Properties

Label 2268.2.t.b.2105.7
Level $2268$
Weight $2$
Character 2268.2105
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2105.7
Root \(-0.811340 + 1.53027i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2105
Dual form 2268.2.t.b.1781.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37166 - 2.37578i) q^{5} +(0.900590 - 2.48776i) q^{7} +O(q^{10})\) \(q+(1.37166 - 2.37578i) q^{5} +(0.900590 - 2.48776i) q^{7} +(0.362306 - 0.209178i) q^{11} -1.53011i q^{13} +(-1.95291 - 3.38253i) q^{17} +(-5.11994 - 2.95600i) q^{19} +(-7.72884 - 4.46225i) q^{23} +(-1.26290 - 2.18740i) q^{25} +6.93257i q^{29} +(3.05626 - 1.76453i) q^{31} +(-4.67507 - 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} -2.12472 q^{41} +11.5569 q^{43} +(0.885373 - 1.53351i) q^{47} +(-5.37787 - 4.48090i) q^{49} +(-3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(2.02728 + 3.51135i) q^{59} +(1.61459 + 0.932184i) q^{61} +(-3.63521 - 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} -8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-0.194094 - 1.08971i) q^{77} +(0.433633 - 0.751074i) q^{79} -6.91761 q^{83} -10.7149 q^{85} +(-4.88864 + 8.46738i) q^{89} +(-3.80655 - 1.37800i) q^{91} +(-14.0456 + 8.10924i) q^{95} +0.231415i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{7} + O(q^{10}) \) \( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.37166 2.37578i 0.613425 1.06248i −0.377234 0.926118i \(-0.623125\pi\)
0.990659 0.136365i \(-0.0435419\pi\)
\(6\) 0 0
\(7\) 0.900590 2.48776i 0.340391 0.940284i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.362306 0.209178i 0.109240 0.0630695i −0.444385 0.895836i \(-0.646578\pi\)
0.553624 + 0.832767i \(0.313244\pi\)
\(12\) 0 0
\(13\) 1.53011i 0.424377i −0.977229 0.212188i \(-0.931941\pi\)
0.977229 0.212188i \(-0.0680590\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.95291 3.38253i −0.473649 0.820385i 0.525896 0.850549i \(-0.323730\pi\)
−0.999545 + 0.0301645i \(0.990397\pi\)
\(18\) 0 0
\(19\) −5.11994 2.95600i −1.17459 0.678152i −0.219836 0.975537i \(-0.570552\pi\)
−0.954758 + 0.297385i \(0.903886\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.72884 4.46225i −1.61157 0.930443i −0.989006 0.147878i \(-0.952756\pi\)
−0.622569 0.782565i \(-0.713911\pi\)
\(24\) 0 0
\(25\) −1.26290 2.18740i −0.252579 0.437480i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.93257i 1.28735i 0.765301 + 0.643673i \(0.222590\pi\)
−0.765301 + 0.643673i \(0.777410\pi\)
\(30\) 0 0
\(31\) 3.05626 1.76453i 0.548921 0.316920i −0.199766 0.979844i \(-0.564018\pi\)
0.748687 + 0.662924i \(0.230685\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.67507 5.55196i −0.790231 0.938453i
\(36\) 0 0
\(37\) −4.54861 + 7.87842i −0.747787 + 1.29520i 0.201095 + 0.979572i \(0.435550\pi\)
−0.948881 + 0.315633i \(0.897783\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.12472 −0.331826 −0.165913 0.986140i \(-0.553057\pi\)
−0.165913 + 0.986140i \(0.553057\pi\)
\(42\) 0 0
\(43\) 11.5569 1.76242 0.881208 0.472730i \(-0.156731\pi\)
0.881208 + 0.472730i \(0.156731\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.885373 1.53351i 0.129145 0.223686i −0.794201 0.607656i \(-0.792110\pi\)
0.923346 + 0.383970i \(0.125443\pi\)
\(48\) 0 0
\(49\) −5.37787 4.48090i −0.768268 0.640129i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.39526 + 1.96025i −0.466374 + 0.269261i −0.714721 0.699410i \(-0.753446\pi\)
0.248346 + 0.968671i \(0.420113\pi\)
\(54\) 0 0
\(55\) 1.14768i 0.154753i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.02728 + 3.51135i 0.263929 + 0.457139i 0.967283 0.253702i \(-0.0816481\pi\)
−0.703353 + 0.710840i \(0.748315\pi\)
\(60\) 0 0
\(61\) 1.61459 + 0.932184i 0.206727 + 0.119354i 0.599789 0.800158i \(-0.295251\pi\)
