Properties

Label 1152.2.w.a.143.4
Level $1152$
Weight $2$
Character 1152.143
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 143.4
Character \(\chi\) \(=\) 1152.143
Dual form 1152.2.w.a.1007.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.352978 + 0.852163i) q^{5} +(3.43393 - 3.43393i) q^{7} +O(q^{10})\) \(q+(-0.352978 + 0.852163i) q^{5} +(3.43393 - 3.43393i) q^{7} +(-1.44650 + 3.49216i) q^{11} +(-0.258636 + 0.107131i) q^{13} +5.30575 q^{17} +(-2.72546 - 6.57983i) q^{19} +(2.23882 - 2.23882i) q^{23} +(2.93394 + 2.93394i) q^{25} +(3.16953 - 1.31286i) q^{29} +3.46749i q^{31} +(1.71417 + 4.13837i) q^{35} +(1.27512 + 0.528171i) q^{37} +(-5.28251 - 5.28251i) q^{41} +(-2.46955 - 1.02292i) q^{43} -0.423698i q^{47} -16.5838i q^{49} +(12.5563 + 5.20097i) q^{53} +(-2.46531 - 2.46531i) q^{55} +(-5.24194 - 2.17128i) q^{59} +(0.0138304 + 0.0333895i) q^{61} -0.258215i q^{65} +(9.82224 - 4.06850i) q^{67} +(4.64969 + 4.64969i) q^{71} +(3.96752 - 3.96752i) q^{73} +(7.02466 + 16.9590i) q^{77} +12.7319 q^{79} +(-0.867335 + 0.359262i) q^{83} +(-1.87281 + 4.52137i) q^{85} +(-4.82033 + 4.82033i) q^{89} +(-0.520260 + 1.25602i) q^{91} +6.56912 q^{95} +8.78058 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(5\) −0.352978 + 0.852163i −0.157856 + 0.381099i −0.982944 0.183906i \(-0.941126\pi\)
0.825087 + 0.565005i \(0.191126\pi\)
\(6\) 0 0
\(7\) 3.43393 3.43393i 1.29790 1.29790i 0.368130 0.929774i \(-0.379998\pi\)
0.929774 0.368130i \(-0.120002\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.44650 + 3.49216i −0.436136 + 1.05293i 0.541135 + 0.840936i \(0.317995\pi\)
−0.977272 + 0.211991i \(0.932005\pi\)
\(12\) 0 0
\(13\) −0.258636 + 0.107131i −0.0717328 + 0.0297127i −0.418261 0.908327i \(-0.637360\pi\)
0.346529 + 0.938039i \(0.387360\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.30575 1.28683 0.643417 0.765516i \(-0.277516\pi\)
0.643417 + 0.765516i \(0.277516\pi\)
\(18\) 0 0
\(19\) −2.72546 6.57983i −0.625263 1.50952i −0.845447 0.534059i \(-0.820666\pi\)
0.220185 0.975458i \(-0.429334\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.23882 2.23882i 0.466825 0.466825i −0.434059 0.900884i \(-0.642919\pi\)
0.900884 + 0.434059i \(0.142919\pi\)
\(24\) 0 0
\(25\) 2.93394 + 2.93394i 0.586789 + 0.586789i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.16953 1.31286i 0.588568 0.243793i −0.0684666 0.997653i \(-0.521811\pi\)
0.657034 + 0.753861i \(0.271811\pi\)
\(30\) 0 0
\(31\) 3.46749i 0.622779i 0.950282 + 0.311390i \(0.100794\pi\)
−0.950282 + 0.311390i \(0.899206\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.71417 + 4.13837i 0.289748 + 0.699513i
\(36\) 0 0
\(37\) 1.27512 + 0.528171i 0.209628 + 0.0868308i 0.485027 0.874499i \(-0.338810\pi\)
−0.275399 + 0.961330i \(0.588810\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.28251 5.28251i −0.824989 0.824989i 0.161830 0.986819i \(-0.448260\pi\)
−0.986819 + 0.161830i \(0.948260\pi\)
\(42\) 0 0
\(43\) −2.46955 1.02292i −0.376603 0.155994i 0.186349 0.982484i \(-0.440334\pi\)
−0.562952 + 0.826489i \(0.690334\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.423698i 0.0618027i −0.999522 0.0309013i \(-0.990162\pi\)
0.999522 0.0309013i \(-0.00983776\pi\)
\(48\) 0 0
\(49\) 16.5838i 2.36911i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.5563 + 5.20097i 1.72474 + 0.714409i 0.999669 + 0.0257295i \(0.00819085\pi\)
0.725066 + 0.688679i \(0.241809\pi\)
\(54\) 0 0
\(55\) −2.46531 2.46531i −0.332422 0.332422i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.24194 2.17128i −0.682442 0.282677i 0.0144054 0.999896i \(-0.495414\pi\)
−0.696847 + 0.717220i \(0.745414\pi\)
\(60\) 0 0
\(61\) 0.0138304 + 0.0333895i 0.00177080 + 0.00427509i 0.924762 0.380545i \(-0.124264\pi\)
