Properties

Label 108.5.g.a.17.2
Level 108
Weight 5
Character 108.17
Analytic conductor 11.164
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{10} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.2
Root \(4.23522 + 4.06612i\) of \(x^{8} - 3 x^{7} + 6 x^{6} + 121 x^{5} + 1104 x^{4} - 1647 x^{3} + 6529 x^{2} + 85254 x + 440076\)
Character \(\chi\) \(=\) 108.17
Dual form 108.5.g.a.89.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-10.6364 - 6.14094i) q^{5} +(7.14202 + 12.3703i) q^{7} +O(q^{10})\) \(q+(-10.6364 - 6.14094i) q^{5} +(7.14202 + 12.3703i) q^{7} +(-90.2145 + 52.0854i) q^{11} +(-37.6173 + 65.1551i) q^{13} +341.998i q^{17} -706.329 q^{19} +(516.421 + 298.156i) q^{23} +(-237.078 - 410.630i) q^{25} +(-1127.90 + 651.194i) q^{29} +(-514.510 + 891.158i) q^{31} -175.435i q^{35} +563.132 q^{37} +(-85.8619 - 49.5724i) q^{41} +(448.257 + 776.404i) q^{43} +(-372.885 + 215.285i) q^{47} +(1098.48 - 1902.63i) q^{49} -5271.47i q^{53} +1279.41 q^{55} +(4883.74 + 2819.63i) q^{59} +(-565.626 - 979.693i) q^{61} +(800.227 - 462.012i) q^{65} +(676.412 - 1171.58i) q^{67} -5681.42i q^{71} +4236.54 q^{73} +(-1288.63 - 743.990i) q^{77} +(3067.71 + 5313.43i) q^{79} +(-6503.75 + 3754.94i) q^{83} +(2100.19 - 3637.64i) q^{85} -8721.70i q^{89} -1074.65 q^{91} +(7512.81 + 4337.53i) q^{95} +(-2720.65 - 4712.31i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 9q^{5} + 13q^{7} + O(q^{10}) \) \( 8q + 9q^{5} + 13q^{7} + 18q^{11} - 5q^{13} + 562q^{19} + 1719q^{23} + 353q^{25} - 2115q^{29} + 187q^{31} + 16q^{37} + 7920q^{41} - 68q^{43} - 13689q^{47} - 327q^{49} - 1818q^{55} + 20052q^{59} - 1937q^{61} - 25965q^{65} + 154q^{67} - 7802q^{73} + 25641q^{77} - 2195q^{79} - 37017q^{83} - 3042q^{85} + 15830q^{91} + 37116q^{95} + 7282q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) −10.6364 6.14094i −0.425457 0.245638i 0.271952 0.962311i \(-0.412331\pi\)
−0.697409 + 0.716673i \(0.745664\pi\)
\(6\) 0 0
\(7\) 7.14202 + 12.3703i 0.145756 + 0.252456i 0.929655 0.368432i \(-0.120105\pi\)
−0.783899 + 0.620888i \(0.786772\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −90.2145 + 52.0854i −0.745575 + 0.430458i −0.824093 0.566455i \(-0.808315\pi\)
0.0785180 + 0.996913i \(0.474981\pi\)
\(12\) 0 0
\(13\) −37.6173 + 65.1551i −0.222588 + 0.385533i −0.955593 0.294690i \(-0.904784\pi\)
0.733005 + 0.680223i \(0.238117\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 341.998i 1.18338i 0.806164 + 0.591692i \(0.201540\pi\)
−0.806164 + 0.591692i \(0.798460\pi\)
\(18\) 0 0
\(19\) −706.329 −1.95659 −0.978295 0.207218i \(-0.933559\pi\)
−0.978295 + 0.207218i \(0.933559\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 516.421 + 298.156i 0.976222 + 0.563622i 0.901127 0.433554i \(-0.142741\pi\)
0.0750946 + 0.997176i \(0.476074\pi\)
\(24\) 0 0
\(25\) −237.078 410.630i −0.379324 0.657009i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1127.90 + 651.194i −1.34114 + 0.774309i −0.986975 0.160873i \(-0.948569\pi\)
−0.354168 + 0.935182i \(0.615236\pi\)
\(30\) 0 0
\(31\) −514.510 + 891.158i −0.535391 + 0.927324i 0.463754 + 0.885964i \(0.346502\pi\)
−0.999144 + 0.0413597i \(0.986831\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 175.435i 0.143212i
\(36\) 0 0
\(37\) 563.132 0.411346 0.205673 0.978621i \(-0.434062\pi\)
0.205673 + 0.978621i \(0.434062\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −85.8619 49.5724i −0.0510779 0.0294898i 0.474244 0.880394i \(-0.342722\pi\)
−0.525321 + 0.850904i \(0.676055\pi\)
\(42\) 0 0
\(43\) 448.257 + 776.404i 0.242432 + 0.419905i 0.961407 0.275132i \(-0.0887215\pi\)
−0.718974 + 0.695037i \(0.755388\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −372.885 + 215.285i −0.168802 + 0.0974581i −0.582021 0.813174i \(-0.697738\pi\)
0.413219 + 0.910632i \(0.364405\pi\)
