 0.988815i \(-0.452347\pi\)
−0.781765 + 0.623573i \(0.785680\pi\)
\(24\) 0 0
\(25\) −142.568 246.935i −1.14054 1.97548i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 233.844i 1.49737i 0.662926 + 0.748685i \(0.269314\pi\)
−0.662926 + 0.748685i \(0.730686\pi\)
\(30\) 0 0
\(31\) −195.398 + 112.813i −1.13208 + 0.653607i −0.944457 0.328635i \(-0.893412\pi\)
−0.187623 + 0.982241i \(0.560078\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −368.793 + 68.3228i −1.78107 + 0.329962i
\(36\) 0 0
\(37\) 135.456 234.617i 0.601860 1.04245i −0.390679 0.920527i \(-0.627760\pi\)
0.992539 0.121925i \(-0.0389069\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −154.432 −0.588248 −0.294124 0.955767i \(-0.595028\pi\)
−0.294124 + 0.955767i \(0.595028\pi\)
\(42\) 0 0
\(43\) 367.102 1.30192 0.650960 0.759112i \(-0.274366\pi\)
0.650960 + 0.759112i \(0.274366\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −263.852 + 457.006i −0.818869 + 1.41832i 0.0876480 + 0.996152i \(0.472065\pi\)
−0.906517 + 0.422170i \(0.861268\pi\)
\(48\) 0 0
\(49\) −53.7086 + 338.769i −0.156585 + 0.987665i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 78.8892 45.5467i 0.204458 0.118044i −0.394275 0.918992i \(-0.629004\pi\)
0.598733 + 0.800949i \(0.295671\pi\)
\(54\) 0 0
\(55\) 361.370i 0.885947i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −312.768 541.729i −0.690150 1.19538i −0.971788 0.235855i \(-0.924211\pi\)
0.281638 0.959521i \(-0.409122\pi\)
\(60\) 0 0
\(61\) −78.8343 45.5150i −0.165470 0.0955344i 0.414978 0.909832i \(-0.363789\pi\)
−0.580448 + 0.814297i \(0.697123\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 581.982 + 336.007i 1.11055 + 0.641178i
\(66\) 0 0
\(67\) −431.509 747.395i −0.786823 1.36282i −0.927904 0.372820i \(-0.878391\pi\)
0.141080 0.989998i \(-0.454942\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 303.596i 0.507468i −0.967274 0.253734i \(-0.918341\pi\)
0.967274 0.253734i \(-0.0816587\pi\)
\(72\) 0 0
\(73\) −999.127 + 576.846i −1.60190 + 0.924859i −0.610797 + 0.791787i \(0.709151\pi\)
−0.991106 + 0.133072i \(0.957516\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −311.508 110.338i −0.461035 0.163300i
\(78\) 0 0
\(79\) 3.48120 6.02961i 0.00495779 0.00858715i −0.863536 0.504287i \(-0.831755\pi\)
0.868494 + 0.495700i \(0.165089\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 815.694 1.07872 0.539362 0.842074i \(-0.318666\pi\)
0.539362 + 0.842074i \(0.318666\pi\)
\(84\) 0 0
\(85\) 927.844 1.18399
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 155.494 269.323i 0.185194 0.320766i −0.758448 0.651734i \(-0.774042\pi\)
0.943642 + 0.330968i \(0.107375\pi\)
\(90\) 0 0
\(91\) 467.343 399.087i 0.538361 0.459733i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 708.998 409.340i 0.765701 0.442078i
\(96\) 0 0
\(97\) 1832.92i 1.91861i 0.282370 + 0.959305i \(0.408879\pi\)
−0.282370 + 0.959305i \(0.591121\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 721.053 + 1248.90i 0.710371 + 1.23040i 0.964718 + 0.263285i \(0.0848060\pi\)
−0.254347 + 0.967113i \(0.581861\pi\)
\(102\) 0 0
\(103\) 928.361 + 535.989i 0.888098 + 0.512744i 0.873320 0.487147i \(-0.161962\pi\)
0.0147781 + 0.999891i \(0.495296\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −722.125 416.919i −0.652434 0.376683i 0.136954 0.990577i \(-0.456269\pi\)
−0.789388 + 0.613894i \(0.789602\pi\)
\(108\) 0 0
\(109\) 922.514 + 1597.84i 0.810650 + 1.40409i 0.912410 + 0.409278i \(0.134219\pi\)
