Properties

Label 1728.3.q.i.449.4
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 449.4
Root \(0.831167 + 1.43962i\) of defining polynomial
Character \(\chi\) \(=\) 1728.449
Dual form 1728.3.q.i.1601.4

$q$-expansion

\(f(q)\) \(=\) \(q+(3.44299 + 1.98781i) q^{5} +(1.80469 + 3.12582i) q^{7} +O(q^{10})\) \(q+(3.44299 + 1.98781i) q^{5} +(1.80469 + 3.12582i) q^{7} +(-11.8326 + 6.83153i) q^{11} +(8.96435 - 15.5267i) q^{13} -21.6750i q^{17} -23.4245 q^{19} +(13.0662 + 7.54376i) q^{23} +(-4.59721 - 7.96260i) q^{25} +(-20.4862 + 11.8277i) q^{29} +(23.5016 - 40.7060i) q^{31} +14.3495i q^{35} -54.6126 q^{37} +(-24.6459 - 14.2293i) q^{41} +(-23.8753 - 41.3532i) q^{43} +(30.5323 - 17.6278i) q^{47} +(17.9862 - 31.1530i) q^{49} -65.0193i q^{53} -54.3192 q^{55} +(76.0156 + 43.8876i) q^{59} +(6.46852 + 11.2038i) q^{61} +(61.7284 - 35.6389i) q^{65} +(1.55595 - 2.69499i) q^{67} +49.5089i q^{71} +102.151 q^{73} +(-42.7082 - 24.6576i) q^{77} +(18.7220 + 32.4275i) q^{79} +(-14.6999 + 8.48702i) q^{83} +(43.0859 - 74.6270i) q^{85} -14.1990i q^{89} +64.7115 q^{91} +(-80.6505 - 46.5636i) q^{95} +(-24.1484 - 41.8262i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) 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
\(5\) 3.44299 + 1.98781i 0.688598 + 0.397562i 0.803087 0.595862i \(-0.203190\pi\)
−0.114488 + 0.993425i \(0.536523\pi\)
\(6\) 0 0
\(7\) 1.80469 + 3.12582i 0.257813 + 0.446545i 0.965656 0.259825i \(-0.0836648\pi\)
−0.707843 + 0.706370i \(0.750331\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.8326 + 6.83153i −1.07569 + 0.621048i −0.929730 0.368243i \(-0.879959\pi\)
−0.145957 + 0.989291i \(0.546626\pi\)
\(12\) 0 0
\(13\) 8.96435 15.5267i 0.689565 1.19436i −0.282413 0.959293i \(-0.591135\pi\)
0.971979 0.235070i \(-0.0755318\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 21.6750i 1.27500i −0.770449 0.637501i \(-0.779968\pi\)
0.770449 0.637501i \(-0.220032\pi\)
\(18\) 0 0
\(19\) −23.4245 −1.23287 −0.616435 0.787406i \(-0.711424\pi\)
−0.616435 + 0.787406i \(0.711424\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 13.0662 + 7.54376i 0.568095 + 0.327990i 0.756388 0.654123i \(-0.226962\pi\)
−0.188293 + 0.982113i \(0.560296\pi\)
\(24\) 0 0
\(25\) −4.59721 7.96260i −0.183888 0.318504i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −20.4862 + 11.8277i −0.706420 + 0.407852i −0.809734 0.586797i \(-0.800389\pi\)
0.103314 + 0.994649i \(0.467055\pi\)
\(30\) 0 0
\(31\) 23.5016 40.7060i 0.758117 1.31310i −0.185693 0.982608i \(-0.559453\pi\)
0.943810 0.330489i \(-0.107214\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 14.3495i 0.409987i
\(36\) 0 0
\(37\) −54.6126 −1.47602 −0.738009 0.674791i \(-0.764234\pi\)
−0.738009 + 0.674791i \(0.764234\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −24.6459 14.2293i −0.601118 0.347056i 0.168363 0.985725i \(-0.446152\pi\)
−0.769481 + 0.638669i \(0.779485\pi\)
\(42\) 0 0
\(43\) −23.8753 41.3532i −0.555239 0.961702i −0.997885 0.0650055i \(-0.979294\pi\)
0.442646 0.896696i \(-0.354040\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 30.5323 17.6278i 0.649623 0.375060i −0.138689 0.990336i \(-0.544289\pi\)
0.788312 + 0.615276i \(0.210955\pi\)
\(48\) 0 0
\(49\) 17.9862 31.1530i 0.367065 0.635775i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 65.0193i 1.22678i −0.789780 0.613390i \(-0.789805\pi\)
0.789780 0.613390i \(-0.210195\pi\)
\(54\) 0 0
\(55\) −54.3192 −0.987621
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 76.0156 + 43.8876i 1.28840 + 0.743858i 0.978369 0.206869i \(-0.0663272\pi\)
0.310031 + 0.950726i \(0.399661\pi\)
\(60\) 0 0
\(61\) 6.46852 + 11.2038i 0.106041 + 0.183669i 0.914163 0.405346i \(-0.132849\pi\)
