Properties

Label 3024.2.q.l.2305.11
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.11
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70368 + 2.95086i) q^{5} +(0.410295 + 2.61374i) q^{7} +O(q^{10})\) \(q+(1.70368 + 2.95086i) q^{5} +(0.410295 + 2.61374i) q^{7} +(-2.69819 + 4.67340i) q^{11} +(1.89598 - 3.28393i) q^{13} +(-0.411976 - 0.713564i) q^{17} +(-0.233611 + 0.404626i) q^{19} +(2.74950 + 4.76227i) q^{23} +(-3.30506 + 5.72452i) q^{25} +(-0.400332 - 0.693396i) q^{29} +9.90732 q^{31} +(-7.01378 + 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(-1.84467 + 3.19507i) q^{41} +(4.36356 + 7.55790i) q^{43} -10.4991 q^{47} +(-6.66332 + 2.14481i) q^{49} +(4.71820 + 8.17217i) q^{53} -18.3874 q^{55} -1.66069 q^{59} +0.948811 q^{61} +12.9206 q^{65} -0.539184 q^{67} -3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(-13.3221 - 5.13490i) q^{77} -7.82899 q^{79} +(-3.79623 - 6.57527i) q^{83} +(1.40375 - 2.43137i) q^{85} +(3.73498 - 6.46917i) q^{89} +(9.36128 + 3.60823i) q^{91} -1.59199 q^{95} +(-3.22500 - 5.58587i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.70368 + 2.95086i 0.761909 + 1.31967i 0.941865 + 0.335991i \(0.109071\pi\)
−0.179956 + 0.983675i \(0.557596\pi\)
\(6\) 0 0
\(7\) 0.410295 + 2.61374i 0.155077 + 0.987902i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.69819 + 4.67340i −0.813535 + 1.40908i 0.0968406 + 0.995300i \(0.469126\pi\)
−0.910375 + 0.413784i \(0.864207\pi\)
\(12\) 0 0
\(13\) 1.89598 3.28393i 0.525850 0.910800i −0.473696 0.880688i \(-0.657080\pi\)
0.999547 0.0301113i \(-0.00958618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.411976 0.713564i −0.0999190 0.173065i 0.811732 0.584030i \(-0.198525\pi\)
−0.911651 + 0.410965i \(0.865192\pi\)
\(18\) 0 0
\(19\) −0.233611 + 0.404626i −0.0535940 + 0.0928275i −0.891578 0.452868i \(-0.850401\pi\)
0.837984 + 0.545695i \(0.183734\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.74950 + 4.76227i 0.573309 + 0.993001i 0.996223 + 0.0868310i \(0.0276740\pi\)
−0.422914 + 0.906170i \(0.638993\pi\)
\(24\) 0 0
\(25\) −3.30506 + 5.72452i −0.661011 + 1.14490i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.400332 0.693396i −0.0743399 0.128760i 0.826459 0.562997i \(-0.190352\pi\)
−0.900799 + 0.434236i \(0.857018\pi\)
\(30\) 0 0
\(31\) 9.90732 1.77941 0.889703 0.456539i \(-0.150911\pi\)
0.889703 + 0.456539i \(0.150911\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −7.01378 + 5.66371i −1.18555 + 0.957342i
\(36\) 0 0
\(37\) 4.34210 7.52074i 0.713837 1.23640i −0.249569 0.968357i \(-0.580289\pi\)
0.963406 0.268045i \(-0.0863777\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.84467 + 3.19507i −0.288090 + 0.498986i −0.973354 0.229309i \(-0.926354\pi\)
0.685264 + 0.728295i \(0.259687\pi\)
\(42\) 0 0
\(43\) 4.36356 + 7.55790i 0.665436 + 1.15257i 0.979167 + 0.203057i \(0.0650878\pi\)
−0.313731 + 0.949512i \(0.601579\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.4991 −1.53146 −0.765728 0.643164i \(-0.777621\pi\)
−0.765728 + 0.643164i \(0.777621\pi\)
\(48\) 0 0
\(49\) −6.66332 + 2.14481i −0.951902 + 0.306402i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.71820 + 8.17217i 0.648095 + 1.12253i 0.983577 + 0.180487i \(0.0577673\pi\)
−0.335483 + 0.942046i \(0.608899\pi\)
\(54\) 0 0
\(55\) −18.3874 −2.47936
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.66069 −0.216203 −0.108102 0.994140i \(-0.534477\pi\)
−0.108102 + 0.994140i \(0.534477\pi\)
\(60\) 0 0
\(61\) 0.948811 0.121483 0.0607414 0.998154i \(-0.480654\pi\)
0.0607414 + 0.998154i \(0.480654\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.9206 1.60260
\(66\) 0 0
\(67\) −0.539184 −0.0658718 −0.0329359 0.999457i \(-0.510486\pi\)
