Properties

Label 2736.2.dc.a.449.1
Level $2736$
Weight $2$
Character 2736.449
Analytic conductor $21.847$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.dc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 342)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2736.449
Dual form 2736.2.dc.a.1889.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{5} +3.44949 q^{7} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{5} +3.44949 q^{7} -6.29253i q^{11} +(-2.17423 - 1.25529i) q^{13} +(-4.22474 + 2.43916i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(-4.89898 - 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(1.22474 - 2.12132i) q^{29} +9.43879i q^{31} +(-4.22474 + 2.43916i) q^{35} +5.97469i q^{37} +(-2.94949 - 5.10867i) q^{43} +(-4.22474 - 2.43916i) q^{47} +4.89898 q^{49} +(-2.44949 + 4.24264i) q^{53} +(4.44949 + 7.70674i) q^{55} +(4.77526 + 8.27098i) q^{59} +(-0.724745 + 1.25529i) q^{61} +3.55051 q^{65} +(-5.84847 - 3.37662i) q^{67} +(3.00000 + 5.19615i) q^{71} +(5.94949 + 10.3048i) q^{73} -21.7060i q^{77} +(-8.17423 + 4.71940i) q^{79} -8.97809i q^{83} +(3.44949 - 5.97469i) q^{85} +(-6.12372 + 10.6066i) q^{89} +(-7.50000 - 4.33013i) q^{91} +(3.67423 - 4.94975i) q^{95} +(-1.65153 + 0.953512i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{7} + O(q^{10}) \) \( 4q + 4q^{7} + 6q^{13} - 12q^{17} - 16q^{19} - 6q^{25} - 12q^{35} - 2q^{43} - 12q^{47} + 8q^{55} + 24q^{59} + 2q^{61} + 24q^{65} + 6q^{67} + 12q^{71} + 14q^{73} - 18q^{79} + 4q^{85} - 30q^{91} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(1\)

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 −0.547723 + 0.316228i −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 0 0
\(7\) 3.44949 1.30378 0.651892 0.758312i \(-0.273975\pi\)
0.651892 + 0.758312i \(0.273975\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.29253i 1.89727i −0.316374 0.948634i \(-0.602466\pi\)
0.316374 0.948634i \(-0.397534\pi\)
\(12\) 0 0
\(13\) −2.17423 1.25529i −0.603024 0.348156i 0.167206 0.985922i \(-0.446525\pi\)
−0.770230 + 0.637766i \(0.779859\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.22474 + 2.43916i −1.02465 + 0.591583i −0.915448 0.402437i \(-0.868163\pi\)
−0.109203 + 0.994019i \(0.534830\pi\)
\(18\) 0 0
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.89898 2.82843i −1.02151 0.589768i −0.106967 0.994263i \(-0.534114\pi\)
−0.914540 + 0.404495i \(0.867447\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.22474 2.12132i 0.227429 0.393919i −0.729616 0.683857i \(-0.760301\pi\)
0.957046 + 0.289938i \(0.0936346\pi\)
\(30\) 0 0
\(31\) 9.43879i 1.69526i 0.530590 + 0.847629i \(0.321970\pi\)
−0.530590 + 0.847629i \(0.678030\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.22474 + 2.43916i −0.714112 + 0.412293i
\(36\) 0 0
\(37\) 5.97469i 0.982233i 0.871094 + 0.491117i \(0.163411\pi\)
−0.871094 + 0.491117i \(0.836589\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −2.94949 5.10867i −0.449793 0.779064i 0.548579 0.836099i \(-0.315169\pi\)
−0.998372 + 0.0570343i \(0.981836\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.22474 2.43916i −0.616242 0.355788i 0.159162 0.987252i \(-0.449121\pi\)
−0.775405 + 0.631465i \(0.782454\pi\)
\(48\) 0 0
\(49\) 4.89898 0.699854
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44949 + 4.24264i −0.336463 + 0.582772i −0.983765 0.179463i \(-0.942564\pi\)
0.647302 + 0.762234i \(0.275897\pi\)
\(54\) 0 0
\(55\) 4.44949 + 7.70674i 0.599969 + 1.03918i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.77526 + 8.27098i 0.621685 + 1.07679i 0.989172 + 0.146762i \(0.0468850\pi\)
