Properties

Label 648.4.i.r.433.2
Level $648$
Weight $4$
Character 648.433
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 433.2
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.4.i.r.217.2

$q$-expansion

\(f(q)\) \(=\) \(q+(7.70820 - 13.3510i) q^{5} +(-11.9164 - 20.6398i) q^{7} +O(q^{10})\) \(q+(7.70820 - 13.3510i) q^{5} +(-11.9164 - 20.6398i) q^{7} +(-7.12461 - 12.3402i) q^{11} +(6.91641 - 11.9796i) q^{13} -80.5836 q^{17} -144.331 q^{19} +(70.5410 - 122.181i) q^{23} +(-56.3328 - 97.5713i) q^{25} +(125.666 + 217.659i) q^{29} +(8.33437 - 14.4355i) q^{31} -367.416 q^{35} +305.164 q^{37} +(-214.663 + 371.806i) q^{41} +(90.8328 + 157.327i) q^{43} +(39.7082 + 68.7766i) q^{47} +(-112.502 + 194.858i) q^{49} -663.830 q^{53} -219.672 q^{55} +(-110.128 + 190.747i) q^{59} +(236.579 + 409.767i) q^{61} +(-106.626 - 184.682i) q^{65} +(323.831 - 560.892i) q^{67} +14.4922 q^{71} +776.003 q^{73} +(-169.800 + 294.101i) q^{77} +(128.913 + 223.284i) q^{79} +(-642.577 - 1112.98i) q^{83} +(-621.155 + 1075.87i) q^{85} -156.255 q^{89} -329.675 q^{91} +(-1112.53 + 1926.97i) q^{95} +(-580.822 - 1006.01i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 4q^{5} + 6q^{7} + 52q^{11} - 26q^{13} - 376q^{17} - 148q^{19} + 148q^{23} - 118q^{25} + 288q^{29} + 248q^{31} - 1416q^{35} + 684q^{37} + 256q^{43} + 132q^{47} - 772q^{49} - 1904q^{53} - 1952q^{55} - 1004q^{59} + 34q^{61} - 668q^{65} + 866q^{67} - 1552q^{71} + 3748q^{73} - 2316q^{77} - 182q^{79} - 1336q^{83} - 16q^{85} - 1752q^{89} - 3036q^{91} - 3028q^{95} + 38q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 7.70820 13.3510i 0.689443 1.19415i −0.282576 0.959245i \(-0.591189\pi\)
0.972018 0.234905i \(-0.0754778\pi\)
\(6\) 0 0
\(7\) −11.9164 20.6398i −0.643426 1.11445i −0.984663 0.174469i \(-0.944179\pi\)
0.341237 0.939977i \(-0.389154\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −7.12461 12.3402i −0.195286 0.338246i 0.751708 0.659496i \(-0.229230\pi\)
−0.946994 + 0.321250i \(0.895897\pi\)
\(12\) 0 0
\(13\) 6.91641 11.9796i 0.147559 0.255580i −0.782766 0.622316i \(-0.786192\pi\)
0.930325 + 0.366737i \(0.119525\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −80.5836 −1.14967 −0.574835 0.818269i \(-0.694934\pi\)
−0.574835 + 0.818269i \(0.694934\pi\)
\(18\) 0 0
\(19\) −144.331 −1.74273 −0.871365 0.490636i \(-0.836765\pi\)
−0.871365 + 0.490636i \(0.836765\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 70.5410 122.181i 0.639514 1.10767i −0.346026 0.938225i \(-0.612469\pi\)
0.985540 0.169445i \(-0.0541977\pi\)
\(24\) 0 0
\(25\) −56.3328 97.5713i −0.450663 0.780570i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 125.666 + 217.659i 0.804673 + 1.39373i 0.916511 + 0.400008i \(0.130993\pi\)
−0.111838 + 0.993726i \(0.535674\pi\)
\(30\) 0 0
\(31\) 8.33437 14.4355i 0.0482870 0.0836355i −0.840872 0.541235i \(-0.817957\pi\)
0.889159 + 0.457599i \(0.151290\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −367.416 −1.77442
\(36\) 0 0
\(37\) 305.164 1.35591 0.677955 0.735103i \(-0.262866\pi\)
0.677955 + 0.735103i \(0.262866\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −214.663 + 371.806i −0.817674 + 1.41625i 0.0897170 + 0.995967i \(0.471404\pi\)
−0.907391 + 0.420286i \(0.861930\pi\)
\(42\) 0 0
\(43\) 90.8328 + 157.327i 0.322137 + 0.557957i 0.980929 0.194368i \(-0.0622656\pi\)
−0.658792 + 0.752325i \(0.728932\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 39.7082 + 68.7766i 0.123235 + 0.213449i 0.921042 0.389464i \(-0.127340\pi\)
−0.797807 + 0.602913i \(0.794006\pi\)
\(48\) 0 0
\(49\) −112.502 + 194.858i −0.327993 + 0.568100i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −663.830 −1.72045 −0.860227 0.509912i \(-0.829678\pi\)
