Properties

Label 1728.3.q.d.1601.1
Level $1728$
Weight $3$
Character 1728.1601
Analytic conductor $47.085$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.1
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1728.1601
Dual form 1728.3.q.d.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.50000 + 2.59808i) q^{5} +(-3.17423 + 5.49794i) q^{7} +O(q^{10})\) \(q+(-4.50000 + 2.59808i) q^{5} +(-3.17423 + 5.49794i) q^{7} +(8.17423 + 4.71940i) q^{11} +(9.84847 + 17.0580i) q^{13} +1.90702i q^{17} -4.69694 q^{19} +(-8.17423 + 4.71940i) q^{23} +(1.00000 - 1.73205i) q^{25} +(-2.84847 - 1.64456i) q^{29} +(20.5227 + 35.5464i) q^{31} -32.9876i q^{35} -17.3031 q^{37} +(53.5454 - 30.9145i) q^{41} +(0.477296 - 0.826701i) q^{43} +(12.2196 + 7.05501i) q^{47} +(4.34847 + 7.53177i) q^{49} -9.53512i q^{53} -49.0454 q^{55} +(79.2650 - 45.7637i) q^{59} +(-37.5454 + 65.0306i) q^{61} +(-88.6362 - 51.1741i) q^{65} +(15.4773 + 26.8075i) q^{67} -85.9026i q^{71} -96.0908 q^{73} +(-51.8939 + 29.9609i) q^{77} +(-14.8712 + 25.7576i) q^{79} +(-76.1288 - 43.9530i) q^{83} +(-4.95459 - 8.58161i) q^{85} +41.3766i q^{89} -125.045 q^{91} +(21.1362 - 12.2030i) q^{95} +(-47.9393 + 83.0333i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{5} + 2 q^{7} + 18 q^{11} + 10 q^{13} + 40 q^{19} - 18 q^{23} + 4 q^{25} + 18 q^{29} + 38 q^{31} - 128 q^{37} + 126 q^{41} + 46 q^{43} - 54 q^{47} - 12 q^{49} - 108 q^{55} + 126 q^{59} - 62 q^{61} - 90 q^{65} + 106 q^{67} - 208 q^{73} - 90 q^{77} + 14 q^{79} - 378 q^{83} - 108 q^{85} - 412 q^{91} - 180 q^{95} + 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −4.50000 + 2.59808i −0.900000 + 0.519615i −0.877200 0.480125i \(-0.840591\pi\)
−0.0227998 + 0.999740i \(0.507258\pi\)
\(6\) 0 0
\(7\) −3.17423 + 5.49794i −0.453462 + 0.785419i −0.998598 0.0529281i \(-0.983145\pi\)
0.545136 + 0.838347i \(0.316478\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 8.17423 + 4.71940i 0.743112 + 0.429036i 0.823200 0.567752i \(-0.192187\pi\)
−0.0800876 + 0.996788i \(0.525520\pi\)
\(12\) 0 0
\(13\) 9.84847 + 17.0580i 0.757575 + 1.31216i 0.944084 + 0.329704i \(0.106949\pi\)
−0.186510 + 0.982453i \(0.559718\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.90702i 0.112178i 0.998426 + 0.0560889i \(0.0178630\pi\)
−0.998426 + 0.0560889i \(0.982137\pi\)
\(18\) 0 0
\(19\) −4.69694 −0.247207 −0.123604 0.992332i \(-0.539445\pi\)
−0.123604 + 0.992332i \(0.539445\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.17423 + 4.71940i −0.355402 + 0.205191i −0.667062 0.745002i \(-0.732448\pi\)
0.311660 + 0.950194i \(0.399115\pi\)
\(24\) 0 0
\(25\) 1.00000 1.73205i 0.0400000 0.0692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.84847 1.64456i −0.0982231 0.0567091i 0.450084 0.892986i \(-0.351394\pi\)
−0.548307 + 0.836277i \(0.684727\pi\)
\(30\) 0 0
\(31\) 20.5227 + 35.5464i 0.662023 + 1.14666i 0.980083 + 0.198587i \(0.0636351\pi\)
−0.318061 + 0.948070i \(0.603032\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 32.9876i 0.942503i
\(36\) 0 0
\(37\) −17.3031 −0.467650 −0.233825 0.972279i \(-0.575124\pi\)
−0.233825 + 0.972279i \(0.575124\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 53.5454 30.9145i 1.30599 0.754011i 0.324562 0.945864i \(-0.394783\pi\)
0.981424 + 0.191853i \(0.0614498\pi\)
\(42\) 0 0
\(43\) 0.477296 0.826701i 0.0110999 0.0192256i −0.860422 0.509582i \(-0.829800\pi\)
0.871522 + 0.490356i \(0.163133\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.2196 + 7.05501i 0.259992 + 0.150107i 0.624331 0.781160i \(-0.285372\pi\)
−0.364339 + 0.931267i \(0.618705\pi\)
\(48\) 0 0
\(49\) 4.34847 + 7.53177i 0.0887443 + 0.153710i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.53512i 0.179908i −0.995946 0.0899539i \(-0.971328\pi\)