−0.808122 + 0.589015i \(0.799516\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 61.7284 35.6389i 0.949667 0.548291i
\(66\) 0 0
\(67\) 1.55595 2.69499i 0.0232232 0.0402237i −0.854180 0.519977i \(-0.825941\pi\)
0.877403 + 0.479753i \(0.159274\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 49.5089i 0.697308i 0.937251 + 0.348654i \(0.113361\pi\)
−0.937251 + 0.348654i \(0.886639\pi\)
\(72\) 0 0
\(73\) 102.151 1.39932 0.699662 0.714474i \(-0.253334\pi\)
0.699662 + 0.714474i \(0.253334\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −42.7082 24.6576i −0.554652 0.320228i
\(78\) 0 0
\(79\) 18.7220 + 32.4275i 0.236988 + 0.410475i 0.959849 0.280519i \(-0.0905065\pi\)
−0.722861 + 0.690994i \(0.757173\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.6999 + 8.48702i −0.177108 + 0.102253i −0.585933 0.810359i \(-0.699272\pi\)
0.408825 + 0.912613i \(0.365939\pi\)
\(84\) 0 0
\(85\) 43.0859 74.6270i 0.506893 0.877964i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.1990i 0.159540i −0.996813 0.0797698i \(-0.974581\pi\)
0.996813 0.0797698i \(-0.0254185\pi\)
\(90\) 0 0
\(91\) 64.7115 0.711116
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −80.6505 46.5636i −0.848952 0.490143i
\(96\) 0 0
\(97\) −24.1484 41.8262i −0.248952 0.431198i 0.714283 0.699857i \(-0.246753\pi\)
−0.963235 + 0.268659i \(0.913420\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −34.5980 + 19.9752i −0.342554 + 0.197774i −0.661401 0.750032i \(-0.730038\pi\)
0.318847 + 0.947806i \(0.396704\pi\)
\(102\) 0 0
\(103\) −10.9749 + 19.0091i −0.106552 + 0.184554i −0.914371 0.404876i \(-0.867315\pi\)
0.807819 + 0.589431i \(0.200648\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.521299i 0.00487195i 0.999997 + 0.00243598i \(0.000775396\pi\)
−0.999997 + 0.00243598i \(0.999225\pi\)
\(108\) 0 0
\(109\) 198.784 1.82371 0.911855 0.410513i \(-0.134650\pi\)
0.911855 + 0.410513i \(0.134650\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −115.971 66.9557i −1.02629 0.592528i −0.110369 0.993891i \(-0.535203\pi\)
−0.915919 + 0.401363i \(0.868537\pi\)
\(114\) 0 0
\(115\) 29.9912 + 51.9462i 0.260793 + 0.451706i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 67.7522 39.1168i 0.569346 0.328712i
\(120\) 0 0
\(121\) 32.8395 56.8797i 0.271401 0.470080i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 135.944i 1.08755i
\(126\) 0 0
\(127\) −45.8769 −0.361235 −0.180618 0.983553i \(-0.557810\pi\)
−0.180618 + 0.983553i \(0.557810\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −167.914 96.9453i −1.28179 0.740040i −0.304612 0.952476i \(-0.598527\pi\)
−0.977175 + 0.212436i \(0.931860\pi\)
\(132\) 0 0
\(133\) −42.2741 73.2208i −0.317850 0.550532i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −149.798 + 86.4859i −1.09342 + 0.631284i −0.934484 0.356005i \(-0.884138\pi\)
−0.158932 + 0.987289i \(0.550805\pi\)
\(138\) 0 0
\(139\) 0.803631 1.39193i 0.00578151 0.0100139i −0.863120 0.504999i \(-0.831493\pi\)
0.868902 + 0.494985i \(0.164826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 244.961i 1.71301i
\(144\) 0 0
\(145\) −94.0450 −0.648586
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 76.1133 + 43.9441i 0.510828 + 0.294927i 0.733174 0.680041i \(-0.238038\pi\)
−0.222346 + 0.974968i \(0.571371\pi\)
\(150\) 0 0
\(151\) −6.64118 11.5029i −0.0439813 0.0761778i 0.843197 0.537605i \(-0.180671\pi\)
−0.887178 + 0.461427i \(0.847338\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 161.832 93.4336i 1.04408 0.602798i
\(156\) 0 0
\(157\) 93.8926 162.627i 0.598042 1.03584i −0.395068 0.918652i \(-0.629279\pi\)
0.993110 0.117188i \(-0.0373879\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 54.4566i 0.338240i
