Properties

Label 1840.2.e.h.369.6
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + 128 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 920)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.6
Root \(0.303680 + 0.303680i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.h.369.11

$q$-expansion

\(f(q)\) \(=\) \(q-0.540724i q^{3} +(2.21535 - 0.303680i) q^{5} -1.15693i q^{7} +2.70762 q^{9} +O(q^{10})\) \(q-0.540724i q^{3} +(2.21535 - 0.303680i) q^{5} -1.15693i q^{7} +2.70762 q^{9} -2.10688 q^{11} -5.59296i q^{13} +(-0.164207 - 1.19789i) q^{15} +0.244199i q^{17} +1.45043 q^{19} -0.625580 q^{21} -1.00000i q^{23} +(4.81556 - 1.34552i) q^{25} -3.08625i q^{27} -4.29653 q^{29} -3.19717 q^{31} +1.13924i q^{33} +(-0.351337 - 2.56301i) q^{35} -0.807940i q^{37} -3.02425 q^{39} -1.59546 q^{41} -5.98219i q^{43} +(5.99832 - 0.822250i) q^{45} +0.624940i q^{47} +5.66151 q^{49} +0.132044 q^{51} +0.536087i q^{53} +(-4.66747 + 0.639817i) q^{55} -0.784283i q^{57} -1.03806 q^{59} +3.77846 q^{61} -3.13253i q^{63} +(-1.69847 - 12.3904i) q^{65} +4.61571i q^{67} -0.540724 q^{69} -6.77489 q^{71} +8.87290i q^{73} +(-0.727553 - 2.60389i) q^{75} +2.43751i q^{77} +14.8521 q^{79} +6.45405 q^{81} +6.11896i q^{83} +(0.0741583 + 0.540985i) q^{85} +2.32323i q^{87} -5.79942 q^{89} -6.47066 q^{91} +1.72879i q^{93} +(3.21321 - 0.440467i) q^{95} -2.38582i q^{97} -5.70462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 2q^{5} - 22q^{9} + O(q^{10}) \) \( 16q - 2q^{5} - 22q^{9} - 14q^{11} - 6q^{15} + 22q^{19} + 12q^{25} - 44q^{29} - 18q^{31} - 20q^{35} + 14q^{41} + 14q^{45} - 78q^{49} + 38q^{51} - 30q^{55} + 64q^{59} + 34q^{61} + 6q^{65} + 6q^{69} - 30q^{71} - 56q^{75} - 4q^{79} + 48q^{81} + 52q^{85} - 92q^{89} + 70q^{91} - 38q^{95} + 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 0.540724i 0.312187i −0.987742 0.156094i \(-0.950110\pi\)
0.987742 0.156094i \(-0.0498901\pi\)
\(4\) 0 0
\(5\) 2.21535 0.303680i 0.990735 0.135810i
\(6\) 0 0
\(7\) 1.15693i 0.437279i −0.975806 0.218639i \(-0.929838\pi\)
0.975806 0.218639i \(-0.0701618\pi\)
\(8\) 0 0
\(9\) 2.70762 0.902539
\(10\) 0 0
\(11\) −2.10688 −0.635247 −0.317624 0.948217i \(-0.602885\pi\)
−0.317624 + 0.948217i \(0.602885\pi\)
\(12\) 0 0
\(13\) 5.59296i 1.55121i −0.631220 0.775604i \(-0.717446\pi\)
0.631220 0.775604i \(-0.282554\pi\)
\(14\) 0 0
\(15\) −0.164207 1.19789i −0.0423981 0.309295i
\(16\) 0 0
\(17\) 0.244199i 0.0592268i 0.999561 + 0.0296134i \(0.00942762\pi\)
−0.999561 + 0.0296134i \(0.990572\pi\)
\(18\) 0 0
\(19\) 1.45043 0.332752 0.166376 0.986062i \(-0.446794\pi\)
0.166376 + 0.986062i \(0.446794\pi\)
\(20\) 0 0
\(21\) −0.625580 −0.136513
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 4.81556 1.34552i 0.963111 0.269103i
\(26\) 0 0
\(27\) 3.08625i 0.593948i
\(28\) 0 0
\(29\) −4.29653 −0.797845 −0.398922 0.916985i \(-0.630616\pi\)
−0.398922 + 0.916985i \(0.630616\pi\)
\(30\) 0 0
\(31\) −3.19717 −0.574229 −0.287114 0.957896i \(-0.592696\pi\)
−0.287114 + 0.957896i \(0.592696\pi\)
\(32\) 0 0
\(33\) 1.13924i 0.198316i
\(34\) 0 0
\(35\) −0.351337 2.56301i −0.0593868 0.433227i
\(36\) 0 0
\(37\) 0.807940i 0.132824i −0.997792 0.0664122i \(-0.978845\pi\)
0.997792 0.0664122i \(-0.0211552\pi\)
\(38\) 0 0
\(39\) −3.02425 −0.484267
\(40\) 0 0
\(41\) −1.59546 −0.249169 −0.124585 0.992209i \(-0.539760\pi\)
−0.124585 + 0.992209i \(0.539760\pi\)
\(42\) 0 0
\(43\) 5.98219i 0.912275i −0.889909 0.456138i \(-0.849232\pi\)
0.889909 0.456138i \(-0.150768\pi\)
\(44\) 0 0
\(45\) 5.99832 0.822250i 0.894177 0.122574i
\(46\) 0 0
\(47\) 0.624940i 0.0911569i 0.998961 + 0.0455784i \(0.0145131\pi\)
−0.998961 + 0.0455784i \(0.985487\pi\)
\(48\) 0 0
