Properties

Label 1520.2.d.d.609.3
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 760)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.3
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.d.609.2

$q$-expansion

\(f(q)\) \(=\) \(q+0.414214i q^{3} +(-2.12132 + 0.707107i) q^{5} +0.414214i q^{7} +2.82843 q^{9} +O(q^{10})\) \(q+0.414214i q^{3} +(-2.12132 + 0.707107i) q^{5} +0.414214i q^{7} +2.82843 q^{9} +1.41421 q^{11} -3.82843i q^{13} +(-0.292893 - 0.878680i) q^{15} -1.00000i q^{17} -1.00000 q^{19} -0.171573 q^{21} +3.24264i q^{23} +(4.00000 - 3.00000i) q^{25} +2.41421i q^{27} +1.82843 q^{29} -0.585786 q^{31} +0.585786i q^{33} +(-0.292893 - 0.878680i) q^{35} -10.8284i q^{37} +1.58579 q^{39} +7.07107 q^{41} +6.24264i q^{43} +(-6.00000 + 2.00000i) q^{45} +8.00000i q^{47} +6.82843 q^{49} +0.414214 q^{51} +3.82843i q^{53} +(-3.00000 + 1.00000i) q^{55} -0.414214i q^{57} +11.5858 q^{59} +0.585786 q^{61} +1.17157i q^{63} +(2.70711 + 8.12132i) q^{65} +8.07107i q^{67} -1.34315 q^{69} +11.0711 q^{71} +8.17157i q^{73} +(1.24264 + 1.65685i) q^{75} +0.585786i q^{77} +4.82843 q^{79} +7.48528 q^{81} -14.4853i q^{83} +(0.707107 + 2.12132i) q^{85} +0.757359i q^{87} +12.2426 q^{89} +1.58579 q^{91} -0.242641i q^{93} +(2.12132 - 0.707107i) q^{95} +3.65685i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q - 4q^{15} - 4q^{19} - 12q^{21} + 16q^{25} - 4q^{29} - 8q^{31} - 4q^{35} + 12q^{39} - 24q^{45} + 16q^{49} - 4q^{51} - 12q^{55} + 52q^{59} + 8q^{61} + 8q^{65} - 28q^{69} + 16q^{71} - 12q^{75} + 8q^{79} - 4q^{81} + 32q^{89} + 12q^{91} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 0.414214i 0.239146i 0.992825 + 0.119573i \(0.0381526\pi\)
−0.992825 + 0.119573i \(0.961847\pi\)
\(4\) 0 0
\(5\) −2.12132 + 0.707107i −0.948683 + 0.316228i
\(6\) 0 0
\(7\) 0.414214i 0.156558i 0.996931 + 0.0782790i \(0.0249425\pi\)
−0.996931 + 0.0782790i \(0.975058\pi\)
\(8\) 0 0
\(9\) 2.82843 0.942809
\(10\) 0 0
\(11\) 1.41421 0.426401 0.213201 0.977008i \(-0.431611\pi\)
0.213201 + 0.977008i \(0.431611\pi\)
\(12\) 0 0
\(13\) 3.82843i 1.06181i −0.847430 0.530907i \(-0.821851\pi\)
0.847430 0.530907i \(-0.178149\pi\)
\(14\) 0 0
\(15\) −0.292893 0.878680i −0.0756247 0.226874i
\(16\) 0 0
\(17\) 1.00000i 0.242536i −0.992620 0.121268i \(-0.961304\pi\)
0.992620 0.121268i \(-0.0386960\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.171573 −0.0374403
\(22\) 0 0
\(23\) 3.24264i 0.676137i 0.941121 + 0.338069i \(0.109774\pi\)
−0.941121 + 0.338069i \(0.890226\pi\)
\(24\) 0 0
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) 0 0
\(27\) 2.41421i 0.464616i
\(28\) 0 0
\(29\) 1.82843 0.339530 0.169765 0.985485i \(-0.445699\pi\)
0.169765 + 0.985485i \(0.445699\pi\)
\(30\) 0 0
\(31\) −0.585786 −0.105210 −0.0526052 0.998615i \(-0.516752\pi\)
−0.0526052 + 0.998615i \(0.516752\pi\)
\(32\) 0 0
\(33\) 0.585786i 0.101972i
\(34\) 0 0
\(35\) −0.292893 0.878680i −0.0495080 0.148524i
\(36\) 0 0
\(37\) 10.8284i 1.78018i −0.455782 0.890091i \(-0.650640\pi\)
0.455782 0.890091i \(-0.349360\pi\)
\(38\) 0 0
\(39\) 1.58579 0.253929
\(40\) 0 0
\(41\) 7.07107 1.10432 0.552158 0.833740i \(-0.313805\pi\)
0.552158 + 0.833740i \(0.313805\pi\)
\(42\) 0 0
\(43\) 6.24264i 0.951994i 0.879447 + 0.475997i \(0.157913\pi\)
−0.879447 + 0.475997i \(0.842087\pi\)
\(44\) 0 0
\(45\) −6.00000 + 2.00000i −0.894427 + 0.298142i
\(46\) 0 0
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) 6.82843 0.975490
\(50\) 0 0
\(51\) 0.414214 0.0580015
\(52\) 0 0
\(53\) 3.82843i 0.525875i 0.964813 + 0.262937i \(0.0846913\pi\)
−0.964813 + 0.262937i \(0.915309\pi\)
\(54\) 0 0
