Properties

Label 1728.3.q.i.449.3
Level $1728$
Weight $3$
Character 1728.449
Analytic conductor $47.085$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.0845896815\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19269881856.9
Defining polynomial: \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.3
Root \(1.91950 + 3.32468i\) of defining polynomial
Character \(\chi\) \(=\) 1728.449
Dual form 1728.3.q.i.1601.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +O(q^{10})\) \(q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +(10.8302 - 6.25280i) q^{11} +(-11.0441 + 19.1289i) q^{13} -12.6991i q^{17} -21.7686 q^{19} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(-25.7787 + 14.8833i) q^{29} +(-6.91549 + 11.9780i) q^{31} +3.26472i q^{35} +8.26807 q^{37} +(-43.8453 - 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} -6.04384i q^{53} +26.1227 q^{55} +(8.01575 + 4.62789i) q^{59} +(-51.9009 - 89.8950i) q^{61} +(-39.9580 + 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} -18.3599i q^{71} -68.5777 q^{73} +(16.9265 + 9.77252i) q^{77} +(-13.3130 - 23.0587i) q^{79} +(-21.0376 + 12.1461i) q^{83} +(13.2634 - 22.9729i) q^{85} +111.730i q^{89} -34.5217 q^{91} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) 1.80902 + 1.04444i 0.361805 + 0.208888i 0.669872 0.742476i \(-0.266349\pi\)
−0.308067 + 0.951365i \(0.599682\pi\)
\(6\) 0 0
\(7\) 0.781452 + 1.35351i 0.111636 + 0.193359i 0.916430 0.400195i \(-0.131058\pi\)
−0.804794 + 0.593554i \(0.797724\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 10.8302 6.25280i 0.984560 0.568436i 0.0809165 0.996721i \(-0.474215\pi\)
0.903644 + 0.428285i \(0.140882\pi\)
\(12\) 0 0
\(13\) −11.0441 + 19.1289i −0.849545 + 1.47145i 0.0320708 + 0.999486i \(0.489790\pi\)
−0.881615 + 0.471969i \(0.843544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 12.6991i 0.747005i −0.927629 0.373503i \(-0.878157\pi\)
0.927629 0.373503i \(-0.121843\pi\)
\(18\) 0 0
\(19\) −21.7686 −1.14572 −0.572859 0.819654i \(-0.694166\pi\)
−0.572859 + 0.819654i \(0.694166\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −28.7989 16.6271i −1.25213 0.722916i −0.280596 0.959826i \(-0.590532\pi\)
−0.971532 + 0.236909i \(0.923866\pi\)
\(24\) 0 0
\(25\) −10.3183 17.8718i −0.412732 0.714872i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −25.7787 + 14.8833i −0.888920 + 0.513218i −0.873589 0.486665i \(-0.838213\pi\)
−0.0153306 + 0.999882i \(0.504880\pi\)
\(30\) 0 0
\(31\) −6.91549 + 11.9780i −0.223080 + 0.386386i −0.955742 0.294207i \(-0.904945\pi\)
0.732662 + 0.680593i \(0.238278\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.26472i 0.0932777i
\(36\) 0 0
\(37\) 8.26807 0.223461 0.111731 0.993739i \(-0.464361\pi\)
0.111731 + 0.993739i \(0.464361\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −43.8453 25.3141i −1.06940 0.617418i −0.141382 0.989955i \(-0.545154\pi\)
−0.928017 + 0.372538i \(0.878488\pi\)
\(42\) 0 0
\(43\) 35.5364 + 61.5508i 0.826427 + 1.43141i 0.900824 + 0.434185i \(0.142964\pi\)
−0.0743965 + 0.997229i \(0.523703\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 57.2470 33.0516i 1.21802 0.703225i 0.253527 0.967328i \(-0.418409\pi\)
0.964495 + 0.264103i \(0.0850759\pi\)
\(48\) 0 0
\(49\) 23.2787 40.3198i 0.475075 0.822854i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.04384i 0.114035i −0.998373 0.0570174i \(-0.981841\pi\)
0.998373 0.0570174i \(-0.0181590\pi\)
\(54\) 0 0
\(55\) 26.1227 0.474958
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.01575 + 4.62789i 0.135860 + 0.0784389i 0.566390 0.824138i \(-0.308340\pi\)
−0.430529 + 0.902577i \(0.641673\pi\)
\(60\) 0 0
\(61\) −51.9009 89.8950i −0.850834 1.47369i −0.880457 0.474127i \(-0.842764\pi\)