\(49\) 5.66151 0.808787
\(50\) 0 0
\(51\) 0.132044 0.0184899
\(52\) 0 0
\(53\) 0.536087i 0.0736372i 0.999322 + 0.0368186i \(0.0117224\pi\)
−0.999322 + 0.0368186i \(0.988278\pi\)
\(54\) 0 0
\(55\) −4.66747 + 0.639817i −0.629362 + 0.0862729i
\(56\) 0 0
\(57\) 0.784283i 0.103881i
\(58\) 0 0
\(59\) −1.03806 −0.135144 −0.0675721 0.997714i \(-0.521525\pi\)
−0.0675721 + 0.997714i \(0.521525\pi\)
\(60\) 0 0
\(61\) 3.77846 0.483783 0.241891 0.970303i \(-0.422232\pi\)
0.241891 + 0.970303i \(0.422232\pi\)
\(62\) 0 0
\(63\) 3.13253i 0.394661i
\(64\) 0 0
\(65\) −1.69847 12.3904i −0.210669 1.53684i
\(66\) 0 0
\(67\) 4.61571i 0.563899i 0.959429 + 0.281949i \(0.0909811\pi\)
−0.959429 + 0.281949i \(0.909019\pi\)
\(68\) 0 0
\(69\) −0.540724 −0.0650955
\(70\) 0 0
\(71\) −6.77489 −0.804032 −0.402016 0.915633i \(-0.631690\pi\)
−0.402016 + 0.915633i \(0.631690\pi\)
\(72\) 0 0
\(73\) 8.87290i 1.03849i 0.854624 + 0.519247i \(0.173788\pi\)
−0.854624 + 0.519247i \(0.826212\pi\)
\(74\) 0 0
\(75\) −0.727553 2.60389i −0.0840106 0.300671i
\(76\) 0 0
\(77\) 2.43751i 0.277780i
\(78\) 0 0
\(79\) 14.8521 1.67099 0.835494 0.549500i \(-0.185182\pi\)
0.835494 + 0.549500i \(0.185182\pi\)
\(80\) 0 0
\(81\) 6.45405 0.717116
\(82\) 0 0
\(83\) 6.11896i 0.671644i 0.941926 + 0.335822i \(0.109014\pi\)
−0.941926 + 0.335822i \(0.890986\pi\)
\(84\) 0 0
\(85\) 0.0741583 + 0.540985i 0.00804360 + 0.0586781i
\(86\) 0 0
\(87\) 2.32323i 0.249077i
\(88\) 0 0
\(89\) −5.79942 −0.614737 −0.307369 0.951591i \(-0.599448\pi\)
−0.307369 + 0.951591i \(0.599448\pi\)
\(90\) 0 0
\(91\) −6.47066 −0.678310
\(92\) 0 0
\(93\) 1.72879i 0.179267i
\(94\) 0 0
\(95\) 3.21321 0.440467i 0.329669 0.0451910i
\(96\) 0 0
\(97\) 2.38582i 0.242244i −0.992638 0.121122i \(-0.961351\pi\)
0.992638 0.121122i \(-0.0386492\pi\)
\(98\) 0 0
\(99\) −5.70462 −0.573336
\(100\) 0 0
\(101\) 8.33379 0.829243 0.414621 0.909994i \(-0.363914\pi\)
0.414621 + 0.909994i \(0.363914\pi\)
\(102\) 0 0
\(103\) 12.4250i 1.22427i −0.790754 0.612135i \(-0.790311\pi\)
0.790754 0.612135i \(-0.209689\pi\)
\(104\) 0 0
\(105\) −1.38588 + 0.189976i −0.135248 + 0.0185398i
\(106\) 0 0
\(107\) 15.5804i 1.50621i −0.657899 0.753106i \(-0.728555\pi\)
0.657899 0.753106i \(-0.271445\pi\)
\(108\) 0 0
\(109\) −9.71396 −0.930428 −0.465214 0.885198i \(-0.654023\pi\)
−0.465214 + 0.885198i \(0.654023\pi\)
\(110\) 0 0
\(111\) −0.436872 −0.0414661
\(112\) 0 0
\(113\) 2.69724i 0.253735i 0.991920 + 0.126867i \(0.0404922\pi\)
−0.991920 + 0.126867i \(0.959508\pi\)
\(114\) 0 0
\(115\) −0.303680 2.21535i −0.0283183 0.206583i
\(116\) 0 0
\(117\) 15.1436i 1.40003i
\(118\) 0 0
\(119\) 0.282521 0.0258986
\(120\) 0 0
\(121\) −6.56107 −0.596461
\(122\) 0 0
\(123\) 0.862705i 0.0777875i
\(124\) 0 0
\(125\) 10.2595 4.44318i 0.917641 0.397410i
\(126\) 0 0
\(127\) 4.40424i 0.390813i −0.980722 0.195406i \(-0.937397\pi\)
0.980722 0.195406i \(-0.0626026\pi\)
\(128\) 0 0
\(129\) −3.23471 −0.284801
\(130\) 0 0
\(131\) −1.65815 −0.144873 −0.0724367 0.997373i \(-0.523078\pi\)
−0.0724367 + 0.997373i \(0.523078\pi\)
\(132\) 0 0
\(133\) 1.67805i 0.145505i
\(134\) 0 0
\(135\) −0.937232 6.83712i −0.0806641 0.588445i
\(136\) 0 0
\(137\) 2.70894i 0.231440i −0.993282 0.115720i \(-0.963082\pi\)
0.993282 0.115720i \(-0.0369176\pi\)
\(138\) 0 0
\(139\) 8.99503 0.762949 0.381474 0.924379i \(-0.375416\pi\)
0.381474 + 0.924379i \(0.375416\pi\)
\(140\) 0 0
\(141\) 0.337920 0.0284580
\(142\) 0 0
\(143\) 11.7837i 0.985400i
\(144\) 0 0
\(145\) −9.51831 + 1.30477i −0.790453 + 0.108355i
\(146\) 0 0
\(147\) 3.06132i 0.252493i
\(148\) 0 0
\(149\) −9.54172 −0.781688 −0.390844 0.920457i \(-0.627817\pi\)
−0.390844 + 0.920457i \(0.627817\pi\)
