Properties

Label 1008.3.cg.h.577.1
Level $1008$
Weight $3$
Character 1008.577
Analytic conductor $27.466$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.cg (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4660106475\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 577.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1008.577
Dual form 1008.3.cg.h.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.24264 + 4.18154i) q^{5} +(6.74264 + 1.88064i) q^{7} +O(q^{10})\) \(q+(-7.24264 + 4.18154i) q^{5} +(6.74264 + 1.88064i) q^{7} +(-3.00000 + 5.19615i) q^{11} +17.8639i q^{13} +(16.2426 + 9.37769i) q^{17} +(14.7426 - 8.51167i) q^{19} +(-6.72792 - 11.6531i) q^{23} +(22.4706 - 38.9202i) q^{25} -33.9411 q^{29} +(-12.7721 - 7.37396i) q^{31} +(-56.6985 + 14.5738i) q^{35} +(-2.98528 - 5.17066i) q^{37} +35.2354i q^{41} -15.4853 q^{43} +(-28.7574 + 16.6031i) q^{47} +(41.9264 + 25.3609i) q^{49} +(-17.2721 + 29.9161i) q^{53} -50.1785i q^{55} +(23.6985 + 13.6823i) q^{59} +(-34.9706 + 20.1903i) q^{61} +(-74.6985 - 129.382i) q^{65} +(-57.1985 + 99.0707i) q^{67} +18.6030 q^{71} +(-101.353 - 58.5161i) q^{73} +(-30.0000 + 29.3939i) q^{77} +(-44.1690 - 76.5030i) q^{79} -75.7601i q^{83} -156.853 q^{85} +(18.0000 - 10.3923i) q^{89} +(-33.5955 + 120.450i) q^{91} +(-71.1838 + 123.294i) q^{95} -30.5826i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{5} + 10q^{7} + O(q^{10}) \) \( 4q - 12q^{5} + 10q^{7} - 12q^{11} + 48q^{17} + 42q^{19} + 24q^{23} + 22q^{25} - 102q^{31} - 108q^{35} + 22q^{37} - 28q^{43} - 132q^{47} - 2q^{49} - 120q^{53} - 24q^{59} - 72q^{61} - 180q^{65} - 110q^{67} + 312q^{71} - 66q^{73} - 120q^{77} + 10q^{79} - 288q^{85} + 72q^{89} + 222q^{91} - 132q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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
\(5\) −7.24264 + 4.18154i −1.44853 + 0.836308i −0.998394 0.0566528i \(-0.981957\pi\)
−0.450134 + 0.892961i \(0.648624\pi\)
\(6\) 0 0
\(7\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.272727 + 0.472377i −0.969559 0.244857i \(-0.921259\pi\)
0.696832 + 0.717234i \(0.254592\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i 0.726590 + 0.687072i \(0.241104\pi\)
−0.726590 + 0.687072i \(0.758896\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16.2426 + 9.37769i 0.955449 + 0.551629i 0.894770 0.446528i \(-0.147340\pi\)
0.0606799 + 0.998157i \(0.480673\pi\)
\(18\) 0 0
\(19\) 14.7426 8.51167i 0.775928 0.447983i −0.0590569 0.998255i \(-0.518809\pi\)
0.834985 + 0.550272i \(0.185476\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.72792 11.6531i −0.292518 0.506657i 0.681886 0.731458i \(-0.261160\pi\)
−0.974405 + 0.224802i \(0.927827\pi\)
\(24\) 0 0
\(25\) 22.4706 38.9202i 0.898823 1.55681i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) 0 0
\(31\) −12.7721 7.37396i −0.412003 0.237870i 0.279647 0.960103i \(-0.409782\pi\)
−0.691650 + 0.722233i \(0.743116\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −56.6985 + 14.5738i −1.61996 + 0.416396i
\(36\) 0 0
\(37\) −2.98528 5.17066i −0.0806833 0.139748i 0.822860 0.568244i \(-0.192377\pi\)
−0.903544 + 0.428496i \(0.859044\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 35.2354i 0.859399i 0.902972 + 0.429700i \(0.141381\pi\)
−0.902972 + 0.429700i \(0.858619\pi\)
\(42\) 0 0
\(43\) −15.4853 −0.360123 −0.180061 0.983655i \(-0.557630\pi\)
−0.180061 + 0.983655i \(0.557630\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −28.7574 + 16.6031i −0.611859 + 0.353257i −0.773693 0.633561i \(-0.781592\pi\)
0.161834 + 0.986818i \(0.448259\pi\)
\(48\) 0 0
\(49\) 41.9264 + 25.3609i 0.855641 + 0.517570i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −17.2721 + 29.9161i −0.325888 + 0.564455i −0.981692 0.190477i \(-0.938997\pi\)
