Properties

Label 1152.2.w.a.431.8
Level $1152$
Weight $2$
Character 1152.431
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 431.8
Character \(\chi\) \(=\) 1152.431
Dual form 1152.2.w.a.719.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +O(q^{10})\) \(q+(2.97412 - 1.23192i) q^{5} +(-0.237717 - 0.237717i) q^{7} +(-2.12394 + 0.879764i) q^{11} +(0.0390635 - 0.0943077i) q^{13} +4.16112 q^{17} +(4.25390 + 1.76202i) q^{19} +(4.84847 + 4.84847i) q^{23} +(3.79221 - 3.79221i) q^{25} +(2.90419 - 7.01132i) q^{29} -9.88480i q^{31} +(-0.999845 - 0.414149i) q^{35} +(0.175641 + 0.424034i) q^{37} +(-7.67919 + 7.67919i) q^{41} +(-2.99581 - 7.23252i) q^{43} +6.10937i q^{47} -6.88698i q^{49} +(4.28258 + 10.3391i) q^{53} +(-5.23304 + 5.23304i) q^{55} +(-1.19303 - 2.88024i) q^{59} +(6.29246 + 2.60642i) q^{61} -0.328605i q^{65} +(5.66771 - 13.6831i) q^{67} +(-3.49288 + 3.49288i) q^{71} +(-1.42542 - 1.42542i) q^{73} +(0.714030 + 0.295761i) q^{77} -1.53778 q^{79} +(2.95890 - 7.14340i) q^{83} +(12.3756 - 5.12616i) q^{85} +(-1.92767 - 1.92767i) q^{89} +(-0.0317046 + 0.0131325i) q^{91} +14.8223 q^{95} -12.9791 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(5\) 2.97412 1.23192i 1.33007 0.550931i 0.399391 0.916781i \(-0.369222\pi\)
0.930674 + 0.365850i \(0.119222\pi\)
\(6\) 0 0
\(7\) −0.237717 0.237717i −0.0898485 0.0898485i 0.660754 0.750603i \(-0.270237\pi\)
−0.750603 + 0.660754i \(0.770237\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.12394 + 0.879764i −0.640391 + 0.265259i −0.679161 0.733989i \(-0.737656\pi\)
0.0387695 + 0.999248i \(0.487656\pi\)
\(12\) 0 0
\(13\) 0.0390635 0.0943077i 0.0108343 0.0261562i −0.918370 0.395723i \(-0.870494\pi\)
0.929204 + 0.369567i \(0.120494\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.16112 1.00922 0.504609 0.863348i \(-0.331636\pi\)
0.504609 + 0.863348i \(0.331636\pi\)
\(18\) 0 0
\(19\) 4.25390 + 1.76202i 0.975912 + 0.404236i 0.812910 0.582390i \(-0.197882\pi\)
0.163002 + 0.986626i \(0.447882\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.84847 + 4.84847i 1.01098 + 1.01098i 0.999939 + 0.0110368i \(0.00351321\pi\)
0.0110368 + 0.999939i \(0.496487\pi\)
\(24\) 0 0
\(25\) 3.79221 3.79221i 0.758441 0.758441i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.90419 7.01132i 0.539294 1.30197i −0.385923 0.922531i \(-0.626117\pi\)
0.925217 0.379439i \(-0.123883\pi\)
\(30\) 0 0
\(31\) 9.88480i 1.77536i −0.460459 0.887681i \(-0.652315\pi\)
0.460459 0.887681i \(-0.347685\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.999845 0.414149i −0.169005 0.0700040i
\(36\) 0 0
\(37\) 0.175641 + 0.424034i 0.0288752 + 0.0697108i 0.937659 0.347556i \(-0.112988\pi\)
−0.908784 + 0.417266i \(0.862988\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.67919 + 7.67919i −1.19929 + 1.19929i −0.224907 + 0.974380i \(0.572208\pi\)
−0.974380 + 0.224907i \(0.927792\pi\)
\(42\) 0 0
\(43\) −2.99581 7.23252i −0.456857 1.10295i −0.969663 0.244445i \(-0.921394\pi\)
0.512807 0.858504i \(-0.328606\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.10937i 0.891143i 0.895246 + 0.445571i \(0.146999\pi\)
−0.895246 + 0.445571i \(0.853001\pi\)
\(48\) 0 0
\(49\) 6.88698i 0.983855i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.28258 + 10.3391i 0.588258 + 1.42018i 0.885167 + 0.465274i \(0.154044\pi\)
−0.296909 + 0.954906i \(0.595956\pi\)
\(54\) 0 0
\(55\) −5.23304 + 5.23304i −0.705623 + 0.705623i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.19303 2.88024i −0.155320 0.374975i 0.826996 0.562208i \(-0.190048\pi\)
−0.982316 + 0.187233i \(0.940048\pi\)
\(60\) 0 0
\(61\) 6.29246 + 2.60642i 0.805667 + 0.333718i 0.747224 0.664573i \(-0.231386\pi\)
0.0584431 + 0.998291i \(0.481386\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.328605i 0.0407584i
