Properties

Label 252.4.t.a.89.6
Level $252$
Weight $4$
Character 252.89
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + 14344616 x^{9} - 18123280 x^{8} - 273588032 x^{7} + 1239640536 x^{6} - 1407381792 x^{5} - 1961185792 x^{4} + 4297169408 x^{3} + 2991779296 x^{2} - 11217342336 x + 7375227456\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.6
Root \(1.09700 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.89
Dual form 252.4.t.a.17.6

$q$-expansion

\(f(q)\) \(=\) \(q+(4.27106 - 7.39769i) q^{5} +(-12.5787 + 13.5933i) q^{7} +O(q^{10})\) \(q+(4.27106 - 7.39769i) q^{5} +(-12.5787 + 13.5933i) q^{7} +(-27.4679 + 15.8586i) q^{11} +9.92568i q^{13} +(63.7751 + 110.462i) q^{17} +(-100.923 - 58.2677i) q^{19} +(55.8271 + 32.2318i) q^{23} +(26.0161 + 45.0612i) q^{25} +113.016i q^{29} +(6.33498 - 3.65751i) q^{31} +(46.8346 + 151.111i) q^{35} +(-184.736 + 319.972i) q^{37} +211.959 q^{41} -432.263 q^{43} +(-200.021 + 346.446i) q^{47} +(-26.5540 - 341.971i) q^{49} +(-121.869 + 70.3612i) q^{53} +270.933i q^{55} +(259.447 + 449.375i) q^{59} +(23.5627 + 13.6039i) q^{61} +(73.4271 + 42.3932i) q^{65} +(68.3597 + 118.403i) q^{67} -604.779i q^{71} +(-41.9780 + 24.2360i) q^{73} +(129.940 - 572.860i) q^{77} +(415.618 - 719.872i) q^{79} -37.2350 q^{83} +1089.55 q^{85} +(235.356 - 407.649i) q^{89} +(-134.922 - 124.852i) q^{91} +(-862.093 + 497.730i) q^{95} +522.691i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{7} + O(q^{10}) \) \( 16q - 4q^{7} - 72q^{19} - 212q^{25} - 708q^{31} + 76q^{37} + 1408q^{43} + 400q^{49} - 1632q^{61} - 1528q^{67} - 2700q^{73} - 364q^{79} + 7392q^{85} + 2472q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) 4.27106 7.39769i 0.382015 0.661670i −0.609335 0.792913i \(-0.708564\pi\)
0.991350 + 0.131243i \(0.0418968\pi\)
\(6\) 0 0
\(7\) −12.5787 + 13.5933i −0.679184 + 0.733968i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −27.4679 + 15.8586i −0.752900 + 0.434687i −0.826741 0.562583i \(-0.809808\pi\)
0.0738410 + 0.997270i \(0.476474\pi\)
\(12\) 0 0
\(13\) 9.92568i 0.211761i 0.994379 + 0.105880i \(0.0337660\pi\)
−0.994379 + 0.105880i \(0.966234\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 63.7751 + 110.462i 0.909866 + 1.57593i 0.814248 + 0.580517i \(0.197149\pi\)
0.0956180 + 0.995418i \(0.469517\pi\)
\(18\) 0 0
\(19\) −100.923 58.2677i −1.21859 0.703554i −0.253974 0.967211i \(-0.581738\pi\)
−0.964616 + 0.263657i \(0.915071\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 55.8271 + 32.2318i 0.506120 + 0.292208i 0.731237 0.682123i \(-0.238943\pi\)
−0.225118 + 0.974332i \(0.572277\pi\)
\(24\) 0 0
\(25\) 26.0161 + 45.0612i 0.208129 + 0.360489i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 113.016i 0.723671i 0.932242 + 0.361836i \(0.117850\pi\)
−0.932242 + 0.361836i \(0.882150\pi\)
\(30\) 0 0
\(31\) 6.33498 3.65751i 0.0367031 0.0211906i −0.481536 0.876426i \(-0.659921\pi\)
0.518239 + 0.855236i \(0.326588\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 46.8346 + 151.111i 0.226185 + 0.729783i
\(36\) 0 0
\(37\) −184.736 + 319.972i −0.820822 + 1.42171i 0.0842481 + 0.996445i \(0.473151\pi\)
−0.905071 + 0.425261i \(0.860182\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 211.959 0.807376 0.403688 0.914897i \(-0.367728\pi\)
0.403688 + 0.914897i \(0.367728\pi\)
\(42\) 0 0
\(43\) −432.263 −1.53301 −0.766506 0.642237i \(-0.778007\pi\)
−0.766506 + 0.642237i \(0.778007\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −200.021 + 346.446i −0.620766 + 1.07520i 0.368577 + 0.929597i \(0.379845\pi\)
