Properties

Label 2736.2.dc.a.449.2
Level $2736$
Weight $2$
Character 2736.449
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 449.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2736.449
Dual form 2736.2.dc.a.1889.2

$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

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

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 −0.200480 0.979698i \(-0.564250\pi\)
0.748203 + 0.663470i \(0.230917\pi\)
\(6\) 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 0.997502 0.0706424i \(-0.0225049\pi\)
0.437573 + 0.899183i \(0.355838\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.77526 + 1.02494i −0.430563 + 0.248585i −0.699586 0.714548i \(-0.746632\pi\)
0.269024 + 0.963134i \(0.413299\pi\)
\(18\) 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 \(-0.132553\pi\)
0.106967 + 0.994263i \(0.465886\pi\)
\(24\) 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 \(-0.906365\pi\)
0.729616 + 0.683857i \(0.239699\pi\)
\(30\) 0 0
\(31\) 0.953512i 0.171256i 0.996327 + 0.0856279i \(0.0272896\pi\)
−0.996327 + 0.0856279i \(0.972710\pi\)
\(32\) 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 \(-0.933835\pi\)
0.978474 0.206369i \(-0.0661648\pi\)
\(38\) 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
\(43\) 1.94949 + 3.37662i 0.297294 + 0.514929i 0.975516 0.219928i \(-0.0705824\pi\)
−0.678222 + 0.734857i \(0.737249\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.77526 1.02494i −0.258948 0.149503i 0.364907 0.931044i \(-0.381101\pi\)
−0.623854 + 0.781541i \(0.714434\pi\)
\(48\) 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 \(-0.724103\pi\)
0.983765 + 0.179463i \(0.0574359\pi\)
\(54\) 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 0.764365 + 0.644784i \(0.223053\pi\)
0.176217 + 0.984351i \(0.443614\pi\)
\(60\) 0 0
\(61\) 1.72474 2.98735i 0.220831 0.382490i −0.734230 0.678901i \(-0.762456\pi\)
0.955061 + 0.296411i \(0.0957898\pi\)
\(62\) 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 0.931169 0.364587i \(-0.118790\pi\)
0.149843 + 0.988710i \(0.452123\pi\)
\(68\) 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
\(73\) 1.05051 + 1.81954i 0.122953 + 0.212961i 0.920931 0.389726i \(-0.127430\pi\)
−0.797978 + 0.602687i \(0.794097\pi\)
\(74\) 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 −0.545733 0.837959i \(-0.683749\pi\)
0.452827 + 0.891598i \(0.350415\pi\)
\(80\) 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 −0.334221 0.942495i \(-0.608473\pi\)
0.983335 0.181803i \(-0.0581933\pi\)
\(90\) 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 −0.687193 + 0.726474i \(0.741158\pi\)
−0.972742 + 0.231890i \(0.925509\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 11.4495 + 6.61037i 1.13927 + 0.657756i 0.946249 0.323439i \(-0.104839\pi\)
0.193018 + 0.981195i \(0.438172\pi\)
\(102\) 0 0
\(103\) 14.4600i 1.42478i 0.701782 + 0.712392i \(0.252388\pi\)
−0.701782 + 0.712392i \(0.747612\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.7980 1.52725 0.763623 0.645662i \(-0.223419\pi\)
0.763623 + 0.645662i \(0.223419\pi\)
\(108\) 0 0
\(109\) −14.6969 + 8.48528i −1.40771 + 0.812743i −0.995167 0.0981950i \(-0.968693\pi\)
−0.412544 + 0.910938i \(0.635360\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.1464 1.61300 0.806500 0.591234i \(-0.201359\pi\)
0.806500 + 0.591234i \(0.201359\pi\)
\(114\) 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 0.137178 0.990546i \(-0.456197\pi\)
−0.789249 + 0.614073i \(0.789530\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.7980 7.38891i 1.11816 0.645572i 0.177232 0.984169i \(-0.443286\pi\)
0.940931 + 0.338598i \(0.109953\pi\)
\(132\) 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 \(-0.246705\pi\)