−0.0329359 + 0.999457i \(0.510486\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.86901 −0.459167 −0.229583 0.973289i \(-0.573736\pi\)
−0.229583 + 0.973289i \(0.573736\pi\)
\(72\) 0 0
\(73\) 2.58943 + 4.48502i 0.303070 + 0.524932i 0.976830 0.214018i \(-0.0686551\pi\)
−0.673760 + 0.738950i \(0.735322\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13.3221 5.13490i −1.51820 0.585176i
\(78\) 0 0
\(79\) −7.82899 −0.880830 −0.440415 0.897794i \(-0.645169\pi\)
−0.440415 + 0.897794i \(0.645169\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.79623 6.57527i −0.416691 0.721729i 0.578914 0.815389i \(-0.303477\pi\)
−0.995604 + 0.0936595i \(0.970143\pi\)
\(84\) 0 0
\(85\) 1.40375 2.43137i 0.152258 0.263719i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.73498 6.46917i 0.395907 0.685730i −0.597310 0.802011i \(-0.703764\pi\)
0.993216 + 0.116280i \(0.0370971\pi\)
\(90\) 0 0
\(91\) 9.36128 + 3.60823i 0.981328 + 0.378245i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.59199 −0.163335
\(96\) 0 0
\(97\) −3.22500 5.58587i −0.327450 0.567159i 0.654555 0.756014i \(-0.272856\pi\)
−0.982005 + 0.188855i \(0.939522\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.09973 + 14.0291i −0.805953 + 1.39595i 0.109692 + 0.993966i \(0.465014\pi\)
−0.915646 + 0.401987i \(0.868320\pi\)
\(102\) 0 0
\(103\) −7.84930 13.5954i −0.773414 1.33959i −0.935681 0.352846i \(-0.885214\pi\)
0.162267 0.986747i \(-0.448119\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.85024 4.93675i 0.275543 0.477254i −0.694729 0.719271i \(-0.744476\pi\)
0.970272 + 0.242017i \(0.0778091\pi\)
\(108\) 0 0
\(109\) −2.19196 3.79659i −0.209952 0.363648i 0.741747 0.670680i \(-0.233997\pi\)
−0.951699 + 0.307032i \(0.900664\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.96607 8.60149i 0.467169 0.809160i −0.532128 0.846664i \(-0.678607\pi\)
0.999296 + 0.0375041i \(0.0119407\pi\)
\(114\) 0 0
\(115\) −9.36852 + 16.2268i −0.873619 + 1.51315i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.69604 1.36957i 0.155476 0.125549i
\(120\) 0 0
\(121\) −9.06045 15.6932i −0.823677 1.42665i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.48623 −0.490703
\(126\) 0 0
\(127\) −16.1122 −1.42973 −0.714864 0.699263i \(-0.753512\pi\)
−0.714864 + 0.699263i \(0.753512\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.97039 12.0731i −0.609006 1.05483i −0.991405 0.130832i \(-0.958235\pi\)
0.382399 0.923997i \(-0.375098\pi\)
\(132\) 0 0
\(133\) −1.15344 0.444583i −0.100016 0.0385502i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.57598 + 9.65787i −0.476388 + 0.825128i −0.999634 0.0270537i \(-0.991388\pi\)
0.523246 + 0.852182i \(0.324721\pi\)
\(138\) 0 0
\(139\) −3.17737 + 5.50337i −0.269501 + 0.466790i −0.968733 0.248105i \(-0.920192\pi\)
0.699232 + 0.714895i \(0.253526\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.2314 + 17.7214i 0.855595 + 1.48193i
\(144\) 0 0
\(145\) 1.36408 2.36265i 0.113280 0.196207i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.76521 9.98564i −0.472304 0.818055i 0.527193 0.849745i \(-0.323244\pi\)
−0.999498 + 0.0316900i \(0.989911\pi\)
\(150\) 0 0
\(151\) −0.347317 + 0.601571i −0.0282643 + 0.0489551i −0.879812 0.475323i \(-0.842331\pi\)
0.851547 + 0.524278i \(0.175665\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 16.8789 + 29.2351i 1.35575 + 2.34822i
\(156\) 0 0
\(157\) −4.04845 −0.323102 −0.161551 0.986864i \(-0.551650\pi\)
−0.161551 + 0.986864i \(0.551650\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −11.3192 + 9.14041i −0.892081 + 0.720365i
\(162\) 0 0
\(163\) 5.05968 8.76363i 0.396305 0.686420i −0.596962 0.802270i \(-0.703626\pi\)