\(48\) 0 0
\(49\) 1098.48 1902.63i 0.457511 0.792432i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5271.47i 1.87664i −0.345773 0.938318i \(-0.612383\pi\)
0.345773 0.938318i \(-0.387617\pi\)
\(54\) 0 0
\(55\) 1279.41 0.422947
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4883.74 + 2819.63i 1.40297 + 0.810005i 0.994696 0.102854i \(-0.0327975\pi\)
0.408274 + 0.912859i \(0.366131\pi\)
\(60\) 0 0
\(61\) −565.626 979.693i −0.152009 0.263287i 0.779957 0.625833i \(-0.215241\pi\)
−0.931966 + 0.362546i \(0.881908\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 800.227 462.012i 0.189403 0.109352i
\(66\) 0 0
\(67\) 676.412 1171.58i 0.150682 0.260989i −0.780796 0.624786i \(-0.785186\pi\)
0.931478 + 0.363797i \(0.118520\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5681.42i 1.12704i −0.826101 0.563522i \(-0.809446\pi\)
0.826101 0.563522i \(-0.190554\pi\)
\(72\) 0 0
\(73\) 4236.54 0.794996 0.397498 0.917603i \(-0.369878\pi\)
0.397498 + 0.917603i \(0.369878\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1288.63 743.990i −0.217343 0.125483i
\(78\) 0 0
\(79\) 3067.71 + 5313.43i 0.491542 + 0.851375i 0.999953 0.00973957i \(-0.00310025\pi\)
−0.508411 + 0.861115i \(0.669767\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6503.75 + 3754.94i −0.944077 + 0.545063i −0.891236 0.453540i \(-0.850161\pi\)
−0.0528411 + 0.998603i \(0.516828\pi\)
\(84\) 0 0
\(85\) 2100.19 3637.64i 0.290684 0.503479i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8721.70i 1.10109i −0.834807 0.550543i \(-0.814421\pi\)
0.834807 0.550543i \(-0.185579\pi\)
\(90\) 0 0
\(91\) −1074.65 −0.129774
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7512.81 + 4337.53i 0.832445 + 0.480612i
\(96\) 0 0
\(97\) −2720.65 4712.31i −0.289154 0.500830i 0.684454 0.729056i \(-0.260041\pi\)
−0.973608 + 0.228226i \(0.926707\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6480.14 + 3741.31i −0.635246 + 0.366759i −0.782781 0.622297i \(-0.786199\pi\)
0.147535 + 0.989057i \(0.452866\pi\)
\(102\) 0 0
\(103\) −6788.27 + 11757.6i −0.639860 + 1.10827i 0.345604 + 0.938381i \(0.387674\pi\)
−0.985463 + 0.169889i \(0.945659\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16741.7i 1.46229i 0.682224 + 0.731143i \(0.261013\pi\)
−0.682224 + 0.731143i \(0.738987\pi\)
\(108\) 0 0
\(109\) −12068.7 −1.01579 −0.507897 0.861418i \(-0.669577\pi\)
−0.507897 + 0.861418i \(0.669577\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −610.202 352.300i −0.0477878 0.0275903i 0.475916 0.879491i \(-0.342117\pi\)
−0.523704 + 0.851901i \(0.675450\pi\)
\(114\) 0 0
\(115\) −3661.92 6342.63i −0.276894 0.479594i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4230.63 + 2442.56i −0.298752 + 0.172485i
\(120\) 0 0
\(121\) −1894.72 + 3281.76i −0.129412 + 0.224148i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 13499.7i 0.863981i
\(126\) 0 0
\(127\) −16050.0 −0.995105 −0.497552 0.867434i \(-0.665768\pi\)
−0.497552 + 0.867434i \(0.665768\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13427.1 + 7752.17i 0.782422 + 0.451732i 0.837288 0.546762i \(-0.184140\pi\)
−0.0548658 + 0.998494i \(0.517473\pi\)
\(132\) 0 0
\(133\) −5044.62 8737.53i −0.285184 0.493953i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 771.295 445.307i 0.0410941 0.0237257i −0.479312 0.877644i \(-0.659114\pi\)
0.520406 + 0.853919i \(0.325781\pi\)
\(138\) 0 0
\(139\) −4679.09 + 8104.42i −0.242176 + 0.419462i −0.961334 0.275385i \(-0.911195\pi\)
0.719158 + 0.694847i \(0.244528\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7837.25i 0.383258i
\(144\) 0 0
\(145\) 15995.8 0.760798
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −35220.7 20334.7i −1.58645 0.915937i −0.993886 0.110412i \(-0.964783\pi\)
−0.592563 0.805524i \(-0.701884\pi\)
