Properties

Label 2736.2.dc.b.1889.1
Level $2736$
Weight $2$
Character 2736.1889
Analytic conductor $21.847$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 1889.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1889
Dual form 2736.2.dc.b.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{5} -1.44949 q^{7} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{5} -1.44949 q^{7} -0.635674i q^{11} +(5.17423 - 2.98735i) q^{13} +(1.77526 + 1.02494i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-4.89898 + 2.82843i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(1.22474 + 2.12132i) q^{29} -0.953512i q^{31} +(1.77526 + 1.02494i) q^{35} +2.51059i q^{37} +(1.94949 - 3.37662i) q^{43} +(1.77526 - 1.02494i) q^{47} -4.89898 q^{49} +(-2.44949 - 4.24264i) q^{53} +(-0.449490 + 0.778539i) q^{55} +(-7.22474 + 12.5136i) q^{59} +(1.72474 + 2.98735i) q^{61} -8.44949 q^{65} +(8.84847 - 5.10867i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(1.05051 - 1.81954i) q^{73} +0.921404i q^{77} +(-0.825765 - 0.476756i) q^{79} -11.8065i q^{83} +(-1.44949 - 2.51059i) q^{85} +(-6.12372 - 10.6066i) q^{89} +(-7.50000 + 4.33013i) q^{91} +(3.67423 + 4.94975i) q^{95} +(-16.3485 - 9.43879i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{7} + O(q^{10}) \) \( 4q + 4q^{7} + 6q^{13} + 12q^{17} - 16q^{19} - 6q^{25} + 12q^{35} - 2q^{43} + 12q^{47} + 8q^{55} - 24q^{59} + 2q^{61} - 24q^{65} + 6q^{67} - 12q^{71} + 14q^{73} - 18q^{79} + 4q^{85} - 30q^{91} - 36q^{97} + O(q^{100}) \)

Character values

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

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

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 0.200480 0.979698i \(-0.435750\pi\)
−0.748203 + 0.663470i \(0.769083\pi\)
\(6\) 0 0
\(7\) −1.44949 −0.547856 −0.273928 0.961750i \(-0.588323\pi\)
−0.273928 + 0.961750i \(0.588323\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.635674i 0.191663i −0.995398 0.0958315i \(-0.969449\pi\)
0.995398 0.0958315i \(-0.0305510\pi\)
\(12\) 0 0
\(13\) 5.17423 2.98735i 1.43507 0.828541i 0.437573 0.899183i \(-0.355838\pi\)
0.997502 + 0.0706424i \(0.0225049\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.77526 + 1.02494i 0.430563 + 0.248585i 0.699586 0.714548i \(-0.253368\pi\)
−0.269024 + 0.963134i \(0.586701\pi\)
\(18\) 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 −0.914540 0.404495i \(-0.867447\pi\)
−0.106967 + 0.994263i \(0.534114\pi\)
\(24\) 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 0.957046 0.289938i \(-0.0936346\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(30\) 0 0
\(31\) 0.953512i 0.171256i −0.996327 0.0856279i \(-0.972710\pi\)
0.996327 0.0856279i \(-0.0272896\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.77526 + 1.02494i 0.300073 + 0.173247i
\(36\) 0 0
\(37\) 2.51059i 0.412738i 0.978474 + 0.206369i \(0.0661648\pi\)
−0.978474 + 0.206369i \(0.933835\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) 1.94949 3.37662i 0.297294 0.514929i −0.678222 0.734857i \(-0.737249\pi\)
0.975516 + 0.219928i \(0.0705824\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.77526 1.02494i 0.258948 0.149503i −0.364907 0.931044i \(-0.618899\pi\)
0.623854 + 0.781541i \(0.285566\pi\)
\(48\) 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 0.647302 0.762234i \(-0.275897\pi\)
−0.983765 + 0.179463i \(0.942564\pi\)
\(54\) 0 0
\(55\) −0.449490 + 0.778539i −0.0606092 + 0.104978i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.22474 + 12.5136i −0.940582 + 1.62914i −0.176217 + 0.984351i \(0.556386\pi\)