0.993267 + 0.115849i \(0.0369590\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.76377 15.1793i 0.678161 1.17461i −0.297374 0.954761i \(-0.596111\pi\)
0.975534 0.219847i \(-0.0705560\pi\)
\(168\) 0 0
\(169\) −0.689486 1.19422i −0.0530374 0.0918634i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.83515 0.595695 0.297848 0.954613i \(-0.403731\pi\)
0.297848 + 0.954613i \(0.403731\pi\)
\(174\) 0 0
\(175\) −16.3185 6.28982i −1.23356 0.475466i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.61920 + 8.00069i 0.345255 + 0.597999i 0.985400 0.170255i \(-0.0544591\pi\)
−0.640145 + 0.768254i \(0.721126\pi\)
\(180\) 0 0
\(181\) 9.45977 0.703139 0.351569 0.936162i \(-0.385648\pi\)
0.351569 + 0.936162i \(0.385648\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 29.5902 2.17552
\(186\) 0 0
\(187\) 4.44636 0.325150
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.0452967 0.00327756 0.00163878 0.999999i \(-0.499478\pi\)
0.00163878 + 0.999999i \(0.499478\pi\)
\(192\) 0 0
\(193\) −18.8198 −1.35468 −0.677340 0.735670i \(-0.736868\pi\)
−0.677340 + 0.735670i \(0.736868\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.3886 1.59512 0.797561 0.603239i \(-0.206123\pi\)
0.797561 + 0.603239i \(0.206123\pi\)
\(198\) 0 0
\(199\) 11.3709 + 19.6949i 0.806060 + 1.39614i 0.915573 + 0.402152i \(0.131738\pi\)
−0.109513 + 0.993985i \(0.534929\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.64811 1.33086i 0.115674 0.0934083i
\(204\) 0 0
\(205\) −12.5709 −0.877993
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.26065 2.18351i −0.0872011 0.151037i
\(210\) 0 0
\(211\) 2.95868 5.12458i 0.203684 0.352791i −0.746029 0.665914i \(-0.768042\pi\)
0.949713 + 0.313123i \(0.101375\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.8682 + 25.7525i −1.01400 + 1.75631i
\(216\) 0 0
\(217\) 4.06492 + 25.8952i 0.275945 + 1.75788i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.12440 −0.210170
\(222\) 0 0
\(223\) 1.20124 + 2.08062i 0.0804412 + 0.139328i 0.903440 0.428716i \(-0.141034\pi\)
−0.822998 + 0.568044i \(0.807700\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.48851 6.04227i 0.231540 0.401040i −0.726721 0.686933i \(-0.758957\pi\)
0.958262 + 0.285893i \(0.0922901\pi\)
\(228\) 0 0
\(229\) 9.60782 + 16.6412i 0.634903 + 1.09968i 0.986536 + 0.163546i \(0.0522931\pi\)
−0.351633 + 0.936138i \(0.614374\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.9002 + 22.3439i −0.845122 + 1.46379i 0.0403930 + 0.999184i \(0.487139\pi\)
−0.885515 + 0.464611i \(0.846194\pi\)
\(234\) 0 0
\(235\) −17.8872 30.9815i −1.16683 2.02101i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.65732 + 11.5308i −0.430626 + 0.745866i −0.996927 0.0783322i \(-0.975041\pi\)
0.566301 + 0.824198i \(0.308374\pi\)
\(240\) 0 0
\(241\) −0.928238 + 1.60776i −0.0597931 + 0.103565i −0.894372 0.447323i \(-0.852377\pi\)
0.834579 + 0.550888i \(0.185711\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −17.6812 16.0084i −1.12961 1.02274i
\(246\) 0 0
\(247\) 0.885843 + 1.53432i 0.0563648 + 0.0976267i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.6947 0.738165 0.369083 0.929397i \(-0.379672\pi\)
0.369083 + 0.929397i \(0.379672\pi\)
\(252\) 0 0
\(253\) −29.6746 −1.86563
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.46594 + 2.53908i 0.0914429 + 0.158384i 0.908118 0.418713i \(-0.137519\pi\)
−0.816676 + 0.577097i \(0.804185\pi\)
\(258\) 0 0
\(259\) 21.4388 + 8.26342i 1.33214 + 0.513464i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 14.1420 24.4946i 0.872032 1.51040i 0.0121407 0.999926i \(-0.496135\pi\)
0.859891 0.510477i \(-0.170531\pi\)
\(264\) 0 0
