Properties

Label 1840.2.e.f.369.12
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 24 x^{10} + 188 x^{8} + 530 x^{6} + 508 x^{4} + 80 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 460)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.12
Root \(-3.16223i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.21923i q^{3} +(1.59013 + 1.57210i) q^{5} +2.43185i q^{7} -7.36343 q^{9} +O(q^{10})\) \(q+3.21923i q^{3} +(1.59013 + 1.57210i) q^{5} +2.43185i q^{7} -7.36343 q^{9} +0.884969 q^{11} -5.10522i q^{13} +(-5.06095 + 5.11898i) q^{15} +0.366626i q^{17} -2.79847 q^{19} -7.82867 q^{21} +1.00000i q^{23} +(0.0570016 + 4.99968i) q^{25} -14.0469i q^{27} -8.02431 q^{29} -7.24179 q^{31} +2.84892i q^{33} +(-3.82311 + 3.86694i) q^{35} -3.10036i q^{37} +16.4349 q^{39} -3.47185 q^{41} +8.56841i q^{43} +(-11.7088 - 11.5760i) q^{45} -5.25528i q^{47} +1.08612 q^{49} -1.18025 q^{51} +11.6413i q^{53} +(1.40721 + 1.39126i) q^{55} -9.00892i q^{57} -9.33209 q^{59} +5.46699 q^{61} -17.9067i q^{63} +(8.02592 - 8.11795i) q^{65} -1.49020i q^{67} -3.21923 q^{69} -8.29949 q^{71} +10.2409i q^{73} +(-16.0951 + 0.183501i) q^{75} +2.15211i q^{77} +6.06522 q^{79} +23.1298 q^{81} +16.2520i q^{83} +(-0.576373 + 0.582981i) q^{85} -25.8321i q^{87} +17.6033 q^{89} +12.4151 q^{91} -23.3130i q^{93} +(-4.44992 - 4.39948i) q^{95} -6.55618i q^{97} -6.51641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 20 q^{9} + O(q^{10}) \) \( 12 q - 20 q^{9} - 4 q^{11} - 2 q^{15} + 8 q^{19} + 8 q^{25} - 10 q^{29} - 18 q^{31} + 10 q^{35} - 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} + 24 q^{51} - 16 q^{55} - 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} + 34 q^{71} - 16 q^{75} + 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} + 8 q^{91} - 12 q^{95} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 3.21923i 1.85862i 0.369298 + 0.929311i \(0.379598\pi\)
−0.369298 + 0.929311i \(0.620402\pi\)
\(4\) 0 0
\(5\) 1.59013 + 1.57210i 0.711126 + 0.703065i
\(6\) 0 0
\(7\) 2.43185i 0.919152i 0.888138 + 0.459576i \(0.151999\pi\)
−0.888138 + 0.459576i \(0.848001\pi\)
\(8\) 0 0
\(9\) −7.36343 −2.45448
\(10\) 0 0
\(11\) 0.884969 0.266828 0.133414 0.991060i \(-0.457406\pi\)
0.133414 + 0.991060i \(0.457406\pi\)
\(12\) 0 0
\(13\) 5.10522i 1.41593i −0.706245 0.707967i \(-0.749612\pi\)
0.706245 0.707967i \(-0.250388\pi\)
\(14\) 0 0
\(15\) −5.06095 + 5.11898i −1.30673 + 1.32171i
\(16\) 0 0
\(17\) 0.366626i 0.0889198i 0.999011 + 0.0444599i \(0.0141567\pi\)
−0.999011 + 0.0444599i \(0.985843\pi\)
\(18\) 0 0
\(19\) −2.79847 −0.642014 −0.321007 0.947077i \(-0.604021\pi\)
−0.321007 + 0.947077i \(0.604021\pi\)
\(20\) 0 0
\(21\) −7.82867 −1.70836
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 0.0570016 + 4.99968i 0.0114003 + 0.999935i
\(26\) 0 0
\(27\) 14.0469i 2.70332i
\(28\) 0 0
\(29\) −8.02431 −1.49008 −0.745038 0.667022i \(-0.767569\pi\)
−0.745038 + 0.667022i \(0.767569\pi\)
\(30\) 0 0
\(31\) −7.24179 −1.30066 −0.650332 0.759650i \(-0.725370\pi\)
−0.650332 + 0.759650i \(0.725370\pi\)
\(32\) 0 0
\(33\) 2.84892i 0.495933i
\(34\) 0 0
\(35\) −3.82311 + 3.86694i −0.646223 + 0.653633i
\(36\) 0 0
\(37\) 3.10036i 0.509697i −0.966981 0.254848i \(-0.917974\pi\)
0.966981 0.254848i \(-0.0820256\pi\)
\(38\) 0 0
\(39\) 16.4349 2.63169
\(40\) 0 0
\(41\) −3.47185 −0.542212 −0.271106 0.962550i \(-0.587389\pi\)
−0.271106 + 0.962550i \(0.587389\pi\)
\(42\) 0 0
\(43\) 8.56841i 1.30667i 0.757069 + 0.653335i \(0.226631\pi\)
−0.757069 + 0.653335i \(0.773369\pi\)
\(44\) 0 0
\(45\) −11.7088 11.5760i −1.74544 1.72566i
\(46\) 0 0
\(47\) 5.25528i 0.766561i −0.923632 0.383281i \(-0.874794\pi\)