0.0296226 0.999561i \(-0.490569\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −39.9580 + 23.0698i −0.614738 + 0.354919i
\(66\) 0 0
\(67\) −19.8853 + 34.4424i −0.296796 + 0.514065i −0.975401 0.220438i \(-0.929251\pi\)
0.678605 + 0.734503i \(0.262585\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 18.3599i 0.258590i −0.991606 0.129295i \(-0.958729\pi\)
0.991606 0.129295i \(-0.0412714\pi\)
\(72\) 0 0
\(73\) −68.5777 −0.939421 −0.469711 0.882820i \(-0.655642\pi\)
−0.469711 + 0.882820i \(0.655642\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16.9265 + 9.77252i 0.219825 + 0.126916i
\(78\) 0 0
\(79\) −13.3130 23.0587i −0.168518 0.291883i 0.769381 0.638791i \(-0.220565\pi\)
−0.937899 + 0.346908i \(0.887232\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −21.0376 + 12.1461i −0.253465 + 0.146338i −0.621350 0.783533i \(-0.713415\pi\)
0.367885 + 0.929871i \(0.380082\pi\)
\(84\) 0 0
\(85\) 13.2634 22.9729i 0.156040 0.270270i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 111.730i 1.25539i 0.778459 + 0.627695i \(0.216001\pi\)
−0.778459 + 0.627695i \(0.783999\pi\)
\(90\) 0 0
\(91\) −34.5217 −0.379359
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −39.3800 22.7360i −0.414526 0.239327i
\(96\) 0 0
\(97\) −2.51182 4.35061i −0.0258951 0.0448516i 0.852787 0.522258i \(-0.174910\pi\)
−0.878683 + 0.477407i \(0.841577\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −86.1052 + 49.7129i −0.852527 + 0.492207i −0.861503 0.507753i \(-0.830476\pi\)
0.00897555 + 0.999960i \(0.497143\pi\)
\(102\) 0 0
\(103\) −13.6160 + 23.5836i −0.132194 + 0.228967i −0.924522 0.381128i \(-0.875536\pi\)
0.792328 + 0.610096i \(0.208869\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 127.242i 1.18918i −0.804030 0.594588i \(-0.797315\pi\)
0.804030 0.594588i \(-0.202685\pi\)
\(108\) 0 0
\(109\) −55.3100 −0.507431 −0.253716 0.967279i \(-0.581653\pi\)
−0.253716 + 0.967279i \(0.581653\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −102.845 59.3775i −0.910131 0.525464i −0.0296577 0.999560i \(-0.509442\pi\)
−0.880473 + 0.474096i \(0.842775\pi\)
\(114\) 0 0
\(115\) −34.7320 60.1576i −0.302017 0.523109i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 17.1884 9.92372i 0.144440 0.0833926i
\(120\) 0 0
\(121\) 17.6950 30.6486i 0.146239 0.253294i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 95.3294i 0.762635i
\(126\) 0 0
\(127\) −74.4516 −0.586233 −0.293116 0.956077i \(-0.594692\pi\)
−0.293116 + 0.956077i \(0.594692\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.08499 + 4.09052i 0.0540839 + 0.0312254i 0.526798 0.849990i \(-0.323392\pi\)
−0.472714 + 0.881216i \(0.656726\pi\)
\(132\) 0 0
\(133\) −17.0111 29.4642i −0.127903 0.221535i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 41.7273 24.0913i 0.304579 0.175849i −0.339919 0.940455i \(-0.610400\pi\)
0.644498 + 0.764606i \(0.277066\pi\)
\(138\) 0 0
\(139\) 119.023 206.155i 0.856284 1.48313i −0.0191645 0.999816i \(-0.506101\pi\)
0.875449 0.483311i \(-0.160566\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 276.226i 1.93165i
\(144\) 0 0
\(145\) −62.1789 −0.428820
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −246.854 142.521i −1.65674 0.956517i −0.974207 0.225658i \(-0.927547\pi\)
−0.682529 0.730859i \(-0.739120\pi\)
\(150\) 0 0
\(151\) 77.2434 + 133.790i 0.511546 + 0.886024i 0.999910 + 0.0133838i \(0.00426032\pi\)
−0.488365 + 0.872640i \(0.662406\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −25.0206 + 14.4456i −0.161423 + 0.0931976i
\(156\) 0 0
\(157\) 119.947 207.754i 0.763993 1.32328i −0.176784 0.984250i \(-0.556569\pi\)
0.940777 0.339026i \(-0.110097\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 51.9730i 0.322814i