−0.101760 + 0.994809i \(0.532447\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1388.90i 1.15626i −0.815946 0.578128i \(-0.803784\pi\)
0.815946 0.578128i \(-0.196216\pi\)
\(114\) 0 0
\(115\) 1413.18 815.899i 1.14591 0.661591i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 283.300 799.821i 0.218236 0.616130i
\(120\) 0 0
\(121\) −506.299 + 876.936i −0.380390 + 0.658855i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3243.04 2.32053
\(126\) 0 0
\(127\) −838.992 −0.586208 −0.293104 0.956080i \(-0.594688\pi\)
−0.293104 + 0.956080i \(0.594688\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −195.038 + 337.815i −0.130080 + 0.225306i −0.923707 0.383099i \(-0.874857\pi\)
0.793627 + 0.608405i \(0.208190\pi\)
\(132\) 0 0
\(133\) −136.380 736.155i −0.0889149 0.479946i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1191.72 + 688.039i −0.743178 + 0.429074i −0.823224 0.567717i \(-0.807827\pi\)
0.0800456 + 0.996791i \(0.474493\pi\)
\(138\) 0 0
\(139\) 953.705i 0.581958i 0.956729 + 0.290979i \(0.0939810\pi\)
−0.956729 + 0.290979i \(0.906019\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 296.055 + 512.782i 0.173128 + 0.299867i
\(144\) 0 0
\(145\) −4101.29 2367.88i −2.34892 1.35615i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2198.94 + 1269.56i 1.20902 + 0.698029i 0.962546 0.271120i \(-0.0873939\pi\)
0.246476 + 0.969149i \(0.420727\pi\)
\(150\) 0 0
\(151\) 515.001 + 892.008i 0.277551 + 0.480733i 0.970776 0.239989i \(-0.0771439\pi\)
−0.693225 + 0.720722i \(0.743811\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4569.33i 2.36786i
\(156\) 0 0
\(157\) 1558.78 899.959i 0.792381 0.457481i −0.0484190 0.998827i \(-0.515418\pi\)
0.840800 + 0.541346i \(0.182085\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −271.834 1467.31i −0.133065 0.718262i
\(162\) 0 0
\(163\) −1312.03 + 2272.50i −0.630466 + 1.09200i 0.356991 + 0.934108i \(0.383803\pi\)
−0.987457 + 0.157891i \(0.949531\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −714.138 −0.330908 −0.165454 0.986217i \(-0.552909\pi\)
−0.165454 + 0.986217i \(0.552909\pi\)
\(168\) 0 0
\(169\) 1095.89 0.498813
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −373.785 + 647.415i −0.164268 + 0.284520i −0.936395 0.350948i \(-0.885859\pi\)
0.772127 + 0.635468i \(0.219193\pi\)
\(174\) 0 0
\(175\) 1763.14 4977.76i 0.761606 2.15019i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3797.55 + 2192.52i −1.58571 + 0.915511i −0.591710 + 0.806151i \(0.701547\pi\)
−0.994002 + 0.109360i \(0.965120\pi\)
\(180\) 0 0
\(181\) 2143.42i 0.880215i 0.897945 + 0.440107i \(0.145060\pi\)
−0.897945 + 0.440107i \(0.854940\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2743.23 + 4751.41i 1.09020 + 1.88827i
\(186\) 0 0
\(187\) 707.993 + 408.760i 0.276864 + 0.159848i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4030.20 2326.84i −1.52678 0.881486i −0.999494 0.0317981i \(-0.989877\pi\)
−0.527285 0.849688i \(-0.676790\pi\)
\(192\) 0 0
\(193\) 1052.69 + 1823.32i 0.392614 + 0.680028i 0.992793 0.119838i \(-0.0382374\pi\)
−0.600179 + 0.799866i \(0.704904\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 707.475i 0.255866i −0.991783 0.127933i \(-0.959166\pi\)
0.991783 0.127933i \(-0.0408342\pi\)
\(198\) 0 0
\(199\) −1115.28 + 643.907i −0.397287 + 0.229374i −0.685313 0.728249i \(-0.740334\pi\)
0.288026 + 0.957623i \(0.407001\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3293.42 + 2812.41i −1.13868 + 0.972377i
