Properties

Label 1620.2.r.h.1189.7
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 1189.7
Root \(-1.76348 + 1.37482i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1189
Dual form 1620.2.r.h.109.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.76348 + 1.37482i) q^{5} +(-4.27415 - 2.46768i) q^{7} +O(q^{10})\) \(q+(1.76348 + 1.37482i) q^{5} +(-4.27415 - 2.46768i) q^{7} +(1.20635 - 2.08945i) q^{11} +(-2.51942 + 1.45459i) q^{13} +6.86869i q^{17} +4.17891 q^{19} +(-2.90917 + 1.67961i) q^{23} +(1.21972 + 4.84895i) q^{25} +(2.59808 - 4.50000i) q^{29} +(3.08945 + 5.35109i) q^{31} +(-4.14474 - 10.2279i) q^{35} +7.84453i q^{37} +(2.93840 + 5.08945i) q^{41} +(4.27415 + 2.46768i) q^{43} +(10.3122 + 5.95376i) q^{47} +(8.67891 + 15.0323i) q^{49} -8.54830i q^{53} +(5.00000 - 2.02619i) q^{55} +(-0.525704 - 0.910546i) q^{59} +(-4.58945 + 7.94917i) q^{61} +(-6.44274 - 0.898624i) q^{65} +(3.50947 - 2.02619i) q^{67} -14.1663 q^{71} -2.02619i q^{73} +(-10.3122 + 5.95376i) q^{77} +(3.00000 - 5.19615i) q^{79} +(-4.49387 - 2.59454i) q^{83} +(-9.44324 + 12.1128i) q^{85} -3.09334 q^{89} +14.3578 q^{91} +(7.36942 + 5.74527i) q^{95} +(-0.764681 - 0.441489i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91} + O(q^{100}) \)

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
\(5\) 1.76348 + 1.37482i 0.788652 + 0.614840i
\(6\) 0 0
\(7\) −4.27415 2.46768i −1.61548 0.932696i −0.988070 0.154005i \(-0.950783\pi\)
−0.627407 0.778692i \(-0.715884\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.20635 2.08945i 0.363727 0.629994i −0.624844 0.780750i \(-0.714837\pi\)
0.988571 + 0.150756i \(0.0481707\pi\)
\(12\) 0 0
\(13\) −2.51942 + 1.45459i −0.698760 + 0.403429i −0.806886 0.590708i \(-0.798849\pi\)
0.108125 + 0.994137i \(0.465515\pi\)
\(14\) 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
\(25\) 1.21972 + 4.84895i 0.243943 + 0.969790i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.59808 4.50000i 0.482451 0.835629i −0.517346 0.855776i \(-0.673080\pi\)
0.999797 + 0.0201471i \(0.00641344\pi\)
\(30\) 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 \(0.223066\pi\)
−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 \(-0.0149101\pi\)
−0.540003 + 0.841663i \(0.681577\pi\)
\(42\) 0 0
\(43\) 4.27415 + 2.46768i 0.651802 + 0.376318i 0.789146 0.614205i \(-0.210523\pi\)
−0.137344 + 0.990523i \(0.543857\pi\)
\(44\) 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 0.829774 0.558099i \(-0.188469\pi\)
−0.898215 + 0.439556i \(0.855136\pi\)
\(60\) 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
\(65\) −6.44274 0.898624i −0.799123 0.111461i
\(66\) 0 0
\(67\) 3.50947 2.02619i 0.428750 0.247539i −0.270064 0.962842i \(-0.587045\pi\)
0.698814 + 0.715303i \(0.253712\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.1663 −1.68123 −0.840614 0.541634i \(-0.817806\pi\)
−0.840614 + 0.541634i \(0.817806\pi\)
\(72\) 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 −0.646440 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
\(85\) −9.44324 + 12.1128i −1.02426 + 1.31382i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.09334 −0.327893 −0.163947 0.986469i \(-0.552422\pi\)
−0.163947 + 0.986469i \(0.552422\pi\)
\(90\) 0 0
\(91\) 14.3578 1.50511
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.36942 + 5.74527i 0.756086 + 0.589452i
\(96\) 0 0
\(97\) −0.764681 0.441489i −0.0776416 0.0448264i 0.460677 0.887568i \(-0.347607\pi\)
−0.538318 + 0.842742i \(0.680940\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.93840 + 5.08945i −0.292382 + 0.506420i −0.974372 0.224941i \(-0.927781\pi\)
0.681991 + 0.731361i \(0.261114\pi\)
\(102\) 0 0
\(103\) −8.54830 + 4.93536i −0.842289 + 0.486296i −0.858042 0.513580i \(-0.828319\pi\)
0.0157525 + 0.999876i \(0.494986\pi\)
\(104\) 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
\(115\) −7.43943 1.03764i −0.693731 0.0967606i
\(116\) 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 0.989695 + 0.143194i \(0.0457373\pi\)
−0.370838 + 0.928698i \(0.620929\pi\)
\(132\) 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 \(-0.985204\pi\)
0.459220 0.888323i \(-0.348129\pi\)
\(150\) 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
\(155\) −1.90862 + 13.6840i −0.153304 + 1.09912i
\(156\) 0 0
\(157\) −6.79357 + 3.92227i −0.542186 + 0.313031i −0.745964 0.665986i \(-0.768011\pi\)
0.203779 + 0.979017i \(0.434678\pi\)
\(158\) 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 −0.185428 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