0.995946 0.0899539i \(-0.0286720\pi\)
\(54\) 0 0
\(55\) −49.0454 −0.891735
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 79.2650 45.7637i 1.34348 0.775656i 0.356160 0.934425i \(-0.384086\pi\)
0.987316 + 0.158769i \(0.0507526\pi\)
\(60\) 0 0
\(61\) −37.5454 + 65.0306i −0.615498 + 1.06607i 0.374798 + 0.927106i \(0.377712\pi\)
−0.990297 + 0.138968i \(0.955621\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −88.6362 51.1741i −1.36363 0.787295i
\(66\) 0 0
\(67\) 15.4773 + 26.8075i 0.231004 + 0.400111i 0.958104 0.286421i \(-0.0924655\pi\)
−0.727100 + 0.686532i \(0.759132\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 85.9026i 1.20990i −0.796265 0.604948i \(-0.793194\pi\)
0.796265 0.604948i \(-0.206806\pi\)
\(72\) 0 0
\(73\) −96.0908 −1.31631 −0.658156 0.752881i \(-0.728663\pi\)
−0.658156 + 0.752881i \(0.728663\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −51.8939 + 29.9609i −0.673946 + 0.389103i
\(78\) 0 0
\(79\) −14.8712 + 25.7576i −0.188243 + 0.326046i −0.944664 0.328038i \(-0.893612\pi\)
0.756422 + 0.654084i \(0.226946\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −76.1288 43.9530i −0.917215 0.529554i −0.0344693 0.999406i \(-0.510974\pi\)
−0.882745 + 0.469852i \(0.844307\pi\)
\(84\) 0 0
\(85\) −4.95459 8.58161i −0.0582893 0.100960i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 41.3766i 0.464905i 0.972608 + 0.232453i \(0.0746751\pi\)
−0.972608 + 0.232453i \(0.925325\pi\)
\(90\) 0 0
\(91\) −125.045 −1.37413
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 21.1362 12.2030i 0.222487 0.128453i
\(96\) 0 0
\(97\) −47.9393 + 83.0333i −0.494219 + 0.856013i −0.999978 0.00666202i \(-0.997879\pi\)
0.505758 + 0.862675i \(0.331213\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −136.772 78.9656i −1.35418 0.781838i −0.365350 0.930870i \(-0.619051\pi\)
−0.988832 + 0.149032i \(0.952384\pi\)
\(102\) 0 0
\(103\) −14.5681 25.2327i −0.141438 0.244978i 0.786600 0.617462i \(-0.211839\pi\)
−0.928038 + 0.372485i \(0.878506\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 171.805i 1.60566i 0.596210 + 0.802829i \(0.296673\pi\)
−0.596210 + 0.802829i \(0.703327\pi\)
\(108\) 0 0
\(109\) −116.272 −1.06672 −0.533360 0.845888i \(-0.679071\pi\)
−0.533360 + 0.845888i \(0.679071\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −175.166 + 101.132i −1.55014 + 0.894976i −0.552015 + 0.833834i \(0.686141\pi\)
−0.998129 + 0.0611424i \(0.980526\pi\)
\(114\) 0 0
\(115\) 24.5227 42.4746i 0.213241 0.369344i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.4847 6.05334i −0.0881067 0.0508684i
\(120\) 0 0
\(121\) −15.9546 27.6342i −0.131856 0.228382i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 119.512i 0.956092i
\(126\) 0 0
\(127\) 10.0908 0.0794552 0.0397276 0.999211i \(-0.487351\pi\)
0.0397276 + 0.999211i \(0.487351\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.29567 2.48010i 0.0327913 0.0189321i −0.483515 0.875336i \(-0.660640\pi\)
0.516306 + 0.856404i \(0.327307\pi\)
\(132\) 0 0
\(133\) 14.9092 25.8235i 0.112099 0.194161i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −203.242 117.342i −1.48352 0.856511i −0.483696 0.875236i \(-0.660706\pi\)
−0.999825 + 0.0187249i \(0.994039\pi\)
\(138\) 0 0
\(139\) 53.2650 + 92.2578i 0.383202 + 0.663725i 0.991518 0.129970i \(-0.0414881\pi\)
−0.608316 + 0.793695i \(0.708155\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 185.915i 1.30011i
\(144\) 0 0
\(145\) 17.0908 0.117868
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −91.0301 + 52.5563i −0.610940 + 0.352727i −0.773333 0.634000i \(-0.781412\pi\)
0.162393 + 0.986726i \(0.448079\pi\)
\(150\) 0 0
\(151\) 142.614 247.014i 0.944460 1.63585i 0.187632 0.982239i \(-0.439919\pi\)