\(162\) 0 0
\(163\) −131.235 −0.805123 −0.402562 0.915393i \(-0.631880\pi\)
−0.402562 + 0.915393i \(0.631880\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −158.636 91.5887i −0.949918 0.548436i −0.0568627 0.998382i \(-0.518110\pi\)
−0.893056 + 0.449946i \(0.851443\pi\)
\(168\) 0 0
\(169\) −76.2192 132.015i −0.451001 0.781157i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 22.6730 13.0903i 0.131058 0.0756662i −0.433038 0.901376i \(-0.642558\pi\)
0.564095 + 0.825710i \(0.309225\pi\)
\(174\) 0 0
\(175\) 16.5931 28.7401i 0.0948176 0.164229i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 175.092i 0.978165i −0.872238 0.489083i \(-0.837332\pi\)
0.872238 0.489083i \(-0.162668\pi\)
\(180\) 0 0
\(181\) 172.814 0.954772 0.477386 0.878694i \(-0.341584\pi\)
0.477386 + 0.878694i \(0.341584\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −188.031 108.560i −1.01638 0.586809i
\(186\) 0 0
\(187\) 148.074 + 256.471i 0.791838 + 1.37150i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 76.1098 43.9420i 0.398481 0.230063i −0.287348 0.957826i \(-0.592773\pi\)
0.685828 + 0.727764i \(0.259440\pi\)
\(192\) 0 0
\(193\) 68.6377 118.884i 0.355636 0.615979i −0.631591 0.775302i \(-0.717598\pi\)
0.987227 + 0.159323i \(0.0509310\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 239.073i 1.21357i −0.794867 0.606784i \(-0.792459\pi\)
0.794867 0.606784i \(-0.207541\pi\)
\(198\) 0 0
\(199\) 250.574 1.25916 0.629582 0.776934i \(-0.283226\pi\)
0.629582 + 0.776934i \(0.283226\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −73.9425 42.6907i −0.364249 0.210299i
\(204\) 0 0
\(205\) −56.5703 97.9826i −0.275953 0.477964i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 277.172 160.025i 1.32618 0.765671i
\(210\) 0 0
\(211\) 118.043 204.456i 0.559445 0.968988i −0.438098 0.898927i \(-0.644348\pi\)
0.997543 0.0700601i \(-0.0223191\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 189.838i 0.882968i
\(216\) 0 0
\(217\) 169.653 0.781810
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −336.542 194.303i −1.52282 0.879198i
\(222\) 0 0
\(223\) −42.8742 74.2603i −0.192261 0.333006i 0.753738 0.657175i \(-0.228249\pi\)
−0.945999 + 0.324169i \(0.894915\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −160.187 + 92.4841i −0.705671 + 0.407419i −0.809456 0.587181i \(-0.800238\pi\)
0.103785 + 0.994600i \(0.466905\pi\)
\(228\) 0 0
\(229\) −128.199 + 222.048i −0.559822 + 0.969640i 0.437689 + 0.899126i \(0.355797\pi\)
−0.997511 + 0.0705135i \(0.977536\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 403.712i 1.73267i −0.499464 0.866335i \(-0.666470\pi\)
0.499464 0.866335i \(-0.333530\pi\)
\(234\) 0 0
\(235\) 140.163 0.596439
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −215.728 124.551i −0.902630 0.521133i −0.0245772 0.999698i \(-0.507824\pi\)
−0.878052 + 0.478565i \(0.841157\pi\)
\(240\) 0 0
\(241\) 85.7023 + 148.441i 0.355611 + 0.615937i 0.987222 0.159349i \(-0.0509394\pi\)
−0.631611 + 0.775285i \(0.717606\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 123.852 71.5063i 0.505520 0.291862i
\(246\) 0 0
\(247\) −209.986 + 363.706i −0.850145 + 1.47249i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 287.980i 1.14733i 0.819089 + 0.573666i \(0.194479\pi\)
−0.819089 + 0.573666i \(0.805521\pi\)
\(252\) 0 0
\(253\) −206.142 −0.814789
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 60.1268 + 34.7142i 0.233957 + 0.135075i 0.612396 0.790551i \(-0.290206\pi\)
−0.378439 + 0.925626i \(0.623539\pi\)
\(258\) 0 0
\(259\) −98.5590 170.709i −0.380537 0.659109i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 68.7357 39.6845i 0.261352 0.150892i −0.363599 0.931556i \(-0.618452\pi\)
