Properties

Label 1008.3.dc.a.737.2
Level $1008$
Weight $3$
Character 1008.737
Analytic conductor $27.466$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.dc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4660106475\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 737.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1008.737
Dual form 1008.3.dc.a.305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{5} +(-6.50000 - 2.59808i) q^{7} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(6.12372 - 3.53553i) q^{11} +15.0000 q^{13} +(-9.79796 + 5.65685i) q^{17} +(-6.50000 + 11.2583i) q^{19} +(19.5959 + 11.3137i) q^{23} +(-11.5000 - 19.9186i) q^{25} -22.6274i q^{29} +(1.50000 + 2.59808i) q^{31} +(-6.12372 - 7.77817i) q^{35} +(-8.50000 + 14.7224i) q^{37} -80.6102i q^{41} +85.0000 q^{43} +(-62.4620 - 36.0624i) q^{47} +(35.5000 + 33.7750i) q^{49} +(29.3939 - 16.9706i) q^{53} +10.0000 q^{55} +(78.3837 - 45.2548i) q^{59} +(36.0000 - 62.3538i) q^{61} +(18.3712 + 10.6066i) q^{65} +(21.5000 + 37.2391i) q^{67} -52.3259i q^{71} +(47.5000 + 82.2724i) q^{73} +(-48.9898 + 7.07107i) q^{77} +(34.5000 - 59.7558i) q^{79} -60.8112i q^{83} -16.0000 q^{85} +(117.576 + 67.8823i) q^{89} +(-97.5000 - 38.9711i) q^{91} +(-15.9217 + 9.19239i) q^{95} +16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 26 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 26 q^{7} + 60 q^{13} - 26 q^{19} - 46 q^{25} + 6 q^{31} - 34 q^{37} + 340 q^{43} + 142 q^{49} + 40 q^{55} + 144 q^{61} + 86 q^{67} + 190 q^{73} + 138 q^{79} - 64 q^{85} - 390 q^{91} + 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.22474 + 0.707107i 0.244949 + 0.141421i 0.617449 0.786611i \(-0.288166\pi\)
−0.372500 + 0.928032i \(0.621499\pi\)
\(6\) 0 0
\(7\) −6.50000 2.59808i −0.928571 0.371154i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.12372 3.53553i 0.556702 0.321412i −0.195119 0.980780i \(-0.562509\pi\)
0.751821 + 0.659367i \(0.229176\pi\)
\(12\) 0 0
\(13\) 15.0000 1.15385 0.576923 0.816798i \(-0.304253\pi\)
0.576923 + 0.816798i \(0.304253\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −9.79796 + 5.65685i −0.576351 + 0.332756i −0.759682 0.650295i \(-0.774645\pi\)
0.183331 + 0.983051i \(0.441312\pi\)
\(18\) 0 0
\(19\) −6.50000 + 11.2583i −0.342105 + 0.592544i −0.984823 0.173559i \(-0.944473\pi\)
0.642718 + 0.766103i \(0.277807\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 19.5959 + 11.3137i 0.851996 + 0.491900i 0.861324 0.508056i \(-0.169636\pi\)
−0.00932753 + 0.999956i \(0.502969\pi\)
\(24\) 0 0
\(25\) −11.5000 19.9186i −0.460000 0.796743i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 22.6274i 0.780256i −0.920761 0.390128i \(-0.872431\pi\)
0.920761 0.390128i \(-0.127569\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.0483871 + 0.0838089i 0.889205 0.457510i \(-0.151259\pi\)
−0.840817 + 0.541319i \(0.817925\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.12372 7.77817i −0.174964 0.222234i
\(36\) 0 0
\(37\) −8.50000 + 14.7224i −0.229730 + 0.397904i −0.957728 0.287675i \(-0.907118\pi\)
0.727998 + 0.685579i \(0.240451\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 80.6102i 1.96610i −0.183333 0.983051i \(-0.558689\pi\)
0.183333 0.983051i \(-0.441311\pi\)
\(42\) 0 0
\(43\) 85.0000 1.97674 0.988372 0.152055i \(-0.0485890\pi\)
0.988372 + 0.152055i \(0.0485890\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −62.4620 36.0624i −1.32898 0.767286i −0.343837 0.939029i \(-0.611727\pi\)
−0.985142 + 0.171743i \(0.945060\pi\)
\(48\) 0 0
\(49\) 35.5000 + 33.7750i 0.724490 + 0.689286i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 29.3939 16.9706i 0.554601 0.320199i −0.196374 0.980529i \(-0.562917\pi\)
0.750976 + 0.660330i \(0.229583\pi\)
\(54\) 0 0
