Properties

Label 1152.2.w.b.431.2
Level $1152$
Weight $2$
Character 1152.431
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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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 431.2
Character \(\chi\) \(=\) 1152.431
Dual form 1152.2.w.b.719.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.70076 + 1.11869i) q^{5} +(1.06647 + 1.06647i) q^{7} +O(q^{10})\) \(q+(-2.70076 + 1.11869i) q^{5} +(1.06647 + 1.06647i) q^{7} +(-5.29504 + 2.19328i) q^{11} +(1.67540 - 4.04478i) q^{13} +3.44484 q^{17} +(-3.23205 - 1.33876i) q^{19} +(-0.703083 - 0.703083i) q^{23} +(2.50711 - 2.50711i) q^{25} +(3.94721 - 9.52941i) q^{29} -4.23846i q^{31} +(-4.07335 - 1.68724i) q^{35} +(-2.04600 - 4.93947i) q^{37} +(-3.53573 + 3.53573i) q^{41} +(3.38340 + 8.16825i) q^{43} -4.33671i q^{47} -4.72526i q^{49} +(-0.541366 - 1.30697i) q^{53} +(11.8470 - 11.8470i) q^{55} +(-3.66093 - 8.83827i) q^{59} +(-1.97197 - 0.816817i) q^{61} +12.7983i q^{65} +(3.55849 - 8.59096i) q^{67} +(1.76501 - 1.76501i) q^{71} +(-1.16342 - 1.16342i) q^{73} +(-7.98610 - 3.30795i) q^{77} -14.4770 q^{79} +(-4.27230 + 10.3143i) q^{83} +(-9.30371 + 3.85372i) q^{85} +(-7.99481 - 7.99481i) q^{89} +(6.10044 - 2.52688i) q^{91} +10.2267 q^{95} +12.8450 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) 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
\(5\) −2.70076 + 1.11869i −1.20782 + 0.500294i −0.893517 0.449029i \(-0.851770\pi\)
−0.314300 + 0.949324i \(0.601770\pi\)
\(6\) 0 0
\(7\) 1.06647 + 1.06647i 0.403090 + 0.403090i 0.879320 0.476231i \(-0.157997\pi\)
−0.476231 + 0.879320i \(0.657997\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.29504 + 2.19328i −1.59651 + 0.661297i −0.990917 0.134475i \(-0.957065\pi\)
−0.605596 + 0.795772i \(0.707065\pi\)
\(12\) 0 0
\(13\) 1.67540 4.04478i 0.464674 1.12182i −0.501783 0.864993i \(-0.667323\pi\)
0.966457 0.256828i \(-0.0826774\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.44484 0.835498 0.417749 0.908563i \(-0.362819\pi\)
0.417749 + 0.908563i \(0.362819\pi\)
\(18\) 0 0
\(19\) −3.23205 1.33876i −0.741483 0.307132i −0.0202218 0.999796i \(-0.506437\pi\)
−0.721261 + 0.692663i \(0.756437\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.703083 0.703083i −0.146603 0.146603i 0.629996 0.776599i \(-0.283057\pi\)
−0.776599 + 0.629996i \(0.783057\pi\)
\(24\) 0 0
\(25\) 2.50711 2.50711i 0.501422 0.501422i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.94721 9.52941i 0.732979 1.76957i 0.100574 0.994930i \(-0.467932\pi\)
0.632405 0.774638i \(-0.282068\pi\)
\(30\) 0 0
\(31\) 4.23846i 0.761250i −0.924729 0.380625i \(-0.875709\pi\)
0.924729 0.380625i \(-0.124291\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.07335 1.68724i −0.688522 0.285195i
\(36\) 0 0
\(37\) −2.04600 4.93947i −0.336360 0.812044i −0.998059 0.0622749i \(-0.980164\pi\)
0.661699 0.749769i \(-0.269836\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.53573 + 3.53573i −0.552188 + 0.552188i −0.927072 0.374884i \(-0.877683\pi\)
0.374884 + 0.927072i \(0.377683\pi\)
\(42\) 0 0
\(43\) 3.38340 + 8.16825i 0.515963 + 1.24565i 0.940364 + 0.340171i \(0.110485\pi\)
−0.424400 + 0.905475i \(0.639515\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.33671i 0.632575i −0.948663 0.316287i \(-0.897564\pi\)
0.948663 0.316287i \(-0.102436\pi\)
\(48\) 0 0
\(49\) 4.72526i 0.675038i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.541366 1.30697i −0.0743624 0.179527i 0.882327 0.470636i \(-0.155976\pi\)
−0.956690 + 0.291110i \(0.905976\pi\)
\(54\) 0 0
\(55\) 11.8470 11.8470i 1.59745 1.59745i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.66093 8.83827i −0.476613 1.15064i −0.961188 0.275895i \(-0.911026\pi\)
0.484575 0.874750i \(-0.338974\pi\)