\(150\) 0 0
\(151\) 12487.2 + 21628.5i 0.547661 + 0.948577i 0.998434 + 0.0559386i \(0.0178151\pi\)
−0.450773 + 0.892639i \(0.648852\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10945.1 6319.16i 0.455572 0.263024i
\(156\) 0 0
\(157\) 16459.2 28508.2i 0.667743 1.15656i −0.310791 0.950478i \(-0.600594\pi\)
0.978534 0.206086i \(-0.0660727\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 8517.75i 0.328604i
\(162\) 0 0
\(163\) 13796.3 0.519262 0.259631 0.965708i \(-0.416399\pi\)
0.259631 + 0.965708i \(0.416399\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9814.14 5666.20i −0.351900 0.203170i 0.313622 0.949548i \(-0.398458\pi\)
−0.665522 + 0.746378i \(0.731791\pi\)
\(168\) 0 0
\(169\) 11450.4 + 19832.6i 0.400910 + 0.694396i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 33922.6 19585.2i 1.13344 0.654389i 0.188639 0.982047i \(-0.439592\pi\)
0.944797 + 0.327657i \(0.106259\pi\)
\(174\) 0 0
\(175\) 3386.43 5865.47i 0.110577 0.191525i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24097.3i 0.752078i −0.926604 0.376039i \(-0.877286\pi\)
0.926604 0.376039i \(-0.122714\pi\)
\(180\) 0 0
\(181\) 10277.1 0.313699 0.156850 0.987623i \(-0.449866\pi\)
0.156850 + 0.987623i \(0.449866\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5989.72 3458.16i −0.175010 0.101042i
\(186\) 0 0
\(187\) −17813.1 30853.2i −0.509397 0.882301i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 30337.2 17515.2i 0.831590 0.480119i −0.0228068 0.999740i \(-0.507260\pi\)
0.854397 + 0.519621i \(0.173927\pi\)
\(192\) 0 0
\(193\) −2620.27 + 4538.45i −0.0703448 + 0.121841i −0.899052 0.437841i \(-0.855743\pi\)
0.828708 + 0.559682i \(0.189077\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 42421.5i 1.09308i 0.837431 + 0.546542i \(0.184056\pi\)
−0.837431 + 0.546542i \(0.815944\pi\)
\(198\) 0 0
\(199\) 31270.0 0.789627 0.394814 0.918761i \(-0.370809\pi\)
0.394814 + 0.918761i \(0.370809\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −16111.0 9301.69i −0.390958 0.225720i
\(204\) 0 0
\(205\) 608.843 + 1054.55i 0.0144876 + 0.0250933i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 63721.1 36789.4i 1.45878 0.842229i
\(210\) 0 0
\(211\) 15562.2 26954.6i 0.349548 0.605435i −0.636621 0.771177i \(-0.719669\pi\)
0.986169 + 0.165742i \(0.0530019\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11010.9i 0.238202i
\(216\) 0 0
\(217\) −14698.6 −0.312145
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22282.9 12865.0i −0.456234 0.263407i
\(222\) 0 0
\(223\) −8013.95 13880.6i −0.161153 0.279124i 0.774130 0.633027i \(-0.218188\pi\)
−0.935282 + 0.353903i \(0.884854\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −58481.7 + 33764.5i −1.13493 + 0.655251i −0.945170 0.326579i \(-0.894104\pi\)
−0.189759 + 0.981831i \(0.560771\pi\)
\(228\) 0 0
\(229\) −39032.9 + 67607.0i −0.744321 + 1.28920i 0.206191 + 0.978512i \(0.433893\pi\)
−0.950512 + 0.310689i \(0.899440\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 61204.9i 1.12739i 0.825983 + 0.563696i \(0.190621\pi\)
−0.825983 + 0.563696i \(0.809379\pi\)
\(234\) 0 0
\(235\) 5288.21 0.0957576
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −37373.3 21577.5i −0.654282 0.377750i 0.135813 0.990735i \(-0.456635\pi\)
−0.790095 + 0.612984i \(0.789969\pi\)
\(240\) 0 0
\(241\) 28103.8 + 48677.2i 0.483873 + 0.838092i 0.999828 0.0185233i \(-0.00589649\pi\)
−0.515956 + 0.856615i \(0.672563\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −23367.9 + 13491.4i −0.389302 + 0.224764i
\(246\) 0 0
\(247\) 26570.2 46020.9i 0.435513 0.754330i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15739.4i 0.249828i −0.992168 0.124914i \(-0.960135\pi\)
0.992168 0.124914i \(-0.0398655\pi\)
\(252\) 0 0
\(253\) −62118.3 −0.970462
