Properties

Label 336.4.h.b.239.18
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.18
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.b.239.17

$q$-expansion

\(f(q)\) \(=\) \(q+(2.33643 + 4.64124i) q^{3} -12.0055i q^{5} -7.00000i q^{7} +(-16.0822 + 21.6878i) q^{9} +O(q^{10})\) \(q+(2.33643 + 4.64124i) q^{3} -12.0055i q^{5} -7.00000i q^{7} +(-16.0822 + 21.6878i) q^{9} +33.9879 q^{11} -13.8712 q^{13} +(55.7206 - 28.0501i) q^{15} -28.7374i q^{17} -75.7520i q^{19} +(32.4887 - 16.3550i) q^{21} +104.296 q^{23} -19.1331 q^{25} +(-138.233 - 23.9692i) q^{27} -242.660i q^{29} -316.604i q^{31} +(79.4103 + 157.746i) q^{33} -84.0388 q^{35} +303.265 q^{37} +(-32.4091 - 64.3795i) q^{39} +382.946i q^{41} -12.0228i q^{43} +(260.374 + 193.076i) q^{45} +314.619 q^{47} -49.0000 q^{49} +(133.377 - 67.1430i) q^{51} +418.518i q^{53} -408.043i q^{55} +(351.583 - 176.989i) q^{57} +477.106 q^{59} +112.267 q^{61} +(151.815 + 112.575i) q^{63} +166.531i q^{65} -180.543i q^{67} +(243.680 + 484.062i) q^{69} +25.4197 q^{71} -349.113 q^{73} +(-44.7032 - 88.8015i) q^{75} -237.915i q^{77} -452.651i q^{79} +(-211.725 - 697.577i) q^{81} -1081.66 q^{83} -345.009 q^{85} +(1126.24 - 566.957i) q^{87} -816.177i q^{89} +97.0984i q^{91} +(1469.44 - 739.724i) q^{93} -909.444 q^{95} -1070.07 q^{97} +(-546.600 + 737.124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 136 q^{9} + O(q^{10}) \) \( 24 q - 136 q^{9} + 96 q^{13} - 112 q^{21} + 168 q^{25} - 320 q^{33} - 864 q^{37} + 592 q^{45} - 1176 q^{49} - 1120 q^{57} - 2304 q^{61} + 1168 q^{69} + 3312 q^{73} - 968 q^{81} - 5808 q^{85} + 1776 q^{93} + 6480 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) 2.33643 + 4.64124i 0.449646 + 0.893207i
\(4\) 0 0
\(5\) 12.0055i 1.07381i −0.843643 0.536904i \(-0.819594\pi\)
0.843643 0.536904i \(-0.180406\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) −16.0822 + 21.6878i −0.595637 + 0.803254i
\(10\) 0 0
\(11\) 33.9879 0.931612 0.465806 0.884887i \(-0.345764\pi\)
0.465806 + 0.884887i \(0.345764\pi\)
\(12\) 0 0
\(13\) −13.8712 −0.295937 −0.147968 0.988992i \(-0.547273\pi\)
−0.147968 + 0.988992i \(0.547273\pi\)
\(14\) 0 0
\(15\) 55.7206 28.0501i 0.959133 0.482834i
\(16\) 0 0
\(17\) 28.7374i 0.409991i −0.978763 0.204996i \(-0.934282\pi\)
0.978763 0.204996i \(-0.0657180\pi\)
\(18\) 0 0
\(19\) 75.7520i 0.914668i −0.889295 0.457334i \(-0.848804\pi\)
0.889295 0.457334i \(-0.151196\pi\)
\(20\) 0 0
\(21\) 32.4887 16.3550i 0.337600 0.169950i
\(22\) 0 0
\(23\) 104.296 0.945530 0.472765 0.881189i \(-0.343256\pi\)
0.472765 + 0.881189i \(0.343256\pi\)
\(24\) 0 0
\(25\) −19.1331 −0.153065
\(26\) 0 0
\(27\) −138.233 23.9692i −0.985297 0.170848i
\(28\) 0 0
\(29\) 242.660i 1.55382i −0.629612 0.776910i \(-0.716786\pi\)
0.629612 0.776910i \(-0.283214\pi\)
\(30\) 0 0
\(31\) 316.604i 1.83432i −0.398523 0.917158i \(-0.630477\pi\)
0.398523 0.917158i \(-0.369523\pi\)
\(32\) 0 0
\(33\) 79.4103 + 157.746i 0.418896 + 0.832122i
\(34\) 0 0
\(35\) −84.0388 −0.405862
\(36\) 0 0
\(37\) 303.265 1.34747 0.673737 0.738971i \(-0.264688\pi\)
0.673737 + 0.738971i \(0.264688\pi\)
\(38\) 0 0
\(39\) −32.4091 64.3795i −0.133067 0.264333i
\(40\) 0 0
\(41\) 382.946i 1.45869i 0.684148 + 0.729343i \(0.260174\pi\)
−0.684148 + 0.729343i \(0.739826\pi\)
\(42\) 0 0
\(43\) 12.0228i 0.0426385i −0.999773 0.0213193i \(-0.993213\pi\)
0.999773 0.0213193i \(-0.00678664\pi\)
\(44\) 0 0
\(45\) 260.374 + 193.076i 0.862541 + 0.639600i
\(46\) 0 0
\(47\) 314.619 0.976424 0.488212 0.872725i \(-0.337649\pi\)
0.488212 + 0.872725i \(0.337649\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 133.377 67.1430i 0.366207 0.184351i
\(52\) 0 0
\(53\) 418.518i 1.08468i 0.840160 + 0.542338i \(0.182461\pi\)
−0.840160 + 0.542338i \(0.817539\pi\)