−0.367487 + 0.930029i \(0.619782\pi\)
\(60\) 0 0
\(61\) −0.724745 + 1.25529i −0.0927941 + 0.160724i −0.908686 0.417481i \(-0.862913\pi\)
0.815892 + 0.578205i \(0.196246\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.55051 0.440387
\(66\) 0 0
\(67\) −5.84847 3.37662i −0.714504 0.412519i 0.0982223 0.995164i \(-0.468684\pi\)
−0.812727 + 0.582645i \(0.802018\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 5.94949 + 10.3048i 0.696335 + 1.20609i 0.969729 + 0.244185i \(0.0785206\pi\)
−0.273393 + 0.961902i \(0.588146\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21.7060i 2.47363i
\(78\) 0 0
\(79\) −8.17423 + 4.71940i −0.919673 + 0.530974i −0.883531 0.468373i \(-0.844840\pi\)
−0.0361424 + 0.999347i \(0.511507\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.97809i 0.985474i −0.870178 0.492737i \(-0.835997\pi\)
0.870178 0.492737i \(-0.164003\pi\)
\(84\) 0 0
\(85\) 3.44949 5.97469i 0.374150 0.648046i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.12372 + 10.6066i −0.649113 + 1.12430i 0.334221 + 0.942495i \(0.391527\pi\)
−0.983335 + 0.181803i \(0.941807\pi\)
\(90\) 0 0
\(91\) −7.50000 4.33013i −0.786214 0.453921i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.67423 4.94975i 0.376969 0.507833i
\(96\) 0 0
\(97\) −1.65153 + 0.953512i −0.167688 + 0.0968144i −0.581495 0.813550i \(-0.697532\pi\)
0.413807 + 0.910364i \(0.364199\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.55051 + 3.78194i 0.651800 + 0.376317i 0.789146 0.614206i \(-0.210524\pi\)
−0.137345 + 0.990523i \(0.543857\pi\)
\(102\) 0 0
\(103\) 10.9959i 1.08346i −0.840554 0.541728i \(-0.817770\pi\)
0.840554 0.541728i \(-0.182230\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.79796 −0.367163 −0.183581 0.983005i \(-0.558769\pi\)
−0.183581 + 0.983005i \(0.558769\pi\)
\(108\) 0 0
\(109\) 14.6969 8.48528i 1.40771 0.812743i 0.412544 0.910938i \(-0.364640\pi\)
0.995167 + 0.0981950i \(0.0313069\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −17.1464 −1.61300 −0.806500 0.591234i \(-0.798641\pi\)
−0.806500 + 0.591234i \(0.798641\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −14.5732 + 8.41385i −1.33592 + 0.771296i
\(120\) 0 0
\(121\) −28.5959 −2.59963
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) 7.34847 + 4.24264i 0.652071 + 0.376473i 0.789249 0.614073i \(-0.210470\pi\)
−0.137178 + 0.990546i \(0.543803\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.79796 + 3.92480i −0.593940 + 0.342912i −0.766654 0.642060i \(-0.778080\pi\)
0.172714 + 0.984972i \(0.444746\pi\)
\(132\) 0 0
\(133\) −13.7980 + 5.97469i −1.19643 + 0.518071i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.550510 + 0.317837i 0.0470333 + 0.0271547i 0.523332 0.852129i \(-0.324689\pi\)
−0.476299 + 0.879283i \(0.658022\pi\)
\(138\) 0 0
\(139\) −3.50000 + 6.06218i −0.296866 + 0.514187i −0.975417 0.220366i \(-0.929275\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.89898 + 13.6814i −0.660546 + 1.14410i
\(144\) 0 0
\(145\) 3.46410i 0.287678i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.5505 + 7.24604i −1.02818 + 0.593619i −0.916462 0.400121i \(-0.868968\pi\)
−0.111716 + 0.993740i \(0.535635\pi\)
\(150\) 0 0
\(151\) 15.4135i 1.25433i −0.778886 0.627166i \(-0.784215\pi\)
0.778886 0.627166i \(-0.215785\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.67423 11.5601i −0.536087 0.928531i
\(156\) 0 0
\(157\) 1.17423 + 2.03383i 0.0937141 + 0.162318i 0.909071 0.416641i \(-0.136793\pi\)
−0.815357 + 0.578958i \(0.803459\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −16.8990 9.75663i −1.33183 0.768930i
