Properties

Label 1620.2.r.h.1189.4
Level $1620$
Weight $2$
Character 1620.1189
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 1189.4
Root \(0.308893 - 2.21463i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1189
Dual form 1620.2.r.h.109.4

$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 0.988070 + 0.154005i \(0.0492170\pi\)
0.627407 + 0.778692i \(0.284116\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.20635 + 2.08945i −0.363727 + 0.629994i −0.988571 0.150756i \(-0.951829\pi\)
0.624844 + 0.780750i \(0.285163\pi\)
\(12\) 0 0
\(13\) 2.51942 1.45459i 0.698760 0.403429i −0.108125 0.994137i \(-0.534485\pi\)
0.806886 + 0.590708i \(0.201151\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.86869i 1.66590i 0.553347 + 0.832951i \(0.313350\pi\)
−0.553347 + 0.832951i \(0.686650\pi\)
\(18\) 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 −0.771635 0.636065i \(-0.780561\pi\)
0.165031 + 0.986288i \(0.447228\pi\)
\(24\) 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 −0.999797 0.0201471i \(-0.993587\pi\)
0.517346 + 0.855776i \(0.326920\pi\)
\(30\) 0 0
\(31\) 3.08945 + 5.35109i 0.554882 + 0.961084i 0.997913 + 0.0645778i \(0.0205701\pi\)
−0.443030 + 0.896507i \(0.646097\pi\)
\(32\) 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 \(-0.776934\pi\)
0.764337 0.644817i \(-0.223066\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.93840 5.08945i −0.458901 0.794839i 0.540003 0.841663i \(-0.318423\pi\)
−0.998903 + 0.0468242i \(0.985090\pi\)
\(42\) 0 0
\(43\) −4.27415 2.46768i −0.651802 0.376318i 0.137344 0.990523i \(-0.456143\pi\)
−0.789146 + 0.614205i \(0.789477\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.3122 + 5.95376i 1.50419 + 0.868445i 0.999988 + 0.00486027i \(0.00154708\pi\)
0.504203 + 0.863585i \(0.331786\pi\)
\(48\) 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 \(-0.800270\pi\)
0.809515 0.587100i \(-0.199730\pi\)
\(54\) 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 0.898215 0.439556i \(-0.144864\pi\)
−0.829774 + 0.558099i \(0.811531\pi\)
\(60\) 0 0
\(61\) −4.58945 + 7.94917i −0.587619 + 1.01779i 0.406924 + 0.913462i \(0.366601\pi\)
−0.994543 + 0.104325i \(0.966732\pi\)
\(62\) 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 −0.698814 0.715303i \(-0.746288\pi\)
0.270064 + 0.962842i \(0.412955\pi\)
\(68\) 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 \(0.0378323\pi\)
−0.992945 + 0.118574i \(0.962168\pi\)
\(74\) 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 −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.49387 2.59454i −0.493267 0.284788i 0.232662 0.972558i \(-0.425256\pi\)
−0.725929 + 0.687770i \(0.758590\pi\)
\(84\) 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 0.538318 0.842742i \(-0.319060\pi\)
−0.460677 + 0.887568i \(0.652393\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.93840 5.08945i 0.292382 0.506420i −0.681991 0.731361i \(-0.738886\pi\)
0.974372 + 0.224941i \(0.0722190\pi\)
\(102\) 0 0
\(103\) 8.54830 4.93536i 0.842289 0.486296i −0.0157525 0.999876i \(-0.505014\pi\)
0.858042 + 0.513580i \(0.171681\pi\)
\(104\) 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 0.168896 0.985634i \(-0.445980\pi\)
0.938032 + 0.346549i \(0.112647\pi\)
\(114\) 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 \(-0.929730\pi\)
0.975731 0.218971i \(-0.0702701\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.08314 12.2684i −0.618857 1.07189i −0.989695 0.143194i \(-0.954263\pi\)
0.370838 0.928698i \(-0.379071\pi\)
\(132\) 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 0.301869 0.953349i \(-0.402389\pi\)
−0.674690 + 0.738101i \(0.735723\pi\)
\(138\) 0 0
\(139\) 2.91055 + 5.04121i 0.246869 + 0.427590i 0.962656 0.270729i \(-0.0872648\pi\)
−0.715786 + 0.698319i \(0.753932\pi\)
\(140\) 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 0.998920 + 0.0464656i \(0.0147958\pi\)
−0.459220 + 0.888323i \(0.651871\pi\)
\(150\) 0 0
\(151\) 3.08945 5.35109i 0.251416 0.435466i −0.712500 0.701672i \(-0.752437\pi\)