\(55\) 10.0000 0.181818
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 78.3837 45.2548i 1.32854 0.767031i 0.343463 0.939166i \(-0.388400\pi\)
0.985073 + 0.172135i \(0.0550665\pi\)
\(60\) 0 0
\(61\) 36.0000 62.3538i 0.590164 1.02219i −0.404046 0.914739i \(-0.632396\pi\)
0.994210 0.107455i \(-0.0342702\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 18.3712 + 10.6066i 0.282633 + 0.163178i
\(66\) 0 0
\(67\) 21.5000 + 37.2391i 0.320896 + 0.555807i 0.980673 0.195654i \(-0.0626828\pi\)
−0.659778 + 0.751461i \(0.729349\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 52.3259i 0.736985i −0.929631 0.368492i \(-0.879874\pi\)
0.929631 0.368492i \(-0.120126\pi\)
\(72\) 0 0
\(73\) 47.5000 + 82.2724i 0.650685 + 1.12702i 0.982957 + 0.183836i \(0.0588515\pi\)
−0.332272 + 0.943184i \(0.607815\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −48.9898 + 7.07107i −0.636231 + 0.0918320i
\(78\) 0 0
\(79\) 34.5000 59.7558i 0.436709 0.756402i −0.560725 0.828002i \(-0.689477\pi\)
0.997433 + 0.0716005i \(0.0228107\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 60.8112i 0.732665i −0.930484 0.366332i \(-0.880613\pi\)
0.930484 0.366332i \(-0.119387\pi\)
\(84\) 0 0
\(85\) −16.0000 −0.188235
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 117.576 + 67.8823i 1.32107 + 0.762722i 0.983900 0.178721i \(-0.0571958\pi\)
0.337173 + 0.941443i \(0.390529\pi\)
\(90\) 0 0
\(91\) −97.5000 38.9711i −1.07143 0.428254i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15.9217 + 9.19239i −0.167597 + 0.0967620i
\(96\) 0 0
\(97\) 16.0000 0.164948 0.0824742 0.996593i \(-0.473718\pi\)
0.0824742 + 0.996593i \(0.473718\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −60.0125 + 34.6482i −0.594183 + 0.343052i −0.766750 0.641946i \(-0.778127\pi\)
0.172567 + 0.984998i \(0.444794\pi\)
\(102\) 0 0
\(103\) −30.5000 + 52.8275i −0.296117 + 0.512889i −0.975244 0.221131i \(-0.929025\pi\)
0.679127 + 0.734020i \(0.262358\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −146.969 84.8528i −1.37355 0.793017i −0.382173 0.924091i \(-0.624824\pi\)
−0.991373 + 0.131074i \(0.958158\pi\)
\(108\) 0 0
\(109\) 32.5000 + 56.2917i 0.298165 + 0.516437i 0.975716 0.219039i \(-0.0702921\pi\)
−0.677551 + 0.735476i \(0.736959\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 137.179i 1.21397i −0.794713 0.606985i \(-0.792379\pi\)
0.794713 0.606985i \(-0.207621\pi\)
\(114\) 0 0
\(115\) 16.0000 + 27.7128i 0.139130 + 0.240981i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 78.3837 11.3137i 0.658686 0.0950732i
\(120\) 0 0
\(121\) −35.5000 + 61.4878i −0.293388 + 0.508164i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 67.8823i 0.543058i
\(126\) 0 0
\(127\) 171.000 1.34646 0.673228 0.739435i \(-0.264907\pi\)
0.673228 + 0.739435i \(0.264907\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 101.654 + 58.6899i 0.775983 + 0.448014i 0.835005 0.550242i \(-0.185465\pi\)
−0.0590215 + 0.998257i \(0.518798\pi\)
\(132\) 0 0
\(133\) 71.5000 56.2917i 0.537594 0.423245i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 186.161 107.480i 1.35884 0.784527i 0.369373 0.929281i \(-0.379572\pi\)
0.989468 + 0.144754i \(0.0462390\pi\)
\(138\) 0 0
\(139\) 83.0000 0.597122 0.298561 0.954391i \(-0.403493\pi\)
0.298561 + 0.954391i \(0.403493\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 91.8559 53.0330i 0.642349 0.370860i
\(144\) 0 0
\(145\) 16.0000 27.7128i 0.110345 0.191123i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −88.1816 50.9117i −0.591823 0.341689i 0.173995 0.984747i \(-0.444332\pi\)
−0.765818 + 0.643057i \(0.777666\pi\)
\(150\) 0 0
\(151\) 20.0000 + 34.6410i 0.132450 + 0.229411i 0.924621 0.380889i \(-0.124382\pi\)
−0.792170 + 0.610300i \(0.791049\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.24264i 0.0273719i
