Properties

Label 1512.2.s.m.865.3
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.9391935744.3
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 12 x^{5} - 76 x^{4} + 84 x^{3} + 245 x^{2} - 1372 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.3
Root \(1.57052 + 2.12920i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.m.1297.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +O(q^{10})\) \(q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +(-1.55868 + 2.69971i) q^{11} -2.32307 q^{13} +(3.09808 - 5.36603i) q^{17} +(3.36125 + 5.82185i) q^{19} +(-2.33369 - 4.04207i) q^{23} +(2.23205 - 3.86603i) q^{25} -9.24884 q^{29} +(-0.326629 + 0.565738i) q^{31} +(-1.14970 - 1.55868i) q^{35} +(-5.41993 - 9.38759i) q^{37} -12.4309 q^{41} +1.77062 q^{43} +(-5.50706 - 9.53850i) q^{47} +(6.82535 - 1.55390i) q^{49} +(-0.398363 + 0.689985i) q^{53} -2.28207 q^{55} +(-0.290731 + 0.503561i) q^{59} +(0.264389 + 0.457934i) q^{61} +(-0.850302 - 1.47277i) q^{65} +(-5.59330 + 9.68788i) q^{67} +6.34674 q^{71} +(-1.48816 + 2.57757i) q^{73} +(3.30029 - 7.55868i) q^{77} +(4.68788 + 8.11964i) q^{79} -11.0527 q^{83} +4.53590 q^{85} +(-5.89237 - 10.2059i) q^{89} +(6.10780 - 0.686487i) q^{91} +(-2.46060 + 4.26189i) q^{95} -1.77062 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 2q^{7} + O(q^{10}) \) \( 8q - 4q^{5} - 2q^{7} - 2q^{11} - 8q^{13} + 4q^{17} - 6q^{19} + 2q^{23} + 4q^{25} + 16q^{29} - 6q^{31} - 2q^{35} - 16q^{41} - 20q^{47} - 6q^{49} - 10q^{53} + 16q^{55} + 22q^{59} + 2q^{61} - 14q^{65} + 2q^{67} + 44q^{71} - 10q^{73} + 54q^{77} + 8q^{79} - 40q^{83} + 64q^{85} - 16q^{89} - 24q^{91} - 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 0.366025 + 0.633975i 0.163692 + 0.283522i 0.936190 0.351495i \(-0.114326\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(6\) 0 0
\(7\) −2.62920 + 0.295509i −0.993743 + 0.111692i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.55868 + 2.69971i −0.469960 + 0.813994i −0.999410 0.0343469i \(-0.989065\pi\)
0.529450 + 0.848341i \(0.322398\pi\)
\(12\) 0 0
\(13\) −2.32307 −0.644303 −0.322152 0.946688i \(-0.604406\pi\)
−0.322152 + 0.946688i \(0.604406\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.09808 5.36603i 0.751394 1.30145i −0.195753 0.980653i \(-0.562715\pi\)
0.947147 0.320799i \(-0.103951\pi\)
\(18\) 0 0
\(19\) 3.36125 + 5.82185i 0.771123 + 1.33562i 0.936948 + 0.349469i \(0.113638\pi\)
−0.165825 + 0.986155i \(0.553029\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.33369 4.04207i −0.486608 0.842829i 0.513274 0.858225i \(-0.328432\pi\)
−0.999881 + 0.0153959i \(0.995099\pi\)
\(24\) 0 0
\(25\) 2.23205 3.86603i 0.446410 0.773205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −9.24884 −1.71747 −0.858733 0.512423i \(-0.828748\pi\)
−0.858733 + 0.512423i \(0.828748\pi\)
\(30\) 0 0
\(31\) −0.326629 + 0.565738i −0.0586643 + 0.101610i −0.893866 0.448334i \(-0.852018\pi\)
0.835202 + 0.549944i \(0.185351\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.14970 1.55868i −0.194334 0.263465i
\(36\) 0 0
\(37\) −5.41993 9.38759i −0.891031 1.54331i −0.838642 0.544683i \(-0.816650\pi\)
−0.0523889 0.998627i \(-0.516684\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.4309 −1.94138 −0.970688 0.240343i \(-0.922740\pi\)
−0.970688 + 0.240343i \(0.922740\pi\)
\(42\) 0 0
\(43\) 1.77062 0.270017 0.135008 0.990844i \(-0.456894\pi\)
0.135008 + 0.990844i \(0.456894\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.50706 9.53850i −0.803287 1.39133i −0.917441 0.397871i \(-0.869749\pi\)
0.114154 0.993463i \(-0.463584\pi\)
\(48\) 0 0
\(49\) 6.82535 1.55390i 0.975050 0.221986i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.398363 + 0.689985i −0.0547194 + 0.0947768i −0.892088 0.451863i \(-0.850760\pi\)