\(55\) −3.00000 + 1.00000i −0.404520 + 0.134840i
\(56\) 0 0
\(57\) 0.414214i 0.0548639i
\(58\) 0 0
\(59\) 11.5858 1.50834 0.754170 0.656679i \(-0.228039\pi\)
0.754170 + 0.656679i \(0.228039\pi\)
\(60\) 0 0
\(61\) 0.585786 0.0750023 0.0375011 0.999297i \(-0.488060\pi\)
0.0375011 + 0.999297i \(0.488060\pi\)
\(62\) 0 0
\(63\) 1.17157i 0.147604i
\(64\) 0 0
\(65\) 2.70711 + 8.12132i 0.335775 + 1.00733i
\(66\) 0 0
\(67\) 8.07107i 0.986038i 0.870019 + 0.493019i \(0.164107\pi\)
−0.870019 + 0.493019i \(0.835893\pi\)
\(68\) 0 0
\(69\) −1.34315 −0.161696
\(70\) 0 0
\(71\) 11.0711 1.31389 0.656947 0.753937i \(-0.271848\pi\)
0.656947 + 0.753937i \(0.271848\pi\)
\(72\) 0 0
\(73\) 8.17157i 0.956410i 0.878248 + 0.478205i \(0.158712\pi\)
−0.878248 + 0.478205i \(0.841288\pi\)
\(74\) 0 0
\(75\) 1.24264 + 1.65685i 0.143488 + 0.191317i
\(76\) 0 0
\(77\) 0.585786i 0.0667566i
\(78\) 0 0
\(79\) 4.82843 0.543240 0.271620 0.962405i \(-0.412441\pi\)
0.271620 + 0.962405i \(0.412441\pi\)
\(80\) 0 0
\(81\) 7.48528 0.831698
\(82\) 0 0
\(83\) 14.4853i 1.58997i −0.606632 0.794983i \(-0.707480\pi\)
0.606632 0.794983i \(-0.292520\pi\)
\(84\) 0 0
\(85\) 0.707107 + 2.12132i 0.0766965 + 0.230089i
\(86\) 0 0
\(87\) 0.757359i 0.0811974i
\(88\) 0 0
\(89\) 12.2426 1.29772 0.648859 0.760909i \(-0.275247\pi\)
0.648859 + 0.760909i \(0.275247\pi\)
\(90\) 0 0
\(91\) 1.58579 0.166236
\(92\) 0 0
\(93\) 0.242641i 0.0251607i
\(94\) 0 0
\(95\) 2.12132 0.707107i 0.217643 0.0725476i
\(96\) 0 0
\(97\) 3.65685i 0.371297i 0.982616 + 0.185649i \(0.0594386\pi\)
−0.982616 + 0.185649i \(0.940561\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −3.89949 −0.388014 −0.194007 0.981000i \(-0.562148\pi\)
−0.194007 + 0.981000i \(0.562148\pi\)
\(102\) 0 0
\(103\) 9.89949i 0.975426i −0.873004 0.487713i \(-0.837831\pi\)
0.873004 0.487713i \(-0.162169\pi\)
\(104\) 0 0
\(105\) 0.363961 0.121320i 0.0355190 0.0118397i
\(106\) 0 0
\(107\) 0.414214i 0.0400435i 0.999800 + 0.0200218i \(0.00637355\pi\)
−0.999800 + 0.0200218i \(0.993626\pi\)
\(108\) 0 0
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) 4.48528 0.425724
\(112\) 0 0
\(113\) 1.07107i 0.100758i 0.998730 + 0.0503788i \(0.0160429\pi\)
−0.998730 + 0.0503788i \(0.983957\pi\)
\(114\) 0 0
\(115\) −2.29289 6.87868i −0.213813 0.641440i
\(116\) 0 0
\(117\) 10.8284i 1.00109i
\(118\) 0 0
\(119\) 0.414214 0.0379709
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 0 0
\(123\) 2.92893i 0.264093i
\(124\) 0 0
\(125\) −6.36396 + 9.19239i −0.569210 + 0.822192i
\(126\) 0 0
\(127\) 16.8284i 1.49328i 0.665228 + 0.746641i \(0.268335\pi\)
−0.665228 + 0.746641i \(0.731665\pi\)
\(128\) 0 0
\(129\) −2.58579 −0.227666
\(130\) 0 0
\(131\) −10.3431 −0.903685 −0.451842 0.892098i \(-0.649233\pi\)
−0.451842 + 0.892098i \(0.649233\pi\)
\(132\) 0 0
\(133\) 0.414214i 0.0359169i
\(134\) 0 0
\(135\) −1.70711 5.12132i −0.146924 0.440773i
\(136\) 0 0
\(137\) 6.31371i 0.539417i 0.962942 + 0.269708i \(0.0869273\pi\)
−0.962942 + 0.269708i \(0.913073\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −3.31371 −0.279065
\(142\) 0 0
\(143\) 5.41421i 0.452759i
\(144\) 0 0
\(145\) −3.87868 + 1.29289i −0.322107 + 0.107369i
\(146\) 0 0
\(147\) 2.82843i 0.233285i
\(148\) 0 0
\(149\) 6.34315 0.519651 0.259825 0.965656i \(-0.416335\pi\)
0.259825 + 0.965656i \(0.416335\pi\)
\(150\) 0 0
\(151\) −16.8284 −1.36948 −0.684739 0.728788i \(-0.740084\pi\)
−0.684739 + 0.728788i \(0.740084\pi\)
\(152\) 0 0
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) 1.24264 0.414214i 0.0998113 0.0332704i
\(156\) 0 0
\(157\) 11.6569i 0.930318i −0.885227 0.465159i \(-0.845997\pi\)