\(156\) 0 0
\(157\) −148.000 256.344i −0.942675 1.63276i −0.760340 0.649525i \(-0.774968\pi\)
−0.182335 0.983237i \(-0.558365\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −97.9796 124.451i −0.608569 0.772986i
\(162\) 0 0
\(163\) 64.0000 110.851i 0.392638 0.680069i −0.600159 0.799881i \(-0.704896\pi\)
0.992797 + 0.119812i \(0.0382292\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 60.8112i 0.364139i 0.983286 + 0.182069i \(0.0582796\pi\)
−0.983286 + 0.182069i \(0.941720\pi\)
\(168\) 0 0
\(169\) 56.0000 0.331361
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −97.9796 56.5685i −0.566356 0.326986i 0.189337 0.981912i \(-0.439366\pi\)
−0.755693 + 0.654926i \(0.772700\pi\)
\(174\) 0 0
\(175\) 23.0000 + 159.349i 0.131429 + 0.910564i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 25.7196 14.8492i 0.143685 0.0829567i −0.426434 0.904519i \(-0.640230\pi\)
0.570119 + 0.821562i \(0.306897\pi\)
\(180\) 0 0
\(181\) 81.0000 0.447514 0.223757 0.974645i \(-0.428168\pi\)
0.223757 + 0.974645i \(0.428168\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −20.8207 + 12.0208i −0.112544 + 0.0649774i
\(186\) 0 0
\(187\) −40.0000 + 69.2820i −0.213904 + 0.370492i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −55.1135 31.8198i −0.288552 0.166596i 0.348736 0.937221i \(-0.386611\pi\)
−0.637289 + 0.770625i \(0.719944\pi\)
\(192\) 0 0
\(193\) 111.500 + 193.124i 0.577720 + 1.00064i 0.995740 + 0.0922029i \(0.0293909\pi\)
−0.418020 + 0.908438i \(0.637276\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 158.392i 0.804020i 0.915635 + 0.402010i \(0.131688\pi\)
−0.915635 + 0.402010i \(0.868312\pi\)
\(198\) 0 0
\(199\) −68.0000 117.779i −0.341709 0.591857i 0.643042 0.765831i \(-0.277672\pi\)
−0.984750 + 0.173975i \(0.944339\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −58.7878 + 147.078i −0.289595 + 0.724523i
\(204\) 0 0
\(205\) 57.0000 98.7269i 0.278049 0.481595i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 91.9239i 0.439827i
\(210\) 0 0
\(211\) −272.000 −1.28910 −0.644550 0.764562i \(-0.722955\pi\)
−0.644550 + 0.764562i \(0.722955\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 104.103 + 60.1041i 0.484201 + 0.279554i
\(216\) 0 0
\(217\) −3.00000 20.7846i −0.0138249 0.0957816i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −146.969 + 84.8528i −0.665020 + 0.383949i
\(222\) 0 0
\(223\) −248.000 −1.11211 −0.556054 0.831146i \(-0.687685\pi\)
−0.556054 + 0.831146i \(0.687685\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −143.295 + 82.7315i −0.631256 + 0.364456i −0.781238 0.624233i \(-0.785412\pi\)
0.149982 + 0.988689i \(0.452078\pi\)
\(228\) 0 0
\(229\) −216.500 + 374.989i −0.945415 + 1.63751i −0.190496 + 0.981688i \(0.561010\pi\)
−0.754918 + 0.655819i \(0.772324\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 197.184 + 113.844i 0.846283 + 0.488602i 0.859395 0.511312i \(-0.170840\pi\)
−0.0131120 + 0.999914i \(0.504174\pi\)
\(234\) 0 0
\(235\) −51.0000 88.3346i −0.217021 0.375892i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 343.654i 1.43788i −0.695071 0.718941i \(-0.744627\pi\)
0.695071 0.718941i \(-0.255373\pi\)
\(240\) 0 0
\(241\) −79.0000 136.832i −0.327801 0.567768i 0.654274 0.756257i \(-0.272974\pi\)
−0.982075 + 0.188490i \(0.939641\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 19.5959 + 66.4680i 0.0799833 + 0.271298i
\(246\) 0 0
\(247\) −97.5000 + 168.875i −0.394737 + 0.683704i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 237.588i 0.946565i 0.880911 + 0.473283i \(0.156931\pi\)
−0.880911 + 0.473283i \(0.843069\pi\)
\(252\) 0 0
\(253\) 160.000 0.632411
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 275.568 + 159.099i 1.07225 + 0.619062i 0.928795 0.370595i \(-0.120846\pi\)