\(60\) 0 0
\(61\) −1.97197 0.816817i −0.252485 0.104583i 0.252851 0.967505i \(-0.418632\pi\)
−0.505336 + 0.862922i \(0.668632\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.7983i 1.58743i
\(66\) 0 0
\(67\) 3.55849 8.59096i 0.434739 1.04955i −0.543001 0.839732i \(-0.682712\pi\)
0.977740 0.209821i \(-0.0672880\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.76501 1.76501i 0.209468 0.209468i −0.594574 0.804041i \(-0.702679\pi\)
0.804041 + 0.594574i \(0.202679\pi\)
\(72\) 0 0
\(73\) −1.16342 1.16342i −0.136168 0.136168i 0.635737 0.771905i \(-0.280696\pi\)
−0.771905 + 0.635737i \(0.780696\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.98610 3.30795i −0.910100 0.376976i
\(78\) 0 0
\(79\) −14.4770 −1.62879 −0.814393 0.580314i \(-0.802930\pi\)
−0.814393 + 0.580314i \(0.802930\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.27230 + 10.3143i −0.468946 + 1.13214i 0.495678 + 0.868507i \(0.334920\pi\)
−0.964624 + 0.263630i \(0.915080\pi\)
\(84\) 0 0
\(85\) −9.30371 + 3.85372i −1.00913 + 0.417995i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.99481 7.99481i −0.847448 0.847448i 0.142366 0.989814i \(-0.454529\pi\)
−0.989814 + 0.142366i \(0.954529\pi\)
\(90\) 0 0
\(91\) 6.10044 2.52688i 0.639500 0.264889i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.2267 1.04923
\(96\) 0 0
\(97\) 12.8450 1.30421 0.652107 0.758127i \(-0.273885\pi\)
0.652107 + 0.758127i \(0.273885\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.195046 + 0.0807908i −0.0194078 + 0.00803898i −0.392366 0.919809i \(-0.628343\pi\)
0.372958 + 0.927848i \(0.378343\pi\)
\(102\) 0 0
\(103\) −7.52990 7.52990i −0.741943 0.741943i 0.231009 0.972952i \(-0.425797\pi\)
−0.972952 + 0.231009i \(0.925797\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.43177 2.66413i 0.621783 0.257551i −0.0494744 0.998775i \(-0.515755\pi\)
0.671257 + 0.741225i \(0.265755\pi\)
\(108\) 0 0
\(109\) −4.89484 + 11.8172i −0.468840 + 1.13188i 0.495830 + 0.868420i \(0.334864\pi\)
−0.964670 + 0.263461i \(0.915136\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.983568 −0.0925263 −0.0462631 0.998929i \(-0.514731\pi\)
−0.0462631 + 0.998929i \(0.514731\pi\)
\(114\) 0 0
\(115\) 2.68539 + 1.11233i 0.250414 + 0.103725i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.67384 + 3.67384i 0.336780 + 0.336780i
\(120\) 0 0
\(121\) 15.4488 15.4488i 1.40443 1.40443i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.62704 3.92802i 0.145527 0.351333i
\(126\) 0 0
\(127\) 5.32766i 0.472754i 0.971661 + 0.236377i \(0.0759600\pi\)
−0.971661 + 0.236377i \(0.924040\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.7023 7.33252i −1.54666 0.640646i −0.563948 0.825811i \(-0.690718\pi\)
−0.982707 + 0.185165i \(0.940718\pi\)
\(132\) 0 0
\(133\) −2.01915 4.87465i −0.175082 0.422686i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0787 + 10.0787i −0.861079 + 0.861079i −0.991464 0.130384i \(-0.958379\pi\)
0.130384 + 0.991464i \(0.458379\pi\)
\(138\) 0 0
\(139\) 4.57378 + 11.0421i 0.387943 + 0.936578i 0.990375 + 0.138408i \(0.0441984\pi\)
−0.602432 + 0.798170i \(0.705802\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 25.0919i 2.09829i
\(144\) 0 0
\(145\) 30.1524i 2.50402i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.47497 5.97511i −0.202758 0.489500i 0.789492 0.613761i \(-0.210344\pi\)
−0.992250 + 0.124261i \(0.960344\pi\)
\(150\) 0 0
\(151\) 5.28519 5.28519i 0.430103 0.430103i −0.458560 0.888663i \(-0.651635\pi\)
0.888663 + 0.458560i \(0.151635\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.74153 + 11.4471i 0.380849 + 0.919451i
\(156\) 0 0
\(157\) 19.9431 + 8.26070i 1.59163 + 0.659276i 0.990201 0.139649i \(-0.0445973\pi\)