0.837368 + 0.546639i \(0.184093\pi\)
\(54\) 0 0
\(55\) −2.28207 −0.307714
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.290731 + 0.503561i −0.0378499 + 0.0655580i −0.884330 0.466863i \(-0.845384\pi\)
0.846480 + 0.532421i \(0.178718\pi\)
\(60\) 0 0
\(61\) 0.264389 + 0.457934i 0.0338515 + 0.0586325i 0.882455 0.470397i \(-0.155889\pi\)
−0.848603 + 0.529030i \(0.822556\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.850302 1.47277i −0.105467 0.182674i
\(66\) 0 0
\(67\) −5.59330 + 9.68788i −0.683330 + 1.18356i 0.290628 + 0.956836i \(0.406136\pi\)
−0.973958 + 0.226726i \(0.927198\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.34674 0.753220 0.376610 0.926372i \(-0.377090\pi\)
0.376610 + 0.926372i \(0.377090\pi\)
\(72\) 0 0
\(73\) −1.48816 + 2.57757i −0.174176 + 0.301682i −0.939876 0.341516i \(-0.889060\pi\)
0.765700 + 0.643198i \(0.222393\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.30029 7.55868i 0.376103 0.861392i
\(78\) 0 0
\(79\) 4.68788 + 8.11964i 0.527427 + 0.913531i 0.999489 + 0.0319654i \(0.0101766\pi\)
−0.472062 + 0.881566i \(0.656490\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −11.0527 −1.21319 −0.606595 0.795011i \(-0.707465\pi\)
−0.606595 + 0.795011i \(0.707465\pi\)
\(84\) 0 0
\(85\) 4.53590 0.491987
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.89237 10.2059i −0.624590 1.08182i −0.988620 0.150434i \(-0.951933\pi\)
0.364030 0.931387i \(-0.381400\pi\)
\(90\) 0 0
\(91\) 6.10780 0.686487i 0.640272 0.0719634i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.46060 + 4.26189i −0.252453 + 0.437261i
\(96\) 0 0
\(97\) −1.77062 −0.179779 −0.0898895 0.995952i \(-0.528651\pi\)
−0.0898895 + 0.995952i \(0.528651\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.67604 + 8.09914i −0.465283 + 0.805894i −0.999214 0.0396337i \(-0.987381\pi\)
0.533931 + 0.845528i \(0.320714\pi\)
\(102\) 0 0
\(103\) −5.30257 9.18432i −0.522477 0.904958i −0.999658 0.0261522i \(-0.991675\pi\)
0.477180 0.878805i \(-0.341659\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.44043 9.42310i −0.525946 0.910965i −0.999543 0.0302237i \(-0.990378\pi\)
0.473597 0.880742i \(-0.342955\pi\)
\(108\) 0 0
\(109\) 1.73561 3.00617i 0.166241 0.287939i −0.770854 0.637012i \(-0.780170\pi\)
0.937095 + 0.349073i \(0.113504\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.3276 1.15969 0.579843 0.814728i \(-0.303114\pi\)
0.579843 + 0.814728i \(0.303114\pi\)
\(114\) 0 0
\(115\) 1.70838 2.95900i 0.159307 0.275928i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.55974 + 15.0238i −0.601331 + 1.37723i
\(120\) 0 0
\(121\) 0.641033 + 1.11030i 0.0582757 + 0.100937i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) −10.1174 −0.897771 −0.448885 0.893589i \(-0.648179\pi\)
−0.448885 + 0.893589i \(0.648179\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.65676 8.06574i −0.406863 0.704707i 0.587674 0.809098i \(-0.300044\pi\)
−0.994536 + 0.104391i \(0.966711\pi\)
\(132\) 0 0
\(133\) −10.5578 14.3135i −0.915476 1.24114i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.71900 + 11.6376i −0.574043 + 0.994271i 0.422102 + 0.906548i \(0.361292\pi\)
−0.996145 + 0.0877228i \(0.972041\pi\)
\(138\) 0 0
\(139\) 8.90453 0.755272 0.377636 0.925954i \(-0.376737\pi\)
0.377636 + 0.925954i \(0.376737\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.62092 6.27162i 0.302797 0.524459i
\(144\) 0 0
\(145\) −3.38531 5.86353i −0.281135 0.486939i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.63397 2.83013i −0.133860 0.231853i 0.791301 0.611427i \(-0.209404\pi\)
−0.925162 + 0.379574i \(0.876071\pi\)
\(150\) 0 0
\(151\) −3.79073 + 6.56574i −0.308485 + 0.534312i −0.978031 0.208458i \(-0.933155\pi\)
0.669546 + 0.742771i \(0.266489\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.478218 −0.0384114
