Properties

Label 1620.2.r.h.109.4
Level $1620$
Weight $2$
Character 1620.109
Analytic conductor $12.936$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.9357651274\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 3 x^{14} - 11 x^{12} - 90 x^{10} - 450 x^{8} - 2250 x^{6} - 6875 x^{4} + 46875 x^{2} + 390625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.4
Root \(0.308893 + 2.21463i\) of defining polynomial
Character \(\chi\) \(=\) 1620.109
Dual form 1620.2.r.h.1189.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.308893 + 2.21463i) q^{5} +(4.27415 - 2.46768i) q^{7} +O(q^{10})\) \(q+(-0.308893 + 2.21463i) q^{5} +(4.27415 - 2.46768i) q^{7} +(-1.20635 - 2.08945i) q^{11} +(2.51942 + 1.45459i) q^{13} -6.86869i q^{17} +4.17891 q^{19} +(-2.90917 - 1.67961i) q^{23} +(-4.80917 - 1.36817i) q^{25} +(-2.59808 - 4.50000i) q^{29} +(3.08945 - 5.35109i) q^{31} +(4.14474 + 10.2279i) q^{35} +7.84453i q^{37} +(-2.93840 + 5.08945i) q^{41} +(-4.27415 + 2.46768i) q^{43} +(10.3122 - 5.95376i) q^{47} +(8.67891 - 15.0323i) q^{49} +8.54830i q^{53} +(5.00000 - 2.02619i) q^{55} +(0.525704 - 0.910546i) q^{59} +(-4.58945 - 7.94917i) q^{61} +(-3.99960 + 5.13026i) q^{65} +(-3.50947 - 2.02619i) q^{67} +14.1663 q^{71} -2.02619i q^{73} +(-10.3122 - 5.95376i) q^{77} +(3.00000 + 5.19615i) q^{79} +(-4.49387 + 2.59454i) q^{83} +(15.2116 + 2.12169i) q^{85} +3.09334 q^{89} +14.3578 q^{91} +(-1.29084 + 9.25473i) q^{95} +(0.764681 - 0.441489i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −0.308893 + 2.21463i −0.138141 + 0.990413i
\(6\) 0 0
\(7\) 4.27415 2.46768i 1.61548 0.932696i 0.627407 0.778692i \(-0.284116\pi\)
0.988070 0.154005i \(-0.0492170\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.20635 2.08945i −0.363727 0.629994i 0.624844 0.780750i \(-0.285163\pi\)
−0.988571 + 0.150756i \(0.951829\pi\)
\(12\) 0 0
\(13\) 2.51942 + 1.45459i 0.698760 + 0.403429i 0.806886 0.590708i \(-0.201151\pi\)
−0.108125 + 0.994137i \(0.534485\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.86869i 1.66590i −0.553347 0.832951i \(-0.686650\pi\)
0.553347 0.832951i \(-0.313350\pi\)
\(18\) 0 0
\(19\) 4.17891 0.958707 0.479354 0.877622i \(-0.340871\pi\)
0.479354 + 0.877622i \(0.340871\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.90917 1.67961i −0.606604 0.350223i 0.165031 0.986288i \(-0.447228\pi\)
−0.771635 + 0.636065i \(0.780561\pi\)
\(24\) 0 0
\(25\) −4.80917 1.36817i −0.961834 0.273634i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.59808 4.50000i −0.482451 0.835629i 0.517346 0.855776i \(-0.326920\pi\)
−0.999797 + 0.0201471i \(0.993587\pi\)
\(30\) 0 0
\(31\) 3.08945 5.35109i 0.554882 0.961084i −0.443030 0.896507i \(-0.646097\pi\)
0.997913 0.0645778i \(-0.0205701\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.14474 + 10.2279i 0.700590 + 1.72883i
\(36\) 0 0
\(37\) 7.84453i 1.28963i 0.764337 + 0.644817i \(0.223066\pi\)
−0.764337 + 0.644817i \(0.776934\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.93840 + 5.08945i −0.458901 + 0.794839i −0.998903 0.0468242i \(-0.985090\pi\)
0.540003 + 0.841663i \(0.318423\pi\)
\(42\) 0 0
\(43\) −4.27415 + 2.46768i −0.651802 + 0.376318i −0.789146 0.614205i \(-0.789477\pi\)
0.137344 + 0.990523i \(0.456143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.3122 5.95376i 1.50419 0.868445i 0.504203 0.863585i \(-0.331786\pi\)
0.999988 0.00486027i \(-0.00154708\pi\)
\(48\) 0 0
\(49\) 8.67891 15.0323i 1.23984 2.14747i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.54830i 1.17420i 0.809515 + 0.587100i \(0.199730\pi\)
−0.809515 + 0.587100i \(0.800270\pi\)
\(54\) 0 0