0.756828 0.653614i \(-0.226748\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −184.704 106.639i −1.19164 0.687994i
\(156\) 0 0
\(157\) −98.5908 170.764i −0.627967 1.08767i −0.987959 0.154715i \(-0.950554\pi\)
0.359992 0.932955i \(-0.382779\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 59.9219i 0.372186i
\(162\) 0 0
\(163\) 249.060 1.52798 0.763988 0.645230i \(-0.223238\pi\)
0.763988 + 0.645230i \(0.223238\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 41.9472 24.2182i 0.251181 0.145019i −0.369124 0.929380i \(-0.620342\pi\)
0.620305 + 0.784361i \(0.287009\pi\)
\(168\) 0 0
\(169\) −109.485 + 189.633i −0.647838 + 1.12209i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 86.9847 + 50.2206i 0.502802 + 0.290293i 0.729870 0.683586i \(-0.239581\pi\)
−0.227068 + 0.973879i \(0.572914\pi\)
\(174\) 0 0
\(175\) 6.34847 + 10.9959i 0.0362770 + 0.0628336i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 285.071i 1.59257i 0.604919 + 0.796287i \(0.293206\pi\)
−0.604919 + 0.796287i \(0.706794\pi\)
\(180\) 0 0
\(181\) −37.1214 −0.205091 −0.102545 0.994728i \(-0.532699\pi\)
−0.102545 + 0.994728i \(0.532699\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 77.8638 44.9547i 0.420885 0.242998i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.0481283 + 0.0833607i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.5227 + 8.96204i 0.0812707 + 0.0469217i 0.540085 0.841611i \(-0.318392\pi\)
−0.458814 + 0.888532i \(0.651726\pi\)
\(192\) 0 0
\(193\) 47.7270 + 82.6657i 0.247290 + 0.428319i 0.962773 0.270311i \(-0.0871265\pi\)
−0.715483 + 0.698630i \(0.753793\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 160.363i 0.814026i −0.913422 0.407013i \(-0.866570\pi\)
0.913422 0.407013i \(-0.133430\pi\)
\(198\) 0 0
\(199\) 6.51531 0.0327402 0.0163701 0.999866i \(-0.494789\pi\)
0.0163701 + 0.999866i \(0.494789\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.0834 10.4405i 0.0890809 0.0514309i
\(204\) 0 0
\(205\) −160.636 + 278.230i −0.783591 + 1.35722i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −38.3939 22.1667i −0.183703 0.106061i
\(210\) 0 0
\(211\) −77.2196 133.748i −0.365970 0.633878i 0.622961 0.782253i \(-0.285929\pi\)
−0.988931 + 0.148374i \(0.952596\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.96021i 0.0230707i
\(216\) 0 0
\(217\) −260.576 −1.20081
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −32.5301 + 18.7813i −0.147195 + 0.0849831i
\(222\) 0 0
\(223\) −46.3865 + 80.3437i −0.208011 + 0.360286i −0.951088 0.308920i \(-0.900032\pi\)
0.743077 + 0.669206i \(0.233366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 147.053 + 84.9010i 0.647810 + 0.374013i 0.787617 0.616166i \(-0.211315\pi\)
−0.139807 + 0.990179i \(0.544648\pi\)
\(228\) 0 0
\(229\) 203.772 + 352.944i 0.889836 + 1.54124i 0.840068 + 0.542480i \(0.182515\pi\)
0.0497675 + 0.998761i \(0.484152\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.2562i 0.0654772i 0.999464 + 0.0327386i \(0.0104229\pi\)
−0.999464 + 0.0327386i \(0.989577\pi\)
\(234\) 0 0
\(235\) −73.3179 −0.311991
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −48.9620 + 28.2682i −0.204862 + 0.118277i −0.598921 0.800808i \(-0.704404\pi\)
0.394059 + 0.919085i \(0.371070\pi\)
\(240\) 0 0
\(241\) −42.1061 + 72.9299i −0.174714 + 0.302614i −0.940062 0.341003i \(-0.889233\pi\)
0.765348 + 0.643617i \(0.222567\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −39.1362 22.5953i −0.159740 0.0922258i
\(246\) 0 0
\(247\) −46.2577 80.1206i −0.187278 0.324375i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 218.903i 0.872123i −0.899917 0.436062i \(-0.856373\pi\)
0.899917 0.436062i \(-0.143627\pi\)
\(252\) 0 0
\(253\) −89.0908 −0.352138