−0.393062 + 0.919512i \(0.628584\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.63521 2.09879i −0.450893 0.260323i
\(66\) 0 0
\(67\) 6.38441 + 11.0581i 0.779979 + 1.35096i 0.931953 + 0.362579i \(0.118104\pi\)
−0.151974 + 0.988385i \(0.548563\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.51021i 1.00998i −0.863126 0.504988i \(-0.831497\pi\)
0.863126 0.504988i \(-0.168503\pi\)
\(72\) 0 0
\(73\) 1.65059 0.952971i 0.193187 0.111537i −0.400286 0.916390i \(-0.631089\pi\)
0.593474 + 0.804853i \(0.297756\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.194094 1.08971i −0.0221190 0.124184i
\(78\) 0 0
\(79\) 0.433633 0.751074i 0.0487875 0.0845024i −0.840600 0.541656i \(-0.817798\pi\)
0.889388 + 0.457153i \(0.151131\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.91761 −0.759306 −0.379653 0.925129i \(-0.623957\pi\)
−0.379653 + 0.925129i \(0.623957\pi\)
\(84\) 0 0
\(85\) −10.7149 −1.16219
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.88864 + 8.46738i −0.518195 + 0.897540i 0.481581 + 0.876401i \(0.340063\pi\)
−0.999777 + 0.0211389i \(0.993271\pi\)
\(90\) 0 0
\(91\) −3.80655 1.37800i −0.399035 0.144454i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −14.0456 + 8.10924i −1.44105 + 0.831990i
\(96\) 0 0
\(97\) 0.231415i 0.0234966i 0.999931 + 0.0117483i \(0.00373968\pi\)
−0.999931 + 0.0117483i \(0.996260\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.14031 12.3674i −0.710487 1.23060i −0.964674 0.263445i \(-0.915141\pi\)
0.254187 0.967155i \(-0.418192\pi\)
\(102\) 0 0
\(103\) 9.30617 + 5.37292i 0.916964 + 0.529410i 0.882665 0.470002i \(-0.155747\pi\)
0.0342991 + 0.999412i \(0.489080\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.50534 3.17851i −0.532221 0.307278i 0.209699 0.977766i \(-0.432751\pi\)
−0.741920 + 0.670488i \(0.766085\pi\)
\(108\) 0 0
\(109\) 2.58036 + 4.46932i 0.247154 + 0.428083i 0.962735 0.270447i \(-0.0871714\pi\)
−0.715581 + 0.698530i \(0.753838\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.6138i 0.998466i −0.866468 0.499233i \(-0.833615\pi\)
0.866468 0.499233i \(-0.166385\pi\)
\(114\) 0 0
\(115\) −21.2027 + 12.2414i −1.97716 + 1.14151i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.1737 + 1.81208i −0.932620 + 0.166113i
\(120\) 0 0
\(121\) −5.41249 + 9.37471i −0.492044 + 0.852246i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.78753 0.607096
\(126\) 0 0
\(127\) 10.2909 0.913169 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.83048 17.0269i 0.858893 1.48765i −0.0140928 0.999901i \(-0.504486\pi\)
0.872986 0.487746i \(-0.162181\pi\)
\(132\) 0 0
\(133\) −11.9648 + 10.0750i −1.03748 + 0.873615i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.66411 2.69282i 0.398481 0.230063i −0.287347 0.957827i \(-0.592773\pi\)
0.685829 + 0.727763i \(0.259440\pi\)
\(138\) 0 0
\(139\) 17.0710i 1.44794i −0.689831 0.723971i \(-0.742315\pi\)
0.689831 0.723971i \(-0.257685\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.320065 0.554369i −0.0267652 0.0463587i
\(144\) 0 0
\(145\) 16.4703 + 9.50912i 1.36778 + 0.789690i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.31162 5.37607i −0.762838 0.440425i 0.0674758 0.997721i \(-0.478505\pi\)
−0.830314 + 0.557296i \(0.811839\pi\)
\(150\) 0 0
\(151\) −3.78223 6.55102i −0.307794 0.533115i 0.670086 0.742284i \(-0.266257\pi\)
−0.977879 + 0.209169i \(0.932924\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.68135i 0.777625i
\(156\) 0 0
\(157\) 10.6317 6.13820i 0.848500 0.489882i −0.0116445 0.999932i \(-0.503707\pi\)
0.860144 + 0.510051i \(0.170373\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −18.0615 + 15.2088i −1.42345 + 1.19862i
\(162\) 0 0