\(162\) 0 0
\(163\) 111.245 0.682483 0.341241 0.939976i \(-0.389153\pi\)
0.341241 + 0.939976i \(0.389153\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 37.9116 + 21.8883i 0.227016 + 0.131068i 0.609195 0.793021i \(-0.291493\pi\)
−0.382179 + 0.924088i \(0.624826\pi\)
\(168\) 0 0
\(169\) −159.443 276.164i −0.943452 1.63411i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −253.383 + 146.291i −1.46464 + 0.845611i −0.999220 0.0394795i \(-0.987430\pi\)
−0.465420 + 0.885090i \(0.654097\pi\)
\(174\) 0 0
\(175\) 16.1265 27.9319i 0.0921514 0.159611i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 194.612i 1.08722i 0.839338 + 0.543610i \(0.182943\pi\)
−0.839338 + 0.543610i \(0.817057\pi\)
\(180\) 0 0
\(181\) −89.3906 −0.493871 −0.246935 0.969032i \(-0.579424\pi\)
−0.246935 + 0.969032i \(0.579424\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 14.9571 + 8.63550i 0.0808494 + 0.0466784i
\(186\) 0 0
\(187\) −79.4048 137.533i −0.424625 0.735472i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −44.9085 + 25.9279i −0.235123 + 0.135748i −0.612933 0.790135i \(-0.710011\pi\)
0.377810 + 0.925883i \(0.376677\pi\)
\(192\) 0 0
\(193\) −29.7763 + 51.5741i −0.154281 + 0.267223i −0.932797 0.360402i \(-0.882640\pi\)
0.778516 + 0.627625i \(0.215973\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 47.4968i 0.241100i −0.992707 0.120550i \(-0.961534\pi\)
0.992707 0.120550i \(-0.0384659\pi\)
\(198\) 0 0
\(199\) −29.5239 −0.148361 −0.0741805 0.997245i \(-0.523634\pi\)
−0.0741805 + 0.997245i \(0.523634\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −40.2896 23.2612i −0.198471 0.114587i
\(204\) 0 0
\(205\) −52.8782 91.5877i −0.257942 0.446769i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −235.758 + 136.115i −1.12803 + 0.651268i
\(210\) 0 0
\(211\) −81.0561 + 140.393i −0.384152 + 0.665371i −0.991651 0.128949i \(-0.958840\pi\)
0.607499 + 0.794320i \(0.292173\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 148.462i 0.690523i
\(216\) 0 0
\(217\) −21.6165 −0.0996151
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 242.920 + 140.250i 1.09918 + 0.634614i
\(222\) 0 0
\(223\) −102.706 177.891i −0.460564 0.797719i 0.538426 0.842673i \(-0.319019\pi\)
−0.998989 + 0.0449536i \(0.985686\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −54.0416 + 31.2009i −0.238069 + 0.137449i −0.614289 0.789081i \(-0.710557\pi\)
0.376220 + 0.926530i \(0.377224\pi\)
\(228\) 0 0
\(229\) 5.73790 9.93834i 0.0250563 0.0433989i −0.853225 0.521542i \(-0.825357\pi\)
0.878282 + 0.478144i \(0.158690\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 177.096i 0.760069i 0.924972 + 0.380035i \(0.124088\pi\)
−0.924972 + 0.380035i \(0.875912\pi\)
\(234\) 0 0
\(235\) 138.082 0.587581
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −231.234 133.503i −0.967505 0.558589i −0.0690305 0.997615i \(-0.521991\pi\)
−0.898475 + 0.439025i \(0.855324\pi\)
\(240\) 0 0
\(241\) 40.7178 + 70.5252i 0.168953 + 0.292636i 0.938052 0.346494i \(-0.112628\pi\)
−0.769099 + 0.639130i \(0.779295\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 84.2233 48.6263i 0.343769 0.198475i
\(246\) 0 0
\(247\) 240.415 416.410i 0.973338 1.68587i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 311.819i 1.24231i 0.783689 + 0.621153i \(0.213336\pi\)
−0.783689 + 0.621153i \(0.786664\pi\)
\(252\) 0 0
\(253\) −415.863 −1.64373
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −335.121 193.482i −1.30397 0.752849i −0.322889 0.946437i \(-0.604654\pi\)
−0.981083 + 0.193588i \(0.937988\pi\)
\(258\) 0 0
\(259\) 6.46110 + 11.1909i 0.0249463 + 0.0432083i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 417.095 240.810i 1.58591 0.915627i 0.591942 0.805981i \(-0.298362\pi\)