0.624951 + 0.780664i \(0.285119\pi\)
\(264\) 0 0
\(265\) 129.246 223.861i 0.487722 0.844758i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 41.6217i 0.154728i 0.997003 + 0.0773638i \(0.0246503\pi\)
−0.997003 + 0.0773638i \(0.975350\pi\)
\(270\) 0 0
\(271\) −98.0065 −0.361648 −0.180824 0.983516i \(-0.557876\pi\)
−0.180824 + 0.983516i \(0.557876\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 108.793 + 62.8119i 0.395612 + 0.228407i
\(276\) 0 0
\(277\) −153.400 265.696i −0.553790 0.959193i −0.997997 0.0632681i \(-0.979848\pi\)
0.444206 0.895924i \(-0.353486\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 54.8876 31.6894i 0.195330 0.112774i −0.399146 0.916888i \(-0.630693\pi\)
0.594475 + 0.804114i \(0.297360\pi\)
\(282\) 0 0
\(283\) −163.299 + 282.842i −0.577027 + 0.999440i 0.418791 + 0.908083i \(0.362454\pi\)
−0.995818 + 0.0913578i \(0.970879\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 102.718i 0.357902i
\(288\) 0 0
\(289\) −180.808 −0.625632
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −62.3120 35.9759i −0.212669 0.122784i 0.389882 0.920865i \(-0.372516\pi\)
−0.602551 + 0.798080i \(0.705849\pi\)
\(294\) 0 0
\(295\) 174.481 + 302.209i 0.591460 + 1.02444i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 234.260 135.250i 0.783477 0.452341i
\(300\) 0 0
\(301\) 86.1750 149.259i 0.286296 0.495879i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 51.4328i 0.168632i
\(306\) 0 0
\(307\) −161.023 −0.524504 −0.262252 0.964999i \(-0.584465\pi\)
−0.262252 + 0.964999i \(0.584465\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 352.553 + 203.547i 1.13361 + 0.654491i 0.944841 0.327530i \(-0.106216\pi\)
0.188771 + 0.982021i \(0.439549\pi\)
\(312\) 0 0
\(313\) 79.7548 + 138.139i 0.254808 + 0.441340i 0.964843 0.262826i \(-0.0846545\pi\)
−0.710035 + 0.704166i \(0.751321\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −364.877 + 210.662i −1.15103 + 0.664549i −0.949139 0.314859i \(-0.898043\pi\)
−0.201894 + 0.979407i \(0.564710\pi\)
\(318\) 0 0
\(319\) 161.602 279.904i 0.506591 0.877441i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 507.728i 1.57191i
\(324\) 0 0
\(325\) −164.844 −0.507212
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 110.203 + 63.6256i 0.334963 + 0.193391i
\(330\) 0 0
\(331\) −64.9715 112.534i −0.196289 0.339982i 0.751034 0.660264i \(-0.229556\pi\)
−0.947322 + 0.320282i \(0.896222\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.7143 6.18588i 0.0319828 0.0184653i
\(336\) 0 0
\(337\) 53.6006 92.8389i 0.159052 0.275486i −0.775475 0.631378i \(-0.782490\pi\)
0.934527 + 0.355892i \(0.115823\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 642.208i 1.88331i
\(342\) 0 0
\(343\) 306.698 0.894163
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −347.832 200.821i −1.00240 0.578735i −0.0934416 0.995625i \(-0.529787\pi\)
−0.908957 + 0.416890i \(0.863120\pi\)
\(348\) 0 0
\(349\) 218.729 + 378.849i 0.626730 + 1.08553i 0.988204 + 0.153146i \(0.0489404\pi\)
−0.361474 + 0.932382i \(0.617726\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −303.639 + 175.306i −0.860167 + 0.496618i −0.864068 0.503375i \(-0.832092\pi\)
0.00390098 + 0.999992i \(0.498758\pi\)
\(354\) 0 0
\(355\) −98.4143 + 170.459i −0.277223 + 0.480165i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 529.816i 1.47581i 0.674904 + 0.737906i \(0.264185\pi\)
−0.674904 + 0.737906i \(0.735815\pi\)
\(360\) 0 0
\(361\) 187.709 0.519969
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 351.704 + 203.056i 0.963572 + 0.556319i
\(366\) 0 0
\(367\) −361.971 626.953i −0.986298 1.70832i −0.636020 0.771673i \(-0.719420\pi\)