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 50887.7 + 29380.0i 0.770454 + 0.444822i 0.833036 0.553218i \(-0.186600\pi\)
−0.0625827 + 0.998040i \(0.519934\pi\)
\(258\) 0 0
\(259\) 4021.91 + 6966.14i 0.0599560 + 0.103847i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −81699.8 + 47169.4i −1.18116 + 0.681944i −0.956283 0.292443i \(-0.905532\pi\)
−0.224879 + 0.974387i \(0.572199\pi\)
\(264\) 0 0
\(265\) −32371.8 + 56069.6i −0.460973 + 0.798428i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 79782.6i 1.10256i 0.834319 + 0.551282i \(0.185861\pi\)
−0.834319 + 0.551282i \(0.814139\pi\)
\(270\) 0 0
\(271\) −76677.1 −1.04406 −0.522032 0.852926i \(-0.674826\pi\)
−0.522032 + 0.852926i \(0.674826\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 42775.7 + 24696.6i 0.565629 + 0.326566i
\(276\) 0 0
\(277\) −56577.9 97995.9i −0.737374 1.27717i −0.953674 0.300842i \(-0.902732\pi\)
0.216300 0.976327i \(-0.430601\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 83614.5 48274.8i 1.05893 0.611376i 0.133797 0.991009i \(-0.457283\pi\)
0.925137 + 0.379633i \(0.123950\pi\)
\(282\) 0 0
\(283\) −15268.5 + 26445.9i −0.190645 + 0.330206i −0.945464 0.325726i \(-0.894391\pi\)
0.754819 + 0.655933i \(0.227725\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1416.19i 0.0171932i
\(288\) 0 0
\(289\) −33441.6 −0.400397
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3511.45 2027.34i −0.0409026 0.0236151i 0.479409 0.877591i \(-0.340851\pi\)
−0.520312 + 0.853976i \(0.674184\pi\)
\(294\) 0 0
\(295\) −34630.4 59981.5i −0.397936 0.689245i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −38852.8 + 22431.7i −0.434590 + 0.250911i
\(300\) 0 0
\(301\) −6402.92 + 11090.2i −0.0706717 + 0.122407i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 13893.9i 0.149357i
\(306\) 0 0
\(307\) 44297.5 0.470005 0.235002 0.971995i \(-0.424490\pi\)
0.235002 + 0.971995i \(0.424490\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 82350.1 + 47544.8i 0.851419 + 0.491567i 0.861129 0.508386i \(-0.169758\pi\)
−0.00971065 + 0.999953i \(0.503091\pi\)
\(312\) 0 0
\(313\) 85286.0 + 147720.i 0.870541 + 1.50782i 0.861438 + 0.507862i \(0.169564\pi\)
0.00910220 + 0.999959i \(0.497103\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −105654. + 60999.2i −1.05140 + 0.607024i −0.923040 0.384704i \(-0.874303\pi\)
−0.128356 + 0.991728i \(0.540970\pi\)
\(318\) 0 0
\(319\) 67835.4 117494.i 0.666615 1.15461i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 241563.i 2.31540i
\(324\) 0 0
\(325\) 35672.9 0.337731
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5326.30 3075.14i −0.0492078 0.0284101i
\(330\) 0 0
\(331\) 47607.1 + 82457.9i 0.434526 + 0.752621i 0.997257 0.0740192i \(-0.0235826\pi\)
−0.562731 + 0.826640i \(0.690249\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −14389.2 + 8307.62i −0.128218 + 0.0740265i
\(336\) 0 0
\(337\) −4204.88 + 7283.07i −0.0370249 + 0.0641291i −0.883944 0.467593i \(-0.845121\pi\)
0.846919 + 0.531722i \(0.178455\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 107194.i 0.921852i
\(342\) 0 0
\(343\) 65677.6 0.558250
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5224.52 3016.38i −0.0433897 0.0250511i 0.478148 0.878279i \(-0.341308\pi\)
−0.521538 + 0.853228i \(0.674642\pi\)
\(348\) 0 0
\(349\) −69799.9 120897.i −0.573065 0.992577i −0.996249 0.0865335i \(-0.972421\pi\)
0.423184 0.906044i \(-0.360912\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 73954.5 42697.7i 0.593493 0.342653i −0.172985 0.984925i \(-0.555341\pi\)
0.766477 + 0.642271i \(0.222008\pi\)
\(354\) 0 0
\(355\) −34889.3 + 60430.1i −0.276844 + 0.479508i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 90712.4i 0.703846i −0.936029 0.351923i \(-0.885528\pi\)
0.936029 0.351923i \(-0.114472\pi\)
\(360\) 0 0
