Properties

Label 1008.3.cg.h.145.1
Level $1008$
Weight $3$
Character 1008.145
Analytic conductor $27.466$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 145.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1008.145
Dual form 1008.3.cg.h.577.1

$q$-expansion

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

Character values

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

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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 −0.450134 0.892961i \(-0.648624\pi\)
−0.998394 + 0.0566528i \(0.981957\pi\)
\(6\) 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 0.696832 0.717234i \(-0.254592\pi\)
−0.969559 + 0.244857i \(0.921259\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i −0.726590 0.687072i \(-0.758896\pi\)
0.726590 0.687072i \(-0.241104\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16.2426 9.37769i 0.955449 0.551629i 0.0606799 0.998157i \(-0.480673\pi\)
0.894770 + 0.446528i \(0.147340\pi\)
\(18\) 0 0
\(19\) 14.7426 + 8.51167i 0.775928 + 0.447983i 0.834985 0.550272i \(-0.185476\pi\)
−0.0590569 + 0.998255i \(0.518809\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.72792 + 11.6531i −0.292518 + 0.506657i −0.974405 0.224802i \(-0.927827\pi\)
0.681886 + 0.731458i \(0.261160\pi\)
\(24\) 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 −0.691650 0.722233i \(-0.743116\pi\)
0.279647 + 0.960103i \(0.409782\pi\)
\(32\) 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 −0.903544 0.428496i \(-0.859044\pi\)
0.822860 + 0.568244i \(0.192377\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 35.2354i 0.859399i −0.902972 0.429700i \(-0.858619\pi\)
0.902972 0.429700i \(-0.141381\pi\)
\(42\) 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 0.161834 0.986818i \(-0.448259\pi\)
−0.773693 + 0.633561i \(0.781592\pi\)
\(48\) 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 0.655803 0.754932i \(-0.272330\pi\)
−0.981692 + 0.190477i \(0.938997\pi\)
\(54\) 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 −0.285535 0.958368i \(-0.592171\pi\)
0.687204 + 0.726465i \(0.258838\pi\)
\(60\) 0 0
\(61\) −34.9706 20.1903i −0.573288 0.330988i 0.185174 0.982706i \(-0.440715\pi\)
−0.758461 + 0.651718i \(0.774049\pi\)
\(62\) 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 −0.877838 0.478958i \(-0.841015\pi\)
0.0241291 0.999709i \(-0.492319\pi\)
\(68\) 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 −0.993134 0.116979i \(-0.962679\pi\)
−0.395260 + 0.918569i \(0.629346\pi\)
\(74\) 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 0.438470 + 0.898746i \(0.355521\pi\)
−0.997572 + 0.0696469i \(0.977813\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 75.7601i 0.912772i 0.889782 + 0.456386i \(0.150856\pi\)
−0.889782 + 0.456386i \(0.849144\pi\)
\(84\) 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 0.597703 0.801717i \(-0.296080\pi\)
−0.395456 + 0.918485i \(0.629413\pi\)
\(90\) 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 \(0.0503892\pi\)
−0.987496 + 0.157642i \(0.949611\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −110.823 + 63.9839i −1.09726 + 0.633504i −0.935500 0.353326i \(-0.885051\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(102\) 0 0
\(103\) 70.1102 + 40.4781i 0.680681 + 0.392992i 0.800112 0.599851i \(-0.204774\pi\)
−0.119430 + 0.992843i \(0.538107\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −84.7279 + 146.753i −0.791850 + 1.37152i 0.132971 + 0.991120i \(0.457548\pi\)
−0.924820 + 0.380404i \(0.875785\pi\)
\(108\) 0 0
\(109\) −89.4706 154.968i −0.820831 1.42172i −0.905064 0.425275i \(-0.860177\pi\)
0.0842335 0.996446i \(-0.473156\pi\)
\(110\) 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 0.494095 0.869408i \(-0.335500\pi\)
−0.505882 + 0.862603i \(0.668833\pi\)
\(132\) 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 0.989332 0.145677i \(-0.0465362\pi\)
−0.620826 + 0.783948i \(0.713203\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i 0.862799 + 0.505548i \(0.168710\pi\)
