Properties

Label 2520.2.bi.r.1801.2
Level $2520$
Weight $2$
Character 2520.1801
Analytic conductor $20.122$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 29 x^{8} + 247 x^{6} + 855 x^{4} + 1212 x^{2} + 588\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1801.2
Root \(-2.19149i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1801
Dual form 2520.2.bi.r.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{5} +(-0.780339 + 2.52806i) q^{7} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{5} +(-0.780339 + 2.52806i) q^{7} +(-2.39788 - 4.15326i) q^{11} +5.94151 q^{13} +(3.41674 + 5.91796i) q^{17} +(-4.26995 + 7.39577i) q^{19} +(4.48961 - 7.77623i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.414934 q^{29} +(-2.80796 - 4.86353i) q^{31} +(-1.79919 - 1.93982i) q^{35} +(-2.79919 + 4.84834i) q^{37} +0.325591 q^{41} +3.90381 q^{43} +(-4.86864 + 8.43273i) q^{47} +(-5.78214 - 3.94548i) q^{49} +(-0.927128 - 1.60583i) q^{53} +4.79577 q^{55} +(4.58830 + 7.94717i) q^{59} +(-6.33063 + 10.9650i) q^{61} +(-2.97076 + 5.14550i) q^{65} +(1.34102 + 2.32271i) q^{67} +5.17660 q^{71} +(4.40454 + 7.62889i) q^{73} +(12.3708 - 2.82104i) q^{77} +(-1.81624 + 3.14582i) q^{79} -9.07619 q^{83} -6.83347 q^{85} +(-0.646788 + 1.12027i) q^{89} +(-4.63640 + 15.0205i) q^{91} +(-4.26995 - 7.39577i) q^{95} -10.0101 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{5} - q^{7} + O(q^{10}) \) \( 10q - 5q^{5} - q^{7} - 2q^{11} + 6q^{13} + 2q^{17} + q^{19} + 8q^{23} - 5q^{25} + 7q^{31} - q^{35} - 11q^{37} + 20q^{41} + 6q^{43} - 23q^{49} - 14q^{53} + 4q^{55} + 4q^{59} - 6q^{61} - 3q^{65} - 7q^{67} - 32q^{71} + 3q^{73} + 8q^{77} - 19q^{79} + 28q^{83} - 4q^{85} - 18q^{89} - 21q^{91} + q^{95} + 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −0.780339 + 2.52806i −0.294941 + 0.955516i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.39788 4.15326i −0.722989 1.25225i −0.959796 0.280697i \(-0.909434\pi\)
0.236807 0.971557i \(-0.423899\pi\)
\(12\) 0 0
\(13\) 5.94151 1.64788 0.823939 0.566678i \(-0.191772\pi\)
0.823939 + 0.566678i \(0.191772\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.41674 + 5.91796i 0.828680 + 1.43532i 0.899074 + 0.437797i \(0.144241\pi\)
−0.0703939 + 0.997519i \(0.522426\pi\)
\(18\) 0 0
\(19\) −4.26995 + 7.39577i −0.979593 + 1.69671i −0.315733 + 0.948848i \(0.602250\pi\)
−0.663860 + 0.747857i \(0.731083\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.48961 7.77623i 0.936148 1.62146i 0.163574 0.986531i \(-0.447698\pi\)
0.772574 0.634925i \(-0.218969\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.414934 0.0770514 0.0385257 0.999258i \(-0.487734\pi\)
0.0385257 + 0.999258i \(0.487734\pi\)
\(30\) 0 0
\(31\) −2.80796 4.86353i −0.504325 0.873516i −0.999987 0.00500080i \(-0.998408\pi\)
0.495663 0.868515i \(-0.334925\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.79919 1.93982i −0.304119 0.327890i
\(36\) 0 0
\(37\) −2.79919 + 4.84834i −0.460184 + 0.797063i −0.998970 0.0453805i \(-0.985550\pi\)
0.538786 + 0.842443i \(0.318883\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.325591 0.0508487 0.0254244 0.999677i \(-0.491906\pi\)
0.0254244 + 0.999677i \(0.491906\pi\)
\(42\) 0 0
\(43\) 3.90381 0.595325 0.297663 0.954671i \(-0.403793\pi\)
0.297663 + 0.954671i \(0.403793\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.86864 + 8.43273i −0.710164 + 1.23004i 0.254631 + 0.967038i \(0.418046\pi\)
−0.964795 + 0.263002i \(0.915287\pi\)
\(48\) 0 0
\(49\) −5.78214 3.94548i −0.826020 0.563641i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.927128 1.60583i −0.127351 0.220578i 0.795299 0.606218i \(-0.207314\pi\)
−0.922649 + 0.385640i \(0.873981\pi\)
\(54\) 0 0
\(55\) 4.79577 0.646661