\(66\) 0 0
\(67\) 5.66771 13.6831i 0.692420 1.67165i −0.0474259 0.998875i \(-0.515102\pi\)
0.739846 0.672776i \(-0.234898\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.49288 + 3.49288i −0.414528 + 0.414528i −0.883313 0.468784i \(-0.844692\pi\)
0.468784 + 0.883313i \(0.344692\pi\)
\(72\) 0 0
\(73\) −1.42542 1.42542i −0.166833 0.166833i 0.618753 0.785586i \(-0.287638\pi\)
−0.785586 + 0.618753i \(0.787638\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.714030 + 0.295761i 0.0813713 + 0.0337051i
\(78\) 0 0
\(79\) −1.53778 −0.173014 −0.0865070 0.996251i \(-0.527570\pi\)
−0.0865070 + 0.996251i \(0.527570\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.95890 7.14340i 0.324781 0.784091i −0.674182 0.738565i \(-0.735504\pi\)
0.998963 0.0455255i \(-0.0144962\pi\)
\(84\) 0 0
\(85\) 12.3756 5.12616i 1.34233 0.556010i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.92767 1.92767i −0.204333 0.204333i 0.597521 0.801853i \(-0.296153\pi\)
−0.801853 + 0.597521i \(0.796153\pi\)
\(90\) 0 0
\(91\) −0.0317046 + 0.0131325i −0.00332354 + 0.00137666i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 14.8223 1.52073
\(96\) 0 0
\(97\) −12.9791 −1.31783 −0.658915 0.752218i \(-0.728984\pi\)
−0.658915 + 0.752218i \(0.728984\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.2765 4.25666i 1.02255 0.423554i 0.192532 0.981291i \(-0.438330\pi\)
0.830018 + 0.557737i \(0.188330\pi\)
\(102\) 0 0
\(103\) 6.66422 + 6.66422i 0.656645 + 0.656645i 0.954585 0.297940i \(-0.0962994\pi\)
−0.297940 + 0.954585i \(0.596299\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.1377 4.61340i 1.07673 0.445994i 0.227366 0.973809i \(-0.426989\pi\)
0.849359 + 0.527815i \(0.176989\pi\)
\(108\) 0 0
\(109\) −3.68462 + 8.89546i −0.352922 + 0.852030i 0.643334 + 0.765585i \(0.277551\pi\)
−0.996257 + 0.0864447i \(0.972449\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.16123 −0.673672 −0.336836 0.941563i \(-0.609357\pi\)
−0.336836 + 0.941563i \(0.609357\pi\)
\(114\) 0 0
\(115\) 20.3928 + 8.44699i 1.90164 + 0.787686i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.989167 0.989167i −0.0906768 0.0906768i
\(120\) 0 0
\(121\) −4.04105 + 4.04105i −0.367368 + 0.367368i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.447173 1.07957i 0.0399964 0.0965599i
\(126\) 0 0
\(127\) 9.41925i 0.835823i 0.908488 + 0.417911i \(0.137238\pi\)
−0.908488 + 0.417911i \(0.862762\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.15026 + 1.30488i 0.275240 + 0.114008i 0.516034 0.856568i \(-0.327408\pi\)
−0.240794 + 0.970576i \(0.577408\pi\)
\(132\) 0 0
\(133\) −0.592361 1.43009i −0.0513642 0.124004i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.26376 + 8.26376i −0.706021 + 0.706021i −0.965696 0.259675i \(-0.916384\pi\)
0.259675 + 0.965696i \(0.416384\pi\)
\(138\) 0 0
\(139\) −0.429473 1.03684i −0.0364274 0.0879436i 0.904619 0.426222i \(-0.140156\pi\)
−0.941046 + 0.338278i \(0.890156\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.234670i 0.0196241i
\(144\) 0 0
\(145\) 24.4302i 2.02882i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.253180 + 0.611230i 0.0207413 + 0.0500739i 0.933911 0.357506i \(-0.116373\pi\)
−0.913170 + 0.407580i \(0.866373\pi\)
\(150\) 0 0
\(151\) −11.4878 + 11.4878i −0.934862 + 0.934862i −0.998005 0.0631423i \(-0.979888\pi\)
0.0631423 + 0.998005i \(0.479888\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.1773 29.3985i −0.978102 2.36135i
\(156\) 0 0
\(157\) −13.7120 5.67968i −1.09433 0.453288i −0.238818 0.971064i \(-0.576760\pi\)
−0.855516 + 0.517777i \(0.826760\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.30512i 0.181669i
\(162\) 0 0
\(163\) −2.66632 + 6.43706i −0.208842 + 0.504189i −0.993241 0.116067i \(-0.962971\pi\)