0.655803 + 0.754932i \(0.272330\pi\)
\(54\) 0 0
\(55\) 50.1785i 0.912336i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 23.6985 + 13.6823i 0.401669 + 0.231904i 0.687204 0.726465i \(-0.258838\pi\)
−0.285535 + 0.958368i \(0.592171\pi\)
\(60\) 0 0
\(61\) −34.9706 + 20.1903i −0.573288 + 0.330988i −0.758461 0.651718i \(-0.774049\pi\)
0.185174 + 0.982706i \(0.440715\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −74.6985 129.382i −1.14921 1.99049i
\(66\) 0 0
\(67\) −57.1985 + 99.0707i −0.853709 + 1.47867i 0.0241291 + 0.999709i \(0.492319\pi\)
−0.877838 + 0.478958i \(0.841015\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 18.6030 0.262015 0.131007 0.991381i \(-0.458179\pi\)
0.131007 + 0.991381i \(0.458179\pi\)
\(72\) 0 0
\(73\) −101.353 58.5161i −1.38839 0.801590i −0.395260 0.918569i \(-0.629346\pi\)
−0.993134 + 0.116979i \(0.962679\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −30.0000 + 29.3939i −0.389610 + 0.381739i
\(78\) 0 0
\(79\) −44.1690 76.5030i −0.559102 0.968393i −0.997572 0.0696469i \(-0.977813\pi\)
0.438470 0.898746i \(-0.355521\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 75.7601i 0.912772i −0.889782 0.456386i \(-0.849144\pi\)
0.889782 0.456386i \(-0.150856\pi\)
\(84\) 0 0
\(85\) −156.853 −1.84533
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 18.0000 10.3923i 0.202247 0.116767i −0.395456 0.918485i \(-0.629413\pi\)
0.597703 + 0.801717i \(0.296080\pi\)
\(90\) 0 0
\(91\) −33.5955 + 120.450i −0.369181 + 1.32362i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −71.1838 + 123.294i −0.749303 + 1.29783i
\(96\) 0 0
\(97\) 30.5826i 0.315284i −0.987496 0.157642i \(-0.949611\pi\)
0.987496 0.157642i \(-0.0503892\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −110.823 63.9839i −1.09726 0.633504i −0.161761 0.986830i \(-0.551717\pi\)
−0.935500 + 0.353326i \(0.885051\pi\)
\(102\) 0 0
\(103\) 70.1102 40.4781i 0.680681 0.392992i −0.119430 0.992843i \(-0.538107\pi\)
0.800112 + 0.599851i \(0.204774\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −84.7279 146.753i −0.791850 1.37152i −0.924820 0.380404i \(-0.875785\pi\)
0.132971 0.991120i \(-0.457548\pi\)
\(108\) 0 0
\(109\) −89.4706 + 154.968i −0.820831 + 1.42172i 0.0842335 + 0.996446i \(0.473156\pi\)
−0.905064 + 0.425275i \(0.860177\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.3970 0.153955 0.0769777 0.997033i \(-0.475473\pi\)
0.0769777 + 0.997033i \(0.475473\pi\)
\(114\) 0 0
\(115\) 97.4558 + 56.2662i 0.847442 + 0.489271i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 91.8823 + 93.7769i 0.772120 + 0.788041i
\(120\) 0 0
\(121\) 42.5000 + 73.6122i 0.351240 + 0.608365i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 166.769i 1.33415i
\(126\) 0 0
\(127\) −167.426 −1.31832 −0.659159 0.752004i \(-0.729088\pi\)
−0.659159 + 0.752004i \(0.729088\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.54416 + 0.891519i −0.0117874 + 0.00680549i −0.505882 0.862603i \(-0.668833\pi\)
0.494095 + 0.869408i \(0.335500\pi\)
\(132\) 0 0
\(133\) 115.412 29.6656i 0.867757 0.223049i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 50.4853 87.4431i 0.368506 0.638271i −0.620826 0.783948i \(-0.713203\pi\)
0.989332 + 0.145677i \(0.0465362\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i −0.862799 0.505548i \(-0.831290\pi\)
0.862799 0.505548i \(-0.168710\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −92.8234 53.5916i −0.649115 0.374766i
\(144\) 0 0
\(145\) 245.823 141.926i 1.69533 0.978801i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 91.4558 + 158.406i 0.613798 + 1.06313i 0.990594 + 0.136833i \(0.0436922\pi\)
−0.376797 + 0.926296i \(0.622974\pi\)
\(150\) 0 0
\(151\) −144.397 + 250.103i −0.956271 + 1.65631i −0.224840 + 0.974396i \(0.572186\pi\)