0.923632 0.383281i \(-0.125206\pi\)
\(48\) 0 0
\(49\) 1.08612 0.155160
\(50\) 0 0
\(51\) −1.18025 −0.165268
\(52\) 0 0
\(53\) 11.6413i 1.59905i 0.600632 + 0.799526i \(0.294916\pi\)
−0.600632 + 0.799526i \(0.705084\pi\)
\(54\) 0 0
\(55\) 1.40721 + 1.39126i 0.189749 + 0.187598i
\(56\) 0 0
\(57\) 9.00892i 1.19326i
\(58\) 0 0
\(59\) −9.33209 −1.21493 −0.607467 0.794345i \(-0.707814\pi\)
−0.607467 + 0.794345i \(0.707814\pi\)
\(60\) 0 0
\(61\) 5.46699 0.699976 0.349988 0.936754i \(-0.386186\pi\)
0.349988 + 0.936754i \(0.386186\pi\)
\(62\) 0 0
\(63\) 17.9067i 2.25604i
\(64\) 0 0
\(65\) 8.02592 8.11795i 0.995493 1.00691i
\(66\) 0 0
\(67\) 1.49020i 0.182057i −0.995848 0.0910285i \(-0.970985\pi\)
0.995848 0.0910285i \(-0.0290154\pi\)
\(68\) 0 0
\(69\) −3.21923 −0.387549
\(70\) 0 0
\(71\) −8.29949 −0.984969 −0.492484 0.870321i \(-0.663911\pi\)
−0.492484 + 0.870321i \(0.663911\pi\)
\(72\) 0 0
\(73\) 10.2409i 1.19860i 0.800523 + 0.599302i \(0.204555\pi\)
−0.800523 + 0.599302i \(0.795445\pi\)
\(74\) 0 0
\(75\) −16.0951 + 0.183501i −1.85850 + 0.0211889i
\(76\) 0 0
\(77\) 2.15211i 0.245256i
\(78\) 0 0
\(79\) 6.06522 0.682391 0.341195 0.939992i \(-0.389168\pi\)
0.341195 + 0.939992i \(0.389168\pi\)
\(80\) 0 0
\(81\) 23.1298 2.56998
\(82\) 0 0
\(83\) 16.2520i 1.78389i 0.452148 + 0.891943i \(0.350658\pi\)
−0.452148 + 0.891943i \(0.649342\pi\)
\(84\) 0 0
\(85\) −0.576373 + 0.582981i −0.0625164 + 0.0632332i
\(86\) 0 0
\(87\) 25.8321i 2.76949i
\(88\) 0 0
\(89\) 17.6033 1.86594 0.932972 0.359949i \(-0.117206\pi\)
0.932972 + 0.359949i \(0.117206\pi\)
\(90\) 0 0
\(91\) 12.4151 1.30146
\(92\) 0 0
\(93\) 23.3130i 2.41744i
\(94\) 0 0
\(95\) −4.44992 4.39948i −0.456553 0.451377i
\(96\) 0 0
\(97\) 6.55618i 0.665679i −0.942984 0.332839i \(-0.891993\pi\)
0.942984 0.332839i \(-0.108007\pi\)
\(98\) 0 0
\(99\) −6.51641 −0.654924
\(100\) 0 0
\(101\) 13.4912 1.34243 0.671213 0.741265i \(-0.265774\pi\)
0.671213 + 0.741265i \(0.265774\pi\)
\(102\) 0 0
\(103\) 12.5460i 1.23619i 0.786103 + 0.618096i \(0.212096\pi\)
−0.786103 + 0.618096i \(0.787904\pi\)
\(104\) 0 0
\(105\) −12.4486 12.3075i −1.21486 1.20108i
\(106\) 0 0
\(107\) 1.46269i 0.141404i −0.997497 0.0707020i \(-0.977476\pi\)
0.997497 0.0707020i \(-0.0225239\pi\)
\(108\) 0 0
\(109\) 19.2173 1.84069 0.920343 0.391113i \(-0.127910\pi\)
0.920343 + 0.391113i \(0.127910\pi\)
\(110\) 0 0
\(111\) 9.98078 0.947334
\(112\) 0 0
\(113\) 0.834901i 0.0785409i 0.999229 + 0.0392705i \(0.0125034\pi\)
−0.999229 + 0.0392705i \(0.987497\pi\)
\(114\) 0 0
\(115\) −1.57210 + 1.59013i −0.146599 + 0.148280i
\(116\) 0 0
\(117\) 37.5920i 3.47538i
\(118\) 0 0
\(119\) −0.891578 −0.0817308
\(120\) 0 0
\(121\) −10.2168 −0.928803
\(122\) 0 0
\(123\) 11.1767i 1.00777i
\(124\) 0 0
\(125\) −7.76935 + 8.03973i −0.694912 + 0.719095i
\(126\) 0 0
\(127\) 7.87453i 0.698751i −0.936983 0.349376i \(-0.886394\pi\)
0.936983 0.349376i \(-0.113606\pi\)
\(128\) 0 0
\(129\) −27.5837 −2.42861
\(130\) 0 0
\(131\) 12.8740 1.12481 0.562403 0.826863i \(-0.309877\pi\)
0.562403 + 0.826863i \(0.309877\pi\)
\(132\) 0 0
\(133\) 6.80546i 0.590108i
\(134\) 0 0
\(135\) 22.0831 22.3363i 1.90061 1.92240i
\(136\) 0 0
\(137\) 3.26675i 0.279097i 0.990215 + 0.139549i \(0.0445651\pi\)
−0.990215 + 0.139549i \(0.955435\pi\)
\(138\) 0 0
\(139\) −12.5578 −1.06514 −0.532570 0.846386i \(-0.678774\pi\)
−0.532570 + 0.846386i \(0.678774\pi\)
\(140\) 0 0
\(141\) 16.9179 1.42475
\(142\) 0 0
\(143\) 4.51797i 0.377811i
\(144\) 0 0
\(145\) −12.7597 12.6150i −1.05963 1.04762i
\(146\) 0 0
\(147\) 3.49647i 0.288384i
\(148\) 0 0
\(149\) 0.188265 0.0154233 0.00771164 0.999970i \(-0.497545\pi\)