\(55\) 5.00000 2.02619i 0.674200 0.273212i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.525704 0.910546i 0.0684408 0.118543i −0.829774 0.558099i \(-0.811531\pi\)
0.898215 + 0.439556i \(0.144864\pi\)
\(60\) 0 0
\(61\) −4.58945 7.94917i −0.587619 1.01779i −0.994543 0.104325i \(-0.966732\pi\)
0.406924 0.913462i \(-0.366601\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.99960 + 5.13026i −0.496089 + 0.636331i
\(66\) 0 0
\(67\) −3.50947 2.02619i −0.428750 0.247539i 0.270064 0.962842i \(-0.412955\pi\)
−0.698814 + 0.715303i \(0.746288\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.1663 1.68123 0.840614 0.541634i \(-0.182194\pi\)
0.840614 + 0.541634i \(0.182194\pi\)
\(72\) 0 0
\(73\) 2.02619i 0.237148i −0.992945 0.118574i \(-0.962168\pi\)
0.992945 0.118574i \(-0.0378323\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.3122 5.95376i −1.17519 0.678494i
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.49387 + 2.59454i −0.493267 + 0.284788i −0.725929 0.687770i \(-0.758590\pi\)
0.232662 + 0.972558i \(0.425256\pi\)
\(84\) 0 0
\(85\) 15.2116 + 2.12169i 1.64993 + 0.230130i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.09334 0.327893 0.163947 0.986469i \(-0.447578\pi\)
0.163947 + 0.986469i \(0.447578\pi\)
\(90\) 0 0
\(91\) 14.3578 1.50511
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.29084 + 9.25473i −0.132437 + 0.949516i
\(96\) 0 0
\(97\) 0.764681 0.441489i 0.0776416 0.0448264i −0.460677 0.887568i \(-0.652393\pi\)
0.538318 + 0.842742i \(0.319060\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.93840 + 5.08945i 0.292382 + 0.506420i 0.974372 0.224941i \(-0.0722190\pi\)
−0.681991 + 0.731361i \(0.738886\pi\)
\(102\) 0 0
\(103\) 8.54830 + 4.93536i 0.842289 + 0.486296i 0.858042 0.513580i \(-0.171681\pi\)
−0.0157525 + 0.999876i \(0.505014\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.7668 + 6.79357i 1.10693 + 0.639085i 0.938032 0.346549i \(-0.112647\pi\)
0.168896 + 0.985634i \(0.445980\pi\)
\(114\) 0 0
\(115\) 4.61834 5.92392i 0.430662 0.552408i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −16.9497 29.3578i −1.55378 2.69123i
\(120\) 0 0
\(121\) 2.58945 4.48507i 0.235405 0.407733i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.51551 10.2279i 0.403879 0.914812i
\(126\) 0 0
\(127\) 4.93536i 0.437943i 0.975731 + 0.218971i \(0.0702701\pi\)
−0.975731 + 0.218971i \(0.929730\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.08314 + 12.2684i −0.618857 + 1.07189i 0.370838 + 0.928698i \(0.379071\pi\)
−0.989695 + 0.143194i \(0.954263\pi\)
\(132\) 0 0
\(133\) 17.8613 10.3122i 1.54877 0.894183i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.36376 + 2.51942i −0.372821 + 0.215248i −0.674690 0.738101i \(-0.735723\pi\)
0.301869 + 0.953349i \(0.402389\pi\)
\(138\) 0 0
\(139\) 2.91055 5.04121i 0.246869 0.427590i −0.715786 0.698319i \(-0.753932\pi\)
0.962656 + 0.270729i \(0.0872648\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.01894i 0.586953i
\(144\) 0 0
\(145\) 10.7684 4.36376i 0.894264 0.362390i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.58788 11.4105i 0.539700 0.934788i −0.459220 0.888323i \(-0.651871\pi\)
0.998920 0.0464656i \(-0.0147958\pi\)
\(150\) 0 0
\(151\) 3.08945 + 5.35109i 0.251416 + 0.435466i 0.963916 0.266207i \(-0.0857704\pi\)
−0.712500 + 0.701672i \(0.752437\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.8964 + 8.49491i 0.875218 + 0.682328i
\(156\) 0 0
\(157\) 6.79357 + 3.92227i 0.542186 + 0.313031i 0.745964 0.665986i \(-0.231989\pi\)
−0.203779 + 0.979017i \(0.565322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −16.5790 −1.30661
\(162\) 0 0
\(163\) 10.7537i 0.842295i 0.906992 + 0.421148i \(0.138373\pi\)