\(150\) 0 0
\(151\) 12.1471 0.988514 0.494257 0.869316i \(-0.335440\pi\)
0.494257 + 0.869316i \(0.335440\pi\)
\(152\) 0 0
\(153\) 0.661196i 0.0534545i
\(154\) 0 0
\(155\) −7.08285 + 0.970918i −0.568909 + 0.0779860i
\(156\) 0 0
\(157\) 19.1756i 1.53038i −0.643806 0.765189i \(-0.722646\pi\)
0.643806 0.765189i \(-0.277354\pi\)
\(158\) 0 0
\(159\) 0.289875 0.0229886
\(160\) 0 0
\(161\) −1.15693 −0.0911789
\(162\) 0 0
\(163\) 17.3397i 1.35815i 0.734071 + 0.679073i \(0.237618\pi\)
−0.734071 + 0.679073i \(0.762382\pi\)
\(164\) 0 0
\(165\) 0.345965 + 2.52381i 0.0269333 + 0.196479i
\(166\) 0 0
\(167\) 0.582642i 0.0450862i 0.999746 + 0.0225431i \(0.00717629\pi\)
−0.999746 + 0.0225431i \(0.992824\pi\)
\(168\) 0 0
\(169\) −18.2812 −1.40624
\(170\) 0 0
\(171\) 3.92721 0.300321
\(172\) 0 0
\(173\) 12.0591i 0.916840i −0.888736 0.458420i \(-0.848416\pi\)
0.888736 0.458420i \(-0.151584\pi\)
\(174\) 0 0
\(175\) −1.55667 5.57126i −0.117673 0.421148i
\(176\) 0 0
\(177\) 0.561305i 0.0421903i
\(178\) 0 0
\(179\) 18.0142 1.34645 0.673223 0.739439i \(-0.264909\pi\)
0.673223 + 0.739439i \(0.264909\pi\)
\(180\) 0 0
\(181\) 3.33577 0.247946 0.123973 0.992286i \(-0.460436\pi\)
0.123973 + 0.992286i \(0.460436\pi\)
\(182\) 0 0
\(183\) 2.04311i 0.151031i
\(184\) 0 0
\(185\) −0.245355 1.78987i −0.0180389 0.131594i
\(186\) 0 0
\(187\) 0.514496i 0.0376237i
\(188\) 0 0
\(189\) −3.57057 −0.259721
\(190\) 0 0
\(191\) 2.90013 0.209846 0.104923 0.994480i \(-0.466540\pi\)
0.104923 + 0.994480i \(0.466540\pi\)
\(192\) 0 0
\(193\) 11.6127i 0.835898i 0.908470 + 0.417949i \(0.137251\pi\)
−0.908470 + 0.417949i \(0.862749\pi\)
\(194\) 0 0
\(195\) −6.69977 + 0.918404i −0.479780 + 0.0657683i
\(196\) 0 0
\(197\) 0.156603i 0.0111575i 0.999984 + 0.00557876i \(0.00177579\pi\)
−0.999984 + 0.00557876i \(0.998224\pi\)
\(198\) 0 0
\(199\) 23.3474 1.65506 0.827528 0.561425i \(-0.189747\pi\)
0.827528 + 0.561425i \(0.189747\pi\)
\(200\) 0 0
\(201\) 2.49583 0.176042
\(202\) 0 0
\(203\) 4.97078i 0.348880i
\(204\) 0 0
\(205\) −3.53451 + 0.484511i −0.246861 + 0.0338397i
\(206\) 0 0
\(207\) 2.70762i 0.188192i
\(208\) 0 0
\(209\) −3.05588 −0.211380
\(210\) 0 0
\(211\) 21.2620 1.46374 0.731870 0.681445i \(-0.238648\pi\)
0.731870 + 0.681445i \(0.238648\pi\)
\(212\) 0 0
\(213\) 3.66335i 0.251008i
\(214\) 0 0
\(215\) −1.81667 13.2526i −0.123896 0.903823i
\(216\) 0 0
\(217\) 3.69890i 0.251098i
\(218\) 0 0
\(219\) 4.79779 0.324205
\(220\) 0 0
\(221\) 1.36579 0.0918731
\(222\) 0 0
\(223\) 28.7628i 1.92610i 0.269328 + 0.963049i \(0.413199\pi\)
−0.269328 + 0.963049i \(0.586801\pi\)
\(224\) 0 0
\(225\) 13.0387 3.64315i 0.869246 0.242876i
\(226\) 0 0
\(227\) 6.08990i 0.404201i −0.979365 0.202100i \(-0.935223\pi\)
0.979365 0.202100i \(-0.0647768\pi\)
\(228\) 0 0
\(229\) −19.9294 −1.31697 −0.658486 0.752593i \(-0.728803\pi\)
−0.658486 + 0.752593i \(0.728803\pi\)
\(230\) 0 0
\(231\) 1.31802 0.0867194
\(232\) 0 0
\(233\) 9.63207i 0.631018i 0.948923 + 0.315509i \(0.102175\pi\)
−0.948923 + 0.315509i \(0.897825\pi\)
\(234\) 0 0
\(235\) 0.189782 + 1.38446i 0.0123800 + 0.0903123i
\(236\) 0 0
\(237\) 8.03087i 0.521661i
\(238\) 0 0
\(239\) 13.2583 0.857607 0.428803 0.903398i \(-0.358935\pi\)
0.428803 + 0.903398i \(0.358935\pi\)
\(240\) 0 0
\(241\) −14.4250 −0.929195 −0.464597 0.885522i \(-0.653801\pi\)
−0.464597 + 0.885522i \(0.653801\pi\)
\(242\) 0 0
\(243\) 12.7486i 0.817823i
\(244\) 0 0
\(245\) 12.5422 1.71929i 0.801294 0.109841i
\(246\) 0 0
\(247\) 8.11220i 0.516167i
\(248\) 0 0
\(249\) 3.30867 0.209678
\(250\) 0 0
\(251\) −18.6789 −1.17900 −0.589500 0.807768i \(-0.700675\pi\)
−0.589500 + 0.807768i \(0.700675\pi\)
\(252\) 0 0