\(54\) 0 0
\(55\) 408.043i 1.00037i
\(56\) 0 0
\(57\) 351.583 176.989i 0.816988 0.411277i
\(58\) 0 0
\(59\) 477.106 1.05278 0.526389 0.850244i \(-0.323546\pi\)
0.526389 + 0.850244i \(0.323546\pi\)
\(60\) 0 0
\(61\) 112.267 0.235644 0.117822 0.993035i \(-0.462409\pi\)
0.117822 + 0.993035i \(0.462409\pi\)
\(62\) 0 0
\(63\) 151.815 + 112.575i 0.303601 + 0.225130i
\(64\) 0 0
\(65\) 166.531i 0.317779i
\(66\) 0 0
\(67\) 180.543i 0.329207i −0.986360 0.164604i \(-0.947366\pi\)
0.986360 0.164604i \(-0.0526345\pi\)
\(68\) 0 0
\(69\) 243.680 + 484.062i 0.425154 + 0.844554i
\(70\) 0 0
\(71\) 25.4197 0.0424896 0.0212448 0.999774i \(-0.493237\pi\)
0.0212448 + 0.999774i \(0.493237\pi\)
\(72\) 0 0
\(73\) −349.113 −0.559734 −0.279867 0.960039i \(-0.590290\pi\)
−0.279867 + 0.960039i \(0.590290\pi\)
\(74\) 0 0
\(75\) −44.7032 88.8015i −0.0688251 0.136719i
\(76\) 0 0
\(77\) 237.915i 0.352116i
\(78\) 0 0
\(79\) 452.651i 0.644648i −0.946629 0.322324i \(-0.895536\pi\)
0.946629 0.322324i \(-0.104464\pi\)
\(80\) 0 0
\(81\) −211.725 697.577i −0.290433 0.956895i
\(82\) 0 0
\(83\) −1081.66 −1.43046 −0.715230 0.698889i \(-0.753678\pi\)
−0.715230 + 0.698889i \(0.753678\pi\)
\(84\) 0 0
\(85\) −345.009 −0.440252
\(86\) 0 0
\(87\) 1126.24 566.957i 1.38788 0.698669i
\(88\) 0 0
\(89\) 816.177i 0.972075i −0.873938 0.486037i \(-0.838442\pi\)
0.873938 0.486037i \(-0.161558\pi\)
\(90\) 0 0
\(91\) 97.0984i 0.111854i
\(92\) 0 0
\(93\) 1469.44 739.724i 1.63842 0.824793i
\(94\) 0 0
\(95\) −909.444 −0.982178
\(96\) 0 0
\(97\) −1070.07 −1.12009 −0.560046 0.828462i \(-0.689216\pi\)
−0.560046 + 0.828462i \(0.689216\pi\)
\(98\) 0 0
\(99\) −546.600 + 737.124i −0.554903 + 0.748321i
\(100\) 0 0
\(101\) 1356.15i 1.33606i 0.744134 + 0.668031i \(0.232863\pi\)
−0.744134 + 0.668031i \(0.767137\pi\)
\(102\) 0 0
\(103\) 757.734i 0.724872i −0.932009 0.362436i \(-0.881945\pi\)
0.932009 0.362436i \(-0.118055\pi\)
\(104\) 0 0
\(105\) −196.351 390.044i −0.182494 0.362518i
\(106\) 0 0
\(107\) 987.341 0.892055 0.446027 0.895019i \(-0.352838\pi\)
0.446027 + 0.895019i \(0.352838\pi\)
\(108\) 0 0
\(109\) −1257.53 −1.10504 −0.552522 0.833498i \(-0.686334\pi\)
−0.552522 + 0.833498i \(0.686334\pi\)
\(110\) 0 0
\(111\) 708.558 + 1407.53i 0.605886 + 1.20357i
\(112\) 0 0
\(113\) 449.026i 0.373812i −0.982378 0.186906i \(-0.940154\pi\)
0.982378 0.186906i \(-0.0598460\pi\)
\(114\) 0 0
\(115\) 1252.13i 1.01532i
\(116\) 0 0
\(117\) 223.079 300.836i 0.176271 0.237712i
\(118\) 0 0
\(119\) −201.162 −0.154962
\(120\) 0 0
\(121\) −175.823 −0.132099
\(122\) 0 0
\(123\) −1777.35 + 894.727i −1.30291 + 0.655892i
\(124\) 0 0
\(125\) 1270.99i 0.909446i
\(126\) 0 0
\(127\) 1557.87i 1.08849i 0.838925 + 0.544247i \(0.183184\pi\)
−0.838925 + 0.544247i \(0.816816\pi\)
\(128\) 0 0
\(129\) 55.8006 28.0904i 0.0380850 0.0191722i
\(130\) 0 0
\(131\) 1864.44 1.24349 0.621743 0.783221i \(-0.286425\pi\)
0.621743 + 0.783221i \(0.286425\pi\)
\(132\) 0 0
\(133\) −530.264 −0.345712
\(134\) 0 0
\(135\) −287.764 + 1659.57i −0.183458 + 1.05802i
\(136\) 0 0
\(137\) 579.299i 0.361261i −0.983551 0.180631i \(-0.942186\pi\)
0.983551 0.180631i \(-0.0578139\pi\)
\(138\) 0 0
\(139\) 1410.44i 0.860661i 0.902671 + 0.430330i \(0.141603\pi\)
−0.902671 + 0.430330i \(0.858397\pi\)
\(140\) 0 0
\(141\) 735.086 + 1460.22i 0.439045 + 0.872149i
\(142\) 0 0
\(143\) −471.453 −0.275698
\(144\) 0 0
\(145\) −2913.26 −1.66851
\(146\) 0 0
\(147\) −114.485 227.421i −0.0642351 0.127601i
\(148\) 0 0
\(149\) 2848.23i 1.56601i 0.622013 + 0.783007i \(0.286315\pi\)
−0.622013 + 0.783007i \(0.713685\pi\)
\(150\) 0 0
\(151\) 556.913i 0.300138i 0.988675 + 0.150069i \(0.0479497\pi\)
−0.988675 + 0.150069i \(0.952050\pi\)
\(152\) 0 0
\(153\) 623.253 + 462.161i 0.329327 + 0.244206i
