Properties

Label 648.4.i.p.217.2
Level $648$
Weight $4$
Character 648.217
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-43})\)
Defining polynomial: \(x^{4} - x^{3} - 10 x^{2} - 11 x + 121\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 217.2
Root \(3.08945 + 1.20635i\) of defining polynomial
Character \(\chi\) \(=\) 648.217
Dual form 648.4.i.p.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(4.67891 + 8.10411i) q^{5} +(-4.17891 + 7.23808i) q^{7} +O(q^{10})\) \(q+(4.67891 + 8.10411i) q^{5} +(-4.17891 + 7.23808i) q^{7} +(14.5367 - 25.1783i) q^{11} +(-18.3945 - 31.8603i) q^{13} +28.4313 q^{17} +73.7891 q^{19} +(-15.2524 - 26.4179i) q^{23} +(18.7156 - 32.4164i) q^{25} +(92.4680 - 160.159i) q^{29} +(95.4313 + 165.292i) q^{31} -78.2109 q^{35} +160.495 q^{37} +(104.789 + 181.500i) q^{41} +(-58.4727 + 101.278i) q^{43} +(-140.799 + 243.870i) q^{47} +(136.573 + 236.552i) q^{49} -397.450 q^{53} +272.064 q^{55} +(189.073 + 327.485i) q^{59} +(148.762 - 257.663i) q^{61} +(172.133 - 298.143i) q^{65} +(413.968 + 717.014i) q^{67} -729.073 q^{71} +1105.44 q^{73} +(121.495 + 210.436i) q^{77} +(532.134 - 921.683i) q^{79} +(295.239 - 511.369i) q^{83} +(133.027 + 230.410i) q^{85} +227.588 q^{89} +307.476 q^{91} +(345.252 + 597.995i) q^{95} +(-642.827 + 1113.41i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} + 6q^{7} + O(q^{10}) \) \( 4q - 4q^{5} + 6q^{7} - 10q^{11} + 40q^{13} - 68q^{17} + 68q^{19} + 98q^{23} - 16q^{25} + 120q^{29} + 200q^{31} - 540q^{35} + 960q^{37} + 192q^{41} + 334q^{43} + 300q^{47} + 410q^{49} - 136q^{53} + 1588q^{55} + 620q^{59} - 200q^{61} + 1370q^{65} + 1406q^{67} - 2780q^{71} + 3604q^{73} + 804q^{77} + 334q^{79} - 500q^{83} + 1100q^{85} - 180q^{89} + 2820q^{91} + 1222q^{95} + 200q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 4.67891 + 8.10411i 0.418494 + 0.724853i 0.995788 0.0916830i \(-0.0292247\pi\)
−0.577294 + 0.816536i \(0.695891\pi\)
\(6\) 0 0
\(7\) −4.17891 + 7.23808i −0.225640 + 0.390820i −0.956511 0.291696i \(-0.905781\pi\)
0.730871 + 0.682515i \(0.239114\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 14.5367 25.1783i 0.398453 0.690142i −0.595082 0.803665i \(-0.702880\pi\)
0.993535 + 0.113524i \(0.0362137\pi\)
\(12\) 0 0
\(13\) −18.3945 31.8603i −0.392441 0.679727i 0.600330 0.799752i \(-0.295036\pi\)
−0.992771 + 0.120025i \(0.961702\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 28.4313 0.405623 0.202812 0.979218i \(-0.434992\pi\)
0.202812 + 0.979218i \(0.434992\pi\)
\(18\) 0 0
\(19\) 73.7891 0.890967 0.445484 0.895290i \(-0.353032\pi\)
0.445484 + 0.895290i \(0.353032\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −15.2524 26.4179i −0.138276 0.239500i 0.788568 0.614947i \(-0.210823\pi\)
−0.926844 + 0.375447i \(0.877489\pi\)
\(24\) 0 0
\(25\) 18.7156 32.4164i 0.149725 0.259331i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 92.4680 160.159i 0.592099 1.02555i −0.401850 0.915705i \(-0.631633\pi\)
0.993949 0.109840i \(-0.0350340\pi\)
\(30\) 0 0
\(31\) 95.4313 + 165.292i 0.552902 + 0.957654i 0.998063 + 0.0622040i \(0.0198129\pi\)
−0.445161 + 0.895450i \(0.646854\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −78.2109 −0.377716
\(36\) 0 0
\(37\) 160.495 0.713115 0.356558 0.934273i \(-0.383950\pi\)
0.356558 + 0.934273i \(0.383950\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 104.789 + 181.500i 0.399154 + 0.691355i 0.993622 0.112765i \(-0.0359706\pi\)
−0.594468 + 0.804119i \(0.702637\pi\)
\(42\) 0 0
\(43\) −58.4727 + 101.278i −0.207372 + 0.359179i −0.950886 0.309541i \(-0.899824\pi\)
0.743514 + 0.668721i \(0.233158\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −140.799 + 243.870i −0.436970 + 0.756854i −0.997454 0.0713113i \(-0.977282\pi\)
0.560484 + 0.828165i \(0.310615\pi\)