\(162\) 0 0
\(163\) 21.6969 1.69944 0.849718 0.527238i \(-0.176772\pi\)
0.849718 + 0.527238i \(0.176772\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.77526 3.07483i 0.137373 0.237938i −0.789128 0.614228i \(-0.789467\pi\)
0.926502 + 0.376291i \(0.122801\pi\)
\(168\) 0 0
\(169\) −3.34847 5.79972i −0.257575 0.446132i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.12372 10.6066i −0.465578 0.806405i 0.533649 0.845706i \(-0.320820\pi\)
−0.999227 + 0.0393009i \(0.987487\pi\)
\(174\) 0 0
\(175\) −5.17423 + 8.96204i −0.391135 + 0.677466i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −19.3485 11.1708i −1.43816 0.830322i −0.440438 0.897783i \(-0.645177\pi\)
−0.997722 + 0.0674605i \(0.978510\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.22474 7.31747i −0.310609 0.537991i
\(186\) 0 0
\(187\) 15.3485 + 26.5843i 1.12239 + 1.94404i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.4422i 0.900285i −0.892957 0.450143i \(-0.851373\pi\)
0.892957 0.450143i \(-0.148627\pi\)
\(192\) 0 0
\(193\) 0.151531 0.0874863i 0.0109074 0.00629740i −0.494536 0.869157i \(-0.664662\pi\)
0.505444 + 0.862860i \(0.331329\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.492810i 0.0351113i 0.999846 + 0.0175556i \(0.00558842\pi\)
−0.999846 + 0.0175556i \(0.994412\pi\)
\(198\) 0 0
\(199\) −3.62372 + 6.27647i −0.256879 + 0.444927i −0.965404 0.260758i \(-0.916028\pi\)
0.708525 + 0.705686i \(0.249361\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.22474 7.31747i 0.296519 0.513586i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.8990 + 25.1701i 0.753898 + 1.74105i
\(210\) 0 0
\(211\) −17.8485 + 10.3048i −1.22874 + 0.709413i −0.966766 0.255662i \(-0.917707\pi\)
−0.261973 + 0.965075i \(0.584373\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.22474 + 4.17121i 0.492724 + 0.284474i
\(216\) 0 0
\(217\) 32.5590i 2.21025i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.2474 0.823853
\(222\) 0 0
\(223\) −5.17423 + 2.98735i −0.346492 + 0.200047i −0.663139 0.748496i \(-0.730776\pi\)
0.316647 + 0.948543i \(0.397443\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.1464 0.739814 0.369907 0.929069i \(-0.379389\pi\)
0.369907 + 0.929069i \(0.379389\pi\)
\(228\) 0 0
\(229\) 5.24745 0.346761 0.173381 0.984855i \(-0.444531\pi\)
0.173381 + 0.984855i \(0.444531\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.24745 + 5.33902i −0.605821 + 0.349771i −0.771328 0.636438i \(-0.780407\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(234\) 0 0
\(235\) 6.89898 0.450040
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.62815i 0.558108i −0.960275 0.279054i \(-0.909979\pi\)
0.960275 0.279054i \(-0.0900209\pi\)
\(240\) 0 0
\(241\) 26.8485 + 15.5010i 1.72946 + 0.998505i 0.892058 + 0.451920i \(0.149261\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 + 3.46410i −0.383326 + 0.221313i
\(246\) 0 0
\(247\) 10.8712 + 1.25529i 0.691716 + 0.0798725i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.22474 0.707107i −0.0773052 0.0446322i 0.460849 0.887478i \(-0.347545\pi\)
−0.538154 + 0.842846i \(0.680878\pi\)
\(252\) 0 0
\(253\) −17.7980 + 30.8270i −1.11895 + 1.93807i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 10.3923i 0.374270 0.648254i −0.615948 0.787787i \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) 0 0
\(259\) 20.6096i 1.28062i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.7980 + 10.8530i −1.15913 + 0.669225i −0.951096 0.308896i \(-0.900040\pi\)