0.601431 + 0.798924i \(0.294597\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.49964i 0.118188i
\(162\) 0 0
\(163\) −4.75817 + 11.4872i −0.372689 + 0.899751i 0.620604 + 0.784124i \(0.286888\pi\)
−0.993293 + 0.115626i \(0.963112\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.4711 13.4711i 1.04243 1.04243i 0.0433679 0.999059i \(-0.486191\pi\)
0.999059 0.0433679i \(-0.0138088\pi\)
\(168\) 0 0
\(169\) −4.36092 4.36092i −0.335455 0.335455i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.48659 0.615768i −0.113024 0.0468160i 0.325455 0.945558i \(-0.394483\pi\)
−0.438479 + 0.898742i \(0.644483\pi\)
\(174\) 0 0
\(175\) 5.34754 0.404236
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.188898 + 0.456040i −0.0141189 + 0.0340860i −0.930782 0.365575i \(-0.880872\pi\)
0.916663 + 0.399661i \(0.130872\pi\)
\(180\) 0 0
\(181\) −20.2286 + 8.37896i −1.50358 + 0.622803i −0.974221 0.225596i \(-0.927567\pi\)
−0.529358 + 0.848398i \(0.677567\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 11.0515 + 11.0515i 0.812522 + 0.812522i
\(186\) 0 0
\(187\) −18.2406 + 7.55549i −1.33388 + 0.552512i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.3059 1.68636 0.843180 0.537632i \(-0.180681\pi\)
0.843180 + 0.537632i \(0.180681\pi\)
\(192\) 0 0
\(193\) −27.0699 −1.94854 −0.974268 0.225392i \(-0.927634\pi\)
−0.974268 + 0.225392i \(0.927634\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.234504 0.0971345i 0.0167077 0.00692055i −0.374314 0.927302i \(-0.622122\pi\)
0.391022 + 0.920381i \(0.372122\pi\)
\(198\) 0 0
\(199\) 2.87064 + 2.87064i 0.203494 + 0.203494i 0.801495 0.598001i \(-0.204038\pi\)
−0.598001 + 0.801495i \(0.704038\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 14.3725 5.95328i 1.00875 0.417838i
\(204\) 0 0
\(205\) 5.59377 13.5045i 0.390686 0.943199i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 20.0501 1.38689
\(210\) 0 0
\(211\) −21.3966 8.86277i −1.47300 0.610138i −0.505462 0.862849i \(-0.668678\pi\)
−0.967542 + 0.252710i \(0.918678\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −18.2755 18.2755i −1.24638 1.24638i
\(216\) 0 0
\(217\) 4.52021 4.52021i 0.306852 0.306852i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.77151 13.9337i 0.388234 0.937279i
\(222\) 0 0
\(223\) 6.32748i 0.423720i −0.977300 0.211860i \(-0.932048\pi\)
0.977300 0.211860i \(-0.0679520\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.62883 + 2.74575i 0.439971 + 0.182242i 0.591662 0.806186i \(-0.298472\pi\)
−0.151691 + 0.988428i \(0.548472\pi\)
\(228\) 0 0
\(229\) −2.56839 6.20065i −0.169724 0.409751i 0.816015 0.578031i \(-0.196179\pi\)
−0.985739 + 0.168280i \(0.946179\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.72679 4.72679i 0.309662 0.309662i −0.535116 0.844779i \(-0.679732\pi\)
0.844779 + 0.535116i \(0.179732\pi\)
\(234\) 0 0
\(235\) 4.85145 + 11.7124i 0.316474 + 0.764035i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5.76879i 0.373152i −0.982441 0.186576i \(-0.940261\pi\)
0.982441 0.186576i \(-0.0597390\pi\)
\(240\) 0 0
\(241\) 20.1679i 1.29913i 0.760308 + 0.649563i \(0.225048\pi\)
−0.760308 + 0.649563i \(0.774952\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.28612 + 12.7618i 0.337718 + 0.815322i
\(246\) 0 0
\(247\) −10.8300 + 10.8300i −0.689095 + 0.689095i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.288817 0.697266i −0.0182300 0.0440110i 0.914502 0.404580i \(-0.132582\pi\)
−0.932732 + 0.360569i \(0.882582\pi\)
\(252\) 0 0
\(253\) 5.26491 + 2.18080i 0.331002 + 0.137105i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.89560i 0.430136i −0.976599 0.215068i \(-0.931003\pi\)
0.976599 0.215068i \(-0.0689973\pi\)
\(258\) 0 0
\(259\) 3.08582 7.44983i 0.191743 0.462910i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.11571 + 3.11571i −0.192123 + 0.192123i −0.796613 0.604490i \(-0.793377\pi\)