−0.764365 + 0.644784i \(0.776947\pi\)
\(60\) 0 0
\(61\) 1.72474 + 2.98735i 0.220831 + 0.382490i 0.955061 0.296411i \(-0.0957898\pi\)
−0.734230 + 0.678901i \(0.762456\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.44949 −1.04803
\(66\) 0 0
\(67\) 8.84847 5.10867i 1.08101 0.624123i 0.149843 0.988710i \(-0.452123\pi\)
0.931169 + 0.364587i \(0.118790\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0 0
\(73\) 1.05051 1.81954i 0.122953 0.212961i −0.797978 0.602687i \(-0.794097\pi\)
0.920931 + 0.389726i \(0.127430\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.921404i 0.105004i
\(78\) 0 0
\(79\) −0.825765 0.476756i −0.0929059 0.0536392i 0.452827 0.891598i \(-0.350415\pi\)
−0.545733 + 0.837959i \(0.683749\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.8065i 1.29593i −0.761669 0.647967i \(-0.775620\pi\)
0.761669 0.647967i \(-0.224380\pi\)
\(84\) 0 0
\(85\) −1.44949 2.51059i −0.157219 0.272312i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.12372 10.6066i −0.649113 1.12430i −0.983335 0.181803i \(-0.941807\pi\)
0.334221 0.942495i \(-0.391527\pi\)
\(90\) 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
\(97\) −16.3485 9.43879i −1.65994 0.958364i −0.972742 0.231890i \(-0.925509\pi\)
−0.687193 0.726474i \(-0.741158\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −11.4495 + 6.61037i −1.13927 + 0.657756i −0.946249 0.323439i \(-0.895161\pi\)
−0.193018 + 0.981195i \(0.561828\pi\)
\(102\) 0 0
\(103\) 14.4600i 1.42478i −0.701782 0.712392i \(-0.747612\pi\)
0.701782 0.712392i \(-0.252388\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.7980 −1.52725 −0.763623 0.645662i \(-0.776581\pi\)
−0.763623 + 0.645662i \(0.776581\pi\)
\(108\) 0 0
\(109\) −14.6969 8.48528i −1.40771 0.812743i −0.412544 0.910938i \(-0.635360\pi\)
−0.995167 + 0.0981950i \(0.968693\pi\)
\(110\) 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
\(119\) −2.57321 1.48565i −0.235886 0.136189i
\(120\) 0 0
\(121\) 10.5959 0.963265
\(122\) 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 \(-0.789530\pi\)
0.137178 + 0.990546i \(0.456197\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12.7980 7.38891i −1.11816 0.645572i −0.177232 0.984169i \(-0.556714\pi\)
−0.940931 + 0.338598i \(0.890047\pi\)
\(132\) 0 0
\(133\) 5.79796 + 2.51059i 0.502747 + 0.217696i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.44949 + 3.14626i −0.465581 + 0.268804i −0.714388 0.699750i \(-0.753295\pi\)
0.248807 + 0.968553i \(0.419962\pi\)
\(138\) 0 0
\(139\) −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i \(-0.262608\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.89898 3.28913i −0.158801 0.275051i
\(144\) 0 0
\(145\) 3.46410i 0.287678i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 17.4495 + 10.0745i 1.42952 + 0.825333i 0.997082 0.0763323i \(-0.0243210\pi\)
0.432435 + 0.901665i \(0.357654\pi\)
\(150\) 0 0
\(151\) 1.55708i 0.126713i −0.997991 0.0633566i \(-0.979819\pi\)
0.997991 0.0633566i \(-0.0201806\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.674235 + 1.16781i −0.0541558 + 0.0938006i
\(156\) 0 0
\(157\) −6.17423 + 10.6941i −0.492758 + 0.853481i −0.999965 0.00834275i \(-0.997344\pi\)
0.507208 + 0.861824i \(0.330678\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.10102 4.09978i 0.559639 0.323108i
\(162\) 0 0
\(163\) −7.69694 −0.602871 −0.301435 0.953487i \(-0.597466\pi\)