−0.862799 + 0.505548i \(0.831290\pi\)
\(140\) 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 −0.376797 0.926296i \(-0.622974\pi\)
0.990594 0.136833i \(-0.0436922\pi\)
\(150\) 0 0
\(151\) −144.397 250.103i −0.956271 1.65631i −0.731432 0.681915i \(-0.761148\pi\)
−0.224840 0.974396i \(-0.572186\pi\)
\(152\) 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 0.114334 0.993442i \(-0.463527\pi\)
0.917513 + 0.397705i \(0.130193\pi\)
\(158\) 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 −0.840344 0.542054i \(-0.817647\pi\)
0.889604 + 0.456732i \(0.150980\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 176.117i 1.05459i −0.849681 0.527297i \(-0.823206\pi\)
0.849681 0.527297i \(-0.176794\pi\)
\(168\) 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 0.950615 0.310373i \(-0.100454\pi\)
0.206517 + 0.978443i \(0.433787\pi\)
\(174\) 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 0.960201 0.279311i \(-0.0901060\pi\)
−0.721991 + 0.691903i \(0.756773\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i −0.999881 0.0154325i \(-0.995087\pi\)
0.999881 0.0154325i \(-0.00491250\pi\)
\(182\) 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 −0.999858 0.0168547i \(-0.994635\pi\)
0.514526 + 0.857475i \(0.327968\pi\)
\(192\) 0 0
\(193\) −113.897 197.275i −0.590140 1.02215i −0.994213 0.107425i \(-0.965739\pi\)
0.404073 0.914727i \(-0.367594\pi\)
\(194\) 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 −0.513499 0.858090i \(-0.671651\pi\)
0.486378 + 0.873748i \(0.338318\pi\)
\(200\) 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 \(0.171327\pi\)
−0.858613 + 0.512625i \(0.828673\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −146.823 + 84.7685i −0.646799 + 0.373430i −0.787229 0.616661i \(-0.788485\pi\)
0.140430 + 0.990091i \(0.455152\pi\)
\(228\) 0 0
\(229\) 30.0442 + 17.3460i 0.131197 + 0.0757467i 0.564162 0.825664i \(-0.309199\pi\)
−0.432965 + 0.901411i \(0.642533\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −127.243 + 220.391i −0.546106 + 0.945883i 0.452431 + 0.891800i \(0.350557\pi\)
−0.998536 + 0.0540833i \(0.982776\pi\)
\(234\) 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 −0.332548 0.943086i \(-0.607908\pi\)
0.650462 + 0.759538i \(0.274575\pi\)
\(242\) 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 \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(252\) 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 0.507235 0.861808i \(-0.330668\pi\)
−0.492730 + 0.870182i \(0.664001\pi\)
\(258\) 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 −0.999043 0.0437468i \(-0.986071\pi\)
0.461635 0.887070i \(-0.347263\pi\)
\(264\) 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 0.262660 0.964888i \(-0.415400\pi\)
0.966948 + 0.254974i \(0.0820669\pi\)
\(270\) 0 0
\(271\) 73.0294 + 42.1636i 0.269481 + 0.155585i 0.628652 0.777687i \(-0.283607\pi\)
−0.359171 + 0.933272i \(0.616940\pi\)
\(272\) 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 0.962833 0.270098i \(-0.0870560\pi\)
−0.715328 + 0.698789i \(0.753723\pi\)
\(278\) 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 −0.767242 0.641357i \(-0.778372\pi\)
0.171811 + 0.985130i \(0.445038\pi\)
\(284\) 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 \(0.134139\pi\)
−0.912513 + 0.409048i \(0.865861\pi\)
\(294\) 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 \(-0.657595\pi\)
0.475120 0.879921i \(-0.342405\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 350.044 202.098i 1.12554 0.649832i 0.182732 0.983163i \(-0.441506\pi\)
0.942810 + 0.333330i \(0.108172\pi\)
\(312\) 0 0
\(313\) −113.706 65.6482i −0.363278 0.209739i 0.307240 0.951632i \(-0.400595\pi\)
−0.670518 + 0.741893i \(0.733928\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −46.9706 + 81.3554i −0.148172 + 0.256642i −0.930552 0.366160i \(-0.880672\pi\)
0.782380 + 0.622802i \(0.214006\pi\)
\(318\) 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 −0.993078 0.117460i \(-0.962525\pi\)