0.143453 + 0.989657i \(0.454179\pi\)
\(258\) 0 0
\(259\) 93.5000 73.6122i 0.361004 0.284217i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 146.969 84.8528i 0.558819 0.322634i −0.193852 0.981031i \(-0.562098\pi\)
0.752671 + 0.658396i \(0.228765\pi\)
\(264\) 0 0
\(265\) 48.0000 0.181132
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −420.087 + 242.538i −1.56166 + 0.901627i −0.564574 + 0.825382i \(0.690960\pi\)
−0.997089 + 0.0762447i \(0.975707\pi\)
\(270\) 0 0
\(271\) 108.000 187.061i 0.398524 0.690264i −0.595020 0.803711i \(-0.702856\pi\)
0.993544 + 0.113447i \(0.0361892\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −140.846 81.3173i −0.512166 0.295699i
\(276\) 0 0
\(277\) −152.500 264.138i −0.550542 0.953566i −0.998236 0.0593790i \(-0.981088\pi\)
0.447694 0.894187i \(-0.352245\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.6274i 0.0805246i 0.999189 + 0.0402623i \(0.0128194\pi\)
−0.999189 + 0.0402623i \(0.987181\pi\)
\(282\) 0 0
\(283\) 78.5000 + 135.966i 0.277385 + 0.480445i 0.970734 0.240157i \(-0.0771989\pi\)
−0.693349 + 0.720602i \(0.743866\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −209.431 + 523.966i −0.729726 + 1.82567i
\(288\) 0 0
\(289\) −80.5000 + 139.430i −0.278547 + 0.482457i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 101.823i 0.347520i 0.984788 + 0.173760i \(0.0555917\pi\)
−0.984788 + 0.173760i \(0.944408\pi\)
\(294\) 0 0
\(295\) 128.000 0.433898
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 293.939 + 169.706i 0.983073 + 0.567577i
\(300\) 0 0
\(301\) −552.500 220.836i −1.83555 0.733676i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 88.1816 50.9117i 0.289120 0.166924i
\(306\) 0 0
\(307\) 11.0000 0.0358306 0.0179153 0.999840i \(-0.494297\pi\)
0.0179153 + 0.999840i \(0.494297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −454.380 + 262.337i −1.46103 + 0.843526i −0.999059 0.0433690i \(-0.986191\pi\)
−0.461971 + 0.886895i \(0.652858\pi\)
\(312\) 0 0
\(313\) −276.500 + 478.912i −0.883387 + 1.53007i −0.0358348 + 0.999358i \(0.511409\pi\)
−0.847552 + 0.530713i \(0.821924\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −117.576 67.8823i −0.370901 0.214140i 0.302951 0.953006i \(-0.402028\pi\)
−0.673852 + 0.738866i \(0.735361\pi\)
\(318\) 0 0
\(319\) −80.0000 138.564i −0.250784 0.434370i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 147.078i 0.455350i
\(324\) 0 0
\(325\) −172.500 298.779i −0.530769 0.919319i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 312.310 + 396.687i 0.949270 + 1.20574i
\(330\) 0 0
\(331\) −30.5000 + 52.8275i −0.0921450 + 0.159600i −0.908413 0.418073i \(-0.862706\pi\)
0.816268 + 0.577673i \(0.196039\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 60.8112i 0.181526i
\(336\) 0 0
\(337\) 135.000 0.400593 0.200297 0.979735i \(-0.435809\pi\)
0.200297 + 0.979735i \(0.435809\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 18.3712 + 10.6066i 0.0538744 + 0.0311044i
\(342\) 0 0
\(343\) −143.000 311.769i −0.416910 0.908948i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −88.1816 + 50.9117i −0.254126 + 0.146720i −0.621652 0.783294i \(-0.713538\pi\)
0.367526 + 0.930013i \(0.380205\pi\)
\(348\) 0 0
\(349\) −152.000 −0.435530 −0.217765 0.976001i \(-0.569877\pi\)
−0.217765 + 0.976001i \(0.569877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 334.355 193.040i 0.947182 0.546856i 0.0549778 0.998488i \(-0.482491\pi\)
0.892205 + 0.451632i \(0.149158\pi\)
\(354\) 0 0
\(355\) 37.0000 64.0859i 0.104225 0.180524i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 39.1918 + 22.6274i 0.109169 + 0.0630290i 0.553591 0.832789i \(-0.313257\pi\)
−0.444421 + 0.895818i \(0.646591\pi\)
\(360\) 0 0