\(163\) 5.91745 10.2493i 0.463490 0.802789i −0.535642 0.844445i \(-0.679930\pi\)
0.999132 + 0.0416566i \(0.0132635\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.5771 −1.05063 −0.525313 0.850909i \(-0.676052\pi\)
−0.525313 + 0.850909i \(0.676052\pi\)
\(168\) 0 0
\(169\) 10.6588 0.819904
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.31085 14.3948i 0.631862 1.09442i −0.355308 0.934749i \(-0.615624\pi\)
0.987171 0.159668i \(-0.0510425\pi\)
\(174\) 0 0
\(175\) −6.57908 + 1.17183i −0.497331 + 0.0885819i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.8080 8.54942i 1.10680 0.639014i 0.168805 0.985650i \(-0.446009\pi\)
0.938000 + 0.346636i \(0.112676\pi\)
\(180\) 0 0
\(181\) 18.2171i 1.35407i −0.735952 0.677034i \(-0.763265\pi\)
0.735952 0.677034i \(-0.236735\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12.4783 + 21.6130i 0.917422 + 1.58902i
\(186\) 0 0
\(187\) −1.41510 0.817009i −0.103482 0.0597456i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.1860 10.4997i −1.31589 0.759730i −0.332826 0.942988i \(-0.608002\pi\)
−0.983065 + 0.183258i \(0.941336\pi\)
\(192\) 0 0
\(193\) 3.48741 + 6.04038i 0.251030 + 0.434796i 0.963810 0.266592i \(-0.0858975\pi\)
−0.712780 + 0.701388i \(0.752564\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.0756i 1.14534i 0.819786 + 0.572670i \(0.194092\pi\)
−0.819786 + 0.572670i \(0.805908\pi\)
\(198\) 0 0
\(199\) −5.44956 + 3.14630i −0.386309 + 0.223036i −0.680560 0.732693i \(-0.738263\pi\)
0.294251 + 0.955728i \(0.404930\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 17.2466 + 6.24341i 1.21047 + 0.438201i
\(204\) 0 0
\(205\) −2.91440 + 5.04788i −0.203550 + 0.352559i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.47331 −0.171083
\(210\) 0 0
\(211\) 2.59627 0.178735 0.0893674 0.995999i \(-0.471515\pi\)
0.0893674 + 0.995999i \(0.471515\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 15.8522 27.4568i 1.08111 1.87254i
\(216\) 0 0
\(217\) −1.63729 9.19236i −0.111147 0.624018i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.17565 + 2.98816i −0.348152 + 0.201006i
\(222\) 0 0
\(223\) 23.9272i 1.60228i −0.598476 0.801141i \(-0.704227\pi\)
0.598476 0.801141i \(-0.295773\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.86609 3.23216i −0.123857 0.214526i 0.797429 0.603413i \(-0.206193\pi\)
−0.921285 + 0.388887i \(0.872860\pi\)
\(228\) 0 0
\(229\) −18.2455 10.5341i −1.20570 0.696111i −0.243882 0.969805i \(-0.578421\pi\)
−0.961817 + 0.273694i \(0.911754\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0542 6.38215i −0.724186 0.418109i 0.0921057 0.995749i \(-0.470640\pi\)
−0.816291 + 0.577640i \(0.803974\pi\)
\(234\) 0 0
\(235\) −2.42886 4.20691i −0.158441 0.274429i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.7618i 0.825494i −0.910846 0.412747i \(-0.864569\pi\)
0.910846 0.412747i \(-0.135431\pi\)
\(240\) 0 0
\(241\) 2.63438 1.52096i 0.169695 0.0979737i −0.412747 0.910846i \(-0.635431\pi\)
0.582442 + 0.812872i \(0.302097\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −18.0223 + 6.63039i −1.15140 + 0.423600i
\(246\) 0 0
\(247\) −4.52301 + 7.83408i −0.287792 + 0.498470i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.32067 −0.398957 −0.199478 0.979902i \(-0.563925\pi\)
−0.199478 + 0.979902i \(0.563925\pi\)
\(252\) 0 0
\(253\) −3.73361 −0.234730
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.2538 + 21.2242i −0.764372 + 1.32393i 0.176206 + 0.984353i \(0.443617\pi\)
−0.940578 + 0.339577i \(0.889716\pi\)
\(258\) 0 0
\(259\) 15.5032 + 18.4111i 0.963320 + 1.14401i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 21.1163 12.1915i 1.30208 0.751759i 0.321323 0.946970i \(-0.395872\pi\)
0.980761 + 0.195211i \(0.0625390\pi\)
\(264\) 0 0