0.00771164 + 0.999970i \(0.497545\pi\)
\(150\) 0 0
\(151\) 18.6708 1.51941 0.759704 0.650269i \(-0.225344\pi\)
0.759704 + 0.650269i \(0.225344\pi\)
\(152\) 0 0
\(153\) 2.69962i 0.218252i
\(154\) 0 0
\(155\) −11.5154 11.3848i −0.924936 0.914451i
\(156\) 0 0
\(157\) 20.0277i 1.59839i 0.601074 + 0.799193i \(0.294740\pi\)
−0.601074 + 0.799193i \(0.705260\pi\)
\(158\) 0 0
\(159\) −37.4759 −2.97203
\(160\) 0 0
\(161\) −2.43185 −0.191656
\(162\) 0 0
\(163\) 3.35607i 0.262867i 0.991325 + 0.131434i \(0.0419580\pi\)
−0.991325 + 0.131434i \(0.958042\pi\)
\(164\) 0 0
\(165\) −4.47878 + 4.53014i −0.348673 + 0.352671i
\(166\) 0 0
\(167\) 2.57745i 0.199449i 0.995015 + 0.0997246i \(0.0317962\pi\)
−0.995015 + 0.0997246i \(0.968204\pi\)
\(168\) 0 0
\(169\) −13.0633 −1.00487
\(170\) 0 0
\(171\) 20.6064 1.57581
\(172\) 0 0
\(173\) 19.4182i 1.47634i 0.674615 + 0.738170i \(0.264310\pi\)
−0.674615 + 0.738170i \(0.735690\pi\)
\(174\) 0 0
\(175\) −12.1584 + 0.138619i −0.919092 + 0.0104786i
\(176\) 0 0
\(177\) 30.0421i 2.25810i
\(178\) 0 0
\(179\) −20.3628 −1.52199 −0.760993 0.648760i \(-0.775288\pi\)
−0.760993 + 0.648760i \(0.775288\pi\)
\(180\) 0 0
\(181\) −22.5629 −1.67709 −0.838543 0.544835i \(-0.816592\pi\)
−0.838543 + 0.544835i \(0.816592\pi\)
\(182\) 0 0
\(183\) 17.5995i 1.30099i
\(184\) 0 0
\(185\) 4.87408 4.92997i 0.358350 0.362459i
\(186\) 0 0
\(187\) 0.324453i 0.0237263i
\(188\) 0 0
\(189\) 34.1598 2.48476
\(190\) 0 0
\(191\) 16.6554 1.20514 0.602571 0.798065i \(-0.294143\pi\)
0.602571 + 0.798065i \(0.294143\pi\)
\(192\) 0 0
\(193\) 14.5214i 1.04527i −0.852556 0.522636i \(-0.824949\pi\)
0.852556 0.522636i \(-0.175051\pi\)
\(194\) 0 0
\(195\) 26.1335 + 25.8373i 1.87146 + 1.85025i
\(196\) 0 0
\(197\) 13.3479i 0.950995i −0.879717 0.475498i \(-0.842268\pi\)
0.879717 0.475498i \(-0.157732\pi\)
\(198\) 0 0
\(199\) 18.7856 1.33168 0.665838 0.746097i \(-0.268074\pi\)
0.665838 + 0.746097i \(0.268074\pi\)
\(200\) 0 0
\(201\) 4.79730 0.338375
\(202\) 0 0
\(203\) 19.5139i 1.36961i
\(204\) 0 0
\(205\) −5.52068 5.45810i −0.385581 0.381210i
\(206\) 0 0
\(207\) 7.36343i 0.511794i
\(208\) 0 0
\(209\) −2.47656 −0.171307
\(210\) 0 0
\(211\) −17.1078 −1.17775 −0.588874 0.808225i \(-0.700429\pi\)
−0.588874 + 0.808225i \(0.700429\pi\)
\(212\) 0 0
\(213\) 26.7180i 1.83068i
\(214\) 0 0
\(215\) −13.4704 + 13.6249i −0.918674 + 0.929207i
\(216\) 0 0
\(217\) 17.6109i 1.19551i
\(218\) 0 0
\(219\) −32.9677 −2.22775
\(220\) 0 0
\(221\) 1.87171 0.125905
\(222\) 0 0
\(223\) 13.5184i 0.905262i −0.891698 0.452631i \(-0.850485\pi\)
0.891698 0.452631i \(-0.149515\pi\)
\(224\) 0 0
\(225\) −0.419727 36.8147i −0.0279818 2.45432i
\(226\) 0 0
\(227\) 8.29581i 0.550612i −0.961357 0.275306i \(-0.911221\pi\)
0.961357 0.275306i \(-0.0887792\pi\)
\(228\) 0 0
\(229\) 6.22318 0.411239 0.205620 0.978632i \(-0.434079\pi\)
0.205620 + 0.978632i \(0.434079\pi\)
\(230\) 0 0
\(231\) −6.92813 −0.455838
\(232\) 0 0
\(233\) 13.6347i 0.893242i 0.894723 + 0.446621i \(0.147373\pi\)
−0.894723 + 0.446621i \(0.852627\pi\)
\(234\) 0 0
\(235\) 8.26183 8.35656i 0.538942 0.545122i
\(236\) 0 0
\(237\) 19.5253i 1.26831i
\(238\) 0 0
\(239\) 11.5281 0.745693 0.372847 0.927893i \(-0.378382\pi\)
0.372847 + 0.927893i \(0.378382\pi\)
\(240\) 0 0
\(241\) −17.5952 −1.13341 −0.566704 0.823921i \(-0.691782\pi\)
−0.566704 + 0.823921i \(0.691782\pi\)
\(242\) 0 0
\(243\) 32.3195i 2.07329i
\(244\) 0 0
\(245\) 1.72707 + 1.70749i 0.110338 + 0.109087i
\(246\) 0 0
\(247\) 14.2868i 0.909049i
\(248\) 0 0
\(249\) −52.3188 −3.31557
\(250\) 0 0
\(251\) −12.5471 −0.791968 −0.395984 0.918257i \(-0.629596\pi\)
−0.395984 + 0.918257i \(0.629596\pi\)
\(252\) 0 0