\(361\) 96.0000 + 166.277i 0.265928 + 0.460601i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 134.350i 0.368083i
\(366\) 0 0
\(367\) 50.5000 + 87.4686i 0.137602 + 0.238334i 0.926588 0.376077i \(-0.122727\pi\)
−0.788986 + 0.614411i \(0.789394\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −235.151 + 33.9411i −0.633830 + 0.0914855i
\(372\) 0 0
\(373\) 155.500 269.334i 0.416890 0.722075i −0.578735 0.815516i \(-0.696453\pi\)
0.995625 + 0.0934411i \(0.0297867\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 339.411i 0.900295i
\(378\) 0 0
\(379\) −91.0000 −0.240106 −0.120053 0.992768i \(-0.538306\pi\)
−0.120053 + 0.992768i \(0.538306\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 284.141 + 164.049i 0.741882 + 0.428326i 0.822753 0.568399i \(-0.192437\pi\)
−0.0808712 + 0.996725i \(0.525770\pi\)
\(384\) 0 0
\(385\) −65.0000 25.9808i −0.168831 0.0674825i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −596.451 + 344.361i −1.53329 + 0.885247i −0.534085 + 0.845431i \(0.679344\pi\)
−0.999207 + 0.0398163i \(0.987323\pi\)
\(390\) 0 0
\(391\) −256.000 −0.654731
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 84.5074 48.7904i 0.213943 0.123520i
\(396\) 0 0
\(397\) 139.500 241.621i 0.351385 0.608617i −0.635107 0.772424i \(-0.719044\pi\)
0.986492 + 0.163807i \(0.0523774\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 22.5000 + 38.9711i 0.0558313 + 0.0967026i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 120.208i 0.295352i
\(408\) 0 0
\(409\) 111.500 + 193.124i 0.272616 + 0.472185i 0.969531 0.244969i \(-0.0787778\pi\)
−0.696915 + 0.717154i \(0.745444\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −627.069 + 90.5097i −1.51833 + 0.219152i
\(414\) 0 0
\(415\) 43.0000 74.4782i 0.103614 0.179466i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 581.242i 1.38721i −0.720355 0.693606i \(-0.756021\pi\)
0.720355 0.693606i \(-0.243979\pi\)
\(420\) 0 0
\(421\) 153.000 0.363420 0.181710 0.983352i \(-0.441837\pi\)
0.181710 + 0.983352i \(0.441837\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 225.353 + 130.108i 0.530242 + 0.306136i
\(426\) 0 0
\(427\) −396.000 + 311.769i −0.927400 + 0.730139i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 121.250 70.0036i 0.281322 0.162421i −0.352700 0.935737i \(-0.614736\pi\)
0.634022 + 0.773315i \(0.281403\pi\)
\(432\) 0 0
\(433\) 137.000 0.316397 0.158199 0.987407i \(-0.449431\pi\)
0.158199 + 0.987407i \(0.449431\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −254.747 + 147.078i −0.582945 + 0.336563i
\(438\) 0 0
\(439\) −300.000 + 519.615i −0.683371 + 1.18363i 0.290574 + 0.956852i \(0.406154\pi\)
−0.973946 + 0.226781i \(0.927180\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 548.686 + 316.784i 1.23857 + 0.715088i 0.968801 0.247838i \(-0.0797201\pi\)
0.269767 + 0.962926i \(0.413053\pi\)
\(444\) 0 0
\(445\) 96.0000 + 166.277i 0.215730 + 0.373656i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 383.252i 0.853568i −0.904354 0.426784i \(-0.859647\pi\)
0.904354 0.426784i \(-0.140353\pi\)
\(450\) 0 0
\(451\) −285.000 493.634i −0.631929 1.09453i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −91.8559 116.673i −0.201881 0.256423i
\(456\) 0 0
\(457\) 119.500 206.980i 0.261488 0.452910i −0.705150 0.709059i \(-0.749120\pi\)
0.966638 + 0.256148i \(0.0824535\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 452.548i 0.981667i 0.871253 + 0.490833i \(0.163308\pi\)
−0.871253 + 0.490833i \(0.836692\pi\)
\(462\) 0 0
\(463\) −211.000 −0.455724 −0.227862 0.973693i \(-0.573173\pi\)
−0.227862 + 0.973693i \(0.573173\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 270.669 + 156.271i 0.579590 + 0.334627i 0.760971 0.648786i \(-0.224723\pi\)
−0.181380 + 0.983413i \(0.558056\pi\)