−0.301435 + 0.953487i \(0.597466\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.22474 7.31747i −0.326921 0.566243i 0.654979 0.755647i \(-0.272678\pi\)
−0.981899 + 0.189404i \(0.939344\pi\)
\(168\) 0 0
\(169\) 11.3485 19.6561i 0.872959 1.51201i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.12372 + 10.6066i −0.465578 + 0.806405i −0.999227 0.0393009i \(-0.987487\pi\)
0.533649 + 0.845706i \(0.320820\pi\)
\(174\) 0 0
\(175\) 2.17423 + 3.76588i 0.164357 + 0.284674i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −4.65153 + 2.68556i −0.345746 + 0.199616i −0.662810 0.748788i \(-0.730636\pi\)
0.317064 + 0.948404i \(0.397303\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.77526 3.07483i 0.130519 0.226066i
\(186\) 0 0
\(187\) 0.651531 1.12848i 0.0476446 0.0825230i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.2706i 1.10494i −0.833532 0.552472i \(-0.813685\pi\)
0.833532 0.552472i \(-0.186315\pi\)
\(192\) 0 0
\(193\) 14.8485 + 8.57277i 1.06882 + 0.617081i 0.927858 0.372934i \(-0.121648\pi\)
0.140958 + 0.990016i \(0.454982\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 20.2918i 1.44573i 0.690989 + 0.722865i \(0.257175\pi\)
−0.690989 + 0.722865i \(0.742825\pi\)
\(198\) 0 0
\(199\) 8.62372 + 14.9367i 0.611320 + 1.05884i 0.991018 + 0.133726i \(0.0426943\pi\)
−0.379699 + 0.925110i \(0.623972\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.77526 3.07483i −0.124598 0.215811i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.10102 + 2.54270i −0.0761592 + 0.175882i
\(210\) 0 0
\(211\) −3.15153 1.81954i −0.216960 0.125262i 0.387582 0.921835i \(-0.373311\pi\)
−0.604542 + 0.796573i \(0.706644\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.77526 + 2.75699i −0.325670 + 0.188025i
\(216\) 0 0
\(217\) 1.38211i 0.0938234i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.2474 0.823853
\(222\) 0 0
\(223\) 2.17423 + 1.25529i 0.145598 + 0.0840608i 0.571029 0.820930i \(-0.306544\pi\)
−0.425432 + 0.904991i \(0.639878\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 23.1464 1.53628 0.768141 0.640280i \(-0.221182\pi\)
0.768141 + 0.640280i \(0.221182\pi\)
\(228\) 0 0
\(229\) −19.2474 −1.27191 −0.635954 0.771727i \(-0.719393\pi\)
−0.635954 + 0.771727i \(0.719393\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.2474 8.80312i −0.998894 0.576711i −0.0909728 0.995853i \(-0.528998\pi\)
−0.907921 + 0.419142i \(0.862331\pi\)
\(234\) 0 0
\(235\) −2.89898 −0.189109
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.4846i 1.45440i 0.686423 + 0.727202i \(0.259180\pi\)
−0.686423 + 0.727202i \(0.740820\pi\)
\(240\) 0 0
\(241\) 12.1515 7.01569i 0.782749 0.451920i −0.0546547 0.998505i \(-0.517406\pi\)
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
\(247\) −25.8712 + 2.98735i −1.64614 + 0.190080i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.22474 + 0.707107i −0.0773052 + 0.0446322i −0.538154 0.842846i \(-0.680878\pi\)
0.460849 + 0.887478i \(0.347545\pi\)
\(252\) 0 0
\(253\) 1.79796 + 3.11416i 0.113037 + 0.195785i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 0 0
\(259\) 3.63907i 0.226121i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.797959 0.460702i −0.0492043 0.0284081i 0.475196 0.879880i \(-0.342377\pi\)
−0.524400 + 0.851472i \(0.675710\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.2247 17.7098i 0.623414 1.07978i −0.365432 0.930838i \(-0.619079\pi\)
0.988845 0.148946i \(-0.0475881\pi\)
\(270\) 0 0
\(271\) 15.6969 27.1879i 0.953521 1.65155i 0.215804 0.976437i \(-0.430763\pi\)