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.1061 6.41212i 0.0432145 0.0249499i −0.478237 0.878231i \(-0.658724\pi\)
0.521452 + 0.853281i \(0.325391\pi\)
\(258\) 0 0
\(259\) 54.9240 95.1311i 0.212062 0.367302i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −291.386 168.232i −1.10793 0.639666i −0.169640 0.985506i \(-0.554261\pi\)
−0.938293 + 0.345840i \(0.887594\pi\)
\(264\) 0 0
\(265\) 24.7730 + 42.9080i 0.0934829 + 0.161917i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 60.4468i 0.224709i −0.993668 0.112355i \(-0.964161\pi\)
0.993668 0.112355i \(-0.0358393\pi\)
\(270\) 0 0
\(271\) 274.636 1.01342 0.506708 0.862118i \(-0.330862\pi\)
0.506708 + 0.862118i \(0.330862\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.3485 9.43879i 0.0594490 0.0343229i
\(276\) 0 0
\(277\) −24.5000 + 42.4352i −0.0884477 + 0.153196i −0.906855 0.421442i \(-0.861524\pi\)
0.818407 + 0.574638i \(0.194857\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 297.121 + 171.543i 1.05737 + 0.610473i 0.924704 0.380688i \(-0.124313\pi\)
0.132666 + 0.991161i \(0.457646\pi\)
\(282\) 0 0
\(283\) −171.704 297.401i −0.606729 1.05089i −0.991776 0.127988i \(-0.959148\pi\)
0.385047 0.922897i \(-0.374185\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 392.519i 1.36766i
\(288\) 0 0
\(289\) 285.363 0.987416
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −248.076 + 143.226i −0.846674 + 0.488828i −0.859527 0.511090i \(-0.829242\pi\)
0.0128532 + 0.999917i \(0.495909\pi\)
\(294\) 0 0
\(295\) −237.795 + 411.873i −0.806085 + 1.39618i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −161.007 92.9577i −0.538486 0.310895i
\(300\) 0 0
\(301\) 3.03010 + 5.24829i 0.0100668 + 0.0174362i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 390.183i 1.27929i
\(306\) 0 0
\(307\) −154.091 −0.501924 −0.250962 0.967997i \(-0.580747\pi\)
−0.250962 + 0.967997i \(0.580747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 62.3411 35.9926i 0.200454 0.115732i −0.396413 0.918072i \(-0.629745\pi\)
0.596867 + 0.802340i \(0.296412\pi\)
\(312\) 0 0
\(313\) 183.803 318.356i 0.587230 1.01711i −0.407363 0.913266i \(-0.633552\pi\)
0.994593 0.103846i \(-0.0331150\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −93.1821 53.7987i −0.293950 0.169712i 0.345772 0.938319i \(-0.387617\pi\)
−0.639722 + 0.768607i \(0.720950\pi\)
\(318\) 0 0
\(319\) −15.5227 26.8861i −0.0486605 0.0842825i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.95717i 0.0277312i
\(324\) 0 0
\(325\) 39.3939 0.121212
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −77.5760 + 44.7885i −0.235793 + 0.136135i
\(330\) 0 0
\(331\) 8.59873 14.8934i 0.0259780 0.0449953i −0.852744 0.522329i \(-0.825063\pi\)
0.878722 + 0.477334i \(0.158397\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −139.296 80.4224i −0.415808 0.240067i
\(336\) 0 0
\(337\) −182.197 315.574i −0.540644 0.936422i −0.998867 0.0475854i \(-0.984847\pi\)
0.458223 0.888837i \(-0.348486\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 387.419i 1.13613i
\(342\) 0 0
\(343\) −366.287 −1.06789
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 505.234 291.697i 1.45601 0.840626i 0.457196 0.889366i \(-0.348854\pi\)
0.998811 + 0.0487402i \(0.0155206\pi\)
\(348\) 0 0
\(349\) 156.379 270.856i 0.448076 0.776091i −0.550185 0.835043i \(-0.685443\pi\)
0.998261 + 0.0589524i \(0.0187760\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 32.5760 + 18.8078i 0.0922834 + 0.0532798i 0.545431 0.838155i \(-0.316366\pi\)
−0.453148 + 0.891435i \(0.649699\pi\)
\(354\) 0 0
\(355\) 223.182 + 386.562i 0.628681 + 1.08891i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 294.028i 0.819019i −0.912306 0.409510i \(-0.865700\pi\)
0.912306 0.409510i \(-0.134300\pi\)
\(360\) 0 0
\(361\) −338.939 −0.938889