\(154\) 0 0
\(155\) −3801.01 −1.96971
\(156\) 0 0
\(157\) −1054.63 −0.536104 −0.268052 0.963405i \(-0.586380\pi\)
−0.268052 + 0.963405i \(0.586380\pi\)
\(158\) 0 0
\(159\) −1942.44 + 977.837i −0.968840 + 0.487720i
\(160\) 0 0
\(161\) 730.071i 0.357377i
\(162\) 0 0
\(163\) 2521.74i 1.21177i 0.795553 + 0.605884i \(0.207180\pi\)
−0.795553 + 0.605884i \(0.792820\pi\)
\(164\) 0 0
\(165\) 1893.83 953.364i 0.893540 0.449814i
\(166\) 0 0
\(167\) −1267.63 −0.587379 −0.293689 0.955901i \(-0.594883\pi\)
−0.293689 + 0.955901i \(0.594883\pi\)
\(168\) 0 0
\(169\) −2004.59 −0.912421
\(170\) 0 0
\(171\) 1642.90 + 1218.26i 0.734710 + 0.544810i
\(172\) 0 0
\(173\) 356.100i 0.156496i 0.996934 + 0.0782479i \(0.0249326\pi\)
−0.996934 + 0.0782479i \(0.975067\pi\)
\(174\) 0 0
\(175\) 133.932i 0.0578532i
\(176\) 0 0
\(177\) 1114.72 + 2214.36i 0.473377 + 0.940349i
\(178\) 0 0
\(179\) 4277.21 1.78600 0.893000 0.450057i \(-0.148596\pi\)
0.893000 + 0.450057i \(0.148596\pi\)
\(180\) 0 0
\(181\) 3200.35 1.31426 0.657128 0.753779i \(-0.271771\pi\)
0.657128 + 0.753779i \(0.271771\pi\)
\(182\) 0 0
\(183\) 262.303 + 521.056i 0.105956 + 0.210479i
\(184\) 0 0
\(185\) 3640.87i 1.44693i
\(186\) 0 0
\(187\) 976.725i 0.381953i
\(188\) 0 0
\(189\) −167.785 + 967.634i −0.0645743 + 0.372407i
\(190\) 0 0
\(191\) −3437.92 −1.30240 −0.651201 0.758905i \(-0.725735\pi\)
−0.651201 + 0.758905i \(0.725735\pi\)
\(192\) 0 0
\(193\) −4846.78 −1.80766 −0.903831 0.427889i \(-0.859258\pi\)
−0.903831 + 0.427889i \(0.859258\pi\)
\(194\) 0 0
\(195\) −772.912 + 389.088i −0.283843 + 0.142888i
\(196\) 0 0
\(197\) 1330.88i 0.481326i −0.970609 0.240663i \(-0.922635\pi\)
0.970609 0.240663i \(-0.0773648\pi\)
\(198\) 0 0
\(199\) 3197.38i 1.13898i −0.821999 0.569489i \(-0.807141\pi\)
0.821999 0.569489i \(-0.192859\pi\)
\(200\) 0 0
\(201\) 837.945 421.827i 0.294050 0.148027i
\(202\) 0 0
\(203\) −1698.62 −0.587289
\(204\) 0 0
\(205\) 4597.48 1.56635
\(206\) 0 0
\(207\) −1677.31 + 2261.95i −0.563193 + 0.759500i
\(208\) 0 0
\(209\) 2574.65i 0.852116i
\(210\) 0 0
\(211\) 85.7881i 0.0279900i −0.999902 0.0139950i \(-0.995545\pi\)
0.999902 0.0139950i \(-0.00445490\pi\)
\(212\) 0 0
\(213\) 59.3912 + 117.979i 0.0191053 + 0.0379520i
\(214\) 0 0
\(215\) −144.340 −0.0457856
\(216\) 0 0
\(217\) −2216.23 −0.693307
\(218\) 0 0
\(219\) −815.678 1620.32i −0.251682 0.499958i
\(220\) 0 0
\(221\) 398.623i 0.121332i
\(222\) 0 0
\(223\) 335.779i 0.100832i 0.998728 + 0.0504158i \(0.0160546\pi\)
−0.998728 + 0.0504158i \(0.983945\pi\)
\(224\) 0 0
\(225\) 307.703 414.957i 0.0911713 0.122950i
\(226\) 0 0
\(227\) 3532.32 1.03281 0.516405 0.856344i \(-0.327270\pi\)
0.516405 + 0.856344i \(0.327270\pi\)
\(228\) 0 0
\(229\) −5711.26 −1.64808 −0.824040 0.566531i \(-0.808285\pi\)
−0.824040 + 0.566531i \(0.808285\pi\)
\(230\) 0 0
\(231\) 1104.22 555.872i 0.314513 0.158328i
\(232\) 0 0
\(233\) 1026.46i 0.288607i 0.989534 + 0.144303i \(0.0460941\pi\)
−0.989534 + 0.144303i \(0.953906\pi\)
\(234\) 0 0
\(235\) 3777.18i 1.04849i
\(236\) 0 0
\(237\) 2100.86 1057.59i 0.575804 0.289863i
\(238\) 0 0
\(239\) 2404.61 0.650800 0.325400 0.945576i \(-0.394501\pi\)
0.325400 + 0.945576i \(0.394501\pi\)
\(240\) 0 0
\(241\) −6537.60 −1.74740 −0.873700 0.486464i \(-0.838286\pi\)
−0.873700 + 0.486464i \(0.838286\pi\)
\(242\) 0 0
\(243\) 2742.94 2612.51i 0.724114 0.689681i
\(244\) 0 0
\(245\) 588.272i 0.153401i
\(246\) 0 0
\(247\) 1050.77i 0.270684i
\(248\) 0 0
\(249\) −2527.23 5020.27i −0.643200 1.27770i
\(250\) 0 0
\(251\) −76.2619 −0.0191777 −0.00958886 0.999954i \(-0.503052\pi\)
−0.00958886 + 0.999954i \(0.503052\pi\)
\(252\) 0 0
\(253\) 3544.80 0.880867
\(254\) 0 0
\(255\) −806.088 1601.27i −0.197958 0.393236i
\(256\) 0 0