\(468\) 0 0
\(469\) −43.0000 297.913i −0.0916844 0.635208i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 520.517 300.520i 1.10046 0.635350i
\(474\) 0 0
\(475\) 299.000 0.629474
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −607.473 + 350.725i −1.26821 + 0.732202i −0.974649 0.223737i \(-0.928174\pi\)
−0.293562 + 0.955940i \(0.594841\pi\)
\(480\) 0 0
\(481\) −127.500 + 220.836i −0.265073 + 0.459119i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19.5959 + 11.3137i 0.0404040 + 0.0233272i
\(486\) 0 0
\(487\) 209.500 + 362.865i 0.430185 + 0.745102i 0.996889 0.0788195i \(-0.0251151\pi\)
−0.566704 + 0.823921i \(0.691782\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 169.706i 0.345633i 0.984954 + 0.172816i \(0.0552867\pi\)
−0.984954 + 0.172816i \(0.944713\pi\)
\(492\) 0 0
\(493\) 128.000 + 221.703i 0.259635 + 0.449701i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −135.947 + 340.118i −0.273535 + 0.684343i
\(498\) 0 0
\(499\) 93.5000 161.947i 0.187375 0.324543i −0.756999 0.653416i \(-0.773335\pi\)
0.944374 + 0.328873i \(0.106669\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 173.948i 0.345822i 0.984937 + 0.172911i \(0.0553172\pi\)
−0.984937 + 0.172911i \(0.944683\pi\)
\(504\) 0 0
\(505\) −98.0000 −0.194059
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 224.128 + 129.401i 0.440331 + 0.254225i 0.703738 0.710460i \(-0.251513\pi\)
−0.263407 + 0.964685i \(0.584846\pi\)
\(510\) 0 0
\(511\) −95.0000 658.179i −0.185910 1.28802i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −74.7094 + 43.1335i −0.145067 + 0.0837544i
\(516\) 0 0
\(517\) −510.000 −0.986460
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −352.727 + 203.647i −0.677018 + 0.390877i −0.798731 0.601689i \(-0.794495\pi\)
0.121712 + 0.992565i \(0.461161\pi\)
\(522\) 0 0
\(523\) −405.500 + 702.347i −0.775335 + 1.34292i 0.159272 + 0.987235i \(0.449085\pi\)
−0.934606 + 0.355684i \(0.884248\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −29.3939 16.9706i −0.0557759 0.0322022i
\(528\) 0 0
\(529\) −8.50000 14.7224i −0.0160681 0.0278307i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1209.15i 2.26858i
\(534\) 0 0
\(535\) −120.000 207.846i −0.224299 0.388497i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 336.805 + 81.3173i 0.624870 + 0.150867i
\(540\) 0 0
\(541\) 172.500 298.779i 0.318854 0.552271i −0.661395 0.750038i \(-0.730035\pi\)
0.980249 + 0.197766i \(0.0633687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 91.9239i 0.168668i
\(546\) 0 0
\(547\) 864.000 1.57952 0.789762 0.613413i \(-0.210204\pi\)
0.789762 + 0.613413i \(0.210204\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 254.747 + 147.078i 0.462336 + 0.266930i
\(552\) 0 0
\(553\) −379.500 + 298.779i −0.686257 + 0.540287i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 821.804 474.469i 1.47541 0.851829i 0.475795 0.879556i \(-0.342160\pi\)
0.999616 + 0.0277272i \(0.00882699\pi\)
\(558\) 0 0
\(559\) 1275.00 2.28086
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −640.542 + 369.817i −1.13773 + 0.656868i −0.945867 0.324554i \(-0.894786\pi\)
−0.191862 + 0.981422i \(0.561453\pi\)
\(564\) 0 0
\(565\) 97.0000 168.009i 0.171681 0.297361i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −665.036 383.959i −1.16878 0.674796i −0.215388 0.976528i \(-0.569102\pi\)
−0.953393 + 0.301732i \(0.902435\pi\)
\(570\) 0 0
\(571\) 238.500 + 413.094i 0.417688 + 0.723457i 0.995706 0.0925665i \(-0.0295071\pi\)
−0.578018 + 0.816024i \(0.696174\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 520.431i 0.905097i
\(576\) 0 0
\(577\) 131.500 + 227.765i 0.227903 + 0.394739i 0.957186 0.289472i \(-0.0934798\pi\)