\(204\) 0 0
\(205\) 1563.76 2708.51i 0.532770 0.922785i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 721.336 0.238736
\(210\) 0 0
\(211\) 1193.83 0.389509 0.194755 0.980852i \(-0.437609\pi\)
0.194755 + 0.980852i \(0.437609\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3717.24 + 6438.46i −1.17913 + 2.04232i
\(216\) 0 0
\(217\) −3938.86 1395.16i −1.23220 0.436451i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1316.61 + 760.144i −0.400745 + 0.231370i
\(222\) 0 0
\(223\) 420.089i 0.126149i −0.998009 0.0630745i \(-0.979909\pi\)
0.998009 0.0630745i \(-0.0200906\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −483.829 838.016i −0.141466 0.245027i 0.786583 0.617485i \(-0.211848\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(228\) 0 0
\(229\) −3018.69 1742.84i −0.871096 0.502927i −0.00338359 0.999994i \(-0.501077\pi\)
−0.867712 + 0.497067i \(0.834410\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1814.94 + 1047.86i 0.510305 + 0.294625i 0.732959 0.680273i \(-0.238139\pi\)
−0.222654 + 0.974897i \(0.571472\pi\)
\(234\) 0 0
\(235\) −5343.49 9255.19i −1.48328 2.56912i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6892.95i 1.86555i −0.360453 0.932777i \(-0.617378\pi\)
0.360453 0.932777i \(-0.382622\pi\)
\(240\) 0 0
\(241\) −2348.99 + 1356.19i −0.627850 + 0.362489i −0.779919 0.625881i \(-0.784740\pi\)
0.152069 + 0.988370i \(0.451406\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5397.68 4372.32i −1.40753 1.14015i
\(246\) 0 0
\(247\) −670.710 + 1161.70i −0.172778 + 0.299261i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6334.19 1.59287 0.796435 0.604724i \(-0.206716\pi\)
0.796435 + 0.604724i \(0.206716\pi\)
\(252\) 0 0
\(253\) 1437.77 0.357281
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2395.68 + 4149.44i −0.581472 + 1.00714i 0.413833 + 0.910353i \(0.364190\pi\)
−0.995305 + 0.0967867i \(0.969144\pi\)
\(258\) 0 0
\(259\) 4933.41 913.966i 1.18358 0.219270i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −200.111 + 115.534i −0.0469177 + 0.0270879i −0.523275 0.852164i \(-0.675290\pi\)
0.476358 + 0.879252i \(0.341957\pi\)
\(264\) 0 0
\(265\) 1844.81i 0.427644i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2356.86 4082.21i −0.534203 0.925266i −0.999201 0.0399551i \(-0.987279\pi\)
0.464999 0.885311i \(-0.346055\pi\)
\(270\) 0 0
\(271\) −3251.50 1877.26i −0.728836 0.420794i 0.0891599 0.996017i \(-0.471582\pi\)
−0.817996 + 0.575223i \(0.804915\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4406.26 + 2543.96i 0.966209 + 0.557841i
\(276\) 0 0
\(277\) 757.120 + 1311.37i 0.164227 + 0.284450i 0.936381 0.350986i \(-0.114154\pi\)
−0.772153 + 0.635436i \(0.780820\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4418.40i 0.938005i 0.883197 + 0.469003i \(0.155387\pi\)
−0.883197 + 0.469003i \(0.844613\pi\)
\(282\) 0 0
\(283\) −4219.93 + 2436.38i −0.886391 + 0.511758i −0.872760 0.488149i \(-0.837672\pi\)
−0.0136304 + 0.999907i \(0.504339\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1857.33 2174.99i −0.382003 0.447337i
\(288\) 0 0
\(289\) 1406.98 2436.96i 0.286378 0.496022i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 340.271 0.0678458 0.0339229 0.999424i \(-0.489200\pi\)
0.0339229 + 0.999424i \(0.489200\pi\)
\(294\) 0 0
\(295\) 12668.2 2.50025
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1336.86 + 2315.52i −0.258571 + 0.447859i
\(300\) 0 0