−0.922992 + 0.384820i \(0.874264\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.258215i 0.0320276i
\(66\) 0 0
\(67\) 9.82224 4.06850i 1.19998 0.497047i 0.308986 0.951067i \(-0.400010\pi\)
0.890992 + 0.454020i \(0.150010\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.64969 + 4.64969i 0.551817 + 0.551817i 0.926965 0.375148i \(-0.122408\pi\)
−0.375148 + 0.926965i \(0.622408\pi\)
\(72\) 0 0
\(73\) 3.96752 3.96752i 0.464363 0.464363i −0.435720 0.900082i \(-0.643506\pi\)
0.900082 + 0.435720i \(0.143506\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.02466 + 16.9590i 0.800534 + 1.93266i
\(78\) 0 0
\(79\) 12.7319 1.43245 0.716224 0.697870i \(-0.245869\pi\)
0.716224 + 0.697870i \(0.245869\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.867335 + 0.359262i −0.0952024 + 0.0394341i −0.429776 0.902935i \(-0.641408\pi\)
0.334574 + 0.942369i \(0.391408\pi\)
\(84\) 0 0
\(85\) −1.87281 + 4.52137i −0.203135 + 0.490411i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.82033 + 4.82033i −0.510954 + 0.510954i −0.914819 0.403865i \(-0.867667\pi\)
0.403865 + 0.914819i \(0.367667\pi\)
\(90\) 0 0
\(91\) −0.520260 + 1.25602i −0.0545381 + 0.131667i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.56912 0.673977
\(96\) 0 0
\(97\) 8.78058 0.891532 0.445766 0.895149i \(-0.352931\pi\)
0.445766 + 0.895149i \(0.352931\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.37141 10.5535i 0.434972 1.05011i −0.542691 0.839933i \(-0.682594\pi\)
0.977662 0.210182i \(-0.0674056\pi\)
\(102\) 0 0
\(103\) −2.54327 + 2.54327i −0.250596 + 0.250596i −0.821215 0.570619i \(-0.806703\pi\)
0.570619 + 0.821215i \(0.306703\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.34953 + 3.25806i −0.130464 + 0.314968i −0.975590 0.219599i \(-0.929525\pi\)
0.845126 + 0.534567i \(0.179525\pi\)
\(108\) 0 0
\(109\) 11.5904 4.80089i 1.11016 0.459842i 0.249165 0.968461i \(-0.419844\pi\)
0.860992 + 0.508619i \(0.169844\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.5004 −1.55223 −0.776115 0.630591i \(-0.782812\pi\)
−0.776115 + 0.630591i \(0.782812\pi\)
\(114\) 0 0
\(115\) 1.11758 + 2.69809i 0.104215 + 0.251598i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 18.2196 18.2196i 1.67019 1.67019i
\(120\) 0 0
\(121\) −2.32465 2.32465i −0.211332 0.211332i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.79663 + 3.22947i −0.697352 + 0.288853i
\(126\) 0 0
\(127\) 9.43014i 0.836790i 0.908265 + 0.418395i \(0.137407\pi\)
−0.908265 + 0.418395i \(0.862593\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.19791 + 14.9631i 0.541514 + 1.30733i 0.923654 + 0.383227i \(0.125187\pi\)
−0.382140 + 0.924104i \(0.624813\pi\)
\(132\) 0 0
\(133\) −31.9537 13.2357i −2.77074 1.14768i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.01737 5.01737i −0.428663 0.428663i 0.459510 0.888173i \(-0.348025\pi\)
−0.888173 + 0.459510i \(0.848025\pi\)
\(138\) 0 0
\(139\) −19.0610 7.89534i −1.61674 0.669674i −0.623083 0.782156i \(-0.714120\pi\)
−0.993654 + 0.112482i \(0.964120\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.05816i 0.0884881i
\(144\) 0 0
\(145\) 3.16437i 0.262787i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −20.8124 8.62076i −1.70502 0.706240i −0.705019 0.709188i \(-0.749062\pi\)
−0.999996 + 0.00294754i \(0.999062\pi\)
\(150\) 0 0
\(151\) −4.68070 4.68070i −0.380910 0.380910i 0.490520 0.871430i \(-0.336807\pi\)
−0.871430 + 0.490520i \(0.836807\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.95487 1.22395i −0.237341 0.0983097i
\(156\) 0 0
\(157\) 6.17384 + 14.9050i 0.492726 + 1.18955i 0.953327 + 0.301939i \(0.0976340\pi\)
−0.460601 + 0.887607i \(0.652366\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.3759i 1.21179i
\(162\) 0 0