0.737717 0.675110i \(-0.235904\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.65153 + 0.953512i −0.0995911 + 0.0574989i
\(276\) 0 0
\(277\) 9.10102 0.546827 0.273414 0.961897i \(-0.411847\pi\)
0.273414 + 0.961897i \(0.411847\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.5732 20.0454i −0.690400 1.19581i −0.971707 0.236190i \(-0.924101\pi\)
0.281307 0.959618i \(-0.409232\pi\)
\(282\) 0 0
\(283\) −7.44949 + 12.9029i −0.442826 + 0.766997i −0.997898 0.0648050i \(-0.979357\pi\)
0.555072 + 0.831802i \(0.312691\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −6.39898 11.0834i −0.376411 0.651962i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −10.6515 −0.622269 −0.311135 0.950366i \(-0.600709\pi\)
−0.311135 + 0.950366i \(0.600709\pi\)
\(294\) 0 0
\(295\) 17.6969 10.2173i 1.03036 0.594876i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −16.8990 + 29.2699i −0.977293 + 1.69272i
\(300\) 0 0
\(301\) −2.82577 + 4.89437i −0.162874 + 0.282107i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.87832i 0.279332i
\(306\) 0 0
\(307\) 13.3485 + 7.70674i 0.761837 + 0.439847i 0.829955 0.557830i \(-0.188366\pi\)
−0.0681177 + 0.997677i \(0.521699\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.16404i 0.292826i 0.989224 + 0.146413i \(0.0467729\pi\)
−0.989224 + 0.146413i \(0.953227\pi\)
\(312\) 0 0
\(313\) −11.3485 19.6561i −0.641453 1.11103i −0.985108 0.171934i \(-0.944998\pi\)
0.343655 0.939096i \(-0.388335\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.67423 + 6.36396i 0.206366 + 0.357436i 0.950567 0.310520i \(-0.100503\pi\)
−0.744201 + 0.667955i \(0.767170\pi\)
\(318\) 0 0
\(319\) 1.34847 0.778539i 0.0754998 0.0435898i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.32577 7.17461i −0.296334 0.399206i
\(324\) 0 0
\(325\) −15.5227 8.96204i −0.861045 0.497124i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.57321 + 1.48565i −0.141866 + 0.0819063i
\(330\) 0 0
\(331\) 18.7026i 1.02799i −0.857794 0.513994i \(-0.828165\pi\)
0.857794 0.513994i \(-0.171835\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −14.4495 −0.789460
\(336\) 0 0
\(337\) 1.80306 + 1.04100i 0.0982190 + 0.0567068i 0.548305 0.836278i \(-0.315273\pi\)
−0.450086 + 0.892985i \(0.648607\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.606123 −0.0328234
\(342\) 0 0
\(343\) 17.2474 0.931275
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.2247 + 16.2956i 1.51518 + 0.874792i 0.999841 + 0.0178073i \(0.00566852\pi\)
0.515342 + 0.856984i \(0.327665\pi\)
\(348\) 0 0
\(349\) 23.2474 1.24441 0.622204 0.782855i \(-0.286238\pi\)
0.622204 + 0.782855i \(0.286238\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.32124i 0.176772i 0.996086 + 0.0883858i \(0.0281708\pi\)
−0.996086 + 0.0883858i \(0.971829\pi\)
\(354\) 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 0.218638 0.975806i \(-0.429839\pi\)
−0.735754 + 0.677249i \(0.763172\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.57321 + 1.48565i −0.134688 + 0.0777623i
\(366\) 0 0
\(367\) −7.17423 12.4261i −0.374492 0.648639i 0.615759 0.787935i \(-0.288850\pi\)
−0.990251 + 0.139295i \(0.955516\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.55051 + 6.14966i 0.184333 + 0.319275i
\(372\) 0 0
\(373\) 12.2993i 0.636835i 0.947951 + 0.318418i \(0.103151\pi\)
−0.947951 + 0.318418i \(0.896849\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.6742 + 7.31747i 0.652756 + 0.376869i
\(378\) 0 0
\(379\) 19.0526i 0.978664i 0.872098 + 0.489332i \(0.162759\pi\)