−0.906992 + 0.421148i \(0.861627\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.40305 + 4.27415i 0.572865 + 0.330744i 0.758293 0.651914i \(-0.226034\pi\)
−0.185428 + 0.982658i \(0.559367\pi\)
\(168\) 0 0
\(169\) −2.26836 3.92892i −0.174489 0.302225i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.2607 9.38811i 1.23628 0.713765i 0.267945 0.963434i \(-0.413655\pi\)
0.968331 + 0.249670i \(0.0803220\pi\)
\(174\) 0 0
\(175\) −23.9313 + 6.01974i −1.80904 + 0.455050i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.97961 −0.596424 −0.298212 0.954500i \(-0.596390\pi\)
−0.298212 + 0.954500i \(0.596390\pi\)
\(180\) 0 0
\(181\) 3.82109 0.284020 0.142010 0.989865i \(-0.454644\pi\)
0.142010 + 0.989865i \(0.454644\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −17.3727 2.42313i −1.27727 0.178152i
\(186\) 0 0
\(187\) −14.3518 + 8.28602i −1.04951 + 0.605934i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.30916 + 5.73164i 0.239443 + 0.414727i 0.960554 0.278092i \(-0.0897020\pi\)
−0.721112 + 0.692819i \(0.756369\pi\)
\(192\) 0 0
\(193\) −18.8513 10.8838i −1.35695 0.783435i −0.367737 0.929930i \(-0.619867\pi\)
−0.989211 + 0.146495i \(0.953201\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4170i 1.09842i 0.835686 + 0.549208i \(0.185070\pi\)
−0.835686 + 0.549208i \(0.814930\pi\)
\(198\) 0 0
\(199\) −20.3578 −1.44313 −0.721564 0.692348i \(-0.756576\pi\)
−0.721564 + 0.692348i \(0.756576\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −22.2091 12.8225i −1.55878 0.899960i
\(204\) 0 0
\(205\) −10.3636 8.07956i −0.723826 0.564301i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.04121 8.73164i −0.348708 0.603980i
\(210\) 0 0
\(211\) −8.08945 + 14.0113i −0.556901 + 0.964581i 0.440852 + 0.897580i \(0.354676\pi\)
−0.997753 + 0.0670010i \(0.978657\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.14474 10.2279i −0.282669 0.697538i
\(216\) 0 0
\(217\) 30.4952i 2.07015i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.99110 17.3051i 0.672074 1.16407i
\(222\) 0 0
\(223\) −22.1354 + 12.7799i −1.48230 + 0.855805i −0.999798 0.0200906i \(-0.993605\pi\)
−0.482500 + 0.875896i \(0.660271\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.3908 + 9.46323i −1.08790 + 0.628097i −0.933015 0.359837i \(-0.882832\pi\)
−0.154880 + 0.987933i \(0.549499\pi\)
\(228\) 0 0
\(229\) 3.41055 5.90724i 0.225375 0.390361i −0.731057 0.682317i \(-0.760973\pi\)
0.956432 + 0.291955i \(0.0943059\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.150248i 0.00984309i 0.999988 + 0.00492154i \(0.00156658\pi\)
−0.999988 + 0.00492154i \(0.998433\pi\)
\(234\) 0 0
\(235\) 10.0000 + 24.6768i 0.652328 + 1.60974i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.51551 7.82109i 0.292084 0.505904i −0.682218 0.731149i \(-0.738985\pi\)
0.974302 + 0.225244i \(0.0723180\pi\)
\(240\) 0 0
\(241\) −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i \(-0.957053\pi\)
0.378963 0.925412i \(-0.376281\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 30.6101 + 23.8640i 1.95561 + 1.52461i
\(246\) 0 0
\(247\) 10.5284 + 6.07858i 0.669907 + 0.386771i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 17.3205 1.09326 0.546630 0.837374i \(-0.315910\pi\)
0.546630 + 0.837374i \(0.315910\pi\)
\(252\) 0 0
\(253\) 8.10477i 0.509543i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.1698 + 11.0677i 1.19578 + 0.690385i 0.959612 0.281327i \(-0.0907744\pi\)
0.236170 + 0.971712i \(0.424108\pi\)
\(258\) 0 0
\(259\) 19.3578 + 33.5287i 1.20284 + 2.08337i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5.81834 + 3.35922i −0.358774 + 0.207138i −0.668543 0.743674i \(-0.733082\pi\)
0.309769 + 0.950812i \(0.399748\pi\)
\(264\) 0 0
