Properties

Label 384.2.f.b.191.3
Level $384$
Weight $2$
Character 384.191
Analytic conductor $3.066$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 191.3
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 384.191
Dual form 384.2.f.b.191.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41421 - 1.00000i) q^{3} -2.82843 q^{5} -2.82843i q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.41421 - 1.00000i) q^{3} -2.82843 q^{5} -2.82843i q^{7} +(1.00000 - 2.82843i) q^{9} +2.00000i q^{11} -4.00000i q^{13} +(-4.00000 + 2.82843i) q^{15} -5.65685i q^{17} -2.82843 q^{19} +(-2.82843 - 4.00000i) q^{21} +8.00000 q^{23} +3.00000 q^{25} +(-1.41421 - 5.00000i) q^{27} -2.82843 q^{29} +8.48528i q^{31} +(2.00000 + 2.82843i) q^{33} +8.00000i q^{35} +4.00000i q^{37} +(-4.00000 - 5.65685i) q^{39} +2.82843 q^{43} +(-2.82843 + 8.00000i) q^{45} -1.00000 q^{49} +(-5.65685 - 8.00000i) q^{51} +8.48528 q^{53} -5.65685i q^{55} +(-4.00000 + 2.82843i) q^{57} +6.00000i q^{59} -4.00000i q^{61} +(-8.00000 - 2.82843i) q^{63} +11.3137i q^{65} +14.1421 q^{67} +(11.3137 - 8.00000i) q^{69} +8.00000 q^{71} -10.0000 q^{73} +(4.24264 - 3.00000i) q^{75} +5.65685 q^{77} -2.82843i q^{79} +(-7.00000 - 5.65685i) q^{81} -6.00000i q^{83} +16.0000i q^{85} +(-4.00000 + 2.82843i) q^{87} +5.65685i q^{89} -11.3137 q^{91} +(8.48528 + 12.0000i) q^{93} +8.00000 q^{95} -6.00000 q^{97} +(5.65685 + 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} - 16q^{15} + 32q^{23} + 12q^{25} + 8q^{33} - 16q^{39} - 4q^{49} - 16q^{57} - 32q^{63} + 32q^{71} - 40q^{73} - 28q^{81} - 16q^{87} + 32q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) 1.41421 1.00000i 0.816497 0.577350i
\(4\) 0 0
\(5\) −2.82843 −1.26491 −0.632456 0.774597i \(-0.717953\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 0 0
\(7\) 2.82843i 1.06904i −0.845154 0.534522i \(-0.820491\pi\)
0.845154 0.534522i \(-0.179509\pi\)
\(8\) 0 0
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 0 0
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0 0
\(15\) −4.00000 + 2.82843i −1.03280 + 0.730297i
\(16\) 0 0
\(17\) 5.65685i 1.37199i −0.727607 0.685994i \(-0.759367\pi\)
0.727607 0.685994i \(-0.240633\pi\)
\(18\) 0 0
\(19\) −2.82843 −0.648886 −0.324443 0.945905i \(-0.605177\pi\)
−0.324443 + 0.945905i \(0.605177\pi\)
\(20\) 0 0
\(21\) −2.82843 4.00000i −0.617213 0.872872i
\(22\) 0 0
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) −1.41421 5.00000i −0.272166 0.962250i
\(28\) 0 0
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) 0 0
\(31\) 8.48528i 1.52400i 0.647576 + 0.762001i \(0.275783\pi\)
−0.647576 + 0.762001i \(0.724217\pi\)
\(32\) 0 0
\(33\) 2.00000 + 2.82843i 0.348155 + 0.492366i
\(34\) 0 0
\(35\) 8.00000i 1.35225i
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 0 0
\(39\) −4.00000 5.65685i −0.640513 0.905822i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 2.82843 0.431331 0.215666 0.976467i \(-0.430808\pi\)
0.215666 + 0.976467i \(0.430808\pi\)
\(44\) 0 0
\(45\) −2.82843 + 8.00000i −0.421637 + 1.19257i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −5.65685 8.00000i −0.792118 1.12022i
\(52\) 0 0
\(53\) 8.48528 1.16554 0.582772 0.812636i \(-0.301968\pi\)
0.582772 + 0.812636i \(0.301968\pi\)
\(54\) 0 0
\(55\) 5.65685i 0.762770i
\(56\) 0 0
