Properties

Label 2268.2.l.n.109.7
Level $2268$
Weight $2$
Character 2268.109
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.7
Root \(-1.30887 - 2.01944i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.n.541.7

$q$-expansion

\(f(q)\) \(=\) \(q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} +O(q^{10})\) \(q+2.30201 q^{5} +(-2.14324 + 1.55130i) q^{7} -4.46291 q^{11} +(1.42148 - 2.46208i) q^{13} +(0.115312 - 0.199726i) q^{17} +(-1.49360 - 2.58700i) q^{19} +0.800587 q^{23} +0.299269 q^{25} +(-3.82751 - 6.62944i) q^{29} +(-2.64324 - 4.57822i) q^{31} +(-4.93376 + 3.57112i) q^{35} +(-1.69333 - 2.93293i) q^{37} +(0.899697 - 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +(2.88818 - 5.00247i) q^{47} +(2.18693 - 6.64961i) q^{49} +(4.31905 - 7.48081i) q^{53} -10.2737 q^{55} +(-4.17793 - 7.23638i) q^{59} +(6.58675 - 11.4086i) q^{61} +(3.27227 - 5.66774i) q^{65} +(3.76545 + 6.52195i) q^{67} -8.59672 q^{71} +(-2.29287 + 3.97137i) q^{73} +(9.56507 - 6.92331i) q^{77} +(-4.83657 + 8.37718i) q^{79} +(-8.46521 - 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(-0.944450 - 1.63584i) q^{89} +(0.772852 + 7.48196i) q^{91} +(-3.43829 - 5.95530i) q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} - 10 q^{43} - 20 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 2.30201 1.02949 0.514746 0.857343i \(-0.327886\pi\)
0.514746 + 0.857343i \(0.327886\pi\)
\(6\) 0 0
\(7\) −2.14324 + 1.55130i −0.810068 + 0.586337i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.46291 −1.34562 −0.672809 0.739816i \(-0.734912\pi\)
−0.672809 + 0.739816i \(0.734912\pi\)
\(12\) 0 0
\(13\) 1.42148 2.46208i 0.394248 0.682858i −0.598757 0.800931i \(-0.704338\pi\)
0.993005 + 0.118073i \(0.0376717\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.115312 0.199726i 0.0279673 0.0484408i −0.851703 0.524025i \(-0.824430\pi\)
0.879670 + 0.475584i \(0.157763\pi\)
\(18\) 0 0
\(19\) −1.49360 2.58700i −0.342656 0.593498i 0.642269 0.766479i \(-0.277993\pi\)
−0.984925 + 0.172982i \(0.944660\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.800587 0.166934 0.0834670 0.996511i \(-0.473401\pi\)
0.0834670 + 0.996511i \(0.473401\pi\)
\(24\) 0 0
\(25\) 0.299269 0.0598538
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.82751 6.62944i −0.710750 1.23106i −0.964576 0.263806i \(-0.915022\pi\)
0.253825 0.967250i \(-0.418311\pi\)
\(30\) 0 0
\(31\) −2.64324 4.57822i −0.474739 0.822273i 0.524842 0.851200i \(-0.324124\pi\)
−0.999582 + 0.0289268i \(0.990791\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.93376 + 3.57112i −0.833958 + 0.603629i
\(36\) 0 0
\(37\) −1.69333 2.93293i −0.278382 0.482171i 0.692601 0.721321i \(-0.256465\pi\)
−0.970983 + 0.239150i \(0.923131\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.899697 1.55832i 0.140509 0.243369i −0.787179 0.616724i \(-0.788459\pi\)
0.927688 + 0.373355i \(0.121793\pi\)
\(42\) 0 0
\(43\) 4.85860 + 8.41533i 0.740929 + 1.28333i 0.952073 + 0.305871i \(0.0989478\pi\)
−0.211144 + 0.977455i \(0.567719\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.88818 5.00247i 0.421284 0.729686i −0.574781 0.818307i \(-0.694913\pi\)
0.996065 + 0.0886214i \(0.0282461\pi\)
\(48\) 0 0
\(49\) 2.18693 6.64961i 0.312419 0.949944i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.31905 7.48081i 0.593267 1.02757i −0.400522 0.916287i \(-0.631171\pi\)
0.993789 0.111281i \(-0.0354954\pi\)
\(54\) 0 0
\(55\) −10.2737 −1.38530
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.17793 7.23638i −0.543920 0.942097i −0.998674 0.0514798i \(-0.983606\pi\)
0.454754 0.890617i \(-0.349727\pi\)
\(60\) 0 0
\(61\) 6.58675 11.4086i 0.843347 1.46072i −0.0437026 0.999045i \(-0.513915\pi\)