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.58830 + 7.94717i 0.597346 + 1.03463i 0.993211 + 0.116325i \(0.0371113\pi\)
−0.395865 + 0.918309i \(0.629555\pi\)
\(60\) 0 0
\(61\) −6.33063 + 10.9650i −0.810554 + 1.40392i 0.101923 + 0.994792i \(0.467500\pi\)
−0.912477 + 0.409128i \(0.865833\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.97076 + 5.14550i −0.368477 + 0.638221i
\(66\) 0 0
\(67\) 1.34102 + 2.32271i 0.163831 + 0.283764i 0.936240 0.351362i \(-0.114281\pi\)
−0.772408 + 0.635126i \(0.780948\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.17660 0.614349 0.307175 0.951653i \(-0.400616\pi\)
0.307175 + 0.951653i \(0.400616\pi\)
\(72\) 0 0
\(73\) 4.40454 + 7.62889i 0.515513 + 0.892894i 0.999838 + 0.0180061i \(0.00573183\pi\)
−0.484325 + 0.874888i \(0.660935\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 12.3708 2.82104i 1.40979 0.321487i
\(78\) 0 0
\(79\) −1.81624 + 3.14582i −0.204343 + 0.353933i −0.949923 0.312483i \(-0.898839\pi\)
0.745580 + 0.666416i \(0.232173\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.07619 −0.996241 −0.498120 0.867108i \(-0.665976\pi\)
−0.498120 + 0.867108i \(0.665976\pi\)
\(84\) 0 0
\(85\) −6.83347 −0.741194
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.646788 + 1.12027i −0.0685594 + 0.118748i −0.898267 0.439449i \(-0.855174\pi\)
0.829708 + 0.558198i \(0.188507\pi\)
\(90\) 0 0
\(91\) −4.63640 + 15.0205i −0.486026 + 1.57457i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.26995 7.39577i −0.438087 0.758790i
\(96\) 0 0
\(97\) −10.0101 −1.01637 −0.508184 0.861248i \(-0.669683\pi\)
−0.508184 + 0.861248i \(0.669683\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.570762 + 0.988589i 0.0567930 + 0.0983683i 0.893024 0.450009i \(-0.148579\pi\)
−0.836231 + 0.548377i \(0.815246\pi\)
\(102\) 0 0
\(103\) −6.58799 + 11.4107i −0.649134 + 1.12433i 0.334196 + 0.942504i \(0.391535\pi\)
−0.983330 + 0.181830i \(0.941798\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.41674 7.65001i 0.426982 0.739554i −0.569621 0.821907i \(-0.692910\pi\)
0.996603 + 0.0823529i \(0.0262435\pi\)
\(108\) 0 0
\(109\) 5.75775 + 9.97272i 0.551493 + 0.955214i 0.998167 + 0.0605170i \(0.0192749\pi\)
−0.446674 + 0.894697i \(0.647392\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.12136 −0.105488 −0.0527442 0.998608i \(-0.516797\pi\)
−0.0527442 + 0.998608i \(0.516797\pi\)
\(114\) 0 0
\(115\) 4.48961 + 7.77623i 0.418658 + 0.725137i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −17.6272 + 4.01968i −1.61588 + 0.368484i
\(120\) 0 0
\(121\) −5.99969 + 10.3918i −0.545426 + 0.944706i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.54674 −0.492194 −0.246097 0.969245i \(-0.579148\pi\)
−0.246097 + 0.969245i \(0.579148\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.19042 3.79391i 0.191378 0.331476i −0.754329 0.656496i \(-0.772038\pi\)
0.945707 + 0.325020i \(0.105371\pi\)
\(132\) 0 0
\(133\) −15.3649 16.5659i −1.33231 1.43644i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.75986 15.1725i −0.748406 1.29628i −0.948587 0.316518i \(-0.897486\pi\)
0.200181 0.979759i \(-0.435847\pi\)
\(138\) 0 0
\(139\) 0.727208 0.0616810 0.0308405 0.999524i \(-0.490182\pi\)
0.0308405 + 0.999524i \(0.490182\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −14.2471 24.6766i −1.19140 2.06356i
\(144\) 0 0
\(145\) −0.207467 + 0.359344i −0.0172292 + 0.0298419i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −10.5776 + 18.3209i −0.866551 + 1.50091i −0.00105144 + 0.999999i \(0.500335\pi\)
−0.865499 + 0.500910i \(0.832999\pi\)
\(150\) 0 0
\(151\) −4.02582 6.97292i −0.327617 0.567449i 0.654422 0.756130i \(-0.272912\pi\)
−0.982038 + 0.188681i \(0.939579\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.61592 0.451082