0.963916 + 0.266207i \(0.0857704\pi\)
\(152\) 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 −0.203779 0.979017i \(-0.565322\pi\)
0.745964 + 0.665986i \(0.231989\pi\)
\(158\) 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 \(-0.861627\pi\)
0.906992 0.421148i \(-0.138373\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.40305 4.27415i 0.572865 0.330744i −0.185428 0.982658i \(-0.559367\pi\)
0.758293 + 0.651914i \(0.226034\pi\)
\(168\) 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 0.968331 0.249670i \(-0.0803220\pi\)
0.267945 + 0.963434i \(0.413655\pi\)
\(174\) 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 −0.721112 0.692819i \(-0.756369\pi\)
0.960554 + 0.278092i \(0.0897020\pi\)
\(192\) 0 0
\(193\) −18.8513 + 10.8838i −1.35695 + 0.783435i −0.989211 0.146495i \(-0.953201\pi\)
−0.367737 + 0.929930i \(0.619867\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4170i 1.09842i −0.835686 0.549208i \(-0.814930\pi\)
0.835686 0.549208i \(-0.185070\pi\)
\(198\) 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 −0.997753 0.0670010i \(-0.978657\pi\)
0.440852 0.897580i \(-0.354676\pi\)
\(212\) 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 −0.482500 0.875896i \(-0.660271\pi\)
−0.999798 + 0.0200906i \(0.993605\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.3908 9.46323i −1.08790 0.628097i −0.154880 0.987933i \(-0.549499\pi\)
−0.933015 + 0.359837i \(0.882832\pi\)
\(228\) 0 0
\(229\) 3.41055 + 5.90724i 0.225375 + 0.390361i 0.956432 0.291955i \(-0.0943059\pi\)
−0.731057 + 0.682317i \(0.760973\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.150248i 0.00984309i −0.999988 0.00492154i \(-0.998433\pi\)
0.999988 0.00492154i \(-0.00156658\pi\)
\(234\) 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 0.974302 0.225244i \(-0.0723180\pi\)
−0.682218 + 0.731149i \(0.738985\pi\)
\(240\) 0 0
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 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 0.236170 0.971712i \(-0.424108\pi\)
0.959612 + 0.281327i \(0.0907744\pi\)
\(258\) 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 0.309769 0.950812i \(-0.399748\pi\)
−0.668543 + 0.743674i \(0.733082\pi\)
\(264\) 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 0.752970 0.658055i \(-0.228620\pi\)
−0.193407 + 0.981119i \(0.561954\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.21712 10.7684i 0.370882 0.642387i −0.618819 0.785533i \(-0.712389\pi\)
0.989701 + 0.143147i \(0.0457221\pi\)
\(282\) 0 0
\(283\) −1.52936 + 0.882978i −0.0909112 + 0.0524876i −0.544766 0.838588i \(-0.683382\pi\)
0.453855 + 0.891075i \(0.350048\pi\)
\(284\) 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 0.121987 0.992532i \(-0.461073\pi\)
0.920551 + 0.390622i \(0.127740\pi\)
\(294\) 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 \(0.0825624\pi\)
−0.966550 + 0.256479i \(0.917438\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.35109 9.26836i −0.303433 0.525561i 0.673479 0.739207i \(-0.264799\pi\)
−0.976911 + 0.213646i \(0.931466\pi\)
\(312\) 0 0
\(313\) 6.02889 + 3.48078i 0.340773 + 0.196745i 0.660614 0.750726i \(-0.270296\pi\)
−0.319841 + 0.947471i \(0.603629\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −29.4821 17.0215i −1.65588 0.956021i −0.974587 0.224008i \(-0.928086\pi\)
−0.681290 0.732013i \(-0.738581\pi\)
\(318\) 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 0.0593863 0.998235i \(-0.481086\pi\)
0.834804 0.550548i \(-0.185581\pi\)
\(332\) 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 −0.248764 0.968564i \(-0.580024\pi\)
0.714419 + 0.699718i \(0.246691\pi\)
\(338\) 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 −0.287952 0.957645i \(-0.592974\pi\)
0.685369 + 0.728196i \(0.259641\pi\)
\(348\) 0 0
\(349\) 10.0895 17.4754i 0.540076 0.935439i −0.458823 0.888528i \(-0.651729\pi\)
0.998899 0.0469115i \(-0.0149379\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −19.0397 10.9926i −1.01338 0.585077i −0.101202 0.994866i \(-0.532269\pi\)