0.887049 0.461675i \(-0.152751\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.27227 5.66774i 0.405875 0.702997i
\(66\) 0 0
\(67\) 3.76545 + 6.52195i 0.460023 + 0.796783i 0.998962 0.0455620i \(-0.0145078\pi\)
−0.538939 + 0.842345i \(0.681175\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.59672 −1.02024 −0.510122 0.860102i \(-0.670400\pi\)
−0.510122 + 0.860102i \(0.670400\pi\)
\(72\) 0 0
\(73\) −2.29287 + 3.97137i −0.268360 + 0.464814i −0.968439 0.249252i \(-0.919815\pi\)
0.700078 + 0.714066i \(0.253148\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9.56507 6.92331i 1.09004 0.788985i
\(78\) 0 0
\(79\) −4.83657 + 8.37718i −0.544156 + 0.942506i 0.454503 + 0.890745i \(0.349817\pi\)
−0.998659 + 0.0517612i \(0.983517\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −8.46521 14.6622i −0.929177 1.60938i −0.784701 0.619874i \(-0.787184\pi\)
−0.144476 0.989508i \(-0.546150\pi\)
\(84\) 0 0
\(85\) 0.265450 0.459773i 0.0287921 0.0498694i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.944450 1.63584i −0.100111 0.173398i 0.811619 0.584187i \(-0.198587\pi\)
−0.911730 + 0.410789i \(0.865253\pi\)
\(90\) 0 0
\(91\) 0.772852 + 7.48196i 0.0810169 + 0.784323i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.43829 5.95530i −0.352762 0.611001i
\(96\) 0 0
\(97\) 7.70796 + 13.3506i 0.782624 + 1.35555i 0.930408 + 0.366525i \(0.119453\pi\)
−0.147784 + 0.989020i \(0.547214\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.81488 0.280091 0.140045 0.990145i \(-0.455275\pi\)
0.140045 + 0.990145i \(0.455275\pi\)
\(102\) 0 0
\(103\) 5.11664 0.504158 0.252079 0.967707i \(-0.418886\pi\)
0.252079 + 0.967707i \(0.418886\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.29487 + 2.24278i 0.125180 + 0.216818i 0.921803 0.387658i \(-0.126716\pi\)
−0.796623 + 0.604476i \(0.793383\pi\)
\(108\) 0 0
\(109\) −8.76728 + 15.1854i −0.839753 + 1.45450i 0.0503474 + 0.998732i \(0.483967\pi\)
−0.890101 + 0.455764i \(0.849366\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.21711 14.2325i 0.773001 1.33888i −0.162910 0.986641i \(-0.552088\pi\)
0.935911 0.352236i \(-0.114579\pi\)
\(114\) 0 0
\(115\) 1.84296 0.171857
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.0626945 + 0.606945i 0.00574720 + 0.0556385i
\(120\) 0 0
\(121\) 8.91756 0.810687
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.8211 −0.967873
\(126\) 0 0
\(127\) 8.13145 0.721549 0.360775 0.932653i \(-0.382512\pi\)
0.360775 + 0.932653i \(0.382512\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.5118 1.09316 0.546582 0.837406i \(-0.315929\pi\)
0.546582 + 0.837406i \(0.315929\pi\)
\(132\) 0 0
\(133\) 7.21435 + 3.22752i 0.625564 + 0.279861i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −16.1934 −1.38349 −0.691746 0.722141i \(-0.743158\pi\)
−0.691746 + 0.722141i \(0.743158\pi\)
\(138\) 0 0
\(139\) 3.07212 5.32107i 0.260574 0.451327i −0.705821 0.708391i \(-0.749422\pi\)
0.966395 + 0.257063i \(0.0827549\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −6.34394 + 10.9880i −0.530507 + 0.918866i
\(144\) 0 0
\(145\) −8.81098 15.2611i −0.731712 1.26736i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.71855 −0.632328 −0.316164 0.948705i \(-0.602395\pi\)
−0.316164 + 0.948705i \(0.602395\pi\)
\(150\) 0 0
\(151\) −14.9176 −1.21397 −0.606987 0.794712i \(-0.707622\pi\)
−0.606987 + 0.794712i \(0.707622\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.08477 10.5391i −0.488740 0.846523i
\(156\) 0 0
\(157\) 0.128610 + 0.222759i 0.0102642 + 0.0177781i 0.871112 0.491085i \(-0.163399\pi\)
−0.860848 + 0.508863i \(0.830066\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.71585 + 1.24195i −0.135228 + 0.0978795i
\(162\) 0 0