0.598263 + 0.801300i \(0.295858\pi\)
\(332\) 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 0.999167 0.0407975i \(-0.0129899\pi\)
−0.534915 + 0.844906i \(0.679657\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i 0.868088 + 0.496411i \(0.165349\pi\)
−0.868088 + 0.496411i \(0.834651\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 537.448 310.296i 1.52252 0.879025i 0.522869 0.852413i \(-0.324862\pi\)
0.999646 0.0266116i \(-0.00847174\pi\)
\(354\) 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 −0.879773 0.475394i \(-0.842305\pi\)
0.851590 + 0.524209i \(0.175639\pi\)
\(360\) 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 −0.0850998 0.996372i \(-0.527121\pi\)
0.820334 + 0.571885i \(0.193788\pi\)
\(368\) 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 0.104125 0.994564i \(-0.466796\pi\)
0.809255 0.587457i \(-0.199871\pi\)
\(374\) 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 0.648143 0.761519i \(-0.275546\pi\)
−0.335423 + 0.942068i \(0.608879\pi\)
\(384\) 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 −0.959226 0.282642i \(-0.908789\pi\)
0.234838 0.972035i \(-0.424544\pi\)
\(390\) 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 −0.0839711 0.996468i \(-0.526760\pi\)
−0.904952 + 0.425513i \(0.860094\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −137.875 + 238.807i −0.343828 + 0.595528i −0.985140 0.171752i \(-0.945057\pi\)
0.641312 + 0.767280i \(0.278390\pi\)
\(402\) 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 −0.884540 0.466465i \(-0.845527\pi\)
−0.0382993 + 0.999266i \(0.512194\pi\)
\(410\) 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 \(-0.882949\pi\)
0.933147 0.359496i \(-0.117051\pi\)
\(420\) 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 0.998912 0.0466317i \(-0.0148487\pi\)
−0.539840 + 0.841767i \(0.681515\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i −0.998693 0.0511184i \(-0.983721\pi\)
0.998693 0.0511184i \(-0.0162786\pi\)
\(434\) 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 0.0532827 0.998579i \(-0.483032\pi\)
−0.838154 + 0.545434i \(0.816365\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 59.2721 102.662i 0.133797 0.231743i −0.791340 0.611376i \(-0.790616\pi\)
0.925137 + 0.379633i \(0.123950\pi\)
\(444\) 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 −0.789388 0.613895i \(-0.789602\pi\)
0.926342 + 0.376682i \(0.122935\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 655.767i 1.42249i −0.702945 0.711244i \(-0.748132\pi\)
0.702945 0.711244i \(-0.251868\pi\)
\(462\) 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 0.231162 0.972915i \(-0.425747\pi\)
−0.726989 + 0.686649i \(0.759081\pi\)
\(468\) 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 −0.233816 0.972281i \(-0.575121\pi\)
0.725112 + 0.688631i \(0.241788\pi\)
\(480\) 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 −0.995877 0.0907186i \(-0.971084\pi\)
0.419374 0.907814i \(-0.362250\pi\)
\(488\) 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 −0.989899 0.141773i \(-0.954720\pi\)
0.617728 + 0.786391i \(0.288053\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 64.6292i 0.128488i 0.997934 + 0.0642438i \(0.0204635\pi\)
−0.997934 + 0.0642438i \(0.979536\pi\)
\(504\) 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 −0.930534 0.366205i \(-0.880657\pi\)
−0.782410 0.622764i \(-0.786010\pi\)
\(510\) 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 −0.157719 0.987484i \(-0.550414\pi\)
0.776327 + 0.630331i \(0.217081\pi\)
\(522\) 0 0
\(523\) 551.904 + 318.642i 1.05527 + 0.609258i 0.924119 0.382105i \(-0.124801\pi\)
0.131147 + 0.991363i \(0.458134\pi\)
\(524\) 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 −0.949842 0.312731i \(-0.898756\pi\)
0.745754 + 0.666222i \(0.232090\pi\)
\(542\) 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 0.570685 0.821169i \(-0.306678\pi\)
−0.996496 + 0.0836431i \(0.973344\pi\)
\(558\) 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 −0.830837 0.556515i \(-0.812138\pi\)