\(163\) 2.13457 0.884169i 0.167193 0.0692534i −0.297517 0.954716i \(-0.596159\pi\)
0.464710 + 0.885463i \(0.346159\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −14.2052 14.2052i −1.09923 1.09923i −0.994500 0.104733i \(-0.966601\pi\)
−0.104733 0.994500i \(-0.533399\pi\)
\(168\) 0 0
\(169\) −9.13697 + 9.13697i −0.702844 + 0.702844i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.53353 + 10.9449i 0.344678 + 0.832127i 0.997230 + 0.0743825i \(0.0236986\pi\)
−0.652552 + 0.757744i \(0.726301\pi\)
\(174\) 0 0
\(175\) 20.1499 1.52319
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.00945 + 3.73184i −0.673398 + 0.278931i −0.693064 0.720876i \(-0.743740\pi\)
0.0196661 + 0.999807i \(0.493740\pi\)
\(180\) 0 0
\(181\) −5.75935 + 13.9043i −0.428089 + 1.03350i 0.551804 + 0.833974i \(0.313940\pi\)
−0.979893 + 0.199524i \(0.936060\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.900176 + 0.900176i −0.0661823 + 0.0661823i
\(186\) 0 0
\(187\) −7.67477 + 18.5285i −0.561235 + 1.35494i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.18207 −0.447319 −0.223660 0.974667i \(-0.571800\pi\)
−0.223660 + 0.974667i \(0.571800\pi\)
\(192\) 0 0
\(193\) −11.2515 −0.809899 −0.404949 0.914339i \(-0.632711\pi\)
−0.404949 + 0.914339i \(0.632711\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.59303 + 6.26014i −0.184746 + 0.446016i −0.988934 0.148359i \(-0.952601\pi\)
0.804187 + 0.594376i \(0.202601\pi\)
\(198\) 0 0
\(199\) −8.67622 + 8.67622i −0.615041 + 0.615041i −0.944255 0.329214i \(-0.893216\pi\)
0.329214 + 0.944255i \(0.393216\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.37568 15.3922i 0.447485 1.08032i
\(204\) 0 0
\(205\) 6.36616 2.63695i 0.444632 0.184173i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 26.9202 1.86211
\(210\) 0 0
\(211\) −3.18497 7.68919i −0.219262 0.529345i 0.775525 0.631317i \(-0.217485\pi\)
−0.994787 + 0.101971i \(0.967485\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.74339 1.74339i 0.118898 0.118898i
\(216\) 0 0
\(217\) 11.9071 + 11.9071i 0.808308 + 0.808308i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.37226 + 0.568409i −0.0923082 + 0.0382353i
\(222\) 0 0
\(223\) 12.9728i 0.868722i 0.900739 + 0.434361i \(0.143026\pi\)
−0.900739 + 0.434361i \(0.856974\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.79613 + 9.16468i 0.251958 + 0.608281i 0.998362 0.0572122i \(-0.0182212\pi\)
−0.746404 + 0.665493i \(0.768221\pi\)
\(228\) 0 0
\(229\) 4.91823 + 2.03720i 0.325006 + 0.134622i 0.539220 0.842165i \(-0.318719\pi\)
−0.214214 + 0.976787i \(0.568719\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.8493 10.8493i −0.710759 0.710759i 0.255935 0.966694i \(-0.417617\pi\)
−0.966694 + 0.255935i \(0.917617\pi\)
\(234\) 0 0
\(235\) 0.361060 + 0.149556i 0.0235529 + 0.00975594i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.69444i 0.497712i 0.968540 + 0.248856i \(0.0800546\pi\)
−0.968540 + 0.248856i \(0.919945\pi\)
\(240\) 0 0
\(241\) 14.5669i 0.938338i −0.883108 0.469169i \(-0.844553\pi\)
0.883108 0.469169i \(-0.155447\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 14.1321 + 5.85370i 0.902866 + 0.373979i
\(246\) 0 0
\(247\) 1.40980 + 1.40980i 0.0897037 + 0.0897037i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.1528 5.86227i −0.893315 0.370023i −0.111669 0.993745i \(-0.535620\pi\)
−0.781646 + 0.623722i \(0.785620\pi\)
\(252\) 0 0
\(253\) 4.57986 + 11.0568i 0.287933 + 0.695132i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.4990i 1.21632i 0.793816 + 0.608159i \(0.208092\pi\)
−0.793816 + 0.608159i \(0.791908\pi\)
\(258\) 0 0
\(259\) 6.19237 2.56496i 0.384775 0.159379i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.65433 + 9.65433i 0.595312 + 0.595312i 0.939061 0.343750i \(-0.111697\pi\)
−0.343750 + 0.939061i \(0.611697\pi\)