\(48\) 0 0
\(49\) 136.573 + 236.552i 0.398173 + 0.689656i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −397.450 −1.03007 −0.515037 0.857168i \(-0.672222\pi\)
−0.515037 + 0.857168i \(0.672222\pi\)
\(54\) 0 0
\(55\) 272.064 0.667002
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 189.073 + 327.485i 0.417208 + 0.722625i 0.995657 0.0930929i \(-0.0296754\pi\)
−0.578450 + 0.815718i \(0.696342\pi\)
\(60\) 0 0
\(61\) 148.762 257.663i 0.312246 0.540826i −0.666602 0.745413i \(-0.732252\pi\)
0.978848 + 0.204588i \(0.0655854\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 172.133 298.143i 0.328468 0.568924i
\(66\) 0 0
\(67\) 413.968 + 717.014i 0.754839 + 1.30742i 0.945454 + 0.325755i \(0.105619\pi\)
−0.190615 + 0.981665i \(0.561048\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −729.073 −1.21866 −0.609332 0.792915i \(-0.708562\pi\)
−0.609332 + 0.792915i \(0.708562\pi\)
\(72\) 0 0
\(73\) 1105.44 1.77236 0.886178 0.463344i \(-0.153351\pi\)
0.886178 + 0.463344i \(0.153351\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 121.495 + 210.436i 0.179814 + 0.311447i
\(78\) 0 0
\(79\) 532.134 921.683i 0.757845 1.31263i −0.186103 0.982530i \(-0.559586\pi\)
0.943948 0.330095i \(-0.107081\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 295.239 511.369i 0.390442 0.676266i −0.602066 0.798447i \(-0.705655\pi\)
0.992508 + 0.122181i \(0.0389887\pi\)
\(84\) 0 0
\(85\) 133.027 + 230.410i 0.169751 + 0.294017i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 227.588 0.271059 0.135529 0.990773i \(-0.456726\pi\)
0.135529 + 0.990773i \(0.456726\pi\)
\(90\) 0 0
\(91\) 307.476 0.354201
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 345.252 + 597.995i 0.372865 + 0.645821i
\(96\) 0 0
\(97\) −642.827 + 1113.41i −0.672878 + 1.16546i 0.304206 + 0.952606i \(0.401609\pi\)
−0.977084 + 0.212853i \(0.931725\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 842.367 1459.02i 0.829888 1.43741i −0.0682378 0.997669i \(-0.521738\pi\)
0.898126 0.439739i \(-0.144929\pi\)
\(102\) 0 0
\(103\) 427.201 + 739.935i 0.408674 + 0.707844i 0.994741 0.102418i \(-0.0326580\pi\)
−0.586068 + 0.810262i \(0.699325\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1369.73 −1.23754 −0.618768 0.785574i \(-0.712368\pi\)
−0.618768 + 0.785574i \(0.712368\pi\)
\(108\) 0 0
\(109\) 1475.06 1.29620 0.648099 0.761556i \(-0.275564\pi\)
0.648099 + 0.761556i \(0.275564\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.50943 7.81057i −0.00375409 0.00650227i 0.864142 0.503248i \(-0.167862\pi\)
−0.867896 + 0.496745i \(0.834528\pi\)
\(114\) 0 0
\(115\) 142.729 247.213i 0.115735 0.200459i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −118.812 + 205.788i −0.0915248 + 0.158526i
\(120\) 0 0
\(121\) 242.867 + 420.658i 0.182470 + 0.316047i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1520.00 1.08762
\(126\) 0 0
\(127\) 2076.05 1.45055 0.725274 0.688460i \(-0.241713\pi\)
0.725274 + 0.688460i \(0.241713\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 887.207 + 1536.69i 0.591723 + 1.02489i 0.994000 + 0.109376i \(0.0348852\pi\)
−0.402278 + 0.915518i \(0.631781\pi\)
\(132\) 0 0
\(133\) −308.358 + 534.091i −0.201038 + 0.348208i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 605.344 1048.49i 0.377504 0.653855i −0.613195 0.789932i \(-0.710116\pi\)
0.990698 + 0.136076i \(0.0434492\pi\)
\(138\) 0 0
\(139\) 366.614 + 634.994i 0.223711 + 0.387478i 0.955932 0.293589i \(-0.0948496\pi\)
−0.732221 + 0.681067i \(0.761516\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1069.59 −0.625477
\(144\) 0 0
\(145\) 1730.60 0.991160
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −257.781 446.489i −0.141733 0.245489i 0.786416 0.617697i \(-0.211934\pi\)
−0.928149 + 0.372208i \(0.878601\pi\)
