Properties

Label 2268.2.t.b.1781.7
Level $2268$
Weight $2$
Character 2268.1781
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 1781.7
Root \(-0.811340 - 1.53027i\) of defining polynomial
Character \(\chi\) \(=\) 2268.1781
Dual form 2268.2.t.b.2105.7

$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

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

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 0.990659 + 0.136365i \(0.0435419\pi\)
−0.377234 + 0.926118i \(0.623125\pi\)
\(6\) 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 0.553624 0.832767i \(-0.313244\pi\)
−0.444385 + 0.895836i \(0.646578\pi\)
\(12\) 0 0
\(13\) 1.53011i 0.424377i 0.977229 + 0.212188i \(0.0680590\pi\)
−0.977229 + 0.212188i \(0.931941\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.95291 + 3.38253i −0.473649 + 0.820385i −0.999545 0.0301645i \(-0.990397\pi\)
0.525896 + 0.850549i \(0.323730\pi\)
\(18\) 0 0
\(19\) −5.11994 + 2.95600i −1.17459 + 0.678152i −0.954758 0.297385i \(-0.903886\pi\)
−0.219836 + 0.975537i \(0.570552\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.72884 + 4.46225i −1.61157 + 0.930443i −0.622569 + 0.782565i \(0.713911\pi\)
−0.989006 + 0.147878i \(0.952756\pi\)
\(24\) 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 \(-0.777410\pi\)
0.765301 0.643673i \(-0.222590\pi\)
\(30\) 0 0
\(31\) 3.05626 + 1.76453i 0.548921 + 0.316920i 0.748687 0.662924i \(-0.230685\pi\)
−0.199766 + 0.979844i \(0.564018\pi\)
\(32\) 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 −0.948881 0.315633i \(-0.897783\pi\)
0.201095 0.979572i \(-0.435550\pi\)
\(38\) 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 0.923346 0.383970i \(-0.125443\pi\)
−0.794201 + 0.607656i \(0.792110\pi\)
\(48\) 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 0.248346 0.968671i \(-0.420113\pi\)
−0.714721 + 0.699410i \(0.753446\pi\)
\(54\) 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 −0.703353 0.710840i \(-0.748315\pi\)
0.967283 + 0.253702i \(0.0816481\pi\)
\(60\) 0 0
\(61\) 1.61459 0.932184i 0.206727 0.119354i −0.393062 0.919512i \(-0.628584\pi\)
0.599789 + 0.800158i \(0.295251\pi\)
\(62\) 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 −0.151974 0.988385i \(-0.548563\pi\)
0.931953 0.362579i \(-0.118104\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.51021i 1.00998i 0.863126 + 0.504988i \(0.168503\pi\)
−0.863126 + 0.504988i \(0.831497\pi\)
\(72\) 0 0
\(73\) 1.65059 + 0.952971i 0.193187 + 0.111537i 0.593474 0.804853i \(-0.297756\pi\)
−0.400286 + 0.916390i \(0.631089\pi\)
\(74\) 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 0.889388 0.457153i \(-0.151131\pi\)
−0.840600 + 0.541656i \(0.817798\pi\)
\(80\) 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 −0.999777 0.0211389i \(-0.993271\pi\)
0.481581 0.876401i \(-0.340063\pi\)
\(90\) 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 \(-0.996260\pi\)
0.999931 0.0117483i \(-0.00373968\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.14031 + 12.3674i −0.710487 + 1.23060i 0.254187 + 0.967155i \(0.418192\pi\)
−0.964674 + 0.263445i \(0.915141\pi\)
\(102\) 0 0
\(103\) 9.30617 5.37292i 0.916964 0.529410i 0.0342991 0.999412i \(-0.489080\pi\)
0.882665 + 0.470002i \(0.155747\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.50534 + 3.17851i −0.532221 + 0.307278i −0.741920 0.670488i \(-0.766085\pi\)
0.209699 + 0.977766i \(0.432751\pi\)
\(108\) 0 0
\(109\) 2.58036 4.46932i 0.247154 0.428083i −0.715581 0.698530i \(-0.753838\pi\)
0.962735 + 0.270447i \(0.0871714\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.6138i 0.998466i 0.866468 + 0.499233i \(0.166385\pi\)
−0.866468 + 0.499233i \(0.833615\pi\)
\(114\) 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 0.872986 + 0.487746i \(0.162181\pi\)
−0.0140928 + 0.999901i \(0.504486\pi\)
\(132\) 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 0.685829 0.727763i \(-0.259440\pi\)
−0.287347 + 0.957827i \(0.592773\pi\)
\(138\) 0 0
\(139\) 17.0710i 1.44794i 0.689831 + 0.723971i \(0.257685\pi\)
−0.689831 + 0.723971i \(0.742315\pi\)