\(264\) 0 0
\(265\) −8.86416 + 8.86416i −0.544521 + 0.544521i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.95451 19.2039i −0.484995 1.17088i −0.957209 0.289397i \(-0.906545\pi\)
0.472214 0.881484i \(-0.343455\pi\)
\(270\) 0 0
\(271\) −19.1213 −1.16154 −0.580770 0.814068i \(-0.697248\pi\)
−0.580770 + 0.814068i \(0.697248\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −14.4898 + 6.00186i −0.873765 + 0.361926i
\(276\) 0 0
\(277\) −0.609964 + 1.47258i −0.0366492 + 0.0884789i −0.941144 0.338005i \(-0.890248\pi\)
0.904495 + 0.426484i \(0.140248\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.76628 + 8.76628i −0.522953 + 0.522953i −0.918462 0.395509i \(-0.870568\pi\)
0.395509 + 0.918462i \(0.370568\pi\)
\(282\) 0 0
\(283\) −7.64026 + 18.4452i −0.454166 + 1.09645i 0.516557 + 0.856253i \(0.327213\pi\)
−0.970723 + 0.240201i \(0.922787\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −36.2795 −2.14151
\(288\) 0 0
\(289\) 11.1510 0.655942
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.73727 21.0936i 0.510437 1.23230i −0.433194 0.901301i \(-0.642613\pi\)
0.943630 0.331002i \(-0.107387\pi\)
\(294\) 0 0
\(295\) 3.70057 3.70057i 0.215456 0.215456i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.339193 + 0.818885i −0.0196160 + 0.0473573i
\(300\) 0 0
\(301\) −11.9929 + 4.96763i −0.691260 + 0.286329i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.0333351 −0.00190876
\(306\) 0 0
\(307\) −2.29860 5.54931i −0.131188 0.316716i 0.844613 0.535378i \(-0.179831\pi\)
−0.975801 + 0.218662i \(0.929831\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.3351 + 12.3351i −0.699460 + 0.699460i −0.964294 0.264834i \(-0.914683\pi\)
0.264834 + 0.964294i \(0.414683\pi\)
\(312\) 0 0
\(313\) 9.07712 + 9.07712i 0.513069 + 0.513069i 0.915465 0.402397i \(-0.131823\pi\)
−0.402397 + 0.915465i \(0.631823\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.7317 6.10208i 0.827416 0.342727i 0.0715366 0.997438i \(-0.477210\pi\)
0.755879 + 0.654711i \(0.227210\pi\)
\(318\) 0 0
\(319\) 12.9676i 0.726045i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −14.4606 34.9110i −0.804609 1.94250i
\(324\) 0 0
\(325\) −1.07314 0.444509i −0.0595271 0.0246569i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.45495 1.45495i −0.0802139 0.0802139i
\(330\) 0 0
\(331\) 20.7207 + 8.58281i 1.13892 + 0.471754i 0.870802 0.491633i \(-0.163600\pi\)
0.268113 + 0.963387i \(0.413600\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.80624i 0.535772i
\(336\) 0 0
\(337\) 12.9981i 0.708052i −0.935236 0.354026i \(-0.884812\pi\)
0.935236 0.354026i \(-0.115188\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.1090 5.01573i −0.655741 0.271617i
\(342\) 0 0
\(343\) −32.9100 32.9100i −1.77697 1.77697i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.4093 10.1107i −1.31036 0.542769i −0.385372 0.922762i \(-0.625927\pi\)
−0.924990 + 0.379992i \(0.875927\pi\)
\(348\) 0 0
\(349\) −3.82444 9.23301i −0.204717 0.494231i 0.787859 0.615856i \(-0.211190\pi\)
−0.992576 + 0.121624i \(0.961190\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.4035i 1.29887i −0.760418 0.649434i \(-0.775006\pi\)
0.760418 0.649434i \(-0.224994\pi\)
\(354\) 0 0
\(355\) −5.60353 + 2.32106i −0.297405 + 0.123189i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.52733 + 6.52733i 0.344500 + 0.344500i 0.858056 0.513556i \(-0.171672\pi\)
−0.513556 + 0.858056i \(0.671672\pi\)
\(360\) 0 0
\(361\) −22.4311 + 22.4311i −1.18058 + 1.18058i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.98053 + 4.78142i 0.103666 + 0.250271i
\(366\) 0 0
\(367\) −19.4291 −1.01419 −0.507096 0.861889i \(-0.669281\pi\)
−0.507096 + 0.861889i \(0.669281\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 60.9771 25.2576i 3.16577 1.31131i