\(265\) −18.9313 2.64051i −1.16294 0.162206i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −30.0646 −1.83307 −0.916536 0.399952i \(-0.869027\pi\)
−0.916536 + 0.399952i \(0.869027\pi\)
\(270\) 0 0
\(271\) −22.3578 −1.35814 −0.679070 0.734073i \(-0.737617\pi\)
−0.679070 + 0.734073i \(0.737617\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.94280 + 11.6990i 0.177458 + 0.705478i
\(276\) 0 0
\(277\) 9.31298 5.37685i 0.559563 0.323064i −0.193407 0.981119i \(-0.561954\pi\)
0.752970 + 0.658055i \(0.228620\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.21712 + 10.7684i 0.370882 + 0.642387i 0.989701 0.143147i \(-0.0457221\pi\)
−0.618819 + 0.785533i \(0.712389\pi\)
\(282\) 0 0
\(283\) −1.52936 0.882978i −0.0909112 0.0524876i 0.453855 0.891075i \(-0.350048\pi\)
−0.544766 + 0.838588i \(0.683382\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 29.0041i 1.71206i
\(288\) 0 0
\(289\) −30.1789 −1.77523
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 17.8454 + 10.3030i 1.04254 + 0.601910i 0.920551 0.390622i \(-0.127740\pi\)
0.121987 + 0.992532i \(0.461073\pi\)
\(294\) 0 0
\(295\) 1.85414 + 1.44550i 0.107952 + 0.0841603i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.88627 8.46327i −0.282581 0.489444i
\(300\) 0 0
\(301\) −12.1789 + 21.0945i −0.701981 + 1.21587i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 19.0221 7.70850i 1.08920 0.441387i
\(306\) 0 0
\(307\) 8.98775i 0.512958i −0.966550 0.256479i \(-0.917438\pi\)
0.966550 0.256479i \(-0.0825624\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.35109 + 9.26836i −0.303433 + 0.525561i −0.976911 0.213646i \(-0.931466\pi\)
0.673479 + 0.739207i \(0.264799\pi\)
\(312\) 0 0
\(313\) 6.02889 3.48078i 0.340773 0.196745i −0.319841 0.947471i \(-0.603629\pi\)
0.660614 + 0.750726i \(0.270296\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −29.4821 + 17.0215i −1.65588 + 0.956021i −0.681290 + 0.732013i \(0.738581\pi\)
−0.974587 + 0.224008i \(0.928086\pi\)
\(318\) 0 0
\(319\) −6.26836 + 10.8571i −0.350961 + 0.607882i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 28.7036i 1.59711i
\(324\) 0 0
\(325\) −10.1262 10.4423i −0.561699 0.579237i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 29.3840 50.8945i 1.61999 2.80591i
\(330\) 0 0
\(331\) 16.2684 + 28.1776i 0.894190 + 1.54878i 0.834804 + 0.550548i \(0.185581\pi\)
0.0593863 + 0.998235i \(0.481086\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.57132 7.14630i 0.304394 0.390444i
\(336\) 0 0
\(337\) 8.54830 + 4.93536i 0.465656 + 0.268846i 0.714419 0.699718i \(-0.246691\pi\)
−0.248764 + 0.968564i \(0.580024\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −14.9078 −0.807303
\(342\) 0 0
\(343\) 51.1196i 2.76020i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.40305 + 4.27415i 0.397416 + 0.229448i 0.685369 0.728196i \(-0.259641\pi\)
−0.287952 + 0.957645i \(0.592974\pi\)
\(348\) 0 0
\(349\) 10.0895 + 17.4754i 0.540076 + 0.935439i 0.998899 + 0.0469115i \(0.0149379\pi\)
−0.458823 + 0.888528i \(0.651729\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −19.0397 + 10.9926i −1.01338 + 0.585077i −0.912180 0.409789i \(-0.865602\pi\)
−0.101202 + 0.994866i \(0.532269\pi\)
\(354\) 0 0
\(355\) −4.37587 + 31.3731i −0.232247 + 1.66511i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.309878 0.0163548 0.00817738 0.999967i \(-0.497397\pi\)
0.00817738 + 0.999967i \(0.497397\pi\)
\(360\) 0 0
\(361\) −1.53673 −0.0808803
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.48727 + 0.625878i 0.234874 + 0.0327599i
\(366\) 0 0
\(367\) −8.54830 + 4.93536i −0.446218 + 0.257624i −0.706231 0.707981i \(-0.749606\pi\)
0.260014 + 0.965605i \(0.416273\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 21.0945 + 36.5367i 1.09517 + 1.89689i