−0.860227 + 0.509912i \(0.829678\pi\)
\(54\) 0 0
\(55\) −219.672 −0.538555
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −110.128 + 190.747i −0.243007 + 0.420900i −0.961569 0.274562i \(-0.911467\pi\)
0.718562 + 0.695462i \(0.244800\pi\)
\(60\) 0 0
\(61\) 236.579 + 409.767i 0.496571 + 0.860086i 0.999992 0.00395500i \(-0.00125892\pi\)
−0.503421 + 0.864041i \(0.667926\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −106.626 184.682i −0.203467 0.352415i
\(66\) 0 0
\(67\) 323.831 560.892i 0.590482 1.02274i −0.403686 0.914898i \(-0.632271\pi\)
0.994168 0.107847i \(-0.0343956\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.4922 0.0242241 0.0121121 0.999927i \(-0.496145\pi\)
0.0121121 + 0.999927i \(0.496145\pi\)
\(72\) 0 0
\(73\) 776.003 1.24417 0.622084 0.782950i \(-0.286286\pi\)
0.622084 + 0.782950i \(0.286286\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −169.800 + 294.101i −0.251305 + 0.435272i
\(78\) 0 0
\(79\) 128.913 + 223.284i 0.183593 + 0.317993i 0.943102 0.332505i \(-0.107894\pi\)
−0.759508 + 0.650498i \(0.774560\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −642.577 1112.98i −0.849784 1.47187i −0.881401 0.472368i \(-0.843399\pi\)
0.0316178 0.999500i \(-0.489934\pi\)
\(84\) 0 0
\(85\) −621.155 + 1075.87i −0.792632 + 1.37288i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −156.255 −0.186102 −0.0930508 0.995661i \(-0.529662\pi\)
−0.0930508 + 0.995661i \(0.529662\pi\)
\(90\) 0 0
\(91\) −329.675 −0.379773
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1112.53 + 1926.97i −1.20151 + 2.08108i
\(96\) 0 0
\(97\) −580.822 1006.01i −0.607975 1.05304i −0.991574 0.129543i \(-0.958649\pi\)
0.383599 0.923500i \(-0.374684\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −842.991 1460.10i −0.830502 1.43847i −0.897641 0.440728i \(-0.854720\pi\)
0.0671386 0.997744i \(-0.478613\pi\)
\(102\) 0 0
\(103\) 382.910 663.220i 0.366304 0.634456i −0.622681 0.782476i \(-0.713957\pi\)
0.988984 + 0.148020i \(0.0472899\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1747.89 −1.57920 −0.789602 0.613619i \(-0.789713\pi\)
−0.789602 + 0.613619i \(0.789713\pi\)
\(108\) 0 0
\(109\) −1211.64 −1.06472 −0.532358 0.846519i \(-0.678694\pi\)
−0.532358 + 0.846519i \(0.678694\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −482.213 + 835.217i −0.401440 + 0.695315i −0.993900 0.110285i \(-0.964824\pi\)
0.592460 + 0.805600i \(0.298157\pi\)
\(114\) 0 0
\(115\) −1087.49 1883.59i −0.881816 1.52735i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 960.267 + 1663.23i 0.739727 + 1.28124i
\(120\) 0 0
\(121\) 563.980 976.842i 0.423726 0.733916i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 190.152 0.136061
\(126\) 0 0
\(127\) −2238.31 −1.56392 −0.781960 0.623329i \(-0.785780\pi\)
−0.781960 + 0.623329i \(0.785780\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −837.155 + 1449.99i −0.558340 + 0.967073i 0.439295 + 0.898343i \(0.355228\pi\)
−0.997635 + 0.0687306i \(0.978105\pi\)
\(132\) 0 0
\(133\) 1719.91 + 2978.97i 1.12132 + 1.94218i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 47.5379 + 82.3381i 0.0296455 + 0.0513476i 0.880468 0.474106i \(-0.157229\pi\)
−0.850822 + 0.525454i \(0.823895\pi\)
\(138\) 0 0
\(139\) −585.320 + 1013.80i −0.357167 + 0.618632i −0.987486 0.157704i \(-0.949591\pi\)
0.630319 + 0.776336i \(0.282924\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −197.107 −0.115265
\(144\) 0 0
\(145\) 3874.63 2.21910
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −429.568 + 744.034i −0.236185 + 0.409085i −0.959616 0.281312i \(-0.909231\pi\)
0.723431 + 0.690396i \(0.242564\pi\)
\(150\) 0 0
\(151\) −1449.41 2510.46i −0.781137 1.35297i −0.931280 0.364305i \(-0.881307\pi\)