\(253\) 0.884969i 0.0556375i
\(254\) 0 0
\(255\) −1.87675 1.85547i −0.117527 0.116194i
\(256\) 0 0
\(257\) 4.88072i 0.304451i 0.988346 + 0.152225i \(0.0486439\pi\)
−0.988346 + 0.152225i \(0.951356\pi\)
\(258\) 0 0
\(259\) 7.53961 0.468489
\(260\) 0 0
\(261\) 59.0864 3.65736
\(262\) 0 0
\(263\) 11.6045i 0.715566i −0.933805 0.357783i \(-0.883533\pi\)
0.933805 0.357783i \(-0.116467\pi\)
\(264\) 0 0
\(265\) −18.3012 + 18.5111i −1.12424 + 1.13713i
\(266\) 0 0
\(267\) 56.6690i 3.46808i
\(268\) 0 0
\(269\) 6.04327 0.368465 0.184232 0.982883i \(-0.441020\pi\)
0.184232 + 0.982883i \(0.441020\pi\)
\(270\) 0 0
\(271\) −3.93401 −0.238974 −0.119487 0.992836i \(-0.538125\pi\)
−0.119487 + 0.992836i \(0.538125\pi\)
\(272\) 0 0
\(273\) 39.9671i 2.41892i
\(274\) 0 0
\(275\) 0.0504447 + 4.42456i 0.00304193 + 0.266811i
\(276\) 0 0
\(277\) 7.92174i 0.475971i 0.971269 + 0.237986i \(0.0764871\pi\)
−0.971269 + 0.237986i \(0.923513\pi\)
\(278\) 0 0
\(279\) 53.3244 3.19245
\(280\) 0 0
\(281\) −6.00419 −0.358180 −0.179090 0.983833i \(-0.557315\pi\)
−0.179090 + 0.983833i \(0.557315\pi\)
\(282\) 0 0
\(283\) 7.65299i 0.454923i 0.973787 + 0.227461i \(0.0730426\pi\)
−0.973787 + 0.227461i \(0.926957\pi\)
\(284\) 0 0
\(285\) 14.1629 14.3253i 0.838940 0.848559i
\(286\) 0 0
\(287\) 8.44301i 0.498375i
\(288\) 0 0
\(289\) 16.8656 0.992093
\(290\) 0 0
\(291\) 21.1058 1.23725
\(292\) 0 0
\(293\) 13.5480i 0.791485i 0.918361 + 0.395743i \(0.129513\pi\)
−0.918361 + 0.395743i \(0.870487\pi\)
\(294\) 0 0
\(295\) −14.8392 14.6710i −0.863971 0.854177i
\(296\) 0 0
\(297\) 12.4310i 0.721323i
\(298\) 0 0
\(299\) 5.10522 0.295243
\(300\) 0 0
\(301\) −20.8371 −1.20103
\(302\) 0 0
\(303\) 43.4313i 2.49506i
\(304\) 0 0
\(305\) 8.69320 + 8.59466i 0.497771 + 0.492129i
\(306\) 0 0
\(307\) 10.0870i 0.575697i −0.957676 0.287848i \(-0.907060\pi\)
0.957676 0.287848i \(-0.0929399\pi\)
\(308\) 0 0
\(309\) −40.3883 −2.29761
\(310\) 0 0
\(311\) 28.2481 1.60180 0.800902 0.598795i \(-0.204354\pi\)
0.800902 + 0.598795i \(0.204354\pi\)
\(312\) 0 0
\(313\) 14.4504i 0.816786i 0.912806 + 0.408393i \(0.133911\pi\)
−0.912806 + 0.408393i \(0.866089\pi\)
\(314\) 0 0
\(315\) 28.1512 28.4740i 1.58614 1.60433i
\(316\) 0 0
\(317\) 14.7835i 0.830324i 0.909748 + 0.415162i \(0.136275\pi\)
−0.909748 + 0.415162i \(0.863725\pi\)
\(318\) 0 0
\(319\) −7.10127 −0.397595
\(320\) 0 0
\(321\) 4.70875 0.262817
\(322\) 0 0
\(323\) 1.02599i 0.0570877i
\(324\) 0 0
\(325\) 25.5245 0.291006i 1.41584 0.0161421i
\(326\) 0 0
\(327\) 61.8649i 3.42114i
\(328\) 0 0
\(329\) 12.7800 0.704586
\(330\) 0 0
\(331\) 20.1494 1.10751 0.553757 0.832679i \(-0.313194\pi\)
0.553757 + 0.832679i \(0.313194\pi\)
\(332\) 0 0
\(333\) 22.8293i 1.25104i
\(334\) 0 0
\(335\) 2.34275 2.36961i 0.127998 0.129465i
\(336\) 0 0
\(337\) 24.0660i 1.31096i 0.755214 + 0.655479i \(0.227533\pi\)
−0.755214 + 0.655479i \(0.772467\pi\)
\(338\) 0 0
\(339\) −2.68774 −0.145978
\(340\) 0 0
\(341\) −6.40876 −0.347054
\(342\) 0 0
\(343\) 19.6642i 1.06177i
\(344\) 0 0
\(345\) −5.11898 5.06095i −0.275597 0.272472i
\(346\) 0 0
\(347\) 26.3788i 1.41609i 0.706168 + 0.708045i \(0.250422\pi\)
−0.706168 + 0.708045i \(0.749578\pi\)
\(348\) 0 0
\(349\) −0.535518 −0.0286656 −0.0143328 0.999897i \(-0.504562\pi\)
−0.0143328 + 0.999897i \(0.504562\pi\)
\(350\) 0 0
\(351\) −71.7124 −3.82773
\(352\) 0 0
\(353\) 5.27606i 0.280816i 0.990094 + 0.140408i \(0.0448415\pi\)
−0.990094 + 0.140408i \(0.955159\pi\)
\(354\) 0 0
\(355\) −13.1972 13.0476i −0.700437 0.692497i
\(356\) 0 0
\(357\) 2.87019i 0.151907i
\(358\) 0 0
\(359\) 20.4351 1.07852 0.539261 0.842139i \(-0.318704\pi\)
0.539261 + 0.842139i \(0.318704\pi\)