0.604490 + 0.796613i \(0.293377\pi\)
\(264\) 0 0
\(265\) 2.92420 + 2.92420i 0.179632 + 0.179632i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.4085 + 5.13977i 0.756560 + 0.313378i 0.727415 0.686198i \(-0.240721\pi\)
0.0291452 + 0.999575i \(0.490721\pi\)
\(270\) 0 0
\(271\) −5.94627 −0.361210 −0.180605 0.983556i \(-0.557806\pi\)
−0.180605 + 0.983556i \(0.557806\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.77645 + 18.7740i −0.468938 + 1.13212i
\(276\) 0 0
\(277\) −8.48544 + 3.51479i −0.509841 + 0.211183i −0.622748 0.782423i \(-0.713984\pi\)
0.112907 + 0.993606i \(0.463984\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.5190 + 12.5190i 0.746823 + 0.746823i 0.973881 0.227058i \(-0.0729107\pi\)
−0.227058 + 0.973881i \(0.572911\pi\)
\(282\) 0 0
\(283\) 16.8466 6.97810i 1.00143 0.414805i 0.179107 0.983830i \(-0.442679\pi\)
0.822321 + 0.569024i \(0.192679\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.54153 −0.445162
\(288\) 0 0
\(289\) −5.13305 −0.301944
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.86190 0.771224i 0.108773 0.0450554i −0.327633 0.944805i \(-0.606251\pi\)
0.436406 + 0.899750i \(0.356251\pi\)
\(294\) 0 0
\(295\) 19.7746 + 19.7746i 1.15132 + 1.15132i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.02177 + 1.66587i −0.232585 + 0.0963398i
\(300\) 0 0
\(301\) −5.10292 + 12.3195i −0.294127 + 0.710086i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.23959 0.357278
\(306\) 0 0
\(307\) 3.70099 + 1.53300i 0.211227 + 0.0874930i 0.485788 0.874077i \(-0.338533\pi\)
−0.274561 + 0.961570i \(0.588533\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.17785 9.17785i −0.520428 0.520428i 0.397273 0.917701i \(-0.369957\pi\)
−0.917701 + 0.397273i \(0.869957\pi\)
\(312\) 0 0
\(313\) −8.66154 + 8.66154i −0.489579 + 0.489579i −0.908173 0.418594i \(-0.862523\pi\)
0.418594 + 0.908173i \(0.362523\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.41379 + 17.8985i −0.416400 + 1.00528i 0.566982 + 0.823730i \(0.308111\pi\)
−0.983382 + 0.181548i \(0.941889\pi\)
\(318\) 0 0
\(319\) 59.1159i 3.30986i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −11.1339 4.61182i −0.619507 0.256608i
\(324\) 0 0
\(325\) −5.94030 14.3411i −0.329508 0.795503i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.62500 4.62500i 0.254984 0.254984i
\(330\) 0 0
\(331\) 3.96293 + 9.56736i 0.217822 + 0.525870i 0.994585 0.103923i \(-0.0331397\pi\)
−0.776763 + 0.629793i \(0.783140\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 27.1830i 1.48517i
\(336\) 0 0
\(337\) 7.50723i 0.408945i −0.978872 0.204472i \(-0.934452\pi\)
0.978872 0.204472i \(-0.0655479\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.29611 + 22.4428i 0.503413 + 1.21535i
\(342\) 0 0
\(343\) 12.5047 12.5047i 0.675190 0.675190i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.18203 2.85368i −0.0634548 0.153194i 0.888971 0.457963i \(-0.151421\pi\)
−0.952426 + 0.304769i \(0.901421\pi\)
\(348\) 0 0
\(349\) 3.41473 + 1.41443i 0.182786 + 0.0757126i 0.472200 0.881492i \(-0.343460\pi\)
−0.289413 + 0.957204i \(0.593460\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.81226i 0.362580i 0.983430 + 0.181290i \(0.0580273\pi\)
−0.983430 + 0.181290i \(0.941973\pi\)
\(354\) 0 0
\(355\) −2.79236 + 6.74136i −0.148203 + 0.357794i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.31414 + 5.31414i −0.280469 + 0.280469i −0.833296 0.552827i \(-0.813549\pi\)
0.552827 + 0.833296i \(0.313549\pi\)
\(360\) 0 0
\(361\) −4.78116 4.78116i −0.251640 0.251640i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.44363 + 1.84061i 0.232590 + 0.0963420i
\(366\) 0 0
\(367\) −29.3775 −1.53349 −0.766745 0.641951i \(-0.778125\pi\)