0.150143 0.988664i \(-0.452027\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −128.486 222.544i −0.0665822 0.115324i
\(156\) 0 0
\(157\) 654.508 1133.64i 0.332710 0.576270i −0.650333 0.759650i \(-0.725370\pi\)
0.983042 + 0.183380i \(0.0587038\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3362.38 −1.64592
\(162\) 0 0
\(163\) −190.988 −0.0917749 −0.0458874 0.998947i \(-0.514612\pi\)
−0.0458874 + 0.998947i \(0.514612\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 720.365 1247.71i 0.333793 0.578147i −0.649459 0.760397i \(-0.725005\pi\)
0.983252 + 0.182250i \(0.0583379\pi\)
\(168\) 0 0
\(169\) 1002.83 + 1736.95i 0.456453 + 0.790599i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 790.663 + 1369.47i 0.347474 + 0.601842i 0.985800 0.167924i \(-0.0537062\pi\)
−0.638326 + 0.769766i \(0.720373\pi\)
\(174\) 0 0
\(175\) −1342.57 + 2325.40i −0.579936 + 1.00448i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −741.836 −0.309762 −0.154881 0.987933i \(-0.549499\pi\)
−0.154881 + 0.987933i \(0.549499\pi\)
\(180\) 0 0
\(181\) 626.786 0.257396 0.128698 0.991684i \(-0.458920\pi\)
0.128698 + 0.991684i \(0.458920\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2352.27 4074.25i 0.934822 1.61916i
\(186\) 0 0
\(187\) 574.127 + 994.417i 0.224515 + 0.388871i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 91.3073 + 158.149i 0.0345904 + 0.0599123i 0.882802 0.469745i \(-0.155654\pi\)
−0.848212 + 0.529657i \(0.822321\pi\)
\(192\) 0 0
\(193\) −859.330 + 1488.40i −0.320497 + 0.555117i −0.980591 0.196066i \(-0.937183\pi\)
0.660094 + 0.751183i \(0.270517\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 119.587 0.0432497 0.0216249 0.999766i \(-0.493116\pi\)
0.0216249 + 0.999766i \(0.493116\pi\)
\(198\) 0 0
\(199\) 707.467 0.252015 0.126008 0.992029i \(-0.459784\pi\)
0.126008 + 0.992029i \(0.459784\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2994.97 5187.43i 1.03549 1.79353i
\(204\) 0 0
\(205\) 3309.33 + 5731.92i 1.12748 + 1.95285i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1028.30 + 1781.08i 0.340332 + 0.589472i
\(210\) 0 0
\(211\) 1194.31 2068.60i 0.389666 0.674922i −0.602738 0.797939i \(-0.705924\pi\)
0.992405 + 0.123017i \(0.0392571\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2800.63 0.888379
\(216\) 0 0
\(217\) −397.263 −0.124276
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −557.349 + 965.357i −0.169644 + 0.293832i
\(222\) 0 0
\(223\) −2811.30 4869.31i −0.844209 1.46221i −0.886306 0.463099i \(-0.846737\pi\)
0.0420975 0.999114i \(-0.486596\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1732.23 3000.31i −0.506485 0.877258i −0.999972 0.00750494i \(-0.997611\pi\)
0.493486 0.869753i \(-0.335722\pi\)
\(228\) 0 0
\(229\) 3041.31 5267.70i 0.877622 1.52009i 0.0236784 0.999720i \(-0.492462\pi\)
0.853943 0.520366i \(-0.174204\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5024.29 1.41267 0.706335 0.707877i \(-0.250347\pi\)
0.706335 + 0.707877i \(0.250347\pi\)
\(234\) 0 0
\(235\) 1224.32 0.339853
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1335.10 2312.46i 0.361341 0.625861i −0.626841 0.779147i \(-0.715652\pi\)
0.988182 + 0.153286i \(0.0489857\pi\)
\(240\) 0 0
\(241\) −377.327 653.549i −0.100854 0.174684i 0.811183 0.584793i \(-0.198824\pi\)
−0.912037 + 0.410109i \(0.865491\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1734.37 + 3004.02i 0.452265 + 0.783345i
\(246\) 0 0
\(247\) −998.254 + 1729.03i −0.257155 + 0.445406i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1588.91 −0.399566 −0.199783 0.979840i \(-0.564024\pi\)
−0.199783 + 0.979840i \(0.564024\pi\)
\(252\) 0 0
\(253\) −2010.31 −0.499554
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2455.88 + 4253.70i −0.596083 + 1.03245i 0.397310 + 0.917685i \(0.369944\pi\)