\(257\) 5213.42i 1.26539i 0.774403 + 0.632693i \(0.218051\pi\)
−0.774403 + 0.632693i \(0.781949\pi\)
\(258\) 0 0
\(259\) 2122.86i 0.509297i
\(260\) 0 0
\(261\) 5262.77 + 3902.50i 1.24811 + 0.925513i
\(262\) 0 0
\(263\) 6662.59 1.56210 0.781051 0.624468i \(-0.214684\pi\)
0.781051 + 0.624468i \(0.214684\pi\)
\(264\) 0 0
\(265\) 5024.54 1.16473
\(266\) 0 0
\(267\) 3788.07 1906.94i 0.868264 0.437089i
\(268\) 0 0
\(269\) 5591.40i 1.26734i −0.773605 0.633669i \(-0.781548\pi\)
0.773605 0.633669i \(-0.218452\pi\)
\(270\) 0 0
\(271\) 2023.00i 0.453462i −0.973957 0.226731i \(-0.927196\pi\)
0.973957 0.226731i \(-0.0728039\pi\)
\(272\) 0 0
\(273\) −450.657 + 226.863i −0.0999084 + 0.0502945i
\(274\) 0 0
\(275\) −650.295 −0.142597
\(276\) 0 0
\(277\) 6383.29 1.38460 0.692300 0.721609i \(-0.256597\pi\)
0.692300 + 0.721609i \(0.256597\pi\)
\(278\) 0 0
\(279\) 6866.47 + 5091.70i 1.47342 + 1.09259i
\(280\) 0 0
\(281\) 7466.36i 1.58507i 0.609824 + 0.792537i \(0.291240\pi\)
−0.609824 + 0.792537i \(0.708760\pi\)
\(282\) 0 0
\(283\) 1593.17i 0.334644i 0.985902 + 0.167322i \(0.0535120\pi\)
−0.985902 + 0.167322i \(0.946488\pi\)
\(284\) 0 0
\(285\) −2124.85 4220.95i −0.441633 0.877289i
\(286\) 0 0
\(287\) 2680.62 0.551332
\(288\) 0 0
\(289\) 4087.16 0.831907
\(290\) 0 0
\(291\) −2500.14 4966.44i −0.503645 1.00047i
\(292\) 0 0
\(293\) 7812.67i 1.55775i 0.627179 + 0.778875i \(0.284210\pi\)
−0.627179 + 0.778875i \(0.715790\pi\)
\(294\) 0 0
\(295\) 5727.92i 1.13048i
\(296\) 0 0
\(297\) −4698.26 814.664i −0.917915 0.159164i
\(298\) 0 0
\(299\) −1446.71 −0.279817
\(300\) 0 0
\(301\) −84.1594 −0.0161158
\(302\) 0 0
\(303\) −6294.23 + 3168.55i −1.19338 + 0.600754i
\(304\) 0 0
\(305\) 1347.82i 0.253036i
\(306\) 0 0
\(307\) 5120.06i 0.951848i −0.879486 0.475924i \(-0.842114\pi\)
0.879486 0.475924i \(-0.157886\pi\)
\(308\) 0 0
\(309\) 3516.83 1770.39i 0.647460 0.325936i
\(310\) 0 0
\(311\) −7740.01 −1.41124 −0.705620 0.708590i \(-0.749332\pi\)
−0.705620 + 0.708590i \(0.749332\pi\)
\(312\) 0 0
\(313\) 4208.89 0.760066 0.380033 0.924973i \(-0.375913\pi\)
0.380033 + 0.924973i \(0.375913\pi\)
\(314\) 0 0
\(315\) 1351.53 1822.62i 0.241746 0.326010i
\(316\) 0 0
\(317\) 8363.38i 1.48181i 0.671609 + 0.740905i \(0.265603\pi\)
−0.671609 + 0.740905i \(0.734397\pi\)
\(318\) 0 0
\(319\) 8247.49i 1.44756i
\(320\) 0 0
\(321\) 2306.85 + 4582.48i 0.401109 + 0.796789i
\(322\) 0 0
\(323\) −2176.92 −0.375006
\(324\) 0 0
\(325\) 265.400 0.0452976
\(326\) 0 0
\(327\) −2938.14 5836.51i −0.496879 0.987033i
\(328\) 0 0
\(329\) 2202.34i 0.369054i
\(330\) 0 0
\(331\) 11782.9i 1.95663i 0.207111 + 0.978317i \(0.433594\pi\)
−0.207111 + 0.978317i \(0.566406\pi\)
\(332\) 0 0
\(333\) −4877.18 + 6577.17i −0.802605 + 1.08236i
\(334\) 0 0
\(335\) −2167.52 −0.353505
\(336\) 0 0
\(337\) 4424.50 0.715187 0.357593 0.933877i \(-0.383597\pi\)
0.357593 + 0.933877i \(0.383597\pi\)
\(338\) 0 0
\(339\) 2084.04 1049.12i 0.333892 0.168083i
\(340\) 0 0
\(341\) 10760.7i 1.70887i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 5811.43 2925.51i 0.906889 0.456534i
\(346\) 0 0
\(347\) −3752.27 −0.580497 −0.290248 0.956951i \(-0.593738\pi\)
−0.290248 + 0.956951i \(0.593738\pi\)
\(348\) 0 0
\(349\) 3908.60 0.599492 0.299746 0.954019i \(-0.403098\pi\)
0.299746 + 0.954019i \(0.403098\pi\)
\(350\) 0 0
\(351\) 1917.46 + 332.482i 0.291586 + 0.0505601i
\(352\) 0 0
\(353\) 2100.72i 0.316742i −0.987380 0.158371i \(-0.949376\pi\)
0.987380 0.158371i \(-0.0506242\pi\)
\(354\) 0 0
\(355\) 305.177i 0.0456257i
\(356\) 0 0
\(357\) −470.001 933.642i −0.0696781 0.138413i
\(358\) 0 0
\(359\) 3016.76 0.443505 0.221752 0.975103i \(-0.428822\pi\)
0.221752 + 0.975103i \(0.428822\pi\)
\(360\) 0 0
\(361\) 1120.64 0.163382
\(362\) 0 0
\(363\) −410.799 816.038i −0.0593976 0.117991i