\(372\) 0 0
\(373\) −4.15808 + 10.0385i −0.215297 + 0.519773i −0.994222 0.107344i \(-0.965765\pi\)
0.778925 + 0.627117i \(0.215765\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.679109 + 0.679109i −0.0349759 + 0.0349759i
\(378\) 0 0
\(379\) −1.96668 + 4.74798i −0.101021 + 0.243887i −0.966307 0.257392i \(-0.917137\pi\)
0.865286 + 0.501279i \(0.167137\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.30106 −0.321969 −0.160985 0.986957i \(-0.551467\pi\)
−0.160985 + 0.986957i \(0.551467\pi\)
\(384\) 0 0
\(385\) −16.9314 −0.862905
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.331782 0.800993i 0.0168220 0.0406119i −0.915245 0.402897i \(-0.868003\pi\)
0.932067 + 0.362285i \(0.118003\pi\)
\(390\) 0 0
\(391\) 11.8786 11.8786i 0.600727 0.600727i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.49407 + 10.8496i −0.226121 + 0.545905i
\(396\) 0 0
\(397\) 11.2798 4.67225i 0.566118 0.234494i −0.0812209 0.996696i \(-0.525882\pi\)
0.647339 + 0.762202i \(0.275882\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.7890 0.538777 0.269388 0.963032i \(-0.413178\pi\)
0.269388 + 0.963032i \(0.413178\pi\)
\(402\) 0 0
\(403\) −0.371474 0.896819i −0.0185045 0.0446737i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.68892 + 3.68892i −0.182853 + 0.182853i
\(408\) 0 0
\(409\) −0.0980818 0.0980818i −0.00484983 0.00484983i 0.704678 0.709528i \(-0.251092\pi\)
−0.709528 + 0.704678i \(0.751092\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −25.4565 + 10.5444i −1.25263 + 0.518857i
\(414\) 0 0
\(415\) 0.865923i 0.0425065i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11.5665 + 27.9241i 0.565063 + 1.36418i 0.905673 + 0.423977i \(0.139366\pi\)
−0.340610 + 0.940205i \(0.610634\pi\)
\(420\) 0 0
\(421\) 18.0670 + 7.48361i 0.880533 + 0.364729i 0.776703 0.629867i \(-0.216890\pi\)
0.103829 + 0.994595i \(0.466890\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 15.5668 + 15.5668i 0.755100 + 0.755100i
\(426\) 0 0
\(427\) 0.162150 + 0.0671647i 0.00784698 + 0.00325033i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.6345i 0.512245i −0.966644 0.256123i \(-0.917555\pi\)
0.966644 0.256123i \(-0.0824451\pi\)
\(432\) 0 0
\(433\) 11.8688i 0.570377i 0.958471 + 0.285189i \(0.0920562\pi\)
−0.958471 + 0.285189i \(0.907944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.8328 8.62924i −0.996569 0.412793i
\(438\) 0 0
\(439\) 11.2613 + 11.2613i 0.537471 + 0.537471i 0.922785 0.385314i \(-0.125907\pi\)
−0.385314 + 0.922785i \(0.625907\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.1370 + 7.09839i 0.814204 + 0.337255i 0.750630 0.660723i \(-0.229750\pi\)
0.0635743 + 0.997977i \(0.479750\pi\)
\(444\) 0 0
\(445\) −2.40624 5.80918i −0.114067 0.275381i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 38.4537i 1.81474i 0.420331 + 0.907371i \(0.361914\pi\)
−0.420331 + 0.907371i \(0.638086\pi\)
\(450\) 0 0
\(451\) 26.0885 10.8062i 1.22846 0.508845i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.886693 0.886693i −0.0415688 0.0415688i
\(456\) 0 0
\(457\) −11.6258 + 11.6258i −0.543833 + 0.543833i −0.924650 0.380817i \(-0.875643\pi\)
0.380817 + 0.924650i \(0.375643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.95672 4.72395i −0.0911337 0.220016i 0.871740 0.489969i \(-0.162992\pi\)
−0.962874 + 0.269953i \(0.912992\pi\)
\(462\) 0 0
\(463\) 24.2082 1.12505 0.562524 0.826781i \(-0.309830\pi\)
0.562524 + 0.826781i \(0.309830\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.35140 + 2.21662i −0.247633 + 0.102573i −0.503048 0.864259i \(-0.667788\pi\)
0.255415 + 0.966832i \(0.417788\pi\)
\(468\) 0 0
\(469\) 19.7579 47.6999i 0.912336 2.20257i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.14442 7.14442i 0.328501 0.328501i
