Properties

Label 1512.2.s.p.865.1
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 865.1
Root \(1.57052 + 2.12920i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.p.1297.1

$q$-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 0.772498 0.635017i \(-0.219007\pi\)
−0.936190 + 0.351495i \(0.885674\pi\)
\(6\) 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 −0.529450 0.848341i \(-0.677602\pi\)
0.999410 + 0.0343469i \(0.0109351\pi\)
\(12\) 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 \(0.437285\pi\)
−0.947147 + 0.320799i \(0.896049\pi\)
\(18\) 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 0.999881 0.0153959i \(-0.00490086\pi\)
−0.513274 + 0.858225i \(0.671568\pi\)
\(24\) 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 \(-0.171252\pi\)
0.858733 + 0.512423i \(0.171252\pi\)
\(30\) 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 \(-0.0772599\pi\)
0.970688 + 0.240343i \(0.0772599\pi\)
\(42\) 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 \(0.130251\pi\)
−0.114154 + 0.993463i \(0.536416\pi\)
\(48\) 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 −0.837368 0.546639i \(-0.815907\pi\)
0.892088 + 0.451863i \(0.149240\pi\)
\(54\) 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 −0.846480 0.532421i \(-0.821282\pi\)
0.884330 + 0.466863i \(0.154616\pi\)
\(60\) 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 \(-0.622910\pi\)
−0.376610 + 0.926372i \(0.622910\pi\)
\(72\) 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 \(-0.292535\pi\)
0.606595 + 0.795011i \(0.292535\pi\)
\(84\) 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 \(0.0480671\pi\)
−0.364030 + 0.931387i \(0.618600\pi\)
\(90\) 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 −0.533931 0.845528i \(-0.679286\pi\)
0.999214 + 0.0396337i \(0.0126191\pi\)
\(102\) 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 \(0.00962198\pi\)
−0.473597 + 0.880742i \(0.657045\pi\)
\(108\) 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 \(-0.696886\pi\)
−0.579843 + 0.814728i \(0.696886\pi\)
\(114\) 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 0.994536 0.104391i \(-0.0332894\pi\)
−0.587674 + 0.809098i \(0.699956\pi\)
\(132\) 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 \(-0.638708\pi\)
0.996145 0.0877228i \(-0.0279590\pi\)
\(138\) 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 0.925162 0.379574i \(-0.123929\pi\)
−0.791301 + 0.611427i \(0.790596\pi\)
\(150\) 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 \(-0.656697\pi\)
−0.472636 + 0.881258i \(0.656697\pi\)
\(168\) 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 \(0.0668721\pi\)
−0.308403 + 0.951256i \(0.599795\pi\)
\(174\) 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 −0.810028 0.586391i \(-0.800548\pi\)
0.912844 + 0.408309i \(0.133881\pi\)
\(180\) 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 0.890660 0.454670i \(-0.150243\pi\)
−0.839086 + 0.543999i \(0.816910\pi\)
\(192\) 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 \(-0.691266\pi\)
−0.565368 + 0.824838i \(0.691266\pi\)
\(198\) 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 −0.626458 0.779455i \(-0.715496\pi\)
0.988257 + 0.152801i \(0.0488294\pi\)
\(228\) 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 0.778418 0.627747i \(-0.216023\pi\)
−0.932853 + 0.360256i \(0.882689\pi\)
\(234\) 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 \(-0.264803\pi\)
0.673470 + 0.739215i \(0.264803\pi\)
\(240\) 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 \(-0.561986\pi\)
−0.193508 + 0.981099i \(0.561986\pi\)
\(252\) 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 0.640580 0.767892i \(-0.278694\pi\)
−0.985304 + 0.170813i \(0.945361\pi\)
\(258\) 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 \(-0.644968\pi\)
0.997677 0.0681153i \(-0.0216986\pi\)
\(264\) 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 \(0.338518\pi\)
−0.999867 + 0.0162879i \(0.994815\pi\)
\(270\) 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 \(-0.793132\pi\)
−0.796147 + 0.605104i \(0.793132\pi\)
\(282\) 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 \(-0.526656\pi\)
−0.0836445 + 0.996496i \(0.526656\pi\)
\(294\) 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 \(0.462798\pi\)
−0.918421 + 0.395604i \(0.870535\pi\)
\(312\) 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 \(-0.984804\pi\)
0.458103 0.888899i \(-0.348529\pi\)
\(318\) 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 \(-0.521584\pi\)
0.897914 0.440171i \(-0.145082\pi\)