\(265\) −16.0766 + 27.8455i −0.987579 + 1.71054i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.79128 8.29874i −0.292129 0.505983i 0.682184 0.731181i \(-0.261030\pi\)
−0.974313 + 0.225198i \(0.927697\pi\)
\(270\) 0 0
\(271\) −9.14220 + 15.8348i −0.555349 + 0.961893i 0.442527 + 0.896755i \(0.354082\pi\)
−0.997876 + 0.0651381i \(0.979251\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −17.8353 30.8917i −1.07551 1.86284i
\(276\) 0 0
\(277\) −2.32776 + 4.03180i −0.139862 + 0.242248i −0.927444 0.373962i \(-0.877999\pi\)
0.787582 + 0.616209i \(0.211332\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.06669 + 15.7040i 0.540873 + 0.936820i 0.998854 + 0.0478580i \(0.0152395\pi\)
−0.457981 + 0.888962i \(0.651427\pi\)
\(282\) 0 0
\(283\) 16.6194 0.987920 0.493960 0.869485i \(-0.335549\pi\)
0.493960 + 0.869485i \(0.335549\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.10796 3.51059i −0.537626 0.207223i
\(288\) 0 0
\(289\) 8.16055 14.1345i 0.480032 0.831441i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.94284 + 3.36510i −0.113502 + 0.196591i −0.917180 0.398473i \(-0.869540\pi\)
0.803678 + 0.595064i \(0.202873\pi\)
\(294\) 0 0
\(295\) −2.82928 4.90046i −0.164727 0.285316i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 20.8520 1.20590
\(300\) 0 0
\(301\) −17.9641 + 14.5062i −1.03543 + 0.836123i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.61647 + 2.79981i 0.0925588 + 0.160317i
\(306\) 0 0
\(307\) 3.48452 0.198872 0.0994361 0.995044i \(-0.468296\pi\)
0.0994361 + 0.995044i \(0.468296\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.9855 −0.736338 −0.368169 0.929759i \(-0.620015\pi\)
−0.368169 + 0.929759i \(0.620015\pi\)
\(312\) 0 0
\(313\) 15.0439 0.850329 0.425164 0.905116i \(-0.360216\pi\)
0.425164 + 0.905116i \(0.360216\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.45839 0.475070 0.237535 0.971379i \(-0.423660\pi\)
0.237535 + 0.971379i \(0.423660\pi\)
\(318\) 0 0
\(319\) 4.32069 0.241912
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.384968 0.0214202
\(324\) 0 0
\(325\) 12.5326 + 21.7072i 0.695186 + 1.20410i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.30774 27.4421i −0.237494 1.51293i
\(330\) 0 0
\(331\) −10.0245 −0.550996 −0.275498 0.961302i \(-0.588843\pi\)
−0.275498 + 0.961302i \(0.588843\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.918597 1.59106i −0.0501883 0.0869287i
\(336\) 0 0
\(337\) −9.33242 + 16.1642i −0.508369 + 0.880522i 0.491584 + 0.870830i \(0.336418\pi\)
−0.999953 + 0.00969119i \(0.996915\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −26.7318 + 46.3009i −1.44761 + 2.50733i
\(342\) 0 0
\(343\) −8.33992 16.5362i −0.450313 0.892871i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.8048 0.848446 0.424223 0.905558i \(-0.360547\pi\)
0.424223 + 0.905558i \(0.360547\pi\)
\(348\) 0 0
\(349\) 4.51578 + 7.82156i 0.241724 + 0.418678i 0.961205 0.275833i \(-0.0889538\pi\)
−0.719481 + 0.694512i \(0.755620\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.23939 12.5390i 0.385314 0.667383i −0.606499 0.795084i \(-0.707427\pi\)
0.991813 + 0.127701i \(0.0407599\pi\)
\(354\) 0 0
\(355\) −6.59155 11.4169i −0.349843 0.605947i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.85517 13.6056i 0.414580 0.718074i −0.580804 0.814043i \(-0.697262\pi\)
0.995384 + 0.0959695i \(0.0305951\pi\)
\(360\) 0 0
\(361\) 9.39085 + 16.2654i 0.494255 + 0.856075i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.82312 + 15.2821i −0.461823 + 0.799902i
\(366\) 0 0
\(367\) −9.42947 + 16.3323i −0.492214 + 0.852540i −0.999960 0.00896710i \(-0.997146\pi\)
0.507746 + 0.861507i \(0.330479\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −19.4241 + 15.6852i −1.00845 + 0.814334i