\(150\) 0 0
\(151\) 576.945 999.299i 0.310935 0.538555i −0.667630 0.744493i \(-0.732691\pi\)
0.978565 + 0.205938i \(0.0660246\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −893.028 + 1546.77i −0.462773 + 0.801546i
\(156\) 0 0
\(157\) 684.754 + 1186.03i 0.348085 + 0.602901i 0.985909 0.167281i \(-0.0534987\pi\)
−0.637824 + 0.770182i \(0.720165\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 254.953 0.124802
\(162\) 0 0
\(163\) −3796.90 −1.82452 −0.912259 0.409613i \(-0.865664\pi\)
−0.912259 + 0.409613i \(0.865664\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1024.45 1774.39i −0.474695 0.822196i 0.524885 0.851173i \(-0.324108\pi\)
−0.999580 + 0.0289774i \(0.990775\pi\)
\(168\) 0 0
\(169\) 421.782 730.547i 0.191981 0.332520i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1012.61 1753.90i 0.445016 0.770789i −0.553038 0.833156i \(-0.686531\pi\)
0.998053 + 0.0623667i \(0.0198648\pi\)
\(174\) 0 0
\(175\) 156.422 + 270.931i 0.0675679 + 0.117031i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3142.50 −1.31219 −0.656094 0.754679i \(-0.727792\pi\)
−0.656094 + 0.754679i \(0.727792\pi\)
\(180\) 0 0
\(181\) 37.6685 0.0154689 0.00773446 0.999970i \(-0.497538\pi\)
0.00773446 + 0.999970i \(0.497538\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 750.943 + 1300.67i 0.298435 + 0.516904i
\(186\) 0 0
\(187\) 413.298 715.852i 0.161622 0.279937i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2117.06 + 3666.86i −0.802016 + 1.38913i 0.116271 + 0.993218i \(0.462906\pi\)
−0.918287 + 0.395915i \(0.870427\pi\)
\(192\) 0 0
\(193\) −1914.65 3316.27i −0.714090 1.23684i −0.963309 0.268394i \(-0.913507\pi\)
0.249219 0.968447i \(-0.419826\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1072.38 0.387838 0.193919 0.981018i \(-0.437880\pi\)
0.193919 + 0.981018i \(0.437880\pi\)
\(198\) 0 0
\(199\) −1078.53 −0.384196 −0.192098 0.981376i \(-0.561529\pi\)
−0.192098 + 0.981376i \(0.561529\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 772.831 + 1338.58i 0.267202 + 0.462808i
\(204\) 0 0
\(205\) −980.597 + 1698.44i −0.334087 + 0.578656i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1072.65 1857.89i 0.355009 0.614893i
\(210\) 0 0
\(211\) 1808.08 + 3131.69i 0.589922 + 1.02177i 0.994242 + 0.107157i \(0.0341747\pi\)
−0.404321 + 0.914617i \(0.632492\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1094.35 −0.347136
\(216\) 0 0
\(217\) −1595.19 −0.499027
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −522.980 905.828i −0.159183 0.275713i
\(222\) 0 0
\(223\) 430.574 745.777i 0.129298 0.223950i −0.794107 0.607778i \(-0.792061\pi\)
0.923405 + 0.383828i \(0.125394\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1542.98 + 2672.52i −0.451150 + 0.781414i −0.998458 0.0555169i \(-0.982319\pi\)
0.547308 + 0.836931i \(0.315653\pi\)
\(228\) 0 0
\(229\) −3095.65 5361.81i −0.893301 1.54724i −0.835893 0.548892i \(-0.815050\pi\)
−0.0574083 0.998351i \(-0.518284\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4325.48 1.21619 0.608093 0.793866i \(-0.291935\pi\)
0.608093 + 0.793866i \(0.291935\pi\)
\(234\) 0 0
\(235\) −2635.13 −0.731477
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1559.24 2700.68i −0.422003 0.730931i 0.574132 0.818763i \(-0.305340\pi\)
−0.996135 + 0.0878315i \(0.972006\pi\)
\(240\) 0 0
\(241\) −361.462 + 626.071i −0.0966134 + 0.167339i −0.910281 0.413991i \(-0.864134\pi\)
0.813667 + 0.581331i \(0.197468\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1278.03 + 2213.61i −0.333267 + 0.577235i
\(246\) 0 0
\(247\) −1357.32 2350.94i −0.349652 0.605615i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6373.89 1.60285 0.801427 0.598093i \(-0.204075\pi\)
0.801427 + 0.598093i \(0.204075\pi\)
\(252\) 0 0