\(140\) 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 −0.830314 0.557296i \(-0.811839\pi\)
0.0674758 + 0.997721i \(0.478505\pi\)
\(150\) 0 0
\(151\) −3.78223 + 6.55102i −0.307794 + 0.533115i −0.977879 0.209169i \(-0.932924\pi\)
0.670086 + 0.742284i \(0.266257\pi\)
\(152\) 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 0.860144 0.510051i \(-0.170373\pi\)
−0.0116445 + 0.999932i \(0.503707\pi\)
\(158\) 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 0.999132 0.0416566i \(-0.0132635\pi\)
−0.535642 + 0.844445i \(0.679930\pi\)
\(164\) 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 0.987171 + 0.159668i \(0.0510425\pi\)
−0.355308 + 0.934749i \(0.615624\pi\)
\(174\) 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 0.938000 0.346636i \(-0.112676\pi\)
0.168805 + 0.985650i \(0.446009\pi\)
\(180\) 0 0
\(181\) 18.2171i 1.35407i 0.735952 + 0.677034i \(0.236735\pi\)
−0.735952 + 0.677034i \(0.763265\pi\)
\(182\) 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 −0.983065 0.183258i \(-0.941336\pi\)
−0.332826 + 0.942988i \(0.608002\pi\)
\(192\) 0 0
\(193\) 3.48741 6.04038i 0.251030 0.434796i −0.712780 0.701388i \(-0.752564\pi\)
0.963810 + 0.266592i \(0.0858975\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.0756i 1.14534i −0.819786 0.572670i \(-0.805908\pi\)
0.819786 0.572670i \(-0.194092\pi\)
\(198\) 0 0
\(199\) −5.44956 3.14630i −0.386309 0.223036i 0.294251 0.955728i \(-0.404930\pi\)
−0.680560 + 0.732693i \(0.738263\pi\)
\(200\) 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 \(0.295773\pi\)
−0.598476 + 0.801141i \(0.704227\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.86609 + 3.23216i −0.123857 + 0.214526i −0.921285 0.388887i \(-0.872860\pi\)
0.797429 + 0.603413i \(0.206193\pi\)
\(228\) 0 0
\(229\) −18.2455 + 10.5341i −1.20570 + 0.696111i −0.961817 0.273694i \(-0.911754\pi\)
−0.243882 + 0.969805i \(0.578421\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0542 + 6.38215i −0.724186 + 0.418109i −0.816291 0.577640i \(-0.803974\pi\)
0.0921057 + 0.995749i \(0.470640\pi\)
\(234\) 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 \(0.135431\pi\)
−0.910846 + 0.412747i \(0.864569\pi\)
\(240\) 0 0
\(241\) 2.63438 + 1.52096i 0.169695 + 0.0979737i 0.582442 0.812872i \(-0.302097\pi\)
−0.412747 + 0.910846i \(0.635431\pi\)
\(242\) 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 −0.940578 0.339577i \(-0.889716\pi\)
0.176206 0.984353i \(-0.443617\pi\)
\(258\) 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 0.980761 0.195211i \(-0.0625390\pi\)
0.321323 + 0.946970i \(0.395872\pi\)
\(264\) 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 −0.674963 0.737852i \(-0.735840\pi\)
0.976480 + 0.215609i \(0.0691737\pi\)
\(270\) 0 0
\(271\) −5.10505 + 2.94740i −0.310110 + 0.179042i −0.646976 0.762511i \(-0.723966\pi\)
0.336866 + 0.941553i \(0.390633\pi\)
\(272\) 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 0.268741 + 0.963213i \(0.413392\pi\)
−0.968537 + 0.248870i \(0.919941\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 25.1680i 1.50140i −0.660644 0.750700i \(-0.729717\pi\)
0.660644 0.750700i \(-0.270283\pi\)
\(282\) 0 0
\(283\) 8.62942 + 4.98220i 0.512966 + 0.296161i 0.734052 0.679093i \(-0.237627\pi\)
−0.221086 + 0.975254i \(0.570960\pi\)
\(284\) 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 \(-0.838932\pi\)
0.874686 0.484691i \(-0.161068\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.00148940 + 0.00257972i −8.44563e−5 + 0.000146283i −0.866068 0.499927i \(-0.833360\pi\)
0.865983 + 0.500073i \(0.166694\pi\)
\(312\) 0 0
\(313\) 10.6154 6.12878i 0.600015 0.346419i −0.169032 0.985611i \(-0.554064\pi\)
0.769048 + 0.639191i \(0.220731\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.0008 11.5475i 1.12336 0.648571i 0.181102 0.983464i \(-0.442034\pi\)
0.942256 + 0.334894i \(0.108700\pi\)
\(318\) 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 0.909670 0.415331i \(-0.136334\pi\)
−0.814522 + 0.580132i \(0.803001\pi\)