0.885227 0.465159i \(-0.154003\pi\)
\(158\) 0 0
\(159\) −1.58579 −0.125761
\(160\) 0 0
\(161\) −1.34315 −0.105855
\(162\) 0 0
\(163\) 17.0711i 1.33711i −0.743663 0.668555i \(-0.766913\pi\)
0.743663 0.668555i \(-0.233087\pi\)
\(164\) 0 0
\(165\) −0.414214 1.24264i −0.0322465 0.0967394i
\(166\) 0 0
\(167\) 19.2132i 1.48676i −0.668868 0.743381i \(-0.733221\pi\)
0.668868 0.743381i \(-0.266779\pi\)
\(168\) 0 0
\(169\) −1.65685 −0.127450
\(170\) 0 0
\(171\) −2.82843 −0.216295
\(172\) 0 0
\(173\) 13.1716i 1.00142i 0.865616 + 0.500708i \(0.166927\pi\)
−0.865616 + 0.500708i \(0.833073\pi\)
\(174\) 0 0
\(175\) 1.24264 + 1.65685i 0.0939348 + 0.125246i
\(176\) 0 0
\(177\) 4.79899i 0.360714i
\(178\) 0 0
\(179\) 10.9706 0.819978 0.409989 0.912090i \(-0.365532\pi\)
0.409989 + 0.912090i \(0.365532\pi\)
\(180\) 0 0
\(181\) −16.4853 −1.22534 −0.612671 0.790338i \(-0.709905\pi\)
−0.612671 + 0.790338i \(0.709905\pi\)
\(182\) 0 0
\(183\) 0.242641i 0.0179365i
\(184\) 0 0
\(185\) 7.65685 + 22.9706i 0.562943 + 1.68883i
\(186\) 0 0
\(187\) 1.41421i 0.103418i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 2.75736 0.199516 0.0997578 0.995012i \(-0.468193\pi\)
0.0997578 + 0.995012i \(0.468193\pi\)
\(192\) 0 0
\(193\) 3.65685i 0.263226i −0.991301 0.131613i \(-0.957984\pi\)
0.991301 0.131613i \(-0.0420156\pi\)
\(194\) 0 0
\(195\) −3.36396 + 1.12132i −0.240898 + 0.0802994i
\(196\) 0 0
\(197\) 4.72792i 0.336850i 0.985714 + 0.168425i \(0.0538682\pi\)
−0.985714 + 0.168425i \(0.946132\pi\)
\(198\) 0 0
\(199\) 1.92893 0.136738 0.0683692 0.997660i \(-0.478220\pi\)
0.0683692 + 0.997660i \(0.478220\pi\)
\(200\) 0 0
\(201\) −3.34315 −0.235807
\(202\) 0 0
\(203\) 0.757359i 0.0531562i
\(204\) 0 0
\(205\) −15.0000 + 5.00000i −1.04765 + 0.349215i
\(206\) 0 0
\(207\) 9.17157i 0.637468i
\(208\) 0 0
\(209\) −1.41421 −0.0978232
\(210\) 0 0
\(211\) 5.10051 0.351133 0.175567 0.984468i \(-0.443824\pi\)
0.175567 + 0.984468i \(0.443824\pi\)
\(212\) 0 0
\(213\) 4.58579i 0.314213i
\(214\) 0 0
\(215\) −4.41421 13.2426i −0.301047 0.903141i
\(216\) 0 0
\(217\) 0.242641i 0.0164715i
\(218\) 0 0
\(219\) −3.38478 −0.228722
\(220\) 0 0
\(221\) −3.82843 −0.257528
\(222\) 0 0
\(223\) 8.82843i 0.591195i −0.955313 0.295598i \(-0.904481\pi\)
0.955313 0.295598i \(-0.0955188\pi\)
\(224\) 0 0
\(225\) 11.3137 8.48528i 0.754247 0.565685i
\(226\) 0 0
\(227\) 8.75736i 0.581246i −0.956838 0.290623i \(-0.906137\pi\)
0.956838 0.290623i \(-0.0938626\pi\)
\(228\) 0 0
\(229\) −6.97056 −0.460628 −0.230314 0.973116i \(-0.573975\pi\)
−0.230314 + 0.973116i \(0.573975\pi\)
\(230\) 0 0
\(231\) −0.242641 −0.0159646
\(232\) 0 0
\(233\) 13.6569i 0.894690i −0.894361 0.447345i \(-0.852370\pi\)
0.894361 0.447345i \(-0.147630\pi\)
\(234\) 0 0
\(235\) −5.65685 16.9706i −0.369012 1.10704i
\(236\) 0 0
\(237\) 2.00000i 0.129914i
\(238\) 0 0
\(239\) 27.7279 1.79357 0.896785 0.442466i \(-0.145896\pi\)
0.896785 + 0.442466i \(0.145896\pi\)
\(240\) 0 0
\(241\) −5.65685 −0.364390 −0.182195 0.983262i \(-0.558320\pi\)
−0.182195 + 0.983262i \(0.558320\pi\)
\(242\) 0 0
\(243\) 10.3431i 0.663513i
\(244\) 0 0
\(245\) −14.4853 + 4.82843i −0.925431 + 0.308477i
\(246\) 0 0
\(247\) 3.82843i 0.243597i
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) −3.55635 −0.224475 −0.112237 0.993681i \(-0.535802\pi\)
−0.112237 + 0.993681i \(0.535802\pi\)
\(252\) 0 0
\(253\) 4.58579i 0.288306i
\(254\) 0 0
\(255\) −0.878680 + 0.292893i −0.0550251 + 0.0183417i
\(256\) 0 0
\(257\) 28.7279i 1.79200i −0.444056 0.895999i \(-0.646461\pi\)
0.444056 0.895999i \(-0.353539\pi\)
\(258\) 0 0