\(301\) 4415.09 + 5170.21i 0.845454 + 0.990053i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1596.54 921.761i 0.299729 0.173049i
\(306\) 0 0
\(307\) 7302.13i 1.35751i 0.734366 + 0.678754i \(0.237480\pi\)
−0.734366 + 0.678754i \(0.762520\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 372.538 + 645.255i 0.0679251 + 0.117650i 0.897988 0.440020i \(-0.145029\pi\)
−0.830063 + 0.557670i \(0.811695\pi\)
\(312\) 0 0
\(313\) 689.742 + 398.223i 0.124558 + 0.0719133i 0.560984 0.827827i \(-0.310423\pi\)
−0.436427 + 0.899740i \(0.643756\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 974.487 + 562.621i 0.172658 + 0.0996843i 0.583839 0.811870i \(-0.301550\pi\)
−0.411180 + 0.911554i \(0.634883\pi\)
\(318\) 0 0
\(319\) −2086.33 3613.64i −0.366183 0.634247i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1852.09i 0.319049i
\(324\) 0 0
\(325\) −8194.03 + 4730.82i −1.39853 + 0.807443i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9609.71 + 1780.30i −1.61034 + 0.298331i
\(330\) 0 0
\(331\) −11.1216 + 19.2632i −0.00184683 + 0.00319880i −0.866947 0.498400i \(-0.833921\pi\)
0.865101 + 0.501599i \(0.167255\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 17477.7 2.85047
\(336\) 0 0
\(337\) 9570.35 1.54697 0.773487 0.633812i \(-0.218511\pi\)
0.773487 + 0.633812i \(0.218511\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2013.01 3486.64i 0.319680 0.553702i
\(342\) 0 0
\(343\) −5417.11 + 3317.91i −0.852759 + 0.522304i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9927.17 5731.45i 1.53579 0.886688i 0.536709 0.843767i \(-0.319667\pi\)
0.999078 0.0429203i \(-0.0136662\pi\)
\(348\) 0 0
\(349\) 1575.13i 0.241590i 0.992677 + 0.120795i \(0.0385443\pi\)
−0.992677 + 0.120795i \(0.961456\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2316.74 + 4012.71i 0.349313 + 0.605028i 0.986128 0.165989i \(-0.0530816\pi\)
−0.636814 + 0.771017i \(0.719748\pi\)
\(354\) 0 0
\(355\) 5324.64 + 3074.18i 0.796064 + 0.459608i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2062.64 1190.86i −0.303236 0.175073i 0.340660 0.940187i \(-0.389350\pi\)
−0.643896 + 0.765113i \(0.722683\pi\)
\(360\) 0 0
\(361\) −2612.41 4524.83i −0.380873 0.659692i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 23364.4i 3.35054i
\(366\) 0 0
\(367\) −990.766 + 572.019i −0.140920 + 0.0813601i −0.568802 0.822474i \(-0.692593\pi\)
0.427882 + 0.903834i \(0.359260\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1590.26 + 563.278i 0.222540 + 0.0788246i
\(372\) 0 0
\(373\) 205.226 355.461i 0.0284884 0.0493434i −0.851430 0.524469i \(-0.824264\pi\)
0.879918 + 0.475125i \(0.157597\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7759.63 1.06006
\(378\) 0 0
\(379\) −6400.00 −0.867403 −0.433702 0.901057i \(-0.642793\pi\)
−0.433702 + 0.901057i \(0.642793\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1742.19 3017.57i 0.232433 0.402586i −0.726090 0.687599i \(-0.758665\pi\)
0.958524 + 0.285013i \(0.0919980\pi\)
\(384\) 0 0
\(385\) 5089.47 4346.15i 0.673723 0.575325i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3641.68 2102.53i 0.474654 0.274042i −0.243532 0.969893i \(-0.578306\pi\)
0.718186 + 0.695851i \(0.244973\pi\)
\(390\) 0 0
\(391\) 3691.59i 0.477472i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 70.5006 + 122.111i 0.00898043 + 0.0155546i
\(396\) 0 0
\(397\) −4699.38 2713.19i −0.594093 0.343000i 0.172621 0.984988i \(-0.444776\pi\)