−0.208036 + 0.978121i \(0.566707\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.77526 13.4671i −0.474066 0.821106i 0.525493 0.850798i \(-0.323881\pi\)
−0.999559 + 0.0296918i \(0.990547\pi\)
\(270\) 0 0
\(271\) −13.6969 23.7238i −0.832030 1.44112i −0.896426 0.443193i \(-0.853845\pi\)
0.0643963 0.997924i \(-0.479488\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.3485 + 9.43879i 0.985850 + 0.569181i
\(276\) 0 0
\(277\) 18.8990 1.13553 0.567765 0.823191i \(-0.307808\pi\)
0.567765 + 0.823191i \(0.307808\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.57321 + 9.65309i −0.332470 + 0.575855i −0.982996 0.183629i \(-0.941215\pi\)
0.650525 + 0.759484i \(0.274549\pi\)
\(282\) 0 0
\(283\) −2.55051 4.41761i −0.151612 0.262600i 0.780208 0.625520i \(-0.215113\pi\)
−0.931820 + 0.362920i \(0.881780\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.39898 5.88721i 0.199940 0.346306i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 25.3485 1.48087 0.740437 0.672126i \(-0.234619\pi\)
0.740437 + 0.672126i \(0.234619\pi\)
\(294\) 0 0
\(295\) −11.6969 6.75323i −0.681022 0.393188i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.10102 + 12.2993i 0.410663 + 0.711289i
\(300\) 0 0
\(301\) −10.1742 17.6223i −0.586433 1.01573i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.04989i 0.117376i
\(306\) 0 0
\(307\) −1.34847 + 0.778539i −0.0769612 + 0.0444336i −0.537987 0.842953i \(-0.680815\pi\)
0.461026 + 0.887387i \(0.347482\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 25.9487i 1.47141i −0.677300 0.735707i \(-0.736850\pi\)
0.677300 0.735707i \(-0.263150\pi\)
\(312\) 0 0
\(313\) 3.34847 5.79972i 0.189267 0.327819i −0.755739 0.654873i \(-0.772722\pi\)
0.945006 + 0.327053i \(0.106056\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.67423 6.36396i 0.206366 0.357436i −0.744201 0.667955i \(-0.767170\pi\)
0.950567 + 0.310520i \(0.100503\pi\)
\(318\) 0 0
\(319\) −13.3485 7.70674i −0.747371 0.431495i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.6742 17.0741i 0.705213 0.950029i
\(324\) 0 0
\(325\) 6.52270 3.76588i 0.361815 0.208894i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.5732 8.41385i −0.803447 0.463871i
\(330\) 0 0
\(331\) 15.2385i 0.837584i −0.908082 0.418792i \(-0.862454\pi\)
0.908082 0.418792i \(-0.137546\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.55051 0.521800
\(336\) 0 0
\(337\) 31.1969 18.0116i 1.69941 0.981152i 0.753085 0.657924i \(-0.228565\pi\)
0.946321 0.323229i \(-0.104768\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 59.3939 3.21636
\(342\) 0 0
\(343\) −7.24745 −0.391325
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −25.7753 + 14.8814i −1.38369 + 0.798873i −0.992594 0.121478i \(-0.961237\pi\)
−0.391094 + 0.920351i \(0.627903\pi\)
\(348\) 0 0
\(349\) −1.24745 −0.0667744 −0.0333872 0.999442i \(-0.510629\pi\)
−0.0333872 + 0.999442i \(0.510629\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.4634i 0.929482i 0.885447 + 0.464741i \(0.153852\pi\)
−0.885447 + 0.464741i \(0.846148\pi\)
\(354\) 0 0
\(355\) −7.34847 4.24264i −0.390016 0.225176i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.79796 + 5.65685i −0.517116 + 0.298557i −0.735754 0.677249i \(-0.763172\pi\)
0.218638 + 0.975806i \(0.429839\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −14.5732 8.41385i −0.762797 0.440401i
\(366\) 0 0
\(367\) 0.174235 0.301783i 0.00909497 0.0157530i −0.861442 0.507856i \(-0.830438\pi\)
0.870537 + 0.492103i \(0.163772\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.44949 + 14.6349i −0.438676 + 0.759809i
\(372\) 0 0
\(373\) 29.2699i 1.51554i −0.652523 0.757769i \(-0.726290\pi\)