−0.731432 + 0.681915i \(0.761148\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 123.338 0.795730
\(156\) 0 0
\(157\) 162.000 + 93.5307i 1.03185 + 0.595737i 0.917513 0.397705i \(-0.130193\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −23.4487 91.2255i −0.145644 0.566618i
\(162\) 0 0
\(163\) 8.02944 + 13.9074i 0.0492604 + 0.0853214i 0.889604 0.456732i \(-0.150980\pi\)
−0.840344 + 0.542054i \(0.817647\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 176.117i 1.05459i 0.849681 + 0.527297i \(0.176794\pi\)
−0.849681 + 0.527297i \(0.823206\pi\)
\(168\) 0 0
\(169\) −150.118 −0.888271
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 200.184 115.576i 1.15713 0.668070i 0.206517 0.978443i \(-0.433787\pi\)
0.950615 + 0.310373i \(0.100454\pi\)
\(174\) 0 0
\(175\) 224.706 220.166i 1.28403 1.25809i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 42.6396 73.8540i 0.238210 0.412592i −0.721991 0.691903i \(-0.756773\pi\)
0.960201 + 0.279311i \(0.0901060\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i 0.999881 + 0.0154325i \(0.00491250\pi\)
−0.999881 + 0.0154325i \(0.995087\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 43.2426 + 24.9662i 0.233744 + 0.134952i
\(186\) 0 0
\(187\) −97.4558 + 56.2662i −0.521154 + 0.300889i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −92.6985 160.558i −0.485332 0.840620i 0.514526 0.857475i \(-0.327968\pi\)
−0.999858 + 0.0168547i \(0.994635\pi\)
\(192\) 0 0
\(193\) −113.897 + 197.275i −0.590140 + 1.02215i 0.404073 + 0.914727i \(0.367594\pi\)
−0.994213 + 0.107425i \(0.965739\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −123.161 −0.625185 −0.312593 0.949887i \(-0.601197\pi\)
−0.312593 + 0.949887i \(0.601197\pi\)
\(198\) 0 0
\(199\) −5.39697 3.11594i −0.0271205 0.0156580i 0.486378 0.873748i \(-0.338318\pi\)
−0.513499 + 0.858090i \(0.671651\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −228.853 63.8309i −1.12735 0.314438i
\(204\) 0 0
\(205\) −147.338 255.197i −0.718722 1.24486i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 102.140i 0.488708i
\(210\) 0 0
\(211\) 124.912 0.591999 0.295999 0.955188i \(-0.404347\pi\)
0.295999 + 0.955188i \(0.404347\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 112.154 64.7523i 0.521648 0.301174i
\(216\) 0 0
\(217\) −72.2498 73.7396i −0.332948 0.339814i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −167.522 + 290.156i −0.758017 + 1.31292i
\(222\) 0 0
\(223\) 228.631i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −146.823 84.7685i −0.646799 0.373430i 0.140430 0.990091i \(-0.455152\pi\)
−0.787229 + 0.616661i \(0.788485\pi\)
\(228\) 0 0
\(229\) 30.0442 17.3460i 0.131197 0.0757467i −0.432965 0.901411i \(-0.642533\pi\)
0.564162 + 0.825664i \(0.309199\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −127.243 220.391i −0.546106 0.945883i −0.998536 0.0540833i \(-0.982776\pi\)
0.452431 0.891800i \(-0.350557\pi\)
\(234\) 0 0
\(235\) 138.853 240.500i 0.590863 1.02340i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 197.147 0.824884 0.412442 0.910984i \(-0.364676\pi\)
0.412442 + 0.910984i \(0.364676\pi\)
\(240\) 0 0
\(241\) 76.6173 + 44.2350i 0.317914 + 0.183548i 0.650462 0.759538i \(-0.274575\pi\)
−0.332548 + 0.943086i \(0.607908\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −409.706 8.36308i −1.67227 0.0341350i
\(246\) 0 0
\(247\) 152.051 + 263.361i 0.615592 + 1.06624i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 215.903i 0.860172i 0.902788 + 0.430086i \(0.141517\pi\)
−0.902788 + 0.430086i \(0.858483\pi\)
\(252\) 0 0
\(253\) 80.7351 0.319111
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.72792 2.15232i 0.0145055 0.00837477i −0.492730 0.870182i \(-0.664001\pi\)