−0.993393 + 0.114762i \(0.963389\pi\)
\(258\) 0 0
\(259\) −3636.46 6298.53i −0.872427 1.51109i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2700.21 + 4676.89i 0.633087 + 1.09654i 0.986917 + 0.161229i \(0.0515457\pi\)
−0.353830 + 0.935310i \(0.615121\pi\)
\(264\) 0 0
\(265\) −5116.93 + 8862.79i −1.18615 + 2.05448i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3234.09 0.733034 0.366517 0.930411i \(-0.380550\pi\)
0.366517 + 0.930411i \(0.380550\pi\)
\(270\) 0 0
\(271\) −6205.83 −1.39106 −0.695530 0.718497i \(-0.744830\pi\)
−0.695530 + 0.718497i \(0.744830\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −802.699 + 1390.32i −0.176017 + 0.304870i
\(276\) 0 0
\(277\) −515.455 892.794i −0.111808 0.193656i 0.804692 0.593693i \(-0.202331\pi\)
−0.916499 + 0.400037i \(0.868997\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1910.66 3309.36i −0.405625 0.702563i 0.588769 0.808301i \(-0.299613\pi\)
−0.994394 + 0.105738i \(0.966279\pi\)
\(282\) 0 0
\(283\) 2201.17 3812.53i 0.462353 0.800818i −0.536725 0.843757i \(-0.680339\pi\)
0.999078 + 0.0429389i \(0.0136721\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10232.0 2.10445
\(288\) 0 0
\(289\) 1580.72 0.321741
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2986.77 5173.24i 0.595526 1.03148i −0.397947 0.917409i \(-0.630277\pi\)
0.993472 0.114072i \(-0.0363896\pi\)
\(294\) 0 0
\(295\) 1697.77 + 2940.63i 0.335079 + 0.580373i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −975.781 1690.10i −0.188732 0.326893i
\(300\) 0 0
\(301\) 2164.80 3749.55i 0.414542 0.718008i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7294.39 1.36943
\(306\) 0 0
\(307\) −219.622 −0.0408290 −0.0204145 0.999792i \(-0.506499\pi\)
−0.0204145 + 0.999792i \(0.506499\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 478.614 828.983i 0.0872659 0.151149i −0.819089 0.573667i \(-0.805520\pi\)
0.906355 + 0.422518i \(0.138854\pi\)
\(312\) 0 0
\(313\) −937.026 1622.98i −0.169214 0.293087i 0.768930 0.639333i \(-0.220789\pi\)
−0.938144 + 0.346246i \(0.887456\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1459.89 2528.60i −0.258661 0.448014i 0.707222 0.706991i \(-0.249948\pi\)
−0.965884 + 0.258977i \(0.916615\pi\)
\(318\) 0 0
\(319\) 1790.64 3101.48i 0.314284 0.544355i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11630.7 2.00356
\(324\) 0 0
\(325\) −1558.48 −0.265997
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 946.358 1639.14i 0.158585 0.274677i
\(330\) 0 0
\(331\) 3324.33 + 5757.91i 0.552030 + 0.956144i 0.998128 + 0.0611596i \(0.0194799\pi\)
−0.446098 + 0.894984i \(0.647187\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4992.31 8646.94i −0.814207 1.41025i
\(336\) 0 0
\(337\) −1943.17 + 3365.67i −0.314098 + 0.544034i −0.979245 0.202678i \(-0.935036\pi\)
0.665147 + 0.746712i \(0.268369\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −237.517 −0.0377192
\(342\) 0 0
\(343\) −2812.20 −0.442695
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2103.88 + 3644.02i −0.325481 + 0.563750i −0.981610 0.190899i \(-0.938860\pi\)
0.656128 + 0.754649i \(0.272193\pi\)
\(348\) 0 0
\(349\) −1505.71 2607.97i −0.230942 0.400004i 0.727143 0.686486i \(-0.240848\pi\)
−0.958086 + 0.286482i \(0.907514\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1249.90 2164.88i −0.188457 0.326417i 0.756279 0.654249i \(-0.227015\pi\)
−0.944736 + 0.327832i \(0.893682\pi\)
\(354\) 0 0
\(355\) 111.709 193.486i 0.0167011 0.0289272i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8319.17 −1.22303 −0.611517 0.791231i \(-0.709440\pi\)
−0.611517 + 0.791231i \(0.709440\pi\)
\(360\) 0 0
\(361\) 13972.5 2.03711