0.784399 + 0.620256i \(0.212971\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.53445 + 6.53445i −0.505651 + 0.505651i −0.913188 0.407538i \(-0.866387\pi\)
0.407538 + 0.913188i \(0.366387\pi\)
\(168\) 0 0
\(169\) 9.18502 + 9.18502i 0.706540 + 0.706540i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.24361 1.34355i −0.246607 0.102148i 0.255956 0.966688i \(-0.417610\pi\)
−0.502563 + 0.864540i \(0.667610\pi\)
\(174\) 0 0
\(175\) −1.80294 −0.136290
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.86789 + 23.8232i −0.737560 + 1.78063i −0.122013 + 0.992528i \(0.538935\pi\)
−0.615547 + 0.788100i \(0.711065\pi\)
\(180\) 0 0
\(181\) 12.1863 5.04772i 0.905799 0.375194i 0.119352 0.992852i \(-0.461918\pi\)
0.786447 + 0.617658i \(0.211918\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.04475 + 1.04475i 0.0768117 + 0.0768117i
\(186\) 0 0
\(187\) −8.83795 + 3.66080i −0.646295 + 0.267704i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.7590 0.923208 0.461604 0.887086i \(-0.347274\pi\)
0.461604 + 0.887086i \(0.347274\pi\)
\(192\) 0 0
\(193\) −12.6078 −0.907531 −0.453766 0.891121i \(-0.649920\pi\)
−0.453766 + 0.891121i \(0.649920\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.666855 + 0.276221i −0.0475115 + 0.0196799i −0.406313 0.913734i \(-0.633186\pi\)
0.358801 + 0.933414i \(0.383186\pi\)
\(198\) 0 0
\(199\) 4.26928 + 4.26928i 0.302641 + 0.302641i 0.842046 0.539405i \(-0.181351\pi\)
−0.539405 + 0.842046i \(0.681351\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.35708 + 0.976336i −0.165435 + 0.0685253i
\(204\) 0 0
\(205\) −13.3787 + 32.2989i −0.934406 + 2.25586i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −10.5852 −0.732193
\(210\) 0 0
\(211\) −15.6370 6.47704i −1.07649 0.445898i −0.227215 0.973845i \(-0.572962\pi\)
−0.849278 + 0.527947i \(0.822962\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.8198 17.8198i −1.21530 1.21530i
\(216\) 0 0
\(217\) −2.34978 + 2.34978i −0.159514 + 0.159514i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.162548 0.392425i 0.0109342 0.0263974i
\(222\) 0 0
\(223\) 29.4910i 1.97487i −0.158038 0.987433i \(-0.550517\pi\)
0.158038 0.987433i \(-0.449483\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −18.5140 7.66873i −1.22881 0.508992i −0.328613 0.944465i \(-0.606581\pi\)
−0.900202 + 0.435473i \(0.856581\pi\)
\(228\) 0 0
\(229\) 2.09503 + 5.05785i 0.138444 + 0.334232i 0.977861 0.209255i \(-0.0671037\pi\)
−0.839418 + 0.543487i \(0.817104\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.699144 + 0.699144i −0.0458024 + 0.0458024i −0.729637 0.683835i \(-0.760311\pi\)
0.683835 + 0.729637i \(0.260311\pi\)
\(234\) 0 0
\(235\) 7.52625 + 18.1700i 0.490958 + 1.18528i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.1034i 1.42975i 0.699253 + 0.714875i \(0.253516\pi\)
−0.699253 + 0.714875i \(0.746484\pi\)
\(240\) 0 0
\(241\) 9.09381i 0.585784i 0.956146 + 0.292892i \(0.0946176\pi\)
−0.956146 + 0.292892i \(0.905382\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −8.48420 20.4827i −0.542036 1.30859i
\(246\) 0 0
\(247\) 0.332345 0.332345i 0.0211466 0.0211466i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.43019 3.45279i −0.0902728 0.217938i 0.872294 0.488981i \(-0.162631\pi\)
−0.962567 + 0.271043i \(0.912631\pi\)
\(252\) 0 0
\(253\) −14.5634 6.03234i −0.915591 0.379250i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.05245i 0.190406i 0.995458 + 0.0952032i \(0.0303501\pi\)
−0.995458 + 0.0952032i \(0.969650\pi\)
\(258\) 0 0
\(259\) 0.0590473 0.142553i 0.00366902 0.00885780i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.44480 + 2.44480i −0.150753 + 0.150753i −0.778454 0.627701i \(-0.783996\pi\)
0.627701 + 0.778454i \(0.283996\pi\)
\(264\) 0 0