−0.766745 + 0.641951i \(0.778125\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.816501 1.97121i 0.0423906 0.102340i
\(372\) 0 0
\(373\) 14.6798 6.08058i 0.760092 0.314840i 0.0312402 0.999512i \(-0.490054\pi\)
0.728852 + 0.684671i \(0.240054\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −31.9312 31.9312i −1.64454 1.64454i
\(378\) 0 0
\(379\) 1.25001 0.517769i 0.0642085 0.0265960i −0.350348 0.936620i \(-0.613937\pi\)
0.414557 + 0.910024i \(0.363937\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −35.2581 −1.80160 −0.900802 0.434230i \(-0.857020\pi\)
−0.900802 + 0.434230i \(0.857020\pi\)
\(384\) 0 0
\(385\) 25.2691 1.28783
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.34556 1.38578i 0.169627 0.0702616i −0.296254 0.955109i \(-0.595738\pi\)
0.465881 + 0.884848i \(0.345738\pi\)
\(390\) 0 0
\(391\) −2.42201 2.42201i −0.122486 0.122486i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 39.0988 16.1953i 1.96728 0.814872i
\(396\) 0 0
\(397\) −2.21822 + 5.35526i −0.111329 + 0.268773i −0.969718 0.244227i \(-0.921466\pi\)
0.858389 + 0.513000i \(0.171466\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.97617 −0.298436 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(402\) 0 0
\(403\) −17.1437 7.10114i −0.853987 0.353733i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21.6672 + 21.6672i 1.07401 + 1.07401i
\(408\) 0 0
\(409\) −5.91961 + 5.91961i −0.292706 + 0.292706i −0.838148 0.545443i \(-0.816362\pi\)
0.545443 + 0.838148i \(0.316362\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.52150 13.3301i 0.271695 0.655931i
\(414\) 0 0
\(415\) 32.6357i 1.60203i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 30.7382 + 12.7322i 1.50166 + 0.622007i 0.973816 0.227336i \(-0.0730017\pi\)
0.527841 + 0.849343i \(0.323002\pi\)
\(420\) 0 0
\(421\) 7.98264 + 19.2718i 0.389050 + 0.939249i 0.990142 + 0.140069i \(0.0447326\pi\)
−0.601092 + 0.799180i \(0.705267\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.63660 8.63660i 0.418937 0.418937i
\(426\) 0 0
\(427\) −1.23194 2.97417i −0.0596179 0.143930i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 29.2128i 1.40713i −0.710630 0.703565i \(-0.751590\pi\)
0.710630 0.703565i \(-0.248410\pi\)
\(432\) 0 0
\(433\) 17.9410i 0.862190i −0.902306 0.431095i \(-0.858127\pi\)
0.902306 0.431095i \(-0.141873\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.33114 + 3.21366i 0.0636771 + 0.153730i
\(438\) 0 0
\(439\) 8.96708 8.96708i 0.427975 0.427975i −0.459963 0.887938i \(-0.652137\pi\)
0.887938 + 0.459963i \(0.152137\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.09257 14.7088i −0.289467 0.698835i 0.710522 0.703675i \(-0.248459\pi\)
−0.999988 + 0.00484090i \(0.998459\pi\)
\(444\) 0 0
\(445\) 30.5358 + 12.6484i 1.44754 + 0.599589i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.66413i 0.172921i 0.996255 + 0.0864604i \(0.0275556\pi\)
−0.996255 + 0.0864604i \(0.972444\pi\)
\(450\) 0 0
\(451\) 10.9670 26.4766i 0.516415 1.24674i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13.6490 + 13.6490i −0.639876 + 0.639876i
\(456\) 0 0
\(457\) −13.9728 13.9728i −0.653622 0.653622i 0.300241 0.953863i \(-0.402933\pi\)
−0.953863 + 0.300241i \(0.902933\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.25638 + 0.934623i 0.105090 + 0.0435297i 0.434609 0.900619i \(-0.356887\pi\)
−0.329519 + 0.944149i \(0.606887\pi\)
\(462\) 0 0
\(463\) −16.4302 −0.763575 −0.381788 0.924250i \(-0.624691\pi\)
−0.381788 + 0.924250i \(0.624691\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.14599 19.6662i 0.376951 0.910041i −0.615582 0.788072i \(-0.711079\pi\)
0.992534 0.121969i \(-0.0389208\pi\)
\(468\) 0 0
\(469\) 12.9571 5.36700i 0.598303 0.247825i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −35.8304 35.8304i −1.64748 1.64748i