\(372\) 0 0
\(373\) 7.78362 + 4.49387i 0.403021 + 0.232684i 0.687786 0.725913i \(-0.258583\pi\)
−0.284766 + 0.958597i \(0.591916\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.1165i 0.778539i
\(378\) 0 0
\(379\) 0.357817 0.0183798 0.00918990 0.999958i \(-0.497075\pi\)
0.00918990 + 0.999958i \(0.497075\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11.8969 6.86869i −0.607904 0.350974i 0.164241 0.986420i \(-0.447483\pi\)
−0.772145 + 0.635447i \(0.780816\pi\)
\(384\) 0 0
\(385\) 16.3708 20.9987i 0.834331 1.07019i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12.8050 22.1789i −0.649239 1.12452i −0.983305 0.181966i \(-0.941754\pi\)
0.334066 0.942550i \(-0.391579\pi\)
\(390\) 0 0
\(391\) −11.5367 + 19.9822i −0.583437 + 1.01054i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −12.4342 + 5.03883i −0.625634 + 0.253531i
\(396\) 0 0
\(397\) 11.0139i 0.552774i 0.961046 + 0.276387i \(0.0891371\pi\)
−0.961046 + 0.276387i \(0.910863\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.3619 + 17.9473i −0.517447 + 0.896244i 0.482348 + 0.875980i \(0.339784\pi\)
−0.999795 + 0.0202642i \(0.993549\pi\)
\(402\) 0 0
\(403\) 15.5672 8.98775i 0.775459 0.447712i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.3908 9.46323i 0.812462 0.469075i
\(408\) 0 0
\(409\) 3.41055 5.90724i 0.168641 0.292094i −0.769302 0.638886i \(-0.779396\pi\)
0.937942 + 0.346792i \(0.112729\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.18908i 0.255338i
\(414\) 0 0
\(415\) −4.35782 10.7537i −0.213917 0.527879i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8.28949 14.3578i 0.404968 0.701425i −0.589350 0.807878i \(-0.700616\pi\)
0.994318 + 0.106453i \(0.0339493\pi\)
\(420\) 0 0
\(421\) −14.8578 25.7345i −0.724126 1.25422i −0.959333 0.282277i \(-0.908910\pi\)
0.235207 0.971945i \(-0.424423\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9.39753 + 33.0327i −0.455847 + 1.60232i
\(426\) 0 0
\(427\) −39.2320 22.6506i −1.89857 1.09614i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.67116 −0.0804972 −0.0402486 0.999190i \(-0.512815\pi\)
−0.0402486 + 0.999190i \(0.512815\pi\)
\(432\) 0 0
\(433\) 36.5737i 1.75762i 0.477170 + 0.878811i \(0.341663\pi\)
−0.477170 + 0.878811i \(0.658337\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.1572 7.01894i −0.581556 0.335761i
\(438\) 0 0
\(439\) 9.26836 + 16.0533i 0.442355 + 0.766181i 0.997864 0.0653296i \(-0.0208099\pi\)
−0.555509 + 0.831511i \(0.687477\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.1306 9.31298i 0.766386 0.442473i −0.0651979 0.997872i \(-0.520768\pi\)
0.831584 + 0.555399i \(0.187435\pi\)
\(444\) 0 0
\(445\) −0.955512 + 6.85060i −0.0452956 + 0.324749i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −25.1783 −1.18824 −0.594120 0.804377i \(-0.702500\pi\)
−0.594120 + 0.804377i \(0.702500\pi\)
\(450\) 0 0
\(451\) 14.1789 0.667659
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.43504 + 31.7972i −0.207918 + 1.49068i
\(456\) 0 0
\(457\) −23.8902 + 13.7930i −1.11753 + 0.645209i −0.940770 0.339044i \(-0.889896\pi\)
−0.176764 + 0.984253i \(0.556563\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.35109 + 9.26836i 0.249225 + 0.431671i 0.963311 0.268387i \(-0.0864907\pi\)
−0.714086 + 0.700058i \(0.753157\pi\)
\(462\) 0 0
\(463\) −25.6449 14.8061i −1.19182 0.688097i −0.233101 0.972453i \(-0.574887\pi\)
−0.958719 + 0.284355i \(0.908221\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.5672i 0.720366i −0.932882 0.360183i \(-0.882714\pi\)
0.932882 0.360183i \(-0.117286\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 10.3122 + 5.95376i 0.474156 + 0.273754i
\(474\) 0 0