\(265\) 10.7552i 0.660686i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.94525 + 8.56542i 0.301517 + 0.522243i 0.976480 0.215609i \(-0.0691737\pi\)
−0.674963 + 0.737852i \(0.735840\pi\)
\(270\) 0 0
\(271\) −5.10505 2.94740i −0.310110 0.179042i 0.336866 0.941553i \(-0.390633\pi\)
−0.646976 + 0.762511i \(0.723966\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.915111 0.528340i −0.0551833 0.0318601i
\(276\) 0 0
\(277\) −11.6469 20.1731i −0.699796 1.21208i −0.968537 0.248870i \(-0.919941\pi\)
0.268741 0.963213i \(-0.413392\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 25.1680i 1.50140i 0.660644 + 0.750700i \(0.270283\pi\)
−0.660644 + 0.750700i \(0.729717\pi\)
\(282\) 0 0
\(283\) 8.62942 4.98220i 0.512966 0.296161i −0.221086 0.975254i \(-0.570960\pi\)
0.734052 + 0.679093i \(0.237627\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.91350 + 5.28579i −0.112951 + 0.312011i
\(288\) 0 0
\(289\) 0.872317 1.51090i 0.0513128 0.0888764i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 13.5813 0.793429 0.396714 0.917942i \(-0.370150\pi\)
0.396714 + 0.917942i \(0.370150\pi\)
\(294\) 0 0
\(295\) 11.1229 0.647603
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.82774 + 11.8260i −0.394858 + 0.683915i
\(300\) 0 0
\(301\) 10.4081 28.7508i 0.599911 1.65717i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.42933 2.55728i 0.253623 0.146429i
\(306\) 0 0
\(307\) 16.9849i 0.969381i 0.874686 + 0.484691i \(0.161068\pi\)
−0.874686 + 0.484691i \(0.838932\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.00148940 0.00257972i −8.44563e−5 0.000146283i 0.865983 0.500073i \(-0.166694\pi\)
−0.866068 + 0.499927i \(0.833360\pi\)
\(312\) 0 0
\(313\) 10.6154 + 6.12878i 0.600015 + 0.346419i 0.769048 0.639191i \(-0.220731\pi\)
−0.169032 + 0.985611i \(0.554064\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.0008 + 11.5475i 1.12336 + 0.648571i 0.942256 0.334894i \(-0.108700\pi\)
0.181102 + 0.983464i \(0.442034\pi\)
\(318\) 0 0
\(319\) 1.45014 + 2.51172i 0.0811922 + 0.140629i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 23.0911i 1.28482i
\(324\) 0 0
\(325\) −3.34697 + 1.93237i −0.185656 + 0.107189i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.01765 3.58366i −0.166368 0.197574i
\(330\) 0 0
\(331\) 1.73106 2.99829i 0.0951479 0.164801i −0.814522 0.580132i \(-0.803001\pi\)
0.909670 + 0.415331i \(0.136334\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 35.0289 1.91383
\(336\) 0 0
\(337\) 18.2604 0.994705 0.497352 0.867549i \(-0.334306\pi\)
0.497352 + 0.867549i \(0.334306\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.738202 1.27860i 0.0399759 0.0692403i
\(342\) 0 0
\(343\) −15.9907 + 9.34339i −0.863414 + 0.504496i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.62386 + 2.66959i −0.248222 + 0.143311i −0.618950 0.785431i \(-0.712442\pi\)
0.370728 + 0.928741i \(0.379108\pi\)
\(348\) 0 0
\(349\) 0.0157983i 0.000845662i −1.00000 0.000422831i \(-0.999865\pi\)
1.00000 0.000422831i \(-0.000134591\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.1543 + 29.7121i 0.913029 + 1.58141i 0.809761 + 0.586760i \(0.199597\pi\)
0.103268 + 0.994654i \(0.467070\pi\)
\(354\) 0 0
\(355\) −20.2184 11.6731i −1.07308 0.619544i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.42754 3.13359i −0.286454 0.165385i 0.349887 0.936792i \(-0.386220\pi\)
−0.636342 + 0.771407i \(0.719553\pi\)
\(360\) 0 0
\(361\) 7.97583 + 13.8145i 0.419781 + 0.727081i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.22861i 0.273678i
\(366\) 0 0
\(367\) −16.4888 + 9.51984i −0.860711 + 0.496931i −0.864250 0.503062i \(-0.832207\pi\)
0.00353959 + 0.999994i \(0.498873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.81890 + 10.2120i 0.0944324 + 0.530179i