\(253\) 2.10688i 0.132458i
\(254\) 0 0
\(255\) 0.292524 0.0400992i 0.0183185 0.00251111i
\(256\) 0 0
\(257\) 25.5035i 1.59087i 0.606042 + 0.795433i \(0.292756\pi\)
−0.606042 + 0.795433i \(0.707244\pi\)
\(258\) 0 0
\(259\) −0.934730 −0.0580813
\(260\) 0 0
\(261\) −11.6333 −0.720086
\(262\) 0 0
\(263\) 18.4521i 1.13780i 0.822405 + 0.568902i \(0.192632\pi\)
−0.822405 + 0.568902i \(0.807368\pi\)
\(264\) 0 0
\(265\) 0.162799 + 1.18762i 0.0100007 + 0.0729549i
\(266\) 0 0
\(267\) 3.13589i 0.191913i
\(268\) 0 0
\(269\) −2.02723 −0.123602 −0.0618012 0.998088i \(-0.519684\pi\)
−0.0618012 + 0.998088i \(0.519684\pi\)
\(270\) 0 0
\(271\) −26.7402 −1.62435 −0.812175 0.583414i \(-0.801716\pi\)
−0.812175 + 0.583414i \(0.801716\pi\)
\(272\) 0 0
\(273\) 3.49884i 0.211760i
\(274\) 0 0
\(275\) −10.1458 + 2.83484i −0.611814 + 0.170947i
\(276\) 0 0
\(277\) 18.8601i 1.13320i −0.823995 0.566598i \(-0.808259\pi\)
0.823995 0.566598i \(-0.191741\pi\)
\(278\) 0 0
\(279\) −8.65672 −0.518264
\(280\) 0 0
\(281\) 6.09240 0.363442 0.181721 0.983350i \(-0.441833\pi\)
0.181721 + 0.983350i \(0.441833\pi\)
\(282\) 0 0
\(283\) 15.6971i 0.933095i 0.884496 + 0.466548i \(0.154502\pi\)
−0.884496 + 0.466548i \(0.845498\pi\)
\(284\) 0 0
\(285\) −0.238171 1.73746i −0.0141080 0.102918i
\(286\) 0 0
\(287\) 1.84584i 0.108956i
\(288\) 0 0
\(289\) 16.9404 0.996492
\(290\) 0 0
\(291\) −1.29007 −0.0756254
\(292\) 0 0
\(293\) 20.3629i 1.18962i 0.803868 + 0.594808i \(0.202772\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(294\) 0 0
\(295\) −2.29967 + 0.315239i −0.133892 + 0.0183539i
\(296\) 0 0
\(297\) 6.50234i 0.377304i
\(298\) 0 0
\(299\) −5.59296 −0.323449
\(300\) 0 0
\(301\) −6.92098 −0.398918
\(302\) 0 0
\(303\) 4.50628i 0.258879i
\(304\) 0 0
\(305\) 8.37062 1.14744i 0.479300 0.0657025i
\(306\) 0 0
\(307\) 6.31386i 0.360351i −0.983634 0.180176i \(-0.942333\pi\)
0.983634 0.180176i \(-0.0576666\pi\)
\(308\) 0 0
\(309\) −6.71848 −0.382201
\(310\) 0 0
\(311\) 2.26901 0.128664 0.0643318 0.997929i \(-0.479508\pi\)
0.0643318 + 0.997929i \(0.479508\pi\)
\(312\) 0 0
\(313\) 25.8886i 1.46331i 0.681676 + 0.731654i \(0.261251\pi\)
−0.681676 + 0.731654i \(0.738749\pi\)
\(314\) 0 0
\(315\) −0.951286 6.93964i −0.0535989 0.391004i
\(316\) 0 0
\(317\) 0.952783i 0.0535136i 0.999642 + 0.0267568i \(0.00851798\pi\)
−0.999642 + 0.0267568i \(0.991482\pi\)
\(318\) 0 0
\(319\) 9.05225 0.506829
\(320\) 0 0
\(321\) −8.42468 −0.470220
\(322\) 0 0
\(323\) 0.354193i 0.0197078i
\(324\) 0 0
\(325\) −7.52542 26.9332i −0.417435 1.49399i
\(326\) 0 0
\(327\) 5.25257i 0.290468i
\(328\) 0 0
\(329\) 0.723012 0.0398609
\(330\) 0 0
\(331\) 14.7188 0.809017 0.404509 0.914534i \(-0.367443\pi\)
0.404509 + 0.914534i \(0.367443\pi\)
\(332\) 0 0
\(333\) 2.18759i 0.119879i
\(334\) 0 0
\(335\) 1.40170 + 10.2254i 0.0765831 + 0.558674i
\(336\) 0 0
\(337\) 23.7550i 1.29402i 0.762482 + 0.647010i \(0.223981\pi\)
−0.762482 + 0.647010i \(0.776019\pi\)
\(338\) 0 0
\(339\) 1.45846 0.0792127
\(340\) 0 0
\(341\) 6.73605 0.364777
\(342\) 0 0
\(343\) 14.6485i 0.790944i
\(344\) 0 0
\(345\) −1.19789 + 0.164207i −0.0644924 + 0.00884062i
\(346\) 0 0
\(347\) 20.8557i 1.11959i 0.828630 + 0.559797i \(0.189121\pi\)
−0.828630 + 0.559797i \(0.810879\pi\)
\(348\) 0 0
\(349\) 12.8328 0.686922 0.343461 0.939167i \(-0.388401\pi\)
0.343461 + 0.939167i \(0.388401\pi\)
\(350\) 0 0
\(351\) −17.2612 −0.921337
\(352\) 0 0
\(353\) 30.4888i 1.62275i 0.584523 + 0.811377i \(0.301282\pi\)
−0.584523 + 0.811377i \(0.698718\pi\)
\(354\) 0 0
\(355\) −15.0088 + 2.05740i −0.796583 + 0.109196i
\(356\) 0 0
\(357\) 0.152766i 0.00808522i
\(358\) 0 0
\(359\) 11.0247 0.581864 0.290932 0.956744i \(-0.406035\pi\)