0.507235 + 0.861808i \(0.330668\pi\)
\(258\) 0 0
\(259\) −10.4045 40.4781i −0.0401720 0.156286i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −141.338 + 244.805i −0.537407 + 0.930817i 0.461635 + 0.887070i \(0.347263\pi\)
−0.999043 + 0.0437468i \(0.986071\pi\)
\(264\) 0 0
\(265\) 288.896i 1.09017i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 330.765 + 190.967i 1.22961 + 0.709914i 0.966948 0.254974i \(-0.0820669\pi\)
0.262660 + 0.964888i \(0.415400\pi\)
\(270\) 0 0
\(271\) 73.0294 42.1636i 0.269481 0.155585i −0.359171 0.933272i \(-0.616940\pi\)
0.628652 + 0.777687i \(0.283607\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 134.823 + 233.521i 0.490267 + 0.849167i
\(276\) 0 0
\(277\) 68.5589 118.747i 0.247505 0.428691i −0.715328 0.698789i \(-0.753723\pi\)
0.962833 + 0.270098i \(0.0870560\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 325.103 1.15695 0.578474 0.815701i \(-0.303648\pi\)
0.578474 + 0.815701i \(0.303648\pi\)
\(282\) 0 0
\(283\) −168.507 97.2876i −0.595432 0.343773i 0.171811 0.985130i \(-0.445038\pi\)
−0.767242 + 0.641357i \(0.778372\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −66.2649 + 237.579i −0.230888 + 0.827803i
\(288\) 0 0
\(289\) 31.3823 + 54.3557i 0.108589 + 0.188082i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 239.702i 0.818095i −0.912513 0.409048i \(-0.865861\pi\)
0.912513 0.409048i \(-0.134139\pi\)
\(294\) 0 0
\(295\) −228.853 −0.775772
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 208.169 120.187i 0.696219 0.401962i
\(300\) 0 0
\(301\) −104.412 29.1222i −0.346883 0.0967515i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 168.853 292.462i 0.553616 0.958891i
\(306\) 0 0
\(307\) 540.272i 1.75984i 0.475120 + 0.879921i \(0.342405\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 350.044 + 202.098i 1.12554 + 0.649832i 0.942810 0.333330i \(-0.108172\pi\)
0.182732 + 0.983163i \(0.441506\pi\)
\(312\) 0 0
\(313\) −113.706 + 65.6482i −0.363278 + 0.209739i −0.670518 0.741893i \(-0.733928\pi\)
0.307240 + 0.951632i \(0.400595\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −46.9706 81.3554i −0.148172 0.256642i 0.782380 0.622802i \(-0.214006\pi\)
−0.930552 + 0.366160i \(0.880672\pi\)
\(318\) 0 0
\(319\) 101.823 176.363i 0.319196 0.552863i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 319.279 0.988481
\(324\) 0 0
\(325\) 695.265 + 401.411i 2.13928 + 1.23511i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −225.125 + 57.8664i −0.684270 + 0.175886i
\(330\) 0 0
\(331\) −130.684 226.351i −0.394815 0.683840i 0.598263 0.801300i \(-0.295858\pi\)
−0.993078 + 0.117460i \(0.962525\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 956.711i 2.85585i
\(336\) 0 0
\(337\) 136.265 0.404347 0.202173 0.979350i \(-0.435200\pi\)
0.202173 + 0.979350i \(0.435200\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 76.6325 44.2438i 0.224729 0.129747i
\(342\) 0 0
\(343\) 235.000 + 249.848i 0.685131 + 0.728420i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 161.095 279.026i 0.464252 0.804108i −0.534915 0.844906i \(-0.679657\pi\)
0.999167 + 0.0407975i \(0.0129899\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i −0.868088 0.496411i \(-0.834651\pi\)
0.868088 0.496411i \(-0.165349\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 537.448 + 310.296i 1.52252 + 0.879025i 0.999646 + 0.0266116i \(0.00847174\pi\)
0.522869 + 0.852413i \(0.324862\pi\)
\(354\) 0 0
\(355\) −134.735 + 77.7893i −0.379535 + 0.219125i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.1177 17.5245i −0.0281831 0.0488146i 0.851590 0.524209i \(-0.175639\pi\)
−0.879773 + 0.475394i \(0.842305\pi\)
\(360\) 0 0
\(361\) −35.6030 + 61.6663i −0.0986234 + 0.170821i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 978.749 2.68151