\(474\) 0 0
\(475\) 11.3085 27.3012i 0.518871 1.25267i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.4282 1.20754 0.603768 0.797160i \(-0.293665\pi\)
0.603768 + 0.797160i \(0.293665\pi\)
\(480\) 0 0
\(481\) −0.386375 −0.0176172
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.09935 + 7.48249i −0.140734 + 0.339762i
\(486\) 0 0
\(487\) 9.32733 9.32733i 0.422662 0.422662i −0.463457 0.886119i \(-0.653391\pi\)
0.886119 + 0.463457i \(0.153391\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.97593 7.18453i 0.134302 0.324233i −0.842394 0.538862i \(-0.818854\pi\)
0.976696 + 0.214629i \(0.0688543\pi\)
\(492\) 0 0
\(493\) 16.8168 6.96573i 0.757389 0.313721i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 31.9334 1.43241
\(498\) 0 0
\(499\) 10.3839 + 25.0689i 0.464846 + 1.12224i 0.966384 + 0.257103i \(0.0827679\pi\)
−0.501538 + 0.865136i \(0.667232\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.53224 3.53224i 0.157495 0.157495i −0.623961 0.781456i \(-0.714478\pi\)
0.781456 + 0.623961i \(0.214478\pi\)
\(504\) 0 0
\(505\) 7.45031 + 7.45031i 0.331535 + 0.331535i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −19.0074 + 7.87311i −0.842487 + 0.348969i −0.761834 0.647773i \(-0.775701\pi\)
−0.0806532 + 0.996742i \(0.525701\pi\)
\(510\) 0 0
\(511\) 27.2484i 1.20540i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.26957 3.06500i −0.0559437 0.135060i
\(516\) 0 0
\(517\) 1.47962 + 0.612879i 0.0650736 + 0.0269544i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.5687 + 12.5687i 0.550643 + 0.550643i 0.926626 0.375984i \(-0.122695\pi\)
−0.375984 + 0.926626i \(0.622695\pi\)
\(522\) 0 0
\(523\) −9.66162 4.00197i −0.422473 0.174994i 0.161310 0.986904i \(-0.448428\pi\)
−0.583783 + 0.811910i \(0.698428\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.3976i 0.801414i
\(528\) 0 0
\(529\) 12.9754i 0.564148i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.93217 + 0.800329i 0.0836914 + 0.0346661i
\(534\) 0 0
\(535\) −2.30004 2.30004i −0.0994395 0.0994395i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 57.9132 + 23.9884i 2.49450 + 1.03326i
\(540\) 0 0
\(541\) −14.6046 35.2587i −0.627901 1.51589i −0.842225 0.539125i \(-0.818755\pi\)
0.214324 0.976763i \(-0.431245\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 11.5715i 0.495669i
\(546\) 0 0
\(547\) 9.22367 3.82057i 0.394376 0.163356i −0.176677 0.984269i \(-0.556535\pi\)
0.571053 + 0.820913i \(0.306535\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17.2769 17.2769i −0.736019 0.736019i
\(552\) 0 0
\(553\) 43.7204 43.7204i 1.85918 1.85918i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.65349 20.8914i −0.366660 0.885196i −0.994293 0.106686i \(-0.965976\pi\)
0.627632 0.778510i \(-0.284024\pi\)
\(558\) 0 0
\(559\) 0.748302 0.0316498
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.53958 + 1.46614i −0.149175 + 0.0617905i −0.456022 0.889969i \(-0.650726\pi\)
0.306847 + 0.951759i \(0.400726\pi\)
\(564\) 0 0
\(565\) 5.82428 14.0611i 0.245029 0.591553i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.855711 + 0.855711i −0.0358733 + 0.0358733i −0.724816 0.688943i \(-0.758075\pi\)
0.688943 + 0.724816i \(0.258075\pi\)
\(570\) 0 0
\(571\) −4.33854 + 10.4742i −0.181562 + 0.438330i −0.988289 0.152595i \(-0.951237\pi\)
0.806726 + 0.590925i \(0.201237\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.1371 0.547856
\(576\) 0 0
\(577\) −2.91000 −0.121145 −0.0605724 0.998164i \(-0.519293\pi\)
−0.0605724 + 0.998164i \(0.519293\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.74469 + 4.21205i −0.0723819 + 0.174745i
\(582\) 0 0
\(583\) −36.3253 + 36.3253i −1.50444 + 1.50444i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.1052 43.7099i 0.747283 1.80410i 0.173996 0.984746i \(-0.444332\pi\)