\(175\) 6.75241 23.7350i 0.510434 1.79420i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.97961 0.596424 0.298212 0.954500i \(-0.403610\pi\)
0.298212 + 0.954500i \(0.403610\pi\)
\(180\) 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
\(185\) −10.7849 + 13.8337i −0.792919 + 1.01707i
\(186\) 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 \(-0.910298\pi\)
0.721112 + 0.692819i \(0.243631\pi\)
\(192\) 0 0
\(193\) 18.8513 10.8838i 1.35695 0.783435i 0.367737 0.929930i \(-0.380133\pi\)
0.989211 + 0.146495i \(0.0467992\pi\)
\(194\) 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
\(205\) −1.81530 + 13.0149i −0.126786 + 0.909002i
\(206\) 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 0.999798 0.0200906i \(-0.00639547\pi\)
0.482500 + 0.875896i \(0.339729\pi\)
\(224\) 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 0.682218 0.731149i \(-0.261015\pi\)
−0.974302 + 0.225244i \(0.927682\pi\)
\(240\) 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
\(245\) −5.36172 + 38.4411i −0.342547 + 2.45591i
\(246\) 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 \(-0.684090\pi\)
−0.546630 + 0.837374i \(0.684090\pi\)
\(252\) 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
\(265\) 11.7524 15.0747i 0.721945 0.926034i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 30.0646 1.83307 0.916536 0.399952i \(-0.130973\pi\)
0.916536 + 0.399952i \(0.130973\pi\)
\(270\) 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
\(275\) 11.6031 + 3.30097i 0.699690 + 0.199056i
\(276\) 0 0
\(277\) −9.31298 5.37685i −0.559563 0.323064i 0.193407 0.981119i \(-0.438046\pi\)
−0.752970 + 0.658055i \(0.771380\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.21712 + 10.7684i −0.370882 + 0.642387i −0.989701 0.143147i \(-0.954278\pi\)
0.618819 + 0.785533i \(0.287611\pi\)
\(282\) 0 0
\(283\) 1.52936 0.882978i 0.0909112 0.0524876i −0.453855 0.891075i \(-0.649952\pi\)
0.544766 + 0.838588i \(0.316618\pi\)
\(284\) 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
\(295\) 0.324773 2.32848i 0.0189090 0.135569i
\(296\) 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 \(-0.0685340\pi\)
−0.673479 + 0.739207i \(0.735201\pi\)
\(312\) 0 0
\(313\) −6.02889 3.48078i −0.340773 0.196745i 0.319841 0.947471i \(-0.396371\pi\)
−0.660614 + 0.750726i \(0.729704\pi\)
\(314\) 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
\(335\) 8.97453 + 1.25176i 0.490331 + 0.0683907i
\(336\) 0 0
\(337\) −8.54830 + 4.93536i −0.465656 + 0.268846i −0.714419 0.699718i \(-0.753309\pi\)
0.248764 + 0.968564i \(0.419976\pi\)
\(338\) 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
\(355\) −24.9819 19.4762i −1.32590 1.03369i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.309878 −0.0163548 −0.00817738 0.999967i \(-0.502603\pi\)
−0.00817738 + 0.999967i \(0.502603\pi\)
\(360\) 0 0
\(361\) −1.53673 −0.0808803
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.78566 3.57315i 0.145808 0.187027i
\(366\) 0 0
\(367\) 8.54830 + 4.93536i 0.446218 + 0.257624i 0.706231 0.707981i \(-0.250394\pi\)
−0.260014 + 0.965605i \(0.583727\pi\)
\(368\) 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 \(-0.741417\pi\)
0.284766 + 0.958597i \(0.408084\pi\)
\(374\) 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
\(385\) −26.3708 3.67816i −1.34398 0.187456i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.8050 22.1789i 0.649239 1.12452i −0.334066 0.942550i \(-0.608421\pi\)
0.983305 0.181966i \(-0.0582459\pi\)
\(390\) 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 0.999795 + 0.0202642i \(0.00645075\pi\)
−0.482348 + 0.875980i \(0.660216\pi\)
\(402\) 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 0.589350 0.807878i \(-0.299384\pi\)
−0.994318 + 0.106453i \(0.966051\pi\)
\(420\) 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
\(425\) −33.3059 + 8.37785i −1.61557 + 0.406385i
\(426\) 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 \(-0.487185\pi\)
0.0402486 + 0.999190i \(0.487185\pi\)
\(432\) 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 −0.555509 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
\(445\) −5.45503 4.25280i −0.258593 0.201602i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 25.1783 1.18824 0.594120 0.804377i \(-0.297500\pi\)
0.594120 + 0.804377i \(0.297500\pi\)
\(450\) 0 0
\(451\) 14.1789 0.667659
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 25.3197 + 19.7395i 1.18701 + 0.925401i
\(456\) 0 0
\(457\) 23.8902 + 13.7930i 1.11753 + 0.645209i 0.940770 0.339044i \(-0.110104\pi\)