−0.989343 + 0.145601i \(0.953488\pi\)
\(48\) 0 0
\(49\) −26.5540 341.971i −0.0774170 0.996999i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −121.869 + 70.3612i −0.315849 + 0.182356i −0.649541 0.760327i \(-0.725039\pi\)
0.333692 + 0.942682i \(0.391706\pi\)
\(54\) 0 0
\(55\) 270.933i 0.664228i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 259.447 + 449.375i 0.572493 + 0.991587i 0.996309 + 0.0858389i \(0.0273570\pi\)
−0.423816 + 0.905748i \(0.639310\pi\)
\(60\) 0 0
\(61\) 23.5627 + 13.6039i 0.0494573 + 0.0285542i 0.524525 0.851395i \(-0.324243\pi\)
−0.475067 + 0.879949i \(0.657576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 73.4271 + 42.3932i 0.140116 + 0.0808958i
\(66\) 0 0
\(67\) 68.3597 + 118.403i 0.124649 + 0.215898i 0.921596 0.388151i \(-0.126886\pi\)
−0.796947 + 0.604050i \(0.793553\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 604.779i 1.01090i −0.862855 0.505451i \(-0.831326\pi\)
0.862855 0.505451i \(-0.168674\pi\)
\(72\) 0 0
\(73\) −41.9780 + 24.2360i −0.0673035 + 0.0388577i −0.533274 0.845942i \(-0.679039\pi\)
0.465971 + 0.884800i \(0.345705\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 129.940 572.860i 0.192312 0.847837i
\(78\) 0 0
\(79\) 415.618 719.872i 0.591907 1.02521i −0.402068 0.915610i \(-0.631708\pi\)
0.993975 0.109604i \(-0.0349582\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −37.2350 −0.0492418 −0.0246209 0.999697i \(-0.507838\pi\)
−0.0246209 + 0.999697i \(0.507838\pi\)
\(84\) 0 0
\(85\) 1089.55 1.39033
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 235.356 407.649i 0.280311 0.485513i −0.691150 0.722711i \(-0.742896\pi\)
0.971461 + 0.237198i \(0.0762290\pi\)
\(90\) 0 0
\(91\) −134.922 124.852i −0.155425 0.143825i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −862.093 + 497.730i −0.931041 + 0.537537i
\(96\) 0 0
\(97\) 522.691i 0.547126i 0.961854 + 0.273563i \(0.0882022\pi\)
−0.961854 + 0.273563i \(0.911798\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −527.361 913.417i −0.519549 0.899885i −0.999742 0.0227221i \(-0.992767\pi\)
0.480193 0.877163i \(-0.340567\pi\)
\(102\) 0 0
\(103\) −643.991 371.808i −0.616061 0.355683i 0.159273 0.987235i \(-0.449085\pi\)
−0.775334 + 0.631552i \(0.782418\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −204.383 118.001i −0.184659 0.106613i 0.404821 0.914396i \(-0.367334\pi\)
−0.589480 + 0.807783i \(0.700667\pi\)
\(108\) 0 0
\(109\) 116.269 + 201.385i 0.102171 + 0.176965i 0.912579 0.408901i \(-0.134088\pi\)
−0.810408 + 0.585866i \(0.800755\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2266.43i 1.88680i −0.331661 0.943398i \(-0.607609\pi\)
0.331661 0.943398i \(-0.392391\pi\)
\(114\) 0 0
\(115\) 476.882 275.328i 0.386691 0.223256i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2303.74 522.549i −1.77465 0.402538i
\(120\) 0 0
\(121\) −162.508 + 281.472i −0.122095 + 0.211474i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1512.23 1.08206
\(126\) 0 0
\(127\) 1675.71 1.17083 0.585414 0.810735i \(-0.300932\pi\)
0.585414 + 0.810735i \(0.300932\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −593.103 + 1027.28i −0.395570 + 0.685147i −0.993174 0.116645i \(-0.962786\pi\)
0.597604 + 0.801791i \(0.296119\pi\)
\(132\) 0 0
\(133\) 2061.52 638.938i 1.34403 0.416564i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2743.44 1583.92i 1.71086 0.987764i 0.777451 0.628943i \(-0.216512\pi\)