−0.766714 + 0.641989i \(0.778110\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7357.88 + 4248.07i 0.916297 + 0.529024i 0.882452 0.470403i \(-0.155891\pi\)
0.0338449 + 0.999427i \(0.489225\pi\)
\(402\) 0 0
\(403\) 3743.47 + 6483.87i 0.462718 + 0.801451i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4834.10i 0.588741i
\(408\) 0 0
\(409\) 5581.42 3222.44i 0.674776 0.389582i −0.123108 0.992393i \(-0.539286\pi\)
0.797884 + 0.602811i \(0.205953\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3868.01 10920.3i 0.460853 1.30109i
\(414\) 0 0
\(415\) −8259.64 + 14306.1i −0.976987 + 1.69219i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14198.4 −1.65546 −0.827728 0.561130i \(-0.810367\pi\)
−0.827728 + 0.561130i \(0.810367\pi\)
\(420\) 0 0
\(421\) 6986.18 0.808754 0.404377 0.914592i \(-0.367488\pi\)
0.404377 + 0.914592i \(0.367488\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6531.80 + 11313.4i −0.745503 + 1.29125i
\(426\) 0 0
\(427\) −307.104 1657.69i −0.0348052 0.187872i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12104.1 + 6988.29i −1.35274 + 0.781007i −0.988633 0.150349i \(-0.951960\pi\)
−0.364111 + 0.931356i \(0.618627\pi\)
\(432\) 0 0
\(433\) 4418.70i 0.490414i −0.969471 0.245207i \(-0.921144\pi\)
0.969471 0.245207i \(-0.0788559\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1628.63 + 2820.87i 0.178279 + 0.308789i
\(438\) 0 0
\(439\) 2497.13 + 1441.72i 0.271484 + 0.156742i 0.629562 0.776950i \(-0.283234\pi\)
−0.358078 + 0.933692i \(0.616568\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11013.8 + 6358.80i 1.18122 + 0.681976i 0.956296 0.292400i \(-0.0944540\pi\)
0.224922 + 0.974377i \(0.427787\pi\)
\(444\) 0 0
\(445\) 3149.03 + 5454.28i 0.335457 + 0.581029i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5375.10i 0.564959i 0.959273 + 0.282479i \(0.0911569\pi\)
−0.959273 + 0.282479i \(0.908843\pi\)
\(450\) 0 0
\(451\) 2386.46 1377.83i 0.249167 0.143856i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2267.15 + 12237.7i 0.233595 + 1.26090i
\(456\) 0 0
\(457\) 2060.59 3569.05i 0.210920 0.365324i −0.741083 0.671414i \(-0.765687\pi\)
0.952003 + 0.306090i \(0.0990208\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6019.06 −0.608103 −0.304052 0.952656i \(-0.598340\pi\)
−0.304052 + 0.952656i \(0.598340\pi\)
\(462\) 0 0
\(463\) −3263.90 −0.327616 −0.163808 0.986492i \(-0.552378\pi\)
−0.163808 + 0.986492i \(0.552378\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 660.961 1144.82i 0.0654938 0.113439i −0.831419 0.555646i \(-0.812471\pi\)
0.896913 + 0.442207i \(0.145804\pi\)
\(468\) 0 0
\(469\) 5336.48 15066.1i 0.525407 1.48334i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5672.90 + 3275.25i −0.551460 + 0.318385i
\(474\) 0 0
\(475\) 11526.6i 1.11343i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1887.69 3269.58i −0.180064 0.311881i 0.761838 0.647768i \(-0.224297\pi\)
−0.941902 + 0.335887i \(0.890964\pi\)
\(480\) 0 0
\(481\) −7785.27 4494.83i −0.737999 0.426084i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −32146.9 18560.0i −3.00972 1.73766i
\(486\) 0 0
\(487\) 6119.80 + 10599.8i 0.569434 + 0.986289i 0.996622 + 0.0821263i \(0.0261711\pi\)
−0.427187 + 0.904163i \(0.640496\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13018.0i 1.19652i −0.801301 0.598261i \(-0.795858\pi\)
0.801301 0.598261i \(-0.204142\pi\)
\(492\) 0 0
\(493\) 9278.28 5356.82i 0.847612 0.489369i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4275.79 3651.31i 0.385906 0.329544i