\(361\) 368579. 2.82824
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −45061.6 26016.3i −0.338237 0.195281i
\(366\) 0 0
\(367\) 12770.7 + 22119.5i 0.0948160 + 0.164226i 0.909532 0.415634i \(-0.136440\pi\)
−0.814716 + 0.579860i \(0.803107\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 65209.9 37649.0i 0.473768 0.273530i
\(372\) 0 0
\(373\) 117264. 203107.i 0.842844 1.45985i −0.0446361 0.999003i \(-0.514213\pi\)
0.887480 0.460846i \(-0.152454\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 97984.7i 0.689407i
\(378\) 0 0
\(379\) −107483. −0.748278 −0.374139 0.927373i \(-0.622062\pi\)
−0.374139 + 0.927373i \(0.622062\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 142398. + 82213.7i 0.970750 + 0.560463i 0.899465 0.436993i \(-0.143957\pi\)
0.0712849 + 0.997456i \(0.477290\pi\)
\(384\) 0 0
\(385\) 9137.60 + 15826.8i 0.0616468 + 0.106775i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −158396. + 91449.9i −1.04675 + 0.604343i −0.921739 0.387811i \(-0.873231\pi\)
−0.125015 + 0.992155i \(0.539898\pi\)
\(390\) 0 0
\(391\) −101969. + 176615.i −0.666981 + 1.15525i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 75354.6i 0.482965i
\(396\) 0 0
\(397\) −277717. −1.76206 −0.881031 0.473059i \(-0.843150\pi\)
−0.881031 + 0.473059i \(0.843150\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 145546. + 84030.8i 0.905128 + 0.522576i 0.878861 0.477079i \(-0.158304\pi\)
0.0262679 + 0.999655i \(0.491638\pi\)
\(402\) 0 0
\(403\) −38709.0 67046.0i −0.238343 0.412822i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −50802.7 + 29331.0i −0.306689 + 0.177067i
\(408\) 0 0
\(409\) 44190.6 76540.3i 0.264170 0.457555i −0.703176 0.711016i \(-0.748235\pi\)
0.967346 + 0.253461i \(0.0815688\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 80551.4i 0.472251i
\(414\) 0 0
\(415\) 92235.5 0.535552
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 131141. + 75714.4i 0.746983 + 0.431271i 0.824603 0.565712i \(-0.191399\pi\)
−0.0776195 + 0.996983i \(0.524732\pi\)
\(420\) 0 0
\(421\) 66110.2 + 114506.i 0.372996 + 0.646048i 0.990025 0.140893i \(-0.0449972\pi\)
−0.617029 + 0.786940i \(0.711664\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 140435. 81080.0i 0.777494 0.448886i
\(426\) 0 0
\(427\) 8079.43 13994.0i 0.0443124 0.0767512i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 231482.i 1.24613i 0.782170 + 0.623065i \(0.214113\pi\)
−0.782170 + 0.623065i \(0.785887\pi\)
\(432\) 0 0
\(433\) −218090. −1.16321 −0.581607 0.813470i \(-0.697576\pi\)
−0.581607 + 0.813470i \(0.697576\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −364763. 210596.i −1.91007 1.10278i
\(438\) 0 0
\(439\) −44778.5 77558.6i −0.232349 0.402440i 0.726150 0.687536i \(-0.241308\pi\)
−0.958499 + 0.285096i \(0.907974\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −228878. + 132143.i −1.16626 + 0.673343i −0.952797 0.303607i \(-0.901809\pi\)
−0.213467 + 0.976950i \(0.568476\pi\)
\(444\) 0 0
\(445\) −53559.5 + 92767.7i −0.270468 + 0.468465i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 33967.2i 0.168487i 0.996445 + 0.0842435i \(0.0268474\pi\)
−0.996445 + 0.0842435i \(0.973153\pi\)
\(450\) 0 0
\(451\) 10328.0 0.0507765
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11430.5 + 6599.40i 0.0552131 + 0.0318773i
\(456\) 0 0
\(457\) −41636.9 72117.2i −0.199363 0.345308i 0.748959 0.662617i \(-0.230554\pi\)
−0.948322 + 0.317309i \(0.897221\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 49805.5 28755.2i 0.234355 0.135305i −0.378224 0.925714i \(-0.623465\pi\)
0.612580 + 0.790409i \(0.290132\pi\)
\(462\) 0 0
\(463\) −40897.0 + 70835.6i −0.190778 + 0.330438i −0.945508 0.325598i \(-0.894434\pi\)
0.754730 + 0.656035i \(0.227768\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 161762.i 0.741726i 0.928688 + 0.370863i \(0.120938\pi\)