\(475\) −20.0971 5.71745i −0.922117 0.262335i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.6501 21.9105i −0.577996 1.00112i −0.995709 0.0925394i \(-0.970502\pi\)
0.417713 0.908579i \(-0.362832\pi\)
\(480\) 0 0
\(481\) −11.4105 + 19.7636i −0.520276 + 0.901145i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.741529 + 1.82986i 0.0336711 + 0.0830896i
\(486\) 0 0
\(487\) 17.9755i 0.814548i 0.913306 + 0.407274i \(0.133521\pi\)
−0.913306 + 0.407274i \(0.866479\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.7853 30.8051i 0.802641 1.39021i −0.115232 0.993339i \(-0.536761\pi\)
0.917872 0.396876i \(-0.129906\pi\)
\(492\) 0 0
\(493\) −30.9091 + 17.8454i −1.39208 + 0.803716i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 60.5488 34.9579i 2.71599 1.56808i
\(498\) 0 0
\(499\) 2.08945 3.61904i 0.0935368 0.162011i −0.815460 0.578813i \(-0.803516\pi\)
0.908997 + 0.416803i \(0.136849\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 37.2519i 1.66098i 0.557032 + 0.830491i \(0.311940\pi\)
−0.557032 + 0.830491i \(0.688060\pi\)
\(504\) 0 0
\(505\) −12.1789 + 4.93536i −0.541954 + 0.219621i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.77398 + 6.53673i −0.167279 + 0.289735i −0.937462 0.348087i \(-0.886831\pi\)
0.770183 + 0.637822i \(0.220165\pi\)
\(510\) 0 0
\(511\) −5.00000 8.66025i −0.221187 0.383107i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13.5705 + 17.4068i −0.597988 + 0.767036i
\(516\) 0 0
\(517\) −24.8802 14.3646i −1.09423 0.631755i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.03102 −0.395656 −0.197828 0.980237i \(-0.563389\pi\)
−0.197828 + 0.980237i \(0.563389\pi\)
\(522\) 0 0
\(523\) 7.58430i 0.331638i 0.986156 + 0.165819i \(0.0530268\pi\)
−0.986156 + 0.165819i \(0.946973\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −36.7550 21.2205i −1.60107 0.924380i
\(528\) 0 0
\(529\) −5.85782 10.1460i −0.254688 0.441132i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −14.8061 + 8.54830i −0.641323 + 0.370268i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −41.8791 −1.80386
\(540\) 0 0
\(541\) 3.35782 0.144364 0.0721819 0.997391i \(-0.477004\pi\)
0.0721819 + 0.997391i \(0.477004\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.16225 15.5024i 0.0926208 0.664050i
\(546\) 0 0
\(547\) 17.0966 9.87073i 0.730998 0.422042i −0.0877892 0.996139i \(-0.527980\pi\)
0.818787 + 0.574097i \(0.194647\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.8571 18.8051i −0.462529 0.801124i
\(552\) 0 0
\(553\) 25.6449 + 14.8061i 1.09053 + 0.629619i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 39.2320i 1.66231i −0.556037 0.831157i \(-0.687679\pi\)
0.556037 0.831157i \(-0.312321\pi\)
\(558\) 0 0
\(559\) −14.3578 −0.607271
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.3122 + 5.95376i 0.434608 + 0.250921i 0.701308 0.712859i \(-0.252600\pi\)
−0.266700 + 0.963780i \(0.585933\pi\)
\(564\) 0 0
\(565\) −18.6799 + 23.9606i −0.785870 + 1.00803i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.22731 + 3.85782i 0.0933738 + 0.161728i 0.908929 0.416952i \(-0.136902\pi\)
−0.815555 + 0.578680i \(0.803568\pi\)
\(570\) 0 0
\(571\) 9.08945 15.7434i 0.380382 0.658841i −0.610735 0.791835i \(-0.709126\pi\)
0.991117 + 0.132994i \(0.0424592\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11.6927 + 12.0578i 0.487619 + 0.502844i
\(576\) 0 0
\(577\) 7.84453i 0.326572i 0.986579 + 0.163286i \(0.0522094\pi\)
−0.986579 + 0.163286i \(0.947791\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.8050 + 22.1789i −0.531241 + 0.920136i
\(582\) 0 0
\(583\) 17.8613 10.3122i 0.739739 0.427088i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.0520 + 5.80351i −0.414890 + 0.239537i −0.692888 0.721045i \(-0.743662\pi\)