\(474\) 0 0
\(475\) −11.4595 + 4.74669i −0.525799 + 0.217793i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.35772 −0.199109 −0.0995545 0.995032i \(-0.531742\pi\)
−0.0995545 + 0.995032i \(0.531742\pi\)
\(480\) 0 0
\(481\) −23.4070 −1.06727
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −34.6914 + 14.3696i −1.57525 + 0.652491i
\(486\) 0 0
\(487\) −10.1865 10.1865i −0.461594 0.461594i 0.437584 0.899178i \(-0.355834\pi\)
−0.899178 + 0.437584i \(0.855834\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −28.0848 + 11.6331i −1.26745 + 0.524994i −0.912187 0.409774i \(-0.865608\pi\)
−0.355260 + 0.934768i \(0.615608\pi\)
\(492\) 0 0
\(493\) 13.5975 32.8273i 0.612402 1.47847i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.76467 0.168869
\(498\) 0 0
\(499\) 20.5327 + 8.50493i 0.919170 + 0.380733i 0.791560 0.611092i \(-0.209269\pi\)
0.127610 + 0.991824i \(0.459269\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6.66355 6.66355i −0.297113 0.297113i 0.542769 0.839882i \(-0.317376\pi\)
−0.839882 + 0.542769i \(0.817376\pi\)
\(504\) 0 0
\(505\) 0.436393 0.436393i 0.0194192 0.0194192i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.13590 9.98494i 0.183320 0.442575i −0.805327 0.592831i \(-0.798010\pi\)
0.988647 + 0.150257i \(0.0480101\pi\)
\(510\) 0 0
\(511\) 2.48152i 0.109776i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 28.7601 + 11.9128i 1.26732 + 0.524942i
\(516\) 0 0
\(517\) 9.51161 + 22.9631i 0.418320 + 1.00991i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.91587 + 2.91587i −0.127746 + 0.127746i −0.768089 0.640343i \(-0.778792\pi\)
0.640343 + 0.768089i \(0.278792\pi\)
\(522\) 0 0
\(523\) −14.2159 34.3201i −0.621616 1.50071i −0.849805 0.527097i \(-0.823280\pi\)
0.228189 0.973617i \(-0.426720\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.6008i 0.636023i
\(528\) 0 0
\(529\) 22.0113i 0.957015i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.37748 + 20.2250i 0.362869 + 0.876043i
\(534\) 0 0
\(535\) −14.3903 + 14.3903i −0.622149 + 0.622149i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.3638 + 25.0204i 0.446401 + 1.07771i
\(540\) 0 0
\(541\) −29.5435 12.2373i −1.27017 0.526123i −0.357157 0.934044i \(-0.616254\pi\)
−0.913017 + 0.407921i \(0.866254\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 37.3912i 1.60166i
\(546\) 0 0
\(547\) 11.8740 28.6664i 0.507696 1.22569i −0.437510 0.899213i \(-0.644140\pi\)
0.945206 0.326474i \(-0.105860\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −25.5152 + 25.5152i −1.08698 + 1.08698i
\(552\) 0 0
\(553\) −15.4393 15.4393i −0.656546 0.656546i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.2393 6.72656i −0.688083 0.285013i 0.0111181 0.999938i \(-0.496461\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(558\) 0 0
\(559\) 38.7074 1.63715
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.7698 38.0718i 0.664620 1.60453i −0.125862 0.992048i \(-0.540170\pi\)
0.790481 0.612486i \(-0.209830\pi\)
\(564\) 0 0
\(565\) 2.65638 1.10031i 0.111755 0.0462904i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.0276 + 11.0276i 0.462302 + 0.462302i 0.899409 0.437107i \(-0.143997\pi\)
−0.437107 + 0.899409i \(0.643997\pi\)
\(570\) 0 0
\(571\) 31.3409 12.9818i 1.31157 0.543272i 0.386231 0.922402i \(-0.373777\pi\)
0.925343 + 0.379130i \(0.123777\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.52541 −0.147020
\(576\) 0 0
\(577\) −2.28631 −0.0951802 −0.0475901 0.998867i \(-0.515154\pi\)
−0.0475901 + 0.998867i \(0.515154\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15.5562 + 6.44359i −0.645380 + 0.267325i
\(582\) 0 0
\(583\) 5.73311 + 5.73311i 0.237441 + 0.237441i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.89005 2.43974i 0.243108 0.100699i −0.257803 0.966198i \(-0.582998\pi\)