\(364\) 0 0
\(365\) 4191.29i 0.601047i
\(366\) 0 0
\(367\) 6833.27i 0.971918i −0.873982 0.485959i \(-0.838470\pi\)
0.873982 0.485959i \(-0.161530\pi\)
\(368\) 0 0
\(369\) −8305.28 6158.62i −1.17170 0.868848i
\(370\) 0 0
\(371\) 2929.62 0.409969
\(372\) 0 0
\(373\) 11866.5 1.64725 0.823627 0.567132i \(-0.191947\pi\)
0.823627 + 0.567132i \(0.191947\pi\)
\(374\) 0 0
\(375\) 5898.97 2969.58i 0.812323 0.408929i
\(376\) 0 0
\(377\) 3365.98i 0.459832i
\(378\) 0 0
\(379\) 13985.9i 1.89554i 0.318956 + 0.947769i \(0.396668\pi\)
−0.318956 + 0.947769i \(0.603332\pi\)
\(380\) 0 0
\(381\) −7230.45 + 3639.85i −0.972250 + 0.489436i
\(382\) 0 0
\(383\) 7569.70 1.00990 0.504952 0.863147i \(-0.331510\pi\)
0.504952 + 0.863147i \(0.331510\pi\)
\(384\) 0 0
\(385\) −2856.30 −0.378106
\(386\) 0 0
\(387\) 260.748 + 193.353i 0.0342495 + 0.0253971i
\(388\) 0 0
\(389\) 2949.39i 0.384422i 0.981354 + 0.192211i \(0.0615657\pi\)
−0.981354 + 0.192211i \(0.938434\pi\)
\(390\) 0 0
\(391\) 2997.20i 0.387659i
\(392\) 0 0
\(393\) 4356.13 + 8653.31i 0.559129 + 1.11069i
\(394\) 0 0
\(395\) −5434.32 −0.692229
\(396\) 0 0
\(397\) −9934.24 −1.25588 −0.627941 0.778261i \(-0.716102\pi\)
−0.627941 + 0.778261i \(0.716102\pi\)
\(398\) 0 0
\(399\) −1238.92 2461.08i −0.155448 0.308792i
\(400\) 0 0
\(401\) 12531.7i 1.56060i −0.625403 0.780302i \(-0.715066\pi\)
0.625403 0.780302i \(-0.284934\pi\)
\(402\) 0 0
\(403\) 4391.68i 0.542842i
\(404\) 0 0
\(405\) −8374.79 + 2541.88i −1.02752 + 0.311869i
\(406\) 0 0
\(407\) 10307.4 1.25532
\(408\) 0 0
\(409\) −9543.29 −1.15375 −0.576877 0.816831i \(-0.695729\pi\)
−0.576877 + 0.816831i \(0.695729\pi\)
\(410\) 0 0
\(411\) 2688.66 1353.49i 0.322681 0.162440i
\(412\) 0 0
\(413\) 3339.74i 0.397913i
\(414\) 0 0
\(415\) 12986.0i 1.53604i
\(416\) 0 0
\(417\) −6546.18 + 3295.39i −0.768748 + 0.386993i
\(418\) 0 0
\(419\) 889.368 0.103696 0.0518478 0.998655i \(-0.483489\pi\)
0.0518478 + 0.998655i \(0.483489\pi\)
\(420\) 0 0
\(421\) 293.443 0.0339704 0.0169852 0.999856i \(-0.494593\pi\)
0.0169852 + 0.999856i \(0.494593\pi\)
\(422\) 0 0
\(423\) −5059.77 + 6823.42i −0.581595 + 0.784316i
\(424\) 0 0
\(425\) 549.838i 0.0627554i
\(426\) 0 0
\(427\) 785.866i 0.0890650i
\(428\) 0 0
\(429\) −1101.52 2188.12i −0.123967 0.246256i
\(430\) 0 0
\(431\) 7891.67 0.881968 0.440984 0.897515i \(-0.354630\pi\)
0.440984 + 0.897515i \(0.354630\pi\)
\(432\) 0 0
\(433\) 10888.9 1.20851 0.604255 0.796791i \(-0.293471\pi\)
0.604255 + 0.796791i \(0.293471\pi\)
\(434\) 0 0
\(435\) −6806.63 13521.1i −0.750236 1.49032i
\(436\) 0 0
\(437\) 7900.61i 0.864846i
\(438\) 0 0
\(439\) 7101.91i 0.772109i 0.922476 + 0.386054i \(0.126162\pi\)
−0.922476 + 0.386054i \(0.873838\pi\)
\(440\) 0 0
\(441\) 788.028 1062.70i 0.0850910 0.114751i
\(442\) 0 0
\(443\) −10843.3 −1.16294 −0.581468 0.813569i \(-0.697522\pi\)
−0.581468 + 0.813569i \(0.697522\pi\)
\(444\) 0 0
\(445\) −9798.66 −1.04382
\(446\) 0 0
\(447\) −13219.3 + 6654.68i −1.39877 + 0.704151i
\(448\) 0 0
\(449\) 11771.1i 1.23722i −0.785698 0.618611i \(-0.787696\pi\)
0.785698 0.618611i \(-0.212304\pi\)
\(450\) 0 0
\(451\) 13015.5i 1.35893i
\(452\) 0 0
\(453\) −2584.76 + 1301.19i −0.268086 + 0.134956i
\(454\) 0 0
\(455\) 1165.72 0.120109
\(456\) 0 0
\(457\) 15242.9 1.56025 0.780125 0.625624i \(-0.215155\pi\)
0.780125 + 0.625624i \(0.215155\pi\)
\(458\) 0 0
\(459\) −688.815 + 3972.48i −0.0700460 + 0.403964i
\(460\) 0 0
\(461\) 537.066i 0.0542595i 0.999632 + 0.0271298i \(0.00863673\pi\)
−0.999632 + 0.0271298i \(0.991363\pi\)
\(462\) 0 0
\(463\) 1043.87i 0.104780i 0.998627 + 0.0523898i \(0.0166838\pi\)
−0.998627 + 0.0523898i \(0.983316\pi\)
\(464\) 0 0
\(465\) −8880.78 17641.4i −0.885670 1.75935i
\(466\) 0 0
\(467\) −1482.78 −0.146927 −0.0734633 0.997298i \(-0.523405\pi\)