−0.248807 + 0.968553i \(0.580038\pi\)
\(138\) 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
\(143\) 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 \(-0.975679\pi\)
−0.432435 + 0.901665i \(0.642346\pi\)
\(150\) 0 0
\(151\) 1.55708i 0.126713i 0.997991 + 0.0633566i \(0.0201806\pi\)
−0.997991 + 0.0633566i \(0.979819\pi\)
\(152\) 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 0.507208 0.861824i \(-0.330678\pi\)
−0.999965 + 0.00834275i \(0.997344\pi\)
\(158\) 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 \(-0.727322\pi\)
0.981899 + 0.189404i \(0.0606557\pi\)
\(168\) 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 \(-0.0125131\pi\)
−0.533649 + 0.845706i \(0.679180\pi\)
\(174\) 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 \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −4.65153 2.68556i −0.345746 0.199616i 0.317064 0.948404i \(-0.397303\pi\)
−0.662810 + 0.748788i \(0.730636\pi\)
\(182\) 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 0.140958 0.990016i \(-0.454982\pi\)
0.927858 + 0.372934i \(0.121648\pi\)
\(194\) 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 −0.379699 0.925110i \(-0.623972\pi\)
0.991018 0.133726i \(-0.0426943\pi\)
\(200\) 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 −0.604542 0.796573i \(-0.706644\pi\)
0.387582 + 0.921835i \(0.373311\pi\)
\(212\) 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 −0.425432 0.904991i \(-0.639878\pi\)
0.571029 + 0.820930i \(0.306544\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.1464 −1.53628 −0.768141 0.640280i \(-0.778818\pi\)
−0.768141 + 0.640280i \(0.778818\pi\)
\(228\) 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 \(-0.471002\pi\)
0.907921 + 0.419142i \(0.137669\pi\)
\(234\) 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 0.837404 0.546585i \(-0.184072\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) 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 \(-0.319122\pi\)
−0.460849 + 0.887478i \(0.652455\pi\)
\(252\) 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 \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) 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 \(-0.657623\pi\)
0.524400 + 0.851472i \(0.324290\pi\)
\(264\) 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 −0.988845 0.148946i \(-0.952412\pi\)
0.365432 0.930838i \(-0.380921\pi\)
\(270\) 0 0
\(271\) 15.6969 + 27.1879i 0.953521 + 1.65155i 0.737717 + 0.675110i \(0.235904\pi\)
0.215804 + 0.976437i \(0.430763\pi\)
\(272\) 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 −0.281307 0.959618i \(-0.590768\pi\)
0.971707 0.236190i \(-0.0758988\pi\)
\(282\) 0 0
\(283\) −7.44949 12.9029i −0.442826 0.766997i 0.555072 0.831802i \(-0.312691\pi\)
−0.997898 + 0.0648050i \(0.979357\pi\)
\(284\) 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 \(-0.399291\pi\)
0.311135 + 0.950366i \(0.399291\pi\)
\(294\) 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 −0.0681177 0.997677i \(-0.521699\pi\)
0.829955 + 0.557830i \(0.188366\pi\)
\(308\) 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 0.343655 + 0.939096i \(0.388335\pi\)
−0.985108 + 0.171934i \(0.944998\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.67423 + 6.36396i −0.206366 + 0.357436i −0.950567 0.310520i \(-0.899497\pi\)
0.744201 + 0.667955i \(0.232830\pi\)
\(318\) 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 \(0.171835\pi\)
−0.857794 + 0.513994i \(0.828165\pi\)
\(332\) 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 −0.450086 0.892985i \(-0.648607\pi\)
0.548305 + 0.836278i \(0.315273\pi\)
\(338\) 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 −0.515342 + 0.856984i \(0.672335\pi\)