0.500911 + 0.865499i \(0.332998\pi\)
\(588\) 0 0
\(589\) −5.67428 + 13.6989i −0.233805 + 0.564454i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.9801 −0.450897 −0.225449 0.974255i \(-0.572385\pi\)
−0.225449 + 0.974255i \(0.572385\pi\)
\(594\) 0 0
\(595\) −14.0321 5.81227i −0.575259 0.238280i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.54515 3.54515i −0.144851 0.144851i 0.630962 0.775813i \(-0.282660\pi\)
−0.775813 + 0.630962i \(0.782660\pi\)
\(600\) 0 0
\(601\) 0.844578 0.844578i 0.0344511 0.0344511i −0.689671 0.724122i \(-0.742245\pi\)
0.724122 + 0.689671i \(0.242245\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −24.4410 + 59.0059i −0.993669 + 2.39893i
\(606\) 0 0
\(607\) 17.9859i 0.730024i −0.931003 0.365012i \(-0.881065\pi\)
0.931003 0.365012i \(-0.118935\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17.5411 7.26575i −0.709636 0.293941i
\(612\) 0 0
\(613\) −6.72419 16.2336i −0.271588 0.655671i 0.727964 0.685615i \(-0.240467\pi\)
−0.999552 + 0.0299448i \(0.990467\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.70935 + 8.70935i −0.350625 + 0.350625i −0.860342 0.509717i \(-0.829750\pi\)
0.509717 + 0.860342i \(0.329750\pi\)
\(618\) 0 0
\(619\) 3.38639 + 8.17546i 0.136110 + 0.328600i 0.977208 0.212284i \(-0.0680901\pi\)
−0.841098 + 0.540883i \(0.818090\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17.0525i 0.683195i
\(624\) 0 0
\(625\) 30.1567i 1.20627i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.04814 17.0157i −0.281028 0.678461i
\(630\) 0 0
\(631\) −2.69060 + 2.69060i −0.107111 + 0.107111i −0.758631 0.651520i \(-0.774132\pi\)
0.651520 + 0.758631i \(0.274132\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.96002 14.3888i −0.236516 0.571000i
\(636\) 0 0
\(637\) −19.1127 7.91673i −0.757272 0.313672i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 37.2166i 1.46997i −0.678084 0.734984i \(-0.737189\pi\)
0.678084 0.734984i \(-0.262811\pi\)
\(642\) 0 0
\(643\) 11.0037 26.5652i 0.433942 1.04763i −0.544063 0.839044i \(-0.683115\pi\)
0.978005 0.208583i \(-0.0668853\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.0988 30.0988i 1.18331 1.18331i 0.204426 0.978882i \(-0.434467\pi\)
0.978882 0.204426i \(-0.0655327\pi\)
\(648\) 0 0
\(649\) 38.7695 + 38.7695i 1.52184 + 1.52184i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.00245 + 1.65787i 0.156628 + 0.0648775i 0.459620 0.888116i \(-0.347986\pi\)
−0.302992 + 0.952993i \(0.597986\pi\)
\(654\) 0 0
\(655\) 56.0125 2.18859
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.32569 + 5.61472i −0.0905962 + 0.218719i −0.962682 0.270634i \(-0.912767\pi\)
0.872086 + 0.489352i \(0.162767\pi\)
\(660\) 0 0
\(661\) 37.0965 15.3659i 1.44288 0.597662i 0.482389 0.875957i \(-0.339769\pi\)
0.960496 + 0.278295i \(0.0897692\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.9065 + 10.9065i 0.422935 + 0.422935i
\(666\) 0 0
\(667\) −9.47519 + 3.92475i −0.366881 + 0.151967i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.2332 0.472256
\(672\) 0 0
\(673\) −13.6208 −0.525043 −0.262521 0.964926i \(-0.584554\pi\)
−0.262521 + 0.964926i \(0.584554\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.5314 4.77647i 0.443189 0.183575i −0.149918 0.988698i \(-0.547901\pi\)
0.593107 + 0.805124i \(0.297901\pi\)
\(678\) 0 0
\(679\) 13.6989 + 13.6989i 0.525715 + 0.525715i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −37.0003 + 15.3260i −1.41578 + 0.586435i −0.953796 0.300454i \(-0.902862\pi\)
−0.461982 + 0.886889i \(0.652862\pi\)
\(684\) 0 0
\(685\) 15.9452 38.4950i 0.609233 1.47082i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.19344 −0.235951
\(690\) 0 0