0.0665378 + 0.997784i \(0.478805\pi\)
\(564\) 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 −0.281752 0.959487i \(-0.590915\pi\)
0.971816 0.235740i \(-0.0757512\pi\)
\(570\) 0 0
\(571\) −357.521 619.245i −0.626132 1.08449i −0.988321 0.152388i \(-0.951304\pi\)
0.362189 0.932105i \(-0.382030\pi\)
\(572\) 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 0.208429 0.978038i \(-0.433165\pi\)
0.951220 + 0.308514i \(0.0998317\pi\)
\(578\) 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 \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 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 −0.253673 0.967290i \(-0.581639\pi\)
−0.964534 + 0.263958i \(0.914972\pi\)
\(594\) 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 −0.957220 0.289363i \(-0.906557\pi\)
0.228014 0.973658i \(-0.426777\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i 0.986203 + 0.165542i \(0.0529375\pi\)
−0.986203 + 0.165542i \(0.947063\pi\)
\(602\) 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 0.382307 0.924035i \(-0.375130\pi\)
−0.609085 + 0.793105i \(0.708463\pi\)
\(608\) 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 0.995124 + 0.0986338i \(0.0314473\pi\)
−0.412143 + 0.911119i \(0.635219\pi\)
\(614\) 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 −0.615487 0.788147i \(-0.711041\pi\)
0.374812 + 0.927101i \(0.377707\pi\)
\(620\) 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 0.941438 0.337186i \(-0.109475\pi\)
−0.762731 + 0.646716i \(0.776142\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i −0.834975 0.550288i \(-0.814518\pi\)
0.834975 0.550288i \(-0.185482\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1021.37 589.687i 1.57862 0.911417i 0.583568 0.812064i \(-0.301656\pi\)
0.995052 0.0993530i \(-0.0316773\pi\)
\(648\) 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 −0.919174 0.393851i \(-0.871143\pi\)
0.800672 + 0.599103i \(0.204476\pi\)
\(654\) 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 −0.389990 0.920819i \(-0.627522\pi\)
0.602458 + 0.798151i \(0.294188\pi\)
\(662\) 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 0.146937 0.989146i \(-0.453059\pi\)
−0.783157 + 0.621824i \(0.786392\pi\)
\(678\) 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 −0.839506 0.543350i \(-0.817156\pi\)
−0.0508015 0.998709i \(-0.516178\pi\)
\(684\) 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 0.988113 0.153731i \(-0.0491290\pi\)
0.360921 + 0.932596i \(0.382462\pi\)
\(692\) 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 −0.941780 0.336229i \(-0.890848\pi\)
0.762073 + 0.647491i \(0.224182\pi\)
\(710\) 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 −0.354931 0.934892i \(-0.615496\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(720\) 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 \(0.0883353\pi\)
−0.961740 + 0.273965i \(0.911665\pi\)
\(728\) 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 0.940547 0.339663i \(-0.110313\pi\)
0.176116 + 0.984369i \(0.443646\pi\)
\(734\) 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 0.923805 0.382863i \(-0.125062\pi\)
−0.793472 + 0.608607i \(0.791729\pi\)
\(740\) 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 −0.966444 0.256877i \(-0.917307\pi\)
0.705684 + 0.708527i \(0.250640\pi\)
\(752\) 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 0.570111 0.821568i \(-0.306900\pi\)
−0.426443 + 0.904514i \(0.640234\pi\)
\(762\) 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 \(-0.922847\pi\)
0.970768 0.240018i \(-0.0771535\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1215.65 701.853i 1.57263 0.907961i 0.576789 0.816893i \(-0.304305\pi\)
0.995845 0.0910674i \(-0.0290279\pi\)
\(774\) 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 −0.619421 0.785059i \(-0.712633\pi\)
0.370170 + 0.928964i \(0.379299\pi\)
\(788\) 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 \(0.142149\pi\)
−0.901932 + 0.431878i \(0.857851\pi\)
\(798\) 0 0
\(799\)