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 432.409 249.651i 1.18468 0.683976i
\(366\) 0 0
\(367\) 16.6135 28.7755i 0.0452684 0.0784072i −0.842503 0.538691i \(-0.818919\pi\)
0.887772 + 0.460284i \(0.152252\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 52.4235 + 30.2667i 0.141303 + 0.0815814i
\(372\) 0 0
\(373\) −112.515 194.881i −0.301648 0.522470i 0.674861 0.737945i \(-0.264203\pi\)
−0.976509 + 0.215475i \(0.930870\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 64.7858i 0.171846i
\(378\) 0 0
\(379\) 166.334 0.438875 0.219438 0.975627i \(-0.429578\pi\)
0.219438 + 0.975627i \(0.429578\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 638.249 368.493i 1.66645 0.962124i 0.696917 0.717152i \(-0.254555\pi\)
0.969530 0.244972i \(-0.0787787\pi\)
\(384\) 0 0
\(385\) 155.682 269.648i 0.404368 0.700386i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −146.682 84.6867i −0.377074 0.217704i 0.299471 0.954106i \(-0.403190\pi\)
−0.676544 + 0.736402i \(0.736523\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.0230179 0.0398682i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 154.546i 0.391255i
\(396\) 0 0
\(397\) 256.272 0.645523 0.322761 0.946480i \(-0.395389\pi\)
0.322761 + 0.946480i \(0.395389\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −226.364 + 130.691i −0.564498 + 0.325913i −0.754949 0.655784i \(-0.772338\pi\)
0.190451 + 0.981697i \(0.439005\pi\)
\(402\) 0 0
\(403\) −404.234 + 700.155i −1.00306 + 1.73736i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −141.439 81.6600i −0.347517 0.200639i
\(408\) 0 0
\(409\) 221.894 + 384.331i 0.542528 + 0.939686i 0.998758 + 0.0498240i \(0.0158660\pi\)
−0.456230 + 0.889862i \(0.650801\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 581.059i 1.40692i
\(414\) 0 0
\(415\) 456.773 1.10066
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.32525 5.38394i 0.0222560 0.0128495i −0.488831 0.872379i \(-0.662576\pi\)
0.511087 + 0.859529i \(0.329243\pi\)
\(420\) 0 0
\(421\) 127.152 220.233i 0.302023 0.523119i −0.674571 0.738210i \(-0.735672\pi\)
0.976594 + 0.215091i \(0.0690048\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.30306 + 1.90702i 0.00777191 + 0.00448711i
\(426\) 0 0
\(427\) −238.356 412.844i −0.558210 0.966849i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 698.663i 1.62103i 0.585719 + 0.810514i \(0.300812\pi\)
−0.585719 + 0.810514i \(0.699188\pi\)
\(432\) 0 0
\(433\) 211.728 0.488978 0.244489 0.969652i \(-0.421380\pi\)
0.244489 + 0.969652i \(0.421380\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 38.3939 22.1667i 0.0878578 0.0507247i
\(438\) 0 0
\(439\) −139.931 + 242.368i −0.318750 + 0.552092i −0.980228 0.197874i \(-0.936596\pi\)
0.661477 + 0.749965i \(0.269930\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −477.400 275.627i −1.07765 0.622183i −0.147391 0.989078i \(-0.547087\pi\)
−0.930262 + 0.366895i \(0.880421\pi\)
\(444\) 0 0
\(445\) −107.499 186.195i −0.241572 0.418415i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 542.865i 1.20905i 0.796585 + 0.604527i \(0.206638\pi\)
−0.796585 + 0.604527i \(0.793362\pi\)
\(450\) 0 0
\(451\) 583.590 1.29399
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 562.704 324.877i 1.23671 0.714016i
\(456\) 0 0
\(457\) −46.1821 + 79.9898i −0.101055 + 0.175032i −0.912120 0.409924i \(-0.865555\pi\)
0.811065 + 0.584957i \(0.198888\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −199.030 114.910i −0.431736 0.249263i 0.268350 0.963321i \(-0.413522\pi\)
−0.700086 + 0.714059i \(0.746855\pi\)
\(462\) 0 0
\(463\) 255.401 + 442.368i 0.551623 + 0.955438i 0.998158 + 0.0606723i \(0.0193245\pi\)
−0.446535 + 0.894766i \(0.647342\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 833.657i 1.78513i 0.450915 + 0.892567i \(0.351098\pi\)