−0.872098 + 0.489332i \(0.837241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.44949 9.43879i 0.278456 0.482300i −0.692545 0.721374i \(-0.743511\pi\)
0.971001 + 0.239075i \(0.0768441\pi\)
\(384\) 0 0
\(385\) 0.651531 1.12848i 0.0332051 0.0575129i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 22.8990 13.2207i 1.16102 0.670318i 0.209475 0.977814i \(-0.432824\pi\)
0.951549 + 0.307496i \(0.0994912\pi\)
\(390\) 0 0
\(391\) −11.5959 −0.586431
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.674235 + 1.16781i 0.0339244 + 0.0587588i
\(396\) 0 0
\(397\) −10.8258 + 18.7508i −0.543330 + 0.941074i 0.455380 + 0.890297i \(0.349503\pi\)
−0.998710 + 0.0507775i \(0.983830\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.123724 0.214297i 0.00617850 0.0107015i −0.862920 0.505341i \(-0.831367\pi\)
0.869098 + 0.494640i \(0.164700\pi\)
\(402\) 0 0
\(403\) −2.84847 4.93369i −0.141892 0.245765i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.59592 0.0791067
\(408\) 0 0
\(409\) −25.0454 + 14.4600i −1.23842 + 0.715000i −0.968770 0.247960i \(-0.920240\pi\)
−0.269645 + 0.962960i \(0.586906\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.4722 18.1384i 0.515303 0.892531i
\(414\) 0 0
\(415\) −8.34847 + 14.4600i −0.409810 + 0.709812i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.74983i 0.183191i −0.995796 0.0915956i \(-0.970803\pi\)
0.995796 0.0915956i \(-0.0291967\pi\)
\(420\) 0 0
\(421\) 1.34847 + 0.778539i 0.0657204 + 0.0379437i 0.532500 0.846430i \(-0.321253\pi\)
−0.466780 + 0.884374i \(0.654586\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.14966i 0.298303i
\(426\) 0 0
\(427\) −2.50000 4.33013i −0.120983 0.209550i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.02270 + 13.8957i 0.386440 + 0.669334i 0.991968 0.126490i \(-0.0403713\pi\)
−0.605528 + 0.795824i \(0.707038\pi\)
\(432\) 0 0
\(433\) 25.1969 14.5475i 1.21089 0.699106i 0.247935 0.968777i \(-0.420248\pi\)
0.962953 + 0.269670i \(0.0869148\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 24.4949 2.82843i 1.17175 0.135302i
\(438\) 0 0
\(439\) 12.5227 + 7.22999i 0.597676 + 0.345068i 0.768127 0.640298i \(-0.221189\pi\)
−0.170451 + 0.985366i \(0.554522\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 25.7753 14.8814i 1.22462 0.707034i 0.258720 0.965952i \(-0.416699\pi\)
0.965899 + 0.258918i \(0.0833660\pi\)
\(444\) 0 0
\(445\) 17.3205i 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −18.2474 −0.861150 −0.430575 0.902555i \(-0.641689\pi\)
−0.430575 + 0.902555i \(0.641689\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 12.2474 0.574169
\(456\) 0 0
\(457\) 19.6969 0.921384 0.460692 0.887560i \(-0.347601\pi\)
0.460692 + 0.887560i \(0.347601\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.12372 + 5.26758i 0.424934 + 0.245336i 0.697186 0.716890i \(-0.254435\pi\)
−0.272252 + 0.962226i \(0.587768\pi\)
\(462\) 0 0
\(463\) −40.1464 −1.86576 −0.932881 0.360184i \(-0.882714\pi\)
−0.932881 + 0.360184i \(0.882714\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.0703i 0.975019i −0.873118 0.487510i \(-0.837905\pi\)
0.873118 0.487510i \(-0.162095\pi\)
\(468\) 0 0
\(469\) −12.8258 + 7.40496i −0.592239 + 0.341929i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.14643 1.23924i −0.0986929 0.0569804i
\(474\) 0 0
\(475\) 1.50000 + 12.9904i 0.0688247 + 0.596040i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.14643 4.70334i 0.372220 0.214901i −0.302208 0.953242i \(-0.597724\pi\)