0.993971 0.109646i \(-0.0349718\pi\)
\(264\) 0 0
\(265\) 6.31243 10.9334i 0.0238205 0.0412583i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 225.818i 0.839474i 0.907646 + 0.419737i \(0.137878\pi\)
−0.907646 + 0.419737i \(0.862122\pi\)
\(270\) 0 0
\(271\) 23.6619 0.0873135 0.0436567 0.999047i \(-0.486099\pi\)
0.0436567 + 0.999047i \(0.486099\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −223.498 129.036i −0.812718 0.469223i
\(276\) 0 0
\(277\) 27.9969 + 48.4920i 0.101072 + 0.175061i 0.912126 0.409909i \(-0.134440\pi\)
−0.811055 + 0.584970i \(0.801106\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −122.023 + 70.4498i −0.434244 + 0.250711i −0.701153 0.713011i \(-0.747331\pi\)
0.266909 + 0.963722i \(0.413998\pi\)
\(282\) 0 0
\(283\) −155.690 + 269.663i −0.550141 + 0.952872i 0.448123 + 0.893972i \(0.352093\pi\)
−0.998264 + 0.0589002i \(0.981241\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 79.1271i 0.275704i
\(288\) 0 0
\(289\) 127.733 0.441983
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −273.621 157.975i −0.933859 0.539164i −0.0458290 0.998949i \(-0.514593\pi\)
−0.888030 + 0.459786i \(0.847926\pi\)
\(294\) 0 0
\(295\) 9.66712 + 16.7439i 0.0327699 + 0.0567591i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 636.116 367.262i 2.12748 1.22830i
\(300\) 0 0
\(301\) −55.5399 + 96.1980i −0.184518 + 0.319595i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 216.829i 0.710916i
\(306\) 0 0
\(307\) −379.819 −1.23720 −0.618598 0.785707i \(-0.712299\pi\)
−0.618598 + 0.785707i \(0.712299\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −335.497 193.699i −1.07877 0.622827i −0.148204 0.988957i \(-0.547349\pi\)
−0.930564 + 0.366130i \(0.880683\pi\)
\(312\) 0 0
\(313\) −100.742 174.491i −0.321860 0.557479i 0.659011 0.752133i \(-0.270975\pi\)
−0.980872 + 0.194654i \(0.937642\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 319.046 184.201i 1.00645 0.581077i 0.0963027 0.995352i \(-0.469298\pi\)
0.910152 + 0.414275i \(0.135965\pi\)
\(318\) 0 0
\(319\) −186.125 + 322.378i −0.583463 + 1.01059i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 276.442i 0.855857i
\(324\) 0 0
\(325\) 455.824 1.40254
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 89.4716 + 51.6564i 0.271950 + 0.157010i
\(330\) 0 0
\(331\) 150.832 + 261.248i 0.455684 + 0.789268i 0.998727 0.0504365i \(-0.0160613\pi\)
−0.543043 + 0.839705i \(0.682728\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −71.9460 + 41.5380i −0.214764 + 0.123994i
\(336\) 0 0
\(337\) 85.5075 148.103i 0.253732 0.439476i −0.710819 0.703375i \(-0.751675\pi\)
0.964550 + 0.263899i \(0.0850087\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 172.965i 0.507227i
\(342\) 0 0
\(343\) 149.347 0.435414
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −264.744 152.850i −0.762950 0.440489i 0.0674041 0.997726i \(-0.478528\pi\)
−0.830354 + 0.557237i \(0.811862\pi\)
\(348\) 0 0
\(349\) 11.1944 + 19.3893i 0.0320756 + 0.0555566i 0.881618 0.471964i \(-0.156455\pi\)
−0.849542 + 0.527521i \(0.823122\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 462.657 267.115i 1.31064 0.756700i 0.328440 0.944525i \(-0.393477\pi\)
0.982203 + 0.187825i \(0.0601437\pi\)
\(354\) 0 0
\(355\) 19.1758 33.2134i 0.0540163 0.0935590i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 217.172i 0.604936i −0.953159 0.302468i \(-0.902189\pi\)
0.953159 0.302468i \(-0.0978106\pi\)
\(360\) 0 0
\(361\) 112.874 0.312669
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −124.059 71.6253i −0.339887 0.196234i
\(366\) 0 0
\(367\) 51.1847 + 88.6546i 0.139468 + 0.241566i 0.927295 0.374330i \(-0.122127\pi\)