\(360\) 0 0
\(361\) −11.1685 −0.587818
\(362\) 0 0
\(363\) 32.8903i 1.72629i
\(364\) 0 0
\(365\) −16.0997 + 16.2843i −0.842696 + 0.852359i
\(366\) 0 0
\(367\) 12.4382i 0.649268i −0.945840 0.324634i \(-0.894759\pi\)
0.945840 0.324634i \(-0.105241\pi\)
\(368\) 0 0
\(369\) 25.5647 1.33085
\(370\) 0 0
\(371\) −28.3098 −1.46977
\(372\) 0 0
\(373\) 2.99999i 0.155334i −0.996979 0.0776669i \(-0.975253\pi\)
0.996979 0.0776669i \(-0.0247471\pi\)
\(374\) 0 0
\(375\) −25.8817 25.0113i −1.33653 1.29158i
\(376\) 0 0
\(377\) 40.9659i 2.10985i
\(378\) 0 0
\(379\) −3.02165 −0.155212 −0.0776059 0.996984i \(-0.524728\pi\)
−0.0776059 + 0.996984i \(0.524728\pi\)
\(380\) 0 0
\(381\) 25.3499 1.29871
\(382\) 0 0
\(383\) 8.15719i 0.416813i 0.978042 + 0.208406i \(0.0668277\pi\)
−0.978042 + 0.208406i \(0.933172\pi\)
\(384\) 0 0
\(385\) −3.38333 + 3.42213i −0.172431 + 0.174408i
\(386\) 0 0
\(387\) 63.0929i 3.20719i
\(388\) 0 0
\(389\) −11.7789 −0.597214 −0.298607 0.954376i \(-0.596522\pi\)
−0.298607 + 0.954376i \(0.596522\pi\)
\(390\) 0 0
\(391\) −0.366626 −0.0185411
\(392\) 0 0
\(393\) 41.4443i 2.09059i
\(394\) 0 0
\(395\) 9.64447 + 9.53514i 0.485266 + 0.479765i
\(396\) 0 0
\(397\) 16.7004i 0.838167i −0.907948 0.419083i \(-0.862351\pi\)
0.907948 0.419083i \(-0.137649\pi\)
\(398\) 0 0
\(399\) 21.9083 1.09679
\(400\) 0 0
\(401\) 9.99936 0.499344 0.249672 0.968330i \(-0.419677\pi\)
0.249672 + 0.968330i \(0.419677\pi\)
\(402\) 0 0
\(403\) 36.9710i 1.84165i
\(404\) 0 0
\(405\) 36.7793 + 36.3624i 1.82758 + 1.80686i
\(406\) 0 0
\(407\) 2.74373i 0.136002i
\(408\) 0 0
\(409\) −2.20305 −0.108934 −0.0544668 0.998516i \(-0.517346\pi\)
−0.0544668 + 0.998516i \(0.517346\pi\)
\(410\) 0 0
\(411\) −10.5164 −0.518736
\(412\) 0 0
\(413\) 22.6942i 1.11671i
\(414\) 0 0
\(415\) −25.5497 + 25.8427i −1.25419 + 1.26857i
\(416\) 0 0
\(417\) 40.4264i 1.97969i
\(418\) 0 0
\(419\) 4.12814 0.201673 0.100836 0.994903i \(-0.467848\pi\)
0.100836 + 0.994903i \(0.467848\pi\)
\(420\) 0 0
\(421\) −15.7354 −0.766899 −0.383449 0.923562i \(-0.625264\pi\)
−0.383449 + 0.923562i \(0.625264\pi\)
\(422\) 0 0
\(423\) 38.6969i 1.88151i
\(424\) 0 0
\(425\) −1.83301 + 0.0208983i −0.0889140 + 0.00101372i
\(426\) 0 0
\(427\) 13.2949i 0.643385i
\(428\) 0 0
\(429\) 14.5444 0.702209
\(430\) 0 0
\(431\) 1.35158 0.0651034 0.0325517 0.999470i \(-0.489637\pi\)
0.0325517 + 0.999470i \(0.489637\pi\)
\(432\) 0 0
\(433\) 39.4114i 1.89399i −0.321244 0.946996i \(-0.604101\pi\)
0.321244 0.946996i \(-0.395899\pi\)
\(434\) 0 0
\(435\) 40.6106 41.0763i 1.94713 1.96946i
\(436\) 0 0
\(437\) 2.79847i 0.133869i
\(438\) 0 0
\(439\) 10.1059 0.482326 0.241163 0.970485i \(-0.422471\pi\)
0.241163 + 0.970485i \(0.422471\pi\)
\(440\) 0 0
\(441\) −7.99756 −0.380836
\(442\) 0 0
\(443\) 6.25526i 0.297197i 0.988898 + 0.148598i \(0.0474761\pi\)
−0.988898 + 0.148598i \(0.952524\pi\)
\(444\) 0 0
\(445\) 27.9914 + 27.6741i 1.32692 + 1.31188i
\(446\) 0 0
\(447\) 0.606068i 0.0286660i
\(448\) 0 0
\(449\) −2.28779 −0.107968 −0.0539839 0.998542i \(-0.517192\pi\)
−0.0539839 + 0.998542i \(0.517192\pi\)
\(450\) 0 0
\(451\) −3.07248 −0.144677
\(452\) 0 0
\(453\) 60.1055i 2.82400i
\(454\) 0 0
\(455\) 19.7416 + 19.5178i 0.925501 + 0.915010i
\(456\) 0 0
\(457\) 14.3062i 0.669217i −0.942357 0.334609i \(-0.891396\pi\)
0.942357 0.334609i \(-0.108604\pi\)
\(458\) 0 0
\(459\) 5.14995 0.240379
\(460\) 0 0
\(461\) −2.38995 −0.111311 −0.0556556 0.998450i \(-0.517725\pi\)
−0.0556556 + 0.998450i \(0.517725\pi\)
\(462\) 0 0
\(463\) 9.52232i 0.442540i −0.975213 0.221270i \(-0.928980\pi\)
0.975213 0.221270i \(-0.0710202\pi\)
\(464\) 0 0