\(265\) 25.4738 + 25.4738i 1.56484 + 1.56484i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −13.7507 5.69573i −0.838395 0.347275i −0.0781745 0.996940i \(-0.524909\pi\)
−0.760221 + 0.649665i \(0.774909\pi\)
\(270\) 0 0
\(271\) −24.0583 −1.46144 −0.730720 0.682677i \(-0.760816\pi\)
−0.730720 + 0.682677i \(0.760816\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.71816 + 11.3907i −0.284516 + 0.686882i
\(276\) 0 0
\(277\) −6.48199 + 2.68493i −0.389465 + 0.161322i −0.568819 0.822463i \(-0.692599\pi\)
0.179354 + 0.983785i \(0.442599\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.59744 4.59744i −0.274260 0.274260i 0.556552 0.830813i \(-0.312124\pi\)
−0.830813 + 0.556552i \(0.812124\pi\)
\(282\) 0 0
\(283\) −17.9590 + 7.43884i −1.06755 + 0.442193i −0.846125 0.532984i \(-0.821070\pi\)
−0.221424 + 0.975178i \(0.571070\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.65094 0.215508
\(288\) 0 0
\(289\) 0.314890 0.0185229
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.0302145 + 0.0125153i −0.00176515 + 0.000731150i −0.383566 0.923514i \(-0.625304\pi\)
0.381801 + 0.924245i \(0.375304\pi\)
\(294\) 0 0
\(295\) −7.09645 7.09645i −0.413171 0.413171i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.646646 0.267850i 0.0373965 0.0154901i
\(300\) 0 0
\(301\) −1.00714 + 2.43145i −0.0580504 + 0.140146i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 21.9254 1.25544
\(306\) 0 0
\(307\) 21.7209 + 8.99707i 1.23967 + 0.513490i 0.903613 0.428350i \(-0.140905\pi\)
0.336062 + 0.941840i \(0.390905\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.59830 3.59830i −0.204041 0.204041i 0.597688 0.801729i \(-0.296086\pi\)
−0.801729 + 0.597688i \(0.796086\pi\)
\(312\) 0 0
\(313\) 1.24094 1.24094i 0.0701421 0.0701421i −0.671165 0.741308i \(-0.734206\pi\)
0.741308 + 0.671165i \(0.234206\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.92298 7.05670i 0.164171 0.396344i −0.820290 0.571948i \(-0.806188\pi\)
0.984461 + 0.175604i \(0.0561879\pi\)
\(318\) 0 0
\(319\) 17.4466i 0.976823i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 17.7010 + 7.33199i 0.984909 + 0.407963i
\(324\) 0 0
\(325\) −0.209497 0.505771i −0.0116208 0.0280551i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.45230 1.45230i 0.0800678 0.0800678i
\(330\) 0 0
\(331\) −11.2439 27.1453i −0.618023 1.49204i −0.853996 0.520280i \(-0.825828\pi\)
0.235973 0.971760i \(-0.424172\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 47.6771i 2.60488i
\(336\) 0 0
\(337\) 13.3438i 0.726882i 0.931617 + 0.363441i \(0.118398\pi\)
−0.931617 + 0.363441i \(0.881602\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.69629 + 20.9947i 0.470930 + 1.13693i
\(342\) 0 0
\(343\) −3.30117 + 3.30117i −0.178246 + 0.178246i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.38445 + 8.17078i 0.181687 + 0.438631i 0.988314 0.152429i \(-0.0487097\pi\)
−0.806628 + 0.591060i \(0.798710\pi\)
\(348\) 0 0
\(349\) 17.9607 + 7.43958i 0.961416 + 0.398232i 0.807510 0.589854i \(-0.200815\pi\)
0.153906 + 0.988085i \(0.450815\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.1730i 1.60594i −0.596016 0.802972i \(-0.703251\pi\)
0.596016 0.802972i \(-0.296749\pi\)
\(354\) 0 0
\(355\) −6.08528 + 14.6912i −0.322973 + 0.779726i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.24818 + 5.24818i −0.276988 + 0.276988i −0.831905 0.554917i \(-0.812750\pi\)
0.554917 + 0.831905i \(0.312750\pi\)
\(360\) 0 0
\(361\) 1.55592 + 1.55592i 0.0818907 + 0.0818907i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.99538 2.48337i −0.313812 0.129985i
\(366\) 0 0
\(367\) 31.3373 1.63580 0.817898 0.575363i \(-0.195139\pi\)
0.817898 + 0.575363i \(0.195139\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.43973 3.47581i 0.0747469 0.180455i