0.674428 + 0.738341i \(0.264390\pi\)
\(480\) 0 0
\(481\) 7.50000 + 12.9904i 0.341971 + 0.592310i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 13.3485 + 23.1202i 0.606123 + 1.04984i
\(486\) 0 0
\(487\) 39.6622i 1.79727i 0.438702 + 0.898633i \(0.355439\pi\)
−0.438702 + 0.898633i \(0.644561\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −26.1464 15.0956i −1.17997 0.681257i −0.223964 0.974597i \(-0.571900\pi\)
−0.956008 + 0.293340i \(0.905233\pi\)
\(492\) 0 0
\(493\) 5.02118i 0.226143i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.34847 7.53177i 0.195056 0.337846i
\(498\) 0 0
\(499\) −21.7474 + 37.6677i −0.973550 + 1.68624i −0.288909 + 0.957357i \(0.593292\pi\)
−0.684641 + 0.728881i \(0.740041\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 35.5176 20.5061i 1.58365 0.914322i 0.589331 0.807891i \(-0.299391\pi\)
0.994320 0.106430i \(-0.0339421\pi\)
\(504\) 0 0
\(505\) 18.6969 0.832003
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.67423 11.5601i −0.295830 0.512393i 0.679347 0.733817i \(-0.262263\pi\)
−0.975178 + 0.221424i \(0.928930\pi\)
\(510\) 0 0
\(511\) −1.52270 + 2.63740i −0.0673605 + 0.116672i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10.2247 + 17.7098i −0.450556 + 0.780386i
\(516\) 0 0
\(517\) −0.651531 1.12848i −0.0286543 0.0496307i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.20204 −0.359338 −0.179669 0.983727i \(-0.557503\pi\)
−0.179669 + 0.983727i \(0.557503\pi\)
\(522\) 0 0
\(523\) −13.5000 + 7.79423i −0.590314 + 0.340818i −0.765222 0.643767i \(-0.777371\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.977296 1.69273i 0.0425717 0.0737363i
\(528\) 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
\(535\) 19.3485 + 11.1708i 0.836507 + 0.482958i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.11416i 0.134136i
\(540\) 0 0
\(541\) −15.1742 26.2825i −0.652391 1.12997i −0.982541 0.186046i \(-0.940433\pi\)
0.330150 0.943929i \(-0.392901\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.0000 + 20.7846i 0.514024 + 0.890315i
\(546\) 0 0
\(547\) 1.80306 1.04100i 0.0770933 0.0445099i −0.460958 0.887422i \(-0.652494\pi\)
0.538051 + 0.842912i \(0.319161\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.22474 10.6066i −0.0521759 0.451856i
\(552\) 0 0
\(553\) 1.19694 + 0.691053i 0.0508990 + 0.0293866i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.5959 13.0458i 0.957420 0.552767i 0.0620418 0.998074i \(-0.480239\pi\)
0.895378 + 0.445307i \(0.146905\pi\)
\(558\) 0 0
\(559\) 23.2952i 0.985282i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.5959 1.07874 0.539370 0.842069i \(-0.318663\pi\)
0.539370 + 0.842069i \(0.318663\pi\)
\(564\) 0 0
\(565\) 21.0000 + 12.1244i 0.883477 + 0.510075i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 31.1010 1.30382 0.651911 0.758295i \(-0.273967\pi\)
0.651911 + 0.758295i \(0.273967\pi\)
\(570\) 0 0
\(571\) 3.69694 0.154712 0.0773560 0.997004i \(-0.475352\pi\)
0.0773560 + 0.997004i \(0.475352\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.6969 + 8.48528i 0.612905 + 0.353861i
\(576\) 0 0
\(577\) 5.79796 0.241372 0.120686 0.992691i \(-0.461491\pi\)
0.120686 + 0.992691i \(0.461491\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 17.1134i 0.709985i
\(582\) 0 0
\(583\) −2.69694 + 1.55708i −0.111696 + 0.0644876i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −24.1237 13.9278i −0.995693 0.574863i −0.0887216 0.996056i \(-0.528278\pi\)
−0.906971 + 0.421193i \(0.861611\pi\)