0.573287 0.819355i \(-0.305668\pi\)
\(588\) 0 0
\(589\) 22.8155 9.45049i 0.940096 0.389401i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −30.7464 −1.26260 −0.631301 0.775538i \(-0.717479\pi\)
−0.631301 + 0.775538i \(0.717479\pi\)
\(594\) 0 0
\(595\) 9.09496 + 21.9572i 0.372857 + 0.900157i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −19.3435 + 19.3435i −0.790354 + 0.790354i −0.981552 0.191198i \(-0.938763\pi\)
0.191198 + 0.981552i \(0.438763\pi\)
\(600\) 0 0
\(601\) −28.4893 28.4893i −1.16210 1.16210i −0.984015 0.178087i \(-0.943009\pi\)
−0.178087 0.984015i \(-0.556991\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.80153 1.16043i 0.113899 0.0471783i
\(606\) 0 0
\(607\) 31.5078i 1.27886i −0.768848 0.639432i \(-0.779170\pi\)
0.768848 0.639432i \(-0.220830\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.0453910 + 0.109584i 0.00183632 + 0.00443328i
\(612\) 0 0
\(613\) −40.5414 16.7928i −1.63745 0.678254i −0.641413 0.767196i \(-0.721651\pi\)
−0.996037 + 0.0889418i \(0.971651\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.1405 + 14.1405i 0.569276 + 0.569276i 0.931926 0.362650i \(-0.118128\pi\)
−0.362650 + 0.931926i \(0.618128\pi\)
\(618\) 0 0
\(619\) 17.7763 + 7.36320i 0.714491 + 0.295952i 0.710162 0.704039i \(-0.248622\pi\)
0.00432943 + 0.999991i \(0.498622\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 33.1054i 1.32634i
\(624\) 0 0
\(625\) 12.9622i 0.518487i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.76546 + 2.80235i 0.269757 + 0.111737i
\(630\) 0 0
\(631\) 14.1654 + 14.1654i 0.563915 + 0.563915i 0.930417 0.366502i \(-0.119445\pi\)
−0.366502 + 0.930417i \(0.619445\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.03602 3.32863i −0.318900 0.132093i
\(636\) 0 0
\(637\) 1.77663 + 4.28917i 0.0703927 + 0.169943i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.51722i 0.138922i −0.997585 0.0694610i \(-0.977872\pi\)
0.997585 0.0694610i \(-0.0221279\pi\)
\(642\) 0 0
\(643\) −28.4159 + 11.7702i −1.12061 + 0.464173i −0.864580 0.502496i \(-0.832415\pi\)
−0.256032 + 0.966668i \(0.582415\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.2793 + 22.2793i 0.875889 + 0.875889i 0.993106 0.117217i \(-0.0373973\pi\)
−0.117217 + 0.993106i \(0.537397\pi\)
\(648\) 0 0
\(649\) 15.1649 15.1649i 0.595275 0.595275i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.57865 + 3.81119i 0.0617772 + 0.149143i 0.951754 0.306863i \(-0.0992794\pi\)
−0.889976 + 0.456007i \(0.849279\pi\)
\(654\) 0 0
\(655\) −14.9387 −0.583704
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.2385 + 5.48357i −0.515699 + 0.213610i −0.625327 0.780363i \(-0.715034\pi\)
0.109627 + 0.993973i \(0.465034\pi\)
\(660\) 0 0
\(661\) −9.61142 + 23.2040i −0.373841 + 0.902532i 0.619251 + 0.785193i \(0.287436\pi\)
−0.993092 + 0.117339i \(0.962564\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 22.5579 22.5579i 0.874758 0.874758i
\(666\) 0 0
\(667\) 4.15674 10.0353i 0.160950 0.388567i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.136607 −0.00527366
\(672\) 0 0
\(673\) −12.4509 −0.479947 −0.239974 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.84859 16.5340i 0.263213 0.635451i −0.735921 0.677067i \(-0.763251\pi\)
0.999134 + 0.0416159i \(0.0132506\pi\)
\(678\) 0 0
\(679\) 30.1519 30.1519i 1.15712 1.15712i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.54777 23.0504i 0.365335 0.881997i −0.629166 0.777271i \(-0.716603\pi\)
0.994501 0.104726i \(-0.0333966\pi\)
\(684\) 0 0
\(685\) 6.04663 2.50460i 0.231030 0.0956958i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.80469 −0.144947
\(690\) 0 0
\(691\) 0.714680 + 1.72539i 0.0271877 + 0.0656369i 0.936890 0.349623i \(-0.113690\pi\)