\(156\) 0 0
\(157\) 5.31351 9.20327i 0.424064 0.734501i −0.572268 0.820067i \(-0.693936\pi\)
0.996333 + 0.0855654i \(0.0272697\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.33019 + 9.93776i 0.577700 + 0.783205i
\(162\) 0 0
\(163\) 9.75839 + 16.9020i 0.764336 + 1.32387i 0.940597 + 0.339526i \(0.110267\pi\)
−0.176260 + 0.984344i \(0.556400\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.2156 0.945272 0.472636 0.881258i \(-0.343303\pi\)
0.472636 + 0.881258i \(0.343303\pi\)
\(168\) 0 0
\(169\) −7.60335 −0.584873
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.80735 15.2548i −0.669610 1.15980i −0.978013 0.208543i \(-0.933128\pi\)
0.308403 0.951256i \(-0.400205\pi\)
\(174\) 0 0
\(175\) −4.72606 + 10.8241i −0.357256 + 0.818227i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.37558 + 2.38258i −0.102816 + 0.178082i −0.912844 0.408309i \(-0.866119\pi\)
0.810028 + 0.586391i \(0.199452\pi\)
\(180\) 0 0
\(181\) 8.07636 0.600311 0.300155 0.953890i \(-0.402961\pi\)
0.300155 + 0.953890i \(0.402961\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.96766 6.87219i 0.291708 0.505254i
\(186\) 0 0
\(187\) 9.65782 + 16.7278i 0.706250 + 1.22326i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.712767 1.23455i −0.0515740 0.0893288i 0.839086 0.543999i \(-0.183090\pi\)
−0.890660 + 0.454670i \(0.849757\pi\)
\(192\) 0 0
\(193\) 2.24656 3.89115i 0.161711 0.280091i −0.773772 0.633465i \(-0.781632\pi\)
0.935482 + 0.353374i \(0.114966\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.8706 1.13074 0.565368 0.824838i \(-0.308734\pi\)
0.565368 + 0.824838i \(0.308734\pi\)
\(198\) 0 0
\(199\) −6.24528 + 10.8171i −0.442716 + 0.766806i −0.997890 0.0649277i \(-0.979318\pi\)
0.555174 + 0.831734i \(0.312652\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 24.3170 2.73311i 1.70672 0.191827i
\(204\) 0 0
\(205\) −4.55002 7.88086i −0.317787 0.550423i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −20.9564 −1.44959
\(210\) 0 0
\(211\) −25.9091 −1.78366 −0.891828 0.452375i \(-0.850577\pi\)
−0.891828 + 0.452375i \(0.850577\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.648091 + 1.12253i 0.0441995 + 0.0765557i
\(216\) 0 0
\(217\) 0.691592 1.58396i 0.0469483 0.107526i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7.19704 + 12.4656i −0.484126 + 0.838530i
\(222\) 0 0
\(223\) 5.05268 0.338353 0.169176 0.985586i \(-0.445889\pi\)
0.169176 + 0.985586i \(0.445889\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.45105 + 9.44149i −0.361799 + 0.626654i −0.988257 0.152801i \(-0.951171\pi\)
0.626458 + 0.779455i \(0.284504\pi\)
\(228\) 0 0
\(229\) 4.35030 + 7.53494i 0.287476 + 0.497923i 0.973207 0.229932i \(-0.0738505\pi\)
−0.685731 + 0.727855i \(0.740517\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.35736 + 4.08307i 0.154436 + 0.267491i 0.932853 0.360256i \(-0.117311\pi\)
−0.778418 + 0.627747i \(0.783977\pi\)
\(234\) 0 0
\(235\) 4.03145 6.98267i 0.262983 0.455499i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.8232 −1.34694 −0.673470 0.739215i \(-0.735197\pi\)
−0.673470 + 0.739215i \(0.735197\pi\)
\(240\) 0 0
\(241\) 7.42577 12.8618i 0.478336 0.828502i −0.521356 0.853339i \(-0.674574\pi\)
0.999692 + 0.0248376i \(0.00790685\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.48339 + 3.75833i 0.222545 + 0.240111i
\(246\) 0 0
\(247\) −7.80841 13.5246i −0.496837 0.860547i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.13148 0.387015 0.193508 0.981099i \(-0.438014\pi\)
0.193508 + 0.981099i \(0.438014\pi\)
\(252\) 0 0
\(253\) 14.5499 0.914744
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.52634 + 9.57191i 0.344724 + 0.597079i 0.985304 0.170813i \(-0.0546393\pi\)
