Properties

Label 648.4.i.p.433.2
Level $648$
Weight $4$
Character 648.433
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 433.2
Root \(3.08945 - 1.20635i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.4.i.p.217.2

$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

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

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
\(5\) 4.67891 8.10411i 0.418494 0.724853i −0.577294 0.816536i \(-0.695891\pi\)
0.995788 + 0.0916830i \(0.0292247\pi\)
\(6\) 0 0
\(7\) −4.17891 7.23808i −0.225640 0.390820i 0.730871 0.682515i \(-0.239114\pi\)
−0.956511 + 0.291696i \(0.905781\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 14.5367 + 25.1783i 0.398453 + 0.690142i 0.993535 0.113524i \(-0.0362137\pi\)
−0.595082 + 0.803665i \(0.702880\pi\)
\(12\) 0 0
\(13\) −18.3945 + 31.8603i −0.392441 + 0.679727i −0.992771 0.120025i \(-0.961702\pi\)
0.600330 + 0.799752i \(0.295036\pi\)
\(14\) 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 −0.926844 0.375447i \(-0.877489\pi\)
0.788568 + 0.614947i \(0.210823\pi\)
\(24\) 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 0.993949 + 0.109840i \(0.0350340\pi\)
−0.401850 + 0.915705i \(0.631633\pi\)
\(30\) 0 0
\(31\) 95.4313 165.292i 0.552902 0.957654i −0.445161 0.895450i \(-0.646854\pi\)
0.998063 0.0622040i \(-0.0198129\pi\)
\(32\) 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 −0.594468 0.804119i \(-0.702637\pi\)
0.993622 + 0.112765i \(0.0359706\pi\)
\(42\) 0 0
\(43\) −58.4727 101.278i −0.207372 0.359179i 0.743514 0.668721i \(-0.233158\pi\)
−0.950886 + 0.309541i \(0.899824\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −140.799 243.870i −0.436970 0.756854i 0.560484 0.828165i \(-0.310615\pi\)
−0.997454 + 0.0713113i \(0.977282\pi\)
\(48\) 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 −0.578450 0.815718i \(-0.696342\pi\)
0.995657 + 0.0930929i \(0.0296754\pi\)
\(60\) 0 0
\(61\) 148.762 + 257.663i 0.312246 + 0.540826i 0.978848 0.204588i \(-0.0655854\pi\)
−0.666602 + 0.745413i \(0.732252\pi\)
\(62\) 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 −0.190615 0.981665i \(-0.561048\pi\)
0.945454 0.325755i \(-0.105619\pi\)
\(68\) 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 0.943948 + 0.330095i \(0.107081\pi\)
−0.186103 + 0.982530i \(0.559586\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 295.239 + 511.369i 0.390442 + 0.676266i 0.992508 0.122181i \(-0.0389887\pi\)
−0.602066 + 0.798447i \(0.705655\pi\)
\(84\) 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 −0.977084 0.212853i \(-0.931725\pi\)
0.304206 0.952606i \(-0.401609\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 842.367 + 1459.02i 0.829888 + 1.43741i 0.898126 + 0.439739i \(0.144929\pi\)
−0.0682378 + 0.997669i \(0.521738\pi\)
\(102\) 0 0
\(103\) 427.201 739.935i 0.408674 0.707844i −0.586068 0.810262i \(-0.699325\pi\)
0.994741 + 0.102418i \(0.0326580\pi\)
\(104\) 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 −0.867896 0.496745i \(-0.834528\pi\)
0.864142 + 0.503248i \(0.167862\pi\)
\(114\) 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 −0.402278 0.915518i \(-0.631781\pi\)
0.994000 0.109376i \(-0.0348852\pi\)
\(132\) 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 0.990698 0.136076i \(-0.0434492\pi\)
−0.613195 + 0.789932i \(0.710116\pi\)
\(138\) 0 0