\(372\) 0 0
\(373\) 12.2609 5.07863i 0.634845 0.262962i −0.0419649 0.999119i \(-0.513362\pi\)
0.676810 + 0.736158i \(0.263362\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.547774 0.547774i −0.0282118 0.0282118i
\(378\) 0 0
\(379\) −23.5487 + 9.75417i −1.20961 + 0.501038i −0.894093 0.447881i \(-0.852179\pi\)
−0.315520 + 0.948919i \(0.602179\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.6719 −0.851896 −0.425948 0.904748i \(-0.640059\pi\)
−0.425948 + 0.904748i \(0.640059\pi\)
\(384\) 0 0
\(385\) 2.48796 0.126798
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.38281 + 0.572777i −0.0701110 + 0.0290409i −0.417463 0.908694i \(-0.637081\pi\)
0.347352 + 0.937735i \(0.387081\pi\)
\(390\) 0 0
\(391\) 20.1750 + 20.1750i 1.02030 + 1.02030i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.57354 + 1.89442i −0.230120 + 0.0953187i
\(396\) 0 0
\(397\) 4.37989 10.5740i 0.219821 0.530694i −0.775044 0.631907i \(-0.782272\pi\)
0.994865 + 0.101213i \(0.0322724\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 23.7727 1.18715 0.593576 0.804778i \(-0.297716\pi\)
0.593576 + 0.804778i \(0.297716\pi\)
\(402\) 0 0
\(403\) −0.932212 0.386135i −0.0464368 0.0192348i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.746100 0.746100i −0.0369828 0.0369828i
\(408\) 0 0
\(409\) −24.1735 + 24.1735i −1.19530 + 1.19530i −0.219743 + 0.975558i \(0.570522\pi\)
−0.975558 + 0.219743i \(0.929478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.401077 + 0.968286i −0.0197357 + 0.0476462i
\(414\) 0 0
\(415\) 24.8904i 1.22182i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.78167 + 2.80906i 0.331306 + 0.137232i 0.542135 0.840291i \(-0.317616\pi\)
−0.210828 + 0.977523i \(0.567616\pi\)
\(420\) 0 0
\(421\) −9.06067 21.8744i −0.441590 1.06609i −0.975391 0.220482i \(-0.929237\pi\)
0.533801 0.845610i \(-0.320763\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 15.7798 15.7798i 0.765433 0.765433i
\(426\) 0 0
\(427\) −0.876233 2.11541i −0.0424039 0.102372i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 22.9164i 1.10384i 0.833896 + 0.551922i \(0.186105\pi\)
−0.833896 + 0.551922i \(0.813895\pi\)
\(432\) 0 0
\(433\) 17.6486i 0.848139i −0.905630 0.424070i \(-0.860601\pi\)
0.905630 0.424070i \(-0.139399\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.0818 + 29.1680i 0.577951 + 1.39530i
\(438\) 0 0
\(439\) −11.5122 + 11.5122i −0.549449 + 0.549449i −0.926281 0.376832i \(-0.877013\pi\)
0.376832 + 0.926281i \(0.377013\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.4242 + 32.4089i 0.637804 + 1.53980i 0.829598 + 0.558360i \(0.188569\pi\)
−0.191794 + 0.981435i \(0.561431\pi\)
\(444\) 0 0
\(445\) −8.10785 3.35838i −0.384349 0.159202i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16.3232i 0.770339i −0.922846 0.385170i \(-0.874143\pi\)
0.922846 0.385170i \(-0.125857\pi\)
\(450\) 0 0
\(451\) 9.55425 23.0660i 0.449892 1.08614i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.0781149 + 0.0781149i −0.00366208 + 0.00366208i
\(456\) 0 0
\(457\) −22.1907 22.1907i −1.03804 1.03804i −0.999247 0.0387901i \(-0.987650\pi\)
−0.0387901 0.999247i \(-0.512350\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15.6722 6.49164i −0.729927 0.302346i −0.0134051 0.999910i \(-0.504267\pi\)
−0.716522 + 0.697564i \(0.754267\pi\)
\(462\) 0 0
\(463\) 21.1826 0.984441 0.492220 0.870471i \(-0.336185\pi\)
0.492220 + 0.870471i \(0.336185\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.30158 10.3849i 0.199053 0.480557i −0.792561 0.609793i \(-0.791253\pi\)
0.991614 + 0.129236i \(0.0412525\pi\)
\(468\) 0 0
\(469\) −4.60000 + 1.90538i −0.212408 + 0.0879824i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.7258 + 12.7258i 0.585134 + 0.585134i