−0.640580 + 0.767892i \(0.721306\pi\)
\(258\) 0 0
\(259\) 17.0242 + 23.0802i 1.05783 + 1.43413i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.04645 + 15.6689i −0.557828 + 0.966187i 0.439849 + 0.898072i \(0.355032\pi\)
−0.997677 + 0.0681153i \(0.978301\pi\)
\(264\) 0 0
\(265\) −0.583244 −0.0358284
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.43087 14.6027i 0.514039 0.890342i −0.485828 0.874054i \(-0.661482\pi\)
0.999867 0.0162879i \(-0.00518482\pi\)
\(270\) 0 0
\(271\) −7.13504 12.3582i −0.433423 0.750710i 0.563743 0.825950i \(-0.309361\pi\)
−0.997165 + 0.0752403i \(0.976028\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.95811 + 12.0518i 0.419590 + 0.726750i
\(276\) 0 0
\(277\) −2.17604 + 3.76901i −0.130746 + 0.226458i −0.923964 0.382479i \(-0.875070\pi\)
0.793219 + 0.608937i \(0.208404\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.6917 1.59229 0.796147 0.605104i \(-0.206868\pi\)
0.796147 + 0.605104i \(0.206868\pi\)
\(282\) 0 0
\(283\) 2.23205 3.86603i 0.132682 0.229811i −0.792028 0.610485i \(-0.790975\pi\)
0.924709 + 0.380674i \(0.124308\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 32.6832 3.67343i 1.92923 0.216836i
\(288\) 0 0
\(289\) −10.6962 18.5263i −0.629185 1.08978i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.86353 0.167289 0.0836445 0.996496i \(-0.473344\pi\)
0.0836445 + 0.996496i \(0.473344\pi\)
\(294\) 0 0
\(295\) −0.425660 −0.0247829
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.42132 + 9.39000i 0.313523 + 0.543037i
\(300\) 0 0
\(301\) −4.65530 + 0.523234i −0.268327 + 0.0301587i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.193546 + 0.335231i −0.0110824 + 0.0191953i
\(306\) 0 0
\(307\) 4.17717 0.238403 0.119202 0.992870i \(-0.461966\pi\)
0.119202 + 0.992870i \(0.461966\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.1401 24.4914i 0.801814 1.38878i −0.116607 0.993178i \(-0.537202\pi\)
0.918421 0.395604i \(-0.129465\pi\)
\(312\) 0 0
\(313\) −7.96638 13.7982i −0.450287 0.779919i 0.548117 0.836402i \(-0.315345\pi\)
−0.998404 + 0.0564825i \(0.982011\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.62792 + 16.6760i 0.540758 + 0.936620i 0.998861 + 0.0477206i \(0.0151957\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(318\) 0 0
\(319\) 14.4160 24.9692i 0.807140 1.39801i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 41.6536 2.31767
\(324\) 0 0
\(325\) −5.18521 + 8.98104i −0.287624 + 0.498179i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.2979 + 23.4512i 0.953661 + 1.29291i
\(330\) 0 0
\(331\) 7.44716 + 12.8989i 0.409333 + 0.708986i 0.994815 0.101700i \(-0.0324281\pi\)
−0.585482 + 0.810685i \(0.699095\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.18916 −0.447421
\(336\) 0 0
\(337\) 34.8279 1.89719 0.948597 0.316486i \(-0.102503\pi\)
0.948597 + 0.316486i \(0.102503\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.01822 1.76361i −0.0551398 0.0955049i
\(342\) 0 0
\(343\) −17.4860 + 6.10247i −0.944155 + 0.329502i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.4641 + 26.7846i −0.830156 + 1.43787i 0.0677573 + 0.997702i \(0.478416\pi\)
−0.897914 + 0.440171i \(0.854918\pi\)
\(348\) 0 0
\(349\) −32.8971 −1.76094 −0.880471 0.474101i \(-0.842773\pi\)
−0.880471 + 0.474101i \(0.842773\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.89676 + 6.74938i −0.207403 + 0.359233i −0.950896 0.309511i \(-0.899835\pi\)
0.743492 + 0.668744i \(0.233168\pi\)
\(354\) 0 0
\(355\) 2.32307 + 4.02367i 0.123296 + 0.213554i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.44043 + 9.42310i 0.287135 + 0.497332i 0.973125 0.230279i \(-0.0739639\pi\)
−0.685990 + 0.727611i \(0.740631\pi\)
\(360\) 0 0
\(361\) −13.0960 + 22.6829i −0.689261 + 1.19384i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.17882 −0.114045