\(366\) 0 0
\(367\) 269.831 + 155.787i 0.735234 + 0.424488i 0.820334 0.571885i \(-0.193788\pi\)
−0.0850998 + 0.996372i \(0.527121\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −172.721 + 169.231i −0.465555 + 0.456149i
\(372\) 0 0
\(373\) 340.691 + 590.094i 0.913380 + 1.58202i 0.809255 + 0.587457i \(0.199871\pi\)
0.104125 + 0.994564i \(0.466796\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 606.320i 1.60828i
\(378\) 0 0
\(379\) 624.779 1.64849 0.824246 0.566231i \(-0.191599\pi\)
0.824246 + 0.566231i \(0.191599\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 119.772 69.1502i 0.312720 0.180549i −0.335423 0.942068i \(-0.608879\pi\)
0.648143 + 0.761519i \(0.275546\pi\)
\(384\) 0 0
\(385\) 94.3675 338.336i 0.245110 0.878794i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −281.787 + 488.069i −0.724388 + 1.25468i 0.234838 + 0.972035i \(0.424544\pi\)
−0.959226 + 0.282642i \(0.908789\pi\)
\(390\) 0 0
\(391\) 252.370i 0.645446i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 639.801 + 369.389i 1.61975 + 0.935163i
\(396\) 0 0
\(397\) −392.603 + 226.669i −0.988923 + 0.570955i −0.904952 0.425513i \(-0.860094\pi\)
−0.0839711 + 0.996468i \(0.526760\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −137.875 238.807i −0.343828 0.595528i 0.641312 0.767280i \(-0.278390\pi\)
−0.985140 + 0.171752i \(0.945057\pi\)
\(402\) 0 0
\(403\) 131.727 228.159i 0.326867 0.566151i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 35.8234 0.0880181
\(408\) 0 0
\(409\) −377.441 217.916i −0.922839 0.532801i −0.0382993 0.999266i \(-0.512194\pi\)
−0.884540 + 0.466465i \(0.845527\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 134.059 + 136.823i 0.324598 + 0.331291i
\(414\) 0 0
\(415\) 316.794 + 548.703i 0.763359 + 1.32218i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 301.257i 0.718991i 0.933147 + 0.359496i \(0.117051\pi\)
−0.933147 + 0.359496i \(0.882949\pi\)
\(420\) 0 0
\(421\) −203.794 −0.484071 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 729.963 421.444i 1.71756 0.991633i
\(426\) 0 0
\(427\) −273.765 + 70.3688i −0.641135 + 0.164798i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 197.860 342.703i 0.459072 0.795136i −0.539840 0.841767i \(-0.681515\pi\)
0.998912 + 0.0466317i \(0.0148487\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i 0.998693 + 0.0511184i \(0.0162786\pi\)
−0.998693 + 0.0511184i \(0.983721\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −198.375 114.532i −0.453947 0.262086i
\(438\) 0 0
\(439\) −344.558 + 198.931i −0.784871 + 0.453146i −0.838154 0.545434i \(-0.816365\pi\)
0.0532827 + 0.998579i \(0.483032\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 59.2721 + 102.662i 0.133797 + 0.231743i 0.925137 0.379633i \(-0.123950\pi\)
−0.791340 + 0.611376i \(0.790616\pi\)
\(444\) 0 0
\(445\) −86.9117 + 150.535i −0.195307 + 0.338282i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −713.897 −1.58997 −0.794985 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(450\) 0 0
\(451\) −183.088 105.706i −0.405961 0.234382i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −260.345 1012.85i −0.572187 2.22605i
\(456\) 0 0
\(457\) 62.5883 + 108.406i 0.136955 + 0.237213i 0.926342 0.376682i \(-0.122935\pi\)
−0.789388 + 0.613895i \(0.789602\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 655.767i 1.42249i 0.702945 + 0.711244i \(0.251868\pi\)
−0.702945 + 0.711244i \(0.748132\pi\)
\(462\) 0 0
\(463\) −869.396 −1.87775 −0.938873 0.344265i \(-0.888128\pi\)
−0.938873 + 0.344265i \(0.888128\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −231.551 + 133.686i −0.495827 + 0.286266i −0.726989 0.686649i \(-0.759081\pi\)
0.231162 + 0.972915i \(0.425747\pi\)
\(468\) 0 0