0.176764 + 0.984253i \(0.443437\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.35109 + 9.26836i −0.249225 + 0.431671i −0.963311 0.268387i \(-0.913509\pi\)
0.714086 + 0.700058i \(0.246843\pi\)
\(462\) 0 0
\(463\) 25.6449 14.8061i 1.19182 0.688097i 0.233101 0.972453i \(-0.425113\pi\)
0.958719 + 0.284355i \(0.0917795\pi\)
\(464\) 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
\(475\) 5.09708 + 20.2633i 0.233870 + 0.929744i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.6501 21.9105i 0.577996 1.00112i −0.417713 0.908579i \(-0.637168\pi\)
0.995709 0.0925394i \(-0.0294984\pi\)
\(480\) 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 −0.917872 0.396876i \(-0.870094\pi\)
0.115232 0.993339i \(-0.463239\pi\)
\(492\) 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 0.937462 0.348087i \(-0.113169\pi\)
−0.770183 + 0.637822i \(0.779835\pi\)
\(510\) 0 0
\(511\) −5.00000 + 8.66025i −0.221187 + 0.383107i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −21.8600 3.04900i −0.963267 0.134355i
\(516\) 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 \(-0.436611\pi\)
0.197828 + 0.980237i \(0.436611\pi\)
\(522\) 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
\(545\) −12.3444 9.62377i −0.528774 0.412237i
\(546\) 0 0
\(547\) −17.0966 9.87073i −0.730998 0.422042i 0.0877892 0.996139i \(-0.472020\pi\)
−0.818787 + 0.574097i \(0.805353\pi\)
\(548\) 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
\(565\) 30.0905 + 4.19698i 1.26592 + 0.176568i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.22731 + 3.85782i −0.0933738 + 0.161728i −0.908929 0.416952i \(-0.863098\pi\)
0.815555 + 0.578680i \(0.196432\pi\)
\(570\) 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 \(0.0522094\pi\)
−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 0.277999 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 0.638290 0.769796i \(-0.279642\pi\)
−0.985808 + 0.167878i \(0.946309\pi\)
\(600\) 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
\(605\) −1.59973 + 11.4694i −0.0650383 + 0.466296i
\(606\) 0 0
\(607\) −4.27415 + 2.46768i −0.173482 + 0.100160i −0.584227 0.811590i \(-0.698602\pi\)
0.410744 + 0.911751i \(0.365269\pi\)
\(608\) 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 −0.404026 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
\(625\) −22.0246 + 11.8287i −0.880984 + 0.473147i
\(626\) 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
\(635\) −6.78526 + 8.70341i −0.269265 + 0.345384i
\(636\) 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 \(-0.715557\pi\)
0.988228 + 0.152990i \(0.0488901\pi\)
\(642\) 0 0
\(643\) −17.8613 + 10.3122i −0.704380 + 0.406674i −0.808977 0.587841i \(-0.799978\pi\)
0.104597 + 0.994515i \(0.466645\pi\)
\(644\) 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
\(655\) −4.37587 + 31.3731i −0.170979 + 1.22585i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 20.7237 35.8945i 0.807282 1.39825i −0.107458 0.994210i \(-0.534271\pi\)
0.914740 0.404043i \(-0.132395\pi\)
\(660\) 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 0.237158 0.971471i \(-0.423784\pi\)
−0.722740 + 0.691120i \(0.757117\pi\)
\(674\) 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
\(695\) −1.79810 + 12.8916i −0.0682057 + 0.489005i
\(696\) 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 \(-0.327291\pi\)
0.516347 + 0.856379i \(0.327291\pi\)
\(702\) 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
\(715\) −9.64981 + 12.3777i −0.360882 + 0.462902i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −40.3960 −1.50652 −0.753259 0.657724i \(-0.771519\pi\)
−0.753259 + 0.657724i \(0.771519\pi\)
\(720\) 0 0
\(721\) 48.7156 1.81426
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.9892 + 7.10922i 0.928075 + 0.264030i
\(726\) 0 0
\(727\) −40.7614 23.5336i −1.51176 0.872813i −0.999906 0.0137388i \(-0.995627\pi\)
−0.511851 0.859074i \(-0.671040\pi\)
\(728\) 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 \(-0.547878\pi\)
0.781324 + 0.624126i \(0.214545\pi\)
\(734\) 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
\(745\) 4.06991 29.1794i 0.149110 1.06905i
\(746\) 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 \(0.0102171\pi\)
−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 \(-0.176661\pi\)
−0.881295 + 0.472566i \(0.843328\pi\)
\(762\) 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
\(785\) −17.3727 2.42313i −0.620060 0.0864851i
\(786\) 0 0
\(787\) −41.5261 + 23.9751i −1.48024 + 0.854620i −0.999750 0.0223775i \(-0.992876\pi\)
−0.480495 + 0.876997i \(0.659543\pi\)
\(788\) 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