\(57\) −4.00000 + 2.82843i −0.529813 + 0.374634i
\(58\) 0 0
\(59\) 6.00000i 0.781133i 0.920575 + 0.390567i \(0.127721\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) 0 0
\(61\) 4.00000i 0.512148i −0.966657 0.256074i \(-0.917571\pi\)
0.966657 0.256074i \(-0.0824290\pi\)
\(62\) 0 0
\(63\) −8.00000 2.82843i −1.00791 0.356348i
\(64\) 0 0
\(65\) 11.3137i 1.40329i
\(66\) 0 0
\(67\) 14.1421 1.72774 0.863868 0.503718i \(-0.168035\pi\)
0.863868 + 0.503718i \(0.168035\pi\)
\(68\) 0 0
\(69\) 11.3137 8.00000i 1.36201 0.963087i
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 4.24264 3.00000i 0.489898 0.346410i
\(76\) 0 0
\(77\) 5.65685 0.644658
\(78\) 0 0
\(79\) 2.82843i 0.318223i −0.987261 0.159111i \(-0.949137\pi\)
0.987261 0.159111i \(-0.0508629\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) 16.0000i 1.73544i
\(86\) 0 0
\(87\) −4.00000 + 2.82843i −0.428845 + 0.303239i
\(88\) 0 0
\(89\) 5.65685i 0.599625i 0.953998 + 0.299813i \(0.0969242\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) −11.3137 −1.18600
\(92\) 0 0
\(93\) 8.48528 + 12.0000i 0.879883 + 1.24434i
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 5.65685 + 2.00000i 0.568535 + 0.201008i
\(100\) 0 0
\(101\) −2.82843 −0.281439 −0.140720 0.990050i \(-0.544942\pi\)
−0.140720 + 0.990050i \(0.544942\pi\)
\(102\) 0 0
\(103\) 8.48528i 0.836080i 0.908429 + 0.418040i \(0.137283\pi\)
−0.908429 + 0.418040i \(0.862717\pi\)
\(104\) 0 0
\(105\) 8.00000 + 11.3137i 0.780720 + 1.10410i
\(106\) 0 0
\(107\) 6.00000i 0.580042i 0.957020 + 0.290021i \(0.0936623\pi\)
−0.957020 + 0.290021i \(0.906338\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 4.00000 + 5.65685i 0.379663 + 0.536925i
\(112\) 0 0
\(113\) 11.3137i 1.06430i 0.846649 + 0.532152i \(0.178617\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −22.6274 −2.11002
\(116\) 0 0
\(117\) −11.3137 4.00000i −1.04595 0.369800i
\(118\) 0 0
\(119\) −16.0000 −1.46672
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 14.1421i 1.25491i −0.778652 0.627456i \(-0.784096\pi\)
0.778652 0.627456i \(-0.215904\pi\)
\(128\) 0 0
\(129\) 4.00000 2.82843i 0.352180 0.249029i
\(130\) 0 0
\(131\) 14.0000i 1.22319i 0.791173 + 0.611593i \(0.209471\pi\)
−0.791173 + 0.611593i \(0.790529\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) 0 0
\(135\) 4.00000 + 14.1421i 0.344265 + 1.21716i
\(136\) 0 0
\(137\) 11.3137i 0.966595i −0.875456 0.483298i \(-0.839439\pi\)
0.875456 0.483298i \(-0.160561\pi\)
\(138\) 0 0
\(139\) 8.48528 0.719712 0.359856 0.933008i \(-0.382826\pi\)
0.359856 + 0.933008i \(0.382826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 8.00000 0.664364
\(146\) 0 0
\(147\) −1.41421 + 1.00000i −0.116642 + 0.0824786i
\(148\) 0 0
\(149\) −2.82843 −0.231714 −0.115857 0.993266i \(-0.536961\pi\)
−0.115857 + 0.993266i \(0.536961\pi\)
\(150\) 0 0
\(151\) 8.48528i 0.690522i 0.938507 + 0.345261i \(0.112210\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(152\) 0 0
\(153\) −16.0000 5.65685i −1.29352 0.457330i
\(154\) 0 0
\(155\) 24.0000i 1.92773i
\(156\) 0 0
\(157\) 20.0000i 1.59617i −0.602542 0.798087i \(-0.705846\pi\)
0.602542 0.798087i \(-0.294154\pi\)
\(158\) 0 0
\(159\) 12.0000 8.48528i 0.951662 0.672927i
\(160\) 0 0
\(161\) 22.6274i 1.78329i
\(162\) 0 0