\(163\) −6.28748 10.8902i −0.492473 0.852989i 0.507489 0.861658i \(-0.330574\pi\)
−0.999962 + 0.00866931i \(0.997240\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.8470 + 18.7875i −0.839363 + 1.45382i 0.0510657 + 0.998695i \(0.483738\pi\)
−0.890428 + 0.455123i \(0.849595\pi\)
\(168\) 0 0
\(169\) 2.45878 + 4.25873i 0.189137 + 0.327595i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.88024 11.9169i 0.523095 0.906026i −0.476544 0.879151i \(-0.658111\pi\)
0.999639 0.0268759i \(-0.00855590\pi\)
\(174\) 0 0
\(175\) −0.641405 + 0.464256i −0.0484856 + 0.0350945i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.448262 0.776412i 0.0335046 0.0580317i −0.848787 0.528735i \(-0.822666\pi\)
0.882292 + 0.470703i \(0.156000\pi\)
\(180\) 0 0
\(181\) −17.4613 −1.29788 −0.648942 0.760838i \(-0.724788\pi\)
−0.648942 + 0.760838i \(0.724788\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.89807 6.75165i −0.286592 0.496391i
\(186\) 0 0
\(187\) −0.514627 + 0.891361i −0.0376333 + 0.0651827i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.734511 + 1.27221i −0.0531474 + 0.0920540i −0.891375 0.453266i \(-0.850259\pi\)
0.838228 + 0.545320i \(0.183592\pi\)
\(192\) 0 0
\(193\) −3.25165 5.63202i −0.234059 0.405402i 0.724940 0.688812i \(-0.241868\pi\)
−0.958999 + 0.283410i \(0.908534\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.9521 0.851552 0.425776 0.904828i \(-0.360001\pi\)
0.425776 + 0.904828i \(0.360001\pi\)
\(198\) 0 0
\(199\) 9.73886 16.8682i 0.690369 1.19575i −0.281348 0.959606i \(-0.590781\pi\)
0.971717 0.236149i \(-0.0758852\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.4875 + 8.27084i 1.29757 + 0.580499i
\(204\) 0 0
\(205\) 2.07112 3.58728i 0.144653 0.250546i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.66581 + 11.5455i 0.461084 + 0.798621i
\(210\) 0 0
\(211\) 6.43611 11.1477i 0.443080 0.767437i −0.554836 0.831960i \(-0.687219\pi\)
0.997916 + 0.0645225i \(0.0205524\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.1846 + 19.3722i 0.762780 + 1.32117i
\(216\) 0 0
\(217\) 12.7673 + 5.71176i 0.866700 + 0.387739i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.327828 0.567815i −0.0220521 0.0381954i
\(222\) 0 0
\(223\) −4.92331 8.52743i −0.329690 0.571039i 0.652761 0.757564i \(-0.273611\pi\)
−0.982450 + 0.186525i \(0.940277\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −24.4507 −1.62285 −0.811426 0.584455i \(-0.801309\pi\)
−0.811426 + 0.584455i \(0.801309\pi\)
\(228\) 0 0
\(229\) −22.0037 −1.45404 −0.727022 0.686615i \(-0.759096\pi\)
−0.727022 + 0.686615i \(0.759096\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.8179 18.7372i −0.708706 1.22752i −0.965337 0.261006i \(-0.915946\pi\)
0.256631 0.966510i \(-0.417388\pi\)
\(234\) 0 0
\(235\) 6.64863 11.5158i 0.433709 0.751206i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.86360 15.3522i 0.573338 0.993051i −0.422882 0.906185i \(-0.638981\pi\)
0.996220 0.0868662i \(-0.0276853\pi\)
\(240\) 0 0
\(241\) 4.31774 0.278130 0.139065 0.990283i \(-0.455590\pi\)
0.139065 + 0.990283i \(0.455590\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.03435 15.3075i 0.321633 0.977960i
\(246\) 0 0
\(247\) −8.49252 −0.540366
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.2938 −0.649741 −0.324870 0.945759i \(-0.605321\pi\)
−0.324870 + 0.945759i \(0.605321\pi\)
\(252\) 0 0
\(253\) −3.57295 −0.224629
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.7914 −0.735525 −0.367763 0.929920i \(-0.619876\pi\)
−0.367763 + 0.929920i \(0.619876\pi\)
\(258\) 0 0
\(259\) 8.17907 + 3.65911i 0.508222 + 0.227366i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5.18719 −0.319856 −0.159928 0.987129i \(-0.551126\pi\)
−0.159928 + 0.987129i \(0.551126\pi\)