\(372\) 0 0
\(373\) −5.41901 + 9.38600i −0.280586 + 0.485989i −0.971529 0.236920i \(-0.923862\pi\)
0.690943 + 0.722909i \(0.257195\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.6076 0.546320
\(378\) 0 0
\(379\) 0.700312 0.0359726 0.0179863 0.999838i \(-0.494274\pi\)
0.0179863 + 0.999838i \(0.494274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 19.0235 32.9497i 0.972056 1.68365i 0.282729 0.959200i \(-0.408760\pi\)
0.689327 0.724451i \(-0.257906\pi\)
\(384\) 0 0
\(385\) −2.85515 1.03359i −0.145512 0.0526767i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −16.6958 + 9.63934i −0.846512 + 0.488734i −0.859473 0.511182i \(-0.829208\pi\)
0.0129603 + 0.999916i \(0.495875\pi\)
\(390\) 0 0
\(391\) 34.8574i 1.76281i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.18959 2.06044i −0.0598549 0.103672i
\(396\) 0 0
\(397\) −17.3610 10.0234i −0.871325 0.503059i −0.00353639 0.999994i \(-0.501126\pi\)
−0.867788 + 0.496934i \(0.834459\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.4232 15.2554i −1.31951 0.761820i −0.335861 0.941912i \(-0.609027\pi\)
−0.983650 + 0.180092i \(0.942360\pi\)
\(402\) 0 0
\(403\) −2.69993 4.67642i −0.134493 0.232949i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.80587i 0.188650i
\(408\) 0 0
\(409\) 0.150631 0.0869667i 0.00744821 0.00430023i −0.496271 0.868168i \(-0.665298\pi\)
0.503719 + 0.863867i \(0.331965\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.5611 1.88109i 0.519680 0.0925624i
\(414\) 0 0
\(415\) −9.48860 + 16.4347i −0.465777 + 0.806749i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.1380 1.37463 0.687316 0.726359i \(-0.258789\pi\)
0.687316 + 0.726359i \(0.258789\pi\)
\(420\) 0 0
\(421\) 3.12259 0.152186 0.0760929 0.997101i \(-0.475755\pi\)
0.0760929 + 0.997101i \(0.475755\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.93264 + 8.54358i −0.239268 + 0.414424i
\(426\) 0 0
\(427\) 3.77313 3.17719i 0.182595 0.153755i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.58876 4.95872i 0.413706 0.238853i −0.278675 0.960385i \(-0.589895\pi\)
0.692381 + 0.721532i \(0.256562\pi\)
\(432\) 0 0
\(433\) 17.1274i 0.823092i 0.911389 + 0.411546i \(0.135011\pi\)
−0.911389 + 0.411546i \(0.864989\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 26.3808 + 45.6929i 1.26196 + 2.18579i
\(438\) 0 0
\(439\) 18.5795 + 10.7269i 0.886750 + 0.511965i 0.872878 0.487938i \(-0.162251\pi\)
0.0138721 + 0.999904i \(0.495584\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.84340 3.37369i −0.277628 0.160289i 0.354721 0.934972i \(-0.384576\pi\)
−0.632349 + 0.774683i \(0.717909\pi\)
\(444\) 0 0
\(445\) 13.4111 + 23.2287i 0.635747 + 1.10115i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.81624i 0.274485i 0.990537 + 0.137243i \(0.0438240\pi\)
−0.990537 + 0.137243i \(0.956176\pi\)
\(450\) 0 0
\(451\) −0.769801 + 0.444445i −0.0362485 + 0.0209281i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.49512 + 7.15338i −0.398258 + 0.335356i
\(456\) 0 0
\(457\) 16.6949 28.9164i 0.780954 1.35265i −0.150432 0.988620i \(-0.548066\pi\)
0.931386 0.364032i \(-0.118600\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 37.0308 1.72469 0.862347 0.506317i \(-0.168993\pi\)
0.862347 + 0.506317i \(0.168993\pi\)
\(462\) 0 0
\(463\) −21.1236 −0.981695 −0.490848 0.871245i \(-0.663313\pi\)
−0.490848 + 0.871245i \(0.663313\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.30470 16.1162i 0.430570 0.745770i −0.566352 0.824163i \(-0.691646\pi\)
0.996922 + 0.0783937i \(0.0249791\pi\)
\(468\) 0 0
\(469\) 33.2596 5.92402i 1.53579 0.273546i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.18715 2.41745i 0.192525 0.111155i
\(474\) 0 0