\(156\) 0 0
\(157\) 9.34948 + 16.1938i 0.746170 + 1.29240i 0.949646 + 0.313324i \(0.101443\pi\)
−0.203477 + 0.979080i \(0.565224\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 16.1553 + 17.4181i 1.27322 + 1.37274i
\(162\) 0 0
\(163\) −6.70642 + 11.6159i −0.525288 + 0.909825i 0.474279 + 0.880375i \(0.342709\pi\)
−0.999566 + 0.0294501i \(0.990624\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.97922 −0.540068 −0.270034 0.962851i \(-0.587035\pi\)
−0.270034 + 0.962851i \(0.587035\pi\)
\(168\) 0 0
\(169\) 22.3016 1.71550
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.48781 + 4.30901i −0.189144 + 0.327608i −0.944965 0.327171i \(-0.893905\pi\)
0.755821 + 0.654779i \(0.227238\pi\)
\(174\) 0 0
\(175\) 2.57953 0.588234i 0.194994 0.0444663i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.40797 2.43867i −0.105236 0.182275i 0.808598 0.588361i \(-0.200227\pi\)
−0.913835 + 0.406086i \(0.866893\pi\)
\(180\) 0 0
\(181\) 11.5922 0.861638 0.430819 0.902438i \(-0.358225\pi\)
0.430819 + 0.902438i \(0.358225\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.79919 4.84834i −0.205801 0.356457i
\(186\) 0 0
\(187\) 16.3859 28.3812i 1.19825 2.07544i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.27279 + 10.8648i −0.453883 + 0.786149i −0.998623 0.0524561i \(-0.983295\pi\)
0.544740 + 0.838605i \(0.316628\pi\)
\(192\) 0 0
\(193\) 6.14867 + 10.6498i 0.442591 + 0.766590i 0.997881 0.0650668i \(-0.0207261\pi\)
−0.555290 + 0.831657i \(0.687393\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7518 0.908525 0.454262 0.890868i \(-0.349903\pi\)
0.454262 + 0.890868i \(0.349903\pi\)
\(198\) 0 0
\(199\) −0.0635238 0.110027i −0.00450309 0.00779957i 0.863765 0.503895i \(-0.168100\pi\)
−0.868268 + 0.496095i \(0.834767\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.323790 + 1.04898i −0.0227256 + 0.0736238i
\(204\) 0 0
\(205\) −0.162795 + 0.281970i −0.0113701 + 0.0196936i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 40.9553 2.83294
\(210\) 0 0
\(211\) 16.5909 1.14217 0.571083 0.820892i \(-0.306523\pi\)
0.571083 + 0.820892i \(0.306523\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.95190 + 3.38080i −0.133119 + 0.230568i
\(216\) 0 0
\(217\) 14.4864 3.30348i 0.983404 0.224255i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 20.3006 + 35.1616i 1.36556 + 2.36523i
\(222\) 0 0
\(223\) −3.00438 −0.201188 −0.100594 0.994928i \(-0.532074\pi\)
−0.100594 + 0.994928i \(0.532074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.270991 0.469370i −0.0179863 0.0311532i 0.856892 0.515496i \(-0.172392\pi\)
−0.874878 + 0.484343i \(0.839059\pi\)
\(228\) 0 0
\(229\) 3.33094 5.76935i 0.220114 0.381249i −0.734728 0.678362i \(-0.762690\pi\)
0.954843 + 0.297112i \(0.0960236\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.1383 22.7562i 0.860717 1.49081i −0.0105206 0.999945i \(-0.503349\pi\)
0.871238 0.490861i \(-0.163318\pi\)
\(234\) 0 0
\(235\) −4.86864 8.43273i −0.317595 0.550091i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −21.1831 −1.37022 −0.685109 0.728440i \(-0.740246\pi\)
−0.685109 + 0.728440i \(0.740246\pi\)
\(240\) 0 0
\(241\) 0.206732 + 0.358071i 0.0133168 + 0.0230654i 0.872607 0.488423i \(-0.162428\pi\)
−0.859290 + 0.511488i \(0.829094\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.30796 3.03474i 0.403001 0.193882i
\(246\) 0 0
\(247\) −25.3699 + 43.9420i −1.61425 + 2.79596i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 21.7010 1.36976 0.684879 0.728657i \(-0.259855\pi\)
0.684879 + 0.728657i \(0.259855\pi\)
\(252\) 0 0
\(253\) −43.0622 −2.70730
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.14755 + 10.6479i −0.383473 + 0.664195i −0.991556 0.129678i \(-0.958606\pi\)
0.608083 + 0.793874i \(0.291939\pi\)