0.277999 + 0.960581i \(0.410329\pi\)
\(588\) 0 0
\(589\) 12.9105 22.3617i 0.531970 0.921399i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.03883i 0.206920i 0.994634 + 0.103460i \(0.0329914\pi\)
−0.994634 + 0.103460i \(0.967009\pi\)
\(594\) 0 0
\(595\) 70.2524 28.4690i 2.88007 1.16711i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.50531 14.7316i 0.347518 0.601918i −0.638290 0.769796i \(-0.720358\pi\)
0.985808 + 0.167878i \(0.0536913\pi\)
\(600\) 0 0
\(601\) 1.67891 + 2.90795i 0.0684841 + 0.118618i 0.898234 0.439517i \(-0.144850\pi\)
−0.829750 + 0.558135i \(0.811517\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.13290 + 7.12009i 0.371305 + 0.289473i
\(606\) 0 0
\(607\) 4.27415 + 2.46768i 0.173482 + 0.100160i 0.584227 0.811590i \(-0.301398\pi\)
−0.410744 + 0.911751i \(0.634731\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 34.6410 1.40143
\(612\) 0 0
\(613\) 37.7170i 1.52337i −0.647945 0.761687i \(-0.724372\pi\)
0.647945 0.761687i \(-0.275628\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.62399 + 2.66966i 0.186155 + 0.107477i 0.590181 0.807271i \(-0.299056\pi\)
−0.404026 + 0.914747i \(0.632390\pi\)
\(618\) 0 0
\(619\) 5.82109 + 10.0824i 0.233969 + 0.405247i 0.958973 0.283499i \(-0.0914951\pi\)
−0.725003 + 0.688745i \(0.758162\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 13.2214 7.63337i 0.529704 0.305825i
\(624\) 0 0
\(625\) 21.2562 + 13.1595i 0.850249 + 0.526381i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 53.8817 2.14840
\(630\) 0 0
\(631\) −22.5367 −0.897173 −0.448586 0.893739i \(-0.648072\pi\)
−0.448586 + 0.893739i \(0.648072\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10.9300 1.52450i −0.433744 0.0604980i
\(636\) 0 0
\(637\) 43.7316 25.2484i 1.73271 1.00038i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.15551 15.8578i −0.361621 0.626346i 0.626607 0.779336i \(-0.284443\pi\)
−0.988228 + 0.152990i \(0.951110\pi\)
\(642\) 0 0
\(643\) 17.8613 + 10.3122i 0.704380 + 0.406674i 0.808977 0.587841i \(-0.200022\pi\)
−0.104597 + 0.994515i \(0.533355\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 44.2709i 1.74047i −0.492639 0.870234i \(-0.663968\pi\)
0.492639 0.870234i \(-0.336032\pi\)
\(648\) 0 0
\(649\) −2.53673 −0.0995752
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.260237 0.150248i −0.0101839 0.00587967i 0.494899 0.868950i \(-0.335205\pi\)
−0.505083 + 0.863071i \(0.668538\pi\)
\(654\) 0 0
\(655\) −24.9819 19.4762i −0.976125 0.760996i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.7237 35.8945i −0.807282 1.39825i −0.914740 0.404043i \(-0.867605\pi\)
0.107458 0.994210i \(-0.465729\pi\)
\(660\) 0 0
\(661\) 23.2156 40.2107i 0.902983 1.56401i 0.0793821 0.996844i \(-0.474705\pi\)
0.823601 0.567169i \(-0.191961\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 17.3205 + 42.7415i 0.671660 + 1.65744i
\(666\) 0 0
\(667\) 17.4550i 0.675861i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −11.0729 + 19.1789i −0.427466 + 0.740394i
\(672\) 0 0
\(673\) 12.5971 7.27293i 0.485582 0.280351i −0.237158 0.971471i \(-0.576216\pi\)
0.722740 + 0.691120i \(0.242883\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29.8724 + 17.2469i −1.14809 + 0.662850i −0.948421 0.317013i \(-0.897320\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(678\) 0 0
\(679\) 2.17891 3.77398i 0.0836188 0.144832i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.5714i 1.70548i 0.522339 + 0.852738i \(0.325060\pi\)
−0.522339 + 0.852738i \(0.674940\pi\)
\(684\) 0 0
\(685\) −4.23164 10.4423i −0.161683 0.398981i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12.4342 + 21.5367i −0.473707 + 0.820484i
\(690\) 0 0