−0.350278 0.936646i \(-0.613913\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 203.239 117.340i 0.547813 0.316280i
\(372\) 0 0
\(373\) 29.6005 51.2696i 0.0793580 0.137452i −0.823615 0.567149i \(-0.808046\pi\)
0.902973 + 0.429697i \(0.141380\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 424.111i 1.12496i
\(378\) 0 0
\(379\) 32.5366 0.0858485 0.0429243 0.999078i \(-0.486333\pi\)
0.0429243 + 0.999078i \(0.486333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −188.264 108.694i −0.491551 0.283797i 0.233666 0.972317i \(-0.424928\pi\)
−0.725218 + 0.688519i \(0.758261\pi\)
\(384\) 0 0
\(385\) −98.0293 169.792i −0.254622 0.441017i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 579.712 334.697i 1.49026 0.860403i 0.490324 0.871540i \(-0.336878\pi\)
0.999938 + 0.0111369i \(0.00354507\pi\)
\(390\) 0 0
\(391\) 163.511 283.210i 0.418188 0.724322i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 148.864i 0.376870i
\(396\) 0 0
\(397\) −22.3088 −0.0561935 −0.0280967 0.999605i \(-0.508945\pi\)
−0.0280967 + 0.999605i \(0.508945\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 77.7666 + 44.8986i 0.193932 + 0.111967i 0.593822 0.804597i \(-0.297618\pi\)
−0.399890 + 0.916563i \(0.630952\pi\)
\(402\) 0 0
\(403\) −421.354 729.806i −1.04554 1.81093i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 646.207 373.088i 1.58773 0.916677i
\(408\) 0 0
\(409\) −308.464 + 534.276i −0.754191 + 1.30630i 0.191584 + 0.981476i \(0.438637\pi\)
−0.945775 + 0.324821i \(0.894696\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 316.814i 0.767105i
\(414\) 0 0
\(415\) −67.4824 −0.162608
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −566.501 327.069i −1.35203 0.780595i −0.363496 0.931596i \(-0.618417\pi\)
−0.988534 + 0.151001i \(0.951750\pi\)
\(420\) 0 0
\(421\) 209.287 + 362.495i 0.497118 + 0.861033i 0.999994 0.00332489i \(-0.00105835\pi\)
−0.502877 + 0.864358i \(0.667725\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −172.590 + 99.6447i −0.406093 + 0.234458i
\(426\) 0 0
\(427\) −23.3474 + 40.4388i −0.0546777 + 0.0947045i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 111.970i 0.259792i 0.991528 + 0.129896i \(0.0414644\pi\)
−0.991528 + 0.129896i \(0.958536\pi\)
\(432\) 0 0
\(433\) −158.770 −0.366673 −0.183337 0.983050i \(-0.558690\pi\)
−0.183337 + 0.983050i \(0.558690\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −306.069 176.709i −0.700387 0.404369i
\(438\) 0 0
\(439\) −61.8211 107.077i −0.140823 0.243912i 0.786984 0.616973i \(-0.211641\pi\)
−0.927807 + 0.373061i \(0.878308\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 680.397 392.827i 1.53588 0.886743i 0.536811 0.843703i \(-0.319629\pi\)
0.999073 0.0430402i \(-0.0137044\pi\)
\(444\) 0 0
\(445\) 28.2250 48.8871i 0.0634269 0.109859i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 387.277i 0.862533i −0.902225 0.431266i \(-0.858067\pi\)
0.902225 0.431266i \(-0.141933\pi\)
\(450\) 0 0
\(451\) 388.831 0.862153
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 222.801 + 128.634i 0.489673 + 0.282713i
\(456\) 0 0
\(457\) 160.668 + 278.284i 0.351570 + 0.608938i 0.986525 0.163612i \(-0.0523145\pi\)
−0.634954 + 0.772550i \(0.718981\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 61.0565 35.2510i 0.132444 0.0764663i −0.432314 0.901723i \(-0.642303\pi\)
0.564758 + 0.825257i \(0.308970\pi\)
\(462\) 0 0
\(463\) −181.170 + 313.796i −0.391297 + 0.677746i −0.992621 0.121259i \(-0.961307\pi\)
0.601324 + 0.799005i \(0.294640\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 478.151i 1.02388i 0.859022 + 0.511939i \(0.171073\pi\)
−0.859022 + 0.511939i \(0.828927\pi\)
\(468\) 0 0
\(469\) 11.2320 0.0239489
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 565.011 + 326.209i 1.19453 + 0.689660i