\(264\) 0 0
\(265\) 9.94251 17.2209i 0.610763 1.05787i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.6103 25.3058i 0.890805 1.54292i 0.0518936 0.998653i \(-0.483474\pi\)
0.838912 0.544268i \(-0.183192\pi\)
\(270\) 0 0
\(271\) 10.2801 + 17.8056i 0.624470 + 1.08161i 0.988643 + 0.150283i \(0.0480184\pi\)
−0.364173 + 0.931331i \(0.618648\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.33561 −0.0805403
\(276\) 0 0
\(277\) −11.9567 −0.718407 −0.359203 0.933259i \(-0.616952\pi\)
−0.359203 + 0.933259i \(0.616952\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.9166 + 25.8363i 0.889850 + 1.54126i 0.840052 + 0.542506i \(0.182524\pi\)
0.0497975 + 0.998759i \(0.484142\pi\)
\(282\) 0 0
\(283\) 4.78547 + 8.28868i 0.284467 + 0.492711i 0.972480 0.232988i \(-0.0748502\pi\)
−0.688013 + 0.725698i \(0.741517\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.489161 + 4.73555i 0.0288742 + 0.279531i
\(288\) 0 0
\(289\) 8.47341 + 14.6764i 0.498436 + 0.863316i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.41014 + 12.8347i −0.432905 + 0.749813i −0.997122 0.0758132i \(-0.975845\pi\)
0.564217 + 0.825626i \(0.309178\pi\)
\(294\) 0 0
\(295\) −9.61765 16.6583i −0.559961 0.969881i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.13802 1.97111i 0.0658134 0.113992i
\(300\) 0 0
\(301\) −23.4678 10.4989i −1.35266 0.605147i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 15.1628 26.2627i 0.868219 1.50380i
\(306\) 0 0
\(307\) −5.88207 −0.335708 −0.167854 0.985812i \(-0.553684\pi\)
−0.167854 + 0.985812i \(0.553684\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.11753 + 14.0600i 0.460303 + 0.797268i 0.998976 0.0452468i \(-0.0144074\pi\)
−0.538673 + 0.842515i \(0.681074\pi\)
\(312\) 0 0
\(313\) −8.84480 + 15.3196i −0.499937 + 0.865917i −1.00000 7.22344e-5i \(-0.999977\pi\)
0.500063 + 0.865989i \(0.333310\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.64009 + 4.57276i −0.148282 + 0.256832i −0.930593 0.366057i \(-0.880708\pi\)
0.782311 + 0.622889i \(0.214041\pi\)
\(318\) 0 0
\(319\) 17.0818 + 29.5866i 0.956398 + 1.65653i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.688922 −0.0383326
\(324\) 0 0
\(325\) 0.425406 0.736824i 0.0235973 0.0408716i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.57029 + 15.2019i 0.0865727 + 0.838109i
\(330\) 0 0
\(331\) 7.80358 13.5162i 0.428923 0.742917i −0.567855 0.823129i \(-0.692226\pi\)
0.996778 + 0.0802120i \(0.0255597\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.66812 + 15.0136i 0.473590 + 0.820282i
\(336\) 0 0
\(337\) −3.77185 + 6.53303i −0.205466 + 0.355877i −0.950281 0.311394i \(-0.899204\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11.7965 + 20.4322i 0.638818 + 1.10646i
\(342\) 0 0
\(343\) 5.62843 + 17.6443i 0.303907 + 0.952702i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.4502 23.2963i −0.722042 1.25061i −0.960180 0.279382i \(-0.909870\pi\)
0.238138 0.971231i \(-0.423463\pi\)
\(348\) 0 0
\(349\) 7.00100 + 12.1261i 0.374755 + 0.649095i 0.990290 0.139014i \(-0.0443934\pi\)
−0.615535 + 0.788109i \(0.711060\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.3311 1.61436 0.807180 0.590306i \(-0.200993\pi\)
0.807180 + 0.590306i \(0.200993\pi\)
\(354\) 0 0
\(355\) −19.7898 −1.05033
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.99876 12.1222i −0.369381 0.639786i 0.620088 0.784532i \(-0.287097\pi\)
−0.989469 + 0.144746i \(0.953763\pi\)
\(360\) 0 0
\(361\) 5.03830 8.72659i 0.265174 0.459294i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.27822 + 9.14215i −0.276275 + 0.478522i
\(366\) 0 0
\(367\) −2.50330 −0.130671 −0.0653356 0.997863i \(-0.520812\pi\)