−0.909703 + 0.415260i \(0.863690\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 13.4562 13.4562i 0.510424 0.510424i
\(696\) 0 0
\(697\) −28.0277 28.0277i −1.06162 1.06162i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 23.2566 9.63319i 0.878388 0.363840i 0.102517 0.994731i \(-0.467310\pi\)
0.775872 + 0.630891i \(0.217310\pi\)
\(702\) 0 0
\(703\) 9.82957i 0.370729i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.2289 51.2512i −0.798396 1.92750i
\(708\) 0 0
\(709\) 37.2006 + 15.4090i 1.39710 + 0.578698i 0.948997 0.315285i \(-0.102100\pi\)
0.448102 + 0.893982i \(0.352100\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.76307 + 7.76307i 0.290729 + 0.290729i
\(714\) 0 0
\(715\) 0.901729 + 0.373508i 0.0337227 + 0.0139684i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.2965i 0.383996i −0.981395 0.191998i \(-0.938503\pi\)
0.981395 0.191998i \(-0.0614968\pi\)
\(720\) 0 0
\(721\) 17.4669i 0.650500i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 13.1511 + 5.44737i 0.488420 + 0.202310i
\(726\) 0 0
\(727\) −13.6565 13.6565i −0.506493 0.506493i 0.406955 0.913448i \(-0.366591\pi\)
−0.913448 + 0.406955i \(0.866591\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −13.1028 5.42737i −0.484626 0.200739i
\(732\) 0 0
\(733\) 12.2351 + 29.5382i 0.451915 + 1.09102i 0.971593 + 0.236657i \(0.0760517\pi\)
−0.519678 + 0.854362i \(0.673948\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 40.1859i 1.48027i
\(738\) 0 0
\(739\) 5.26176 2.17949i 0.193557 0.0801739i −0.283800 0.958884i \(-0.591595\pi\)
0.477356 + 0.878710i \(0.341595\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −17.0314 17.0314i −0.624823 0.624823i 0.321938 0.946761i \(-0.395666\pi\)
−0.946761 + 0.321938i \(0.895666\pi\)
\(744\) 0 0
\(745\) 14.6926 14.6926i 0.538295 0.538295i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.55375 + 15.8221i 0.239469 + 0.578129i
\(750\) 0 0
\(751\) −5.21219 −0.190196 −0.0950978 0.995468i \(-0.530316\pi\)
−0.0950978 + 0.995468i \(0.530316\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.64090 2.33654i 0.205293 0.0850353i
\(756\) 0 0
\(757\) 5.99669 14.4773i 0.217953 0.526186i −0.776650 0.629932i \(-0.783083\pi\)
0.994604 + 0.103746i \(0.0330828\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.7870 + 16.7870i −0.608528 + 0.608528i −0.942561 0.334033i \(-0.891590\pi\)
0.334033 + 0.942561i \(0.391590\pi\)
\(762\) 0 0
\(763\) 23.3146 56.2865i 0.844046 2.03771i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.58837 0.0573526
\(768\) 0 0
\(769\) 33.1933 1.19698 0.598491 0.801129i \(-0.295767\pi\)
0.598491 + 0.801129i \(0.295767\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5.41657 + 13.0767i −0.194820 + 0.470338i −0.990858 0.134909i \(-0.956926\pi\)
0.796038 + 0.605247i \(0.206926\pi\)
\(774\) 0 0
\(775\) −10.1734 + 10.1734i −0.365440 + 0.365440i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −20.3608 + 49.1552i −0.729500 + 1.76117i
\(780\) 0 0
\(781\) −22.9632 + 9.51169i −0.821689 + 0.340355i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14.8807 −0.531115
\(786\) 0 0
\(787\) −18.2278 44.0057i −0.649750 1.56864i −0.813136 0.582073i \(-0.802242\pi\)
0.163387 0.986562i \(-0.447758\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −56.6614 + 56.6614i −2.01465 + 2.01465i
\(792\) 0 0
\(793\) −0.00715408 0.00715408i −0.000254049 0.000254049i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 33.3377 13.8089i 1.18088 0.489138i 0.296107 0.955155i \(-0.404311\pi\)
0.884776 + 0.466017i \(0.154311\pi\)
\(798\) 0 0
\(799\) 2.24803i 0.0795298i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.11619 + 19.5942i 0.286414 + 0.691465i
\(804\) 0 0
\(805\) 13.1028 + 5.42734i 0.461812 + 0.191289i