\(259\) 4.48528 0.278702
\(260\) 0 0
\(261\) 5.17157 0.320112
\(262\) 0 0
\(263\) 15.6569i 0.965443i 0.875774 + 0.482721i \(0.160352\pi\)
−0.875774 + 0.482721i \(0.839648\pi\)
\(264\) 0 0
\(265\) −2.70711 8.12132i −0.166296 0.498889i
\(266\) 0 0
\(267\) 5.07107i 0.310344i
\(268\) 0 0
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) −15.3848 −0.934559 −0.467279 0.884110i \(-0.654766\pi\)
−0.467279 + 0.884110i \(0.654766\pi\)
\(272\) 0 0
\(273\) 0.656854i 0.0397546i
\(274\) 0 0
\(275\) 5.65685 4.24264i 0.341121 0.255841i
\(276\) 0 0
\(277\) 3.31371i 0.199101i 0.995032 + 0.0995507i \(0.0317406\pi\)
−0.995032 + 0.0995507i \(0.968259\pi\)
\(278\) 0 0
\(279\) −1.65685 −0.0991933
\(280\) 0 0
\(281\) −3.75736 −0.224145 −0.112073 0.993700i \(-0.535749\pi\)
−0.112073 + 0.993700i \(0.535749\pi\)
\(282\) 0 0
\(283\) 9.51472i 0.565591i −0.959180 0.282796i \(-0.908738\pi\)
0.959180 0.282796i \(-0.0912618\pi\)
\(284\) 0 0
\(285\) 0.292893 + 0.878680i 0.0173495 + 0.0520485i
\(286\) 0 0
\(287\) 2.92893i 0.172889i
\(288\) 0 0
\(289\) 16.0000 0.941176
\(290\) 0 0
\(291\) −1.51472 −0.0887944
\(292\) 0 0
\(293\) 10.7990i 0.630884i 0.948945 + 0.315442i \(0.102153\pi\)
−0.948945 + 0.315442i \(0.897847\pi\)
\(294\) 0 0
\(295\) −24.5772 + 8.19239i −1.43094 + 0.476979i
\(296\) 0 0
\(297\) 3.41421i 0.198113i
\(298\) 0 0
\(299\) 12.4142 0.717933
\(300\) 0 0
\(301\) −2.58579 −0.149042
\(302\) 0 0
\(303\) 1.61522i 0.0927922i
\(304\) 0 0
\(305\) −1.24264 + 0.414214i −0.0711534 + 0.0237178i
\(306\) 0 0
\(307\) 32.2843i 1.84256i 0.388899 + 0.921280i \(0.372855\pi\)
−0.388899 + 0.921280i \(0.627145\pi\)
\(308\) 0 0
\(309\) 4.10051 0.233270
\(310\) 0 0
\(311\) −23.2426 −1.31797 −0.658985 0.752156i \(-0.729014\pi\)
−0.658985 + 0.752156i \(0.729014\pi\)
\(312\) 0 0
\(313\) 6.65685i 0.376268i 0.982143 + 0.188134i \(0.0602439\pi\)
−0.982143 + 0.188134i \(0.939756\pi\)
\(314\) 0 0
\(315\) −0.828427 2.48528i −0.0466766 0.140030i
\(316\) 0 0
\(317\) 6.79899i 0.381869i −0.981603 0.190935i \(-0.938848\pi\)
0.981603 0.190935i \(-0.0611519\pi\)
\(318\) 0 0
\(319\) 2.58579 0.144776
\(320\) 0 0
\(321\) −0.171573 −0.00957626
\(322\) 0 0
\(323\) 1.00000i 0.0556415i
\(324\) 0 0
\(325\) −11.4853 15.3137i −0.637089 0.849452i
\(326\) 0 0
\(327\) 2.07107i 0.114530i
\(328\) 0 0
\(329\) −3.31371 −0.182691
\(330\) 0 0
\(331\) −19.3848 −1.06548 −0.532742 0.846278i \(-0.678838\pi\)
−0.532742 + 0.846278i \(0.678838\pi\)
\(332\) 0 0
\(333\) 30.6274i 1.67837i
\(334\) 0 0
\(335\) −5.70711 17.1213i −0.311813 0.935438i
\(336\) 0 0
\(337\) 12.7279i 0.693334i −0.937988 0.346667i \(-0.887313\pi\)
0.937988 0.346667i \(-0.112687\pi\)
\(338\) 0 0
\(339\) −0.443651 −0.0240958
\(340\) 0 0
\(341\) −0.828427 −0.0448618
\(342\) 0 0
\(343\) 5.72792i 0.309279i
\(344\) 0 0
\(345\) 2.84924 0.949747i 0.153398 0.0511327i
\(346\) 0 0
\(347\) 15.1716i 0.814453i 0.913327 + 0.407226i \(0.133504\pi\)
−0.913327 + 0.407226i \(0.866496\pi\)
\(348\) 0 0
\(349\) −28.6274 −1.53239 −0.766195 0.642608i \(-0.777852\pi\)
−0.766195 + 0.642608i \(0.777852\pi\)
\(350\) 0 0
\(351\) 9.24264 0.493336
\(352\) 0 0
\(353\) 36.1127i 1.92208i 0.276401 + 0.961042i \(0.410858\pi\)
−0.276401 + 0.961042i \(0.589142\pi\)
\(354\) 0 0
\(355\) −23.4853 + 7.82843i −1.24647 + 0.415490i
\(356\) 0 0
\(357\) 0.171573i 0.00908060i
\(358\) 0 0
\(359\) −6.07107 −0.320419 −0.160209 0.987083i \(-0.551217\pi\)
−0.160209 + 0.987083i \(0.551217\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 3.72792i 0.195665i
\(364\) 0 0
\(365\) −5.77817 17.3345i −0.302443 0.907330i
\(366\) 0 0
\(367\) 33.4558i 1.74638i −0.487379 0.873190i \(-0.662047\pi\)