\(474\) 0 0
\(475\) 107.687 + 186.520i 0.226710 + 0.392674i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −790.996 + 456.682i −1.65135 + 0.953407i −0.674830 + 0.737973i \(0.735783\pi\)
−0.976518 + 0.215434i \(0.930883\pi\)
\(480\) 0 0
\(481\) −489.567 + 847.955i −1.01781 + 1.76290i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 192.010i 0.395896i
\(486\) 0 0
\(487\) −700.870 −1.43916 −0.719579 0.694411i \(-0.755665\pi\)
−0.719579 + 0.694411i \(0.755665\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 479.646 + 276.924i 0.976876 + 0.564000i 0.901326 0.433142i \(-0.142595\pi\)
0.0755505 + 0.997142i \(0.475929\pi\)
\(492\) 0 0
\(493\) 256.366 + 444.039i 0.520012 + 0.900687i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −154.756 + 89.3482i −0.311380 + 0.179775i
\(498\) 0 0
\(499\) 162.874 282.107i 0.326401 0.565344i −0.655394 0.755287i \(-0.727497\pi\)
0.981795 + 0.189944i \(0.0608306\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 610.492i 1.21370i 0.794816 + 0.606851i \(0.207567\pi\)
−0.794816 + 0.606851i \(0.792433\pi\)
\(504\) 0 0
\(505\) −158.827 −0.314510
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 774.630 + 447.233i 1.52187 + 0.878650i 0.999666 + 0.0258270i \(0.00822190\pi\)
0.522200 + 0.852823i \(0.325111\pi\)
\(510\) 0 0
\(511\) 184.350 + 319.304i 0.360764 + 0.624862i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −75.5729 + 43.6320i −0.146744 + 0.0847224i
\(516\) 0 0
\(517\) −240.850 + 417.164i −0.465860 + 0.806894i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 244.209i 0.468732i 0.972148 + 0.234366i \(0.0753014\pi\)
−0.972148 + 0.234366i \(0.924699\pi\)
\(522\) 0 0
\(523\) −4.79146 −0.00916150 −0.00458075 0.999990i \(-0.501458\pi\)
−0.00458075 + 0.999990i \(0.501458\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −882.305 509.399i −1.67420 0.966601i
\(528\) 0 0
\(529\) −150.683 260.991i −0.284846 0.493367i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −441.868 + 255.113i −0.829021 + 0.478636i
\(534\) 0 0
\(535\) −1.03624 + 1.79483i −0.00193690 + 0.00335482i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 491.492i 0.911859i
\(540\) 0 0
\(541\) −406.633 −0.751633 −0.375816 0.926694i \(-0.622638\pi\)
−0.375816 + 0.926694i \(0.622638\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 684.413 + 395.146i 1.25580 + 0.725038i
\(546\) 0 0
\(547\) 250.283 + 433.503i 0.457556 + 0.792509i 0.998831 0.0483358i \(-0.0153918\pi\)
−0.541276 + 0.840845i \(0.682058\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 479.879 277.058i 0.870924 0.502828i
\(552\) 0 0
\(553\) −67.5750 + 117.043i −0.122197 + 0.211652i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 549.645i 0.986796i −0.869804 0.493398i \(-0.835755\pi\)
0.869804 0.493398i \(-0.164245\pi\)
\(558\) 0 0
\(559\) −856.105 −1.53149
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −799.025 461.317i −1.41923 0.819391i −0.422996 0.906132i \(-0.639022\pi\)
−0.996231 + 0.0867404i \(0.972355\pi\)
\(564\) 0 0
\(565\) −266.191 461.056i −0.471134 0.816027i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −281.820 + 162.709i −0.495289 + 0.285955i −0.726766 0.686885i \(-0.758978\pi\)
0.231477 + 0.972840i \(0.425644\pi\)
\(570\) 0 0
\(571\) 64.8487 112.321i 0.113570 0.196710i −0.803637 0.595120i \(-0.797105\pi\)
0.917207 + 0.398410i \(0.130438\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 138.721i 0.241254i
\(576\) 0 0
\(577\) 401.374 0.695621 0.347811 0.937565i \(-0.386925\pi\)
0.347811 + 0.937565i \(0.386925\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −53.0577 30.6329i −0.0913214 0.0527244i
\(582\) 0 0