\(691\) −6.40367 2.65249i −0.243607 0.100905i 0.257539 0.966268i \(-0.417088\pi\)
−0.501147 + 0.865362i \(0.667088\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.7054 24.7054i −0.937129 0.937129i
\(696\) 0 0
\(697\) −12.1800 + 12.1800i −0.461352 + 0.461352i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7.95095 19.1953i 0.300303 0.724996i −0.699642 0.714494i \(-0.746657\pi\)
0.999945 0.0105021i \(-0.00334297\pi\)
\(702\) 0 0
\(703\) 18.7037i 0.705424i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.294173 0.121850i −0.0110635 0.00458266i
\(708\) 0 0
\(709\) 0.602133 + 1.45368i 0.0226136 + 0.0545940i 0.934783 0.355219i \(-0.115594\pi\)
−0.912169 + 0.409813i \(0.865594\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.97999 + 2.97999i −0.111602 + 0.111602i
\(714\) 0 0
\(715\) −28.0701 67.7673i −1.04976 2.53435i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 36.1660i 1.34877i 0.738382 + 0.674383i \(0.235590\pi\)
−0.738382 + 0.674383i \(0.764410\pi\)
\(720\) 0 0
\(721\) 16.0609i 0.598139i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13.9952 33.7874i −0.519768 1.25483i
\(726\) 0 0
\(727\) 3.48345 3.48345i 0.129194 0.129194i −0.639553 0.768747i \(-0.720881\pi\)
0.768747 + 0.639553i \(0.220881\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.6553 + 28.1383i 0.431086 + 1.04073i
\(732\) 0 0
\(733\) −9.32567 3.86282i −0.344452 0.142677i 0.203750 0.979023i \(-0.434687\pi\)
−0.548201 + 0.836347i \(0.684687\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 53.2942i 1.96312i
\(738\) 0 0
\(739\) −18.2859 + 44.1460i −0.672657 + 1.62394i 0.104421 + 0.994533i \(0.466701\pi\)
−0.777078 + 0.629404i \(0.783299\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −26.3660 + 26.3660i −0.967273 + 0.967273i −0.999481 0.0322079i \(-0.989746\pi\)
0.0322079 + 0.999481i \(0.489746\pi\)
\(744\) 0 0
\(745\) 13.3686 + 13.3686i 0.489789 + 0.489789i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 9.70055 + 4.01810i 0.354450 + 0.146818i
\(750\) 0 0
\(751\) −31.9193 −1.16475 −0.582377 0.812919i \(-0.697877\pi\)
−0.582377 + 0.812919i \(0.697877\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.36155 + 20.1866i −0.304308 + 0.734664i
\(756\) 0 0
\(757\) 25.8156 10.6932i 0.938284 0.388650i 0.139469 0.990226i \(-0.455461\pi\)
0.798815 + 0.601577i \(0.205461\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14.4436 + 14.4436i 0.523579 + 0.523579i 0.918650 0.395072i \(-0.129280\pi\)
−0.395072 + 0.918650i \(0.629280\pi\)
\(762\) 0 0
\(763\) −17.8229 + 7.38250i −0.645234 + 0.267265i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −41.8824 −1.51229
\(768\) 0 0
\(769\) 21.6737 0.781574 0.390787 0.920481i \(-0.372203\pi\)
0.390787 + 0.920481i \(0.372203\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5.45257 + 2.25853i −0.196115 + 0.0812336i −0.478580 0.878044i \(-0.658848\pi\)
0.282464 + 0.959278i \(0.408848\pi\)
\(774\) 0 0
\(775\) −10.6263 10.6263i −0.381708 0.381708i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16.1611 6.69416i 0.579033 0.239843i
\(780\) 0 0
\(781\) −5.47463 + 13.2169i −0.195898 + 0.472939i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −63.1027 −2.25223
\(786\) 0 0
\(787\) 38.9288 + 16.1249i 1.38766 + 0.574789i 0.946519 0.322647i \(-0.104573\pi\)
0.441144 + 0.897436i \(0.354573\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.04895 1.04895i −0.0372964 0.0372964i
\(792\) 0 0
\(793\) −6.60770 + 6.60770i −0.234646 + 0.234646i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13.4105 + 32.3759i −0.475025 + 1.14681i 0.486890 + 0.873463i \(0.338131\pi\)
−0.961915 + 0.273349i \(0.911869\pi\)
\(798\) 0 0
\(799\) 14.9393i 0.528515i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.71205 + 3.60865i 0.307442 + 0.127346i
\(804\) 0 0