0.487379 0.873190i \(-0.337953\pi\)
\(368\) 0 0
\(369\) 20.0000 1.04116
\(370\) 0 0
\(371\) −1.58579 −0.0823299
\(372\) 0 0
\(373\) 27.9706i 1.44826i −0.689663 0.724130i \(-0.742241\pi\)
0.689663 0.724130i \(-0.257759\pi\)
\(374\) 0 0
\(375\) −3.80761 2.63604i −0.196624 0.136124i
\(376\) 0 0
\(377\) 7.00000i 0.360518i
\(378\) 0 0
\(379\) −3.38478 −0.173864 −0.0869321 0.996214i \(-0.527706\pi\)
−0.0869321 + 0.996214i \(0.527706\pi\)
\(380\) 0 0
\(381\) −6.97056 −0.357113
\(382\) 0 0
\(383\) 20.7279i 1.05915i 0.848264 + 0.529574i \(0.177648\pi\)
−0.848264 + 0.529574i \(0.822352\pi\)
\(384\) 0 0
\(385\) −0.414214 1.24264i −0.0211103 0.0633308i
\(386\) 0 0
\(387\) 17.6569i 0.897548i
\(388\) 0 0
\(389\) −7.89949 −0.400520 −0.200260 0.979743i \(-0.564179\pi\)
−0.200260 + 0.979743i \(0.564179\pi\)
\(390\) 0 0
\(391\) 3.24264 0.163987
\(392\) 0 0
\(393\) 4.28427i 0.216113i
\(394\) 0 0
\(395\) −10.2426 + 3.41421i −0.515363 + 0.171788i
\(396\) 0 0
\(397\) 22.6274i 1.13564i −0.823154 0.567819i \(-0.807787\pi\)
0.823154 0.567819i \(-0.192213\pi\)
\(398\) 0 0
\(399\) 0.171573 0.00858939
\(400\) 0 0
\(401\) −6.10051 −0.304645 −0.152322 0.988331i \(-0.548675\pi\)
−0.152322 + 0.988331i \(0.548675\pi\)
\(402\) 0 0
\(403\) 2.24264i 0.111714i
\(404\) 0 0
\(405\) −15.8787 + 5.29289i −0.789018 + 0.263006i
\(406\) 0 0
\(407\) 15.3137i 0.759072i
\(408\) 0 0
\(409\) −2.58579 −0.127859 −0.0639295 0.997954i \(-0.520363\pi\)
−0.0639295 + 0.997954i \(0.520363\pi\)
\(410\) 0 0
\(411\) −2.61522 −0.128999
\(412\) 0 0
\(413\) 4.79899i 0.236143i
\(414\) 0 0
\(415\) 10.2426 + 30.7279i 0.502791 + 1.50837i
\(416\) 0 0
\(417\) 1.65685i 0.0811365i
\(418\) 0 0
\(419\) −27.2132 −1.32945 −0.664726 0.747087i \(-0.731452\pi\)
−0.664726 + 0.747087i \(0.731452\pi\)
\(420\) 0 0
\(421\) 13.1421 0.640508 0.320254 0.947332i \(-0.396232\pi\)
0.320254 + 0.947332i \(0.396232\pi\)
\(422\) 0 0
\(423\) 22.6274i 1.10018i
\(424\) 0 0
\(425\) −3.00000 4.00000i −0.145521 0.194029i
\(426\) 0 0
\(427\) 0.242641i 0.0117422i
\(428\) 0 0
\(429\) 2.24264 0.108276
\(430\) 0 0
\(431\) 5.41421 0.260793 0.130397 0.991462i \(-0.458375\pi\)
0.130397 + 0.991462i \(0.458375\pi\)
\(432\) 0 0
\(433\) 5.07107i 0.243700i 0.992549 + 0.121850i \(0.0388827\pi\)
−0.992549 + 0.121850i \(0.961117\pi\)
\(434\) 0 0
\(435\) −0.535534 1.60660i −0.0256769 0.0770307i
\(436\) 0 0
\(437\) 3.24264i 0.155117i
\(438\) 0 0
\(439\) −30.7279 −1.46656 −0.733282 0.679925i \(-0.762012\pi\)
−0.733282 + 0.679925i \(0.762012\pi\)
\(440\) 0 0
\(441\) 19.3137 0.919700
\(442\) 0 0
\(443\) 15.5563i 0.739104i −0.929210 0.369552i \(-0.879511\pi\)
0.929210 0.369552i \(-0.120489\pi\)
\(444\) 0 0
\(445\) −25.9706 + 8.65685i −1.23112 + 0.410374i
\(446\) 0 0
\(447\) 2.62742i 0.124273i
\(448\) 0 0
\(449\) 35.9411 1.69617 0.848083 0.529863i \(-0.177757\pi\)
0.848083 + 0.529863i \(0.177757\pi\)
\(450\) 0 0
\(451\) 10.0000 0.470882
\(452\) 0 0
\(453\) 6.97056i 0.327506i
\(454\) 0 0
\(455\) −3.36396 + 1.12132i −0.157705 + 0.0525683i
\(456\) 0 0
\(457\) 16.3137i 0.763123i −0.924343 0.381562i \(-0.875386\pi\)
0.924343 0.381562i \(-0.124614\pi\)
\(458\) 0 0
\(459\) 2.41421 0.112686
\(460\) 0 0
\(461\) −7.27208 −0.338694 −0.169347 0.985556i \(-0.554166\pi\)
−0.169347 + 0.985556i \(0.554166\pi\)
\(462\) 0 0
\(463\) 22.1421i 1.02903i −0.857481 0.514516i \(-0.827972\pi\)
0.857481 0.514516i \(-0.172028\pi\)
\(464\) 0 0
\(465\) 0.171573 + 0.514719i 0.00795650 + 0.0238695i
\(466\) 0 0
\(467\) 21.8995i 1.01339i −0.862126 0.506694i \(-0.830867\pi\)
0.862126 0.506694i \(-0.169133\pi\)
\(468\) 0 0