−0.999841 + 0.0178073i \(0.994331\pi\)
\(348\) 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 \(-0.570161\pi\)
0.735754 + 0.677249i \(0.236828\pi\)
\(360\) 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 −0.990251 0.139295i \(-0.955516\pi\)
0.615759 + 0.787935i \(0.288850\pi\)
\(368\) 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 \(-0.896849\pi\)
0.947951 0.318418i \(-0.103151\pi\)
\(374\) 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 \(-0.837241\pi\)
0.872098 0.489332i \(-0.162759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.44949 9.43879i −0.278456 0.482300i 0.692545 0.721374i \(-0.256489\pi\)
−0.971001 + 0.239075i \(0.923156\pi\)
\(384\) 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 \(-0.567176\pi\)
−0.951549 + 0.307496i \(0.900509\pi\)
\(390\) 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 −0.998710 0.0507775i \(-0.983830\pi\)
0.455380 0.890297i \(-0.349503\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.123724 0.214297i −0.00617850 0.0107015i 0.862920 0.505341i \(-0.168633\pi\)
−0.869098 + 0.494640i \(0.835300\pi\)
\(402\) 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 −0.269645 0.962960i \(-0.586906\pi\)
−0.968770 + 0.247960i \(0.920240\pi\)
\(410\) 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 −0.466780 0.884374i \(-0.654586\pi\)
0.532500 + 0.846430i \(0.321253\pi\)
\(422\) 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 \(-0.959629\pi\)
0.605528 + 0.795824i \(0.292962\pi\)
\(432\) 0 0
\(433\) 25.1969 + 14.5475i 1.21089 + 0.699106i 0.962953 0.269670i \(-0.0869148\pi\)
0.247935 + 0.968777i \(0.420248\pi\)
\(434\) 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 −0.170451 0.985366i \(-0.554522\pi\)
0.768127 + 0.640298i \(0.221189\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −25.7753 14.8814i −1.22462 0.707034i −0.258720 0.965952i \(-0.583301\pi\)
−0.965899 + 0.258918i \(0.916634\pi\)
\(444\) 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 \(-0.358311\pi\)
0.430575 + 0.902555i \(0.358311\pi\)
\(450\) 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 \(-0.745565\pi\)
0.272252 + 0.962226i \(0.412232\pi\)
\(462\) 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 \(-0.402276\pi\)
−0.674428 + 0.738341i \(0.735610\pi\)
\(480\) 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 \(-0.644561\pi\)
0.438702 0.898633i \(-0.355439\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.1464 15.0956i 1.17997 0.681257i 0.223964 0.974597i \(-0.428100\pi\)
0.956008 + 0.293340i \(0.0947669\pi\)
\(492\) 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 −0.684641 0.728881i \(-0.740041\pi\)
−0.288909 0.957357i \(-0.593292\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −35.5176 20.5061i −1.58365 0.914322i −0.994320 0.106430i \(-0.966058\pi\)
−0.589331 0.807891i \(-0.700609\pi\)
\(504\) 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 \(-0.737737\pi\)
0.975178 + 0.221424i \(0.0710704\pi\)
\(510\) 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 \(-0.442497\pi\)
0.179669 + 0.983727i \(0.442497\pi\)
\(522\) 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
\(527\) −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 0.330150 + 0.943929i \(0.392901\pi\)
−0.982541 + 0.186046i \(0.940433\pi\)
\(542\) 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 0.538051 0.842912i \(-0.319161\pi\)
−0.460958 + 0.887422i \(0.652494\pi\)
\(548\) 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 \(-0.519761\pi\)
−0.895378 + 0.445307i \(0.853095\pi\)
\(558\) 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 \(-0.681337\pi\)
−0.539370 + 0.842069i \(0.681337\pi\)
\(564\) 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 \(-0.726033\pi\)