\(465\) 36.6503 37.0706i 1.69962 1.71911i
\(466\) 0 0
\(467\) 6.14501i 0.284357i 0.989841 + 0.142178i \(0.0454107\pi\)
−0.989841 + 0.142178i \(0.954589\pi\)
\(468\) 0 0
\(469\) 3.62394 0.167338
\(470\) 0 0
\(471\) −64.4738 −2.97080
\(472\) 0 0
\(473\) 7.58278i 0.348657i
\(474\) 0 0
\(475\) −0.159518 13.9915i −0.00731917 0.641972i
\(476\) 0 0
\(477\) 85.7197i 3.92483i
\(478\) 0 0
\(479\) −1.40986 −0.0644180 −0.0322090 0.999481i \(-0.510254\pi\)
−0.0322090 + 0.999481i \(0.510254\pi\)
\(480\) 0 0
\(481\) −15.8281 −0.721697
\(482\) 0 0
\(483\) 7.82867i 0.356217i
\(484\) 0 0
\(485\) 10.3070 10.4251i 0.468015 0.473382i
\(486\) 0 0
\(487\) 31.2993i 1.41831i −0.705054 0.709154i \(-0.749077\pi\)
0.705054 0.709154i \(-0.250923\pi\)
\(488\) 0 0
\(489\) −10.8039 −0.488571
\(490\) 0 0
\(491\) 25.9254 1.17000 0.584999 0.811034i \(-0.301095\pi\)
0.584999 + 0.811034i \(0.301095\pi\)
\(492\) 0 0
\(493\) 2.94192i 0.132497i
\(494\) 0 0
\(495\) −10.3619 10.2444i −0.465733 0.460454i
\(496\) 0 0
\(497\) 20.1831i 0.905336i
\(498\) 0 0
\(499\) −8.04562 −0.360172 −0.180086 0.983651i \(-0.557638\pi\)
−0.180086 + 0.983651i \(0.557638\pi\)
\(500\) 0 0
\(501\) −8.29740 −0.370701
\(502\) 0 0
\(503\) 5.50490i 0.245451i −0.992441 0.122726i \(-0.960836\pi\)
0.992441 0.122726i \(-0.0391635\pi\)
\(504\) 0 0
\(505\) 21.4527 + 21.2095i 0.954634 + 0.943812i
\(506\) 0 0
\(507\) 42.0538i 1.86767i
\(508\) 0 0
\(509\) 8.26586 0.366378 0.183189 0.983078i \(-0.441358\pi\)
0.183189 + 0.983078i \(0.441358\pi\)
\(510\) 0 0
\(511\) −24.9043 −1.10170
\(512\) 0 0
\(513\) 39.3098i 1.73557i
\(514\) 0 0
\(515\) −19.7235 + 19.9497i −0.869122 + 0.879088i
\(516\) 0 0
\(517\) 4.65076i 0.204540i
\(518\) 0 0
\(519\) −62.5116 −2.74396
\(520\) 0 0
\(521\) 11.9776 0.524747 0.262374 0.964966i \(-0.415495\pi\)
0.262374 + 0.964966i \(0.415495\pi\)
\(522\) 0 0
\(523\) 0.711546i 0.0311137i −0.999879 0.0155569i \(-0.995048\pi\)
0.999879 0.0155569i \(-0.00495210\pi\)
\(524\) 0 0
\(525\) −0.446247 39.1408i −0.0194758 1.70824i
\(526\) 0 0
\(527\) 2.65503i 0.115655i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 68.7162 2.98203
\(532\) 0 0
\(533\) 17.7246i 0.767737i
\(534\) 0 0
\(535\) 2.29950 2.32587i 0.0994161 0.100556i
\(536\) 0 0
\(537\) 65.5524i 2.82880i
\(538\) 0 0
\(539\) 0.961182 0.0414011
\(540\) 0 0
\(541\) 34.9533 1.50276 0.751381 0.659869i \(-0.229388\pi\)
0.751381 + 0.659869i \(0.229388\pi\)
\(542\) 0 0
\(543\) 72.6351i 3.11707i
\(544\) 0 0
\(545\) 30.5580 + 30.2115i 1.30896 + 1.29412i
\(546\) 0 0
\(547\) 17.8478i 0.763118i −0.924345 0.381559i \(-0.875387\pi\)
0.924345 0.381559i \(-0.124613\pi\)
\(548\) 0 0
\(549\) −40.2558 −1.71808
\(550\) 0 0
\(551\) 22.4558 0.956650
\(552\) 0 0
\(553\) 14.7497i 0.627221i
\(554\) 0 0
\(555\) 15.8707 + 15.6908i 0.673674 + 0.666037i
\(556\) 0 0
\(557\) 3.29661i 0.139682i 0.997558 + 0.0698410i \(0.0222492\pi\)
−0.997558 + 0.0698410i \(0.977751\pi\)
\(558\) 0 0
\(559\) 43.7437 1.85016
\(560\) 0 0
\(561\) −1.04449 −0.0440983
\(562\) 0 0
\(563\) 4.44153i 0.187188i 0.995610 + 0.0935941i \(0.0298356\pi\)
−0.995610 + 0.0935941i \(0.970164\pi\)
\(564\) 0 0
\(565\) −1.31255 + 1.32760i −0.0552193 + 0.0558525i
\(566\) 0 0
\(567\) 56.2481i 2.36220i
\(568\) 0 0
\(569\) 6.00088 0.251570 0.125785 0.992058i \(-0.459855\pi\)
0.125785 + 0.992058i \(0.459855\pi\)
\(570\) 0 0
\(571\) −18.1609 −0.760008 −0.380004 0.924985i \(-0.624077\pi\)
−0.380004 + 0.924985i \(0.624077\pi\)
\(572\) 0 0
\(573\) 53.6175i 2.23990i
\(574\) 0 0
\(575\) −4.99968 + 0.0570016i −0.208501 + 0.00237713i
\(576\) 0 0
\(577\) 10.0474i 0.418279i −0.977886 0.209140i \(-0.932934\pi\)
0.977886 0.209140i \(-0.0670663\pi\)