\(348\) 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 −0.743492 0.668744i \(-0.766832\pi\)
0.950896 + 0.309511i \(0.100165\pi\)
\(354\) 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 0.685990 0.727611i \(-0.259369\pi\)
−0.973125 + 0.230279i \(0.926036\pi\)
\(360\) 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 0.608827 0.793303i \(-0.291640\pi\)
−0.991434 + 0.130608i \(0.958307\pi\)
\(384\) 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 \(-0.481541\pi\)
0.835591 0.549352i \(-0.185125\pi\)
\(390\) 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 \(0.0123199\pi\)
−0.466115 + 0.884724i \(0.654347\pi\)
\(402\) 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 \(-0.258371\pi\)
0.688269 + 0.725455i \(0.258371\pi\)
\(420\) 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 −0.762006 0.647570i \(-0.775785\pi\)
0.941815 + 0.336131i \(0.109119\pi\)
\(432\) 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 0.987509 0.157565i \(-0.0503642\pi\)
−0.630209 + 0.776425i \(0.717031\pi\)
\(444\) 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 \(-0.565104\pi\)
−0.203108 + 0.979156i \(0.565104\pi\)
\(450\) 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 \(-0.601613\pi\)
−0.313833 + 0.949478i \(0.601613\pi\)
\(462\) 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 \(0.135353\pi\)
−0.0982167 + 0.995165i \(0.531314\pi\)
\(468\) 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 −0.659406 0.751787i \(-0.729192\pi\)
0.980770 + 0.195168i \(0.0625253\pi\)
\(480\) 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 \(-0.700205\pi\)
−0.588307 + 0.808638i \(0.700205\pi\)
\(492\) 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 \(-0.287081\pi\)
0.620128 + 0.784500i \(0.287081\pi\)
\(504\) 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 0.777829 0.628475i \(-0.216321\pi\)
−0.933190 + 0.359382i \(0.882987\pi\)
\(510\) 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 −0.703431 0.710764i \(-0.748350\pi\)
0.967255 + 0.253807i \(0.0816829\pi\)
\(522\) 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 \(-0.611581\pi\)
0.985063 0.172195i \(-0.0550859\pi\)
\(558\) 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 −0.995867 0.0908278i \(-0.971049\pi\)
0.576592 + 0.817032i \(0.304382\pi\)
\(564\) 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 0.754776 0.655982i \(-0.227745\pi\)
−0.945485 + 0.325664i \(0.894412\pi\)
\(570\) 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 \(-0.613194\pi\)
−0.348161 + 0.937435i \(0.613194\pi\)
\(588\) 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 0.931141 0.364660i \(-0.118815\pi\)
−0.781375 + 0.624062i \(0.785481\pi\)
\(594\) 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 −0.686950 0.726704i \(-0.741051\pi\)
0.972820 + 0.231564i \(0.0743843\pi\)
\(600\) 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 \(-0.225314\pi\)
0.759766 + 0.650197i \(0.225314\pi\)
\(618\) 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 \(0.378946\pi\)
−0.989751 + 0.142807i \(0.954387\pi\)
\(642\) 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 −0.872761 0.488148i \(-0.837673\pi\)
0.859129 + 0.511759i \(0.171006\pi\)
\(648\) 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 0.987808 0.155677i \(-0.0497559\pi\)
−0.628724 + 0.777628i \(0.716423\pi\)
\(654\) 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 \(-0.508783\pi\)
−0.0275878 + 0.999619i \(0.508783\pi\)
\(660\) 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 \(0.00329040\pi\)
−0.491021 + 0.871148i \(0.663376\pi\)
\(678\) 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 −0.892569 0.450911i \(-0.851099\pi\)
0.836785 + 0.547532i \(0.184432\pi\)
\(684\) 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 \(-0.530406\pi\)
−0.0953785 + 0.995441i \(0.530406\pi\)
\(702\) 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 \(0.0644372\pi\)
−0.315671 + 0.948869i \(0.602229\pi\)
\(720\) 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 \(-0.376938\pi\)
0.377051 + 0.926192i \(0.376938\pi\)
\(744\) 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 0.701398 0.712769i \(-0.252559\pi\)
−0.967976 + 0.251044i \(0.919226\pi\)
\(762\) 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 −0.866216 0.499669i \(-0.833455\pi\)
0.865834 + 0.500331i \(0.166788\pi\)
\(774\) 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 \(-0.317937\pi\)
0.541287 + 0.840838i \(0.317937\pi\)
\(798\) 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