−0.651911 + 0.758295i \(0.726033\pi\)
\(570\) 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 \(-0.471722\pi\)
0.906971 + 0.421193i \(0.138389\pi\)
\(588\) 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 \(-0.229848\pi\)
−0.197190 + 0.980365i \(0.563182\pi\)
\(594\) 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 −0.170548 0.985349i \(-0.554554\pi\)
0.938611 0.344976i \(-0.112113\pi\)
\(600\) 0 0
\(601\) 10.2173i 0.416774i −0.978046 0.208387i \(-0.933179\pi\)
0.978046 0.208387i \(-0.0668213\pi\)
\(602\) 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 \(0.0139620\pi\)
−0.999038 + 0.0438489i \(0.986038\pi\)
\(608\) 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 0.609639 0.792680i \(-0.291315\pi\)
−0.991300 + 0.131623i \(0.957981\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 28.1010 + 16.2241i 1.13130 + 0.653159i 0.944263 0.329193i \(-0.106777\pi\)
0.187042 + 0.982352i \(0.440110\pi\)
\(618\) 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 −0.684096 0.729392i \(-0.739803\pi\)
0.973720 + 0.227749i \(0.0731366\pi\)
\(632\) 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 −0.814980 0.579489i \(-0.803252\pi\)
−0.0943619 0.995538i \(-0.530081\pi\)
\(642\) 0 0
\(643\) 21.2980 + 36.8891i 0.839910 + 1.45477i 0.889970 + 0.456020i \(0.150725\pi\)
−0.0500601 + 0.998746i \(0.515941\pi\)
\(644\) 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 \(-0.762101\pi\)
0.955391 + 0.295343i \(0.0954339\pi\)
\(660\) 0 0
\(661\) −23.6969 13.6814i −0.921704 0.532146i −0.0375258 0.999296i \(-0.511948\pi\)
−0.884178 + 0.467150i \(0.845281\pi\)
\(662\) 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 \(0.119687\pi\)
−0.930138 + 0.367211i \(0.880313\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −37.3485 −1.43542 −0.717709 0.696343i \(-0.754809\pi\)
−0.717709 + 0.696343i \(0.754809\pi\)
\(678\) 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 \(-0.680278\pi\)
−0.536564 + 0.843860i \(0.680278\pi\)
\(684\) 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 \(-0.761579\pi\)
0.223518 + 0.974700i \(0.428246\pi\)
\(702\) 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 −0.919455 0.393195i \(-0.871370\pi\)
0.800244 + 0.599674i \(0.204703\pi\)
\(710\) 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 \(-0.546302\pi\)
0.784404 + 0.620250i \(0.212969\pi\)
\(720\) 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 0.941531 0.336927i \(-0.109388\pi\)
−0.762553 + 0.646926i \(0.776054\pi\)
\(728\) 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 0.878201 + 0.478292i \(0.158744\pi\)
−0.0248879 + 0.999690i \(0.507923\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −23.6969 41.0443i −0.869356 1.50577i −0.862656 0.505792i \(-0.831200\pi\)
−0.00670079 0.999978i \(-0.502133\pi\)
\(744\) 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 −0.0118820 0.999929i \(-0.503782\pi\)
−0.871905 + 0.489675i \(0.837116\pi\)
\(752\) 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 0.555393 0.831588i \(-0.312568\pi\)
−0.997873 + 0.0651902i \(0.979235\pi\)
\(758\) 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 −0.841673 0.539987i \(-0.818429\pi\)
0.888479 + 0.458917i \(0.151763\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.47219 + 7.74607i −0.160854 + 0.278607i −0.935175 0.354186i \(-0.884758\pi\)
0.774321 + 0.632792i \(0.218091\pi\)
\(774\) 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 \(-0.858842\pi\)
0.903272 0.429068i \(-0.141158\pi\)
\(788\) 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 \(-0.735694\pi\)
−0.674623 + 0.738162i \(0.735694\pi\)
\(798\) 0 0
\(799\) 4.20204 0.148658
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.15663 0.667783i 0.0408167