\(469\) −3.34315 −0.154372
\(470\) 0 0
\(471\) 4.82843 0.222482
\(472\) 0 0
\(473\) 8.82843i 0.405932i
\(474\) 0 0
\(475\) −4.00000 + 3.00000i −0.183533 + 0.137649i
\(476\) 0 0
\(477\) 10.8284i 0.495800i
\(478\) 0 0
\(479\) 33.4558 1.52864 0.764318 0.644839i \(-0.223076\pi\)
0.764318 + 0.644839i \(0.223076\pi\)
\(480\) 0 0
\(481\) −41.4558 −1.89022
\(482\) 0 0
\(483\) 0.556349i 0.0253148i
\(484\) 0 0
\(485\) −2.58579 7.75736i −0.117415 0.352244i
\(486\) 0 0
\(487\) 7.17157i 0.324975i 0.986711 + 0.162487i \(0.0519517\pi\)
−0.986711 + 0.162487i \(0.948048\pi\)
\(488\) 0 0
\(489\) 7.07107 0.319765
\(490\) 0 0
\(491\) −17.7574 −0.801378 −0.400689 0.916214i \(-0.631229\pi\)
−0.400689 + 0.916214i \(0.631229\pi\)
\(492\) 0 0
\(493\) 1.82843i 0.0823482i
\(494\) 0 0
\(495\) −8.48528 + 2.82843i −0.381385 + 0.127128i
\(496\) 0 0
\(497\) 4.58579i 0.205701i
\(498\) 0 0
\(499\) 18.9289 0.847375 0.423688 0.905808i \(-0.360735\pi\)
0.423688 + 0.905808i \(0.360735\pi\)
\(500\) 0 0
\(501\) 7.95837 0.355554
\(502\) 0 0
\(503\) 32.8995i 1.46692i −0.679735 0.733458i \(-0.737905\pi\)
0.679735 0.733458i \(-0.262095\pi\)
\(504\) 0 0
\(505\) 8.27208 2.75736i 0.368103 0.122701i
\(506\) 0 0
\(507\) 0.686292i 0.0304793i
\(508\) 0 0
\(509\) −9.65685 −0.428033 −0.214016 0.976830i \(-0.568655\pi\)
−0.214016 + 0.976830i \(0.568655\pi\)
\(510\) 0 0
\(511\) −3.38478 −0.149734
\(512\) 0 0
\(513\) 2.41421i 0.106590i
\(514\) 0 0
\(515\) 7.00000 + 21.0000i 0.308457 + 0.925371i
\(516\) 0 0
\(517\) 11.3137i 0.497576i
\(518\) 0 0
\(519\) −5.45584 −0.239485
\(520\) 0 0
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 0 0
\(523\) 20.2132i 0.883862i 0.897049 + 0.441931i \(0.145706\pi\)
−0.897049 + 0.441931i \(0.854294\pi\)
\(524\) 0 0
\(525\) −0.686292 + 0.514719i −0.0299522 + 0.0224642i
\(526\) 0 0
\(527\) 0.585786i 0.0255173i
\(528\) 0 0
\(529\) 12.4853 0.542838
\(530\) 0 0
\(531\) 32.7696 1.42208
\(532\) 0 0
\(533\) 27.0711i 1.17258i
\(534\) 0 0
\(535\) −0.292893 0.878680i −0.0126629 0.0379886i
\(536\) 0 0
\(537\) 4.54416i 0.196095i
\(538\) 0 0
\(539\) 9.65685 0.415950
\(540\) 0 0
\(541\) 30.0416 1.29159 0.645795 0.763511i \(-0.276526\pi\)
0.645795 + 0.763511i \(0.276526\pi\)
\(542\) 0 0
\(543\) 6.82843i 0.293036i
\(544\) 0 0
\(545\) −10.6066 + 3.53553i −0.454337 + 0.151446i
\(546\) 0 0
\(547\) 23.9411i 1.02365i −0.859090 0.511824i \(-0.828970\pi\)
0.859090 0.511824i \(-0.171030\pi\)
\(548\) 0 0
\(549\) 1.65685 0.0707128
\(550\) 0 0
\(551\) −1.82843 −0.0778936
\(552\) 0 0
\(553\) 2.00000i 0.0850487i
\(554\) 0 0
\(555\) −9.51472 + 3.17157i −0.403877 + 0.134626i
\(556\) 0 0
\(557\) 43.3137i 1.83526i 0.397435 + 0.917630i \(0.369900\pi\)
−0.397435 + 0.917630i \(0.630100\pi\)
\(558\) 0 0
\(559\) 23.8995 1.01084
\(560\) 0 0
\(561\) 0.585786 0.0247319
\(562\) 0 0
\(563\) 44.9706i 1.89528i 0.319336 + 0.947642i \(0.396540\pi\)
−0.319336 + 0.947642i \(0.603460\pi\)
\(564\) 0 0
\(565\) −0.757359 2.27208i −0.0318623 0.0955870i
\(566\) 0 0
\(567\) 3.10051i 0.130209i
\(568\) 0 0
\(569\) 8.97056 0.376066 0.188033 0.982163i \(-0.439789\pi\)
0.188033 + 0.982163i \(0.439789\pi\)
\(570\) 0 0
\(571\) −47.6985 −1.99612 −0.998060 0.0622637i \(-0.980168\pi\)
−0.998060 + 0.0622637i \(0.980168\pi\)
\(572\) 0 0
\(573\) 1.14214i 0.0477134i
\(574\) 0 0
\(575\) 9.72792 + 12.9706i 0.405682 + 0.540910i
\(576\) 0 0
\(577\) 25.0000i 1.04076i 0.853934 + 0.520382i \(0.174210\pi\)
−0.853934 + 0.520382i \(0.825790\pi\)
\(578\) 0 0
\(579\) 1.51472 0.0629496
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) 0 0
\(583\) 5.41421i 0.224234i
\(584\) 0 0