−0.787827 + 0.615896i \(0.788794\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.18042 4.72297i 0.0220497 0.0127304i
\(372\) 0 0
\(373\) −243.458 + 421.682i −0.652702 + 1.13051i 0.329762 + 0.944064i \(0.393031\pi\)
−0.982464 + 0.186450i \(0.940302\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 657.490i 1.74401i
\(378\) 0 0
\(379\) 553.727 1.46102 0.730510 0.682901i \(-0.239282\pi\)
0.730510 + 0.682901i \(0.239282\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 184.612 + 106.586i 0.482016 + 0.278292i 0.721256 0.692668i \(-0.243565\pi\)
−0.239240 + 0.970960i \(0.576898\pi\)
\(384\) 0 0
\(385\) 20.4136 + 35.3574i 0.0530224 + 0.0918375i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −82.4958 + 47.6290i −0.212071 + 0.122439i −0.602274 0.798290i \(-0.705738\pi\)
0.390202 + 0.920729i \(0.372405\pi\)
\(390\) 0 0
\(391\) −211.149 + 365.720i −0.540022 + 0.935346i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 55.6184i 0.140806i
\(396\) 0 0
\(397\) 481.407 1.21261 0.606306 0.795231i \(-0.292651\pi\)
0.606306 + 0.795231i \(0.292651\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 517.354 + 298.694i 1.29016 + 0.744874i 0.978682 0.205380i \(-0.0658430\pi\)
0.311477 + 0.950254i \(0.399176\pi\)
\(402\) 0 0
\(403\) −152.750 264.571i −0.379033 0.656505i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 89.5446 51.6986i 0.220011 0.127024i
\(408\) 0 0
\(409\) −53.7260 + 93.0562i −0.131359 + 0.227521i −0.924201 0.381907i \(-0.875268\pi\)
0.792841 + 0.609428i \(0.208601\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 14.4659i 0.0350264i
\(414\) 0 0
\(415\) −50.7433 −0.122273
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −39.6993 22.9204i −0.0947477 0.0547026i 0.451878 0.892080i \(-0.350754\pi\)
−0.546625 + 0.837377i \(0.684088\pi\)
\(420\) 0 0
\(421\) 5.53062 + 9.57932i 0.0131369 + 0.0227537i 0.872519 0.488580i \(-0.162485\pi\)
−0.859382 + 0.511334i \(0.829152\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −226.956 + 131.033i −0.534013 + 0.308313i
\(426\) 0 0
\(427\) 81.1161 140.497i 0.189967 0.329033i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 590.788i 1.37074i 0.728196 + 0.685369i \(0.240359\pi\)
−0.728196 + 0.685369i \(0.759641\pi\)
\(432\) 0 0
\(433\) −13.9683 −0.0322594 −0.0161297 0.999870i \(-0.505134\pi\)
−0.0161297 + 0.999870i \(0.505134\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 626.914 + 361.949i 1.43459 + 0.828258i
\(438\) 0 0
\(439\) −35.9051 62.1894i −0.0817883 0.141662i 0.822230 0.569156i \(-0.192730\pi\)
−0.904018 + 0.427494i \(0.859396\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 581.028 335.457i 1.31158 0.757239i 0.329219 0.944254i \(-0.393214\pi\)
0.982357 + 0.187015i \(0.0598812\pi\)
\(444\) 0 0
\(445\) −116.695 + 202.122i −0.262236 + 0.454206i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 830.401i 1.84945i 0.380642 + 0.924723i \(0.375703\pi\)
−0.380642 + 0.924723i \(0.624297\pi\)
\(450\) 0 0
\(451\) −633.136 −1.40385
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −62.4505 36.0558i −0.137254 0.0792435i
\(456\) 0 0
\(457\) 423.113 + 732.854i 0.925850 + 1.60362i 0.790188 + 0.612864i \(0.209983\pi\)
0.135661 + 0.990755i \(0.456684\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 109.019 62.9423i 0.236484 0.136534i −0.377076 0.926182i \(-0.623070\pi\)
0.613560 + 0.789648i \(0.289737\pi\)
\(462\) 0 0
\(463\) −307.121 + 531.950i −0.663329 + 1.14892i 0.316407 + 0.948624i \(0.397524\pi\)
−0.979735 + 0.200296i \(0.935810\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 172.270i 0.368887i 0.982843 + 0.184444i \(0.0590484\pi\)
−0.982843 + 0.184444i \(0.940952\pi\)
\(468\) 0 0