\(139\) 366.614 634.994i 0.223711 0.387478i −0.732221 0.681067i \(-0.761516\pi\)
0.955932 + 0.293589i \(0.0948496\pi\)
\(140\) 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 −0.928149 0.372208i \(-0.878601\pi\)
0.786416 + 0.617697i \(0.211934\pi\)
\(150\) 0 0
\(151\) 576.945 + 999.299i 0.310935 + 0.538555i 0.978565 0.205938i \(-0.0660246\pi\)
−0.667630 + 0.744493i \(0.732691\pi\)
\(152\) 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 −0.637824 0.770182i \(-0.720165\pi\)
0.985909 + 0.167281i \(0.0534987\pi\)
\(158\) 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 −0.999580 0.0289774i \(-0.990775\pi\)
0.524885 + 0.851173i \(0.324108\pi\)
\(168\) 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 0.998053 0.0623667i \(-0.0198648\pi\)
−0.553038 + 0.833156i \(0.686531\pi\)
\(174\) 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 −0.918287 0.395915i \(-0.870427\pi\)
0.116271 0.993218i \(-0.462906\pi\)
\(192\) 0 0
\(193\) −1914.65 + 3316.27i −0.714090 + 1.23684i 0.249219 + 0.968447i \(0.419826\pi\)
−0.963309 + 0.268394i \(0.913507\pi\)
\(194\) 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 −0.404321 0.914617i \(-0.632492\pi\)
0.994242 0.107157i \(-0.0341747\pi\)
\(212\) 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 0.923405 0.383828i \(-0.125394\pi\)
−0.794107 + 0.607778i \(0.792061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1542.98 2672.52i −0.451150 0.781414i 0.547308 0.836931i \(-0.315653\pi\)
−0.998458 + 0.0555169i \(0.982319\pi\)
\(228\) 0 0
\(229\) −3095.65 + 5361.81i −0.893301 + 1.54724i −0.0574083 + 0.998351i \(0.518284\pi\)
−0.835893 + 0.548892i \(0.815050\pi\)
\(230\) 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 −0.996135 0.0878315i \(-0.972006\pi\)
0.574132 + 0.818763i \(0.305340\pi\)
\(240\) 0 0
\(241\) −361.462 626.071i −0.0966134 0.167339i 0.813667 0.581331i \(-0.197468\pi\)
−0.910281 + 0.413991i \(0.864134\pi\)
\(242\) 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 −0.999048 0.0436203i \(-0.986111\pi\)
0.537300 + 0.843391i \(0.319444\pi\)
\(258\) 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 0.767774 0.640721i \(-0.221364\pi\)
−0.938767 + 0.344552i \(0.888031\pi\)
\(264\) 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 0.648321 0.761367i \(-0.275471\pi\)
−0.983524 + 0.180779i \(0.942138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2420.90 + 4193.12i 0.513946 + 0.890180i 0.999869 + 0.0161788i \(0.00515008\pi\)
−0.485923 + 0.874001i \(0.661517\pi\)
\(282\) 0 0
\(283\) −359.725 + 623.062i −0.0755598 + 0.130873i −0.901330 0.433134i \(-0.857408\pi\)
0.825770 + 0.564007i \(0.190741\pi\)
\(284\) 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 0.476234 + 0.879319i \(0.342002\pi\)
−0.999629 + 0.0272288i \(0.991332\pi\)
\(294\) 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 −0.847564 0.530693i \(-0.821932\pi\)
0.883375 + 0.468666i \(0.155265\pi\)
\(312\) 0 0
\(313\) −558.235 966.891i −0.100809 0.174607i 0.811209 0.584756i \(-0.198810\pi\)
−0.912018 + 0.410150i \(0.865476\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 654.340 + 1133.35i 0.115935 + 0.200805i 0.918153 0.396226i \(-0.129680\pi\)
−0.802218 + 0.597031i \(0.796347\pi\)
\(318\) 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 0.999854 + 0.0170616i \(0.00543113\pi\)
−0.485151 + 0.874430i \(0.661236\pi\)