\(332\) 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 0.370728 0.928741i \(-0.379108\pi\)
−0.618950 + 0.785431i \(0.712442\pi\)
\(348\) 0 0
\(349\) 0.0157983i 0.000845662i 1.00000 0.000422831i \(0.000134591\pi\)
−1.00000 0.000422831i \(0.999865\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.1543 29.7121i 0.913029 1.58141i 0.103268 0.994654i \(-0.467070\pi\)
0.809761 0.586760i \(-0.199597\pi\)
\(354\) 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 −0.636342 0.771407i \(-0.719553\pi\)
0.349887 + 0.936792i \(0.386220\pi\)
\(360\) 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 0.00353959 0.999994i \(-0.498873\pi\)
−0.864250 + 0.503062i \(0.832207\pi\)
\(368\) 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 0.690943 0.722909i \(-0.257195\pi\)
−0.971529 + 0.236920i \(0.923862\pi\)
\(374\) 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 0.689327 + 0.724451i \(0.257906\pi\)
0.282729 + 0.959200i \(0.408760\pi\)
\(384\) 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 0.0129603 0.999916i \(-0.495875\pi\)
−0.859473 + 0.511182i \(0.829208\pi\)
\(390\) 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 −0.867788 0.496934i \(-0.834459\pi\)
−0.00353639 + 0.999994i \(0.501126\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.4232 + 15.2554i −1.31951 + 0.761820i −0.983650 0.180092i \(-0.942360\pi\)
−0.335861 + 0.941912i \(0.609027\pi\)
\(402\) 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 0.503719 0.863867i \(-0.331965\pi\)
−0.496271 + 0.868168i \(0.665298\pi\)
\(410\) 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 0.692381 0.721532i \(-0.256562\pi\)
−0.278675 + 0.960385i \(0.589895\pi\)
\(432\) 0 0
\(433\) 17.1274i 0.823092i −0.911389 0.411546i \(-0.864989\pi\)
0.911389 0.411546i \(-0.135011\pi\)
\(434\) 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 0.0138721 0.999904i \(-0.495584\pi\)
0.872878 + 0.487938i \(0.162251\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.84340 + 3.37369i −0.277628 + 0.160289i −0.632349 0.774683i \(-0.717909\pi\)
0.354721 + 0.934972i \(0.384576\pi\)
\(444\) 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 \(-0.956176\pi\)
0.990537 0.137243i \(-0.0438240\pi\)
\(450\) 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 0.931386 + 0.364032i \(0.118600\pi\)
−0.150432 + 0.988620i \(0.548066\pi\)
\(458\) 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 0.996922 0.0783937i \(-0.0249791\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(468\) 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 −0.654539 0.756028i \(-0.727137\pi\)
0.982009 + 0.188834i \(0.0604707\pi\)
\(480\) 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 −0.965153 0.261687i \(-0.915721\pi\)
0.709204 + 0.705003i \(0.249054\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.2087i 0.460711i −0.973107 0.230356i \(-0.926011\pi\)
0.973107 0.230356i \(-0.0739889\pi\)
\(492\) 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 0.996719 0.0809379i \(-0.0257915\pi\)
−0.568454 + 0.822715i \(0.692458\pi\)
\(500\) 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 0.999853 0.0171449i \(-0.00545767\pi\)
−0.514774 + 0.857326i \(0.672124\pi\)
\(510\) 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 −0.846663 0.532129i \(-0.821392\pi\)
0.884169 + 0.467168i \(0.154726\pi\)
\(522\) 0 0
\(523\) 7.16320 4.13568i 0.313225 0.180841i −0.335144 0.942167i \(-0.608785\pi\)
0.648369 + 0.761326i \(0.275452\pi\)
\(524\) 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 0.559057 0.829129i \(-0.311163\pi\)
−0.997575 + 0.0695932i \(0.977830\pi\)
\(542\) 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 0.776198 0.630489i \(-0.217146\pi\)
−0.157920 + 0.987452i \(0.550479\pi\)
\(558\) 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 −0.637093 0.770787i \(-0.719863\pi\)
0.986068 + 0.166345i \(0.0531965\pi\)
\(564\) 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 −0.610808 0.791779i \(-0.709155\pi\)
0.380296 + 0.924865i \(0.375822\pi\)
\(570\) 0 0
\(571\) −22.8703 + 39.6125i −0.957092 + 1.65773i −0.227585 + 0.973758i \(0.573083\pi\)