\(258\) 0 0
\(259\) −10.0726 10.8599i −0.625879 0.674799i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.41915 + 4.19010i 0.149171 + 0.258373i 0.930921 0.365219i \(-0.119006\pi\)
−0.781750 + 0.623592i \(0.785673\pi\)
\(264\) 0 0
\(265\) 1.85426 0.113906
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.01754 5.22653i −0.183983 0.318667i 0.759251 0.650798i \(-0.225566\pi\)
−0.943233 + 0.332131i \(0.892232\pi\)
\(270\) 0 0
\(271\) 14.0748 24.3782i 0.854980 1.48087i −0.0216828 0.999765i \(-0.506902\pi\)
0.876663 0.481105i \(-0.159764\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.39788 + 4.15326i −0.144598 + 0.250451i
\(276\) 0 0
\(277\) −2.51943 4.36378i −0.151378 0.262194i 0.780356 0.625335i \(-0.215038\pi\)
−0.931734 + 0.363141i \(0.881704\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.05865 0.421084 0.210542 0.977585i \(-0.432477\pi\)
0.210542 + 0.977585i \(0.432477\pi\)
\(282\) 0 0
\(283\) 11.4422 + 19.8186i 0.680171 + 1.17809i 0.974928 + 0.222519i \(0.0714278\pi\)
−0.294758 + 0.955572i \(0.595239\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.254071 + 0.823112i −0.0149974 + 0.0485868i
\(288\) 0 0
\(289\) −14.8482 + 25.7178i −0.873421 + 1.51281i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.8308 −1.10011 −0.550053 0.835130i \(-0.685392\pi\)
−0.550053 + 0.835130i \(0.685392\pi\)
\(294\) 0 0
\(295\) −9.17660 −0.534282
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 26.6751 46.2026i 1.54266 2.67196i
\(300\) 0 0
\(301\) −3.04630 + 9.86905i −0.175586 + 0.568842i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.33063 10.9650i −0.362491 0.627852i
\(306\) 0 0
\(307\) −17.1788 −0.980449 −0.490224 0.871596i \(-0.663085\pi\)
−0.490224 + 0.871596i \(0.663085\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.19415 5.53243i −0.181124 0.313715i 0.761140 0.648588i \(-0.224640\pi\)
−0.942263 + 0.334873i \(0.891307\pi\)
\(312\) 0 0
\(313\) 0.754520 1.30687i 0.0426480 0.0738685i −0.843913 0.536479i \(-0.819754\pi\)
0.886561 + 0.462611i \(0.153087\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.4093 + 23.2255i −0.753140 + 1.30448i 0.193154 + 0.981168i \(0.438128\pi\)
−0.946294 + 0.323308i \(0.895205\pi\)
\(318\) 0 0
\(319\) −0.994965 1.72333i −0.0557073 0.0964879i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −58.3571 −3.24708
\(324\) 0 0
\(325\) −2.97076 5.14550i −0.164788 0.285421i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −17.5192 18.8886i −0.965866 1.04136i
\(330\) 0 0
\(331\) −0.780259 + 1.35145i −0.0428869 + 0.0742823i −0.886672 0.462399i \(-0.846989\pi\)
0.843785 + 0.536681i \(0.180322\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.68204 −0.146535
\(336\) 0 0
\(337\) 22.7841 1.24113 0.620564 0.784156i \(-0.286904\pi\)
0.620564 + 0.784156i \(0.286904\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.4663 + 23.3244i −0.729242 + 1.26308i
\(342\) 0 0
\(343\) 14.4864 11.5388i 0.782194 0.623035i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.74622 + 3.02453i 0.0937417 + 0.162365i 0.909083 0.416616i \(-0.136784\pi\)
−0.815341 + 0.578981i \(0.803451\pi\)
\(348\) 0 0
\(349\) 0.192385 0.0102981 0.00514907 0.999987i \(-0.498361\pi\)
0.00514907 + 0.999987i \(0.498361\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.69716 11.5998i −0.356454 0.617396i 0.630912 0.775854i \(-0.282681\pi\)
−0.987366 + 0.158459i \(0.949348\pi\)
\(354\) 0 0
\(355\) −2.58830 + 4.48307i −0.137373 + 0.237936i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.50465 16.4625i 0.501636 0.868859i −0.498362 0.866969i \(-0.666065\pi\)
0.999998 0.00189015i \(-0.000601655\pi\)
\(360\) 0 0
\(361\) −26.9649 46.7046i −1.41921 2.45814i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.80908 −0.461089