\(163\) 8.48528 0.664619 0.332309 0.943170i \(-0.392172\pi\)
0.332309 + 0.943170i \(0.392172\pi\)
\(164\) 0 0
\(165\) −5.65685 8.00000i −0.440386 0.622799i
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −2.82843 + 8.00000i −0.216295 + 0.611775i
\(172\) 0 0
\(173\) −2.82843 −0.215041 −0.107521 0.994203i \(-0.534291\pi\)
−0.107521 + 0.994203i \(0.534291\pi\)
\(174\) 0 0
\(175\) 8.48528i 0.641427i
\(176\) 0 0
\(177\) 6.00000 + 8.48528i 0.450988 + 0.637793i
\(178\) 0 0
\(179\) 18.0000i 1.34538i −0.739923 0.672692i \(-0.765138\pi\)
0.739923 0.672692i \(-0.234862\pi\)
\(180\) 0 0
\(181\) 12.0000i 0.891953i −0.895045 0.445976i \(-0.852856\pi\)
0.895045 0.445976i \(-0.147144\pi\)
\(182\) 0 0
\(183\) −4.00000 5.65685i −0.295689 0.418167i
\(184\) 0 0
\(185\) 11.3137i 0.831800i
\(186\) 0 0
\(187\) 11.3137 0.827340
\(188\) 0 0
\(189\) −14.1421 + 4.00000i −1.02869 + 0.290957i
\(190\) 0 0
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 0 0
\(195\) 11.3137 + 16.0000i 0.810191 + 1.14578i
\(196\) 0 0
\(197\) −14.1421 −1.00759 −0.503793 0.863825i \(-0.668062\pi\)
−0.503793 + 0.863825i \(0.668062\pi\)
\(198\) 0 0
\(199\) 8.48528i 0.601506i 0.953702 + 0.300753i \(0.0972379\pi\)
−0.953702 + 0.300753i \(0.902762\pi\)
\(200\) 0 0
\(201\) 20.0000 14.1421i 1.41069 0.997509i
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 8.00000 22.6274i 0.556038 1.57271i
\(208\) 0 0
\(209\) 5.65685i 0.391293i
\(210\) 0 0
\(211\) 2.82843 0.194717 0.0973585 0.995249i \(-0.468961\pi\)
0.0973585 + 0.995249i \(0.468961\pi\)
\(212\) 0 0
\(213\) 11.3137 8.00000i 0.775203 0.548151i
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 24.0000 1.62923
\(218\) 0 0
\(219\) −14.1421 + 10.0000i −0.955637 + 0.675737i
\(220\) 0 0
\(221\) −22.6274 −1.52208
\(222\) 0 0
\(223\) 2.82843i 0.189405i −0.995506 0.0947027i \(-0.969810\pi\)
0.995506 0.0947027i \(-0.0301901\pi\)
\(224\) 0 0
\(225\) 3.00000 8.48528i 0.200000 0.565685i
\(226\) 0 0
\(227\) 22.0000i 1.46019i −0.683345 0.730096i \(-0.739475\pi\)
0.683345 0.730096i \(-0.260525\pi\)
\(228\) 0 0
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 8.00000 5.65685i 0.526361 0.372194i
\(232\) 0 0
\(233\) 28.2843i 1.85296i 0.376339 + 0.926482i \(0.377183\pi\)
−0.376339 + 0.926482i \(0.622817\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.82843 4.00000i −0.183726 0.259828i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) −15.5563 1.00000i −0.997940 0.0641500i
\(244\) 0 0
\(245\) 2.82843 0.180702
\(246\) 0 0
\(247\) 11.3137i 0.719874i
\(248\) 0 0
\(249\) −6.00000 8.48528i −0.380235 0.537733i
\(250\) 0 0
\(251\) 2.00000i 0.126239i 0.998006 + 0.0631194i \(0.0201049\pi\)
−0.998006 + 0.0631194i \(0.979895\pi\)
\(252\) 0 0
\(253\) 16.0000i 1.00591i
\(254\) 0 0
\(255\) 16.0000 + 22.6274i 1.00196 + 1.41698i
\(256\) 0 0
\(257\) 11.3137i 0.705730i −0.935674 0.352865i \(-0.885208\pi\)
0.935674 0.352865i \(-0.114792\pi\)
\(258\) 0 0
\(259\) 11.3137 0.703000
\(260\) 0 0
\(261\) −2.82843 + 8.00000i −0.175075 + 0.495188i
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) 5.65685 + 8.00000i 0.346194 + 0.489592i
\(268\) 0 0
\(269\) −14.1421 −0.862261 −0.431131 0.902290i \(-0.641885\pi\)
−0.431131 + 0.902290i \(0.641885\pi\)
\(270\) 0 0
\(271\) 19.7990i 1.20270i 0.798985 + 0.601351i \(0.205371\pi\)