−0.928688 + 0.370863i \(0.879062\pi\)
\(468\) 0 0
\(469\) 19323.8 0.0878511
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −80878.6 46695.3i −0.361503 0.208714i
\(474\) 0 0
\(475\) 167455. + 290040.i 0.742182 + 1.28550i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −111249. + 64229.4i −0.484868 + 0.279939i −0.722443 0.691430i \(-0.756981\pi\)
0.237575 + 0.971369i \(0.423648\pi\)
\(480\) 0 0
\(481\) −21183.5 + 36690.9i −0.0915605 + 0.158587i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 66829.5i 0.284109i
\(486\) 0 0
\(487\) −255021. −1.07527 −0.537636 0.843177i \(-0.680682\pi\)
−0.537636 + 0.843177i \(0.680682\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 151163. + 87274.1i 0.627023 + 0.362012i 0.779598 0.626280i \(-0.215423\pi\)
−0.152575 + 0.988292i \(0.548757\pi\)
\(492\) 0 0
\(493\) −222707. 385740.i −0.916305 1.58709i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 70281.2 40576.9i 0.284529 0.164273i
\(498\) 0 0
\(499\) −104865. + 181631.i −0.421141 + 0.729438i −0.996051 0.0887787i \(-0.971704\pi\)
0.574910 + 0.818216i \(0.305037\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 288148.i 1.13888i 0.822031 + 0.569442i \(0.192841\pi\)
−0.822031 + 0.569442i \(0.807159\pi\)
\(504\) 0 0
\(505\) 91900.8 0.360360
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −73335.8 42340.5i −0.283061 0.163426i 0.351747 0.936095i \(-0.385588\pi\)
−0.634809 + 0.772669i \(0.718921\pi\)
\(510\) 0 0
\(511\) 30257.4 + 52407.4i 0.115875 + 0.200702i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 144406. 83372.8i 0.544466 0.314347i
\(516\) 0 0
\(517\) 22426.4 38843.7i 0.0839032 0.145325i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 80148.3i 0.295270i −0.989042 0.147635i \(-0.952834\pi\)
0.989042 0.147635i \(-0.0471660\pi\)
\(522\) 0 0
\(523\) 127783. 0.467163 0.233581 0.972337i \(-0.424955\pi\)
0.233581 + 0.972337i \(0.424955\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −304774. 175962.i −1.09738 0.633573i
\(528\) 0 0
\(529\) 37873.6 + 65598.9i 0.135340 + 0.234415i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6459.79 3729.56i 0.0227386 0.0131281i
\(534\) 0 0
\(535\) 102810. 178072.i 0.359193 0.622140i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 228860.i 0.787756i
\(540\) 0 0
\(541\) 1167.97 0.00399060 0.00199530 0.999998i \(-0.499365\pi\)
0.00199530 + 0.999998i \(0.499365\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 128367. + 74112.9i 0.432177 + 0.249518i
\(546\) 0 0
\(547\) −138903. 240586.i −0.464232 0.804074i 0.534934 0.844894i \(-0.320336\pi\)
−0.999167 + 0.0408196i \(0.987003\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 796669. 459957.i 2.62407 1.51501i
\(552\) 0 0
\(553\) −43819.3 + 75897.3i −0.143290 + 0.248185i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 127126.i 0.409755i −0.978788 0.204877i \(-0.934320\pi\)
0.978788 0.204877i \(-0.0656795\pi\)
\(558\) 0 0
\(559\) −67448.9 −0.215850
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −107207. 61896.1i −0.338226 0.195275i 0.321261 0.946991i \(-0.395893\pi\)
−0.659487 + 0.751716i \(0.729227\pi\)
\(564\) 0 0
\(565\) 4326.91 + 7494.43i 0.0135544 + 0.0234770i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −53531.2 + 30906.3i −0.165342 + 0.0954601i −0.580388 0.814340i \(-0.697099\pi\)
0.415046 + 0.909801i \(0.363766\pi\)
\(570\) 0 0
\(571\) 102067. 176786.i 0.313050 0.542219i −0.665971 0.745978i \(-0.731982\pi\)
0.979021 + 0.203759i \(0.0653158\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 282745.i 0.855182i
\(576\) 0 0
\(577\) 555504. 1.66854 0.834269 0.551358i \(-0.185890\pi\)
0.834269 + 0.551358i \(0.185890\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −92899.9 53635.8i −0.275209 0.158892i