−0.912180 + 0.409789i \(0.865602\pi\)
\(354\) 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 0.260014 0.965605i \(-0.416273\pi\)
−0.706231 + 0.707981i \(0.749606\pi\)
\(368\) 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 −0.284766 0.958597i \(-0.591916\pi\)
0.687786 + 0.725913i \(0.258583\pi\)
\(374\) 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 −0.772145 0.635447i \(-0.780816\pi\)
0.164241 + 0.986420i \(0.447483\pi\)
\(384\) 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 0.334066 + 0.942550i \(0.391579\pi\)
−0.983305 + 0.181966i \(0.941754\pi\)
\(390\) 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 \(-0.910863\pi\)
0.961046 0.276387i \(-0.0891371\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.3619 17.9473i −0.517447 0.896244i −0.999795 0.0202642i \(-0.993549\pi\)
0.482348 0.875980i \(-0.339784\pi\)
\(402\) 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 0.937942 0.346792i \(-0.112729\pi\)
−0.769302 + 0.638886i \(0.779396\pi\)
\(410\) 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 0.994318 0.106453i \(-0.0339493\pi\)
−0.589350 + 0.807878i \(0.700616\pi\)
\(420\) 0 0
\(421\) −14.8578 + 25.7345i −0.724126 + 1.25422i 0.235207 + 0.971945i \(0.424423\pi\)
−0.959333 + 0.282277i \(0.908910\pi\)
\(422\) 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 \(-0.658337\pi\)
0.477170 0.878811i \(-0.341663\pi\)
\(434\) 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 −0.555509 0.831511i \(-0.687477\pi\)
0.997864 + 0.0653296i \(0.0208099\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.1306 + 9.31298i 0.766386 + 0.442473i 0.831584 0.555399i \(-0.187435\pi\)
−0.0651979 + 0.997872i \(0.520768\pi\)
\(444\) 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 −0.176764 0.984253i \(-0.556563\pi\)
−0.940770 + 0.339044i \(0.889896\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.35109 9.26836i 0.249225 0.431671i −0.714086 0.700058i \(-0.753157\pi\)
0.963311 + 0.268387i \(0.0864907\pi\)
\(462\) 0 0
\(463\) −25.6449 + 14.8061i −1.19182 + 0.688097i −0.958719 0.284355i \(-0.908221\pi\)
−0.233101 + 0.972453i \(0.574887\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.5672i 0.720366i 0.932882 + 0.360183i \(0.117286\pi\)
−0.932882 + 0.360183i \(0.882714\pi\)
\(468\) 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 0.417713 + 0.908579i \(0.362832\pi\)
−0.995709 + 0.0925394i \(0.970502\pi\)
\(480\) 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 \(-0.866479\pi\)
0.913306 0.407274i \(-0.133521\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.7853 + 30.8051i 0.802641 + 1.39021i 0.917872 + 0.396876i \(0.129906\pi\)
−0.115232 + 0.993339i \(0.536761\pi\)
\(492\) 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 0.908997 0.416803i \(-0.136849\pi\)
−0.815460 + 0.578813i \(0.803516\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 37.2519i 1.66098i −0.557032 0.830491i \(-0.688060\pi\)
0.557032 0.830491i \(-0.311940\pi\)
\(504\) 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 0.770183 0.637822i \(-0.220165\pi\)
−0.937462 + 0.348087i \(0.886831\pi\)
\(510\) 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 \(-0.946973\pi\)
0.986156 0.165819i \(-0.0530268\pi\)
\(524\) 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 0.818787 0.574097i \(-0.194647\pi\)
−0.0877892 + 0.996139i \(0.527980\pi\)
\(548\) 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 \(0.312321\pi\)
−0.556037 + 0.831157i \(0.687679\pi\)
\(558\) 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 −0.266700 0.963780i \(-0.585933\pi\)
0.701308 + 0.712859i \(0.252600\pi\)
\(564\) 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 −0.815555 0.578680i \(-0.803568\pi\)
0.908929 + 0.416952i \(0.136902\pi\)
\(570\) 0 0
\(571\) 9.08945 + 15.7434i 0.380382 + 0.658841i 0.991117 0.132994i \(-0.0424592\pi\)
−0.610735 + 0.791835i \(0.709126\pi\)
\(572\) 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 \(-0.947791\pi\)
0.986579 0.163286i \(-0.0522094\pi\)