−0.450915 + 0.892567i \(0.648902\pi\)
\(468\) 0 0
\(469\) −196.514 −0.419007
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.80306 4.50510i 0.0164970 0.00952452i
\(474\) 0 0
\(475\) −4.69694 + 8.13534i −0.00988829 + 0.0171270i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −569.144 328.595i −1.18819 0.686003i −0.230296 0.973121i \(-0.573969\pi\)
−0.957895 + 0.287118i \(0.907303\pi\)
\(480\) 0 0
\(481\) −170.409 295.156i −0.354280 0.613631i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 498.200i 1.02722i
\(486\) 0 0
\(487\) −351.666 −0.722107 −0.361054 0.932545i \(-0.617583\pi\)
−0.361054 + 0.932545i \(0.617583\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 212.539 122.709i 0.432869 0.249917i −0.267699 0.963503i \(-0.586263\pi\)
0.700568 + 0.713586i \(0.252930\pi\)
\(492\) 0 0
\(493\) 3.13622 5.43210i 0.00636151 0.0110185i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 472.287 + 272.675i 0.950276 + 0.548642i
\(498\) 0 0
\(499\) 315.113 + 545.792i 0.631489 + 1.09377i 0.987247 + 0.159193i \(0.0508892\pi\)
−0.355758 + 0.934578i \(0.615777\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 286.891i 0.570360i 0.958474 + 0.285180i \(0.0920534\pi\)
−0.958474 + 0.285180i \(0.907947\pi\)
\(504\) 0 0
\(505\) 820.635 1.62502
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 755.454 436.161i 1.48419 0.856898i 0.484353 0.874873i \(-0.339055\pi\)
0.999838 + 0.0179741i \(0.00572163\pi\)
\(510\) 0 0
\(511\) 305.015 528.301i 0.596898 1.03386i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 131.113 + 75.6981i 0.254588 + 0.146987i
\(516\) 0 0
\(517\) 66.5908 + 115.339i 0.128802 + 0.223092i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 206.132i 0.395646i 0.980238 + 0.197823i \(0.0633872\pi\)
−0.980238 + 0.197823i \(0.936613\pi\)
\(522\) 0 0
\(523\) −884.817 −1.69181 −0.845906 0.533333i \(-0.820939\pi\)
−0.845906 + 0.533333i \(0.820939\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −67.7878 + 39.1373i −0.128630 + 0.0742643i
\(528\) 0 0
\(529\) −219.955 + 380.973i −0.415793 + 0.720175i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1054.68 + 608.920i 1.97876 + 1.14244i
\(534\) 0 0
\(535\) −446.363 773.124i −0.834324 1.44509i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 82.0886i 0.152298i
\(540\) 0 0
\(541\) 509.151 0.941129 0.470565 0.882365i \(-0.344050\pi\)
0.470565 + 0.882365i \(0.344050\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 523.226 302.085i 0.960048 0.554284i
\(546\) 0 0
\(547\) 274.022 474.620i 0.500955 0.867679i −0.499045 0.866576i \(-0.666316\pi\)
0.999999 0.00110267i \(-0.000350992\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.3791 + 7.72442i 0.0242815 + 0.0140189i
\(552\) 0 0
\(553\) −94.4092 163.522i −0.170722 0.295699i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 406.542i 0.729879i 0.931031 + 0.364939i \(0.118910\pi\)
−0.931031 + 0.364939i \(0.881090\pi\)
\(558\) 0 0
\(559\) 18.8025 0.0336360
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −525.220 + 303.236i −0.932895 + 0.538607i −0.887726 0.460372i \(-0.847716\pi\)
−0.0451687 + 0.998979i \(0.514383\pi\)
\(564\) 0 0
\(565\) 525.499 910.191i 0.930087 1.61096i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 224.954 + 129.877i 0.395350 + 0.228255i 0.684476 0.729036i \(-0.260031\pi\)
−0.289126 + 0.957291i \(0.593365\pi\)
\(570\) 0 0
\(571\) −43.9166 76.0657i −0.0769117 0.133215i 0.825004 0.565126i \(-0.191173\pi\)
−0.901916 + 0.431911i \(0.857839\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.8776i 0.0328306i
\(576\) 0 0
\(577\) −132.091 −0.228927 −0.114463 0.993427i \(-0.536515\pi\)