\(372\) 0 0
\(373\) 16.8568 + 29.1969i 0.872814 + 1.51176i 0.859073 + 0.511853i \(0.171041\pi\)
0.0137417 + 0.999906i \(0.495626\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.03609 −0.156367
\(378\) 0 0
\(379\) 33.7263 1.73241 0.866203 0.499693i \(-0.166554\pi\)
0.866203 + 0.499693i \(0.166554\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.16201 + 15.8691i 0.468157 + 0.810871i 0.999338 0.0363870i \(-0.0115849\pi\)
−0.531181 + 0.847258i \(0.678252\pi\)
\(384\) 0 0
\(385\) −7.54427 48.0600i −0.384491 2.44936i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.13744 3.70216i 0.108373 0.187707i −0.806739 0.590909i \(-0.798769\pi\)
0.915111 + 0.403202i \(0.132103\pi\)
\(390\) 0 0
\(391\) 2.26545 3.92388i 0.114569 0.198439i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13.3381 23.1023i −0.671112 1.16240i
\(396\) 0 0
\(397\) 17.9312 31.0577i 0.899939 1.55874i 0.0723687 0.997378i \(-0.476944\pi\)
0.827570 0.561362i \(-0.189723\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.7007 20.2663i −0.584307 1.01205i −0.994961 0.100259i \(-0.968033\pi\)
0.410654 0.911791i \(-0.365300\pi\)
\(402\) 0 0
\(403\) 18.7841 32.5350i 0.935702 1.62068i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 23.4316 + 40.5848i 1.16146 + 2.01171i
\(408\) 0 0
\(409\) 34.8032 1.72091 0.860453 0.509530i \(-0.170181\pi\)
0.860453 + 0.509530i \(0.170181\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.681372 4.34062i −0.0335281 0.213588i
\(414\) 0 0
\(415\) 12.9351 22.4043i 0.634961 1.09978i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.90894 + 5.03843i −0.142111 + 0.246143i −0.928291 0.371854i \(-0.878722\pi\)
0.786180 + 0.617997i \(0.212056\pi\)
\(420\) 0 0
\(421\) −17.7765 30.7898i −0.866375 1.50061i −0.865676 0.500605i \(-0.833111\pi\)
−0.000699237 1.00000i \(-0.500223\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.44642 0.264190
\(426\) 0 0
\(427\) 0.389292 + 2.47995i 0.0188392 + 0.120013i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.48374 + 4.30196i 0.119637 + 0.207218i 0.919624 0.392800i \(-0.128493\pi\)
−0.799987 + 0.600018i \(0.795160\pi\)
\(432\) 0 0
\(433\) 22.9062 1.10080 0.550401 0.834900i \(-0.314475\pi\)
0.550401 + 0.834900i \(0.314475\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.56925 −0.122904
\(438\) 0 0
\(439\) 8.05894 0.384632 0.192316 0.981333i \(-0.438400\pi\)
0.192316 + 0.981333i \(0.438400\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.77766 0.179482 0.0897410 0.995965i \(-0.471396\pi\)
0.0897410 + 0.995965i \(0.471396\pi\)
\(444\) 0 0
\(445\) 25.4528 1.20658
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −33.5069 −1.58129 −0.790644 0.612276i \(-0.790254\pi\)
−0.790644 + 0.612276i \(0.790254\pi\)
\(450\) 0 0
\(451\) −9.95457 17.2418i −0.468742 0.811885i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.30125 + 33.7711i 0.248527 + 1.58321i
\(456\) 0 0
\(457\) 0.739506 0.0345926 0.0172963 0.999850i \(-0.494494\pi\)
0.0172963 + 0.999850i \(0.494494\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.30465 + 5.72383i 0.153913 + 0.266585i 0.932663 0.360750i \(-0.117479\pi\)
−0.778750 + 0.627335i \(0.784146\pi\)
\(462\) 0 0
\(463\) −5.96606 + 10.3335i −0.277266 + 0.480239i −0.970704 0.240277i \(-0.922762\pi\)
0.693438 + 0.720516i \(0.256095\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.11184 8.85396i 0.236548 0.409713i −0.723174 0.690666i \(-0.757317\pi\)
0.959721 + 0.280954i \(0.0906507\pi\)
\(468\) 0 0
\(469\) −0.221225 1.40929i −0.0102152 0.0650749i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −47.0948 −2.16542
\(474\) 0 0