0.652523 0.757769i \(-0.273710\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.32577 + 3.07483i −0.274291 + 0.158362i
\(378\) 0 0
\(379\) 19.0526i 0.978664i −0.872098 0.489332i \(-0.837241\pi\)
0.872098 0.489332i \(-0.162759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.550510 0.953512i −0.0281298 0.0487222i 0.851618 0.524163i \(-0.175622\pi\)
−0.879748 + 0.475441i \(0.842288\pi\)
\(384\) 0 0
\(385\) 15.3485 + 26.5843i 0.782230 + 1.35486i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −13.1010 7.56388i −0.664248 0.383504i 0.129646 0.991560i \(-0.458616\pi\)
−0.793894 + 0.608057i \(0.791949\pi\)
\(390\) 0 0
\(391\) 27.5959 1.39559
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.67423 11.5601i 0.335817 0.581652i
\(396\) 0 0
\(397\) −18.1742 31.4787i −0.912139 1.57987i −0.811037 0.584994i \(-0.801097\pi\)
−0.101101 0.994876i \(-0.532237\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1237 + 20.9989i 0.605430 + 1.04864i 0.991983 + 0.126368i \(0.0403321\pi\)
−0.386553 + 0.922267i \(0.626335\pi\)
\(402\) 0 0
\(403\) 11.8485 20.5222i 0.590214 1.02228i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 37.5959 1.86356
\(408\) 0 0
\(409\) 19.0454 + 10.9959i 0.941735 + 0.543711i 0.890504 0.454976i \(-0.150352\pi\)
0.0512311 + 0.998687i \(0.483685\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.4722 + 28.5307i 0.810544 + 1.40390i
\(414\) 0 0
\(415\) 6.34847 + 10.9959i 0.311634 + 0.539766i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.5344i 1.19859i 0.800530 + 0.599293i \(0.204552\pi\)
−0.800530 + 0.599293i \(0.795448\pi\)
\(420\) 0 0
\(421\) −13.3485 + 7.70674i −0.650565 + 0.375604i −0.788672 0.614814i \(-0.789231\pi\)
0.138108 + 0.990417i \(0.455898\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 14.6349i 0.709899i
\(426\) 0 0
\(427\) −2.50000 + 4.33013i −0.120983 + 0.209550i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14.0227 24.2880i 0.675450 1.16991i −0.300887 0.953660i \(-0.597283\pi\)
0.976337 0.216254i \(-0.0693839\pi\)
\(432\) 0 0
\(433\) −4.19694 2.42310i −0.201692 0.116447i 0.395752 0.918357i \(-0.370484\pi\)
−0.597444 + 0.801910i \(0.703817\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 24.4949 + 2.82843i 1.17175 + 0.135302i
\(438\) 0 0
\(439\) −9.52270 + 5.49794i −0.454494 + 0.262402i −0.709726 0.704478i \(-0.751181\pi\)
0.255232 + 0.966880i \(0.417848\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −28.2247 16.2956i −1.34100 0.774226i −0.354044 0.935229i \(-0.615194\pi\)
−0.986954 + 0.161003i \(0.948527\pi\)
\(444\) 0 0
\(445\) 17.3205i 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.24745 −0.294835 −0.147418 0.989074i \(-0.547096\pi\)
−0.147418 + 0.989074i \(0.547096\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 12.2474 0.574169
\(456\) 0 0
\(457\) −9.69694 −0.453604 −0.226802 0.973941i \(-0.572827\pi\)
−0.226802 + 0.973941i \(0.572827\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.12372 1.80348i 0.145486 0.0839966i −0.425490 0.904963i \(-0.639898\pi\)
0.570976 + 0.820967i \(0.306565\pi\)
\(462\) 0 0
\(463\) −5.85357 −0.272039 −0.136019 0.990706i \(-0.543431\pi\)
−0.136019 + 0.990706i \(0.543431\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.21393i 0.333821i 0.985972 + 0.166910i \(0.0533791\pi\)
−0.985972 + 0.166910i \(0.946621\pi\)
\(468\) 0 0
\(469\) −20.1742 11.6476i −0.931560 0.537836i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −32.1464 + 18.5597i −1.47809 + 0.853378i
\(474\) 0 0