\(366\) 0 0
\(367\) 0.773990 + 1.34059i 0.0404019 + 0.0699782i 0.885519 0.464603i \(-0.153803\pi\)
−0.845117 + 0.534581i \(0.820469\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.78311 1.09074i 0.248327 0.0566282i
\(372\) 0 0
\(373\) 15.0952 26.1457i 0.781601 1.35377i −0.149408 0.988776i \(-0.547737\pi\)
0.931009 0.364997i \(-0.118930\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.46534 0.126971
\(378\) 0 0
\(379\) −18.2959 −0.939796 −0.469898 0.882721i \(-0.655709\pi\)
−0.469898 + 0.882721i \(0.655709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.3590 21.4064i 0.631514 1.09382i −0.355728 0.934590i \(-0.615767\pi\)
0.987242 0.159226i \(-0.0508997\pi\)
\(384\) 0 0
\(385\) −3.74233 + 12.1240i −0.190727 + 0.617895i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.2496 + 19.4848i 0.570375 + 0.987918i 0.996527 + 0.0832670i \(0.0265354\pi\)
−0.426152 + 0.904651i \(0.640131\pi\)
\(390\) 0 0
\(391\) 61.3592 3.10307
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.81624 3.14582i −0.0913851 0.158284i
\(396\) 0 0
\(397\) 15.3594 26.6032i 0.770865 1.33518i −0.166225 0.986088i \(-0.553158\pi\)
0.937090 0.349089i \(-0.113509\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.3218 24.8062i 0.715199 1.23876i −0.247684 0.968841i \(-0.579669\pi\)
0.962883 0.269920i \(-0.0869972\pi\)
\(402\) 0 0
\(403\) −16.6835 28.8967i −0.831066 1.43945i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 26.8485 1.33083
\(408\) 0 0
\(409\) −5.07506 8.79027i −0.250946 0.434651i 0.712841 0.701326i \(-0.247408\pi\)
−0.963786 + 0.266675i \(0.914075\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −23.6713 + 5.39799i −1.16479 + 0.265618i
\(414\) 0 0
\(415\) 4.53809 7.86021i 0.222766 0.385842i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.59691 0.126868 0.0634338 0.997986i \(-0.479795\pi\)
0.0634338 + 0.997986i \(0.479795\pi\)
\(420\) 0 0
\(421\) −9.28805 −0.452672 −0.226336 0.974049i \(-0.572675\pi\)
−0.226336 + 0.974049i \(0.572675\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.41674 5.91796i 0.165736 0.287063i
\(426\) 0 0
\(427\) −22.7800 24.5606i −1.10240 1.18857i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.8655 + 32.6760i 0.908718 + 1.57395i 0.815847 + 0.578268i \(0.196271\pi\)
0.0928719 + 0.995678i \(0.470395\pi\)
\(432\) 0 0
\(433\) 36.7159 1.76445 0.882226 0.470826i \(-0.156044\pi\)
0.882226 + 0.470826i \(0.156044\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 38.3408 + 66.4082i 1.83409 + 3.17673i
\(438\) 0 0
\(439\) 8.66191 15.0029i 0.413410 0.716048i −0.581850 0.813296i \(-0.697671\pi\)
0.995260 + 0.0972486i \(0.0310042\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.30542 + 5.72516i −0.157045 + 0.272011i −0.933802 0.357790i \(-0.883530\pi\)
0.776756 + 0.629801i \(0.216864\pi\)
\(444\) 0 0
\(445\) −0.646788 1.12027i −0.0306607 0.0531059i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.2861 0.910168 0.455084 0.890449i \(-0.349609\pi\)
0.455084 + 0.890449i \(0.349609\pi\)
\(450\) 0 0
\(451\) −0.780729 1.35226i −0.0367631 0.0636755i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.6899 11.5255i −0.501151 0.540323i
\(456\) 0 0
\(457\) 9.51700 16.4839i 0.445186 0.771086i −0.552879 0.833262i \(-0.686471\pi\)
0.998065 + 0.0621761i \(0.0198041\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.71780 −0.219730 −0.109865 0.993947i \(-0.535042\pi\)
−0.109865 + 0.993947i \(0.535042\pi\)
\(462\) 0 0
\(463\) 25.3128 1.17639 0.588193 0.808721i \(-0.299840\pi\)
0.588193 + 0.808721i \(0.299840\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.18992 + 14.1854i −0.378984 + 0.656420i −0.990915 0.134492i \(-0.957060\pi\)
0.611931 + 0.790911i \(0.290393\pi\)
\(468\) 0 0