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5981.59 10360.4i 0.857783 1.48572i
\(366\) 0 0
\(367\) 2229.93 + 3862.34i 0.317169 + 0.549354i 0.979896 0.199508i \(-0.0639343\pi\)
−0.662727 + 0.748861i \(0.730601\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7910.47 + 13701.3i 1.10698 + 1.91735i
\(372\) 0 0
\(373\) 589.703 1021.39i 0.0818596 0.141785i −0.822189 0.569214i \(-0.807247\pi\)
0.904049 + 0.427429i \(0.140581\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3476.62 0.474947
\(378\) 0 0
\(379\) 8413.88 1.14035 0.570174 0.821524i \(-0.306876\pi\)
0.570174 + 0.821524i \(0.306876\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 800.972 1387.32i 0.106861 0.185089i −0.807636 0.589681i \(-0.799253\pi\)
0.914497 + 0.404593i \(0.132587\pi\)
\(384\) 0 0
\(385\) 2617.70 + 4533.99i 0.346520 + 0.600191i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2601.21 4505.44i −0.339041 0.587236i 0.645212 0.764004i \(-0.276769\pi\)
−0.984253 + 0.176768i \(0.943436\pi\)
\(390\) 0 0
\(391\) −5684.45 + 9845.75i −0.735230 + 1.27346i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3974.76 0.506309
\(396\) 0 0
\(397\) 4310.87 0.544979 0.272489 0.962159i \(-0.412153\pi\)
0.272489 + 0.962159i \(0.412153\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3120.29 5404.51i 0.388579 0.673038i −0.603680 0.797227i \(-0.706300\pi\)
0.992259 + 0.124189i \(0.0396329\pi\)
\(402\) 0 0
\(403\) −115.288 199.684i −0.0142504 0.0246823i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2174.18 3765.78i −0.264791 0.458631i
\(408\) 0 0
\(409\) −1023.83 + 1773.33i −0.123778 + 0.214390i −0.921255 0.388960i \(-0.872834\pi\)
0.797477 + 0.603350i \(0.206168\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5249.31 0.625427
\(414\) 0 0
\(415\) −19812.5 −2.34351
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2980.06 5161.62i 0.347459 0.601817i −0.638338 0.769756i \(-0.720378\pi\)
0.985797 + 0.167939i \(0.0537111\pi\)
\(420\) 0 0
\(421\) −155.783 269.825i −0.0180342 0.0312362i 0.856867 0.515537i \(-0.172407\pi\)
−0.874902 + 0.484301i \(0.839074\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4539.50 + 7862.65i 0.518113 + 0.897398i
\(426\) 0 0
\(427\) 5638.34 9765.90i 0.639013 1.10680i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −17105.0 −1.91164 −0.955821 0.293950i \(-0.905030\pi\)
−0.955821 + 0.293950i \(0.905030\pi\)
\(432\) 0 0
\(433\) 2582.96 0.286672 0.143336 0.989674i \(-0.454217\pi\)
0.143336 + 0.989674i \(0.454217\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10181.3 + 17634.5i −1.11450 + 1.93037i
\(438\) 0 0
\(439\) 3398.93 + 5887.13i 0.369527 + 0.640039i 0.989492 0.144590i \(-0.0461864\pi\)
−0.619965 + 0.784630i \(0.712853\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5227.04 + 9053.50i 0.560596 + 0.970981i 0.997444 + 0.0714458i \(0.0227613\pi\)
−0.436848 + 0.899535i \(0.643905\pi\)
\(444\) 0 0
\(445\) −1204.45 + 2086.17i −0.128306 + 0.222233i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −17208.6 −1.80873 −0.904367 0.426755i \(-0.859657\pi\)
−0.904367 + 0.426755i \(0.859657\pi\)
\(450\) 0 0
\(451\) 6117.55 0.638723
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2541.20 + 4401.49i −0.261832 + 0.453506i
\(456\) 0 0
\(457\) −7894.04 13672.9i −0.808025 1.39954i −0.914230 0.405196i \(-0.867203\pi\)
0.106205 0.994344i \(-0.466130\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2591.59 + 4488.76i 0.261827 + 0.453497i 0.966727 0.255809i \(-0.0823417\pi\)
−0.704901 + 0.709306i \(0.749008\pi\)
\(462\) 0 0
\(463\) 2916.69 5051.86i 0.292765 0.507083i −0.681698 0.731634i \(-0.738758\pi\)
0.974462 + 0.224551i \(0.0720914\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6315.33 −0.625779 −0.312889 0.949790i \(-0.601297\pi\)