\(475\) 14.9325i 0.685149i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.16703 + 12.4137i 0.327470 + 0.567194i 0.982009 0.188834i \(-0.0604707\pi\)
−0.654539 + 0.756028i \(0.727137\pi\)
\(480\) 0 0
\(481\) 12.0549 + 6.95988i 0.549655 + 0.317343i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.549791 + 0.317422i 0.0249647 + 0.0144134i
\(486\) 0 0
\(487\) −5.64829 9.78313i −0.255949 0.443316i 0.709204 0.705003i \(-0.249054\pi\)
−0.965153 + 0.261687i \(0.915721\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.2087i 0.460711i 0.973107 + 0.230356i \(0.0739889\pi\)
−0.973107 + 0.230356i \(0.926011\pi\)
\(492\) 0 0
\(493\) 23.4496 13.5387i 1.05612 0.609751i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −21.1713 7.66422i −0.949665 0.343787i
\(498\) 0 0
\(499\) 9.56672 16.5701i 0.428265 0.741777i −0.568454 0.822715i \(-0.692458\pi\)
0.996719 + 0.0809379i \(0.0257915\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0.268917 0.0119904 0.00599520 0.999982i \(-0.498092\pi\)
0.00599520 + 0.999982i \(0.498092\pi\)
\(504\) 0 0
\(505\) −39.1763 −1.74332
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.9439 18.9553i 0.485079 0.840181i −0.514774 0.857326i \(-0.672124\pi\)
0.999853 + 0.0171449i \(0.00545767\pi\)
\(510\) 0 0
\(511\) −0.884252 4.96452i −0.0391170 0.219617i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 25.5298 14.7396i 1.12498 0.649506i
\(516\) 0 0
\(517\) 0.740802i 0.0325804i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.856074 + 1.48276i 0.0375053 + 0.0649610i 0.884169 0.467168i \(-0.154726\pi\)
−0.846663 + 0.532129i \(0.821392\pi\)
\(522\) 0 0
\(523\) 7.16320 + 4.13568i 0.313225 + 0.180841i 0.648369 0.761326i \(-0.275452\pi\)
−0.335144 + 0.942167i \(0.608785\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.9372 6.89193i −0.519992 0.300217i
\(528\) 0 0
\(529\) 28.3233 + 49.0574i 1.23145 + 2.13293i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.25106i 0.140819i
\(534\) 0 0
\(535\) −15.1029 + 8.71966i −0.652955 + 0.376984i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.88574 0.498528i −0.124298 0.0214731i
\(540\) 0 0
\(541\) −10.1997 + 17.6664i −0.438518 + 0.759536i −0.997575 0.0695932i \(-0.977830\pi\)
0.559057 + 0.829129i \(0.311163\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14.1575 0.606441
\(546\) 0 0
\(547\) −37.9261 −1.62160 −0.810801 0.585322i \(-0.800968\pi\)
−0.810801 + 0.585322i \(0.800968\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 20.4927 35.4943i 0.873017 1.51211i
\(552\) 0 0
\(553\) −1.47796 1.75518i −0.0628494 0.0746380i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.5919 8.42463i 0.618278 0.356963i −0.157920 0.987452i \(-0.550479\pi\)
0.776198 + 0.630489i \(0.217146\pi\)
\(558\) 0 0
\(559\) 17.6834i 0.747928i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8.28035 + 14.3420i 0.348975 + 0.604443i 0.986068 0.166345i \(-0.0531965\pi\)
−0.637093 + 0.770787i \(0.719863\pi\)
\(564\) 0 0
\(565\) −25.2162 14.5586i −1.06085 0.612484i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.49856 3.17460i −0.230512 0.133086i 0.380296 0.924865i \(-0.375822\pi\)
−0.610808 + 0.791779i \(0.709155\pi\)
\(570\) 0 0
\(571\) −22.8703 39.6125i −0.957092 1.65773i −0.729507 0.683973i \(-0.760250\pi\)
−0.227585 0.973758i \(-0.573083\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22.5414i 0.940043i
\(576\) 0 0
\(577\) 15.3719 8.87497i 0.639940 0.369470i −0.144651 0.989483i \(-0.546206\pi\)
0.784592 + 0.620013i \(0.212873\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.22993 + 17.2093i −0.258461 + 0.713963i
\(582\) 0 0
\(583\) −0.820082 + 1.42042i −0.0339643 + 0.0588280i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.82297 −0.364163 −0.182081 0.983283i \(-0.558283\pi\)