\(469\) −62.1576 −0.132532
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 769.729 + 444.403i 1.62733 + 0.939542i
\(474\) 0 0
\(475\) 224.615 + 389.045i 0.472874 + 0.819042i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −174.532 + 100.766i −0.364367 + 0.210367i −0.670995 0.741462i \(-0.734133\pi\)
0.306628 + 0.951829i \(0.400799\pi\)
\(480\) 0 0
\(481\) −91.3132 + 158.159i −0.189840 + 0.328813i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.4938i 0.0216367i
\(486\) 0 0
\(487\) 801.178 1.64513 0.822565 0.568671i \(-0.192542\pi\)
0.822565 + 0.568671i \(0.192542\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −625.711 361.255i −1.27436 0.735753i −0.298555 0.954392i \(-0.596505\pi\)
−0.975806 + 0.218640i \(0.929838\pi\)
\(492\) 0 0
\(493\) 189.005 + 327.366i 0.383376 + 0.664028i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.8503 14.3474i 0.0500007 0.0288679i
\(498\) 0 0
\(499\) −69.4409 + 120.275i −0.139160 + 0.241032i −0.927179 0.374619i \(-0.877774\pi\)
0.788019 + 0.615651i \(0.211107\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 794.533i 1.57959i −0.613372 0.789794i \(-0.710187\pi\)
0.613372 0.789794i \(-0.289813\pi\)
\(504\) 0 0
\(505\) −207.689 −0.411264
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −179.929 103.882i −0.353495 0.204090i 0.312729 0.949843i \(-0.398757\pi\)
−0.666224 + 0.745752i \(0.732090\pi\)
\(510\) 0 0
\(511\) −53.5902 92.8209i −0.104873 0.181646i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −49.2634 + 28.4422i −0.0956571 + 0.0552276i
\(516\) 0 0
\(517\) 413.330 715.908i 0.799477 1.38474i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 248.275i 0.476535i −0.971200 0.238267i \(-0.923421\pi\)
0.971200 0.238267i \(-0.0765795\pi\)
\(522\) 0 0
\(523\) −108.678 −0.207797 −0.103898 0.994588i \(-0.533132\pi\)
−0.103898 + 0.994588i \(0.533132\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 152.109 + 87.8204i 0.288633 + 0.166642i
\(528\) 0 0
\(529\) 288.420 + 499.557i 0.545216 + 0.944343i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 968.463 559.142i 1.81700 1.04905i
\(534\) 0 0
\(535\) 132.896 230.183i 0.248405 0.430249i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 582.227i 1.08020i
\(540\) 0 0
\(541\) 20.0646 0.0370880 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −100.057 57.7680i −0.183591 0.105996i
\(546\) 0 0
\(547\) 86.6937 + 150.158i 0.158489 + 0.274512i 0.934324 0.356424i \(-0.116004\pi\)
−0.775835 + 0.630936i \(0.782671\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 561.167 323.990i 1.01845 0.588003i
\(552\) 0 0
\(553\) 20.8069 36.0386i 0.0376254 0.0651692i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 434.666i 0.780370i −0.920737 0.390185i \(-0.872411\pi\)
0.920737 0.390185i \(-0.127589\pi\)
\(558\) 0 0
\(559\) −1569.87 −2.80835
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −86.8277 50.1300i −0.154223 0.0890409i 0.420902 0.907106i \(-0.361714\pi\)
−0.575126 + 0.818065i \(0.695047\pi\)
\(564\) 0 0
\(565\) −124.032 214.830i −0.219526 0.380231i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −44.1556 + 25.4932i −0.0776020 + 0.0448036i −0.538299 0.842754i \(-0.680933\pi\)
0.460697 + 0.887558i \(0.347600\pi\)
\(570\) 0 0
\(571\) 430.481 745.615i 0.753907 1.30581i −0.192009 0.981393i \(-0.561500\pi\)
0.945916 0.324412i \(-0.105166\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 686.252i 1.19348i
\(576\) 0 0
\(577\) 59.3431 0.102848 0.0514239 0.998677i \(-0.483624\pi\)
0.0514239 + 0.998677i \(0.483624\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −32.8797 18.9831i −0.0565916 0.0326732i
\(582\) 0 0