−0.0734633 + 0.997298i \(0.523405\pi\)
\(468\) 0 0
\(469\) −1263.80 −0.124429
\(470\) 0 0
\(471\) −2464.06 4894.77i −0.241057 0.478851i
\(472\) 0 0
\(473\) 408.629i 0.0397226i
\(474\) 0 0
\(475\) 1449.37i 0.140004i
\(476\) 0 0
\(477\) −9076.75 6730.69i −0.871270 0.646074i
\(478\) 0 0
\(479\) 722.425 0.0689111 0.0344556 0.999406i \(-0.489030\pi\)
0.0344556 + 0.999406i \(0.489030\pi\)
\(480\) 0 0
\(481\) −4206.65 −0.398767
\(482\) 0 0
\(483\) 3388.43 1705.76i 0.319211 0.160693i
\(484\) 0 0
\(485\) 12846.7i 1.20276i
\(486\) 0 0
\(487\) 3750.20i 0.348948i −0.984662 0.174474i \(-0.944177\pi\)
0.984662 0.174474i \(-0.0558226\pi\)
\(488\) 0 0
\(489\) −11704.0 + 5891.87i −1.08236 + 0.544866i
\(490\) 0 0
\(491\) −5139.62 −0.472399 −0.236199 0.971705i \(-0.575902\pi\)
−0.236199 + 0.971705i \(0.575902\pi\)
\(492\) 0 0
\(493\) −6973.42 −0.637053
\(494\) 0 0
\(495\) 8849.58 + 6562.23i 0.803553 + 0.595860i
\(496\) 0 0
\(497\) 177.938i 0.0160595i
\(498\) 0 0
\(499\) 13413.4i 1.20334i 0.798746 + 0.601668i \(0.205497\pi\)
−0.798746 + 0.601668i \(0.794503\pi\)
\(500\) 0 0
\(501\) −2961.73 5883.38i −0.264113 0.524651i
\(502\) 0 0
\(503\) −9602.30 −0.851184 −0.425592 0.904915i \(-0.639934\pi\)
−0.425592 + 0.904915i \(0.639934\pi\)
\(504\) 0 0
\(505\) 16281.3 1.43467
\(506\) 0 0
\(507\) −4683.58 9303.78i −0.410267 0.814981i
\(508\) 0 0
\(509\) 20047.2i 1.74573i −0.487962 0.872865i \(-0.662260\pi\)
0.487962 0.872865i \(-0.337740\pi\)
\(510\) 0 0
\(511\) 2443.79i 0.211560i
\(512\) 0 0
\(513\) −1815.72 + 10471.5i −0.156269 + 0.901220i
\(514\) 0 0
\(515\) −9097.02 −0.778374
\(516\) 0 0
\(517\) 10693.2 0.909649
\(518\) 0 0
\(519\) −1652.75 + 832.002i −0.139783 + 0.0703677i
\(520\) 0 0
\(521\) 14178.2i 1.19224i 0.802894 + 0.596121i \(0.203292\pi\)
−0.802894 + 0.596121i \(0.796708\pi\)
\(522\) 0 0
\(523\) 3326.40i 0.278114i 0.990284 + 0.139057i \(0.0444071\pi\)
−0.990284 + 0.139057i \(0.955593\pi\)
\(524\) 0 0
\(525\) −621.610 + 312.922i −0.0516749 + 0.0260134i
\(526\) 0 0
\(527\) −9098.40 −0.752054
\(528\) 0 0
\(529\) −1289.38 −0.105974
\(530\) 0 0
\(531\) −7672.92 + 10347.4i −0.627074 + 0.845648i
\(532\) 0 0
\(533\) 5311.92i 0.431679i
\(534\) 0 0
\(535\) 11853.6i 0.957896i
\(536\) 0 0
\(537\) 9993.40 + 19851.6i 0.803067 + 1.59527i
\(538\) 0 0
\(539\) −1665.41 −0.133087
\(540\) 0 0
\(541\) 1153.72 0.0916867 0.0458434 0.998949i \(-0.485402\pi\)
0.0458434 + 0.998949i \(0.485402\pi\)
\(542\) 0 0
\(543\) 7477.40 + 14853.6i 0.590950 + 1.17390i
\(544\) 0 0
\(545\) 15097.4i 1.18661i
\(546\) 0 0
\(547\) 25250.9i 1.97377i 0.161436 + 0.986883i \(0.448387\pi\)
−0.161436 + 0.986883i \(0.551613\pi\)
\(548\) 0 0
\(549\) −1805.49 + 2434.82i −0.140358 + 0.189282i
\(550\) 0 0
\(551\) −18381.9 −1.42123
\(552\) 0 0
\(553\) −3168.56 −0.243654
\(554\) 0 0
\(555\) 16898.1 8506.62i 1.29241 0.650606i
\(556\) 0 0
\(557\) 6469.49i 0.492138i −0.969252 0.246069i \(-0.920861\pi\)
0.969252 0.246069i \(-0.0791391\pi\)
\(558\) 0 0
\(559\) 166.770i 0.0126183i
\(560\) 0 0
\(561\) 4533.22 2282.05i 0.341163 0.171744i
\(562\) 0 0
\(563\) 19640.7 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(564\) 0 0
\(565\) −5390.80 −0.401403
\(566\) 0 0
\(567\) −4883.04 + 1482.08i −0.361672 + 0.109773i
\(568\) 0 0
\(569\) 8396.74i 0.618646i 0.950957 + 0.309323i \(0.100102\pi\)
−0.950957 + 0.309323i \(0.899898\pi\)
\(570\) 0 0
\(571\) 4362.50i 0.319728i −0.987139 0.159864i \(-0.948894\pi\)
0.987139 0.159864i \(-0.0511056\pi\)
\(572\) 0 0
\(573\) −8032.45 15956.2i −0.585620 1.16332i
\(574\) 0 0
\(575\) −1995.51 −0.144728
\(576\) 0 0
\(577\) 19329.8 1.39465 0.697324 0.716756i \(-0.254374\pi\)
0.697324 + 0.716756i \(0.254374\pi\)
\(578\) 0 0
\(579\) −11324.2 22495.1i −0.812808 1.61462i