\(474\) 0 0
\(475\) 22.8136 9.44971i 1.04676 0.433583i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −36.0607 −1.64766 −0.823828 0.566840i \(-0.808166\pi\)
−0.823828 + 0.566840i \(0.808166\pi\)
\(480\) 0 0
\(481\) 0.0468509 0.00213622
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −38.6014 + 15.9892i −1.75280 + 0.726033i
\(486\) 0 0
\(487\) 6.99084 + 6.99084i 0.316785 + 0.316785i 0.847531 0.530746i \(-0.178088\pi\)
−0.530746 + 0.847531i \(0.678088\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.37664 2.64129i 0.287774 0.119200i −0.234127 0.972206i \(-0.575223\pi\)
0.521901 + 0.853006i \(0.325223\pi\)
\(492\) 0 0
\(493\) 12.0847 29.1749i 0.544266 1.31397i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.66063 0.0744895
\(498\) 0 0
\(499\) −7.43198 3.07843i −0.332701 0.137809i 0.210078 0.977685i \(-0.432628\pi\)
−0.542779 + 0.839875i \(0.682628\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.67081 2.67081i −0.119086 0.119086i 0.645053 0.764138i \(-0.276835\pi\)
−0.764138 + 0.645053i \(0.776835\pi\)
\(504\) 0 0
\(505\) 25.3196 25.3196i 1.12671 1.12671i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.36796 + 22.6162i −0.415227 + 1.00245i 0.568484 + 0.822694i \(0.307530\pi\)
−0.983712 + 0.179753i \(0.942470\pi\)
\(510\) 0 0
\(511\) 0.677694i 0.0299794i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 28.0299 + 11.6104i 1.23515 + 0.511615i
\(516\) 0 0
\(517\) −5.37480 12.9759i −0.236384 0.570680i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22.3821 + 22.3821i −0.980579 + 0.980579i −0.999815 0.0192357i \(-0.993877\pi\)
0.0192357 + 0.999815i \(0.493877\pi\)
\(522\) 0 0
\(523\) −2.70300 6.52561i −0.118194 0.285345i 0.853700 0.520765i \(-0.174353\pi\)
−0.971894 + 0.235420i \(0.924353\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 41.1318i 1.79173i
\(528\) 0 0
\(529\) 24.0153i 1.04414i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.424230 + 1.02418i 0.0183755 + 0.0443623i
\(534\) 0 0
\(535\) 27.4416 27.4416i 1.18640 1.18640i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.05892 + 14.6275i 0.260976 + 0.630052i
\(540\) 0 0
\(541\) −3.90965 1.61943i −0.168089 0.0696246i 0.297052 0.954861i \(-0.403996\pi\)
−0.465141 + 0.885237i \(0.653996\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 30.9953i 1.32769i
\(546\) 0 0
\(547\) −6.81941 + 16.4635i −0.291577 + 0.703929i −0.999998 0.00186067i \(-0.999408\pi\)
0.708421 + 0.705790i \(0.249408\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 24.7082 24.7082i 1.05261 1.05261i
\(552\) 0 0
\(553\) 0.365556 + 0.365556i 0.0155450 + 0.0155450i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.65431 1.51367i −0.154838 0.0641361i 0.303918 0.952698i \(-0.401705\pi\)
−0.458757 + 0.888562i \(0.651705\pi\)
\(558\) 0 0
\(559\) −0.799109 −0.0337987
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.27091 3.06826i 0.0535626 0.129312i −0.894833 0.446401i \(-0.852706\pi\)
0.948396 + 0.317089i \(0.102706\pi\)
\(564\) 0 0
\(565\) −21.2983 + 8.82206i −0.896028 + 0.371147i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.04933 8.04933i −0.337446 0.337446i 0.517960 0.855405i \(-0.326692\pi\)
−0.855405 + 0.517960i \(0.826692\pi\)
\(570\) 0 0
\(571\) −24.5752 + 10.1794i −1.02844 + 0.425994i −0.832150 0.554551i \(-0.812890\pi\)
−0.196292 + 0.980546i \(0.562890\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 36.7728 1.53353
\(576\) 0 0
\(577\) 6.56790 0.273425 0.136713 0.990611i \(-0.456346\pi\)
0.136713 + 0.990611i \(0.456346\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.40149 + 0.994728i −0.0996304 + 0.0412683i
\(582\) 0 0
\(583\) −18.1919 18.1919i −0.753430 0.753430i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.5921 + 6.87268i −0.684830 + 0.283666i −0.697844 0.716249i \(-0.745857\pi\)