0.290932 + 0.956744i \(0.406035\pi\)
\(360\) 0 0
\(361\) −16.8963 −0.889276
\(362\) 0 0
\(363\) 3.54773i 0.186207i
\(364\) 0 0
\(365\) 2.69453 + 19.6566i 0.141038 + 1.02887i
\(366\) 0 0
\(367\) 18.5124i 0.966340i 0.875527 + 0.483170i \(0.160515\pi\)
−0.875527 + 0.483170i \(0.839485\pi\)
\(368\) 0 0
\(369\) −4.31990 −0.224885
\(370\) 0 0
\(371\) 0.620215 0.0322000
\(372\) 0 0
\(373\) 26.4707i 1.37060i −0.728260 0.685301i \(-0.759670\pi\)
0.728260 0.685301i \(-0.240330\pi\)
\(374\) 0 0
\(375\) −2.40254 5.54758i −0.124066 0.286476i
\(376\) 0 0
\(377\) 24.0303i 1.23762i
\(378\) 0 0
\(379\) 10.8785 0.558791 0.279395 0.960176i \(-0.409866\pi\)
0.279395 + 0.960176i \(0.409866\pi\)
\(380\) 0 0
\(381\) −2.38148 −0.122007
\(382\) 0 0
\(383\) 21.6026i 1.10384i 0.833897 + 0.551920i \(0.186105\pi\)
−0.833897 + 0.551920i \(0.813895\pi\)
\(384\) 0 0
\(385\) 0.740224 + 5.39994i 0.0377253 + 0.275206i
\(386\) 0 0
\(387\) 16.1975i 0.823364i
\(388\) 0 0
\(389\) 29.4117 1.49123 0.745617 0.666374i \(-0.232155\pi\)
0.745617 + 0.666374i \(0.232155\pi\)
\(390\) 0 0
\(391\) 0.244199 0.0123497
\(392\) 0 0
\(393\) 0.896603i 0.0452276i
\(394\) 0 0
\(395\) 32.9025 4.51028i 1.65551 0.226937i
\(396\) 0 0
\(397\) 33.2753i 1.67004i −0.550219 0.835021i \(-0.685456\pi\)
0.550219 0.835021i \(-0.314544\pi\)
\(398\) 0 0
\(399\) −0.907360 −0.0454248
\(400\) 0 0
\(401\) 33.7280 1.68429 0.842147 0.539248i \(-0.181292\pi\)
0.842147 + 0.539248i \(0.181292\pi\)
\(402\) 0 0
\(403\) 17.8816i 0.890748i
\(404\) 0 0
\(405\) 14.2980 1.95997i 0.710472 0.0973915i
\(406\) 0 0
\(407\) 1.70223i 0.0843764i
\(408\) 0 0
\(409\) −22.6282 −1.11889 −0.559445 0.828867i \(-0.688986\pi\)
−0.559445 + 0.828867i \(0.688986\pi\)
\(410\) 0 0
\(411\) −1.46479 −0.0722527
\(412\) 0 0
\(413\) 1.20097i 0.0590956i
\(414\) 0 0
\(415\) 1.85821 + 13.5556i 0.0912159 + 0.665421i
\(416\) 0 0
\(417\) 4.86383i 0.238183i
\(418\) 0 0
\(419\) −34.6846 −1.69446 −0.847228 0.531230i \(-0.821730\pi\)
−0.847228 + 0.531230i \(0.821730\pi\)
\(420\) 0 0
\(421\) −0.348044 −0.0169626 −0.00848131 0.999964i \(-0.502700\pi\)
−0.00848131 + 0.999964i \(0.502700\pi\)
\(422\) 0 0
\(423\) 1.69210i 0.0822726i
\(424\) 0 0
\(425\) 0.328573 + 1.17595i 0.0159381 + 0.0570420i
\(426\) 0 0
\(427\) 4.37142i 0.211548i
\(428\) 0 0
\(429\) 6.37172 0.307629
\(430\) 0 0
\(431\) −21.2559 −1.02386 −0.511930 0.859027i \(-0.671069\pi\)
−0.511930 + 0.859027i \(0.671069\pi\)
\(432\) 0 0
\(433\) 29.3363i 1.40981i 0.709301 + 0.704906i \(0.249011\pi\)
−0.709301 + 0.704906i \(0.750989\pi\)
\(434\) 0 0
\(435\) 0.705521 + 5.14678i 0.0338271 + 0.246769i
\(436\) 0 0
\(437\) 1.45043i 0.0693835i
\(438\) 0 0
\(439\) 20.2210 0.965096 0.482548 0.875870i \(-0.339711\pi\)
0.482548 + 0.875870i \(0.339711\pi\)
\(440\) 0 0
\(441\) 15.3292 0.729962
\(442\) 0 0
\(443\) 33.8124i 1.60648i 0.595657 + 0.803239i \(0.296892\pi\)
−0.595657 + 0.803239i \(0.703108\pi\)
\(444\) 0 0
\(445\) −12.8478 + 1.76117i −0.609042 + 0.0834875i
\(446\) 0 0
\(447\) 5.15944i 0.244033i
\(448\) 0 0
\(449\) −17.7383 −0.837120 −0.418560 0.908189i \(-0.637465\pi\)
−0.418560 + 0.908189i \(0.637465\pi\)
\(450\) 0 0
\(451\) 3.36144 0.158284
\(452\) 0 0
\(453\) 6.56821i 0.308601i
\(454\) 0 0
\(455\) −14.3348 + 1.96501i −0.672025 + 0.0921212i
\(456\) 0 0
\(457\) 31.7861i 1.48689i 0.668797 + 0.743445i \(0.266810\pi\)
−0.668797 + 0.743445i \(0.733190\pi\)
\(458\) 0 0
\(459\) 0.753657 0.0351777
\(460\) 0 0
\(461\) 17.2206 0.802044 0.401022 0.916068i \(-0.368655\pi\)
0.401022 + 0.916068i \(0.368655\pi\)
\(462\) 0 0
\(463\) 40.0085i 1.85935i 0.368376 + 0.929677i \(0.379914\pi\)
−0.368376 + 0.929677i \(0.620086\pi\)
\(464\) 0 0