\(253\) −886.877 −0.220385
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1902.41 3295.07i −0.461748 0.799771i 0.537300 0.843391i \(-0.319444\pi\)
−0.999048 + 0.0436203i \(0.986111\pi\)
\(258\) 0 0
\(259\) −670.695 + 1161.68i −0.160907 + 0.278699i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −729.311 + 1263.20i −0.170993 + 0.296169i −0.938767 0.344552i \(-0.888031\pi\)
0.767774 + 0.640721i \(0.221364\pi\)
\(264\) 0 0
\(265\) −1859.63 3220.98i −0.431080 0.746653i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2240.99 0.507940 0.253970 0.967212i \(-0.418264\pi\)
0.253970 + 0.967212i \(0.418264\pi\)
\(270\) 0 0
\(271\) −3077.92 −0.689927 −0.344963 0.938616i \(-0.612109\pi\)
−0.344963 + 0.938616i \(0.612109\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −544.128 942.457i −0.119317 0.206663i
\(276\) 0 0
\(277\) −1545.35 + 2676.63i −0.335203 + 0.580588i −0.983524 0.180779i \(-0.942138\pi\)
0.648321 + 0.761367i \(0.275471\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2420.90 4193.12i 0.513946 0.890180i −0.485923 0.874001i \(-0.661517\pi\)
0.999869 0.0161788i \(-0.00515008\pi\)
\(282\) 0 0
\(283\) −359.725 623.062i −0.0755598 0.130873i 0.825770 0.564007i \(-0.190741\pi\)
−0.901330 + 0.433134i \(0.857408\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1751.62 −0.360260
\(288\) 0 0
\(289\) −4104.66 −0.835470
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2625.01 4546.65i −0.523395 0.906548i −0.999629 0.0272288i \(-0.991332\pi\)
0.476234 0.879319i \(-0.342002\pi\)
\(294\) 0 0
\(295\) −1769.31 + 3064.54i −0.349198 + 0.604829i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −561.120 + 971.889i −0.108530 + 0.187979i
\(300\) 0 0
\(301\) −488.704 846.460i −0.0935829 0.162090i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2784.17 0.522692
\(306\) 0 0
\(307\) −5823.45 −1.08261 −0.541306 0.840826i \(-0.682070\pi\)
−0.541306 + 0.840826i \(0.682070\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 196.407 + 340.187i 0.0358110 + 0.0620265i 0.883375 0.468666i \(-0.155265\pi\)
−0.847564 + 0.530693i \(0.821932\pi\)
\(312\) 0 0
\(313\) −558.235 + 966.891i −0.100809 + 0.174607i −0.912018 0.410150i \(-0.865476\pi\)
0.811209 + 0.584756i \(0.198810\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 654.340 1133.35i 0.115935 0.200805i −0.802218 0.597031i \(-0.796347\pi\)
0.918153 + 0.396226i \(0.129680\pi\)
\(318\) 0 0
\(319\) −2688.36 4656.38i −0.471848 0.817264i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2097.92 0.361397
\(324\) 0 0
\(325\) −1377.06 −0.235033
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1176.77 2038.22i −0.197196 0.341553i
\(330\) 0 0
\(331\) 3099.55 5368.58i 0.514703 0.891492i −0.485151 0.874430i \(-0.661236\pi\)
0.999854 0.0170616i \(-0.00543113\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3873.84 + 6709.68i −0.631792 + 1.09430i
\(336\) 0 0
\(337\) −403.851 699.491i −0.0652794 0.113067i 0.831538 0.555467i \(-0.187461\pi\)
−0.896818 + 0.442400i \(0.854127\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5549.03 0.881223
\(342\) 0 0
\(343\) −5149.64 −0.810655
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 746.608 + 1293.16i 0.115504 + 0.200059i 0.917981 0.396624i \(-0.129818\pi\)
−0.802477 + 0.596683i \(0.796485\pi\)
\(348\) 0 0
\(349\) 249.305 431.809i 0.0382378 0.0662299i −0.846273 0.532749i \(-0.821159\pi\)
0.884511 + 0.466519i \(0.154492\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6002.66 + 10396.9i −0.905069 + 1.56762i −0.0842436 + 0.996445i \(0.526847\pi\)
−0.820825 + 0.571180i \(0.806486\pi\)
\(354\) 0 0
\(355\) −3411.27 5908.49i −0.510004 0.883352i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6842.79 −1.00599 −0.502993 0.864291i \(-0.667768\pi\)