−0.729507 + 0.683973i \(0.760250\pi\)
\(572\) 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 0.784592 0.620013i \(-0.212873\pi\)
−0.144651 + 0.989483i \(0.546206\pi\)
\(578\) 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 0.939976 0.341241i \(-0.110847\pi\)
−0.765511 + 0.643422i \(0.777514\pi\)
\(594\) 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 0.432952 0.901417i \(-0.357472\pi\)
−0.564174 + 0.825656i \(0.690805\pi\)
\(600\) 0 0
\(601\) 7.09036i 0.289222i −0.989489 0.144611i \(-0.953807\pi\)
0.989489 0.144611i \(-0.0461930\pi\)
\(602\) 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 0.235500 0.971874i \(-0.424327\pi\)
0.959418 + 0.281988i \(0.0909939\pi\)
\(608\) 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 −0.999472 0.0324944i \(-0.989655\pi\)
0.527877 + 0.849321i \(0.322988\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.1277i 1.81677i −0.418133 0.908386i \(-0.637316\pi\)
0.418133 0.908386i \(-0.362684\pi\)
\(618\) 0 0
\(619\) 7.97914 + 4.60676i 0.320709 + 0.185161i 0.651708 0.758470i \(-0.274053\pi\)
−0.331000 + 0.943631i \(0.607386\pi\)
\(620\) 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 0.135550 0.990771i \(-0.456720\pi\)
−0.790258 + 0.612775i \(0.790053\pi\)
\(642\) 0 0
\(643\) 2.32244i 0.0915882i −0.998951 0.0457941i \(-0.985418\pi\)
0.998951 0.0457941i \(-0.0145818\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.9310 22.3971i 0.508370 0.880522i −0.491583 0.870831i \(-0.663582\pi\)
0.999953 0.00969167i \(-0.00308500\pi\)
\(648\) 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 −0.0518258 0.998656i \(-0.516504\pi\)
0.838949 + 0.544211i \(0.183171\pi\)
\(654\) 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 \(-0.900299\pi\)
0.951347 0.308122i \(-0.0997006\pi\)
\(660\) 0 0
\(661\) 15.8006 + 9.12248i 0.614572 + 0.354823i 0.774753 0.632264i \(-0.217874\pi\)
−0.160181 + 0.987088i \(0.551208\pi\)
\(662\) 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 0.984440 + 0.175722i \(0.0562261\pi\)
−0.340040 + 0.940411i \(0.610441\pi\)
\(678\) 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 0.0880282 0.996118i \(-0.471943\pi\)
−0.818649 + 0.574294i \(0.805277\pi\)
\(684\) 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 0.00256453 0.999997i \(-0.499184\pi\)
0.867305 + 0.497777i \(0.165850\pi\)
\(692\) 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 \(0.126627\pi\)
−0.921911 + 0.387402i \(0.873373\pi\)
\(702\) 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 0.918804 0.394714i \(-0.129156\pi\)
−0.801234 + 0.598351i \(0.795823\pi\)
\(710\) 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 0.564109 0.825700i \(-0.309220\pi\)
−0.997132 + 0.0756828i \(0.975886\pi\)
\(720\) 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 \(-0.982884\pi\)
0.998555 0.0537457i \(-0.0171160\pi\)
\(728\) 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 −0.677950 0.735108i \(-0.737131\pi\)
0.297647 + 0.954676i \(0.403798\pi\)
\(734\) 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 −0.353151 0.935566i \(-0.614890\pi\)
0.986800 0.161945i \(-0.0517767\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.81826i 0.103392i −0.998663 0.0516960i \(-0.983537\pi\)
0.998663 0.0516960i \(-0.0164627\pi\)
\(744\) 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 0.786955 0.617011i \(-0.211657\pi\)
−0.927824 + 0.373017i \(0.878323\pi\)
\(752\) 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 0.836236 0.548369i \(-0.184751\pi\)
−0.893020 + 0.450017i \(0.851418\pi\)
\(762\) 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 \(0.0367627\pi\)
−0.993338 + 0.115237i \(0.963237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23.9779 41.5309i 0.862425 1.49376i −0.00715621 0.999974i \(-0.502278\pi\)
0.869581 0.493790i \(-0.164389\pi\)
\(774\) 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 0.403855 0.914823i \(-0.367670\pi\)
−0.590333 + 0.807160i \(0.701003\pi\)
\(788\) 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