\(366\) 0 0
\(367\) 7.83491 13.5705i 0.408979 0.708372i −0.585797 0.810458i \(-0.699218\pi\)
0.994776 + 0.102086i \(0.0325517\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.843478 1.93183i 0.0437912 0.100295i
\(372\) 0 0
\(373\) 19.0119 + 32.9297i 0.984401 + 1.70503i 0.644568 + 0.764547i \(0.277037\pi\)
0.339834 + 0.940486i \(0.389629\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 21.4857 1.10657
\(378\) 0 0
\(379\) 20.8663 1.07183 0.535915 0.844272i \(-0.319967\pi\)
0.535915 + 0.844272i \(0.319967\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.48777 + 12.9692i 0.382607 + 0.662695i 0.991434 0.130608i \(-0.0416929\pi\)
−0.608827 + 0.793303i \(0.708360\pi\)
\(384\) 0 0
\(385\) 6.00000 0.674371i 0.305788 0.0343691i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −17.6235 + 30.5248i −0.893548 + 1.54767i −0.0579573 + 0.998319i \(0.518459\pi\)
−0.835591 + 0.549352i \(0.814875\pi\)
\(390\) 0 0
\(391\) −28.9198 −1.46254
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.43176 + 5.94399i −0.172671 + 0.299075i
\(396\) 0 0
\(397\) 7.85297 + 13.6017i 0.394129 + 0.682652i 0.992990 0.118201i \(-0.0377129\pi\)
−0.598860 + 0.800854i \(0.704380\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.6760 18.4914i −0.533136 0.923419i −0.999251 0.0386945i \(-0.987680\pi\)
0.466115 0.884724i \(-0.345653\pi\)
\(402\) 0 0
\(403\) 0.758782 1.31425i 0.0377976 0.0654674i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 33.7917 1.67499
\(408\) 0 0
\(409\) −16.3158 + 28.2598i −0.806764 + 1.39736i 0.108330 + 0.994115i \(0.465450\pi\)
−0.915094 + 0.403241i \(0.867884\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.615582 1.40987i 0.0302908 0.0693753i
\(414\) 0 0
\(415\) −4.04556 7.00712i −0.198589 0.343966i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.1770 −1.37654 −0.688269 0.725455i \(-0.741629\pi\)
−0.688269 + 0.725455i \(0.741629\pi\)
\(420\) 0 0
\(421\) 7.62246 0.371496 0.185748 0.982597i \(-0.440529\pi\)
0.185748 + 0.982597i \(0.440529\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −13.8301 23.9545i −0.670860 1.16196i
\(426\) 0 0
\(427\) −0.830453 1.12587i −0.0401884 0.0544847i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.73294 + 6.46565i −0.179809 + 0.311439i −0.941815 0.336131i \(-0.890881\pi\)
0.762006 + 0.647570i \(0.224215\pi\)
\(432\) 0 0
\(433\) −12.3348 −0.592770 −0.296385 0.955069i \(-0.595781\pi\)
−0.296385 + 0.955069i \(0.595781\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.6882 27.1728i 0.750469 1.29985i
\(438\) 0 0
\(439\) −16.0360 27.7752i −0.765357 1.32564i −0.940058 0.341015i \(-0.889229\pi\)
0.174701 0.984622i \(-0.444104\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.52028 13.0255i −0.357299 0.618861i 0.630209 0.776425i \(-0.282969\pi\)
−0.987509 + 0.157565i \(0.949636\pi\)
\(444\) 0 0
\(445\) 4.31351 7.47122i 0.204480 0.354170i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.60757 0.406216 0.203108 0.979156i \(-0.434896\pi\)
0.203108 + 0.979156i \(0.434896\pi\)
\(450\) 0 0
\(451\) 19.3758 33.5598i 0.912369 1.58027i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.67083 + 3.62092i 0.125210 + 0.169751i
\(456\) 0 0
\(457\) −11.0027 19.0572i −0.514683 0.891457i −0.999855 0.0170385i \(-0.994576\pi\)
0.485172 0.874419i \(-0.338757\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.4766 0.627666 0.313833 0.949478i \(-0.398387\pi\)
0.313833 + 0.949478i \(0.398387\pi\)
\(462\) 0 0
\(463\) −36.6560 −1.70355 −0.851775 0.523907i \(-0.824474\pi\)
−0.851775 + 0.523907i \(0.824474\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.5632 30.4204i −0.812730 1.40769i −0.910947 0.412524i \(-0.864647\pi\)
0.0982167 0.995165i \(-0.468686\pi\)
\(468\) 0 0