\(469\) −6.91840 + 1.57767i −0.319462 + 0.0728499i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.36088 16.2135i −0.430414 0.745498i
\(474\) 0 0
\(475\) 8.53989 0.391837
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.07541 + 8.79086i 0.231901 + 0.401665i 0.958368 0.285537i \(-0.0921720\pi\)
−0.726466 + 0.687202i \(0.758839\pi\)
\(480\) 0 0
\(481\) −16.6314 + 28.8065i −0.758328 + 1.31346i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.00504 8.66898i 0.227267 0.393638i
\(486\) 0 0
\(487\) −4.28938 7.42942i −0.194370 0.336659i 0.752324 0.658794i \(-0.228933\pi\)
−0.946694 + 0.322134i \(0.895600\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −31.2669 −1.41106 −0.705528 0.708682i \(-0.749290\pi\)
−0.705528 + 0.708682i \(0.749290\pi\)
\(492\) 0 0
\(493\) 1.41772 + 2.45557i 0.0638510 + 0.110593i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.03951 + 13.0867i −0.181197 + 0.587020i
\(498\) 0 0
\(499\) 3.76279 6.51734i 0.168446 0.291756i −0.769428 0.638734i \(-0.779459\pi\)
0.937874 + 0.346977i \(0.112792\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.11292 −0.317149 −0.158575 0.987347i \(-0.550690\pi\)
−0.158575 + 0.987347i \(0.550690\pi\)
\(504\) 0 0
\(505\) −1.14152 −0.0507972
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.57400 + 13.1185i −0.335711 + 0.581469i −0.983621 0.180248i \(-0.942310\pi\)
0.647910 + 0.761717i \(0.275643\pi\)
\(510\) 0 0
\(511\) −22.7233 + 5.18181i −1.00522 + 0.229230i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.58799 11.4107i −0.290302 0.502817i
\(516\) 0 0
\(517\) 46.6977 2.05376
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.76801 + 11.7225i 0.296512 + 0.513574i 0.975336 0.220728i \(-0.0708432\pi\)
−0.678823 + 0.734302i \(0.737510\pi\)
\(522\) 0 0
\(523\) 11.3787 19.7085i 0.497557 0.861794i −0.502439 0.864613i \(-0.667564\pi\)
0.999996 + 0.00281888i \(0.000897277\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 19.1881 33.2348i 0.835847 1.44773i
\(528\) 0 0
\(529\) −28.8132 49.9059i −1.25275 2.16982i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.93450 0.0837926
\(534\) 0 0
\(535\) 4.41674 + 7.65001i 0.190952 + 0.330739i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.52171 + 33.4755i −0.108618 + 1.44189i
\(540\) 0 0
\(541\) −10.8916 + 18.8648i −0.468267 + 0.811062i −0.999342 0.0362623i \(-0.988455\pi\)
0.531075 + 0.847325i \(0.321788\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11.5155 −0.493270
\(546\) 0 0
\(547\) −4.26935 −0.182544 −0.0912721 0.995826i \(-0.529093\pi\)
−0.0912721 + 0.995826i \(0.529093\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.77175 + 3.06876i −0.0754790 + 0.130733i
\(552\) 0 0
\(553\) −6.53554 7.04637i −0.277919 0.299642i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.3255 24.8125i −0.606991 1.05134i −0.991733 0.128315i \(-0.959043\pi\)
0.384743 0.923024i \(-0.374290\pi\)
\(558\) 0 0
\(559\) 23.1945 0.981024
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10.0489 17.4053i −0.423512 0.733544i 0.572768 0.819717i \(-0.305870\pi\)
−0.996280 + 0.0861730i \(0.972536\pi\)
\(564\) 0 0
\(565\) 0.560679 0.971124i 0.0235879 0.0408555i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.32186 9.21773i 0.223104 0.386427i −0.732645 0.680611i \(-0.761714\pi\)
0.955749 + 0.294184i \(0.0950478\pi\)
\(570\) 0 0
\(571\) −4.75837 8.24174i −0.199132 0.344906i 0.749115 0.662439i \(-0.230479\pi\)
−0.948247 + 0.317533i \(0.897145\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.97922 −0.374459
\(576\) 0 0
\(577\) −8.84321 15.3169i −0.368148 0.637650i 0.621128 0.783709i \(-0.286675\pi\)
−0.989276 + 0.146058i \(0.953341\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.08251 22.9451i 0.293832 0.951924i