−0.0653356 + 0.997863i \(0.520812\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.34824 + 22.7333i 0.121915 + 1.18025i
\(372\) 0 0
\(373\) 17.6062 0.911616 0.455808 0.890078i \(-0.349350\pi\)
0.455808 + 0.890078i \(0.349350\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −21.7629 −1.12085
\(378\) 0 0
\(379\) 10.5474 0.541781 0.270891 0.962610i \(-0.412682\pi\)
0.270891 + 0.962610i \(0.412682\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 21.6837 1.10798 0.553992 0.832522i \(-0.313104\pi\)
0.553992 + 0.832522i \(0.313104\pi\)
\(384\) 0 0
\(385\) 22.0189 15.9376i 1.12219 0.812254i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.9330 0.706434 0.353217 0.935541i \(-0.385088\pi\)
0.353217 + 0.935541i \(0.385088\pi\)
\(390\) 0 0
\(391\) 0.0923174 0.159898i 0.00466869 0.00808641i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −11.1338 + 19.2844i −0.560204 + 0.970303i
\(396\) 0 0
\(397\) 13.9542 + 24.1694i 0.700342 + 1.21303i 0.968346 + 0.249610i \(0.0803025\pi\)
−0.268004 + 0.963418i \(0.586364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −34.9049 −1.74307 −0.871534 0.490335i \(-0.836874\pi\)
−0.871534 + 0.490335i \(0.836874\pi\)
\(402\) 0 0
\(403\) −15.0293 −0.748660
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.55717 + 13.0894i 0.374595 + 0.648818i
\(408\) 0 0
\(409\) 10.3369 + 17.9041i 0.511128 + 0.885300i 0.999917 + 0.0128979i \(0.00410563\pi\)
−0.488789 + 0.872402i \(0.662561\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 20.1801 + 9.02806i 0.992998 + 0.444242i
\(414\) 0 0
\(415\) −19.4870 33.7525i −0.956581 1.65685i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.9859 + 34.6166i −0.976376 + 1.69113i −0.301061 + 0.953605i \(0.597341\pi\)
−0.675316 + 0.737529i \(0.735993\pi\)
\(420\) 0 0
\(421\) −12.5082 21.6649i −0.609614 1.05588i −0.991304 0.131592i \(-0.957991\pi\)
0.381690 0.924290i \(-0.375342\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.0345093 0.0597719i 0.00167395 0.00289936i
\(426\) 0 0
\(427\) 3.58118 + 34.6693i 0.173305 + 1.67777i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.05181 + 12.2141i −0.339674 + 0.588332i −0.984371 0.176106i \(-0.943650\pi\)
0.644698 + 0.764438i \(0.276983\pi\)
\(432\) 0 0
\(433\) 1.58941 0.0763821 0.0381911 0.999270i \(-0.487840\pi\)
0.0381911 + 0.999270i \(0.487840\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.19576 2.07112i −0.0572009 0.0990749i
\(438\) 0 0
\(439\) 12.1884 21.1109i 0.581721 1.00757i −0.413555 0.910479i \(-0.635713\pi\)
0.995276 0.0970905i \(-0.0309536\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.28200 + 16.0769i −0.441001 + 0.763836i −0.997764 0.0668352i \(-0.978710\pi\)
0.556763 + 0.830671i \(0.312043\pi\)
\(444\) 0 0
\(445\) −2.17414 3.76572i −0.103064 0.178512i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 21.4616 1.01284 0.506418 0.862288i \(-0.330969\pi\)
0.506418 + 0.862288i \(0.330969\pi\)
\(450\) 0 0
\(451\) −4.01527 + 6.95465i −0.189072 + 0.327482i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.77912 + 17.2236i 0.0834062 + 0.807454i
\(456\) 0 0
\(457\) −7.56371 + 13.1007i −0.353816 + 0.612827i −0.986915 0.161244i \(-0.948449\pi\)
0.633099 + 0.774071i \(0.281783\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.5385 + 28.6455i 0.770273 + 1.33415i 0.937413 + 0.348219i \(0.113213\pi\)
−0.167140 + 0.985933i \(0.553453\pi\)
\(462\) 0 0
\(463\) −13.4223 + 23.2481i −0.623788 + 1.08043i 0.364986 + 0.931013i \(0.381074\pi\)
−0.988774 + 0.149419i \(0.952260\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.93579 + 10.2811i 0.274675 + 0.475752i 0.970053 0.242893i \(-0.0780963\pi\)
−0.695378 + 0.718644i \(0.744763\pi\)
\(468\) 0 0