\(469\) 11.8430 27.1242i 0.546860 1.25248i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.75983 + 4.78016i −0.126897 + 0.219792i
\(474\) 0 0
\(475\) 30.0099 1.37695
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.03340 + 12.1822i −0.321364 + 0.556619i −0.980770 0.195168i \(-0.937475\pi\)
0.659406 + 0.751787i \(0.270808\pi\)
\(480\) 0 0
\(481\) 12.5909 + 21.8080i 0.574094 + 0.994360i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.648091 1.12253i −0.0294283 0.0509713i
\(486\) 0 0
\(487\) −5.66064 + 9.80452i −0.256508 + 0.444285i −0.965304 0.261128i \(-0.915905\pi\)
0.708796 + 0.705414i \(0.249239\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.0720 1.17661 0.588307 0.808638i \(-0.299795\pi\)
0.588307 + 0.808638i \(0.299795\pi\)
\(492\) 0 0
\(493\) −28.6536 + 49.6295i −1.29049 + 2.23520i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.6868 + 1.87552i −0.748507 + 0.0841285i
\(498\) 0 0
\(499\) −1.21793 2.10952i −0.0545222 0.0944352i 0.837476 0.546474i \(-0.184030\pi\)
−0.891998 + 0.452039i \(0.850697\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.8161 −1.24026 −0.620128 0.784500i \(-0.712919\pi\)
−0.620128 + 0.784500i \(0.712919\pi\)
\(504\) 0 0
\(505\) −6.84620 −0.304652
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.50510 + 6.07102i 0.155361 + 0.269093i 0.933190 0.359382i \(-0.117013\pi\)
−0.777829 + 0.628475i \(0.783679\pi\)
\(510\) 0 0
\(511\) 3.15098 7.21672i 0.139391 0.319249i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.88175 6.72339i 0.171050 0.296268i
\(516\) 0 0
\(517\) 34.3350 1.51005
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.02189 + 10.4302i −0.263824 + 0.456956i −0.967255 0.253807i \(-0.918317\pi\)
0.703431 + 0.710764i \(0.251650\pi\)
\(522\) 0 0
\(523\) 5.47350 + 9.48039i 0.239340 + 0.414548i 0.960525 0.278194i \(-0.0897357\pi\)
−0.721185 + 0.692742i \(0.756402\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.02384 + 3.50540i 0.0881601 + 0.152698i
\(528\) 0 0
\(529\) 0.607804 1.05275i 0.0264263 0.0457716i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.8778 1.25084
\(534\) 0 0
\(535\) 3.98267 6.89819i 0.172186 0.298235i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.44345 + 20.8485i −0.277539 + 0.898009i
\(540\) 0 0
\(541\) 2.21066 + 3.82897i 0.0950436 + 0.164620i 0.909627 0.415426i \(-0.136368\pi\)
−0.814583 + 0.580047i \(0.803034\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.54111 0.108849
\(546\) 0 0
\(547\) 15.2438 0.651780 0.325890 0.945408i \(-0.394336\pi\)
0.325890 + 0.945408i \(0.394336\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −31.0876 53.8454i −1.32438 2.29389i
\(552\) 0 0
\(553\) −14.7248 19.9628i −0.626161 0.848906i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.1436 + 26.2296i −0.641657 + 1.11138i 0.343406 + 0.939187i \(0.388419\pi\)
−0.985063 + 0.172195i \(0.944914\pi\)
\(558\) 0 0
\(559\) −4.11327 −0.173973
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.94838 17.2311i 0.419274 0.726204i −0.576592 0.817032i \(-0.695618\pi\)
0.995867 + 0.0908278i \(0.0289513\pi\)
\(564\) 0 0
\(565\) 4.51223 + 7.81540i 0.189831 + 0.328797i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.54912 + 7.87931i 0.190709 + 0.330318i 0.945485 0.325664i \(-0.105588\pi\)
−0.754776 + 0.655982i \(0.772255\pi\)
\(570\) 0 0
\(571\) 3.65287 6.32696i 0.152868 0.264775i −0.779413 0.626511i \(-0.784482\pi\)
0.932281 + 0.361736i \(0.117816\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20.8356 −0.868906
\(576\) 0 0
\(577\) −21.5215 + 37.2763i −0.895952 + 1.55183i −0.0633297 + 0.997993i \(0.520172\pi\)
−0.832622 + 0.553841i \(0.813161\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 29.0597 3.26617i 1.20560 0.135503i
\(582\) 0 0