\(475\) 1.50000 12.9904i 0.0688247 0.596040i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.1464 + 15.0956i 1.19466 + 0.689738i 0.959360 0.282185i \(-0.0910592\pi\)
0.235301 + 0.971923i \(0.424392\pi\)
\(480\) 0 0
\(481\) 7.50000 12.9904i 0.341971 0.592310i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.34847 2.33562i 0.0612308 0.106055i
\(486\) 0 0
\(487\) 22.6916i 1.02826i −0.857713 0.514128i \(-0.828116\pi\)
0.857713 0.514128i \(-0.171884\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.14643 + 4.70334i −0.367643 + 0.212259i −0.672428 0.740162i \(-0.734749\pi\)
0.304785 + 0.952421i \(0.401415\pi\)
\(492\) 0 0
\(493\) 11.9494i 0.538173i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.3485 + 17.9241i 0.464192 + 0.804005i
\(498\) 0 0
\(499\) 2.74745 + 4.75872i 0.122993 + 0.213030i 0.920947 0.389689i \(-0.127417\pi\)
−0.797954 + 0.602719i \(0.794084\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 35.5176 + 20.5061i 1.58365 + 0.914322i 0.994320 + 0.106430i \(0.0339421\pi\)
0.589331 + 0.807891i \(0.299391\pi\)
\(504\) 0 0
\(505\) −10.6969 −0.476008
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.674235 + 1.16781i −0.0298849 + 0.0517622i −0.880581 0.473896i \(-0.842847\pi\)
0.850696 + 0.525658i \(0.176181\pi\)
\(510\) 0 0
\(511\) 20.5227 + 35.5464i 0.907871 + 1.57248i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.77526 + 13.4671i 0.342619 + 0.593433i
\(516\) 0 0
\(517\) −15.3485 + 26.5843i −0.675025 + 1.16918i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 27.7980 1.21785 0.608925 0.793228i \(-0.291601\pi\)
0.608925 + 0.793228i \(0.291601\pi\)
\(522\) 0 0
\(523\) −13.5000 7.79423i −0.590314 0.340818i 0.174908 0.984585i \(-0.444037\pi\)
−0.765222 + 0.643767i \(0.777371\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.0227 39.8765i −1.00288 1.73705i
\(528\) 0 0
\(529\) 4.50000 + 7.79423i 0.195652 + 0.338880i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.65153 2.68556i 0.201103 0.116107i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 30.8270i 1.32781i
\(540\) 0 0
\(541\) −7.82577 + 13.5546i −0.336456 + 0.582759i −0.983763 0.179470i \(-0.942562\pi\)
0.647307 + 0.762229i \(0.275895\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.0000 + 20.7846i −0.514024 + 0.890315i
\(546\) 0 0
\(547\) 31.1969 + 18.0116i 1.33388 + 0.770119i 0.985893 0.167379i \(-0.0535303\pi\)
0.347992 + 0.937497i \(0.386864\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.22474 + 10.6066i −0.0521759 + 0.451856i
\(552\) 0 0
\(553\) −28.1969 + 16.2795i −1.19906 + 0.692275i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.5959 + 9.58166i 0.703192 + 0.405988i 0.808535 0.588448i \(-0.200261\pi\)
−0.105343 + 0.994436i \(0.533594\pi\)
\(558\) 0 0
\(559\) 14.8099i 0.626393i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.5959 0.573000 0.286500 0.958080i \(-0.407508\pi\)
0.286500 + 0.958080i \(0.407508\pi\)
\(564\) 0 0
\(565\) 21.0000 12.1244i 0.883477 0.510075i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −40.8990 −1.71457 −0.857287 0.514838i \(-0.827852\pi\)
−0.857287 + 0.514838i \(0.827852\pi\)
\(570\) 0 0
\(571\) −25.6969 −1.07538 −0.537692 0.843142i \(-0.680704\pi\)
−0.537692 + 0.843142i \(0.680704\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.6969 8.48528i 0.612905 0.353861i
\(576\) 0 0
\(577\) −13.7980 −0.574417 −0.287208 0.957868i \(-0.592727\pi\)
−0.287208 + 0.957868i \(0.592727\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 30.9698i 1.28485i
\(582\) 0 0
\(583\) 26.6969 + 15.4135i 1.10567 + 0.638361i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.8763 6.85677i 0.490186 0.283009i −0.234465 0.972124i \(-0.575334\pi\)