0.0130142 + 0.999915i \(0.495857\pi\)
\(588\) 0 0
\(589\) 17.4172 42.0490i 0.717665 1.73260i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 28.8208 1.18353 0.591765 0.806111i \(-0.298431\pi\)
0.591765 + 0.806111i \(0.298431\pi\)
\(594\) 0 0
\(595\) −4.16047 1.72332i −0.170563 0.0706494i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17.4840 + 17.4840i 0.714377 + 0.714377i 0.967448 0.253071i \(-0.0814405\pi\)
−0.253071 + 0.967448i \(0.581440\pi\)
\(600\) 0 0
\(601\) 33.1960 33.1960i 1.35409 1.35409i 0.473065 0.881028i \(-0.343148\pi\)
0.881028 0.473065i \(-0.156852\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.04030 + 16.9968i −0.286229 + 0.691017i
\(606\) 0 0
\(607\) 15.7874i 0.640790i −0.947284 0.320395i \(-0.896184\pi\)
0.947284 0.320395i \(-0.103816\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.576160 + 0.238653i 0.0233090 + 0.00965488i
\(612\) 0 0
\(613\) −1.45651 3.51632i −0.0588278 0.142023i 0.891733 0.452563i \(-0.149490\pi\)
−0.950560 + 0.310540i \(0.899490\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.98815 5.98815i 0.241074 0.241074i −0.576220 0.817294i \(-0.695473\pi\)
0.817294 + 0.576220i \(0.195473\pi\)
\(618\) 0 0
\(619\) 7.03768 + 16.9905i 0.282868 + 0.682905i 0.999900 0.0141358i \(-0.00449972\pi\)
−0.717032 + 0.697041i \(0.754500\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.916479i 0.0367179i
\(624\) 0 0
\(625\) 23.0533i 0.922132i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.730862 + 1.76446i 0.0291414 + 0.0703535i
\(630\) 0 0
\(631\) 19.0530 19.0530i 0.758486 0.758486i −0.217561 0.976047i \(-0.569810\pi\)
0.976047 + 0.217561i \(0.0698100\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 11.6037 + 28.0139i 0.460481 + 1.11170i
\(636\) 0 0
\(637\) −0.649495 0.269030i −0.0257339 0.0106593i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.84179i 0.191239i 0.995418 + 0.0956197i \(0.0304833\pi\)
−0.995418 + 0.0956197i \(0.969517\pi\)
\(642\) 0 0
\(643\) 1.99669 4.82043i 0.0787417 0.190099i −0.879606 0.475702i \(-0.842194\pi\)
0.958348 + 0.285603i \(0.0921939\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.0278 23.0278i 0.905316 0.905316i −0.0905742 0.995890i \(-0.528870\pi\)
0.995890 + 0.0905742i \(0.0288702\pi\)
\(648\) 0 0
\(649\) 5.06786 + 5.06786i 0.198931 + 0.198931i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25.3058 + 10.4820i 0.990294 + 0.410193i 0.818229 0.574893i \(-0.194956\pi\)
0.172065 + 0.985086i \(0.444956\pi\)
\(654\) 0 0
\(655\) 10.9768 0.428897
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.74923 21.1225i 0.340821 0.822816i −0.656812 0.754055i \(-0.728095\pi\)
0.997633 0.0687611i \(-0.0219046\pi\)
\(660\) 0 0
\(661\) 14.1409 5.85735i 0.550017 0.227824i −0.0903280 0.995912i \(-0.528792\pi\)
0.640345 + 0.768088i \(0.278792\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.52350 3.52350i −0.136635 0.136635i
\(666\) 0 0
\(667\) 48.0751 19.9133i 1.86147 0.771048i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −15.6578 −0.604464
\(672\) 0 0
\(673\) 38.4339 1.48152 0.740758 0.671772i \(-0.234466\pi\)
0.740758 + 0.671772i \(0.234466\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.0186 4.56407i 0.423481 0.175412i −0.160757 0.986994i \(-0.551394\pi\)
0.584238 + 0.811583i \(0.301394\pi\)
\(678\) 0 0
\(679\) 3.08535 + 3.08535i 0.118405 + 0.118405i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.4586 18.4153i 1.70116 0.704643i 0.701195 0.712970i \(-0.252650\pi\)
0.999965 + 0.00832649i \(0.00265043\pi\)
\(684\) 0 0
\(685\) −14.3971 + 34.7577i −0.550085 + 1.32802i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.14235 0.0435199
\(690\) 0 0