\(583\) −37.7909 65.4558i −0.0648215 0.112274i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −534.777 + 308.754i −0.911034 + 0.525986i −0.880764 0.473556i \(-0.842970\pi\)
−0.0302706 + 0.999542i \(0.509637\pi\)
\(588\) 0 0
\(589\) 150.541 260.744i 0.255587 0.442690i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 342.310i 0.577251i −0.957442 0.288626i \(-0.906802\pi\)
0.957442 0.288626i \(-0.0931983\pi\)
\(594\) 0 0
\(595\) 41.4589 0.0696789
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 379.292 + 218.984i 0.633209 + 0.365583i 0.781994 0.623286i \(-0.214203\pi\)
−0.148785 + 0.988870i \(0.547536\pi\)
\(600\) 0 0
\(601\) 304.452 + 527.327i 0.506576 + 0.877416i 0.999971 + 0.00761053i \(0.00242253\pi\)
−0.493395 + 0.869806i \(0.664244\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 64.0212 36.9627i 0.105820 0.0610953i
\(606\) 0 0
\(607\) 540.751 936.608i 0.890858 1.54301i 0.0520102 0.998647i \(-0.483437\pi\)
0.838848 0.544365i \(-0.183230\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1460.10i 2.38968i
\(612\) 0 0
\(613\) 222.279 0.362609 0.181304 0.983427i \(-0.441968\pi\)
0.181304 + 0.983427i \(0.441968\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 31.0310 + 17.9158i 0.0502934 + 0.0290369i 0.524936 0.851142i \(-0.324089\pi\)
−0.474642 + 0.880179i \(0.657423\pi\)
\(618\) 0 0
\(619\) −161.494 279.717i −0.260896 0.451885i 0.705584 0.708626i \(-0.250685\pi\)
−0.966480 + 0.256741i \(0.917351\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −151.228 + 87.3114i −0.242741 + 0.140147i
\(624\) 0 0
\(625\) −158.391 + 274.342i −0.253426 + 0.438947i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 104.997i 0.166927i
\(630\) 0 0
\(631\) 794.037 1.25838 0.629189 0.777252i \(-0.283387\pi\)
0.629189 + 0.777252i \(0.283387\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −134.685 77.7602i −0.212102 0.122457i
\(636\) 0 0
\(637\) 514.183 + 890.591i 0.807194 + 1.39810i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 753.063 434.781i 1.17483 0.678286i 0.220013 0.975497i \(-0.429390\pi\)
0.954812 + 0.297211i \(0.0960566\pi\)
\(642\) 0 0
\(643\) 31.2519 54.1299i 0.0486033 0.0841834i −0.840700 0.541501i \(-0.817856\pi\)
0.889304 + 0.457317i \(0.151190\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 761.439i 1.17688i 0.808542 + 0.588438i \(0.200257\pi\)
−0.808542 + 0.588438i \(0.799743\pi\)
\(648\) 0 0
\(649\) 115.749 0.178350
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 129.622 + 74.8371i 0.198502 + 0.114605i 0.595956 0.803017i \(-0.296773\pi\)
−0.397455 + 0.917622i \(0.630106\pi\)
\(654\) 0 0
\(655\) 8.54461 + 14.7997i 0.0130452 + 0.0225950i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 564.273 325.783i 0.856256 0.494360i −0.00650063 0.999979i \(-0.502069\pi\)
0.862757 + 0.505619i \(0.168736\pi\)
\(660\) 0 0
\(661\) −596.672 + 1033.47i −0.902681 + 1.56349i −0.0786818 + 0.996900i \(0.525071\pi\)
−0.824000 + 0.566590i \(0.808262\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 71.0685i 0.106870i
\(666\) 0 0
\(667\) 989.865 1.48405
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1124.19 649.051i −1.67539 0.967290i
\(672\) 0 0
\(673\) −74.7771 129.518i −0.111110 0.192448i 0.805108 0.593128i \(-0.202107\pi\)
−0.916218 + 0.400680i \(0.868774\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −607.487 + 350.733i −0.897322 + 0.518069i −0.876331 0.481710i \(-0.840016\pi\)
−0.0209919 + 0.999780i \(0.506682\pi\)
\(678\) 0 0
\(679\) 3.92574 6.79958i 0.00578165 0.0100141i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 503.096i 0.736597i 0.929708 + 0.368299i \(0.120060\pi\)
−0.929708 + 0.368299i \(0.879940\pi\)
\(684\) 0 0
\(685\) 100.648 0.146931