0.933406 0.358821i \(-0.116821\pi\)
\(138\) 0 0
\(139\) 607.821i 0.370897i −0.982654 0.185448i \(-0.940626\pi\)
0.982654 0.185448i \(-0.0593738\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −157.408 272.638i −0.0920496 0.159435i
\(144\) 0 0
\(145\) 836.055 + 482.696i 0.478832 + 0.276454i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1117.57 645.230i −0.614463 0.354760i 0.160247 0.987077i \(-0.448771\pi\)
−0.774710 + 0.632317i \(0.782104\pi\)
\(150\) 0 0
\(151\) −1452.49 2515.79i −0.782796 1.35584i −0.930307 0.366782i \(-0.880459\pi\)
0.147510 0.989060i \(-0.452874\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 62.4857i 0.0323805i
\(156\) 0 0
\(157\) −1022.35 + 590.254i −0.519697 + 0.300047i −0.736811 0.676099i \(-0.763669\pi\)
0.217114 + 0.976146i \(0.430336\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1140.37 + 353.440i −0.558220 + 0.173012i
\(162\) 0 0
\(163\) −803.791 + 1392.21i −0.386244 + 0.668994i −0.991941 0.126701i \(-0.959561\pi\)
0.605697 + 0.795695i \(0.292894\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2621.57 1.21475 0.607374 0.794416i \(-0.292223\pi\)
0.607374 + 0.794416i \(0.292223\pi\)
\(168\) 0 0
\(169\) 2098.48 0.955157
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1321.78 + 2289.40i −0.580887 + 1.00613i 0.414488 + 0.910055i \(0.363961\pi\)
−0.995375 + 0.0960706i \(0.969373\pi\)
\(174\) 0 0
\(175\) −939.777 213.166i −0.405945 0.0920791i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3594.15 + 2075.08i −1.50078 + 0.866475i −0.500779 + 0.865575i \(0.666953\pi\)
−1.00000 0.000899820i \(0.999714\pi\)
\(180\) 0 0
\(181\) 4040.50i 1.65927i 0.558304 + 0.829636i \(0.311452\pi\)
−0.558304 + 0.829636i \(0.688548\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1578.04 + 2733.24i 0.627133 + 1.08623i
\(186\) 0 0
\(187\) −3503.54 2022.77i −1.37008 0.791014i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3227.37 + 1863.32i 1.22264 + 0.705892i 0.965480 0.260477i \(-0.0838797\pi\)
0.257161 + 0.966369i \(0.417213\pi\)
\(192\) 0 0
\(193\) −668.472 1157.83i −0.249314 0.431825i 0.714022 0.700124i \(-0.246872\pi\)
−0.963336 + 0.268299i \(0.913539\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3451.92i 1.24842i −0.781256 0.624210i \(-0.785421\pi\)
0.781256 0.624210i \(-0.214579\pi\)
\(198\) 0 0
\(199\) −4621.37 + 2668.15i −1.64623 + 0.950453i −0.667682 + 0.744447i \(0.732713\pi\)
−0.978551 + 0.206006i \(0.933953\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1536.25 1421.59i −0.531151 0.491506i
\(204\) 0 0
\(205\) 905.289 1568.01i 0.308430 0.534216i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3696.18 1.22330
\(210\) 0 0
\(211\) 1800.90 0.587578 0.293789 0.955870i \(-0.405084\pi\)
0.293789 + 0.955870i \(0.405084\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1846.22 + 3197.75i −0.585634 + 1.01435i
\(216\) 0 0
\(217\) −29.9682 + 132.120i −0.00937501 + 0.0413312i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1096.41 + 633.011i −0.333721 + 0.192674i
\(222\) 0 0
\(223\) 2815.72i 0.845535i 0.906238 + 0.422768i \(0.138941\pi\)
−0.906238 + 0.422768i \(0.861059\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1976.56 + 3423.50i 0.577925 + 1.00100i 0.995717 + 0.0924528i \(0.0294707\pi\)
−0.417792 + 0.908543i \(0.637196\pi\)
\(228\) 0 0
\(229\) −2132.66 1231.29i −0.615416 0.355311i 0.159666 0.987171i \(-0.448958\pi\)
−0.775082 + 0.631860i \(0.782292\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4505.33 + 2601.16i 1.26676 + 0.731362i 0.974373 0.224939i \(-0.0722182\pi\)