\(469\) −18.1878 8.13674i −0.839833 0.375720i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −21.6835 37.5569i −0.997007 1.72687i
\(474\) 0 0
\(475\) −0.446989 0.774208i −0.0205093 0.0355231i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.4395 −0.796830 −0.398415 0.917205i \(-0.630440\pi\)
−0.398415 + 0.917205i \(0.630440\pi\)
\(480\) 0 0
\(481\) −9.62815 −0.439006
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.7438 + 30.7332i 0.805706 + 1.39552i
\(486\) 0 0
\(487\) 18.3889 31.8504i 0.833279 1.44328i −0.0621458 0.998067i \(-0.519794\pi\)
0.895424 0.445214i \(-0.146872\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.54050 + 7.86437i −0.204910 + 0.354914i −0.950104 0.311933i \(-0.899023\pi\)
0.745194 + 0.666847i \(0.232357\pi\)
\(492\) 0 0
\(493\) −1.76543 −0.0795110
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 18.4248 13.3361i 0.826466 0.598206i
\(498\) 0 0
\(499\) 6.82522 0.305539 0.152769 0.988262i \(-0.451181\pi\)
0.152769 + 0.988262i \(0.451181\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.09211 −0.182458 −0.0912291 0.995830i \(-0.529080\pi\)
−0.0912291 + 0.995830i \(0.529080\pi\)
\(504\) 0 0
\(505\) 6.47989 0.288351
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 28.7982 1.27646 0.638228 0.769847i \(-0.279668\pi\)
0.638228 + 0.769847i \(0.279668\pi\)
\(510\) 0 0
\(511\) −1.24662 12.0685i −0.0551473 0.533880i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11.7786 0.519026
\(516\) 0 0
\(517\) −12.8897 + 22.3256i −0.566888 + 0.981878i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.92170 10.2567i 0.259434 0.449353i −0.706656 0.707557i \(-0.749797\pi\)
0.966090 + 0.258204i \(0.0831306\pi\)
\(522\) 0 0
\(523\) 6.86664 + 11.8934i 0.300257 + 0.520061i 0.976194 0.216899i \(-0.0695942\pi\)
−0.675937 + 0.736959i \(0.736261\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.21919 −0.0531087
\(528\) 0 0
\(529\) −22.3591 −0.972133
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.55781 4.43025i −0.110791 0.191896i
\(534\) 0 0
\(535\) 2.98081 + 5.16291i 0.128872 + 0.223212i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.76008 + 29.6766i −0.420396 + 1.27826i
\(540\) 0 0
\(541\) 21.7425 + 37.6592i 0.934784 + 1.61909i 0.775019 + 0.631938i \(0.217740\pi\)
0.159765 + 0.987155i \(0.448926\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −20.1824 + 34.9570i −0.864519 + 1.49739i
\(546\) 0 0
\(547\) −11.0307 19.1058i −0.471640 0.816904i 0.527834 0.849348i \(-0.323004\pi\)
−0.999474 + 0.0324437i \(0.989671\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.4336 + 19.8035i −0.487086 + 0.843657i
\(552\) 0 0
\(553\) −2.62961 25.4573i −0.111823 1.08255i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.0925 27.8730i 0.681862 1.18102i −0.292551 0.956250i \(-0.594504\pi\)
0.974412 0.224769i \(-0.0721627\pi\)
\(558\) 0 0
\(559\) 27.6256 1.16844
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.69369 + 2.93355i 0.0713804 + 0.123635i 0.899507 0.436907i \(-0.143926\pi\)
−0.828126 + 0.560542i \(0.810593\pi\)
\(564\) 0 0
\(565\) 18.9159 32.7633i 0.795798 1.37836i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −20.1737 + 34.9419i −0.845726 + 1.46484i 0.0392637 + 0.999229i \(0.487499\pi\)
−0.884989 + 0.465611i \(0.845835\pi\)
\(570\) 0 0
\(571\) 5.21928 + 9.04006i 0.218420 + 0.378315i 0.954325 0.298770i \(-0.0965763\pi\)
−0.735905 + 0.677085i \(0.763243\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.239591 0.00999164
\(576\) 0 0
\(577\) 5.55156 9.61559i 0.231114 0.400302i −0.727022 0.686614i \(-0.759096\pi\)
0.958136 + 0.286312i \(0.0924295\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 40.8884 + 18.2924i 1.69634 + 0.758898i
\(582\) 0 0