−0.798985 + 0.601351i \(0.794629\pi\)
\(272\) 0 0
\(273\) −16.0000 + 11.3137i −0.968364 + 0.684737i
\(274\) 0 0
\(275\) 6.00000i 0.361814i
\(276\) 0 0
\(277\) 12.0000i 0.721010i −0.932757 0.360505i \(-0.882604\pi\)
0.932757 0.360505i \(-0.117396\pi\)
\(278\) 0 0
\(279\) 24.0000 + 8.48528i 1.43684 + 0.508001i
\(280\) 0 0
\(281\) 5.65685i 0.337460i −0.985662 0.168730i \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) 0 0
\(283\) −25.4558 −1.51319 −0.756596 0.653882i \(-0.773139\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) 0 0
\(285\) 11.3137 8.00000i 0.670166 0.473879i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.0000 −0.882353
\(290\) 0 0
\(291\) −8.48528 + 6.00000i −0.497416 + 0.351726i
\(292\) 0 0
\(293\) 31.1127 1.81762 0.908812 0.417207i \(-0.136991\pi\)
0.908812 + 0.417207i \(0.136991\pi\)
\(294\) 0 0
\(295\) 16.9706i 0.988064i
\(296\) 0 0
\(297\) 10.0000 2.82843i 0.580259 0.164122i
\(298\) 0 0
\(299\) 32.0000i 1.85061i
\(300\) 0 0
\(301\) 8.00000i 0.461112i
\(302\) 0 0
\(303\) −4.00000 + 2.82843i −0.229794 + 0.162489i
\(304\) 0 0
\(305\) 11.3137i 0.647821i
\(306\) 0 0
\(307\) −8.48528 −0.484281 −0.242140 0.970241i \(-0.577849\pi\)
−0.242140 + 0.970241i \(0.577849\pi\)
\(308\) 0 0
\(309\) 8.48528 + 12.0000i 0.482711 + 0.682656i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −2.00000 −0.113047 −0.0565233 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) 0 0
\(315\) 22.6274 + 8.00000i 1.27491 + 0.450749i
\(316\) 0 0
\(317\) 31.1127 1.74746 0.873732 0.486408i \(-0.161693\pi\)
0.873732 + 0.486408i \(0.161693\pi\)
\(318\) 0 0
\(319\) 5.65685i 0.316723i
\(320\) 0 0
\(321\) 6.00000 + 8.48528i 0.334887 + 0.473602i
\(322\) 0 0
\(323\) 16.0000i 0.890264i
\(324\) 0 0
\(325\) 12.0000i 0.665640i
\(326\) 0 0
\(327\) −4.00000 5.65685i −0.221201 0.312825i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.82843 −0.155464 −0.0777322 0.996974i \(-0.524768\pi\)
−0.0777322 + 0.996974i \(0.524768\pi\)
\(332\) 0 0
\(333\) 11.3137 + 4.00000i 0.619987 + 0.219199i
\(334\) 0 0
\(335\) −40.0000 −2.18543
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 0 0
\(339\) 11.3137 + 16.0000i 0.614476 + 0.869001i
\(340\) 0 0
\(341\) −16.9706 −0.919007
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) −32.0000 + 22.6274i −1.72282 + 1.21822i
\(346\) 0 0
\(347\) 2.00000i 0.107366i 0.998558 + 0.0536828i \(0.0170960\pi\)
−0.998558 + 0.0536828i \(0.982904\pi\)
\(348\) 0 0
\(349\) 28.0000i 1.49881i 0.662114 + 0.749403i \(0.269659\pi\)
−0.662114 + 0.749403i \(0.730341\pi\)
\(350\) 0 0
\(351\) −20.0000 + 5.65685i −1.06752 + 0.301941i
\(352\) 0 0
\(353\) 22.6274i 1.20434i 0.798369 + 0.602168i \(0.205696\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) −22.6274 −1.20094
\(356\) 0 0
\(357\) −22.6274 + 16.0000i −1.19757 + 0.846810i
\(358\) 0 0
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) −11.0000 −0.578947
\(362\) 0 0
\(363\) 9.89949 7.00000i 0.519589 0.367405i
\(364\) 0 0
\(365\) 28.2843 1.48047
\(366\) 0 0
\(367\) 8.48528i 0.442928i 0.975169 + 0.221464i \(0.0710835\pi\)
−0.975169 + 0.221464i \(0.928916\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 24.0000i 1.24602i
\(372\) 0 0