0.292384 + 0.956301i \(0.405552\pi\)
\(234\) 0 0
\(235\) 1708.60 + 2959.38i 0.474284 + 0.821485i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1510.80i 0.408894i 0.978878 + 0.204447i \(0.0655396\pi\)
−0.978878 + 0.204447i \(0.934460\pi\)
\(240\) 0 0
\(241\) −1360.97 + 785.759i −0.363768 + 0.210022i −0.670732 0.741699i \(-0.734020\pi\)
0.306964 + 0.951721i \(0.400687\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2643.21 1264.14i −0.689259 0.329644i
\(246\) 0 0
\(247\) 578.346 1001.73i 0.148985 0.258050i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3863.31 0.971514 0.485757 0.874094i \(-0.338544\pi\)
0.485757 + 0.874094i \(0.338544\pi\)
\(252\) 0 0
\(253\) −2044.61 −0.508077
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2911.09 + 5042.16i −0.706572 + 1.22382i 0.259549 + 0.965730i \(0.416426\pi\)
−0.966121 + 0.258089i \(0.916907\pi\)
\(258\) 0 0
\(259\) −2025.74 6536.00i −0.485997 1.56806i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −935.656 + 540.201i −0.219373 + 0.126655i −0.605660 0.795724i \(-0.707091\pi\)
0.386287 + 0.922379i \(0.373757\pi\)
\(264\) 0 0
\(265\) 1202.07i 0.278651i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1142.76 + 1979.32i 0.259016 + 0.448630i 0.965979 0.258622i \(-0.0832683\pi\)
−0.706962 + 0.707251i \(0.749935\pi\)
\(270\) 0 0
\(271\) −1966.85 1135.56i −0.440877 0.254540i 0.263093 0.964771i \(-0.415257\pi\)
−0.703969 + 0.710230i \(0.748591\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1429.22 825.159i −0.313400 0.180942i
\(276\) 0 0
\(277\) −824.549 1428.16i −0.178853 0.309783i 0.762635 0.646829i \(-0.223905\pi\)
−0.941488 + 0.337046i \(0.890572\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7573.33i 1.60778i −0.594776 0.803892i \(-0.702759\pi\)
0.594776 0.803892i \(-0.297241\pi\)
\(282\) 0 0
\(283\) 4526.00 2613.09i 0.950682 0.548877i 0.0573894 0.998352i \(-0.481722\pi\)
0.893293 + 0.449475i \(0.148389\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2666.16 + 2881.21i −0.548357 + 0.592588i
\(288\) 0 0
\(289\) −5678.02 + 9834.62i −1.15571 + 2.00175i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4924.11 0.981808 0.490904 0.871214i \(-0.336667\pi\)
0.490904 + 0.871214i \(0.336667\pi\)
\(294\) 0 0
\(295\) 4432.45 0.874805
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −319.922 + 554.122i −0.0618782 + 0.107176i
\(300\) 0 0
\(301\) 5437.30 5875.87i 1.04120 1.12518i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 201.275 116.206i 0.0377869 0.0218163i
\(306\) 0 0
\(307\) 10064.5i 1.87105i 0.353256 + 0.935527i \(0.385075\pi\)
−0.353256 + 0.935527i \(0.614925\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1150.12 1992.06i −0.209701 0.363214i 0.741919 0.670490i \(-0.233916\pi\)
−0.951620 + 0.307276i \(0.900583\pi\)
\(312\) 0 0
\(313\) 898.271 + 518.617i 0.162215 + 0.0936548i 0.578910 0.815392i \(-0.303478\pi\)
−0.416695 + 0.909046i \(0.636812\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7214.93 4165.54i −1.27833 0.738044i −0.301789 0.953375i \(-0.597584\pi\)
−0.976541 + 0.215330i \(0.930917\pi\)
\(318\) 0 0
\(319\) −1792.27 3104.31i −0.314570 0.544852i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 14864.1i 2.56056i
\(324\) 0 0
\(325\) −447.263 + 258.227i −0.0763375 + 0.0440735i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2193.34 7076.77i −0.367546 1.18588i
\(330\) 0 0
\(331\) 1397.99 2421.39i 0.232146 0.402089i −0.726293 0.687385i \(-0.758759\pi\)