\(578\) 0 0
\(579\) 46.7476 1.94277
\(580\) 0 0
\(581\) −39.5223 −1.63966
\(582\) 0 0
\(583\) 10.3022i 0.426672i
\(584\) 0 0
\(585\) −59.0983 + 59.7759i −2.44341 + 2.47143i
\(586\) 0 0
\(587\) 42.3593i 1.74836i 0.485605 + 0.874178i \(0.338599\pi\)
−0.485605 + 0.874178i \(0.661401\pi\)
\(588\) 0 0
\(589\) 20.2660 0.835044
\(590\) 0 0
\(591\) 42.9698 1.76754
\(592\) 0 0
\(593\) 19.6741i 0.807917i −0.914777 0.403958i \(-0.867634\pi\)
0.914777 0.403958i \(-0.132366\pi\)
\(594\) 0 0
\(595\) −1.41772 1.40165i −0.0581209 0.0574620i
\(596\) 0 0
\(597\) 60.4751i 2.47508i
\(598\) 0 0
\(599\) −18.2740 −0.746655 −0.373328 0.927700i \(-0.621783\pi\)
−0.373328 + 0.927700i \(0.621783\pi\)
\(600\) 0 0
\(601\) −8.17793 −0.333585 −0.166792 0.985992i \(-0.553341\pi\)
−0.166792 + 0.985992i \(0.553341\pi\)
\(602\) 0 0
\(603\) 10.9730i 0.446855i
\(604\) 0 0
\(605\) −16.2460 16.0619i −0.660496 0.653008i
\(606\) 0 0
\(607\) 21.7927i 0.884538i −0.896883 0.442269i \(-0.854174\pi\)
0.896883 0.442269i \(-0.145826\pi\)
\(608\) 0 0
\(609\) 62.8197 2.54558
\(610\) 0 0
\(611\) −26.8294 −1.08540
\(612\) 0 0
\(613\) 15.2379i 0.615455i 0.951475 + 0.307727i \(0.0995685\pi\)
−0.951475 + 0.307727i \(0.900432\pi\)
\(614\) 0 0
\(615\) 17.5709 17.7723i 0.708525 0.716649i
\(616\) 0 0
\(617\) 20.2945i 0.817024i 0.912753 + 0.408512i \(0.133952\pi\)
−0.912753 + 0.408512i \(0.866048\pi\)
\(618\) 0 0
\(619\) 2.08510 0.0838073 0.0419037 0.999122i \(-0.486658\pi\)
0.0419037 + 0.999122i \(0.486658\pi\)
\(620\) 0 0
\(621\) 14.0469 0.563681
\(622\) 0 0
\(623\) 42.8085i 1.71509i
\(624\) 0 0
\(625\) −24.9935 + 0.569979i −0.999740 + 0.0227992i
\(626\) 0 0
\(627\) 7.97262i 0.318396i
\(628\) 0 0
\(629\) 1.13667 0.0453221
\(630\) 0 0
\(631\) −39.0512 −1.55461 −0.777303 0.629127i \(-0.783413\pi\)
−0.777303 + 0.629127i \(0.783413\pi\)
\(632\) 0 0
\(633\) 55.0738i 2.18899i
\(634\) 0 0
\(635\) 12.3795 12.5215i 0.491267 0.496900i
\(636\) 0 0
\(637\) 5.54488i 0.219696i
\(638\) 0 0
\(639\) 61.1127 2.41758
\(640\) 0 0
\(641\) −21.8361 −0.862475 −0.431238 0.902238i \(-0.641923\pi\)
−0.431238 + 0.902238i \(0.641923\pi\)
\(642\) 0 0
\(643\) 16.3727i 0.645676i −0.946454 0.322838i \(-0.895363\pi\)
0.946454 0.322838i \(-0.104637\pi\)
\(644\) 0 0
\(645\) −43.8615 43.3643i −1.72705 1.70747i
\(646\) 0 0
\(647\) 20.9991i 0.825560i 0.910831 + 0.412780i \(0.135442\pi\)
−0.910831 + 0.412780i \(0.864558\pi\)
\(648\) 0 0
\(649\) −8.25861 −0.324179
\(650\) 0 0
\(651\) 56.6936 2.22200
\(652\) 0 0
\(653\) 23.2756i 0.910846i 0.890275 + 0.455423i \(0.150512\pi\)
−0.890275 + 0.455423i \(0.849488\pi\)
\(654\) 0 0
\(655\) 20.4713 + 20.2392i 0.799878 + 0.790811i
\(656\) 0 0
\(657\) 75.4080i 2.94195i
\(658\) 0 0
\(659\) −2.09639 −0.0816637 −0.0408318 0.999166i \(-0.513001\pi\)
−0.0408318 + 0.999166i \(0.513001\pi\)
\(660\) 0 0
\(661\) −31.3184 −1.21814 −0.609072 0.793115i \(-0.708458\pi\)
−0.609072 + 0.793115i \(0.708458\pi\)
\(662\) 0 0
\(663\) 6.02545i 0.234009i
\(664\) 0 0
\(665\) 10.6989 10.8215i 0.414884 0.419641i
\(666\) 0 0
\(667\) 8.02431i 0.310703i
\(668\) 0 0
\(669\) 43.5190 1.68254
\(670\) 0 0
\(671\) 4.83812 0.186773
\(672\) 0 0
\(673\) 44.3377i 1.70909i −0.519377 0.854545i \(-0.673836\pi\)
0.519377 0.854545i \(-0.326164\pi\)
\(674\) 0 0
\(675\) 70.2298 0.800695i 2.70315 0.0308188i
\(676\) 0 0
\(677\) 3.03772i 0.116749i 0.998295 + 0.0583746i \(0.0185918\pi\)
−0.998295 + 0.0583746i \(0.981408\pi\)
\(678\) 0 0
\(679\) 15.9436 0.611860
\(680\) 0 0
\(681\) 26.7061 1.02338
\(682\) 0 0
\(683\) 22.6750i 0.867635i −0.901001 0.433817i \(-0.857166\pi\)
0.901001 0.433817i \(-0.142834\pi\)
\(684\) 0 0
\(685\) −5.13566 + 5.19454i −0.196223 + 0.198473i