\(332\) 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 −0.896818 0.442400i \(-0.854127\pi\)
0.831538 + 0.555467i \(0.187461\pi\)
\(338\) 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 −0.802477 0.596683i \(-0.796485\pi\)
0.917981 + 0.396624i \(0.129818\pi\)
\(348\) 0 0
\(349\) 249.305 + 431.809i 0.0382378 + 0.0662299i 0.884511 0.466519i \(-0.154492\pi\)
−0.846273 + 0.532749i \(0.821159\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6002.66 10396.9i −0.905069 1.56762i −0.820825 0.571180i \(-0.806486\pi\)
−0.0842436 0.996445i \(-0.526847\pi\)
\(354\) 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 0.869985 0.493079i \(-0.164129\pi\)
−0.862011 + 0.506890i \(0.830795\pi\)
\(368\) 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 −0.926421 0.376489i \(-0.877131\pi\)
0.789260 + 0.614059i \(0.210464\pi\)
\(374\) 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 0.198087 + 0.980185i \(0.436527\pi\)
−0.947908 + 0.318544i \(0.896806\pi\)
\(384\) 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 0.716825 0.697254i \(-0.245595\pi\)
−0.962252 + 0.272161i \(0.912262\pi\)
\(390\) 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 −0.985522 0.169546i \(-0.945770\pi\)
0.639592 + 0.768715i \(0.279103\pi\)
\(402\) 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 0.0708190 0.997489i \(-0.477439\pi\)
0.828441 0.560076i \(-0.189228\pi\)
\(410\) 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 −0.444192 0.895932i \(-0.646509\pi\)
0.997996 0.0632842i \(-0.0201575\pi\)
\(420\) 0 0
\(421\) 2998.70 + 5193.90i 0.347144 + 0.601271i 0.985741 0.168270i \(-0.0538182\pi\)
−0.638597 + 0.769541i \(0.720485\pi\)
\(422\) 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 −0.794322 0.607497i \(-0.792174\pi\)
−0.128947 0.991651i \(-0.541160\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3584.85 + 6209.14i 0.384473 + 0.665926i 0.991696 0.128605i \(-0.0410499\pi\)
−0.607223 + 0.794531i \(0.707717\pi\)
\(444\) 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 0.840856 0.541259i \(-0.182052\pi\)
−0.889172 + 0.457573i \(0.848719\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2549.51 4415.88i −0.257576 0.446134i 0.708016 0.706196i \(-0.249590\pi\)
−0.965592 + 0.260062i \(0.916257\pi\)
\(462\) 0 0
\(463\) 458.859 794.767i 0.0460583 0.0797753i −0.842077 0.539357i \(-0.818667\pi\)
0.888135 + 0.459582i \(0.152001\pi\)
\(464\) 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 0.857769 + 0.514036i \(0.171850\pi\)
0.0162836 + 0.999867i \(0.494817\pi\)
\(480\) 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 −0.940991 0.338432i \(-0.890104\pi\)
0.763586 + 0.645706i \(0.223437\pi\)
\(492\) 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 −0.335689 0.941973i \(-0.608969\pi\)
0.983617 0.180271i \(-0.0576974\pi\)
\(500\) 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 −0.737015 0.675877i \(-0.763765\pi\)
0.953834 + 0.300335i \(0.0970984\pi\)
\(510\) 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 0.941038 0.338301i \(-0.109852\pi\)
−0.763496 + 0.645812i \(0.776519\pi\)
\(548\) 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 −0.468350 0.883543i \(-0.655151\pi\)
0.999346 0.0361685i \(-0.0115153\pi\)
\(564\) 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 0.591130 0.806577i \(-0.298682\pi\)
−0.994081 + 0.108645i \(0.965349\pi\)
\(570\) 0 0