\(583\) −19.2755 + 33.3862i −0.798310 + 1.38271i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.3875 + 35.3122i 0.841482 + 1.45749i 0.888642 + 0.458602i \(0.151650\pi\)
−0.0471601 + 0.998887i \(0.515017\pi\)
\(588\) 0 0
\(589\) −7.89589 + 13.6761i −0.325345 + 0.563513i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14.7930 25.6221i −0.607474 1.05218i −0.991655 0.128918i \(-0.958850\pi\)
0.384182 0.923258i \(-0.374484\pi\)
\(594\) 0 0
\(595\) 0.144324 + 1.39720i 0.00591669 + 0.0572794i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.17760 15.8961i −0.374987 0.649496i 0.615338 0.788263i \(-0.289019\pi\)
−0.990325 + 0.138767i \(0.955686\pi\)
\(600\) 0 0
\(601\) 15.9250 + 27.5828i 0.649593 + 1.12513i 0.983220 + 0.182423i \(0.0583939\pi\)
−0.333628 + 0.942705i \(0.608273\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.5283 0.834596
\(606\) 0 0
\(607\) 23.6903 0.961560 0.480780 0.876841i \(-0.340353\pi\)
0.480780 + 0.876841i \(0.340353\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.21099 14.2219i −0.332181 0.575354i
\(612\) 0 0
\(613\) 13.3159 23.0638i 0.537824 0.931539i −0.461197 0.887298i \(-0.652580\pi\)
0.999021 0.0442411i \(-0.0140870\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.72483 + 8.18364i −0.190214 + 0.329461i −0.945321 0.326141i \(-0.894252\pi\)
0.755107 + 0.655602i \(0.227585\pi\)
\(618\) 0 0
\(619\) −36.0947 −1.45077 −0.725385 0.688344i \(-0.758338\pi\)
−0.725385 + 0.688344i \(0.758338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.56185 + 2.04086i 0.182767 + 0.0817652i
\(624\) 0 0
\(625\) −26.4068 −1.05627
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.781045 −0.0311423
\(630\) 0 0
\(631\) 0.0100579 0.000400401 0.000200200 1.00000i \(-0.499936\pi\)
0.000200200 1.00000i \(0.499936\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 18.7187 0.742829
\(636\) 0 0
\(637\) −13.2632 14.8367i −0.525506 0.587851i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.90453 0.193717 0.0968587 0.995298i \(-0.469121\pi\)
0.0968587 + 0.995298i \(0.469121\pi\)
\(642\) 0 0
\(643\) 22.0655 38.2186i 0.870180 1.50720i 0.00837033 0.999965i \(-0.497336\pi\)
0.861810 0.507231i \(-0.169331\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.8813 43.0957i 0.978186 1.69427i 0.309192 0.950999i \(-0.399941\pi\)
0.668993 0.743268i \(-0.266725\pi\)
\(648\) 0 0
\(649\) 18.6457 + 32.2953i 0.731908 + 1.26770i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13.9716 −0.546749 −0.273375 0.961908i \(-0.588140\pi\)
−0.273375 + 0.961908i \(0.588140\pi\)
\(654\) 0 0
\(655\) 28.8024 1.12540
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.9827 22.4867i −0.505733 0.875956i −0.999978 0.00663317i \(-0.997889\pi\)
0.494245 0.869323i \(-0.335445\pi\)
\(660\) 0 0
\(661\) −12.7681 22.1150i −0.496622 0.860174i 0.503370 0.864071i \(-0.332093\pi\)
−0.999992 + 0.00389626i \(0.998760\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.6075 + 7.42979i 0.644013 + 0.288115i
\(666\) 0 0
\(667\) −3.06425 5.30744i −0.118648 0.205505i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −29.3961 + 50.9155i −1.13482 + 1.96557i
\(672\) 0 0
\(673\) 2.71472 + 4.70203i 0.104645 + 0.181250i 0.913593 0.406630i \(-0.133296\pi\)
−0.808948 + 0.587880i \(0.799963\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.07571 + 12.2555i −0.271942 + 0.471017i −0.969359 0.245648i \(-0.920999\pi\)
0.697417 + 0.716665i \(0.254332\pi\)
\(678\) 0 0
\(679\) −37.2307 16.6561i −1.42878 0.639202i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.553330 0.958397i 0.0211726 0.0366720i −0.855245 0.518224i \(-0.826593\pi\)
0.876418 + 0.481552i \(0.159927\pi\)
\(684\) 0 0
\(685\) −37.2773 −1.42429
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12.2789 21.2677i −0.467789 0.810234i