−0.729283 + 0.684212i \(0.760146\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −157.992 + 395.273i −0.271931 + 0.680332i
\(582\) 0 0
\(583\) 120.000 207.846i 0.205832 0.356511i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 531.744i 0.905868i −0.891544 0.452934i \(-0.850377\pi\)
0.891544 0.452934i \(-0.149623\pi\)
\(588\) 0 0
\(589\) −39.0000 −0.0662139
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 694.430 + 400.930i 1.17105 + 0.676104i 0.953926 0.300041i \(-0.0970004\pi\)
0.217120 + 0.976145i \(0.430334\pi\)
\(594\) 0 0
\(595\) 104.000 + 41.5692i 0.174790 + 0.0698642i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 676.059 390.323i 1.12865 0.651624i 0.185052 0.982729i \(-0.440755\pi\)
0.943594 + 0.331104i \(0.107421\pi\)
\(600\) 0 0
\(601\) 383.000 0.637271 0.318636 0.947877i \(-0.396775\pi\)
0.318636 + 0.947877i \(0.396775\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −86.9569 + 50.2046i −0.143730 + 0.0829828i
\(606\) 0 0
\(607\) −382.500 + 662.509i −0.630148 + 1.09145i 0.357373 + 0.933962i \(0.383673\pi\)
−0.987521 + 0.157487i \(0.949661\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −936.930 540.937i −1.53344 0.885330i
\(612\) 0 0
\(613\) −204.000 353.338i −0.332790 0.576408i 0.650268 0.759705i \(-0.274657\pi\)
−0.983058 + 0.183296i \(0.941323\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 914.996i 1.48298i −0.670966 0.741488i \(-0.734120\pi\)
0.670966 0.741488i \(-0.265880\pi\)
\(618\) 0 0
\(619\) −473.500 820.126i −0.764943 1.32492i −0.940276 0.340412i \(-0.889434\pi\)
0.175333 0.984509i \(-0.443900\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −587.878 746.705i −0.943624 1.19856i
\(624\) 0 0
\(625\) −239.500 + 414.826i −0.383200 + 0.663722i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 192.333i 0.305776i
\(630\) 0 0
\(631\) 760.000 1.20444 0.602219 0.798331i \(-0.294284\pi\)
0.602219 + 0.798331i \(0.294284\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 209.431 + 120.915i 0.329813 + 0.190418i
\(636\) 0 0
\(637\) 532.500 + 506.625i 0.835950 + 0.795329i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 401.716 231.931i 0.626703 0.361827i −0.152771 0.988262i \(-0.548820\pi\)
0.779474 + 0.626435i \(0.215486\pi\)
\(642\) 0 0
\(643\) 19.0000 0.0295490 0.0147745 0.999891i \(-0.495297\pi\)
0.0147745 + 0.999891i \(0.495297\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1003.07 579.120i 1.55033 0.895086i 0.552220 0.833698i \(-0.313781\pi\)
0.998114 0.0613872i \(-0.0195524\pi\)
\(648\) 0 0
\(649\) 320.000 554.256i 0.493066 0.854016i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −892.839 515.481i −1.36729 0.789404i −0.376707 0.926332i \(-0.622944\pi\)
−0.990581 + 0.136928i \(0.956277\pi\)
\(654\) 0 0
\(655\) 83.0000 + 143.760i 0.126718 + 0.219481i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 972.979i 1.47645i −0.674556 0.738224i \(-0.735665\pi\)
0.674556 0.738224i \(-0.264335\pi\)
\(660\) 0 0
\(661\) 200.500 + 347.276i 0.303328 + 0.525380i 0.976888 0.213753i \(-0.0685688\pi\)
−0.673559 + 0.739133i \(0.735235\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 127.373 18.3848i 0.191539 0.0276463i
\(666\) 0 0
\(667\) 256.000 443.405i 0.383808 0.664775i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 509.117i 0.758743i
\(672\) 0 0
\(673\) 665.000 0.988113 0.494056 0.869430i \(-0.335514\pi\)
0.494056 + 0.869430i \(0.335514\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 793.635 + 458.205i 1.17228 + 0.676817i 0.954216 0.299117i \(-0.0966921\pi\)
0.218065 + 0.975934i \(0.430025\pi\)
\(678\) 0 0
\(679\) −104.000 41.5692i −0.153166 0.0612212i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −117.576 + 67.8823i −0.172146 + 0.0993884i −0.583597 0.812043i \(-0.698355\pi\)
0.411452 + 0.911432i \(0.365022\pi\)
\(684\) 0 0