\(588\) 0 0
\(589\) −1.65153 + 3.81405i −0.0680501 + 0.157155i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −13.4722 + 7.77817i −0.553237 + 0.319411i −0.750426 0.660954i \(-0.770152\pi\)
0.197190 + 0.980365i \(0.436818\pi\)
\(594\) 0 0
\(595\) 2.10102 + 3.63907i 0.0861334 + 0.149188i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.7980 32.5590i −0.768064 1.33033i −0.938611 0.344976i \(-0.887887\pi\)
0.170548 0.985349i \(-0.445446\pi\)
\(600\) 0 0
\(601\) 10.2173i 0.416774i 0.978046 + 0.208387i \(0.0668213\pi\)
−0.978046 + 0.208387i \(0.933179\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12.9773 7.49245i −0.527602 0.304611i
\(606\) 0 0
\(607\) 2.16064i 0.0876979i −0.999038 0.0438489i \(-0.986038\pi\)
0.999038 0.0438489i \(-0.0139620\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.12372 10.6066i 0.247739 0.429097i
\(612\) 0 0
\(613\) −9.44949 + 16.3670i −0.381661 + 0.661057i −0.991300 0.131623i \(-0.957981\pi\)
0.609639 + 0.792680i \(0.291315\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.1010 + 16.2241i −1.13130 + 0.653159i −0.944263 0.329193i \(-0.893223\pi\)
−0.187042 + 0.982352i \(0.559890\pi\)
\(618\) 0 0
\(619\) 36.3939 1.46279 0.731397 0.681952i \(-0.238869\pi\)
0.731397 + 0.681952i \(0.238869\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.87628 + 15.3742i 0.355620 + 0.615953i
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.57321 + 4.45694i −0.102601 + 0.177710i
\(630\) 0 0
\(631\) 7.27526 + 12.6011i 0.289623 + 0.501642i 0.973720 0.227749i \(-0.0731366\pi\)
−0.684096 + 0.729392i \(0.739803\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) −25.3485 + 14.6349i −1.00434 + 0.579858i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.0227 39.8765i 0.909342 1.57503i 0.0943619 0.995538i \(-0.469919\pi\)
0.814980 0.579489i \(-0.196748\pi\)
\(642\) 0 0
\(643\) 21.2980 36.8891i 0.839910 1.45477i −0.0500601 0.998746i \(-0.515941\pi\)
0.889970 0.456020i \(-0.150725\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.97129i 0.116814i −0.998293 0.0584068i \(-0.981398\pi\)
0.998293 0.0584068i \(-0.0186020\pi\)
\(648\) 0 0
\(649\) 7.95459 + 4.59259i 0.312245 + 0.180275i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.3908i 1.50235i 0.660103 + 0.751175i \(0.270513\pi\)
−0.660103 + 0.751175i \(0.729487\pi\)
\(654\) 0 0
\(655\) 10.4495 + 18.0990i 0.408295 + 0.707188i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −5.69694 9.86739i −0.221921 0.384379i 0.733470 0.679722i \(-0.237899\pi\)
−0.955391 + 0.295343i \(0.904566\pi\)
\(660\) 0 0
\(661\) −23.6969 + 13.6814i −0.921704 + 0.532146i −0.884178 0.467150i \(-0.845281\pi\)
−0.0375258 + 0.999296i \(0.511948\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.32577 7.17461i −0.206524 0.278219i
\(666\) 0 0
\(667\) −12.0000 6.92820i −0.464642 0.268261i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.89898 1.09638i 0.0733093 0.0423251i
\(672\) 0 0
\(673\) 19.0526i 0.734422i −0.930138 0.367211i \(-0.880313\pi\)
0.930138 0.367211i \(-0.119687\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 37.3485 1.43542 0.717709 0.696343i \(-0.245191\pi\)
0.717709 + 0.696343i \(0.245191\pi\)
\(678\) 0 0
\(679\) 23.6969 + 13.6814i 0.909405 + 0.525045i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 28.0454 1.07313 0.536564 0.843860i \(-0.319722\pi\)
0.536564 + 0.843860i \(0.319722\pi\)
\(684\) 0 0
\(685\) 8.89898 0.340013
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −25.3485 14.6349i −0.965700 0.557547i