\(498\) 0 0
\(499\) 8603.67 14902.0i 0.771850 1.33688i −0.164697 0.986344i \(-0.552665\pi\)
0.936548 0.350540i \(-0.114002\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 19760.5 1.75164 0.875821 0.482635i \(-0.160320\pi\)
0.875821 + 0.482635i \(0.160320\pi\)
\(504\) 0 0
\(505\) −29205.3 −2.57350
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2351.82 4073.48i 0.204799 0.354722i −0.745270 0.666763i \(-0.767679\pi\)
0.950069 + 0.312041i \(0.101013\pi\)
\(510\) 0 0
\(511\) −20140.6 7133.88i −1.74357 0.617582i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −18801.0 + 10854.8i −1.60868 + 0.928772i
\(516\) 0 0
\(517\) 9416.26i 0.801019i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7971.12 + 13806.4i 0.670290 + 1.16098i 0.977822 + 0.209438i \(0.0671635\pi\)
−0.307532 + 0.951538i \(0.599503\pi\)
\(522\) 0 0
\(523\) −17362.2 10024.0i −1.45161 0.838090i −0.453041 0.891490i \(-0.649661\pi\)
−0.998573 + 0.0533995i \(0.982994\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8952.22 + 5168.56i 0.739971 + 0.427222i
\(528\) 0 0
\(529\) −2837.30 4914.35i −0.233196 0.403908i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5124.50i 0.416448i
\(534\) 0 0
\(535\) 14624.3 8443.37i 1.18180 0.682315i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2192.50 5714.25i −0.175209 0.456642i
\(540\) 0 0
\(541\) −1931.85 + 3346.06i −0.153524 + 0.265912i −0.932521 0.361117i \(-0.882396\pi\)
0.778997 + 0.627028i \(0.215729\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −37365.2 −2.93678
\(546\) 0 0
\(547\) −18674.5 −1.45972 −0.729859 0.683598i \(-0.760414\pi\)
−0.729859 + 0.683598i \(0.760414\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4726.57 8186.66i 0.365442 0.632965i
\(552\) 0 0
\(553\) 126.788 23.4888i 0.00974968 0.00180623i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1489.14 859.753i 0.113280 0.0654020i −0.442290 0.896872i \(-0.645834\pi\)
0.555569 + 0.831470i \(0.312500\pi\)
\(558\) 0 0
\(559\) 12181.5i 0.921689i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6596.37 + 11425.3i 0.493790 + 0.855270i 0.999974 0.00715535i \(-0.00227764\pi\)
−0.506184 + 0.862426i \(0.668944\pi\)
\(564\) 0 0
\(565\) 24359.4 + 14063.9i 1.81382 + 1.04721i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −21405.5 12358.4i −1.57709 0.910533i −0.995263 0.0972193i \(-0.969005\pi\)
−0.581826 0.813313i \(-0.697661\pi\)
\(570\) 0 0
\(571\) −1032.73 1788.73i −0.0756887 0.131097i 0.825697 0.564114i \(-0.190782\pi\)
−0.901386 + 0.433017i \(0.857449\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22974.9i 1.66630i
\(576\) 0 0
\(577\) −6759.61 + 3902.66i −0.487706 + 0.281577i −0.723622 0.690196i \(-0.757524\pi\)
0.235916 + 0.971773i \(0.424191\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 9810.25 + 11488.1i 0.700512 + 0.820321i
\(582\) 0 0
\(583\) −812.727 + 1407.68i −0.0577353 + 0.100001i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6297.78 −0.442823 −0.221412 0.975180i \(-0.571066\pi\)
−0.221412 + 0.975180i \(0.571066\pi\)
\(588\) 0 0
\(589\) 9120.93 0.638067
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9115.60 + 15788.7i −0.631253 + 1.09336i 0.356043 + 0.934470i \(0.384126\pi\)
−0.987296 + 0.158893i \(0.949208\pi\)
\(594\) 0 0
\(595\) 11159.1 + 13067.6i 0.768869 + 0.900368i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7161.55 + 4134.72i −0.488503 + 0.282037i −0.723953 0.689849i \(-0.757677\pi\)