\(580\) 0 0
\(581\) 7571.65i 0.540663i
\(582\) 0 0
\(583\) 14224.5i 1.01050i
\(584\) 0 0
\(585\) −3611.71 2678.19i −0.255257 0.189281i
\(586\) 0 0
\(587\) 21737.9 1.52848 0.764241 0.644931i \(-0.223114\pi\)
0.764241 + 0.644931i \(0.223114\pi\)
\(588\) 0 0
\(589\) −23983.4 −1.67779
\(590\) 0 0
\(591\) 6176.93 3109.50i 0.429924 0.216426i
\(592\) 0 0
\(593\) 20354.5i 1.40954i 0.709435 + 0.704771i \(0.248950\pi\)
−0.709435 + 0.704771i \(0.751050\pi\)
\(594\) 0 0
\(595\) 2415.06i 0.166400i
\(596\) 0 0
\(597\) 14839.8 7470.46i 1.01734 0.512137i
\(598\) 0 0
\(599\) −24269.5 −1.65547 −0.827733 0.561122i \(-0.810370\pi\)
−0.827733 + 0.561122i \(0.810370\pi\)
\(600\) 0 0
\(601\) 20775.4 1.41006 0.705029 0.709178i \(-0.250934\pi\)
0.705029 + 0.709178i \(0.250934\pi\)
\(602\) 0 0
\(603\) 3915.60 + 2903.53i 0.264437 + 0.196088i
\(604\) 0 0
\(605\) 2110.85i 0.141849i
\(606\) 0 0
\(607\) 3498.28i 0.233922i −0.993136 0.116961i \(-0.962685\pi\)
0.993136 0.116961i \(-0.0373153\pi\)
\(608\) 0 0
\(609\) −3968.70 7883.69i −0.264072 0.524570i
\(610\) 0 0
\(611\) −4364.15 −0.288960
\(612\) 0 0
\(613\) 14449.4 0.952047 0.476024 0.879433i \(-0.342078\pi\)
0.476024 + 0.879433i \(0.342078\pi\)
\(614\) 0 0
\(615\) 10741.7 + 21338.0i 0.704303 + 1.39908i
\(616\) 0 0
\(617\) 14078.2i 0.918585i 0.888285 + 0.459293i \(0.151897\pi\)
−0.888285 + 0.459293i \(0.848103\pi\)
\(618\) 0 0
\(619\) 7166.47i 0.465339i −0.972556 0.232670i \(-0.925254\pi\)
0.972556 0.232670i \(-0.0747461\pi\)
\(620\) 0 0
\(621\) −14417.2 2499.89i −0.931628 0.161541i
\(622\) 0 0
\(623\) −5713.24 −0.367410
\(624\) 0 0
\(625\) −17650.6 −1.12964
\(626\) 0 0
\(627\) 11949.6 6015.48i 0.761116 0.383150i
\(628\) 0 0
\(629\) 8715.07i 0.552453i
\(630\) 0 0
\(631\) 8130.21i 0.512929i −0.966554 0.256465i \(-0.917442\pi\)
0.966554 0.256465i \(-0.0825577\pi\)
\(632\) 0 0
\(633\) 398.163 200.438i 0.0250009 0.0125856i
\(634\) 0 0
\(635\) 18703.1 1.16883
\(636\) 0 0
\(637\) 679.689 0.0422767
\(638\) 0 0
\(639\) −408.804 + 551.298i −0.0253084 + 0.0341299i
\(640\) 0 0
\(641\) 21601.6i 1.33106i −0.746370 0.665531i \(-0.768205\pi\)
0.746370 0.665531i \(-0.231795\pi\)
\(642\) 0 0
\(643\) 21818.4i 1.33816i −0.743192 0.669078i \(-0.766689\pi\)
0.743192 0.669078i \(-0.233311\pi\)
\(644\) 0 0
\(645\) −337.240 669.916i −0.0205873 0.0408960i
\(646\) 0 0
\(647\) 26057.5 1.58335 0.791673 0.610945i \(-0.209210\pi\)
0.791673 + 0.610945i \(0.209210\pi\)
\(648\) 0 0
\(649\) 16215.8 0.980781
\(650\) 0 0
\(651\) −5178.06 10286.1i −0.311742 0.619266i
\(652\) 0 0
\(653\) 8250.21i 0.494419i 0.968962 + 0.247209i \(0.0795136\pi\)
−0.968962 + 0.247209i \(0.920486\pi\)
\(654\) 0 0
\(655\) 22383.6i 1.33527i
\(656\) 0 0
\(657\) 5614.51 7571.51i 0.333398 0.449608i
\(658\) 0 0
\(659\) 7630.25 0.451035 0.225518 0.974239i \(-0.427593\pi\)
0.225518 + 0.974239i \(0.427593\pi\)
\(660\) 0 0
\(661\) 1683.25 0.0990480 0.0495240 0.998773i \(-0.484230\pi\)
0.0495240 + 0.998773i \(0.484230\pi\)
\(662\) 0 0
\(663\) −1850.10 + 931.354i −0.108374 + 0.0545562i
\(664\) 0 0
\(665\) 6366.11i 0.371229i
\(666\) 0 0
\(667\) 25308.4i 1.46918i
\(668\) 0 0
\(669\) −1558.43 + 784.524i −0.0900634 + 0.0453385i
\(670\) 0 0
\(671\) 3815.71 0.219529
\(672\) 0 0
\(673\) −16361.7 −0.937143 −0.468571 0.883426i \(-0.655231\pi\)
−0.468571 + 0.883426i \(0.655231\pi\)
\(674\) 0 0
\(675\) 2644.84 + 458.607i 0.150815 + 0.0261508i
\(676\) 0 0
\(677\) 13383.2i 0.759763i −0.925035 0.379882i \(-0.875965\pi\)
0.925035 0.379882i \(-0.124035\pi\)
\(678\) 0 0
\(679\) 7490.47i 0.423355i
\(680\) 0 0
\(681\) 8253.00 + 16394.3i 0.464399 + 0.922514i
\(682\) 0 0
\(683\) −15026.1 −0.841810 −0.420905 0.907105i \(-0.638287\pi\)
−0.420905 + 0.907105i \(0.638287\pi\)
\(684\) 0 0
\(685\) −6954.80 −0.387926