\(690\) 0 0
\(691\) 0.696938 0.0265128 0.0132564 0.999912i \(-0.495780\pi\)
0.0132564 + 0.999912i \(0.495780\pi\)
\(692\) 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 0.732356 0.680922i \(-0.238421\pi\)
−0.223518 + 0.974700i \(0.571754\pi\)
\(702\) 0 0
\(703\) 4.34847 10.0424i 0.164006 0.378755i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.5959 9.58166i 0.624154 0.360355i
\(708\) 0 0
\(709\) −3.17423 5.49794i −0.119211 0.206479i 0.800244 0.599674i \(-0.204703\pi\)
−0.919455 + 0.393195i \(0.871370\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.69694 + 4.67123i 0.101001 + 0.174939i
\(714\) 0 0
\(715\) 5.37113i 0.200869i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.1464 9.89949i −0.639454 0.369189i 0.144950 0.989439i \(-0.453698\pi\)
−0.784404 + 0.620250i \(0.787031\pi\)
\(720\) 0 0
\(721\) 20.9596i 0.780576i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.67423 6.36396i 0.136458 0.236352i
\(726\) 0 0
\(727\) 4.82577 8.35847i 0.178978 0.309999i −0.762553 0.646926i \(-0.776054\pi\)
0.941531 + 0.336927i \(0.109388\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.92168 3.99624i 0.256008 0.147806i
\(732\) 0 0
\(733\) −30.6969 −1.13382 −0.566909 0.823781i \(-0.691861\pi\)
−0.566909 + 0.823781i \(0.691861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.24745 5.62475i −0.119621 0.207190i
\(738\) 0 0
\(739\) 23.1969 40.1783i 0.853313 1.47798i −0.0248879 0.999690i \(-0.507923\pi\)
0.878201 0.478292i \(-0.158744\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 23.6969 41.0443i 0.869356 1.50577i 0.00670079 0.999978i \(-0.497867\pi\)
0.862656 0.505792i \(-0.168800\pi\)
\(744\) 0 0
\(745\) −14.2474 24.6773i −0.521986 0.904107i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 22.8990 0.836711
\(750\) 0 0
\(751\) −24.2196 + 13.9832i −0.883787 + 0.510255i −0.871905 0.489675i \(-0.837116\pi\)
−0.0118820 + 0.999929i \(0.503782\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.10102 + 1.90702i −0.0400702 + 0.0694037i
\(756\) 0 0
\(757\) −12.1742 + 21.0864i −0.442480 + 0.766398i −0.997873 0.0651902i \(-0.979235\pi\)
0.555393 + 0.831588i \(0.312568\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 44.8262i 1.62495i −0.582996 0.812475i \(-0.698120\pi\)
0.582996 0.812475i \(-0.301880\pi\)
\(762\) 0 0
\(763\) 21.3031 + 12.2993i 0.771223 + 0.445266i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 86.3312i 3.11724i
\(768\) 0 0
\(769\) 1.29796 + 2.24813i 0.0468056 + 0.0810697i 0.888479 0.458917i \(-0.151763\pi\)
−0.841673 + 0.539987i \(0.818429\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.47219 + 7.74607i 0.160854 + 0.278607i 0.935175 0.354186i \(-0.115242\pi\)
−0.774321 + 0.632792i \(0.781909\pi\)
\(774\) 0 0
\(775\) −2.47730 + 1.43027i −0.0889871 + 0.0513767i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 3.30306 + 1.90702i 0.118193 + 0.0682387i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.1237 8.73169i 0.539789 0.311647i
\(786\) 0 0
\(787\) 24.0737i 0.858136i 0.903272 + 0.429068i \(0.141158\pi\)
−0.903272 + 0.429068i \(0.858842\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.8536 0.883691
\(792\) 0 0
\(793\) 17.8485 + 10.3048i 0.633818 + 0.365935i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 38.0908 1.34925 0.674623 0.738162i \(-0.264306\pi\)
0.674623 + 0.738162i \(0.264306\pi\)
\(798\) 0 0
\(799\) 4.20204 0.148658
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.15663 0.667783i −0.0408167