\(465\) 0.524999 + 3.82987i 0.0243462 + 0.177606i
\(466\) 0 0
\(467\) 11.9947i 0.555049i 0.960719 + 0.277524i \(0.0895140\pi\)
−0.960719 + 0.277524i \(0.910486\pi\)
\(468\) 0 0
\(469\) 5.34006 0.246581
\(470\) 0 0
\(471\) −10.3687 −0.477764
\(472\) 0 0
\(473\) 12.6037i 0.579520i
\(474\) 0 0
\(475\) 6.98463 1.95158i 0.320477 0.0895446i
\(476\) 0 0
\(477\) 1.45152i 0.0664604i
\(478\) 0 0
\(479\) −20.8249 −0.951514 −0.475757 0.879577i \(-0.657826\pi\)
−0.475757 + 0.879577i \(0.657826\pi\)
\(480\) 0 0
\(481\) −4.51877 −0.206038
\(482\) 0 0
\(483\) 0.625580i 0.0284649i
\(484\) 0 0
\(485\) −0.724528 5.28544i −0.0328991 0.239999i
\(486\) 0 0
\(487\) 16.5640i 0.750584i −0.926907 0.375292i \(-0.877542\pi\)
0.926907 0.375292i \(-0.122458\pi\)
\(488\) 0 0
\(489\) 9.37597 0.423996
\(490\) 0 0
\(491\) −28.8494 −1.30196 −0.650978 0.759097i \(-0.725641\pi\)
−0.650978 + 0.759097i \(0.725641\pi\)
\(492\) 0 0
\(493\) 1.04921i 0.0472538i
\(494\) 0 0
\(495\) −12.6377 + 1.73238i −0.568024 + 0.0778647i
\(496\) 0 0
\(497\) 7.83808i 0.351586i
\(498\) 0 0
\(499\) −14.0289 −0.628021 −0.314011 0.949419i \(-0.601673\pi\)
−0.314011 + 0.949419i \(0.601673\pi\)
\(500\) 0 0
\(501\) 0.315048 0.0140753
\(502\) 0 0
\(503\) 23.2157i 1.03514i −0.855642 0.517568i \(-0.826838\pi\)
0.855642 0.517568i \(-0.173162\pi\)
\(504\) 0 0
\(505\) 18.4623 2.53081i 0.821560 0.112619i
\(506\) 0 0
\(507\) 9.88507i 0.439011i
\(508\) 0 0
\(509\) 17.6290 0.781394 0.390697 0.920519i \(-0.372234\pi\)
0.390697 + 0.920519i \(0.372234\pi\)
\(510\) 0 0
\(511\) 10.2653 0.454111
\(512\) 0 0
\(513\) 4.47638i 0.197637i
\(514\) 0 0
\(515\) −3.77322 27.5257i −0.166268 1.21293i
\(516\) 0 0
\(517\) 1.31667i 0.0579072i
\(518\) 0 0
\(519\) −6.52067 −0.286226
\(520\) 0 0
\(521\) −1.64734 −0.0721711 −0.0360855 0.999349i \(-0.511489\pi\)
−0.0360855 + 0.999349i \(0.511489\pi\)
\(522\) 0 0
\(523\) 40.1998i 1.75781i −0.476994 0.878907i \(-0.658274\pi\)
0.476994 0.878907i \(-0.341726\pi\)
\(524\) 0 0
\(525\) −3.01252 + 0.841729i −0.131477 + 0.0367360i
\(526\) 0 0
\(527\) 0.780744i 0.0340098i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −2.81067 −0.121973
\(532\) 0 0
\(533\) 8.92336i 0.386513i
\(534\) 0 0
\(535\) −4.73145 34.5160i −0.204559 1.49226i
\(536\) 0 0
\(537\) 9.74072i 0.420343i
\(538\) 0 0
\(539\) −11.9281 −0.513780
\(540\) 0 0
\(541\) 26.8419 1.15403 0.577013 0.816735i \(-0.304218\pi\)
0.577013 + 0.816735i \(0.304218\pi\)
\(542\) 0 0
\(543\) 1.80373i 0.0774055i
\(544\) 0 0
\(545\) −21.5198 + 2.94994i −0.921808 + 0.126361i
\(546\) 0 0
\(547\) 20.7472i 0.887087i −0.896253 0.443544i \(-0.853721\pi\)
0.896253 0.443544i \(-0.146279\pi\)
\(548\) 0 0
\(549\) 10.2306 0.436633
\(550\) 0 0
\(551\) −6.23181 −0.265484
\(552\) 0 0
\(553\) 17.1828i 0.730687i
\(554\) 0 0
\(555\) −0.967826 + 0.132670i −0.0410819 + 0.00563151i
\(556\) 0 0
\(557\) 18.1711i 0.769933i 0.922931 + 0.384966i \(0.125787\pi\)
−0.922931 + 0.384966i \(0.874213\pi\)
\(558\) 0 0
\(559\) −33.4581 −1.41513
\(560\) 0 0
\(561\) −0.278201 −0.0117456
\(562\) 0 0
\(563\) 22.9947i 0.969110i 0.874761 + 0.484555i \(0.161018\pi\)
−0.874761 + 0.484555i \(0.838982\pi\)
\(564\) 0 0
\(565\) 0.819098 + 5.97532i 0.0344597 + 0.251384i
\(566\) 0 0
\(567\) 7.46688i 0.313580i
\(568\) 0 0
\(569\) −27.0829 −1.13537 −0.567687 0.823245i \(-0.692162\pi\)
−0.567687 + 0.823245i \(0.692162\pi\)
\(570\) 0 0
\(571\) 10.5631 0.442053 0.221027 0.975268i \(-0.429059\pi\)
0.221027 + 0.975268i \(0.429059\pi\)
\(572\) 0 0
\(573\) 1.56817i 0.0655112i
\(574\) 0 0
\(575\) −1.34552 4.81556i −0.0561119 0.200823i
\(576\) 0 0
\(577\) 2.51016i 0.104499i −0.998634 0.0522496i \(-0.983361\pi\)
0.998634 0.0522496i \(-0.0166392\pi\)