\(475\) −1.54419 2.67462i −0.0708524 0.122720i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.01896 + 1.76488i −0.0465573 + 0.0806395i −0.888365 0.459138i \(-0.848158\pi\)
0.841808 + 0.539778i \(0.181492\pi\)
\(480\) 0 0
\(481\) −16.4651 28.5184i −0.750743 1.30033i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.9888 19.0331i 0.498974 0.864248i
\(486\) 0 0
\(487\) 17.5958 + 30.4767i 0.797340 + 1.38103i 0.921343 + 0.388751i \(0.127093\pi\)
−0.124003 + 0.992282i \(0.539573\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.5708 30.4335i 0.792958 1.37344i −0.131170 0.991360i \(-0.541873\pi\)
0.924128 0.382083i \(-0.124793\pi\)
\(492\) 0 0
\(493\) −0.329855 + 0.571326i −0.0148559 + 0.0257312i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.58744 10.1126i −0.0712062 0.453612i
\(498\) 0 0
\(499\) −2.32633 4.02932i −0.104141 0.180377i 0.809246 0.587470i \(-0.199876\pi\)
−0.913387 + 0.407093i \(0.866543\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0660 −0.537997 −0.268999 0.963141i \(-0.586693\pi\)
−0.268999 + 0.963141i \(0.586693\pi\)
\(504\) 0 0
\(505\) −55.1974 −2.45625
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.1739 + 19.3537i 0.495273 + 0.857838i 0.999985 0.00544958i \(-0.00173466\pi\)
−0.504712 + 0.863288i \(0.668401\pi\)
\(510\) 0 0
\(511\) −10.6603 + 8.60829i −0.471583 + 0.380808i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 26.7454 46.3244i 1.17854 2.04130i
\(516\) 0 0
\(517\) 28.3287 49.0667i 1.24589 2.15795i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.854260 1.47962i −0.0374258 0.0648234i 0.846706 0.532061i \(-0.178582\pi\)
−0.884132 + 0.467238i \(0.845249\pi\)
\(522\) 0 0
\(523\) −10.6036 + 18.3659i −0.463662 + 0.803087i −0.999140 0.0414627i \(-0.986798\pi\)
0.535478 + 0.844549i \(0.320132\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.08158 7.06951i −0.177796 0.307952i
\(528\) 0 0
\(529\) −3.61945 + 6.26907i −0.157367 + 0.272568i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.99494 + 12.1156i 0.302984 + 0.524784i
\(534\) 0 0
\(535\) 19.4236 0.839754
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.95532 36.9275i 0.342660 1.59058i
\(540\) 0 0
\(541\) 4.79443 8.30419i 0.206129 0.357025i −0.744363 0.667775i \(-0.767247\pi\)
0.950492 + 0.310750i \(0.100580\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.46882 12.9364i 0.319929 0.554133i
\(546\) 0 0
\(547\) −5.65927 9.80214i −0.241973 0.419109i 0.719303 0.694696i \(-0.244461\pi\)
−0.961276 + 0.275587i \(0.911128\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.374088 0.0159367
\(552\) 0 0
\(553\) −3.21220 20.4630i −0.136596 0.870174i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.68102 2.91162i −0.0712272 0.123369i 0.828212 0.560415i \(-0.189358\pi\)
−0.899439 + 0.437045i \(0.856025\pi\)
\(558\) 0 0
\(559\) 33.0929 1.39968
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.0914 0.804606 0.402303 0.915506i \(-0.368210\pi\)
0.402303 + 0.915506i \(0.368210\pi\)
\(564\) 0 0
\(565\) 33.8424 1.42376
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.62726 −0.110140 −0.0550702 0.998482i \(-0.517538\pi\)
−0.0550702 + 0.998482i \(0.517538\pi\)
\(570\) 0 0
\(571\) −9.98226 −0.417745 −0.208872 0.977943i \(-0.566979\pi\)
−0.208872 + 0.977943i \(0.566979\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −36.3489 −1.51586
\(576\) 0 0
\(577\) 6.05761 + 10.4921i 0.252182 + 0.436791i 0.964126 0.265444i \(-0.0855187\pi\)
−0.711945 + 0.702236i \(0.752185\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 15.6285 12.6202i 0.648379 0.523573i
\(582\) 0 0
\(583\) −50.9224 −2.10899
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.1857 26.3025i −0.626782 1.08562i −0.988193 0.153212i \(-0.951038\pi\)