\(373\) 36.0000i 1.86401i 0.362446 + 0.932005i \(0.381942\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 8.00000 5.65685i 0.413118 0.292119i
\(376\) 0 0
\(377\) 11.3137i 0.582686i
\(378\) 0 0
\(379\) 25.4558 1.30758 0.653789 0.756677i \(-0.273178\pi\)
0.653789 + 0.756677i \(0.273178\pi\)
\(380\) 0 0
\(381\) −14.1421 20.0000i −0.724524 1.02463i
\(382\) 0 0
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 0 0
\(385\) −16.0000 −0.815436
\(386\) 0 0
\(387\) 2.82843 8.00000i 0.143777 0.406663i
\(388\) 0 0
\(389\) 8.48528 0.430221 0.215110 0.976590i \(-0.430989\pi\)
0.215110 + 0.976590i \(0.430989\pi\)
\(390\) 0 0
\(391\) 45.2548i 2.28864i
\(392\) 0 0
\(393\) 14.0000 + 19.7990i 0.706207 + 0.998727i
\(394\) 0 0
\(395\) 8.00000i 0.402524i
\(396\) 0 0
\(397\) 28.0000i 1.40528i 0.711546 + 0.702640i \(0.247995\pi\)
−0.711546 + 0.702640i \(0.752005\pi\)
\(398\) 0 0
\(399\) 8.00000 + 11.3137i 0.400501 + 0.566394i
\(400\) 0 0
\(401\) 5.65685i 0.282490i 0.989975 + 0.141245i \(0.0451105\pi\)
−0.989975 + 0.141245i \(0.954889\pi\)
\(402\) 0 0
\(403\) 33.9411 1.69073
\(404\) 0 0
\(405\) 19.7990 + 16.0000i 0.983820 + 0.795046i
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 0 0
\(411\) −11.3137 16.0000i −0.558064 0.789222i
\(412\) 0 0
\(413\) 16.9706 0.835067
\(414\) 0 0
\(415\) 16.9706i 0.833052i
\(416\) 0 0
\(417\) 12.0000 8.48528i 0.587643 0.415526i
\(418\) 0 0
\(419\) 6.00000i 0.293119i −0.989202 0.146560i \(-0.953180\pi\)
0.989202 0.146560i \(-0.0468200\pi\)
\(420\) 0 0
\(421\) 28.0000i 1.36464i −0.731055 0.682318i \(-0.760972\pi\)
0.731055 0.682318i \(-0.239028\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 16.9706i 0.823193i
\(426\) 0 0
\(427\) −11.3137 −0.547509
\(428\) 0 0
\(429\) 11.3137 8.00000i 0.546231 0.386244i
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 0 0
\(435\) 11.3137 8.00000i 0.542451 0.383571i
\(436\) 0 0
\(437\) −22.6274 −1.08242
\(438\) 0 0
\(439\) 8.48528i 0.404980i 0.979284 + 0.202490i \(0.0649034\pi\)
−0.979284 + 0.202490i \(0.935097\pi\)
\(440\) 0 0
\(441\) −1.00000 + 2.82843i −0.0476190 + 0.134687i
\(442\) 0 0
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 0 0
\(445\) 16.0000i 0.758473i
\(446\) 0 0
\(447\) −4.00000 + 2.82843i −0.189194 + 0.133780i
\(448\) 0 0
\(449\) 16.9706i 0.800890i 0.916321 + 0.400445i \(0.131145\pi\)
−0.916321 + 0.400445i \(0.868855\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 8.48528 + 12.0000i 0.398673 + 0.563809i
\(454\) 0 0
\(455\) 32.0000 1.50018
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) −28.2843 + 8.00000i −1.32020 + 0.373408i
\(460\) 0 0
\(461\) −25.4558 −1.18560 −0.592798 0.805351i \(-0.701977\pi\)
−0.592798 + 0.805351i \(0.701977\pi\)
\(462\) 0 0
\(463\) 8.48528i 0.394344i 0.980369 + 0.197172i \(0.0631758\pi\)
−0.980369 + 0.197172i \(0.936824\pi\)
\(464\) 0 0
\(465\) −24.0000 33.9411i −1.11297 1.57398i
\(466\) 0 0
\(467\) 42.0000i 1.94353i 0.235954 + 0.971764i \(0.424178\pi\)
−0.235954 + 0.971764i \(0.575822\pi\)
\(468\) 0 0
\(469\) 40.0000i 1.84703i
\(470\) 0 0
\(471\) −20.0000 28.2843i −0.921551 1.30327i
\(472\) 0 0
\(473\) 5.65685i 0.260102i
\(474\) 0 0
\(475\) −8.48528 −0.389331
\(476\) 0 0
\(477\) 8.48528 24.0000i 0.388514 1.09888i
\(478\) 0 0
\(479\) −32.0000 −1.46212 −0.731059 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 0 0