\(582\) 0 0
\(583\) −4.44629 + 7.70120i −0.184146 + 0.318951i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.4738 −0.679946 −0.339973 0.940435i \(-0.610418\pi\)
−0.339973 + 0.940435i \(0.610418\pi\)
\(588\) 0 0
\(589\) 47.9594 1.97613
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.41612 9.38099i 0.222413 0.385231i −0.733127 0.680092i \(-0.761940\pi\)
0.955540 + 0.294861i \(0.0952732\pi\)
\(594\) 0 0
\(595\) 5.33243 17.2754i 0.218608 0.708222i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11.3633 + 19.6818i 0.464292 + 0.804177i 0.999169 0.0407528i \(-0.0129756\pi\)
−0.534878 + 0.844930i \(0.679642\pi\)
\(600\) 0 0
\(601\) −3.36346 −0.137198 −0.0685991 0.997644i \(-0.521853\pi\)
−0.0685991 + 0.997644i \(0.521853\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.99969 10.3918i −0.243922 0.422486i
\(606\) 0 0
\(607\) −12.6564 + 21.9215i −0.513707 + 0.889767i 0.486166 + 0.873866i \(0.338395\pi\)
−0.999874 + 0.0159007i \(0.994938\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −28.9271 + 50.1032i −1.17026 + 2.02696i
\(612\) 0 0
\(613\) 7.97790 + 13.8181i 0.322224 + 0.558109i 0.980947 0.194277i \(-0.0622361\pi\)
−0.658722 + 0.752386i \(0.728903\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.2040 1.49778 0.748888 0.662697i \(-0.230588\pi\)
0.748888 + 0.662697i \(0.230588\pi\)
\(618\) 0 0
\(619\) 19.6698 + 34.0690i 0.790594 + 1.36935i 0.925600 + 0.378504i \(0.123561\pi\)
−0.135006 + 0.990845i \(0.543105\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.32739 2.50931i −0.0932450 0.100533i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −38.2564 −1.52538
\(630\) 0 0
\(631\) 0.331822 0.0132096 0.00660481 0.999978i \(-0.497898\pi\)
0.00660481 + 0.999978i \(0.497898\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.77337 4.80362i 0.110058 0.190626i
\(636\) 0 0
\(637\) −34.3547 23.4421i −1.36118 0.928812i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −14.8039 25.6411i −0.584718 1.01276i −0.994911 0.100763i \(-0.967872\pi\)
0.410192 0.911999i \(-0.365462\pi\)
\(642\) 0 0
\(643\) −3.27639 −0.129208 −0.0646042 0.997911i \(-0.520578\pi\)
−0.0646042 + 0.997911i \(0.520578\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.4487 18.0976i −0.410779 0.711490i 0.584196 0.811613i \(-0.301410\pi\)
−0.994975 + 0.100122i \(0.968077\pi\)
\(648\) 0 0
\(649\) 22.0044 38.1128i 0.863749 1.49606i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.93656 + 10.2824i −0.232315 + 0.402382i −0.958489 0.285129i \(-0.907963\pi\)
0.726174 + 0.687511i \(0.241297\pi\)
\(654\) 0 0
\(655\) 2.19042 + 3.79391i 0.0855866 + 0.148240i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14.5722 0.567653 0.283827 0.958876i \(-0.408396\pi\)
0.283827 + 0.958876i \(0.408396\pi\)
\(660\) 0 0
\(661\) −8.37367 14.5036i −0.325698 0.564126i 0.655955 0.754800i \(-0.272266\pi\)
−0.981653 + 0.190674i \(0.938933\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 22.0289 5.02346i 0.854245 0.194801i
\(666\) 0 0
\(667\) 1.86289 3.22663i 0.0721315 0.124935i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 60.7204 2.34409
\(672\) 0 0
\(673\) 41.7595 1.60971 0.804855 0.593471i \(-0.202243\pi\)
0.804855 + 0.593471i \(0.202243\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13.5380 23.4485i 0.520308 0.901199i −0.479414 0.877589i \(-0.659151\pi\)
0.999721 0.0236102i \(-0.00751605\pi\)
\(678\) 0 0
\(679\) 7.81125 25.3060i 0.299768 0.971156i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −15.5859 26.9955i −0.596377 1.03295i −0.993351 0.115125i \(-0.963273\pi\)
0.396974 0.917830i \(-0.370060\pi\)
\(684\) 0 0
\(685\) 17.5197 0.669394
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.50854 9.54107i −0.209859 0.363486i
\(690\) 0 0