−0.502993 + 0.864291i \(0.667768\pi\)
\(360\) 0 0
\(361\) −1414.17 −0.206177
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5172.26 + 8958.61i 0.741721 + 1.28470i
\(366\) 0 0
\(367\) 56.0606 97.0999i 0.00797368 0.0138108i −0.862011 0.506890i \(-0.830795\pi\)
0.869985 + 0.493079i \(0.164129\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1660.91 2876.78i 0.232426 0.402574i
\(372\) 0 0
\(373\) −988.085 1711.41i −0.137161 0.237570i 0.789260 0.614059i \(-0.210464\pi\)
−0.926421 + 0.376489i \(0.877131\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6803.63 −0.929455
\(378\) 0 0
\(379\) −669.717 −0.0907679 −0.0453840 0.998970i \(-0.514451\pi\)
−0.0453840 + 0.998970i \(0.514451\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5620.25 9734.57i −0.749821 1.29873i −0.947908 0.318544i \(-0.896806\pi\)
0.198087 0.980185i \(-0.436527\pi\)
\(384\) 0 0
\(385\) −1136.93 + 1969.22i −0.150502 + 0.260677i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1882.99 + 3261.43i −0.245427 + 0.425092i −0.962252 0.272161i \(-0.912262\pi\)
0.716825 + 0.697254i \(0.245595\pi\)
\(390\) 0 0
\(391\) −433.644 751.093i −0.0560878 0.0971468i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9959.22 1.26861
\(396\) 0 0
\(397\) −2005.69 −0.253558 −0.126779 0.991931i \(-0.540464\pi\)
−0.126779 + 0.991931i \(0.540464\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2777.83 4811.34i −0.345930 0.599169i 0.639592 0.768715i \(-0.279103\pi\)
−0.985522 + 0.169546i \(0.945770\pi\)
\(402\) 0 0
\(403\) 3510.83 6080.93i 0.433962 0.751645i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2333.08 4041.01i 0.284143 0.492150i
\(408\) 0 0
\(409\) 7438.24 + 12883.4i 0.899260 + 1.55756i 0.828441 + 0.560076i \(0.189228\pi\)
0.0708190 + 0.997489i \(0.477439\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3160.48 −0.376555
\(414\) 0 0
\(415\) 5525.59 0.653592
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4749.82 + 8226.92i 0.553803 + 0.959216i 0.997996 + 0.0632842i \(0.0201575\pi\)
−0.444192 + 0.895932i \(0.646509\pi\)
\(420\) 0 0
\(421\) 2998.70 5193.90i 0.347144 0.601271i −0.638597 0.769541i \(-0.720485\pi\)
0.985741 + 0.168270i \(0.0538182\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 532.109 921.640i 0.0607320 0.105191i
\(426\) 0 0
\(427\) 1243.32 + 2153.50i 0.140910 + 0.244064i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15607.1 −1.74424 −0.872121 0.489291i \(-0.837256\pi\)
−0.872121 + 0.489291i \(0.837256\pi\)
\(432\) 0 0
\(433\) −1204.46 −0.133678 −0.0668390 0.997764i \(-0.521291\pi\)
−0.0668390 + 0.997764i \(0.521291\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1125.46 1949.35i −0.123199 0.213387i
\(438\) 0 0
\(439\) −8492.29 + 14709.1i −0.923269 + 1.59915i −0.128947 + 0.991651i \(0.541160\pi\)
−0.794322 + 0.607497i \(0.792174\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3584.85 6209.14i 0.384473 0.665926i −0.607223 0.794531i \(-0.707717\pi\)
0.991696 + 0.128605i \(0.0410499\pi\)
\(444\) 0 0
\(445\) 1064.86 + 1844.39i 0.113437 + 0.196478i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4648.71 0.488611 0.244305 0.969698i \(-0.421440\pi\)
0.244305 + 0.969698i \(0.421440\pi\)
\(450\) 0 0
\(451\) 6093.16 0.636177
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1438.65 + 2491.82i 0.148231 + 0.256744i
\(456\) 0 0
\(457\) −472.024 + 817.569i −0.0483158 + 0.0836855i −0.889172 0.457573i \(-0.848719\pi\)
0.840856 + 0.541259i \(0.182052\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2549.51 + 4415.88i −0.257576 + 0.446134i −0.965592 0.260062i \(-0.916257\pi\)
0.708016 + 0.706196i \(0.249590\pi\)
\(462\) 0 0
\(463\) 458.859 + 794.767i 0.0460583 + 0.0797753i 0.888135 0.459582i \(-0.152001\pi\)