0.361411 0.932407i \(-0.382295\pi\)
\(588\) 0 0
\(589\) −2.31446 + 4.00875i −0.0953655 + 0.165178i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 20.5788 35.6434i 0.845068 1.46370i −0.0404940 0.999180i \(-0.512893\pi\)
0.885562 0.464521i \(-0.153774\pi\)
\(594\) 0 0
\(595\) 6.93093 + 2.67147i 0.284141 + 0.109520i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.11041 −0.331382 −0.165691 0.986178i \(-0.552986\pi\)
−0.165691 + 0.986178i \(0.552986\pi\)
\(600\) 0 0
\(601\) 15.8320 + 27.4218i 0.645801 + 1.11856i 0.984116 + 0.177527i \(0.0568098\pi\)
−0.338315 + 0.941033i \(0.609857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 30.8722 53.4723i 1.25513 2.17396i
\(606\) 0 0
\(607\) 11.5131 + 19.9412i 0.467300 + 0.809388i 0.999302 0.0373552i \(-0.0118933\pi\)
−0.532002 + 0.846743i \(0.678560\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −19.9062 + 34.4785i −0.805317 + 1.39485i
\(612\) 0 0
\(613\) 11.4750 + 19.8752i 0.463470 + 0.802753i 0.999131 0.0416796i \(-0.0132709\pi\)
−0.535661 + 0.844433i \(0.679938\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.1183 + 19.2574i −0.447605 + 0.775274i −0.998230 0.0594788i \(-0.981056\pi\)
0.550625 + 0.834753i \(0.314389\pi\)
\(618\) 0 0
\(619\) 2.75302 4.76836i 0.110653 0.191657i −0.805381 0.592758i \(-0.798039\pi\)
0.916034 + 0.401101i \(0.131372\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.4412 + 7.10800i 0.738831 + 0.284776i
\(624\) 0 0
\(625\) 7.17850 + 12.4335i 0.287140 + 0.497341i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.15538 −0.285303
\(630\) 0 0
\(631\) −32.9276 −1.31083 −0.655413 0.755271i \(-0.727505\pi\)
−0.655413 + 0.755271i \(0.727505\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −27.4501 47.5449i −1.08932 1.88676i
\(636\) 0 0
\(637\) −5.59009 + 25.9484i −0.221488 + 1.02811i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.945880 + 1.63831i −0.0373600 + 0.0647095i −0.884101 0.467296i \(-0.845228\pi\)
0.846741 + 0.532006i \(0.178562\pi\)
\(642\) 0 0
\(643\) 22.8742 39.6193i 0.902070 1.56243i 0.0772675 0.997010i \(-0.475380\pi\)
0.824803 0.565421i \(-0.191286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.98067 15.5550i −0.353066 0.611529i 0.633719 0.773564i \(-0.281528\pi\)
−0.986785 + 0.162035i \(0.948194\pi\)
\(648\) 0 0
\(649\) 4.48085 7.76106i 0.175889 0.304648i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.0741 19.1809i −0.433363 0.750607i 0.563797 0.825913i \(-0.309340\pi\)
−0.997160 + 0.0753063i \(0.976007\pi\)
\(654\) 0 0
\(655\) 23.7506 41.1373i 0.928015 1.60737i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.39543 + 9.34515i 0.210176 + 0.364035i 0.951769 0.306814i \(-0.0992630\pi\)
−0.741594 + 0.670850i \(0.765930\pi\)
\(660\) 0 0
\(661\) −5.13907 −0.199887 −0.0999434 0.994993i \(-0.531866\pi\)
−0.0999434 + 0.994993i \(0.531866\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.653187 4.16106i −0.0253295 0.161359i
\(666\) 0 0
\(667\) 2.20142 3.81298i 0.0852395 0.147639i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.56007 + 4.43417i −0.0988304 + 0.171179i
\(672\) 0 0
\(673\) 10.9290 + 18.9295i 0.421281 + 0.729680i 0.996065 0.0886254i \(-0.0282474\pi\)
−0.574784 + 0.818305i \(0.694914\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.7296 0.450807 0.225403 0.974266i \(-0.427630\pi\)
0.225403 + 0.974266i \(0.427630\pi\)
\(678\) 0 0
\(679\) 13.2768 10.7212i 0.509518 0.411442i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.260358 + 0.450954i 0.00996234 + 0.0172553i 0.870964 0.491348i \(-0.163496\pi\)
−0.861001 + 0.508603i \(0.830162\pi\)
\(684\) 0 0
\(685\) −37.9987 −1.45186