\(583\) −1.24184 2.15093i −0.0514318 0.0890825i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.8705 0.696321 0.348161 0.937435i \(-0.386806\pi\)
0.348161 + 0.937435i \(0.386806\pi\)
\(588\) 0 0
\(589\) −4.39153 −0.180950
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.64703 6.31684i −0.149766 0.259401i 0.781375 0.624062i \(-0.214519\pi\)
−0.931141 + 0.364660i \(0.881185\pi\)
\(594\) 0 0
\(595\) −11.9258 + 1.34040i −0.488909 + 0.0549510i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.99650 + 12.1183i −0.285869 + 0.495140i −0.972820 0.231564i \(-0.925616\pi\)
0.686950 + 0.726704i \(0.258949\pi\)
\(600\) 0 0
\(601\) 22.8953 0.933919 0.466960 0.884279i \(-0.345349\pi\)
0.466960 + 0.884279i \(0.345349\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.469269 + 0.812797i −0.0190785 + 0.0330449i
\(606\) 0 0
\(607\) −19.9017 34.4708i −0.807785 1.39913i −0.914395 0.404824i \(-0.867333\pi\)
0.106609 0.994301i \(-0.466001\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.7933 + 22.1586i 0.517560 + 0.896441i
\(612\) 0 0
\(613\) 13.2934 23.0248i 0.536915 0.929965i −0.462153 0.886800i \(-0.652923\pi\)
0.999068 0.0431643i \(-0.0137439\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −37.7444 −1.51953 −0.759766 0.650197i \(-0.774686\pi\)
−0.759766 + 0.650197i \(0.774686\pi\)
\(618\) 0 0
\(619\) −8.26311 + 14.3121i −0.332122 + 0.575253i −0.982928 0.183992i \(-0.941098\pi\)
0.650805 + 0.759245i \(0.274431\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.5081 + 25.0920i 0.741512 + 1.00529i
\(624\) 0 0
\(625\) −8.62436 14.9378i −0.344974 0.597513i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −67.1654 −2.67806
\(630\) 0 0
\(631\) −13.9880 −0.556854 −0.278427 0.960457i \(-0.589813\pi\)
−0.278427 + 0.960457i \(0.589813\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.70321 6.41415i −0.146957 0.254538i
\(636\) 0 0
\(637\) −15.8558 + 3.60982i −0.628228 + 0.143026i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.6604 27.1247i 0.618550 1.07136i −0.371201 0.928553i \(-0.621054\pi\)
0.989751 0.142807i \(-0.0456128\pi\)
\(642\) 0 0
\(643\) 25.2347 0.995160 0.497580 0.867418i \(-0.334222\pi\)
0.497580 + 0.867418i \(0.334222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.346742 0.600574i 0.0136318 0.0236110i −0.859129 0.511759i \(-0.828994\pi\)
0.872761 + 0.488148i \(0.162327\pi\)
\(648\) 0 0
\(649\) −0.906313 1.56978i −0.0355759 0.0616192i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.17598 15.8933i −0.359084 0.621951i 0.628724 0.777628i \(-0.283577\pi\)
−0.987808 + 0.155677i \(0.950244\pi\)
\(654\) 0 0
\(655\) 3.40898 5.90453i 0.133200 0.230709i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.41641 0.0551756 0.0275878 0.999619i \(-0.491217\pi\)
0.0275878 + 0.999619i \(0.491217\pi\)
\(660\) 0 0
\(661\) 6.57229 11.3835i 0.255633 0.442769i −0.709435 0.704771i \(-0.751050\pi\)
0.965067 + 0.262003i \(0.0843829\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.20998 11.9325i 0.202035 0.462722i
\(666\) 0 0
\(667\) 21.5839 + 37.3844i 0.835732 + 1.44753i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.64839 −0.0636353
\(672\) 0 0
\(673\) 42.8801 1.65291 0.826453 0.563006i \(-0.190355\pi\)
0.826453 + 0.563006i \(0.190355\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.2418 22.9355i −0.508925 0.881484i −0.999947 0.0103369i \(-0.996710\pi\)
0.491021 0.871148i \(-0.336624\pi\)
\(678\) 0 0
\(679\) 4.65530 0.523234i 0.178654 0.0200799i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.45787 2.52511i 0.0557839 0.0966206i −0.836785 0.547532i \(-0.815568\pi\)
0.892569 + 0.450911i \(0.148901\pi\)
\(684\) 0 0
\(685\) −9.83729 −0.375864
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.925425 1.60288i 0.0352559 0.0610650i