\(578\) 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 0.277999 0.960581i \(-0.410329\pi\)
−0.692888 + 0.721045i \(0.743662\pi\)
\(588\) 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 \(-0.967009\pi\)
0.994634 0.103460i \(-0.0329914\pi\)
\(594\) 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 0.985808 0.167878i \(-0.0536913\pi\)
−0.638290 + 0.769796i \(0.720358\pi\)
\(600\) 0 0
\(601\) 1.67891 2.90795i 0.0684841 0.118618i −0.829750 0.558135i \(-0.811517\pi\)
0.898234 + 0.439517i \(0.144850\pi\)
\(602\) 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 −0.410744 0.911751i \(-0.634731\pi\)
0.584227 + 0.811590i \(0.301398\pi\)
\(608\) 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 \(0.275628\pi\)
−0.647945 + 0.761687i \(0.724372\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.62399 2.66966i 0.186155 0.107477i −0.404026 0.914747i \(-0.632390\pi\)
0.590181 + 0.807271i \(0.299056\pi\)
\(618\) 0 0
\(619\) 5.82109 10.0824i 0.233969 0.405247i −0.725003 0.688745i \(-0.758162\pi\)
0.958973 + 0.283499i \(0.0914951\pi\)
\(620\) 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 −0.988228 0.152990i \(-0.951110\pi\)
0.626607 + 0.779336i \(0.284443\pi\)
\(642\) 0 0
\(643\) 17.8613 10.3122i 0.704380 0.406674i −0.104597 0.994515i \(-0.533355\pi\)
0.808977 + 0.587841i \(0.200022\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 44.2709i 1.74047i 0.492639 + 0.870234i \(0.336032\pi\)
−0.492639 + 0.870234i \(0.663968\pi\)
\(648\) 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 −0.505083 0.863071i \(-0.668538\pi\)
0.494899 + 0.868950i \(0.335205\pi\)
\(654\) 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 0.107458 + 0.994210i \(0.465729\pi\)
−0.914740 + 0.404043i \(0.867605\pi\)
\(660\) 0 0
\(661\) 23.2156 + 40.2107i 0.902983 + 1.56401i 0.823601 + 0.567169i \(0.191961\pi\)
0.0793821 + 0.996844i \(0.474705\pi\)
\(662\) 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 0.722740 0.691120i \(-0.242883\pi\)
−0.237158 + 0.971471i \(0.576216\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29.8724 17.2469i −1.14809 0.662850i −0.199669 0.979863i \(-0.563987\pi\)
−0.948421 + 0.317013i \(0.897320\pi\)
\(678\) 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 \(-0.674940\pi\)
0.522339 0.852738i \(-0.325060\pi\)
\(684\) 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 −0.410731 0.911757i \(-0.634726\pi\)
0.994970 0.100175i \(-0.0319402\pi\)
\(692\) 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 −0.682476 0.730908i \(-0.739097\pi\)
0.974223 + 0.225587i \(0.0724301\pi\)
\(710\) 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 0.999906 + 0.0137388i \(0.00437333\pi\)
0.511851 + 0.859074i \(0.328960\pi\)
\(728\) 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 −0.781324 0.624126i \(-0.785455\pi\)
0.149847 + 0.988709i \(0.452122\pi\)
\(734\) 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 0.586239 0.810138i \(-0.300608\pi\)
0.994720 0.102628i \(-0.0327253\pi\)
\(744\) 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 0.918179 0.396166i \(-0.129659\pi\)
−0.802179 + 0.597084i \(0.796326\pi\)
\(752\) 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 \(-0.989783\pi\)
0.999485 0.0320924i \(-0.0102171\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.866025 + 1.50000i 0.0313934 + 0.0543750i 0.881295 0.472566i \(-0.156672\pi\)
−0.849902 + 0.526941i \(0.823339\pi\)
\(762\) 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 0.999140 0.0414599i \(-0.0132009\pi\)
−0.535475 + 0.844551i \(0.679868\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30.6837i 1.10362i 0.833971 + 0.551809i \(0.186062\pi\)
−0.833971 + 0.551809i \(0.813938\pi\)
\(774\) 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 0.480495 0.876997i \(-0.340457\pi\)
0.999750 + 0.0223775i \(0.00712359\pi\)
\(788\) 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 −0.669374 0.742926i \(-0.733438\pi\)
0.308706 + 0.951158i \(0.400104\pi\)
\(798\) 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