\(686\) 0 0
\(687\) −13343.9 26507.3i −0.741053 1.47208i
\(688\) 0 0
\(689\) 5805.34i 0.320996i
\(690\) 0 0
\(691\) 1932.62i 0.106397i −0.998584 0.0531986i \(-0.983058\pi\)
0.998584 0.0531986i \(-0.0169416\pi\)
\(692\) 0 0
\(693\) 5159.87 + 3826.20i 0.282839 + 0.209734i
\(694\) 0 0
\(695\) 16933.1 0.924185
\(696\) 0 0
\(697\) 11004.9 0.598049
\(698\) 0 0
\(699\) −4764.03 + 2398.24i −0.257785 + 0.129771i
\(700\) 0 0
\(701\) 3730.63i 0.201004i 0.994937 + 0.100502i \(0.0320449\pi\)
−0.994937 + 0.100502i \(0.967955\pi\)
\(702\) 0 0
\(703\) 22972.9i 1.23249i
\(704\) 0 0
\(705\) 17530.8 8825.10i 0.936521 0.471451i
\(706\) 0 0
\(707\) 9493.07 0.504984
\(708\) 0 0
\(709\) −19110.7 −1.01230 −0.506149 0.862446i \(-0.668931\pi\)
−0.506149 + 0.862446i \(0.668931\pi\)
\(710\) 0 0
\(711\) 9817.02 + 7279.62i 0.517816 + 0.383976i
\(712\) 0 0
\(713\) 33020.5i 1.73440i
\(714\) 0 0
\(715\) 5660.05i 0.296047i
\(716\) 0 0
\(717\) 5618.20 + 11160.4i 0.292630 + 0.581299i
\(718\) 0 0
\(719\) 9718.45 0.504085 0.252043 0.967716i \(-0.418898\pi\)
0.252043 + 0.967716i \(0.418898\pi\)
\(720\) 0 0
\(721\) −5304.14 −0.273976
\(722\) 0 0
\(723\) −15274.6 30342.5i −0.785712 1.56079i
\(724\) 0 0
\(725\) 4642.84i 0.237836i
\(726\) 0 0
\(727\) 20385.8i 1.03998i −0.854172 0.519991i \(-0.825935\pi\)
0.854172 0.519991i \(-0.174065\pi\)
\(728\) 0 0
\(729\) 18534.0 + 6626.70i 0.941622 + 0.336671i
\(730\) 0 0
\(731\) −345.504 −0.0174814
\(732\) 0 0
\(733\) −14957.5 −0.753709 −0.376855 0.926272i \(-0.622994\pi\)
−0.376855 + 0.926272i \(0.622994\pi\)
\(734\) 0 0
\(735\) −2730.31 + 1374.45i −0.137019 + 0.0689762i
\(736\) 0 0
\(737\) 6136.29i 0.306693i
\(738\) 0 0
\(739\) 31710.5i 1.57847i 0.614090 + 0.789236i \(0.289523\pi\)
−0.614090 + 0.789236i \(0.710477\pi\)
\(740\) 0 0
\(741\) −4876.88 + 2455.05i −0.241777 + 0.121712i
\(742\) 0 0
\(743\) −26608.9 −1.31384 −0.656922 0.753958i \(-0.728142\pi\)
−0.656922 + 0.753958i \(0.728142\pi\)
\(744\) 0 0
\(745\) 34194.5 1.68160
\(746\) 0 0
\(747\) 17395.6 23459.0i 0.852035 1.14902i
\(748\) 0 0
\(749\) 6911.39i 0.337165i
\(750\) 0 0
\(751\) 20486.9i 0.995445i −0.867336 0.497723i \(-0.834170\pi\)
0.867336 0.497723i \(-0.165830\pi\)
\(752\) 0 0
\(753\) −178.180 353.950i −0.00862318 0.0171297i
\(754\) 0 0
\(755\) 6686.04 0.322291
\(756\) 0 0
\(757\) 7557.64 0.362863 0.181431 0.983404i \(-0.441927\pi\)
0.181431 + 0.983404i \(0.441927\pi\)
\(758\) 0 0
\(759\) 8282.16 + 16452.2i 0.396078 + 0.786797i
\(760\) 0 0
\(761\) 7134.66i 0.339857i 0.985456 + 0.169928i \(0.0543537\pi\)
−0.985456 + 0.169928i \(0.945646\pi\)
\(762\) 0 0
\(763\) 8802.73i 0.417667i
\(764\) 0 0
\(765\) 5548.50 7482.50i 0.262231 0.353634i
\(766\) 0 0
\(767\) −6618.03 −0.311556
\(768\) 0 0
\(769\) −15189.2 −0.712270 −0.356135 0.934434i \(-0.615906\pi\)
−0.356135 + 0.934434i \(0.615906\pi\)
\(770\) 0 0
\(771\) −24196.7 + 12180.8i −1.13025 + 0.568976i
\(772\) 0 0
\(773\) 30376.4i 1.41340i 0.707511 + 0.706702i \(0.249818\pi\)
−0.707511 + 0.706702i \(0.750182\pi\)
\(774\) 0 0
\(775\) 6057.64i 0.280770i
\(776\) 0 0
\(777\) 9852.69 4959.91i 0.454908 0.229003i
\(778\) 0 0
\(779\) 29008.9 1.33421
\(780\) 0 0
\(781\) 863.961 0.0395838
\(782\) 0 0
\(783\) −5816.37 + 33543.7i −0.265466 + 1.53097i
\(784\) 0 0
\(785\) 12661.4i 0.575673i
\(786\) 0 0
\(787\) 19109.2i 0.865528i −0.901507 0.432764i \(-0.857538\pi\)
0.901507 0.432764i \(-0.142462\pi\)
\(788\) 0 0
\(789\) 15566.7 + 30922.7i 0.702393 + 1.39528i
\(790\) 0 0
\(791\) −3143.18 −0.141288
\(792\) 0 0
\(793\) −1557.27 −0.0697356
\(794\) 0 0
\(795\) 11739.5 + 23320.1i 0.523718 + 1.04035i
\(796\) 0 0
\(797\) 15055.1i 0.669109i −0.942376 0.334554i \(-0.891414\pi\)
0.942376 0.334554i \(-0.108586\pi\)
\(798\) 0 0
\(799\) 9041.36i 0.400326i