\(690\) 0 0
\(691\) −11.6078 20.1053i −0.441582 0.764842i 0.556225 0.831031i \(-0.312249\pi\)
−0.997807 + 0.0661896i \(0.978916\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.25928 + 5.64525i 0.123632 + 0.214136i
\(696\) 0 0
\(697\) −38.5118 + 66.7044i −1.45874 + 2.52661i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.05056 0.190757 0.0953785 0.995441i \(-0.469594\pi\)
0.0953785 + 0.995441i \(0.469594\pi\)
\(702\) 0 0
\(703\) 36.4354 63.1080i 1.37419 2.38016i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.90086 22.6760i 0.372360 0.852820i
\(708\) 0 0
\(709\) −10.0106 17.3388i −0.375954 0.651172i 0.614515 0.788905i \(-0.289352\pi\)
−0.990469 + 0.137733i \(0.956018\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.04900 0.114186
\(714\) 0 0
\(715\) 5.30140 0.198261
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.8022 30.8343i −0.663909 1.14992i −0.979580 0.201056i \(-0.935563\pi\)
0.315671 0.948869i \(-0.397771\pi\)
\(720\) 0 0
\(721\) 16.6555 + 22.5804i 0.620285 + 0.840939i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −20.6439 + 35.7562i −0.766694 + 1.32795i
\(726\) 0 0
\(727\) −0.634146 −0.0235192 −0.0117596 0.999931i \(-0.503743\pi\)
−0.0117596 + 0.999931i \(0.503743\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.48551 9.50118i 0.202889 0.351414i
\(732\) 0 0
\(733\) 12.3817 + 21.4458i 0.457330 + 0.792119i 0.998819 0.0485888i \(-0.0154724\pi\)
−0.541489 + 0.840708i \(0.682139\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −17.4363 30.2006i −0.642275 1.11245i
\(738\) 0 0
\(739\) −2.35897 + 4.08585i −0.0867760 + 0.150300i −0.906147 0.422964i \(-0.860990\pi\)
0.819371 + 0.573264i \(0.194323\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20.5554 −0.754103 −0.377051 0.926192i \(-0.623062\pi\)
−0.377051 + 0.926192i \(0.623062\pi\)
\(744\) 0 0
\(745\) 1.19615 2.07180i 0.0438236 0.0759048i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 17.0886 + 23.1675i 0.624403 + 0.846521i
\(750\) 0 0
\(751\) −0.777351 1.34641i −0.0283659 0.0491312i 0.851494 0.524364i \(-0.175697\pi\)
−0.879860 + 0.475233i \(0.842364\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.55002 −0.201986
\(756\) 0 0
\(757\) 10.9305 0.397274 0.198637 0.980073i \(-0.436349\pi\)
0.198637 + 0.980073i \(0.436349\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.35386 + 12.7373i 0.266577 + 0.461725i 0.967976 0.251044i \(-0.0807739\pi\)
−0.701398 + 0.712769i \(0.747441\pi\)
\(762\) 0 0
\(763\) −3.67491 + 8.41669i −0.133041 + 0.304705i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.675388 1.16981i 0.0243868 0.0422392i
\(768\) 0 0
\(769\) −24.3159 −0.876855 −0.438428 0.898766i \(-0.644464\pi\)
−0.438428 + 0.898766i \(0.644464\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.0106190 0.0183927i 0.000381939 0.000661538i −0.865834 0.500331i \(-0.833212\pi\)
0.866216 + 0.499669i \(0.166545\pi\)
\(774\) 0 0
\(775\) 1.45811 + 2.52551i 0.0523767 + 0.0907191i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −41.7832 72.3707i −1.49704 2.59295i
\(780\) 0 0
\(781\) −9.89254 + 17.1344i −0.353983 + 0.613116i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.77952 0.277663
\(786\) 0 0
\(787\) 6.00510 10.4011i 0.214059 0.370761i −0.738922 0.673791i \(-0.764665\pi\)
0.952981 + 0.303030i \(0.0979982\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −32.4118 + 3.64292i −1.15243 + 0.129527i
\(792\) 0 0
\(793\) −0.614193 1.06381i −0.0218106 0.0377771i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.5623 −1.08257 −0.541287 0.840838i \(-0.682063\pi\)
−0.541287 + 0.840838i \(0.682063\pi\)
\(798\) 0 0
\(799\) −68.2451 −2.41434
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.63914 8.03523i −0.163712 0.283557i
\(804\) 0 0