\(483\) −22.6274 32.0000i −1.02958 1.45605i
\(484\) 0 0
\(485\) 16.9706 0.770594
\(486\) 0 0
\(487\) 42.4264i 1.92252i 0.275636 + 0.961262i \(0.411111\pi\)
−0.275636 + 0.961262i \(0.588889\pi\)
\(488\) 0 0
\(489\) 12.0000 8.48528i 0.542659 0.383718i
\(490\) 0 0
\(491\) 22.0000i 0.992846i 0.868081 + 0.496423i \(0.165354\pi\)
−0.868081 + 0.496423i \(0.834646\pi\)
\(492\) 0 0
\(493\) 16.0000i 0.720604i
\(494\) 0 0
\(495\) −16.0000 5.65685i −0.719147 0.254257i
\(496\) 0 0
\(497\) 22.6274i 1.01498i
\(498\) 0 0
\(499\) −19.7990 −0.886325 −0.443162 0.896441i \(-0.646143\pi\)
−0.443162 + 0.896441i \(0.646143\pi\)
\(500\) 0 0
\(501\) −11.3137 + 8.00000i −0.505459 + 0.357414i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 8.00000 0.355995
\(506\) 0 0
\(507\) −4.24264 + 3.00000i −0.188422 + 0.133235i
\(508\) 0 0
\(509\) −25.4558 −1.12831 −0.564155 0.825669i \(-0.690798\pi\)
−0.564155 + 0.825669i \(0.690798\pi\)
\(510\) 0 0
\(511\) 28.2843i 1.25122i
\(512\) 0 0
\(513\) 4.00000 + 14.1421i 0.176604 + 0.624391i
\(514\) 0 0
\(515\) 24.0000i 1.05757i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −4.00000 + 2.82843i −0.175581 + 0.124154i
\(520\) 0 0
\(521\) 33.9411i 1.48699i −0.668743 0.743494i \(-0.733167\pi\)
0.668743 0.743494i \(-0.266833\pi\)
\(522\) 0 0
\(523\) 14.1421 0.618392 0.309196 0.950998i \(-0.399940\pi\)
0.309196 + 0.950998i \(0.399940\pi\)
\(524\) 0 0
\(525\) −8.48528 12.0000i −0.370328 0.523723i
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 16.9706 + 6.00000i 0.736460 + 0.260378i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 16.9706i 0.733701i
\(536\) 0 0
\(537\) −18.0000 25.4558i −0.776757 1.09850i
\(538\) 0 0
\(539\) 2.00000i 0.0861461i
\(540\) 0 0
\(541\) 28.0000i 1.20381i 0.798566 + 0.601907i \(0.205592\pi\)
−0.798566 + 0.601907i \(0.794408\pi\)
\(542\) 0 0
\(543\) −12.0000 16.9706i −0.514969 0.728277i
\(544\) 0 0
\(545\) 11.3137i 0.484626i
\(546\) 0 0
\(547\) −25.4558 −1.08841 −0.544207 0.838951i \(-0.683169\pi\)
−0.544207 + 0.838951i \(0.683169\pi\)
\(548\) 0 0
\(549\) −11.3137 4.00000i −0.482857 0.170716i
\(550\) 0 0
\(551\) 8.00000 0.340811
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) −11.3137 16.0000i −0.480240 0.679162i
\(556\) 0 0
\(557\) −36.7696 −1.55798 −0.778988 0.627039i \(-0.784267\pi\)
−0.778988 + 0.627039i \(0.784267\pi\)
\(558\) 0 0
\(559\) 11.3137i 0.478519i
\(560\) 0 0
\(561\) 16.0000 11.3137i 0.675521 0.477665i
\(562\) 0 0
\(563\) 42.0000i 1.77009i 0.465506 + 0.885044i \(0.345872\pi\)
−0.465506 + 0.885044i \(0.654128\pi\)
\(564\) 0 0
\(565\) 32.0000i 1.34625i
\(566\) 0 0
\(567\) −16.0000 + 19.7990i −0.671937 + 0.831479i
\(568\) 0 0
\(569\) 11.3137i 0.474295i 0.971474 + 0.237148i \(0.0762125\pi\)
−0.971474 + 0.237148i \(0.923787\pi\)
\(570\) 0 0
\(571\) 42.4264 1.77549 0.887745 0.460336i \(-0.152271\pi\)
0.887745 + 0.460336i \(0.152271\pi\)
\(572\) 0 0
\(573\) −22.6274 + 16.0000i −0.945274 + 0.668410i
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 0 0
\(579\) −2.82843 + 2.00000i −0.117545 + 0.0831172i
\(580\) 0 0
\(581\) −16.9706 −0.704058
\(582\) 0 0
\(583\) 16.9706i 0.702849i
\(584\) 0 0
\(585\) 32.0000 + 11.3137i 1.32304 + 0.467764i
\(586\) 0 0
\(587\) 26.0000i 1.07313i −0.843857 0.536567i \(-0.819721\pi\)
0.843857 0.536567i \(-0.180279\pi\)