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 35.7825 1.36320
\(690\) 0 0
\(691\) 46.1912 1.75720 0.878599 0.477561i \(-0.158479\pi\)
0.878599 + 0.477561i \(0.158479\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −21.6529 −0.821342
\(696\) 0 0
\(697\) 3.03985 0.115143
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 32.7166 1.23569 0.617844 0.786301i \(-0.288006\pi\)
0.617844 + 0.786301i \(0.288006\pi\)
\(702\) 0 0
\(703\) 2.02872 + 3.51385i 0.0765148 + 0.132527i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −39.9919 15.4145i −1.50405 0.579723i
\(708\) 0 0
\(709\) −33.4551 −1.25643 −0.628216 0.778039i \(-0.716215\pi\)
−0.628216 + 0.778039i \(0.716215\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 27.2401 + 47.1813i 1.02015 + 1.76695i
\(714\) 0 0
\(715\) −34.8622 + 60.3831i −1.30377 + 2.25820i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.42685 + 16.3278i −0.351562 + 0.608924i −0.986523 0.163621i \(-0.947683\pi\)
0.634961 + 0.772544i \(0.281016\pi\)
\(720\) 0 0
\(721\) 32.3143 26.0942i 1.20345 0.971798i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.29248 0.196558
\(726\) 0 0
\(727\) −19.3107 33.4471i −0.716194 1.24048i −0.962497 0.271291i \(-0.912549\pi\)
0.246303 0.969193i \(-0.420784\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.59537 6.22736i 0.132979 0.230327i
\(732\) 0 0
\(733\) 9.35591 + 16.2049i 0.345569 + 0.598542i 0.985457 0.169926i \(-0.0543527\pi\)
−0.639888 + 0.768468i \(0.721019\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.45482 2.51982i 0.0535890 0.0928189i
\(738\) 0 0
\(739\) 7.15949 + 12.4006i 0.263366 + 0.456163i 0.967134 0.254266i \(-0.0818340\pi\)
−0.703768 + 0.710430i \(0.748501\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.2068 + 24.6069i −0.521197 + 0.902740i 0.478499 + 0.878088i \(0.341181\pi\)
−0.999696 + 0.0246519i \(0.992152\pi\)
\(744\) 0 0
\(745\) 19.6442 34.0247i 0.719706 1.24657i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14.0729 + 5.42426i 0.514211 + 0.198198i
\(750\) 0 0
\(751\) 15.7209 + 27.2294i 0.573663 + 0.993614i 0.996185 + 0.0872612i \(0.0278115\pi\)
−0.422522 + 0.906353i \(0.638855\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.36687 −0.0861392
\(756\) 0 0
\(757\) 0.405916 0.0147533 0.00737663 0.999973i \(-0.497652\pi\)
0.00737663 + 0.999973i \(0.497652\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.65688 + 4.60184i 0.0963117 + 0.166817i 0.910155 0.414267i \(-0.135962\pi\)
−0.813844 + 0.581084i \(0.802629\pi\)
\(762\) 0 0
\(763\) 9.02397 7.28696i 0.326690 0.263806i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.14863 + 5.45359i −0.113691 + 0.196918i
\(768\) 0 0
\(769\) 11.9430 20.6858i 0.430674 0.745949i −0.566258 0.824228i \(-0.691609\pi\)
0.996931 + 0.0782793i \(0.0249426\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.8525 22.2613i −0.462274 0.800682i 0.536800 0.843710i \(-0.319633\pi\)
−0.999074 + 0.0430274i \(0.986300\pi\)
\(774\) 0 0
\(775\) −32.7442 + 56.7147i −1.17621 + 2.03725i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.861872 1.49281i −0.0308798 0.0534853i
\(780\) 0 0
\(781\) 10.4393 18.0814i 0.373548 0.647004i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.89727 11.9464i −0.246174 0.426386i
\(786\) 0 0
\(787\) 16.1109 0.574292 0.287146 0.957887i \(-0.407293\pi\)
0.287146 + 0.957887i \(0.407293\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.5196 + 9.45089i 0.871818 + 0.336035i
\(792\) 0 0
\(793\) 1.79893 3.11583i 0.0638818 0.110646i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.556852 + 0.964495i −0.0197247 + 0.0341642i −0.875719 0.482821i \(-0.839612\pi\)
0.855995 + 0.516985i \(0.172946\pi\)