\(585\) 7.65685 + 22.9706i 0.316572 + 0.949716i
\(586\) 0 0
\(587\) 32.3848i 1.33666i −0.743864 0.668331i \(-0.767009\pi\)
0.743864 0.668331i \(-0.232991\pi\)
\(588\) 0 0
\(589\) 0.585786 0.0241369
\(590\) 0 0
\(591\) −1.95837 −0.0805566
\(592\) 0 0
\(593\) 42.0000i 1.72473i −0.506284 0.862367i \(-0.668981\pi\)
0.506284 0.862367i \(-0.331019\pi\)
\(594\) 0 0
\(595\) −0.878680 + 0.292893i −0.0360224 + 0.0120075i
\(596\) 0 0
\(597\) 0.798990i 0.0327005i
\(598\) 0 0
\(599\) −33.5563 −1.37108 −0.685538 0.728037i \(-0.740433\pi\)
−0.685538 + 0.728037i \(0.740433\pi\)
\(600\) 0 0
\(601\) 0.443651 0.0180969 0.00904845 0.999959i \(-0.497120\pi\)
0.00904845 + 0.999959i \(0.497120\pi\)
\(602\) 0 0
\(603\) 22.8284i 0.929645i
\(604\) 0 0
\(605\) 19.0919 6.36396i 0.776195 0.258732i
\(606\) 0 0
\(607\) 30.4853i 1.23736i 0.785643 + 0.618680i \(0.212332\pi\)
−0.785643 + 0.618680i \(0.787668\pi\)
\(608\) 0 0
\(609\) −0.313708 −0.0127121
\(610\) 0 0
\(611\) 30.6274 1.23905
\(612\) 0 0
\(613\) 2.72792i 0.110180i −0.998481 0.0550899i \(-0.982455\pi\)
0.998481 0.0550899i \(-0.0175445\pi\)
\(614\) 0 0
\(615\) −2.07107 6.21320i −0.0835135 0.250541i
\(616\) 0 0
\(617\) 31.7990i 1.28018i 0.768300 + 0.640090i \(0.221103\pi\)
−0.768300 + 0.640090i \(0.778897\pi\)
\(618\) 0 0
\(619\) 6.38478 0.256626 0.128313 0.991734i \(-0.459044\pi\)
0.128313 + 0.991734i \(0.459044\pi\)
\(620\) 0 0
\(621\) −7.82843 −0.314144
\(622\) 0 0
\(623\) 5.07107i 0.203168i
\(624\) 0 0
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 0 0
\(627\) 0.585786i 0.0233941i
\(628\) 0 0
\(629\) −10.8284 −0.431758
\(630\) 0 0
\(631\) 5.02944 0.200219 0.100109 0.994976i \(-0.468081\pi\)
0.100109 + 0.994976i \(0.468081\pi\)
\(632\) 0 0
\(633\) 2.11270i 0.0839722i
\(634\) 0 0
\(635\) −11.8995 35.6985i −0.472217 1.41665i
\(636\) 0 0
\(637\) 26.1421i 1.03579i
\(638\) 0 0
\(639\) 31.3137 1.23875
\(640\) 0 0
\(641\) 3.21320 0.126914 0.0634570 0.997985i \(-0.479787\pi\)
0.0634570 + 0.997985i \(0.479787\pi\)
\(642\) 0 0
\(643\) 36.8284i 1.45237i −0.687499 0.726186i \(-0.741291\pi\)
0.687499 0.726186i \(-0.258709\pi\)
\(644\) 0 0
\(645\) 5.48528 1.82843i 0.215983 0.0719942i
\(646\) 0 0
\(647\) 2.07107i 0.0814221i −0.999171 0.0407110i \(-0.987038\pi\)
0.999171 0.0407110i \(-0.0129623\pi\)
\(648\) 0 0
\(649\) 16.3848 0.643159
\(650\) 0 0
\(651\) 0.100505 0.00393910
\(652\) 0 0
\(653\) 24.2843i 0.950317i 0.879900 + 0.475158i \(0.157609\pi\)
−0.879900 + 0.475158i \(0.842391\pi\)
\(654\) 0 0
\(655\) 21.9411 7.31371i 0.857311 0.285770i
\(656\) 0 0
\(657\) 23.1127i 0.901712i
\(658\) 0 0
\(659\) 10.8995 0.424584 0.212292 0.977206i \(-0.431907\pi\)
0.212292 + 0.977206i \(0.431907\pi\)
\(660\) 0 0
\(661\) 26.5147 1.03130 0.515652 0.856798i \(-0.327550\pi\)
0.515652 + 0.856798i \(0.327550\pi\)
\(662\) 0 0
\(663\) 1.58579i 0.0615868i
\(664\) 0 0
\(665\) 0.292893 + 0.878680i 0.0113579 + 0.0340737i
\(666\) 0 0
\(667\) 5.92893i 0.229569i
\(668\) 0 0
\(669\) 3.65685 0.141382
\(670\) 0 0
\(671\) 0.828427 0.0319811
\(672\) 0 0
\(673\) 28.0000i 1.07932i 0.841883 + 0.539660i \(0.181447\pi\)
−0.841883 + 0.539660i \(0.818553\pi\)
\(674\) 0 0
\(675\) 7.24264 + 9.65685i 0.278769 + 0.371692i
\(676\) 0 0
\(677\) 32.6569i 1.25510i 0.778574 + 0.627552i \(0.215943\pi\)
−0.778574 + 0.627552i \(0.784057\pi\)
\(678\) 0 0
\(679\) −1.51472 −0.0581296
\(680\) 0 0
\(681\) 3.62742 0.139003
\(682\) 0 0
\(683\) 0.686292i 0.0262602i −0.999914 0.0131301i \(-0.995820\pi\)
0.999914 0.0131301i \(-0.00417956\pi\)
\(684\) 0 0
\(685\) −4.46447 13.3934i −0.170578 0.511735i
\(686\) 0 0
\(687\) 2.88730i 0.110157i