\(571\) 6070.81 10514.9i 0.444931 0.770642i −0.553117 0.833104i \(-0.686562\pi\)
0.998047 + 0.0624614i \(0.0198950\pi\)
\(572\) 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 0.844816 + 0.535057i \(0.179710\pi\)
0.0409650 + 0.999161i \(0.486957\pi\)
\(588\) 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 −0.202495 + 0.979283i \(0.564905\pi\)
−0.746836 + 0.665008i \(0.768428\pi\)
\(600\) 0 0
\(601\) 8056.88 + 13954.9i 0.546833 + 0.947143i 0.998489 + 0.0549509i \(0.0175002\pi\)
−0.451656 + 0.892192i \(0.649166\pi\)
\(602\) 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 −0.812958 0.582322i \(-0.802144\pi\)
0.910785 + 0.412881i \(0.135478\pi\)
\(608\) 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 −0.483867 0.875142i \(-0.660768\pi\)
0.999828 0.0185297i \(-0.00589853\pi\)
\(618\) 0 0
\(619\) 6164.41 + 10677.1i 0.400272 + 0.693292i 0.993759 0.111552i \(-0.0355823\pi\)
−0.593486 + 0.804844i \(0.702249\pi\)
\(620\) 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 0.600715 0.799463i \(-0.294882\pi\)
−0.992713 + 0.120503i \(0.961549\pi\)
\(642\) 0 0
\(643\) 7088.18 12277.1i 0.434729 0.752972i −0.562545 0.826767i \(-0.690178\pi\)
0.997273 + 0.0737946i \(0.0235109\pi\)
\(644\) 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 −0.994252 0.107062i \(-0.965856\pi\)
0.589845 + 0.807517i \(0.299189\pi\)
\(654\) 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 0.987539 0.157374i \(-0.0503030\pi\)
−0.630060 + 0.776547i \(0.716970\pi\)
\(660\) 0 0
\(661\) 5002.37 8664.35i 0.294356 0.509840i −0.680479 0.732768i \(-0.738228\pi\)
0.974835 + 0.222928i \(0.0715614\pi\)
\(662\) 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 0.688490 0.725246i \(-0.258274\pi\)
−0.972326 + 0.233627i \(0.924940\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9424.73 16324.1i −0.535040 0.926716i −0.999161 0.0409446i \(-0.986963\pi\)
0.464122 0.885771i \(-0.346370\pi\)
\(678\) 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 0.954492 0.298238i \(-0.0963989\pi\)
−0.735527 + 0.677495i \(0.763066\pi\)
\(692\) 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 0.862258 0.506469i \(-0.169050\pi\)
−0.869744 + 0.493503i \(0.835716\pi\)
\(710\) 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 0.895982 0.444089i \(-0.146473\pi\)
−0.832584 + 0.553899i \(0.813139\pi\)
\(728\) 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 −0.708821 0.705388i \(-0.750773\pi\)
0.965295 + 0.261163i \(0.0841060\pi\)
\(734\) 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 −0.897064 0.441900i \(-0.854304\pi\)
0.831229 + 0.555930i \(0.187638\pi\)
\(744\) 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 −0.999579 0.0290186i \(-0.990762\pi\)
0.524920 + 0.851151i \(0.324095\pi\)
\(752\) 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 −0.318544 + 0.947908i \(0.603194\pi\)
−0.661641 + 0.749821i \(0.730140\pi\)
\(762\) 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 0.486918 + 0.873448i \(0.338121\pi\)
−0.999887 + 0.0150403i \(0.995212\pi\)
\(770\) 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 −0.989473 0.144719i \(-0.953772\pi\)
0.620067 + 0.784549i \(0.287105\pi\)
\(788\) 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 −0.489680 0.871902i \(-0.662886\pi\)
0.999929 0.0118755i \(-0.00378019\pi\)
\(798\) 0 0
\(799\) −4003.08 6933.54i −0.177245 0.306997i
\(800\) 0 0
\(801\) 0 0