−0.182081 + 0.983283i \(0.558283\pi\)
\(588\) 0 0
\(589\) −20.8638 −0.859679
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.24849 7.35860i 0.174465 0.302181i −0.765511 0.643422i \(-0.777514\pi\)
0.939976 + 0.341241i \(0.110847\pi\)
\(594\) 0 0
\(595\) −9.64972 + 26.6560i −0.395600 + 1.09279i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.21158 + 1.85421i −0.131222 + 0.0757609i −0.564174 0.825656i \(-0.690805\pi\)
0.432952 + 0.901417i \(0.357472\pi\)
\(600\) 0 0
\(601\) 7.09036i 0.289222i 0.989489 + 0.144611i \(0.0461930\pi\)
−0.989489 + 0.144611i \(0.953807\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 14.8482 + 25.7178i 0.603664 + 1.04558i
\(606\) 0 0
\(607\) 29.4396 + 16.9970i 1.19492 + 0.689886i 0.959418 0.281988i \(-0.0909939\pi\)
0.235500 + 0.971874i \(0.424327\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.34644 1.35472i −0.0949270 0.0548061i
\(612\) 0 0
\(613\) −11.6761 20.2237i −0.471595 0.816827i 0.527877 0.849321i \(-0.322988\pi\)
−0.999472 + 0.0324944i \(0.989655\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.1277i 1.81677i 0.418133 + 0.908386i \(0.362684\pi\)
−0.418133 + 0.908386i \(0.637316\pi\)
\(618\) 0 0
\(619\) 7.97914 4.60676i 0.320709 0.185161i −0.331000 0.943631i \(-0.607386\pi\)
0.651708 + 0.758470i \(0.274053\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 16.6621 + 19.7874i 0.667554 + 0.792765i
\(624\) 0 0
\(625\) 15.6247 27.0627i 0.624987 1.08251i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 35.5320 1.41675
\(630\) 0 0
\(631\) 17.6136 0.701188 0.350594 0.936528i \(-0.385980\pi\)
0.350594 + 0.936528i \(0.385980\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14.1156 24.4489i 0.560160 0.970226i
\(636\) 0 0
\(637\) −6.85628 + 8.22875i −0.271656 + 0.326035i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.5759 + 9.57009i −0.654708 + 0.377996i −0.790258 0.612775i \(-0.790053\pi\)
0.135550 + 0.990771i \(0.456720\pi\)
\(642\) 0 0
\(643\) 2.32244i 0.0915882i 0.998951 + 0.0457941i \(0.0145818\pi\)
−0.998951 + 0.0457941i \(0.985418\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.9310 + 22.3971i 0.508370 + 0.880522i 0.999953 + 0.00969167i \(0.00308500\pi\)
−0.491583 + 0.870831i \(0.663582\pi\)
\(648\) 0 0
\(649\) 1.46899 + 0.848123i 0.0576630 + 0.0332918i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20.1140 + 11.6128i 0.787123 + 0.454446i 0.838949 0.544211i \(-0.183171\pi\)
−0.0518258 + 0.998656i \(0.516504\pi\)
\(654\) 0 0
\(655\) −26.9681 46.7102i −1.05373 1.82512i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 15.8196i 0.616245i 0.951347 + 0.308122i \(0.0997006\pi\)
−0.951347 + 0.308122i \(0.900299\pi\)
\(660\) 0 0
\(661\) 15.8006 9.12248i 0.614572 0.354823i −0.160181 0.987088i \(-0.551208\pi\)
0.774753 + 0.632264i \(0.217874\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.52447 + 42.2452i 0.291787 + 1.63820i
\(666\) 0 0
\(667\) 30.9349 53.5807i 1.19780 2.07465i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.779968 0.0301103
\(672\) 0 0
\(673\) −28.8367 −1.11157 −0.555787 0.831325i \(-0.687583\pi\)
−0.555787 + 0.831325i \(0.687583\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16.7668 29.0409i 0.644400 1.11613i −0.340040 0.940411i \(-0.610441\pi\)
0.984440 0.175722i \(-0.0562261\pi\)
\(678\) 0 0
\(679\) 0.575703 + 0.208410i 0.0220935 + 0.00799803i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19.0943 + 11.0241i −0.730621 + 0.421824i −0.818649 0.574294i \(-0.805277\pi\)
0.0880282 + 0.996118i \(0.471943\pi\)
\(684\) 0 0
\(685\) 14.7745i 0.564506i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.99941 + 5.19512i 0.114268 + 0.197918i
\(690\) 0 0