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 115.612 + 66.7487i 0.167797 + 0.0968776i
\(690\) 0 0
\(691\) −329.413 570.561i −0.476720 0.825703i 0.522924 0.852379i \(-0.324841\pi\)
−0.999644 + 0.0266761i \(0.991508\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 430.633 248.626i 0.619615 0.357735i
\(696\) 0 0
\(697\) −321.466 + 556.796i −0.461214 + 0.798846i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 172.963i 0.246738i 0.992361 + 0.123369i \(0.0393698\pi\)
−0.992361 + 0.123369i \(0.960630\pi\)
\(702\) 0 0
\(703\) −179.985 −0.256024
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −134.574 77.6964i −0.190345 0.109896i
\(708\) 0 0
\(709\) 527.267 + 913.254i 0.743677 + 1.28809i 0.950810 + 0.309774i \(0.100253\pi\)
−0.207133 + 0.978313i \(0.566413\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 398.317 229.969i 0.558650 0.322537i
\(714\) 0 0
\(715\) −288.501 + 499.699i −0.403498 + 0.698879i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1164.78i 1.62000i 0.586432 + 0.809998i \(0.300532\pi\)
−0.586432 + 0.809998i \(0.699468\pi\)
\(720\) 0 0
\(721\) −42.5611 −0.0590306
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 531.983 + 307.141i 0.733770 + 0.423642i
\(726\) 0 0
\(727\) 492.209 + 852.530i 0.677041 + 1.17267i 0.975868 + 0.218362i \(0.0700712\pi\)
−0.298827 + 0.954307i \(0.596595\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 781.639 451.280i 1.06927 0.617345i
\(732\) 0 0
\(733\) −246.459 + 426.879i −0.336233 + 0.582372i −0.983721 0.179703i \(-0.942486\pi\)
0.647488 + 0.762076i \(0.275820\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 497.355i 0.674837i
\(738\) 0 0
\(739\) −571.150 −0.772869 −0.386435 0.922317i \(-0.626293\pi\)
−0.386435 + 0.922317i \(0.626293\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −910.255 525.536i −1.22511 0.707316i −0.259105 0.965849i \(-0.583427\pi\)
−0.966002 + 0.258533i \(0.916761\pi\)
\(744\) 0 0
\(745\) −297.709 515.648i −0.399610 0.692144i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 172.224 99.4334i 0.229938 0.132755i
\(750\) 0 0
\(751\) 42.3053 73.2749i 0.0563319 0.0975698i −0.836484 0.547991i \(-0.815393\pi\)
0.892816 + 0.450421i \(0.148726\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 322.705i 0.427423i
\(756\) 0 0
\(757\) −1007.63 −1.33109 −0.665543 0.746360i \(-0.731800\pi\)
−0.665543 + 0.746360i \(0.731800\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −393.981 227.465i −0.517715 0.298903i 0.218285 0.975885i \(-0.429954\pi\)
−0.735999 + 0.676983i \(0.763287\pi\)
\(762\) 0 0
\(763\) −43.2221 74.8629i −0.0566476 0.0981165i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −177.053 + 102.222i −0.230838 + 0.133275i
\(768\) 0 0
\(769\) 352.232 610.084i 0.458039 0.793347i −0.540818 0.841139i \(-0.681885\pi\)
0.998857 + 0.0477927i \(0.0152187\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1021.43i 1.32138i 0.750658 + 0.660691i \(0.229737\pi\)
−0.750658 + 0.660691i \(0.770263\pi\)
\(774\) 0 0
\(775\) 285.424 0.368289
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 954.453 + 551.054i 1.22523 + 0.707386i
\(780\) 0 0
\(781\) −114.801 198.840i −0.146992 0.254597i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 433.974 250.555i 0.552833 0.319178i
\(786\) 0 0
\(787\) −202.007 + 349.886i −0.256680 + 0.444582i −0.965350 0.260957i \(-0.915962\pi\)
0.708671 + 0.705539i \(0.249295\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 185.603i 0.234643i
\(792\) 0 0
\(793\) 2292.79 2.89129
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 765.042 + 441.697i 0.959902 + 0.554200i 0.896143 0.443766i \(-0.146358\pi\)
0.0637592 + 0.997965i \(0.479691\pi\)
\(798\) 0 0
\(799\) −419.725 726.985i −0.525313 0.909869i