0.235450 + 0.971886i \(0.424343\pi\)
\(600\) 0 0
\(601\) 11106.1i 0.753788i −0.926256 0.376894i \(-0.876992\pi\)
0.926256 0.376894i \(-0.123008\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10253.5 17759.5i −0.689030 1.19343i
\(606\) 0 0
\(607\) −10414.3 6012.71i −0.696382 0.402056i 0.109616 0.993974i \(-0.465038\pi\)
−0.805999 + 0.591917i \(0.798371\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15164.8 + 8755.40i 1.00409 + 0.579714i
\(612\) 0 0
\(613\) 2027.75 + 3512.16i 0.133605 + 0.231411i 0.925064 0.379812i \(-0.124011\pi\)
−0.791459 + 0.611223i \(0.790678\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7236.59i 0.472178i 0.971731 + 0.236089i \(0.0758658\pi\)
−0.971731 + 0.236089i \(0.924134\pi\)
\(618\) 0 0
\(619\) 13803.6 7969.54i 0.896309 0.517484i 0.0203081 0.999794i \(-0.493535\pi\)
0.876001 + 0.482310i \(0.160202\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5663.20 1049.17i 0.364192 0.0674703i
\(624\) 0 0
\(625\) −15017.8 + 26011.5i −0.961136 + 1.66474i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12411.9 −0.786798
\(630\) 0 0
\(631\) 25310.1 1.59680 0.798399 0.602129i \(-0.205681\pi\)
0.798399 + 0.602129i \(0.205681\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8495.55 14714.7i 0.530922 0.919584i
\(636\) 0 0
\(637\) 11241.3 + 1782.21i 0.699213 + 0.110854i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21593.9 12467.2i 1.33059 0.768216i 0.345199 0.938530i \(-0.387812\pi\)
0.985390 + 0.170314i \(0.0544782\pi\)
\(642\) 0 0
\(643\) 12466.1i 0.764563i 0.924046 + 0.382282i \(0.124862\pi\)
−0.924046 + 0.382282i \(0.875138\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12339.6 21372.8i −0.749799 1.29869i −0.947919 0.318513i \(-0.896817\pi\)
0.198119 0.980178i \(-0.436517\pi\)
\(648\) 0 0
\(649\) 9666.52 + 5580.97i 0.584659 + 0.337553i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16498.1 + 9525.16i 0.988697 + 0.570825i 0.904885 0.425657i \(-0.139957\pi\)
0.0838127 + 0.996482i \(0.473290\pi\)
\(654\) 0 0
\(655\) −3949.87 6841.37i −0.235625 0.408114i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5983.49i 0.353693i −0.984238 0.176847i \(-0.943410\pi\)
0.984238 0.176847i \(-0.0565897\pi\)
\(660\) 0 0
\(661\) −12000.7 + 6928.61i −0.706162 + 0.407703i −0.809638 0.586929i \(-0.800337\pi\)
0.103476 + 0.994632i \(0.467003\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 14292.1 + 5062.32i 0.833419 + 0.295201i
\(666\) 0 0
\(667\) 9421.03 16317.7i 0.546902 0.947263i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1624.32 0.0934519
\(672\) 0 0
\(673\) −21469.4 −1.22970 −0.614849 0.788645i \(-0.710783\pi\)
−0.614849 + 0.788645i \(0.710783\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10221.4 17703.9i 0.580265 1.00505i −0.415183 0.909738i \(-0.636282\pi\)
0.995448 0.0953099i \(-0.0303842\pi\)
\(678\) 0 0
\(679\) −25814.6 + 22044.3i −1.45902 + 1.24593i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16958.6 9791.08i 0.950080 0.548529i 0.0569740 0.998376i \(-0.481855\pi\)
0.893106 + 0.449847i \(0.148521\pi\)
\(684\) 0 0
\(685\) 27868.1i 1.55443i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1511.37 2617.77i −0.0835685 0.144745i
\(690\) 0 0
\(691\) 10137.3 + 5852.75i 0.558089 + 0.322213i 0.752378 0.658731i \(-0.228907\pi\)
−0.194289 + 0.980944i \(0.562240\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −16726.6 9657.13i −0.912917 0.527073i