\(691\) 22.8662 + 13.2018i 0.869869 + 0.502219i 0.867305 0.497777i \(-0.165850\pi\)
0.00256453 + 0.999997i \(0.499184\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −40.5569 23.4156i −1.53841 0.888203i
\(696\) 0 0
\(697\) 4.14938 + 7.18694i 0.157169 + 0.272225i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 20.5140i 0.774804i −0.921911 0.387402i \(-0.873373\pi\)
0.921911 0.387402i \(-0.126627\pi\)
\(702\) 0 0
\(703\) 46.5772 26.8913i 1.75669 1.01423i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −37.1975 + 6.62541i −1.39896 + 0.249174i
\(708\) 0 0
\(709\) 3.13054 5.42226i 0.117570 0.203637i −0.801234 0.598351i \(-0.795823\pi\)
0.918804 + 0.394714i \(0.129156\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31.4951 −1.17950
\(714\) 0 0
\(715\) −1.75608 −0.0656737
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11.6111 + 20.1111i −0.433023 + 0.750017i −0.997132 0.0756828i \(-0.975886\pi\)
0.564109 + 0.825700i \(0.309220\pi\)
\(720\) 0 0
\(721\) 21.7476 18.3127i 0.809922 0.682001i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.1643 8.75512i 0.563189 0.325157i
\(726\) 0 0
\(727\) 2.89828i 0.107491i 0.998555 + 0.0537457i \(0.0171160\pi\)
−0.998555 + 0.0537457i \(0.982884\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −22.5696 39.0917i −0.834767 1.44586i
\(732\) 0 0
\(733\) −10.2963 5.94457i −0.380302 0.219568i 0.297647 0.954676i \(-0.403798\pi\)
−0.677950 + 0.735108i \(0.737131\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.62622 + 2.67095i 0.170409 + 0.0983858i
\(738\) 0 0
\(739\) 17.2254 + 29.8354i 0.633648 + 1.09751i 0.986800 + 0.161945i \(0.0517767\pi\)
−0.353151 + 0.935566i \(0.614890\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.81826i 0.103392i 0.998663 + 0.0516960i \(0.0164627\pi\)
−0.998663 + 0.0516960i \(0.983537\pi\)
\(744\) 0 0
\(745\) −25.5447 + 14.7483i −0.935887 + 0.540335i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.8654 + 10.8334i −0.470092 + 0.395844i
\(750\) 0 0
\(751\) −3.86045 + 6.68649i −0.140870 + 0.243993i −0.927824 0.373017i \(-0.878323\pi\)
0.786955 + 0.617011i \(0.211657\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20.7517 −0.755233
\(756\) 0 0
\(757\) 1.17924 0.0428603 0.0214302 0.999770i \(-0.493178\pi\)
0.0214302 + 0.999770i \(0.493178\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.56644 + 2.71316i −0.0567835 + 0.0983520i −0.893020 0.450017i \(-0.851418\pi\)
0.836236 + 0.548369i \(0.184751\pi\)
\(762\) 0 0
\(763\) 13.4424 2.39429i 0.486648 0.0866791i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.37276 3.10196i 0.193999 0.112005i
\(768\) 0 0
\(769\) 6.39124i 0.230474i −0.993338 0.115237i \(-0.963237\pi\)
0.993338 0.115237i \(-0.0367627\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23.9779 + 41.5309i 0.862425 + 1.49376i 0.869581 + 0.493790i \(0.164389\pi\)
−0.00715621 + 0.999974i \(0.502278\pi\)
\(774\) 0 0
\(775\) −7.71948 4.45685i −0.277292 0.160095i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.8784 + 6.28067i 0.389761 + 0.225028i
\(780\) 0 0
\(781\) −1.78015 3.08331i −0.0636987 0.110329i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 33.6781i 1.20202i
\(786\) 0 0
\(787\) −5.23136 + 3.02033i −0.186478 + 0.107663i −0.590333 0.807160i \(-0.701003\pi\)
0.403855 + 0.914823i \(0.367670\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −26.4047 9.55872i −0.938842 0.339869i
\(792\) 0 0
\(793\) 1.42635 2.47050i 0.0506510 0.0877301i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.56500 −0.0554352 −0.0277176 0.999616i \(-0.508824\pi\)
−0.0277176 + 0.999616i \(0.508824\pi\)
\(798\) 0 0
\(799\) −6.91620 −0.244678
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0.398681 0.690535i 0.0140691 0.0243685i