−0.842077 + 0.539357i \(0.818667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19073.2 1.88994 0.944969 0.327160i \(-0.106092\pi\)
0.944969 + 0.327160i \(0.106092\pi\)
\(468\) 0 0
\(469\) −6919.74 −0.681287
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1700.00 + 2944.49i 0.165256 + 0.286232i
\(474\) 0 0
\(475\) 1381.01 2391.98i 0.133400 0.231056i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9163.06 15870.9i 0.874052 1.51390i 0.0162836 0.999867i \(-0.494817\pi\)
0.857769 0.514036i \(-0.171850\pi\)
\(480\) 0 0
\(481\) −2952.24 5113.42i −0.279855 0.484724i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −12030.9 −1.12638
\(486\) 0 0
\(487\) 18087.7 1.68302 0.841512 0.540238i \(-0.181666\pi\)
0.841512 + 0.540238i \(0.181666\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1930.14 3343.10i −0.177405 0.307275i 0.763586 0.645706i \(-0.223437\pi\)
−0.940991 + 0.338432i \(0.890104\pi\)
\(492\) 0 0
\(493\) 2628.98 4553.53i 0.240169 0.415985i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3046.73 5277.09i 0.274979 0.476278i
\(498\) 0 0
\(499\) 7222.33 + 12509.4i 0.647928 + 1.12224i 0.983617 + 0.180271i \(0.0576974\pi\)
−0.335689 + 0.941973i \(0.608969\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2074.88 0.183925 0.0919625 0.995762i \(-0.470686\pi\)
0.0919625 + 0.995762i \(0.470686\pi\)
\(504\) 0 0
\(505\) 15765.4 1.38921
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2489.86 + 4312.56i 0.216819 + 0.375542i 0.953834 0.300335i \(-0.0970984\pi\)
−0.737015 + 0.675877i \(0.763765\pi\)
\(510\) 0 0
\(511\) −4619.54 + 8001.27i −0.399914 + 0.692672i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3997.67 + 6924.17i −0.342055 + 0.592457i
\(516\) 0 0
\(517\) 4093.50 + 7090.15i 0.348224 + 0.603142i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8212.49 −0.690587 −0.345293 0.938495i \(-0.612221\pi\)
−0.345293 + 0.938495i \(0.612221\pi\)
\(522\) 0 0
\(523\) 12630.6 1.05602 0.528009 0.849239i \(-0.322939\pi\)
0.528009 + 0.849239i \(0.322939\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2713.23 + 4699.46i 0.224270 + 0.388447i
\(528\) 0 0
\(529\) 5618.23 9731.06i 0.461760 0.799791i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3855.09 6677.22i 0.313288 0.542631i
\(534\) 0 0
\(535\) −6408.82 11100.4i −0.517902 0.897032i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7941.32 0.634614
\(540\) 0 0
\(541\) 22132.0 1.75883 0.879416 0.476054i \(-0.157933\pi\)
0.879416 + 0.476054i \(0.157933\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6901.69 + 11954.1i 0.542451 + 0.939553i
\(546\) 0 0
\(547\) 2271.34 3934.07i 0.177542 0.307511i −0.763496 0.645812i \(-0.776519\pi\)
0.941038 + 0.338301i \(0.109852\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6823.13 11818.0i 0.527541 0.913728i
\(552\) 0 0
\(553\) 4447.48 + 7703.26i 0.342000 + 0.592361i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22330.0 −1.69866 −0.849330 0.527862i \(-0.822994\pi\)
−0.849330 + 0.527862i \(0.822994\pi\)
\(558\) 0 0
\(559\) 4302.31 0.325525
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7093.39 + 12286.1i 0.530996 + 0.919712i 0.999346 + 0.0361685i \(0.0115153\pi\)
−0.468350 + 0.883543i \(0.655151\pi\)
\(564\) 0 0
\(565\) 42.1985 73.0899i 0.00314213 0.00544233i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5469.16 + 9472.86i −0.402951 + 0.697932i −0.994081 0.108645i \(-0.965349\pi\)
0.591130 + 0.806577i \(0.298682\pi\)
\(570\) 0 0
\(571\) 6070.81 + 10514.9i 0.444931 + 0.770642i 0.998047 0.0624614i \(-0.0198950\pi\)
−0.553117 + 0.833104i \(0.686562\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1141.83 −0.0828132
\(576\) 0 0
\(577\) −14080.0 −1.01587 −0.507936 0.861395i \(-0.669592\pi\)
−0.507936 + 0.861395i \(0.669592\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2467.56 + 4273.93i 0.176199 + 0.305185i