−0.312889 + 0.949790i \(0.601297\pi\)
\(468\) 0 0
\(469\) −15435.6 −1.51972
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1294.30 2241.79i 0.125818 0.217923i
\(474\) 0 0
\(475\) 8130.59 + 14082.6i 0.785383 + 1.36032i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4867.94 + 8431.52i 0.464346 + 0.804271i 0.999172 0.0406913i \(-0.0129560\pi\)
−0.534826 + 0.844963i \(0.679623\pi\)
\(480\) 0 0
\(481\) 2110.64 3655.73i 0.200077 0.346543i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17908.4 −1.67665
\(486\) 0 0
\(487\) 13447.9 1.25130 0.625649 0.780104i \(-0.284834\pi\)
0.625649 + 0.780104i \(0.284834\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3514.04 + 6086.50i −0.322987 + 0.559430i −0.981103 0.193487i \(-0.938020\pi\)
0.658116 + 0.752917i \(0.271354\pi\)
\(492\) 0 0
\(493\) −10126.6 17539.8i −0.925109 1.60234i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −172.695 299.117i −0.0155864 0.0269965i
\(498\) 0 0
\(499\) −827.722 + 1433.66i −0.0742563 + 0.128616i −0.900763 0.434312i \(-0.856992\pi\)
0.826506 + 0.562927i \(0.190325\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1909.16 −0.169235 −0.0846174 0.996414i \(-0.526967\pi\)
−0.0846174 + 0.996414i \(0.526967\pi\)
\(504\) 0 0
\(505\) −25991.8 −2.29033
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4432.85 7677.92i 0.386017 0.668601i −0.605893 0.795546i \(-0.707184\pi\)
0.991910 + 0.126945i \(0.0405173\pi\)
\(510\) 0 0
\(511\) −9247.17 16016.6i −0.800530 1.38656i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5903.10 10224.5i −0.505091 0.874843i
\(516\) 0 0
\(517\) 565.811 980.014i 0.0481322 0.0833674i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9256.80 −0.778403 −0.389201 0.921153i \(-0.627249\pi\)
−0.389201 + 0.921153i \(0.627249\pi\)
\(522\) 0 0
\(523\) 13607.5 1.13770 0.568849 0.822442i \(-0.307389\pi\)
0.568849 + 0.822442i \(0.307389\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −671.613 + 1163.27i −0.0555141 + 0.0961533i
\(528\) 0 0
\(529\) −3868.57 6700.56i −0.317956 0.550716i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2969.39 + 5143.13i 0.241310 + 0.417962i
\(534\) 0 0
\(535\) −13473.1 + 23336.1i −1.08877 + 1.88581i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3206.12 0.256210
\(540\) 0 0
\(541\) −483.548 −0.0384276 −0.0192138 0.999815i \(-0.506116\pi\)
−0.0192138 + 0.999815i \(0.506116\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −9339.57 + 16176.6i −0.734061 + 1.27143i
\(546\) 0 0
\(547\) 2355.64 + 4080.09i 0.184131 + 0.318925i 0.943283 0.331988i \(-0.107719\pi\)
−0.759152 + 0.650913i \(0.774386\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −18137.5 31415.0i −1.40233 2.42890i
\(552\) 0 0
\(553\) 3072.37 5321.50i 0.236257 0.409210i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 21650.7 1.64698 0.823492 0.567327i \(-0.192023\pi\)
0.823492 + 0.567327i \(0.192023\pi\)
\(558\) 0 0
\(559\) 2512.95 0.190137
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7011.50 12144.3i 0.524866 0.909094i −0.474715 0.880140i \(-0.657449\pi\)
0.999581 0.0289545i \(-0.00921780\pi\)
\(564\) 0 0
\(565\) 7433.99 + 12876.0i 0.553540 + 0.958760i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2437.67 + 4222.16i 0.179600 + 0.311076i 0.941744 0.336332i \(-0.109186\pi\)
−0.762144 + 0.647408i \(0.775853\pi\)
\(570\) 0 0
\(571\) 12984.6 22489.9i 0.951640 1.64829i 0.209765 0.977752i \(-0.432730\pi\)
0.741876 0.670537i \(-0.233936\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −15895.1 −1.15282
\(576\) 0 0
\(577\) −23113.1 −1.66761 −0.833806 0.552058i \(-0.813843\pi\)
−0.833806 + 0.552058i \(0.813843\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15314.4 + 26525.4i −1.09354 + 1.89408i