\(588\) 0 0
\(589\) 24.0000i 0.988903i
\(590\) 0 0
\(591\) −20.0000 + 14.1421i −0.822690 + 0.581730i
\(592\) 0 0
\(593\) 22.6274i 0.929197i −0.885522 0.464598i \(-0.846199\pi\)
0.885522 0.464598i \(-0.153801\pi\)
\(594\) 0 0
\(595\) 45.2548 1.85527
\(596\) 0 0
\(597\) 8.48528 + 12.0000i 0.347279 + 0.491127i
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 14.1421 40.0000i 0.575912 1.62893i
\(604\) 0 0
\(605\) −19.7990 −0.804943
\(606\) 0 0
\(607\) 36.7696i 1.49243i −0.665705 0.746215i \(-0.731869\pi\)
0.665705 0.746215i \(-0.268131\pi\)
\(608\) 0 0
\(609\) 8.00000 + 11.3137i 0.324176 + 0.458455i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 12.0000i 0.484675i −0.970192 0.242338i \(-0.922086\pi\)
0.970192 0.242338i \(-0.0779142\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.65685i 0.227736i −0.993496 0.113868i \(-0.963676\pi\)
0.993496 0.113868i \(-0.0363242\pi\)
\(618\) 0 0
\(619\) −25.4558 −1.02316 −0.511578 0.859237i \(-0.670939\pi\)
−0.511578 + 0.859237i \(0.670939\pi\)
\(620\) 0 0
\(621\) −11.3137 40.0000i −0.454003 1.60514i
\(622\) 0 0
\(623\) 16.0000 0.641026
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) −5.65685 8.00000i −0.225913 0.319489i
\(628\) 0 0
\(629\) 22.6274 0.902214
\(630\) 0 0
\(631\) 25.4558i 1.01338i −0.862128 0.506691i \(-0.830869\pi\)
0.862128 0.506691i \(-0.169131\pi\)
\(632\) 0 0
\(633\) 4.00000 2.82843i 0.158986 0.112420i
\(634\) 0 0
\(635\) 40.0000i 1.58735i
\(636\) 0 0
\(637\) 4.00000i 0.158486i
\(638\) 0 0
\(639\) 8.00000 22.6274i 0.316475 0.895127i
\(640\) 0 0
\(641\) 39.5980i 1.56403i −0.623262 0.782013i \(-0.714193\pi\)
0.623262 0.782013i \(-0.285807\pi\)
\(642\) 0 0
\(643\) −25.4558 −1.00388 −0.501940 0.864902i \(-0.667380\pi\)
−0.501940 + 0.864902i \(0.667380\pi\)
\(644\) 0 0
\(645\) −11.3137 + 8.00000i −0.445477 + 0.315000i
\(646\) 0 0
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 0 0
\(651\) 33.9411 24.0000i 1.33026 0.940634i
\(652\) 0 0
\(653\) 42.4264 1.66027 0.830137 0.557560i \(-0.188262\pi\)
0.830137 + 0.557560i \(0.188262\pi\)
\(654\) 0 0
\(655\) 39.5980i 1.54722i
\(656\) 0 0
\(657\) −10.0000 + 28.2843i −0.390137 + 1.10347i
\(658\) 0 0
\(659\) 14.0000i 0.545363i 0.962104 + 0.272681i \(0.0879105\pi\)
−0.962104 + 0.272681i \(0.912090\pi\)
\(660\) 0 0
\(661\) 4.00000i 0.155582i 0.996970 + 0.0777910i \(0.0247867\pi\)
−0.996970 + 0.0777910i \(0.975213\pi\)
\(662\) 0 0
\(663\) −32.0000 + 22.6274i −1.24278 + 0.878776i
\(664\) 0 0
\(665\) 22.6274i 0.877454i
\(666\) 0 0
\(667\) −22.6274 −0.876137
\(668\) 0 0
\(669\) −2.82843 4.00000i −0.109353 0.154649i
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −38.0000 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) 0 0
\(675\) −4.24264 15.0000i −0.163299 0.577350i
\(676\) 0 0
\(677\) −25.4558 −0.978348 −0.489174 0.872186i \(-0.662702\pi\)
−0.489174 + 0.872186i \(0.662702\pi\)
\(678\) 0 0
\(679\) 16.9706i 0.651270i
\(680\) 0 0
\(681\) −22.0000 31.1127i −0.843042 1.19224i
\(682\) 0 0
\(683\) 18.0000i 0.688751i 0.938832 + 0.344375i \(0.111909\pi\)
−0.938832 + 0.344375i \(0.888091\pi\)
\(684\) 0 0
\(685\) 32.0000i 1.22266i
\(686\) 0 0
\(687\) 4.00000 + 5.65685i 0.152610 + 0.215822i
\(688\) 0 0
\(689\) 33.9411i 1.29305i
\(690\) 0 0