\(685\) 304.000 0.443796
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 440.908 254.558i 0.639925 0.369461i
\(690\) 0 0
\(691\) 110.500 191.392i 0.159913 0.276978i −0.774924 0.632054i \(-0.782212\pi\)
0.934837 + 0.355077i \(0.115545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 101.654 + 58.6899i 0.146264 + 0.0844458i
\(696\) 0 0
\(697\) 456.000 + 789.815i 0.654232 + 1.13316i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 192.333i 0.274370i −0.990545 0.137185i \(-0.956195\pi\)
0.990545 0.137185i \(-0.0438054\pi\)
\(702\) 0 0
\(703\) −110.500 191.392i −0.157183 0.272250i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 480.100 69.2965i 0.679066 0.0980148i
\(708\) 0 0
\(709\) 164.000 284.056i 0.231312 0.400644i −0.726883 0.686762i \(-0.759032\pi\)
0.958194 + 0.286118i \(0.0923649\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 67.8823i 0.0952065i
\(714\) 0 0
\(715\) 150.000 0.209790
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −878.142 506.996i −1.22134 0.705140i −0.256135 0.966641i \(-0.582449\pi\)
−0.965203 + 0.261501i \(0.915782\pi\)
\(720\) 0 0
\(721\) 335.500 264.138i 0.465326 0.366349i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −450.706 + 260.215i −0.621664 + 0.358918i
\(726\) 0 0
\(727\) −1069.00 −1.47043 −0.735213 0.677836i \(-0.762918\pi\)
−0.735213 + 0.677836i \(0.762918\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −832.827 + 480.833i −1.13930 + 0.657774i
\(732\) 0 0
\(733\) −247.500 + 428.683i −0.337653 + 0.584833i −0.983991 0.178219i \(-0.942967\pi\)
0.646337 + 0.763052i \(0.276300\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 263.320 + 152.028i 0.357286 + 0.206279i
\(738\) 0 0
\(739\) 226.500 + 392.310i 0.306495 + 0.530865i 0.977593 0.210503i \(-0.0675103\pi\)
−0.671098 + 0.741369i \(0.734177\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 538.815i 0.725189i 0.931947 + 0.362594i \(0.118109\pi\)
−0.931947 + 0.362594i \(0.881891\pi\)
\(744\) 0 0
\(745\) −72.0000 124.708i −0.0966443 0.167393i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 734.847 + 933.381i 0.981104 + 1.24617i
\(750\) 0 0
\(751\) −169.500 + 293.583i −0.225699 + 0.390922i −0.956529 0.291637i \(-0.905800\pi\)
0.730830 + 0.682560i \(0.239133\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 56.5685i 0.0749252i
\(756\) 0 0
\(757\) 198.000 0.261559 0.130779 0.991411i \(-0.458252\pi\)
0.130779 + 0.991411i \(0.458252\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −313.535 181.019i −0.412004 0.237870i 0.279647 0.960103i \(-0.409783\pi\)
−0.691650 + 0.722233i \(0.743116\pi\)
\(762\) 0 0
\(763\) −65.0000 450.333i −0.0851900 0.590214i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1175.76 678.823i 1.53293 0.885036i
\(768\) 0 0
\(769\) −929.000 −1.20806 −0.604031 0.796961i \(-0.706440\pi\)
−0.604031 + 0.796961i \(0.706440\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −148.194 + 85.5599i −0.191713 + 0.110686i −0.592784 0.805361i \(-0.701971\pi\)
0.401071 + 0.916047i \(0.368638\pi\)
\(774\) 0 0
\(775\) 34.5000 59.7558i 0.0445161 0.0771042i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 907.536 + 523.966i 1.16500 + 0.672614i
\(780\) 0 0
\(781\) −185.000 320.429i −0.236876 0.410281i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 418.607i 0.533258i
\(786\) 0 0
\(787\) 45.0000 + 77.9423i 0.0571792 + 0.0990372i 0.893198 0.449663i \(-0.148456\pi\)
−0.836019 + 0.548701i \(0.815123\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −356.401 + 891.662i −0.450570 + 1.12726i
\(792\) 0 0
\(793\) 540.000 935.307i 0.680958 1.17945i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1154.00i 1.44793i −0.689838 0.723964i \(-0.742318\pi\)
0.689838 0.723964i \(-0.257682\pi\)
\(798\) 0