\(582\) 0 0
\(583\) 4729.53 + 8191.78i 0.335981 + 0.581937i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2735.83 4738.59i −0.192368 0.333190i 0.753667 0.657257i \(-0.228283\pi\)
−0.946034 + 0.324066i \(0.894950\pi\)
\(588\) 0 0
\(589\) −1202.91 + 2083.50i −0.0841512 + 0.145754i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22609.2 −1.56568 −0.782841 0.622222i \(-0.786230\pi\)
−0.782841 + 0.622222i \(0.786230\pi\)
\(594\) 0 0
\(595\) 29607.7 2.04000
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1854.45 + 3211.99i −0.126495 + 0.219096i −0.922316 0.386436i \(-0.873706\pi\)
0.795821 + 0.605532i \(0.207039\pi\)
\(600\) 0 0
\(601\) 5239.08 + 9074.36i 0.355585 + 0.615892i 0.987218 0.159376i \(-0.0509483\pi\)
−0.631633 + 0.775268i \(0.717615\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −8694.54 15059.4i −0.584270 1.01199i
\(606\) 0 0
\(607\) −5356.78 + 9278.22i −0.358196 + 0.620414i −0.987660 0.156616i \(-0.949941\pi\)
0.629463 + 0.777030i \(0.283275\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1098.55 0.0727376
\(612\) 0 0
\(613\) 7860.62 0.517924 0.258962 0.965887i \(-0.416619\pi\)
0.258962 + 0.965887i \(0.416619\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4264.00 + 7385.47i −0.278221 + 0.481893i −0.970943 0.239312i \(-0.923078\pi\)
0.692722 + 0.721205i \(0.256411\pi\)
\(618\) 0 0
\(619\) 4011.45 + 6948.03i 0.260474 + 0.451155i 0.966368 0.257163i \(-0.0827877\pi\)
−0.705894 + 0.708318i \(0.749454\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1862.00 + 3225.08i 0.119743 + 0.207400i
\(624\) 0 0
\(625\) 8507.33 14735.1i 0.544469 0.943048i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24591.2 −1.55885
\(630\) 0 0
\(631\) −3984.40 −0.251373 −0.125687 0.992070i \(-0.540113\pi\)
−0.125687 + 0.992070i \(0.540113\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −17253.3 + 29883.7i −1.07823 + 1.86755i
\(636\) 0 0
\(637\) 1556.21 + 2695.44i 0.0967966 + 0.167657i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7375.12 12774.1i −0.454446 0.787123i 0.544210 0.838949i \(-0.316829\pi\)
−0.998656 + 0.0518255i \(0.983496\pi\)
\(642\) 0 0
\(643\) −4905.37 + 8496.35i −0.300854 + 0.521094i −0.976330 0.216288i \(-0.930605\pi\)
0.675476 + 0.737382i \(0.263938\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5683.55 0.345353 0.172677 0.984979i \(-0.444758\pi\)
0.172677 + 0.984979i \(0.444758\pi\)
\(648\) 0 0
\(649\) 3138.47 0.189824
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1702.76 + 2949.27i −0.102043 + 0.176744i −0.912526 0.409018i \(-0.865871\pi\)
0.810483 + 0.585762i \(0.199205\pi\)
\(654\) 0 0
\(655\) 12905.9 + 22353.7i 0.769887 + 1.33348i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9524.57 + 16497.0i 0.563011 + 0.975164i 0.997232 + 0.0743575i \(0.0236906\pi\)
−0.434220 + 0.900807i \(0.642976\pi\)
\(660\) 0 0
\(661\) −10211.2 + 17686.4i −0.600864 + 1.04073i 0.391827 + 0.920039i \(0.371843\pi\)
−0.992691 + 0.120688i \(0.961490\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 53029.7 3.09233
\(666\) 0 0
\(667\) 35458.3 2.05840
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3371.07 5838.86i 0.193947 0.335926i
\(672\) 0 0
\(673\) −4306.73 7459.47i −0.246675 0.427253i 0.715926 0.698176i \(-0.246005\pi\)
−0.962601 + 0.270923i \(0.912671\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5234.56 9066.52i −0.297164 0.514704i 0.678322 0.734765i \(-0.262708\pi\)
−0.975486 + 0.220061i \(0.929374\pi\)
\(678\) 0 0
\(679\) −13842.6 + 23976.1i −0.782373 + 1.35511i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9490.28 −0.531677 −0.265839 0.964018i \(-0.585649\pi\)
−0.265839 + 0.964018i \(0.585649\pi\)
\(684\) 0 0