\(696\) 0 0
\(697\) 3537.67 + 6127.43i 0.192251 + 0.332988i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17998.6i 0.969752i 0.874583 + 0.484876i \(0.161135\pi\)
−0.874583 + 0.484876i \(0.838865\pi\)
\(702\) 0 0
\(703\) −9484.38 + 5475.81i −0.508834 + 0.293775i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8917.29 + 25175.5i −0.474355 + 1.33921i
\(708\) 0 0
\(709\) 11891.5 20596.7i 0.629895 1.09101i −0.357677 0.933845i \(-0.616431\pi\)
0.987572 0.157166i \(-0.0502356\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18179.9 0.954899
\(714\) 0 0
\(715\) −11991.3 −0.627202
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16513.5 28602.2i 0.856536 1.48356i −0.0186774 0.999826i \(-0.505946\pi\)
0.875213 0.483738i \(-0.160721\pi\)
\(720\) 0 0
\(721\) 3616.49 + 19521.2i 0.186803 + 1.00833i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 57744.2 33338.6i 2.95802 1.70782i
\(726\) 0 0
\(727\) 6816.11i 0.347724i −0.984770 0.173862i \(-0.944375\pi\)
0.984770 0.173862i \(-0.0556247\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8409.46 14565.6i −0.425493 0.736975i
\(732\) 0 0
\(733\) 20701.4 + 11951.9i 1.04314 + 0.602258i 0.920722 0.390220i \(-0.127601\pi\)
0.122420 + 0.992478i \(0.460934\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13336.4 + 7699.76i 0.666556 + 0.384836i
\(738\) 0 0
\(739\) −4558.07 7894.81i −0.226889 0.392984i 0.729995 0.683452i \(-0.239522\pi\)
−0.956885 + 0.290468i \(0.906189\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32818.5i 1.62045i 0.586121 + 0.810224i \(0.300654\pi\)
−0.586121 + 0.810224i \(0.699346\pi\)
\(744\) 0 0
\(745\) −44532.5 + 25710.9i −2.18999 + 1.26439i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2813.09 15184.5i −0.137234 0.740762i
\(750\) 0 0
\(751\) 4620.07 8002.20i 0.224486 0.388821i −0.731679 0.681649i \(-0.761263\pi\)
0.956165 + 0.292828i \(0.0945964\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20859.4 −1.00550
\(756\) 0 0
\(757\) 16610.7 0.797523 0.398761 0.917055i \(-0.369440\pi\)
0.398761 + 0.917055i \(0.369440\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1121.42 1942.35i 0.0534184 0.0925234i −0.838080 0.545548i \(-0.816322\pi\)
0.891498 + 0.453024i \(0.149655\pi\)
\(762\) 0 0
\(763\) −11408.8 + 32209.6i −0.541317 + 1.52826i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −17976.2 + 10378.5i −0.846261 + 0.488589i
\(768\) 0 0
\(769\) 9182.73i 0.430608i −0.976547 0.215304i \(-0.930926\pi\)
0.976547 0.215304i \(-0.0690743\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4272.40 + 7400.02i 0.198794 + 0.344321i 0.948138 0.317860i \(-0.102964\pi\)
−0.749344 + 0.662181i \(0.769631\pi\)
\(774\) 0 0
\(775\) 55714.9 + 32167.0i 2.58237 + 1.49093i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5406.51 + 3121.45i 0.248663 + 0.143566i
\(780\) 0 0
\(781\) 2708.65 + 4691.53i 0.124101 + 0.214950i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 36451.6i 1.65734i
\(786\) 0 0
\(787\) 20236.4 11683.5i 0.916583 0.529190i 0.0340400 0.999420i \(-0.489163\pi\)
0.882544 + 0.470231i \(0.155829\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19561.1 16704.1i 0.879281 0.750861i
\(792\) 0 0
\(793\) −1510.32 + 2615.95i −0.0676331 + 0.117144i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8319.18 −0.369737 −0.184869 0.982763i \(-0.559186\pi\)
−0.184869 + 0.982763i \(0.559186\pi\)
\(798\) 0 0
\(799\) 24177.0 1.07049
\(800\) 0 0
\(801\) 0 0
\(802\) 0