−0.114463 + 0.993427i \(0.536515\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 483.302 279.034i 0.831844 0.480266i
\(582\) 0 0
\(583\) 45.0000 77.9423i 0.0771870 0.133692i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −491.614 283.833i −0.837502 0.483532i 0.0189125 0.999821i \(-0.493980\pi\)
−0.856414 + 0.516289i \(0.827313\pi\)
\(588\) 0 0
\(589\) −96.3939 166.959i −0.163657 0.283462i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 77.0321i 0.129902i −0.997888 0.0649512i \(-0.979311\pi\)
0.997888 0.0649512i \(-0.0206892\pi\)
\(594\) 0 0
\(595\) 62.9082 0.105728
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 764.917 441.625i 1.27699 0.737270i 0.300696 0.953720i \(-0.402781\pi\)
0.976294 + 0.216450i \(0.0694479\pi\)
\(600\) 0 0
\(601\) 397.545 688.569i 0.661473 1.14571i −0.318755 0.947837i \(-0.603265\pi\)
0.980229 0.197868i \(-0.0634018\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 143.591 + 82.9025i 0.237341 + 0.137029i
\(606\) 0 0
\(607\) 148.372 + 256.987i 0.244434 + 0.423373i 0.961972 0.273147i \(-0.0880644\pi\)
−0.717538 + 0.696519i \(0.754731\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 277.924i 0.454868i
\(612\) 0 0
\(613\) 517.181 0.843688 0.421844 0.906668i \(-0.361383\pi\)
0.421844 + 0.906668i \(0.361383\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 229.909 132.738i 0.372623 0.215134i −0.301981 0.953314i \(-0.597648\pi\)
0.674604 + 0.738180i \(0.264314\pi\)
\(618\) 0 0
\(619\) −98.5227 + 170.646i −0.159164 + 0.275681i −0.934568 0.355786i \(-0.884213\pi\)
0.775403 + 0.631466i \(0.217547\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −227.486 131.339i −0.365146 0.210817i
\(624\) 0 0
\(625\) 335.500 + 581.103i 0.536800 + 0.929765i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 32.9973i 0.0524600i
\(630\) 0 0
\(631\) −160.879 −0.254958 −0.127479 0.991841i \(-0.540689\pi\)
−0.127479 + 0.991841i \(0.540689\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −45.4087 + 26.2167i −0.0715097 + 0.0412862i
\(636\) 0 0
\(637\) −85.6515 + 148.353i −0.134461 + 0.232893i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 267.894 + 154.669i 0.417931 + 0.241293i 0.694192 0.719790i \(-0.255762\pi\)
−0.276261 + 0.961083i \(0.589095\pi\)
\(642\) 0 0
\(643\) 197.296 + 341.726i 0.306836 + 0.531456i 0.977668 0.210153i \(-0.0673963\pi\)
−0.670832 + 0.741609i \(0.734063\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 418.736i 0.647196i 0.946195 + 0.323598i \(0.104892\pi\)
−0.946195 + 0.323598i \(0.895108\pi\)
\(648\) 0 0
\(649\) 863.908 1.33114
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −459.621 + 265.363i −0.703861 + 0.406375i −0.808784 0.588106i \(-0.799874\pi\)
0.104923 + 0.994480i \(0.466540\pi\)
\(654\) 0 0
\(655\) −12.8870 + 22.3209i −0.0196748 + 0.0340778i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 310.204 + 179.096i 0.470719 + 0.271770i 0.716541 0.697545i \(-0.245724\pi\)
−0.245822 + 0.969315i \(0.579058\pi\)
\(660\) 0 0
\(661\) −111.136 192.493i −0.168133 0.291214i 0.769631 0.638489i \(-0.220440\pi\)
−0.937763 + 0.347275i \(0.887107\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 154.941i 0.232994i
\(666\) 0 0
\(667\) 31.0454 0.0465448
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −613.810 + 354.383i −0.914769 + 0.528142i
\(672\) 0 0
\(673\) 144.606 250.464i 0.214867 0.372161i −0.738364 0.674402i \(-0.764401\pi\)
0.953231 + 0.302241i \(0.0977348\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 402.227 + 232.226i 0.594131 + 0.343022i 0.766729 0.641971i \(-0.221883\pi\)
−0.172598 + 0.984992i \(0.555216\pi\)
\(678\) 0 0
\(679\) −304.341 527.134i −0.448220 0.776339i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1126.36i 1.64913i −0.565767 0.824565i \(-0.691420\pi\)