\(582\) 0 0
\(583\) 274567. + 475563.i 0.807813 + 1.39917i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6076.70 + 3508.38i −0.0176357 + 0.0101820i −0.508792 0.860890i \(-0.669908\pi\)
0.491156 + 0.871071i \(0.336574\pi\)
\(588\) 0 0
\(589\) 363414. 629451.i 1.04754 1.81439i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 77064.9i 0.219153i −0.993978 0.109576i \(-0.965051\pi\)
0.993978 0.109576i \(-0.0349494\pi\)
\(594\) 0 0
\(595\) 59998.4 0.169475
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −473683. 273481.i −1.32018 0.762208i −0.336425 0.941710i \(-0.609218\pi\)
−0.983757 + 0.179503i \(0.942551\pi\)
\(600\) 0 0
\(601\) 269988. + 467633.i 0.747473 + 1.29466i 0.949030 + 0.315184i \(0.102066\pi\)
−0.201558 + 0.979477i \(0.564600\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 40306.2 23270.8i 0.110119 0.0635770i
\(606\) 0 0
\(607\) −249663. + 432429.i −0.677606 + 1.17365i 0.298094 + 0.954536i \(0.403649\pi\)
−0.975700 + 0.219111i \(0.929684\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32393.8i 0.0867719i
\(612\) 0 0
\(613\) 80551.4 0.214364 0.107182 0.994239i \(-0.465817\pi\)
0.107182 + 0.994239i \(0.465817\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −385247. 222423.i −1.01197 0.584263i −0.100205 0.994967i \(-0.531950\pi\)
−0.911769 + 0.410703i \(0.865283\pi\)
\(618\) 0 0
\(619\) −280471. 485789.i −0.731992 1.26785i −0.956031 0.293267i \(-0.905258\pi\)
0.224039 0.974580i \(-0.428076\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 107890. 62290.6i 0.277976 0.160489i
\(624\) 0 0
\(625\) −65272.6 + 113055.i −0.167098 + 0.289422i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 192590.i 0.486780i
\(630\) 0 0
\(631\) 621772. 1.56161 0.780805 0.624775i \(-0.214809\pi\)
0.780805 + 0.624775i \(0.214809\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 170715. + 98562.4i 0.423374 + 0.244435i
\(636\) 0 0
\(637\) 82643.9 + 143144.i 0.203672 + 0.352771i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 279418. 161322.i 0.680045 0.392624i −0.119827 0.992795i \(-0.538234\pi\)
0.799872 + 0.600171i \(0.204901\pi\)
\(642\) 0 0
\(643\) 244906. 424190.i 0.592350 1.02598i −0.401565 0.915830i \(-0.631534\pi\)
0.993915 0.110149i \(-0.0351329\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26885.7i 0.0642263i 0.999484 + 0.0321132i \(0.0102237\pi\)
−0.999484 + 0.0321132i \(0.989776\pi\)
\(648\) 0 0
\(649\) −587446. −1.39469
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 618540. + 357114.i 1.45058 + 0.837492i 0.998514 0.0544925i \(-0.0173541\pi\)
0.452065 + 0.891985i \(0.350687\pi\)
\(654\) 0 0
\(655\) −95211.2 164911.i −0.221925 0.384385i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −203254. + 117349.i −0.468024 + 0.270214i −0.715412 0.698703i \(-0.753761\pi\)
0.247388 + 0.968916i \(0.420428\pi\)
\(660\) 0 0
\(661\) −313281. + 542619.i −0.717020 + 1.24191i 0.245155 + 0.969484i \(0.421161\pi\)
−0.962175 + 0.272431i \(0.912172\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 123915.i 0.280208i
\(666\) 0 0
\(667\) −776630. −1.74567
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 102055. + 58921.7i 0.226668 + 0.130867i
\(672\) 0 0
\(673\) −320999. 555987.i −0.708718 1.22754i −0.965333 0.261022i \(-0.915940\pi\)
0.256614 0.966514i \(-0.417393\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −568932. + 328473.i −1.24132 + 0.716675i −0.969362 0.245635i \(-0.921004\pi\)
−0.271955 + 0.962310i \(0.587670\pi\)
\(678\) 0 0
\(679\) 38861.9 67310.9i 0.0842917 0.145998i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 76710.6i 0.164442i −0.996614 0.0822212i \(-0.973799\pi\)
0.996614 0.0822212i \(-0.0262014\pi\)
\(684\) 0 0
\(685\) −10938.4 −0.0233117
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 343463. + 198299.i 0.723505 + 0.417716i