\(469\) −571.985 + 560.428i −1.21958 + 1.19494i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 46.4558 80.4639i 0.0982153 0.170114i
\(474\) 0 0
\(475\) 765.048i 1.61063i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 235.331 + 135.868i 0.491296 + 0.283650i 0.725112 0.688631i \(-0.241788\pi\)
−0.233816 + 0.972281i \(0.575121\pi\)
\(480\) 0 0
\(481\) 92.3680 53.3287i 0.192033 0.110870i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 127.882 + 221.499i 0.263675 + 0.456698i
\(486\) 0 0
\(487\) −280.757 + 486.285i −0.576503 + 0.998532i 0.419374 + 0.907814i \(0.362250\pi\)
−0.995877 + 0.0907186i \(0.971084\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −406.441 −0.827781 −0.413891 0.910327i \(-0.635830\pi\)
−0.413891 + 0.910327i \(0.635830\pi\)
\(492\) 0 0
\(493\) −551.294 318.289i −1.11824 0.645618i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 125.434 + 34.9856i 0.252381 + 0.0703935i
\(498\) 0 0
\(499\) −185.713 321.665i −0.372171 0.644619i 0.617728 0.786391i \(-0.288053\pi\)
−0.989899 + 0.141773i \(0.954720\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 64.6292i 0.128488i −0.997934 0.0642438i \(-0.979536\pi\)
0.997934 0.0642438i \(-0.0204635\pi\)
\(504\) 0 0
\(505\) 1070.21 2.11922
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −871.889 + 503.385i −1.71294 + 0.988969i −0.782410 + 0.622764i \(0.786010\pi\)
−0.930534 + 0.366205i \(0.880657\pi\)
\(510\) 0 0
\(511\) −573.338 585.161i −1.12199 1.14513i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −338.522 + 586.337i −0.657324 + 1.13852i
\(516\) 0 0
\(517\) 199.237i 0.385371i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 322.294 + 186.077i 0.618607 + 0.357153i 0.776327 0.630331i \(-0.217081\pi\)
−0.157719 + 0.987484i \(0.550414\pi\)
\(522\) 0 0
\(523\) 551.904 318.642i 1.05527 0.609258i 0.131147 0.991363i \(-0.458134\pi\)
0.924119 + 0.382105i \(0.124801\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −138.302 239.545i −0.262432 0.454545i
\(528\) 0 0
\(529\) 173.970 301.325i 0.328866 0.569613i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −629.440 −1.18094
\(534\) 0 0
\(535\) 1227.31 + 708.586i 2.29403 + 1.32446i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −257.558 + 141.773i −0.477845 + 0.263030i
\(540\) 0 0
\(541\) −110.412 191.239i −0.204088 0.353491i 0.745754 0.666222i \(-0.232090\pi\)
−0.949842 + 0.312731i \(0.898756\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1496.50i 2.74587i
\(546\) 0 0
\(547\) 160.676 0.293741 0.146870 0.989156i \(-0.453080\pi\)
0.146870 + 0.989156i \(0.453080\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −500.382 + 288.896i −0.908134 + 0.524311i
\(552\) 0 0
\(553\) −153.942 598.898i −0.278375 1.08300i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −237.177 + 410.802i −0.425811 + 0.737526i −0.996496 0.0836431i \(-0.973344\pi\)
0.570685 + 0.821169i \(0.306678\pi\)
\(558\) 0 0
\(559\) 276.627i 0.494860i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −430.301 248.434i −0.764300 0.441269i 0.0665378 0.997784i \(-0.478805\pi\)
−0.830837 + 0.556515i \(0.812138\pi\)
\(564\) 0 0
\(565\) −126.000 + 72.7461i −0.223009 + 0.128754i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 392.647 + 680.084i 0.690065 + 1.19523i 0.971816 + 0.235740i \(0.0757512\pi\)
−0.281752 + 0.959487i \(0.590915\pi\)
\(570\) 0 0
\(571\) −357.521 + 619.245i −0.626132 + 1.08449i 0.362189 + 0.932105i \(0.382030\pi\)
−0.988321 + 0.152388i \(0.951304\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −604.721 −1.05169
\(576\) 0 0
\(577\) 669.117 + 386.315i 1.15965 + 0.669524i 0.951220 0.308514i \(-0.0998317\pi\)
0.208429 + 0.978038i \(0.433165\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 142.477 510.823i 0.245228 0.879214i