0.724652 + 0.689115i \(0.242001\pi\)
\(588\) 0 0
\(589\) −16.3485 37.7552i −0.673627 1.55567i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −13.4722 7.77817i −0.553237 0.319411i 0.197190 0.980365i \(-0.436818\pi\)
−0.750426 + 0.660954i \(0.770152\pi\)
\(594\) 0 0
\(595\) 11.8990 20.6096i 0.487811 0.844913i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −0.797959 + 1.38211i −0.0326037 + 0.0564713i −0.881867 0.471499i \(-0.843713\pi\)
0.849263 + 0.527970i \(0.177047\pi\)
\(600\) 0 0
\(601\) 6.75323i 0.275470i 0.990469 + 0.137735i \(0.0439822\pi\)
−0.990469 + 0.137735i \(0.956018\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 35.0227 20.2204i 1.42388 0.822075i
\(606\) 0 0
\(607\) 40.2658i 1.63434i −0.576399 0.817168i \(-0.695543\pi\)
0.576399 0.817168i \(-0.304457\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.12372 + 10.6066i 0.247739 + 0.429097i
\(612\) 0 0
\(613\) −4.55051 7.88171i −0.183793 0.318339i 0.759376 0.650652i \(-0.225504\pi\)
−0.943169 + 0.332313i \(0.892171\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.8990 + 21.8810i 1.52576 + 0.880895i 0.999533 + 0.0305482i \(0.00972531\pi\)
0.526222 + 0.850347i \(0.323608\pi\)
\(618\) 0 0
\(619\) −22.3939 −0.900086 −0.450043 0.893007i \(-0.648591\pi\)
−0.450043 + 0.893007i \(0.648591\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21.1237 + 36.5874i −0.846304 + 1.46584i
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14.5732 25.2415i −0.581072 1.00645i
\(630\) 0 0
\(631\) 9.72474 16.8438i 0.387136 0.670539i −0.604927 0.796281i \(-0.706798\pi\)
0.992063 + 0.125742i \(0.0401311\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12.0000 −0.476205
\(636\) 0 0
\(637\) −10.6515 6.14966i −0.422029 0.243659i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.977296 1.69273i −0.0386009 0.0668587i 0.846080 0.533057i \(-0.178957\pi\)
−0.884680 + 0.466198i \(0.845623\pi\)
\(642\) 0 0
\(643\) 1.70204 + 2.94802i 0.0671219 + 0.116259i 0.897633 0.440743i \(-0.145285\pi\)
−0.830511 + 0.557002i \(0.811952\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.8277i 0.661565i 0.943707 + 0.330783i \(0.107313\pi\)
−0.943707 + 0.330783i \(0.892687\pi\)
\(648\) 0 0
\(649\) 52.0454 30.0484i 2.04296 1.17950i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.1066i 0.395501i 0.980252 + 0.197750i \(0.0633636\pi\)
−0.980252 + 0.197750i \(0.936636\pi\)
\(654\) 0 0
\(655\) 5.55051 9.61377i 0.216876 0.375641i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23.6969 + 41.0443i −0.923102 + 1.59886i −0.128516 + 0.991707i \(0.541021\pi\)
−0.794586 + 0.607151i \(0.792312\pi\)
\(660\) 0 0
\(661\) 5.69694 + 3.28913i 0.221585 + 0.127932i 0.606684 0.794943i \(-0.292499\pi\)
−0.385099 + 0.922875i \(0.625833\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 12.6742 17.0741i 0.491486 0.662105i
\(666\) 0 0
\(667\) −12.0000 + 6.92820i −0.464642 + 0.268261i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.89898 + 4.56048i 0.304937 + 0.176055i
\(672\) 0 0
\(673\) 19.0526i 0.734422i 0.930138 + 0.367211i \(0.119687\pi\)
−0.930138 + 0.367211i \(0.880313\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −22.6515 −0.870569 −0.435285 0.900293i \(-0.643352\pi\)
−0.435285 + 0.900293i \(0.643352\pi\)
\(678\) 0 0
\(679\) −5.69694 + 3.28913i −0.218628 + 0.126225i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.0454 0.613960 0.306980 0.951716i \(-0.400681\pi\)
0.306980 + 0.951716i \(0.400681\pi\)
\(684\) 0 0
\(685\) −0.898979 −0.0343482
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 10.6515 6.14966i 0.405791 0.234284i