\(690\) 0 0
\(691\) 285435. + 494387.i 0.597793 + 1.03541i 0.993146 + 0.116878i \(0.0372887\pi\)
−0.395354 + 0.918529i \(0.629378\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 99537.6 57468.1i 0.206071 0.118975i
\(696\) 0 0
\(697\) 16953.7 29364.6i 0.0348978 0.0604447i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4271.71i 0.00869292i −0.999991 0.00434646i \(-0.998616\pi\)
0.999991 0.00434646i \(-0.00138353\pi\)
\(702\) 0 0
\(703\) −397757. −0.804835
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −92562.7 53441.1i −0.185181 0.106914i
\(708\) 0 0
\(709\) −74221.7 128556.i −0.147652 0.255740i 0.782707 0.622390i \(-0.213838\pi\)
−0.930359 + 0.366650i \(0.880505\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −531408. + 306809.i −1.04532 + 0.603516i
\(714\) 0 0
\(715\) −48128.1 + 83360.3i −0.0941427 + 0.163060i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 549881.i 1.06368i 0.846845 + 0.531840i \(0.178499\pi\)
−0.846845 + 0.531840i \(0.821501\pi\)
\(720\) 0 0
\(721\) −193928. −0.373052
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 534800. + 308767.i 1.01746 + 0.587429i
\(726\) 0 0
\(727\) −322003. 557726.i −0.609244 1.05524i −0.991365 0.131130i \(-0.958139\pi\)
0.382121 0.924112i \(-0.375194\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −265528. + 153303.i −0.496908 + 0.286890i
\(732\) 0 0
\(733\) −416415. + 721253.i −0.775031 + 1.34239i 0.159747 + 0.987158i \(0.448932\pi\)
−0.934777 + 0.355234i \(0.884401\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 140925.i 0.259449i
\(738\) 0 0
\(739\) 472487. 0.865170 0.432585 0.901593i \(-0.357602\pi\)
0.432585 + 0.901593i \(0.357602\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −847338. 489211.i −1.53490 0.886173i −0.999126 0.0418100i \(-0.986688\pi\)
−0.535771 0.844363i \(-0.679979\pi\)
\(744\) 0 0
\(745\) 249749. + 432577.i 0.449977 + 0.779383i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −207101. + 119570.i −0.369163 + 0.213136i
\(750\) 0 0
\(751\) 83140.6 144004.i 0.147412 0.255325i −0.782858 0.622200i \(-0.786239\pi\)
0.930270 + 0.366875i \(0.119572\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 306733.i 0.538105i
\(756\) 0 0
\(757\) −238453. −0.416114 −0.208057 0.978117i \(-0.566714\pi\)
−0.208057 + 0.978117i \(0.566714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 518174. + 299168.i 0.894759 + 0.516589i 0.875496 0.483225i \(-0.160535\pi\)
0.0192628 + 0.999814i \(0.493868\pi\)
\(762\) 0 0
\(763\) −86194.6 149294.i −0.148058 0.256444i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −367426. + 212134.i −0.624568 + 0.360594i
\(768\) 0 0
\(769\) −333662. + 577919.i −0.564227 + 0.977270i 0.432894 + 0.901445i \(0.357492\pi\)
−0.997121 + 0.0758248i \(0.975841\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 848153.i 1.41943i −0.704487 0.709717i \(-0.748823\pi\)
0.704487 0.709717i \(-0.251177\pi\)
\(774\) 0 0
\(775\) 487916. 0.812347
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 60646.7 + 35014.4i 0.0999384 + 0.0576995i
\(780\) 0 0
\(781\) 295919. + 512547.i 0.485145 + 0.840295i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −350134. + 202150.i −0.568192 + 0.328046i
\(786\) 0 0
\(787\) 483866. 838081.i 0.781225 1.35312i −0.150004 0.988685i \(-0.547929\pi\)
0.931229 0.364436i \(-0.118738\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10064.6i 0.0160858i
\(792\) 0 0
\(793\) 85109.3 0.135341
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 583828. + 337073.i 0.919111 + 0.530649i 0.883351 0.468711i \(-0.155282\pi\)
0.0357599 + 0.999360i \(0.488615\pi\)
\(798\) 0 0
\(799\) −73627.0 127526.i −0.115330 0.199758i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −382197. + 220662.i −0.592729 + 0.342212i