\(582\) 0 0
\(583\) −103.632 179.497i −0.177757 0.307885i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 436.477i 0.743572i 0.928318 + 0.371786i \(0.121254\pi\)
−0.928318 + 0.371786i \(0.878746\pi\)
\(588\) 0 0
\(589\) −251.059 −0.426246
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −722.397 + 417.076i −1.21821 + 0.703332i −0.964534 0.263958i \(-0.914972\pi\)
−0.253673 + 0.967290i \(0.581639\pi\)
\(594\) 0 0
\(595\) −1057.60 294.983i −1.77748 0.495770i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −436.794 + 756.549i −0.729205 + 1.26302i 0.228014 + 0.973658i \(0.426777\pi\)
−0.957220 + 0.289363i \(0.906557\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i −0.986203 0.165542i \(-0.947063\pi\)
0.986203 0.165542i \(-0.0529375\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −615.624 355.431i −1.01756 0.587489i
\(606\) 0 0
\(607\) −137.654 + 79.4748i −0.226778 + 0.130930i −0.609085 0.793105i \(-0.708463\pi\)
0.382307 + 0.924035i \(0.375130\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −296.595 513.718i −0.485426 0.840782i
\(612\) 0 0
\(613\) 357.368 618.979i 0.582981 1.00975i −0.412143 0.911119i \(-0.635219\pi\)
0.995124 0.0986338i \(-0.0314473\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 639.381 1.03627 0.518137 0.855298i \(-0.326626\pi\)
0.518137 + 0.855298i \(0.326626\pi\)
\(618\) 0 0
\(619\) −148.978 86.0126i −0.240676 0.138954i 0.374812 0.927101i \(-0.377707\pi\)
−0.615487 + 0.788147i \(0.711041\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 140.912 36.2201i 0.226182 0.0581382i
\(624\) 0 0
\(625\) −135.588 234.846i −0.216941 0.375753i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 111.980i 0.178029i
\(630\) 0 0
\(631\) 1141.06 1.80833 0.904166 0.427180i \(-0.140493\pi\)
0.904166 + 0.427180i \(0.140493\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1212.61 700.100i 1.90962 1.10252i
\(636\) 0 0
\(637\) −453.044 + 748.968i −0.711215 + 1.17577i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 114.551 198.409i 0.178707 0.309530i −0.762731 0.646716i \(-0.776142\pi\)
0.941438 + 0.337186i \(0.109475\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i 0.834975 + 0.550288i \(0.185482\pi\)
−0.834975 + 0.550288i \(0.814518\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1021.37 + 589.687i 1.57862 + 0.911417i 0.995052 + 0.0993530i \(0.0316773\pi\)
0.583568 + 0.812064i \(0.301656\pi\)
\(648\) 0 0
\(649\) −142.191 + 82.0940i −0.219092 + 0.126493i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −77.3818 134.029i −0.118502 0.205252i 0.800672 0.599103i \(-0.204476\pi\)
−0.919174 + 0.393851i \(0.871143\pi\)
\(654\) 0 0
\(655\) 7.45584 12.9139i 0.0113830 0.0197159i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 591.308 0.897280 0.448640 0.893712i \(-0.351908\pi\)
0.448640 + 0.893712i \(0.351908\pi\)
\(660\) 0 0
\(661\) 140.441 + 81.0837i 0.212468 + 0.122668i 0.602458 0.798151i \(-0.294188\pi\)
−0.389990 + 0.920819i \(0.627522\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −711.838 + 697.456i −1.07043 + 1.04881i
\(666\) 0 0
\(667\) 228.353 + 395.519i 0.342359 + 0.592983i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 242.283i 0.361078i
\(672\) 0 0
\(673\) 42.3238 0.0628883 0.0314441 0.999506i \(-0.489989\pi\)
0.0314441 + 0.999506i \(0.489989\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −430.721 + 248.677i −0.636220 + 0.367322i −0.783157 0.621824i \(-0.786392\pi\)
0.146937 + 0.989146i \(0.453059\pi\)
\(678\) 0 0
\(679\) 57.5147 206.207i 0.0847050 0.303693i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −608.080 + 1053.23i −0.890308 + 1.54206i −0.0508015 + 0.998709i \(0.516178\pi\)
−0.839506 + 0.543350i \(0.817156\pi\)
\(684\) 0 0