\(690\) 0 0
\(691\) −11.4539 + 19.8387i −0.435725 + 0.754698i −0.997355 0.0726910i \(-0.976841\pi\)
0.561629 + 0.827389i \(0.310175\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.07207 12.2492i 0.268259 0.464638i
\(696\) 0 0
\(697\) −0.207492 0.359387i −0.00785932 0.0136127i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.4056 0.430782 0.215391 0.976528i \(-0.430897\pi\)
0.215391 + 0.976528i \(0.430897\pi\)
\(702\) 0 0
\(703\) −5.05832 + 8.76127i −0.190778 + 0.330438i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.03295 + 4.36672i −0.226892 + 0.164227i
\(708\) 0 0
\(709\) 18.5336 32.1011i 0.696042 1.20558i −0.273786 0.961791i \(-0.588276\pi\)
0.969828 0.243790i \(-0.0783908\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.11614 3.66527i −0.0792502 0.137265i
\(714\) 0 0
\(715\) −14.6038 + 25.2946i −0.546153 + 0.945965i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.459342 + 0.795604i 0.0171306 + 0.0296710i 0.874464 0.485091i \(-0.161214\pi\)
−0.857333 + 0.514762i \(0.827880\pi\)
\(720\) 0 0
\(721\) −10.9662 + 7.93745i −0.408402 + 0.295606i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.14545 1.98399i −0.0425411 0.0736834i
\(726\) 0 0
\(727\) 7.34433 + 12.7208i 0.272386 + 0.471787i 0.969472 0.245201i \(-0.0788538\pi\)
−0.697086 + 0.716987i \(0.745521\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.24102 0.0828871
\(732\) 0 0
\(733\) −22.8624 −0.844441 −0.422220 0.906493i \(-0.638749\pi\)
−0.422220 + 0.906493i \(0.638749\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.8049 29.1069i −0.619015 1.07217i
\(738\) 0 0
\(739\) 19.6692 34.0681i 0.723544 1.25321i −0.236027 0.971746i \(-0.575845\pi\)
0.959571 0.281468i \(-0.0908212\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.8663 + 18.8210i −0.398647 + 0.690477i −0.993559 0.113314i \(-0.963853\pi\)
0.594912 + 0.803791i \(0.297187\pi\)
\(744\) 0 0
\(745\) −17.7682 −0.650977
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.25444 2.79808i −0.228532 0.102240i
\(750\) 0 0
\(751\) 20.6143 0.752225 0.376113 0.926574i \(-0.377261\pi\)
0.376113 + 0.926574i \(0.377261\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −34.3404 −1.24978
\(756\) 0 0
\(757\) 17.8453 0.648600 0.324300 0.945954i \(-0.394871\pi\)
0.324300 + 0.945954i \(0.394871\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.9427 1.23042 0.615211 0.788362i \(-0.289071\pi\)
0.615211 + 0.788362i \(0.289071\pi\)
\(762\) 0 0
\(763\) −4.76672 46.1466i −0.172567 1.67062i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −23.7554 −0.857757
\(768\) 0 0
\(769\) 20.3452 35.2389i 0.733665 1.27075i −0.221641 0.975128i \(-0.571141\pi\)
0.955306 0.295617i \(-0.0955253\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.17562 + 3.76829i −0.0782517 + 0.135536i −0.902496 0.430699i \(-0.858267\pi\)
0.824244 + 0.566235i \(0.191600\pi\)
\(774\) 0 0
\(775\) −0.791039 1.37012i −0.0284150 0.0492162i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.37516 −0.192585
\(780\) 0 0
\(781\) 38.3664 1.37286
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.296062 + 0.512795i 0.0105669 + 0.0183024i
\(786\) 0 0
\(787\) −18.8110 32.5816i −0.670539 1.16141i −0.977751 0.209767i \(-0.932730\pi\)
0.307213 0.951641i \(-0.400604\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.46760 + 43.2508i 0.158850 + 1.53782i
\(792\) 0 0
\(793\) −18.7259 32.4342i −0.664976 1.15177i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 22.1570 38.3771i 0.784842 1.35939i −0.144251 0.989541i \(-0.546077\pi\)
0.929093 0.369845i \(-0.120589\pi\)
\(798\) 0 0
\(799\) −0.666084 1.15369i −0.0235644 0.0408147i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\)