\(578\) 0 0
\(579\) 6.27925 0.260957
\(580\) 0 0
\(581\) 7.07922 0.293695
\(582\) 0 0
\(583\) 1.12947i 0.0467778i
\(584\) 0 0
\(585\) −4.59881 33.5484i −0.190137 1.38705i
\(586\) 0 0
\(587\) 43.0923i 1.77861i 0.457315 + 0.889305i \(0.348811\pi\)
−0.457315 + 0.889305i \(0.651189\pi\)
\(588\) 0 0
\(589\) −4.63727 −0.191076
\(590\) 0 0
\(591\) 0.0846792 0.00348324
\(592\) 0 0
\(593\) 29.7306i 1.22089i −0.792059 0.610444i \(-0.790991\pi\)
0.792059 0.610444i \(-0.209009\pi\)
\(594\) 0 0
\(595\) 0.625882 0.0857960i 0.0256587 0.00351729i
\(596\) 0 0
\(597\) 12.6245i 0.516687i
\(598\) 0 0
\(599\) −22.9491 −0.937674 −0.468837 0.883285i \(-0.655327\pi\)
−0.468837 + 0.883285i \(0.655327\pi\)
\(600\) 0 0
\(601\) 3.49920 0.142735 0.0713677 0.997450i \(-0.477264\pi\)
0.0713677 + 0.997450i \(0.477264\pi\)
\(602\) 0 0
\(603\) 12.4976i 0.508941i
\(604\) 0 0
\(605\) −14.5351 + 1.99247i −0.590934 + 0.0810053i
\(606\) 0 0
\(607\) 42.5670i 1.72774i −0.503714 0.863871i \(-0.668033\pi\)
0.503714 0.863871i \(-0.331967\pi\)
\(608\) 0 0
\(609\) 2.68782 0.108916
\(610\) 0 0
\(611\) 3.49526 0.141403
\(612\) 0 0
\(613\) 28.0072i 1.13120i 0.824679 + 0.565600i \(0.191356\pi\)
−0.824679 + 0.565600i \(0.808644\pi\)
\(614\) 0 0
\(615\) 0.261987 + 1.91119i 0.0105643 + 0.0770668i
\(616\) 0 0
\(617\) 3.14856i 0.126756i 0.997990 + 0.0633781i \(0.0201874\pi\)
−0.997990 + 0.0633781i \(0.979813\pi\)
\(618\) 0 0
\(619\) 13.1433 0.528275 0.264137 0.964485i \(-0.414913\pi\)
0.264137 + 0.964485i \(0.414913\pi\)
\(620\) 0 0
\(621\) −3.08625 −0.123847
\(622\) 0 0
\(623\) 6.70953i 0.268812i
\(624\) 0 0
\(625\) 21.3792 12.9588i 0.855167 0.518353i
\(626\) 0 0
\(627\) 1.65239i 0.0659900i
\(628\) 0 0
\(629\) 0.197298 0.00786677
\(630\) 0 0
\(631\) 35.4545 1.41142 0.705711 0.708500i \(-0.250628\pi\)
0.705711 + 0.708500i \(0.250628\pi\)
\(632\) 0 0
\(633\) 11.4969i 0.456961i
\(634\) 0 0
\(635\) −1.33748 9.75693i −0.0530763 0.387192i
\(636\) 0 0
\(637\) 31.6646i 1.25460i
\(638\) 0 0
\(639\) −18.3438 −0.725670
\(640\) 0 0
\(641\) 9.79611 0.386923 0.193462 0.981108i \(-0.438029\pi\)
0.193462 + 0.981108i \(0.438029\pi\)
\(642\) 0 0
\(643\) 15.6613i 0.617621i −0.951124 0.308810i \(-0.900069\pi\)
0.951124 0.308810i \(-0.0999308\pi\)
\(644\) 0 0
\(645\) −7.16602 + 0.982319i −0.282162 + 0.0386788i
\(646\) 0 0
\(647\) 38.6953i 1.52127i 0.649180 + 0.760634i \(0.275112\pi\)
−0.649180 + 0.760634i \(0.724888\pi\)
\(648\) 0 0
\(649\) 2.18707 0.0858500
\(650\) 0 0
\(651\) 2.00009 0.0783896
\(652\) 0 0
\(653\) 37.8261i 1.48025i 0.672469 + 0.740125i \(0.265234\pi\)
−0.672469 + 0.740125i \(0.734766\pi\)
\(654\) 0 0
\(655\) −3.67339 + 0.503548i −0.143531 + 0.0196753i
\(656\) 0 0
\(657\) 24.0244i 0.937282i
\(658\) 0 0
\(659\) 9.00852 0.350922 0.175461 0.984486i \(-0.443858\pi\)
0.175461 + 0.984486i \(0.443858\pi\)
\(660\) 0 0
\(661\) −26.0490 −1.01319 −0.506594 0.862185i \(-0.669096\pi\)
−0.506594 + 0.862185i \(0.669096\pi\)
\(662\) 0 0
\(663\) 0.738517i 0.0286816i
\(664\) 0 0
\(665\) −0.509590 3.71746i −0.0197611 0.144157i
\(666\) 0 0
\(667\) 4.29653i 0.166362i
\(668\) 0 0
\(669\) 15.5527 0.601303
\(670\) 0 0
\(671\) −7.96076 −0.307322
\(672\) 0 0
\(673\) 4.68835i 0.180722i −0.995909 0.0903612i \(-0.971198\pi\)
0.995909 0.0903612i \(-0.0288022\pi\)
\(674\) 0 0
\(675\) −4.15260 14.8620i −0.159834 0.572038i
\(676\) 0 0
\(677\) 31.1370i 1.19669i −0.801238 0.598346i \(-0.795825\pi\)
0.801238 0.598346i \(-0.204175\pi\)
\(678\) 0 0
\(679\) −2.76023 −0.105928
\(680\) 0 0
\(681\) −3.29296 −0.126186
\(682\) 0 0
\(683\) 15.2671i 0.584180i −0.956391 0.292090i \(-0.905649\pi\)
0.956391 0.292090i \(-0.0943507\pi\)
\(684\) 0 0