\(691\) 8.16704 14.1457i 0.310689 0.538129i −0.667823 0.744320i \(-0.732774\pi\)
0.978512 + 0.206192i \(0.0661070\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.363604 + 0.629780i −0.0137923 + 0.0238889i
\(696\) 0 0
\(697\) 1.11246 + 1.92683i 0.0421373 + 0.0729840i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 49.6205 1.87414 0.937070 0.349143i \(-0.113527\pi\)
0.937070 + 0.349143i \(0.113527\pi\)
\(702\) 0 0
\(703\) −23.9048 41.4043i −0.901587 1.56159i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.94460 + 0.671484i −0.110743 + 0.0252538i
\(708\) 0 0
\(709\) −9.48953 + 16.4363i −0.356387 + 0.617280i −0.987354 0.158529i \(-0.949325\pi\)
0.630968 + 0.775809i \(0.282658\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −50.4266 −1.88849
\(714\) 0 0
\(715\) 28.4941 1.06562
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.13828 + 15.8280i −0.340800 + 0.590283i −0.984582 0.174926i \(-0.944031\pi\)
0.643781 + 0.765210i \(0.277365\pi\)
\(720\) 0 0
\(721\) −23.7061 25.5591i −0.882862 0.951869i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.207467 0.359344i −0.00770514 0.0133457i
\(726\) 0 0
\(727\) −27.2878 −1.01205 −0.506024 0.862519i \(-0.668885\pi\)
−0.506024 + 0.862519i \(0.668885\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 13.3383 + 23.1026i 0.493334 + 0.854480i
\(732\) 0 0
\(733\) 17.8175 30.8609i 0.658106 1.13987i −0.322999 0.946399i \(-0.604691\pi\)
0.981105 0.193474i \(-0.0619755\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.43121 11.1392i 0.236897 0.410317i
\(738\) 0 0
\(739\) 6.37114 + 11.0351i 0.234366 + 0.405934i 0.959088 0.283107i \(-0.0913652\pi\)
−0.724722 + 0.689041i \(0.758032\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.5025 0.458674 0.229337 0.973347i \(-0.426344\pi\)
0.229337 + 0.973347i \(0.426344\pi\)
\(744\) 0 0
\(745\) −10.5776 18.3209i −0.387533 0.671227i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.8931 + 17.1354i 0.580721 + 0.626113i
\(750\) 0 0
\(751\) 4.50331 7.79997i 0.164328 0.284625i −0.772088 0.635515i \(-0.780788\pi\)
0.936417 + 0.350890i \(0.114121\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.05164 0.293029
\(756\) 0 0
\(757\) 46.1180 1.67619 0.838094 0.545526i \(-0.183670\pi\)
0.838094 + 0.545526i \(0.183670\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.70540 + 4.68588i −0.0980705 + 0.169863i −0.910886 0.412658i \(-0.864600\pi\)
0.812815 + 0.582521i \(0.197934\pi\)
\(762\) 0 0
\(763\) −29.7046 + 6.77382i −1.07538 + 0.245229i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 27.2614 + 47.2182i 0.984353 + 1.70495i
\(768\) 0 0
\(769\) 4.36121 0.157269 0.0786346 0.996904i \(-0.474944\pi\)
0.0786346 + 0.996904i \(0.474944\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.38010 + 7.58655i 0.157541 + 0.272869i 0.933981 0.357322i \(-0.116310\pi\)
−0.776440 + 0.630191i \(0.782977\pi\)
\(774\) 0 0
\(775\) −2.80796 + 4.86353i −0.100865 + 0.174703i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.39026 + 2.40799i −0.0498111 + 0.0862753i
\(780\) 0 0
\(781\) −12.4129 21.4997i −0.444168 0.769321i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −18.6990 −0.667394
\(786\) 0 0
\(787\) 0.0341019 + 0.0590662i 0.00121560 + 0.00210548i 0.866633 0.498947i \(-0.166280\pi\)
−0.865417 + 0.501052i \(0.832946\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.875040 2.83486i 0.0311128 0.100796i
\(792\) 0 0
\(793\) −37.6135 + 65.1485i −1.33569 + 2.31349i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38.0302 −1.34710 −0.673550 0.739142i \(-0.735231\pi\)
−0.673550 + 0.739142i \(0.735231\pi\)
\(798\) 0 0
\(799\) −66.5394 −2.35400
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 21.1232 36.5864i 0.745420 1.29111i
\(804\) 0