\(685\) 1465.73 0.0817556
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4591.32 + 7952.39i −0.253868 + 0.439713i
\(690\) 0 0
\(691\) −7907.36 13696.0i −0.435326 0.754007i 0.561996 0.827140i \(-0.310034\pi\)
−0.997322 + 0.0731330i \(0.976700\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9023.54 + 15629.2i 0.492493 + 0.853022i
\(696\) 0 0
\(697\) 17298.3 29961.5i 0.940056 1.62822i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −15790.6 −0.850791 −0.425395 0.905008i \(-0.639865\pi\)
−0.425395 + 0.905008i \(0.639865\pi\)
\(702\) 0 0
\(703\) −44044.7 −2.36298
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20090.8 + 34798.4i −1.06873 + 1.85110i
\(708\) 0 0
\(709\) −13771.4 23852.8i −0.729474 1.26349i −0.957106 0.289738i \(-0.906432\pi\)
0.227632 0.973747i \(-0.426902\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1175.83 2036.60i −0.0617604 0.106972i
\(714\) 0 0
\(715\) −1519.34 + 2631.57i −0.0794687 + 0.137644i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 19578.6 1.01552 0.507761 0.861498i \(-0.330473\pi\)
0.507761 + 0.861498i \(0.330473\pi\)
\(720\) 0 0
\(721\) −18251.7 −0.942756
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 14158.2 24522.7i 0.725272 1.25621i
\(726\) 0 0
\(727\) −10474.0 18141.5i −0.534330 0.925487i −0.999195 0.0401059i \(-0.987230\pi\)
0.464865 0.885382i \(-0.346103\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7319.63 12678.0i −0.370351 0.641466i
\(732\) 0 0
\(733\) 412.674 714.773i 0.0207946 0.0360174i −0.855441 0.517901i \(-0.826714\pi\)
0.876235 + 0.481883i \(0.160047\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9228.69 −0.461253
\(738\) 0 0
\(739\) 22821.1 1.13598 0.567988 0.823037i \(-0.307722\pi\)
0.567988 + 0.823037i \(0.307722\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −6028.23 + 10441.2i −0.297650 + 0.515545i −0.975598 0.219565i \(-0.929536\pi\)
0.677948 + 0.735110i \(0.262870\pi\)
\(744\) 0 0
\(745\) 6622.40 + 11470.3i 0.325672 + 0.564081i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 20828.6 + 36076.1i 1.01610 + 1.75994i
\(750\) 0 0
\(751\) 3861.16 6687.72i 0.187611 0.324951i −0.756842 0.653597i \(-0.773259\pi\)
0.944453 + 0.328646i \(0.106592\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −44689.5 −2.15420
\(756\) 0 0
\(757\) −1440.60 −0.0691671 −0.0345835 0.999402i \(-0.511010\pi\)
−0.0345835 + 0.999402i \(0.511010\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15361.3 26606.5i 0.731729 1.26739i −0.224414 0.974494i \(-0.572047\pi\)
0.956144 0.292899i \(-0.0946198\pi\)
\(762\) 0 0
\(763\) 14438.4 + 25008.1i 0.685066 + 1.18657i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1523.38 + 2638.57i 0.0717157 + 0.124215i
\(768\) 0 0
\(769\) 20140.4 34884.3i 0.944451 1.63584i 0.187604 0.982245i \(-0.439928\pi\)
0.756847 0.653592i \(-0.226739\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4282.45 −0.199261 −0.0996306 0.995024i \(-0.531766\pi\)
−0.0996306 + 0.995024i \(0.531766\pi\)
\(774\) 0 0
\(775\) −1877.99 −0.0870446
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 30982.5 53663.3i 1.42499 2.46815i
\(780\) 0 0
\(781\) −103.252 178.837i −0.00473064 0.00819371i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10090.2 17476.7i −0.458768 0.794610i
\(786\) 0 0
\(787\) 6285.82 10887.4i 0.284708 0.493129i −0.687830 0.725872i \(-0.741437\pi\)
0.972538 + 0.232743i \(0.0747700\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22985.0 1.03319
\(792\) 0 0
\(793\) 6545.11 0.293094
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14037.0 24312.8i 0.623860 1.08056i −0.364900 0.931047i \(-0.618897\pi\)
0.988760 0.149510i \(-0.0477697\pi\)
\(798\) 0 0
\(799\) −3199.83 5542.27i −0.141679 0.245396i
\(800\) 0 0