\(583\) 444.181 + 769.345i 0.761889 + 1.31963i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 650.079 375.323i 1.10746 0.639392i 0.169290 0.985566i \(-0.445853\pi\)
0.938170 + 0.346174i \(0.112519\pi\)
\(588\) 0 0
\(589\) −550.515 + 953.519i −0.934660 + 1.61888i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 969.193i 1.63439i 0.576362 + 0.817195i \(0.304472\pi\)
−0.576362 + 0.817195i \(0.695528\pi\)
\(594\) 0 0
\(595\) 311.027 0.522735
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.76897 5.64012i −0.0163088 0.00941589i 0.491823 0.870695i \(-0.336331\pi\)
−0.508132 + 0.861279i \(0.669664\pi\)
\(600\) 0 0
\(601\) −425.209 736.483i −0.707502 1.22543i −0.965781 0.259359i \(-0.916489\pi\)
0.258279 0.966070i \(-0.416845\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 226.132 130.557i 0.373772 0.215797i
\(606\) 0 0
\(607\) 91.2085 157.978i 0.150261 0.260260i −0.781062 0.624453i \(-0.785322\pi\)
0.931323 + 0.364193i \(0.118655\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 632.088i 1.03451i
\(612\) 0 0
\(613\) 334.345 0.545425 0.272712 0.962096i \(-0.412079\pi\)
0.272712 + 0.962096i \(0.412079\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 154.140 + 88.9929i 0.249822 + 0.144235i 0.619683 0.784852i \(-0.287261\pi\)
−0.369861 + 0.929087i \(0.620595\pi\)
\(618\) 0 0
\(619\) 529.724 + 917.510i 0.855775 + 1.48225i 0.875925 + 0.482448i \(0.160252\pi\)
−0.0201500 + 0.999797i \(0.506414\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 44.3836 25.6249i 0.0712417 0.0411314i
\(624\) 0 0
\(625\) 155.301 268.989i 0.248482 0.430383i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1183.73i 1.88193i
\(630\) 0 0
\(631\) 950.275 1.50598 0.752991 0.658031i \(-0.228610\pi\)
0.752991 + 0.658031i \(0.228610\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −157.954 91.1946i −0.248746 0.143614i
\(636\) 0 0
\(637\) −322.469 558.532i −0.506230 0.876817i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 74.1661 42.8198i 0.115704 0.0668016i −0.441031 0.897492i \(-0.645387\pi\)
0.556735 + 0.830690i \(0.312054\pi\)
\(642\) 0 0
\(643\) 139.447 241.529i 0.216869 0.375629i −0.736980 0.675915i \(-0.763749\pi\)
0.953849 + 0.300286i \(0.0970821\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 654.758i 1.01199i −0.862536 0.505995i \(-0.831125\pi\)
0.862536 0.505995i \(-0.168875\pi\)
\(648\) 0 0
\(649\) −1199.28 −1.84789
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −159.696 92.2004i −0.244557 0.141195i 0.372712 0.927947i \(-0.378428\pi\)
−0.617269 + 0.786752i \(0.711761\pi\)
\(654\) 0 0
\(655\) −385.418 667.563i −0.588424 1.01918i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 165.641 95.6328i 0.251352 0.145118i −0.369031 0.929417i \(-0.620310\pi\)
0.620383 + 0.784299i \(0.286977\pi\)
\(660\) 0 0
\(661\) −66.6012 + 115.357i −0.100758 + 0.174518i −0.911997 0.410196i \(-0.865460\pi\)
0.811239 + 0.584715i \(0.198794\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 336.131i 0.505461i
\(666\) 0 0
\(667\) −356.901 −0.535085
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −153.078 88.3797i −0.228134 0.131713i
\(672\) 0 0
\(673\) 661.521 + 1145.79i 0.982943 + 1.70251i 0.650742 + 0.759299i \(0.274458\pi\)
0.332201 + 0.943208i \(0.392209\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 288.213 166.400i 0.425720 0.245790i −0.271801 0.962353i \(-0.587619\pi\)
0.697522 + 0.716564i \(0.254286\pi\)
\(678\) 0 0
\(679\) 87.1607 150.967i 0.128366 0.222337i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 190.785i 0.279333i −0.990199 0.139667i \(-0.955397\pi\)
0.990199 0.139667i \(-0.0446031\pi\)
\(684\) 0 0
\(685\) −687.671 −1.00390
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1009.54 582.856i −1.46522 0.845945i