0.565767 0.824565i \(-0.308580\pi\)
\(684\) 0 0
\(685\) 1219.45 1.78022
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 162.650 93.9063i 0.236067 0.136294i
\(690\) 0 0
\(691\) 518.841 898.658i 0.750855 1.30052i −0.196554 0.980493i \(-0.562975\pi\)
0.947409 0.320025i \(-0.103691\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −479.385 276.773i −0.689763 0.398235i
\(696\) 0 0
\(697\) 58.9546 + 102.112i 0.0845833 + 0.146503i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 778.180i 1.11010i 0.831817 + 0.555050i \(0.187301\pi\)
−0.831817 + 0.555050i \(0.812699\pi\)
\(702\) 0 0
\(703\) 81.2714 0.115607
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 868.296 501.311i 1.22814 0.709068i
\(708\) 0 0
\(709\) −586.014 + 1015.01i −0.826536 + 1.43160i 0.0742031 + 0.997243i \(0.476359\pi\)
−0.900739 + 0.434360i \(0.856975\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −335.515 193.710i −0.470568 0.271682i
\(714\) 0 0
\(715\) −483.022 836.619i −0.675556 1.17010i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 515.416i 0.716851i 0.933558 + 0.358426i \(0.116686\pi\)
−0.933558 + 0.358426i \(0.883314\pi\)
\(720\) 0 0
\(721\) 184.970 0.256547
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.69694 + 3.28913i −0.00785785 + 0.00453673i
\(726\) 0 0
\(727\) 420.704 728.681i 0.578685 1.00231i −0.416945 0.908932i \(-0.636899\pi\)
0.995630 0.0933809i \(-0.0297674\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.57654 + 0.910215i 0.00215669 + 0.00124516i
\(732\) 0 0
\(733\) 303.181 + 525.125i 0.413617 + 0.716405i 0.995282 0.0970229i \(-0.0309320\pi\)
−0.581665 + 0.813428i \(0.697599\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 292.174i 0.396437i
\(738\) 0 0
\(739\) 389.362 0.526877 0.263439 0.964676i \(-0.415143\pi\)
0.263439 + 0.964676i \(0.415143\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −904.779 + 522.375i −1.21774 + 0.703061i −0.964434 0.264325i \(-0.914851\pi\)
−0.253304 + 0.967387i \(0.581517\pi\)
\(744\) 0 0
\(745\) 273.090 473.006i 0.366564 0.634908i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −944.574 545.350i −1.26111 0.728105i
\(750\) 0 0
\(751\) 645.916 + 1118.76i 0.860074 + 1.48969i 0.871857 + 0.489761i \(0.162916\pi\)
−0.0117826 + 0.999931i \(0.503751\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1482.08i 1.96302i
\(756\) 0 0
\(757\) −1042.36 −1.37697 −0.688483 0.725252i \(-0.741723\pi\)
−0.688483 + 0.725252i \(0.741723\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 281.607 162.586i 0.370048 0.213647i −0.303431 0.952853i \(-0.598132\pi\)
0.673479 + 0.739206i \(0.264799\pi\)
\(762\) 0 0
\(763\) 369.076 639.258i 0.483717 0.837822i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1561.28 + 901.405i 2.03557 + 1.17523i
\(768\) 0 0
\(769\) −171.348 296.783i −0.222819 0.385934i 0.732844 0.680397i \(-0.238193\pi\)
−0.955663 + 0.294463i \(0.904859\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 532.579i 0.688977i −0.938791 0.344488i \(-0.888052\pi\)
0.938791 0.344488i \(-0.111948\pi\)
\(774\) 0 0
\(775\) 82.0908 0.105924
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −251.499 + 145.203i −0.322849 + 0.186397i
\(780\) 0 0
\(781\) 405.409 702.188i 0.519089 0.899089i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 887.317 + 512.293i 1.13034 + 0.652602i
\(786\) 0 0
\(787\) −51.9768 90.0264i −0.0660442 0.114392i 0.831113 0.556104i \(-0.187704\pi\)
−0.897157 + 0.441712i \(0.854371\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1284.07i 1.62335i
\(792\) 0 0
\(793\) −1479.06 −1.86514
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −956.331 + 552.138i −1.19991 + 0.692770i −0.960536 0.278156i \(-0.910277\pi\)
−0.239378 + 0.970927i \(0.576943\pi\)
\(798\) 0 </