\(691\) 31.1127 1.18358 0.591791 0.806091i \(-0.298421\pi\)
0.591791 + 0.806091i \(0.298421\pi\)
\(692\) 0 0
\(693\) 5.65685 16.0000i 0.214886 0.607790i
\(694\) 0 0
\(695\) −24.0000 −0.910372
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 28.2843 + 40.0000i 1.06981 + 1.51294i
\(700\) 0 0
\(701\) 31.1127 1.17511 0.587555 0.809184i \(-0.300091\pi\)
0.587555 + 0.809184i \(0.300091\pi\)
\(702\) 0 0
\(703\) 11.3137i 0.426705i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.00000i 0.300871i
\(708\) 0 0
\(709\) 4.00000i 0.150223i 0.997175 + 0.0751116i \(0.0239313\pi\)
−0.997175 + 0.0751116i \(0.976069\pi\)
\(710\) 0 0
\(711\) −8.00000 2.82843i −0.300023 0.106074i
\(712\) 0 0
\(713\) 67.8823i 2.54221i
\(714\) 0 0
\(715\) −22.6274 −0.846217
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) 19.7990 14.0000i 0.736332 0.520666i
\(724\) 0 0
\(725\) −8.48528 −0.315135
\(726\) 0 0
\(727\) 31.1127i 1.15391i 0.816777 + 0.576953i \(0.195758\pi\)
−0.816777 + 0.576953i \(0.804242\pi\)
\(728\) 0 0
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 0 0
\(731\) 16.0000i 0.591781i
\(732\) 0 0
\(733\) 36.0000i 1.32969i −0.746981 0.664845i \(-0.768498\pi\)
0.746981 0.664845i \(-0.231502\pi\)
\(734\) 0 0
\(735\) 4.00000 2.82843i 0.147542 0.104328i
\(736\) 0 0
\(737\) 28.2843i 1.04186i
\(738\) 0 0
\(739\) −42.4264 −1.56068 −0.780340 0.625355i \(-0.784954\pi\)
−0.780340 + 0.625355i \(0.784954\pi\)
\(740\) 0 0
\(741\) 11.3137 + 16.0000i 0.415619 + 0.587775i
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 8.00000 0.293097
\(746\) 0 0
\(747\) −16.9706 6.00000i −0.620920 0.219529i
\(748\) 0 0
\(749\) 16.9706 0.620091
\(750\) 0 0
\(751\) 2.82843i 0.103211i −0.998668 0.0516054i \(-0.983566\pi\)
0.998668 0.0516054i \(-0.0164338\pi\)
\(752\) 0 0
\(753\) 2.00000 + 2.82843i 0.0728841 + 0.103074i
\(754\) 0 0
\(755\) 24.0000i 0.873449i
\(756\) 0 0
\(757\) 12.0000i 0.436147i −0.975932 0.218074i \(-0.930023\pi\)
0.975932 0.218074i \(-0.0699773\pi\)
\(758\) 0 0
\(759\) 16.0000 + 22.6274i 0.580763 + 0.821323i
\(760\) 0 0
\(761\) 22.6274i 0.820243i 0.912031 + 0.410122i \(0.134514\pi\)
−0.912031 + 0.410122i \(0.865486\pi\)
\(762\) 0 0
\(763\) −11.3137 −0.409584
\(764\) 0 0
\(765\) 45.2548 + 16.0000i 1.63619 + 0.578481i
\(766\) 0 0
\(767\) 24.0000 0.866590
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −11.3137 16.0000i −0.407453 0.576226i
\(772\) 0 0
\(773\) −2.82843 −0.101731 −0.0508657 0.998706i \(-0.516198\pi\)
−0.0508657 + 0.998706i \(0.516198\pi\)
\(774\) 0 0
\(775\) 25.4558i 0.914401i
\(776\) 0 0
\(777\) 16.0000 11.3137i 0.573997 0.405877i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 16.0000i 0.572525i
\(782\) 0 0
\(783\) 4.00000 + 14.1421i 0.142948 + 0.505399i
\(784\) 0 0
\(785\) 56.5685i 2.01902i
\(786\) 0 0
\(787\) 31.1127 1.10905 0.554524 0.832168i \(-0.312900\pi\)
0.554524 + 0.832168i \(0.312900\pi\)
\(788\) 0 0
\(789\) −33.9411 + 24.0000i −1.20834 + 0.854423i
\(790\) 0 0
\(791\) 32.0000 1.13779
\(792\) 0 0
\(793\) −16.0000 −0.568177
\(794\) 0 0
\(795\) −33.9411 + 24.0000i −1.20377 + 0.851192i
\(796\) 0 0
\(797\) −14.1421 −0.500940 −0.250470 0.968124i \(-0.580585\pi\)
−0.250470 + 0.968124i \(0.580585\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 16.0000 + 5.65685i 0.565332 + 0.199875i
\(802\) 0