\(685\) 844.425i 1.23274i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −534.418 308.546i −0.775642 0.447817i
\(690\) 0 0
\(691\) 932.182 538.196i 1.34903 0.778865i 0.360921 0.932596i \(-0.382462\pi\)
0.988113 + 0.153731i \(0.0491290\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 587.683 + 1017.90i 0.845588 + 1.46460i
\(696\) 0 0
\(697\) −330.426 + 572.315i −0.474069 + 0.821112i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 695.897 0.992720 0.496360 0.868117i \(-0.334670\pi\)
0.496360 + 0.868117i \(0.334670\pi\)
\(702\) 0 0
\(703\) −88.0219 50.8194i −0.125209 0.0722894i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −626.912 639.839i −0.886721 0.905006i
\(708\) 0 0
\(709\) −127.412 220.684i −0.179707 0.311261i 0.762073 0.647491i \(-0.224182\pi\)
−0.941780 + 0.336229i \(0.890848\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 198.446i 0.278325i
\(714\) 0 0
\(715\) 896.382 1.25368
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −964.925 + 557.100i −1.34204 + 0.774826i −0.987106 0.160066i \(-0.948829\pi\)
−0.354931 + 0.934892i \(0.615496\pi\)
\(720\) 0 0
\(721\) 548.852 141.078i 0.761238 0.195669i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −762.676 + 1320.99i −1.05197 + 1.82206i
\(726\) 0 0
\(727\) 398.345i 0.547930i −0.961740 0.273965i \(-0.911665\pi\)
0.961740 0.273965i \(-0.0883353\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −251.522 145.216i −0.344079 0.198654i
\(732\) 0 0
\(733\) 818.514 472.569i 1.11666 0.644706i 0.176116 0.984369i \(-0.443646\pi\)
0.940547 + 0.339663i \(0.110313\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −343.191 594.424i −0.465659 0.806546i
\(738\) 0 0
\(739\) 96.3162 166.825i 0.130333 0.225744i −0.793472 0.608607i \(-0.791729\pi\)
0.923805 + 0.382863i \(0.125062\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −911.616 −1.22694 −0.613470 0.789718i \(-0.710227\pi\)
−0.613470 + 0.789718i \(0.710227\pi\)
\(744\) 0 0
\(745\) −1324.76 764.853i −1.77821 1.02665i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −295.301 1148.85i −0.394260 1.53384i
\(750\) 0 0
\(751\) −195.831 339.189i −0.260760 0.451650i 0.705684 0.708527i \(-0.250640\pi\)
−0.966444 + 0.256877i \(0.917307\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2415.21i 3.19895i
\(756\) 0 0
\(757\) −152.823 −0.201879 −0.100940 0.994893i \(-0.532185\pi\)
−0.100940 + 0.994893i \(0.532185\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 109.331 63.1223i 0.143667 0.0829465i −0.426443 0.904514i \(-0.640234\pi\)
0.570111 + 0.821568i \(0.306900\pi\)
\(762\) 0 0
\(763\) −894.706 + 876.629i −1.17262 + 1.14892i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −244.419 + 423.347i −0.318669 + 0.551951i
\(768\) 0 0
\(769\) 369.148i 0.480037i 0.970768 + 0.240018i \(0.0771535\pi\)
−0.970768 + 0.240018i \(0.922847\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1215.65 + 701.853i 1.57263 + 0.907961i 0.995845 + 0.0910674i \(0.0290279\pi\)
0.576789 + 0.816893i \(0.304305\pi\)
\(774\) 0 0
\(775\) −573.992 + 331.394i −0.740634 + 0.427605i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 299.912 + 519.462i 0.384996 + 0.666832i
\(780\) 0 0
\(781\) −55.8091 + 96.6642i −0.0714585 + 0.123770i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1564.41 −1.99288
\(786\) 0 0
\(787\) −196.161 113.253i −0.249251 0.143905i 0.370170 0.928964i \(-0.379299\pi\)
−0.619421 + 0.785059i \(0.712633\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 117.302 + 32.7174i 0.148295 + 0.0413621i
\(792\) 0 0
\(793\) −360.676 624.709i −0.454825 0.787780i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 688.414i 0.863756i −0.901932 0.431878i \(-0.857851\pi\)
0.901932 0.431878i \(-0.142149\pi\)
\(798\) 0 0
\(799\) −622.794 </