\(686\) 0 0
\(687\) 20.0338i 0.764338i
\(688\) 0 0
\(689\) 59.4313 2.26415
\(690\) 0 0
\(691\) 18.2394 0.693860 0.346930 0.937891i \(-0.387224\pi\)
0.346930 + 0.937891i \(0.387224\pi\)
\(692\) 0 0
\(693\) 15.8469i 0.601974i
\(694\) 0 0
\(695\) −19.9685 19.7421i −0.757448 0.748862i
\(696\) 0 0
\(697\) 1.27287i 0.0482134i
\(698\) 0 0
\(699\) −43.8934 −1.66020
\(700\) 0 0
\(701\) 17.4315 0.658378 0.329189 0.944264i \(-0.393225\pi\)
0.329189 + 0.944264i \(0.393225\pi\)
\(702\) 0 0
\(703\) 8.67629i 0.327232i
\(704\) 0 0
\(705\) 26.9017 + 26.5967i 1.01318 + 1.00169i
\(706\) 0 0
\(707\) 32.8086i 1.23389i
\(708\) 0 0
\(709\) 32.4207 1.21758 0.608792 0.793330i \(-0.291654\pi\)
0.608792 + 0.793330i \(0.291654\pi\)
\(710\) 0 0
\(711\) −44.6608 −1.67491
\(712\) 0 0
\(713\) 7.24179i 0.271207i
\(714\) 0 0
\(715\) 7.10270 7.18414i 0.265626 0.268671i
\(716\) 0 0
\(717\) 37.1117i 1.38596i
\(718\) 0 0
\(719\) 0.494269 0.0184331 0.00921656 0.999958i \(-0.497066\pi\)
0.00921656 + 0.999958i \(0.497066\pi\)
\(720\) 0 0
\(721\) −30.5099 −1.13625
\(722\) 0 0
\(723\) 56.6430i 2.10658i
\(724\) 0 0
\(725\) −0.457399 40.1189i −0.0169874 1.48998i
\(726\) 0 0
\(727\) 4.25774i 0.157911i 0.996878 + 0.0789555i \(0.0251585\pi\)
−0.996878 + 0.0789555i \(0.974842\pi\)
\(728\) 0 0
\(729\) −34.6543 −1.28349
\(730\) 0 0
\(731\) −3.14140 −0.116189
\(732\) 0 0
\(733\) 14.8525i 0.548589i −0.961646 0.274295i \(-0.911556\pi\)
0.961646 0.274295i \(-0.0884443\pi\)
\(734\) 0 0
\(735\) −5.49680 + 5.55982i −0.202752 + 0.205077i
\(736\) 0 0
\(737\) 1.31878i 0.0485780i
\(738\) 0 0
\(739\) −42.1389 −1.55010 −0.775052 0.631898i \(-0.782276\pi\)
−0.775052 + 0.631898i \(0.782276\pi\)
\(740\) 0 0
\(741\) −45.9926 −1.68958
\(742\) 0 0
\(743\) 3.97014i 0.145650i 0.997345 + 0.0728252i \(0.0232015\pi\)
−0.997345 + 0.0728252i \(0.976798\pi\)
\(744\) 0 0
\(745\) 0.299365 + 0.295971i 0.0109679 + 0.0108436i
\(746\) 0 0
\(747\) 119.670i 4.37851i
\(748\) 0 0
\(749\) 3.55705 0.129972
\(750\) 0 0
\(751\) −51.5382 −1.88066 −0.940328 0.340269i \(-0.889482\pi\)
−0.940328 + 0.340269i \(0.889482\pi\)
\(752\) 0 0
\(753\) 40.3921i 1.47197i
\(754\) 0 0
\(755\) 29.6889 + 29.3524i 1.08049 + 1.06824i
\(756\) 0 0
\(757\) 39.9808i 1.45313i −0.687099 0.726564i \(-0.741116\pi\)
0.687099 0.726564i \(-0.258884\pi\)
\(758\) 0 0
\(759\) −2.84892 −0.103409
\(760\) 0 0
\(761\) −20.6683 −0.749226 −0.374613 0.927181i \(-0.622224\pi\)
−0.374613 + 0.927181i \(0.622224\pi\)
\(762\) 0 0
\(763\) 46.7336i 1.69187i
\(764\) 0 0
\(765\) 4.24408 4.29274i 0.153445 0.155204i
\(766\) 0 0
\(767\) 47.6424i 1.72027i
\(768\) 0 0
\(769\) 0.0670558 0.00241809 0.00120905 0.999999i \(-0.499615\pi\)
0.00120905 + 0.999999i \(0.499615\pi\)
\(770\) 0 0
\(771\) −15.7121 −0.565859
\(772\) 0 0
\(773\) 21.2074i 0.762778i −0.924415 0.381389i \(-0.875446\pi\)
0.924415 0.381389i \(-0.124554\pi\)
\(774\) 0 0
\(775\) −0.412794 36.2066i −0.0148280 1.30058i
\(776\) 0 0
\(777\) 24.2717i 0.870744i
\(778\) 0 0
\(779\) 9.71588 0.348108
\(780\) 0 0
\(781\) −7.34480 −0.262817
\(782\) 0 0
\(783\) 112.716i 4.02816i
\(784\) 0 0
\(785\) −31.4856 + 31.8466i −1.12377 + 1.13665i
\(786\) 0 0
\(787\) 19.1047i 0.681010i −0.940243 0.340505i \(-0.889402\pi\)
0.940243 0.340505i \(-0.110598\pi\)
\(788\) 0 0
\(789\) 37.3577 1.32997
\(790\) 0 0
\(791\) −2.03035 −0.0721910
\(792\) 0 0
\(793\) 27.9102i 0.991121i
\(794\) 0 0
\(795\) −59.5914 58.9159i −2.11349 2.08953i
\(796\) 0 0
\(797\) 51.0751i 1.80917i −0.426290 0.904587i \(-0.640180\pi\)
0.426290 0.904587i \(-0.359820\pi\)
\(798\) 0 0
\(799\) 1.92672 0.0681625
\(800\) 0 0
\(801\) −129.621 −4.57992
\(802\) 0