\(688\) 0 0
\(689\) 14.6569 0.558382
\(690\) 0 0
\(691\) 43.4558 1.65314 0.826569 0.562835i \(-0.190289\pi\)
0.826569 + 0.562835i \(0.190289\pi\)
\(692\) 0 0
\(693\) 1.65685i 0.0629387i
\(694\) 0 0
\(695\) 8.48528 2.82843i 0.321865 0.107288i
\(696\) 0 0
\(697\) 7.07107i 0.267836i
\(698\) 0 0
\(699\) 5.65685 0.213962
\(700\) 0 0
\(701\) −0.970563 −0.0366576 −0.0183288 0.999832i \(-0.505835\pi\)
−0.0183288 + 0.999832i \(0.505835\pi\)
\(702\) 0 0
\(703\) 10.8284i 0.408402i
\(704\) 0 0
\(705\) 7.02944 2.34315i 0.264744 0.0882480i
\(706\) 0 0
\(707\) 1.61522i 0.0607467i
\(708\) 0 0
\(709\) −33.3137 −1.25112 −0.625561 0.780175i \(-0.715130\pi\)
−0.625561 + 0.780175i \(0.715130\pi\)
\(710\) 0 0
\(711\) 13.6569 0.512172
\(712\) 0 0
\(713\) 1.89949i 0.0711366i
\(714\) 0 0
\(715\) 3.82843 + 11.4853i 0.143175 + 0.429525i
\(716\) 0 0
\(717\) 11.4853i 0.428926i
\(718\) 0 0
\(719\) 27.5858 1.02878 0.514388 0.857557i \(-0.328019\pi\)
0.514388 + 0.857557i \(0.328019\pi\)
\(720\) 0 0
\(721\) 4.10051 0.152711
\(722\) 0 0
\(723\) 2.34315i 0.0871425i
\(724\) 0 0
\(725\) 7.31371 5.48528i 0.271624 0.203718i
\(726\) 0 0
\(727\) 44.2132i 1.63978i −0.572523 0.819888i \(-0.694035\pi\)
0.572523 0.819888i \(-0.305965\pi\)
\(728\) 0 0
\(729\) 18.1716 0.673021
\(730\) 0 0
\(731\) 6.24264 0.230892
\(732\) 0 0
\(733\) 34.6274i 1.27899i 0.768794 + 0.639496i \(0.220857\pi\)
−0.768794 + 0.639496i \(0.779143\pi\)
\(734\) 0 0
\(735\) −2.00000 6.00000i −0.0737711 0.221313i
\(736\) 0 0
\(737\) 11.4142i 0.420448i
\(738\) 0 0
\(739\) 4.58579 0.168691 0.0843454 0.996437i \(-0.473120\pi\)
0.0843454 + 0.996437i \(0.473120\pi\)
\(740\) 0 0
\(741\) −1.58579 −0.0582553
\(742\) 0 0
\(743\) 5.75736i 0.211217i −0.994408 0.105609i \(-0.966321\pi\)
0.994408 0.105609i \(-0.0336790\pi\)
\(744\) 0 0
\(745\) −13.4558 + 4.48528i −0.492984 + 0.164328i
\(746\) 0 0
\(747\) 40.9706i 1.49903i
\(748\) 0 0
\(749\) −0.171573 −0.00626914
\(750\) 0 0
\(751\) −38.2426 −1.39549 −0.697747 0.716344i \(-0.745814\pi\)
−0.697747 + 0.716344i \(0.745814\pi\)
\(752\) 0 0
\(753\) 1.47309i 0.0536823i
\(754\) 0 0
\(755\) 35.6985 11.8995i 1.29920 0.433067i
\(756\) 0 0
\(757\) 27.6569i 1.00521i 0.864517 + 0.502603i \(0.167624\pi\)
−0.864517 + 0.502603i \(0.832376\pi\)
\(758\) 0 0
\(759\) −1.89949 −0.0689473
\(760\) 0 0
\(761\) −37.9706 −1.37643 −0.688216 0.725506i \(-0.741606\pi\)
−0.688216 + 0.725506i \(0.741606\pi\)
\(762\) 0 0
\(763\) 2.07107i 0.0749777i
\(764\) 0 0
\(765\) 2.00000 + 6.00000i 0.0723102 + 0.216930i
\(766\) 0 0
\(767\) 44.3553i 1.60158i
\(768\) 0 0
\(769\) −8.79899 −0.317300 −0.158650 0.987335i \(-0.550714\pi\)
−0.158650 + 0.987335i \(0.550714\pi\)
\(770\) 0 0
\(771\) 11.8995 0.428550
\(772\) 0 0
\(773\) 9.00000i 0.323708i 0.986815 + 0.161854i \(0.0517473\pi\)
−0.986815 + 0.161854i \(0.948253\pi\)
\(774\) 0 0
\(775\) −2.34315 + 1.75736i −0.0841683 + 0.0631262i
\(776\) 0 0
\(777\) 1.85786i 0.0666505i
\(778\) 0 0
\(779\) −7.07107 −0.253347
\(780\) 0 0
\(781\) 15.6569 0.560246
\(782\) 0 0
\(783\) 4.41421i 0.157751i
\(784\) 0 0
\(785\) 8.24264 + 24.7279i 0.294192 + 0.882577i
\(786\) 0 0
\(787\) 31.2426i 1.11368i −0.830620 0.556840i \(-0.812014\pi\)
0.830620 0.556840i \(-0.187986\pi\)
\(788\) 0 0
\(789\) −6.48528 −0.230882
\(790\) 0 0
\(791\) −0.443651 −0.0157744
\(792\) 0 0
\(793\) 2.24264i 0.0796385i
\(794\) 0 0
\(795\) 3.36396 1.12132i 0.119307 0.0397691i
\(796\) 0 0
\(797\) 6.85786i 0.242918i −0.992596 0.121459i \(-0.961243\pi\)
0.992596 0.121459i \(-0.0387573\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 34.6274 1.22350
\(802\) 0 0
\(803\) 11.5563i