\(691\) 2.14643 + 0.889080i 0.0816540 + 0.0338222i 0.423137 0.906066i \(-0.360929\pi\)
−0.341483 + 0.939888i \(0.610929\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.55461 2.55461i −0.0969017 0.0969017i
\(696\) 0 0
\(697\) −31.9540 + 31.9540i −1.21034 + 1.21034i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.0073 26.5740i 0.415740 1.00368i −0.567828 0.823147i \(-0.692216\pi\)
0.983568 0.180537i \(-0.0577837\pi\)
\(702\) 0 0
\(703\) 2.11328i 0.0797040i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.45478 1.43101i −0.129930 0.0538189i
\(708\) 0 0
\(709\) 2.62019 + 6.32569i 0.0984031 + 0.237566i 0.965413 0.260724i \(-0.0839613\pi\)
−0.867010 + 0.498290i \(0.833961\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 47.9261 47.9261i 1.79485 1.79485i
\(714\) 0 0
\(715\) 0.289095 + 0.697937i 0.0108115 + 0.0261014i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17.1528i 0.639691i 0.947470 + 0.319845i \(0.103631\pi\)
−0.947470 + 0.319845i \(0.896369\pi\)
\(720\) 0 0
\(721\) 3.16839i 0.117997i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −15.5751 37.6017i −0.578445 1.39649i
\(726\) 0 0
\(727\) 7.52775 7.52775i 0.279189 0.279189i −0.553596 0.832785i \(-0.686745\pi\)
0.832785 + 0.553596i \(0.186745\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.4659 30.0954i −0.461068 1.11312i
\(732\) 0 0
\(733\) −7.56986 3.13554i −0.279599 0.115814i 0.238477 0.971148i \(-0.423352\pi\)
−0.518076 + 0.855334i \(0.673352\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34.0482i 1.25418i
\(738\) 0 0
\(739\) −3.52118 + 8.50088i −0.129529 + 0.312710i −0.975317 0.220808i \(-0.929130\pi\)
0.845789 + 0.533518i \(0.179130\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −6.66625 + 6.66625i −0.244561 + 0.244561i −0.818734 0.574173i \(-0.805324\pi\)
0.574173 + 0.818734i \(0.305324\pi\)
\(744\) 0 0
\(745\) 1.50597 + 1.50597i 0.0551745 + 0.0551745i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.74431 1.55094i −0.136814 0.0566702i
\(750\) 0 0
\(751\) −8.17302 −0.298238 −0.149119 0.988819i \(-0.547644\pi\)
−0.149119 + 0.988819i \(0.547644\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20.0140 + 48.3180i −0.728383 + 1.75847i
\(756\) 0 0
\(757\) −17.8950 + 7.41237i −0.650406 + 0.269407i −0.683395 0.730049i \(-0.739497\pi\)
0.0329891 + 0.999456i \(0.489497\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 30.8536 + 30.8536i 1.11844 + 1.11844i 0.991970 + 0.126471i \(0.0403650\pi\)
0.126471 + 0.991970i \(0.459635\pi\)
\(762\) 0 0
\(763\) 2.99049 1.23870i 0.108263 0.0448441i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.318233 −0.0114907
\(768\) 0 0
\(769\) 36.0834 1.30120 0.650599 0.759421i \(-0.274518\pi\)
0.650599 + 0.759421i \(0.274518\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14.9974 6.21213i 0.539419 0.223435i −0.0963038 0.995352i \(-0.530702\pi\)
0.635723 + 0.771917i \(0.280702\pi\)
\(774\) 0 0
\(775\) −37.4852 37.4852i −1.34651 1.34651i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −46.1974 + 19.1356i −1.65519 + 0.685604i
\(780\) 0 0
\(781\) 4.34575 10.4916i 0.155503 0.375418i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −47.7779 −1.70527
\(786\) 0 0
\(787\) −43.7262 18.1120i −1.55867 0.645623i −0.573813 0.818986i \(-0.694536\pi\)
−0.984858 + 0.173364i \(0.944536\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.70234 + 1.70234i 0.0605284 + 0.0605284i
\(792\) 0 0
\(793\) 0.491611 0.491611i 0.0174576 0.0174576i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.6617 + 25.7396i −0.377656 + 0.911742i 0.614748 + 0.788723i \(0.289258\pi\)
−0.992404 + 0.123019i \(0.960742\pi\)
\(798\) 0 0
\(799\) 25.4218i 0.899358i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.28155 + 1.77347i 0.151092 + 0.0625845i
\(804\) 0 0