\(685\) −0.822652 6.00125i −0.0314319 0.229296i
\(686\) 0 0
\(687\) 10.7763i 0.411142i
\(688\) 0 0
\(689\) 2.99831 0.114227
\(690\) 0 0
\(691\) 30.3229 1.15354 0.576768 0.816908i \(-0.304314\pi\)
0.576768 + 0.816908i \(0.304314\pi\)
\(692\) 0 0
\(693\) 6.59985i 0.250707i
\(694\) 0 0
\(695\) 19.9271 2.73161i 0.755880 0.103616i
\(696\) 0 0
\(697\) 0.389610i 0.0147575i
\(698\) 0 0
\(699\) 5.20829 0.196996
\(700\) 0 0
\(701\) −19.7545 −0.746118 −0.373059 0.927808i \(-0.621691\pi\)
−0.373059 + 0.927808i \(0.621691\pi\)
\(702\) 0 0
\(703\) 1.17186i 0.0441975i
\(704\) 0 0
\(705\) 0.748611 0.102620i 0.0281943 0.00386488i
\(706\) 0 0
\(707\) 9.64161i 0.362610i
\(708\) 0 0
\(709\) −7.45728 −0.280064 −0.140032 0.990147i \(-0.544721\pi\)
−0.140032 + 0.990147i \(0.544721\pi\)
\(710\) 0 0
\(711\) 40.2137 1.50813
\(712\) 0 0
\(713\) 3.19717i 0.119735i
\(714\) 0 0
\(715\) 3.57847 + 26.1050i 0.133827 + 0.976271i
\(716\) 0 0
\(717\) 7.16907i 0.267734i
\(718\) 0 0
\(719\) 48.4683 1.80756 0.903781 0.427995i \(-0.140780\pi\)
0.903781 + 0.427995i \(0.140780\pi\)
\(720\) 0 0
\(721\) −14.3748 −0.535347
\(722\) 0 0
\(723\) 7.79993i 0.290083i
\(724\) 0 0
\(725\) −20.6902 + 5.78105i −0.768413 + 0.214703i
\(726\) 0 0
\(727\) 49.7498i 1.84512i −0.385856 0.922559i \(-0.626094\pi\)
0.385856 0.922559i \(-0.373906\pi\)
\(728\) 0 0
\(729\) 12.4687 0.461802
\(730\) 0 0
\(731\) 1.46084 0.0540312
\(732\) 0 0
\(733\) 12.1579i 0.449063i 0.974467 + 0.224531i \(0.0720851\pi\)
−0.974467 + 0.224531i \(0.927915\pi\)
\(734\) 0 0
\(735\) −0.929661 6.78189i −0.0342911 0.250154i
\(736\) 0 0
\(737\) 9.72474i 0.358215i
\(738\) 0 0
\(739\) −20.5807 −0.757075 −0.378537 0.925586i \(-0.623573\pi\)
−0.378537 + 0.925586i \(0.623573\pi\)
\(740\) 0 0
\(741\) −4.38646 −0.161141
\(742\) 0 0
\(743\) 22.7862i 0.835944i −0.908460 0.417972i \(-0.862741\pi\)
0.908460 0.417972i \(-0.137259\pi\)
\(744\) 0 0
\(745\) −21.1383 + 2.89763i −0.774446 + 0.106161i
\(746\) 0 0
\(747\) 16.5678i 0.606185i
\(748\) 0 0
\(749\) −18.0254 −0.658634
\(750\) 0 0
\(751\) −1.69147 −0.0617226 −0.0308613 0.999524i \(-0.509825\pi\)
−0.0308613 + 0.999524i \(0.509825\pi\)
\(752\) 0 0
\(753\) 10.1001i 0.368069i
\(754\) 0 0
\(755\) 26.9100 3.68883i 0.979355 0.134250i
\(756\) 0 0
\(757\) 25.7514i 0.935952i −0.883741 0.467976i \(-0.844983\pi\)
0.883741 0.467976i \(-0.155017\pi\)
\(758\) 0 0
\(759\) 1.13924 0.0413518
\(760\) 0 0
\(761\) 41.5286 1.50541 0.752706 0.658357i \(-0.228748\pi\)
0.752706 + 0.658357i \(0.228748\pi\)
\(762\) 0 0
\(763\) 11.2384i 0.406856i
\(764\) 0 0
\(765\) 0.200792 + 1.46478i 0.00725966 + 0.0529593i
\(766\) 0 0
\(767\) 5.80584i 0.209637i
\(768\) 0 0
\(769\) −0.962676 −0.0347150 −0.0173575 0.999849i \(-0.505525\pi\)
−0.0173575 + 0.999849i \(0.505525\pi\)
\(770\) 0 0
\(771\) 13.7904 0.496648
\(772\) 0 0
\(773\) 42.5570i 1.53067i 0.643633 + 0.765334i \(0.277426\pi\)
−0.643633 + 0.765334i \(0.722574\pi\)
\(774\) 0 0
\(775\) −15.3962 + 4.30185i −0.553046 + 0.154527i
\(776\) 0 0
\(777\) 0.505431i 0.0181322i
\(778\) 0 0
\(779\) −2.31411 −0.0829115
\(780\) 0 0
\(781\) 14.2739 0.510759
\(782\) 0 0
\(783\) 13.2601i 0.473879i
\(784\) 0 0
\(785\) −5.82325 42.4806i −0.207841 1.51620i
\(786\) 0 0
\(787\) 32.0542i 1.14261i −0.820738 0.571304i \(-0.806438\pi\)
0.820738 0.571304i \(-0.193562\pi\)
\(788\) 0 0
\(789\) 9.97749 0.355208
\(790\) 0 0
\(791\) 3.12051 0.110953
\(792\) 0 0
\(793\) 21.1328i 0.750447i
\(794\) 0 0
\(795\) 0.642175 0.0880293i 0.0227756 0.00312208i
\(796\) 0 0
\(797\) 42.6339i 1.51017i 0.655628 + 0.755084i \(0.272404\pi\)
−0.655628 + 0.755084i \(0.727596\pi\)
\(798\) 0 0
\(799\) −0.152609 −0.00539893
\(800\) 0 0
\(801\) −15.7026 −0.554825
\(802\)