\(582\) 0 0
\(583\) −5777.62 + 10007.1i −0.410437 + 0.710898i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12597.5 21819.5i 0.885781 1.53422i 0.0409650 0.999161i \(-0.486957\pi\)
0.844816 0.535057i \(-0.179710\pi\)
\(588\) 0 0
\(589\) 7041.79 + 12196.7i 0.492618 + 0.853239i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24086.1 −1.66796 −0.833978 0.551798i \(-0.813942\pi\)
−0.833978 + 0.551798i \(0.813942\pi\)
\(594\) 0 0
\(595\) −2223.64 −0.153210
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13917.4 24105.7i −0.949332 1.64429i −0.746836 0.665008i \(-0.768428\pi\)
−0.202495 0.979283i \(-0.564905\pi\)
\(600\) 0 0
\(601\) 8056.88 13954.9i 0.546833 0.947143i −0.451656 0.892192i \(-0.649166\pi\)
0.998489 0.0549509i \(-0.0175002\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2272.71 + 3936.44i −0.152725 + 0.264528i
\(606\) 0 0
\(607\) 1462.99 + 2533.97i 0.0978268 + 0.169441i 0.910785 0.412881i \(-0.135478\pi\)
−0.812958 + 0.582322i \(0.802144\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10359.7 0.685939
\(612\) 0 0
\(613\) −11350.9 −0.747896 −0.373948 0.927450i \(-0.621996\pi\)
−0.373948 + 0.927450i \(0.621996\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7907.60 + 13696.4i 0.515961 + 0.893671i 0.999828 + 0.0185297i \(0.00589853\pi\)
−0.483867 + 0.875142i \(0.660768\pi\)
\(618\) 0 0
\(619\) 6164.41 10677.1i 0.400272 0.693292i −0.593486 0.804844i \(-0.702249\pi\)
0.993759 + 0.111552i \(0.0355823\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −951.068 + 1647.30i −0.0611617 + 0.105935i
\(624\) 0 0
\(625\) 4772.50 + 8266.21i 0.305440 + 0.529037i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4563.08 0.289256
\(630\) 0 0
\(631\) 25545.6 1.61165 0.805826 0.592152i \(-0.201722\pi\)
0.805826 + 0.592152i \(0.201722\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9713.64 + 16824.5i 0.607046 + 1.05143i
\(636\) 0 0
\(637\) 5024.41 8702.54i 0.312519 0.541298i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6361.66 + 11018.7i −0.391998 + 0.678960i −0.992713 0.120503i \(-0.961549\pi\)
0.600715 + 0.799463i \(0.294882\pi\)
\(642\) 0 0
\(643\) 7088.18 + 12277.1i 0.434729 + 0.752972i 0.997273 0.0737946i \(-0.0235109\pi\)
−0.562545 + 0.826767i \(0.690178\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25409.1 −1.54395 −0.771975 0.635653i \(-0.780731\pi\)
−0.771975 + 0.635653i \(0.780731\pi\)
\(648\) 0 0
\(649\) 10994.0 0.664952
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6748.22 11688.3i −0.404408 0.700455i 0.589845 0.807517i \(-0.299189\pi\)
−0.994252 + 0.107062i \(0.965856\pi\)
\(654\) 0 0
\(655\) −8302.32 + 14380.0i −0.495265 + 0.857824i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6047.54 10474.7i 0.357479 0.619172i −0.630060 0.776547i \(-0.716970\pi\)
0.987539 + 0.157374i \(0.0503030\pi\)
\(660\) 0 0
\(661\) 5002.37 + 8664.35i 0.294356 + 0.509840i 0.974835 0.222928i \(-0.0715614\pi\)
−0.680479 + 0.732768i \(0.738228\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5771.11 −0.336533
\(666\) 0 0
\(667\) −5641.42 −0.327491
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4325.02 7491.15i −0.248831 0.430988i
\(672\) 0 0
\(673\) −4955.53 + 8583.23i −0.283836 + 0.491618i −0.972326 0.233627i \(-0.924940\pi\)
0.688490 + 0.725246i \(0.258274\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9424.73 + 16324.1i −0.535040 + 0.926716i 0.464122 + 0.885771i \(0.346370\pi\)
−0.999161 + 0.0409446i \(0.986963\pi\)
\(678\) 0 0
\(679\) −5372.63 9305.67i −0.303656 0.525948i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17224.5 0.964973 0.482486 0.875903i \(-0.339734\pi\)
0.482486 + 0.875903i \(0.339734\pi\)
\(684\) 0 0
\(685\) 11329.4 0.631932