\(691\) 15.3578 + 26.6005i 0.584239 + 1.01193i 0.994970 + 0.100175i \(0.0319402\pi\)
−0.410731 + 0.911757i \(0.634726\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.2654 + 8.00298i 0.389388 + 0.303570i
\(696\) 0 0
\(697\) 34.9579 + 20.1829i 1.32412 + 0.764484i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.3420 −1.03269 −0.516347 0.856379i \(-0.672709\pi\)
−0.516347 + 0.856379i \(0.672709\pi\)
\(702\) 0 0
\(703\) 32.7816i 1.23638i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25.1183 + 14.5021i 0.944671 + 0.545406i
\(708\) 0 0
\(709\) 7.76836 + 13.4552i 0.291747 + 0.505321i 0.974223 0.225587i \(-0.0724301\pi\)
−0.682476 + 0.730908i \(0.739097\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −17.9755 + 10.3782i −0.673188 + 0.388665i
\(714\) 0 0
\(715\) 15.5444 + 2.16810i 0.581326 + 0.0810825i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.3960 1.50652 0.753259 0.657724i \(-0.228481\pi\)
0.753259 + 0.657724i \(0.228481\pi\)
\(720\) 0 0
\(721\) 48.7156 1.81426
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.33783 + 25.1959i 0.235381 + 0.935751i
\(726\) 0 0
\(727\) 40.7614 23.5336i 1.51176 0.872813i 0.511851 0.859074i \(-0.328960\pi\)
0.999906 0.0137388i \(-0.00437333\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.9497 + 29.3578i 0.626909 + 1.08584i
\(732\) 0 0
\(733\) −17.0966 9.87073i −0.631477 0.364584i 0.149847 0.988709i \(-0.452122\pi\)
−0.781324 + 0.624126i \(0.785455\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.77717i 0.360147i
\(738\) 0 0
\(739\) 22.8945 0.842189 0.421095 0.907017i \(-0.361646\pi\)
0.421095 + 0.907017i \(0.361646\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 43.0938 + 24.8802i 1.58096 + 0.912767i 0.994720 + 0.102628i \(0.0327253\pi\)
0.586239 + 0.810138i \(0.300608\pi\)
\(744\) 0 0
\(745\) 23.2352 + 18.1144i 0.851271 + 0.663659i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3.17891 5.50603i 0.116000 0.200918i −0.802179 0.597084i \(-0.796326\pi\)
0.918179 + 0.396166i \(0.129659\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.8050 + 5.18908i −0.466022 + 0.188850i
\(756\) 0 0
\(757\) 1.76596i 0.0641847i 0.999485 + 0.0320924i \(0.0102171\pi\)
−0.999485 + 0.0320924i \(0.989783\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.866025 1.50000i 0.0313934 0.0543750i −0.849902 0.526941i \(-0.823339\pi\)
0.881295 + 0.472566i \(0.156672\pi\)
\(762\) 0 0
\(763\) −29.9191 + 17.2738i −1.08314 + 0.625353i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.64893 1.52936i 0.0956474 0.0552221i
\(768\) 0 0
\(769\) 12.8578 22.2704i 0.463665 0.803091i −0.535475 0.844551i \(-0.679868\pi\)
0.999140 + 0.0414599i \(0.0132009\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30.6837i 1.10362i −0.833971 0.551809i \(-0.813938\pi\)
0.833971 0.551809i \(-0.186062\pi\)
\(774\) 0 0
\(775\) −22.1789 + 21.5074i −0.796690 + 0.772569i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.2793 + 21.2684i −0.439951 + 0.762018i
\(780\) 0 0
\(781\) −17.0895 29.5998i −0.611509 1.05916i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10.7849 + 13.8337i −0.384928 + 0.493745i
\(786\) 0 0
\(787\) 41.5261 + 23.9751i 1.48024 + 0.854620i 0.999750 0.0223775i \(-0.00712359\pi\)
0.480495 + 0.876997i \(0.340457\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 67.0574 2.38429
\(792\) 0 0
\(793\) 26.7030i 0.948252i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.1821 5.87864i −0.360668 0.208232i 0.308706 0.951158i \(-0.400104\pi\)
−0.669374 + 0.742926i \(0.733438\pi\)
\(798\) 0 0
\(799\) −40.8945 70.8314i −1.44674 2.50584i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.23364 + 2.44429i −0.149402 + 0.0862572i
\(804\) 0