\(690\) 0 0
\(691\) −360.135 623.771i −0.521179 0.902708i −0.999697 0.0246304i \(-0.992159\pi\)
0.478518 0.878078i \(-0.341174\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.53379 3.19493i 0.00796228 0.00459703i
\(696\) 0 0
\(697\) −308.421 + 534.200i −0.442497 + 0.766428i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 145.736i 0.207897i 0.994583 + 0.103949i \(0.0331477\pi\)
−0.994583 + 0.103949i \(0.966852\pi\)
\(702\) 0 0
\(703\) 1279.28 1.81974
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −124.877 72.0980i −0.176630 0.101977i
\(708\) 0 0
\(709\) 394.430 + 683.173i 0.556319 + 0.963572i 0.997800 + 0.0663017i \(0.0211200\pi\)
−0.441481 + 0.897271i \(0.645547\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 614.153 354.581i 0.861365 0.497309i
\(714\) 0 0
\(715\) −486.936 + 843.398i −0.681029 + 1.17958i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 721.671i 1.00372i 0.864950 + 0.501858i \(0.167350\pi\)
−0.864950 + 0.501858i \(0.832650\pi\)
\(720\) 0 0
\(721\) −79.2252 −0.109882
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 188.358 + 108.749i 0.259805 + 0.149998i
\(726\) 0 0
\(727\) 543.433 + 941.253i 0.747500 + 1.29471i 0.949018 + 0.315223i \(0.102079\pi\)
−0.201518 + 0.979485i \(0.564587\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −896.332 + 517.498i −1.22617 + 0.707931i
\(732\) 0 0
\(733\) 352.753 610.985i 0.481245 0.833541i −0.518523 0.855063i \(-0.673518\pi\)
0.999768 + 0.0215227i \(0.00685140\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 42.5181i 0.0576908i
\(738\) 0 0
\(739\) −1183.74 −1.60182 −0.800909 0.598786i \(-0.795650\pi\)
−0.800909 + 0.598786i \(0.795650\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 187.727 + 108.384i 0.252661 + 0.145874i 0.620982 0.783825i \(-0.286734\pi\)
−0.368321 + 0.929699i \(0.620067\pi\)
\(744\) 0 0
\(745\) 174.705 + 302.598i 0.234503 + 0.406172i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.62949 + 0.940784i −0.00217555 + 0.00125605i
\(750\) 0 0
\(751\) −76.7045 + 132.856i −0.102137 + 0.176906i −0.912565 0.408932i \(-0.865901\pi\)
0.810428 + 0.585838i \(0.199235\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 52.8056i 0.0699412i
\(756\) 0 0
\(757\) 585.893 0.773967 0.386983 0.922087i \(-0.373517\pi\)
0.386983 + 0.922087i \(0.373517\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 290.563 + 167.757i 0.381817 + 0.220442i 0.678609 0.734500i \(-0.262583\pi\)
−0.296791 + 0.954942i \(0.595917\pi\)
\(762\) 0 0
\(763\) 358.744 + 621.364i 0.470176 + 0.814369i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1362.86 786.848i 1.77687 1.02588i
\(768\) 0 0
\(769\) 613.797 1063.13i 0.798175 1.38248i −0.122628 0.992453i \(-0.539132\pi\)
0.920803 0.390028i \(-0.127535\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 512.944i 0.663576i 0.943354 + 0.331788i \(0.107652\pi\)
−0.943354 + 0.331788i \(0.892348\pi\)
\(774\) 0 0
\(775\) −432.168 −0.557636
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 577.318 + 333.315i 0.741101 + 0.427875i
\(780\) 0 0
\(781\) −338.221 585.816i −0.433062 0.750085i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 646.543 373.282i 0.823622 0.475518i
\(786\) 0 0
\(787\) 284.387 492.573i 0.361356 0.625886i −0.626828 0.779157i \(-0.715647\pi\)
0.988184 + 0.153271i \(0.0489807\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 483.337i 0.611046i
\(792\) 0 0
\(793\) 231.944 0.292490
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1026.79 + 592.819i 1.28832 + 0.743813i 0.978355 0.206934i \(-0.0663485\pi\)
0.309967 + 0.950747i \(0.399682\pi\)
\(798\) 0 0
\(799\) −382.084 661.789i −0.478203 0.828271i