\(690\) 0 0
\(691\) −28.6969 −1.09168 −0.545841 0.837888i \(-0.683790\pi\)
−0.545841 + 0.837888i \(0.683790\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.89949i 0.375509i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.4722 7.77817i 0.508838 0.293778i −0.223518 0.974700i \(-0.571754\pi\)
0.732356 + 0.680922i \(0.238421\pi\)
\(702\) 0 0
\(703\) −10.3485 23.8988i −0.390300 0.901359i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 22.5959 + 13.0458i 0.849807 + 0.490636i
\(708\) 0 0
\(709\) 4.17423 7.22999i 0.156767 0.271528i −0.776934 0.629582i \(-0.783226\pi\)
0.933701 + 0.358054i \(0.116560\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 26.6969 46.2405i 0.999808 1.73172i
\(714\) 0 0
\(715\) 22.3417i 0.835532i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.1464 + 9.89949i −0.639454 + 0.369189i −0.784404 0.620250i \(-0.787031\pi\)
0.144950 + 0.989439i \(0.453698\pi\)
\(720\) 0 0
\(721\) 37.9301i 1.41259i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.67423 + 6.36396i 0.136458 + 0.236352i
\(726\) 0 0
\(727\) 12.1742 + 21.0864i 0.451517 + 0.782051i 0.998481 0.0551057i \(-0.0175496\pi\)
−0.546963 + 0.837157i \(0.684216\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 24.9217 + 14.3885i 0.921762 + 0.532179i
\(732\) 0 0
\(733\) −1.30306 −0.0481297 −0.0240648 0.999710i \(-0.507661\pi\)
−0.0240648 + 0.999710i \(0.507661\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.2474 + 36.8017i −0.782660 + 1.35561i
\(738\) 0 0
\(739\) −6.19694 10.7334i −0.227958 0.394835i 0.729245 0.684253i \(-0.239872\pi\)
−0.957203 + 0.289418i \(0.906538\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.69694 + 9.86739i 0.209000 + 0.361999i 0.951400 0.307958i \(-0.0996457\pi\)
−0.742400 + 0.669957i \(0.766312\pi\)
\(744\) 0 0
\(745\) 10.2474 17.7491i 0.375437 0.650277i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13.1010 −0.478701
\(750\) 0 0
\(751\) 27.2196 + 15.7153i 0.993259 + 0.573458i 0.906247 0.422749i \(-0.138935\pi\)
0.0870120 + 0.996207i \(0.472268\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10.8990 + 18.8776i 0.396654 + 0.687026i
\(756\) 0 0
\(757\) −4.82577 8.35847i −0.175395 0.303794i 0.764903 0.644146i \(-0.222787\pi\)
−0.940298 + 0.340352i \(0.889454\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.25702i 0.118067i 0.998256 + 0.0590335i \(0.0188019\pi\)
−0.998256 + 0.0590335i \(0.981198\pi\)
\(762\) 0 0
\(763\) 50.6969 29.2699i 1.83535 1.05964i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 23.9774i 0.865774i
\(768\) 0 0
\(769\) −18.2980 + 31.6930i −0.659841 + 1.14288i 0.320815 + 0.947142i \(0.396043\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.4722 38.9230i 0.808269 1.39996i −0.105793 0.994388i \(-0.533738\pi\)
0.914062 0.405574i \(-0.132928\pi\)
\(774\) 0 0
\(775\) −24.5227 14.1582i −0.880882 0.508577i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 32.6969 18.8776i 1.16999 0.675493i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.87628 1.66062i −0.102659 0.0592700i
\(786\) 0 0
\(787\) 7.10318i 0.253201i −0.991954 0.126600i \(-0.959593\pi\)
0.991954 0.126600i \(-0.0404066\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −59.1464 −2.10300
\(792\) 0 0
\(793\) 3.15153 1.81954i 0.111914 0.0646137i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 50.0908 1.77431 0.887154 0.461474i \(-0.152679\pi\)
0.887154 + 0.461474i \(0.152679\pi\)
\(798\) 0 0
\(799\) 23.7980 0.841911
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 64.8434 37.4373i 2.28827 1.32113i