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7310.91 + 12662.9i 0.404243 + 0.700170i
\(690\) 0 0
\(691\) 3977.32 6888.91i 0.218964 0.379257i −0.735527 0.677495i \(-0.763066\pi\)
0.954492 + 0.298238i \(0.0963989\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3430.71 + 5942.16i −0.187243 + 0.324315i
\(696\) 0 0
\(697\) 2979.29 + 5160.28i 0.161906 + 0.280430i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3771.49 −0.203206 −0.101603 0.994825i \(-0.532397\pi\)
−0.101603 + 0.994825i \(0.532397\pi\)
\(702\) 0 0
\(703\) 11842.8 0.635362
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7040.35 + 12194.2i 0.374512 + 0.648673i
\(708\) 0 0
\(709\) −141.333 + 244.795i −0.00748640 + 0.0129668i −0.869744 0.493503i \(-0.835716\pi\)
0.862258 + 0.506469i \(0.169050\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2911.10 5042.18i 0.152906 0.264840i
\(714\) 0 0
\(715\) −5004.49 8668.04i −0.261759 0.453379i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8779.02 −0.455358 −0.227679 0.973736i \(-0.573114\pi\)
−0.227679 + 0.973736i \(0.573114\pi\)
\(720\) 0 0
\(721\) −7140.94 −0.368852
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3461.19 5994.96i −0.177304 0.307100i
\(726\) 0 0
\(727\) 1242.74 2152.49i 0.0633985 0.109809i −0.832584 0.553899i \(-0.813139\pi\)
0.895982 + 0.444089i \(0.146473\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1662.45 + 2879.45i −0.0841150 + 0.145691i
\(732\) 0 0
\(733\) 5089.78 + 8815.75i 0.256474 + 0.444225i 0.965295 0.261163i \(-0.0841060\pi\)
−0.708821 + 0.705388i \(0.750773\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24071.0 1.20307
\(738\) 0 0
\(739\) 3318.26 0.165175 0.0825874 0.996584i \(-0.473682\pi\)
0.0825874 + 0.996584i \(0.473682\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1333.34 2309.41i −0.0658350 0.114030i 0.831229 0.555930i \(-0.187638\pi\)
−0.897064 + 0.441900i \(0.854304\pi\)
\(744\) 0 0
\(745\) 2412.26 4178.16i 0.118629 0.205471i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5723.96 9914.18i 0.279237 0.483653i
\(750\) 0 0
\(751\) −9768.80 16920.1i −0.474659 0.822133i 0.524920 0.851151i \(-0.324095\pi\)
−0.999579 + 0.0290186i \(0.990762\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10797.9 0.520498
\(756\) 0 0
\(757\) −30037.2 −1.44217 −0.721084 0.692848i \(-0.756356\pi\)
−0.721084 + 0.692848i \(0.756356\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20577.1 35640.6i −0.980184 1.69773i −0.661641 0.749821i \(-0.730140\pi\)
−0.318544 0.947908i \(-0.603194\pi\)
\(762\) 0 0
\(763\) −6164.16 + 10676.6i −0.292474 + 0.506579i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6955.84 12047.9i 0.327459 0.567175i
\(768\) 0 0
\(769\) −10939.1 18947.0i −0.512969 0.888488i −0.999887 0.0150403i \(-0.995212\pi\)
0.486918 0.873448i \(-0.338121\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23321.1 1.08512 0.542561 0.840016i \(-0.317455\pi\)
0.542561 + 0.840016i \(0.317455\pi\)
\(774\) 0 0
\(775\) 7144.23 0.331133
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7732.29 + 13392.7i 0.355633 + 0.615974i
\(780\) 0 0
\(781\) −10598.3 + 18356.9i −0.485581 + 0.841050i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6407.81 + 11098.6i −0.291343 + 0.504621i
\(786\) 0 0
\(787\) −8155.78 14126.2i −0.369406 0.639829i 0.620067 0.784549i \(-0.287105\pi\)
−0.989473 + 0.144719i \(0.953772\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 75.3780 0.00338829
\(792\) 0 0
\(793\) −10945.6 −0.490152
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11480.7 + 19885.2i 0.510249 + 0.883778i 0.999929 + 0.0118755i \(0.00378019\pi\)
−0.489680 + 0.871902i \(0.662886\pi\)
\(798\) 0 0
\(799\) −4003.08 + 6933.54i −0.177245 + 0.306997i
\(800\) 0 0
\(801\) 0 0
\(802\) 0