0.958440 + 0.285296i \(0.0920918\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1167.87 0.190471
\(336\) 0 0
\(337\) 4675.27 0.755721 0.377861 0.925863i \(-0.376660\pi\)
0.377861 + 0.925863i \(0.376660\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −116.006 + 200.928i −0.0184225 + 0.0319087i
\(342\) 0 0
\(343\) 4982.51 + 3940.58i 0.784345 + 0.620324i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2303.50 + 1329.93i −0.356364 + 0.205747i −0.667485 0.744623i \(-0.732629\pi\)
0.311120 + 0.950370i \(0.399296\pi\)
\(348\) 0 0
\(349\) 12826.3i 1.96727i −0.180181 0.983633i \(-0.557668\pi\)
0.180181 0.983633i \(-0.442332\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4113.76 + 7125.25i 0.620265 + 1.07433i 0.989436 + 0.144969i \(0.0463083\pi\)
−0.369171 + 0.929361i \(0.620358\pi\)
\(354\) 0 0
\(355\) −4473.97 2583.05i −0.668883 0.386180i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.38244 4.26226i −0.00108532 0.000626611i 0.499457 0.866339i \(-0.333533\pi\)
−0.500543 + 0.865712i \(0.666866\pi\)
\(360\) 0 0
\(361\) 3360.74 + 5820.98i 0.489976 + 0.848663i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 414.054i 0.0593769i
\(366\) 0 0
\(367\) 6325.97 3652.30i 0.899763 0.519478i 0.0226398 0.999744i \(-0.492793\pi\)
0.877123 + 0.480265i \(0.159460\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 576.514 2541.65i 0.0806768 0.355676i
\(372\) 0 0
\(373\) 4253.40 7367.10i 0.590436 1.02266i −0.403738 0.914875i \(-0.632289\pi\)
0.994174 0.107790i \(-0.0343774\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1121.76 −0.153245
\(378\) 0 0
\(379\) 7735.02 1.04834 0.524171 0.851613i \(-0.324375\pi\)
0.524171 + 0.851613i \(0.324375\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3963.43 6864.86i 0.528777 0.915869i −0.470659 0.882315i \(-0.655984\pi\)
0.999437 0.0335545i \(-0.0106827\pi\)
\(384\) 0 0
\(385\) −3682.86 3407.97i −0.487522 0.451133i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9283.67 + 5359.93i −1.21003 + 0.698609i −0.962765 0.270339i \(-0.912864\pi\)
−0.247262 + 0.968949i \(0.579531\pi\)
\(390\) 0 0
\(391\) 8222.34i 1.06348i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3550.26 6149.23i −0.452235 0.783295i
\(396\) 0 0
\(397\) −4886.86 2821.43i −0.617795 0.356684i 0.158215 0.987405i \(-0.449426\pi\)
−0.776010 + 0.630721i \(0.782759\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −159.937 92.3395i −0.0199174 0.0114993i 0.490008 0.871718i \(-0.336994\pi\)
−0.509926 + 0.860218i \(0.670327\pi\)
\(402\) 0 0
\(403\) 36.3032 + 62.8790i 0.00448733 + 0.00777228i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11718.6i 1.42720i
\(408\) 0 0
\(409\) −2321.40 + 1340.26i −0.280651 + 0.162034i −0.633718 0.773564i \(-0.718472\pi\)
0.353067 + 0.935598i \(0.385139\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9371.97 2125.81i −1.11662 0.253279i
\(414\) 0 0
\(415\) −159.033 + 275.453i −0.0188111 + 0.0325818i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12735.7 1.48492 0.742460 0.669890i \(-0.233659\pi\)
0.742460 + 0.669890i \(0.233659\pi\)
\(420\) 0 0
\(421\) 3317.68 0.384070 0.192035 0.981388i \(-0.438491\pi\)
0.192035 + 0.981388i \(0.438491\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3318.36 + 5747.56i −0.378739 + 0.655994i
\(426\) 0 0
\(427\) −481.309 + 149.175i −0.0545485 + 0.0169065i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7748.89 4473.82i 0.866011 0.499992i −9.69024e−6 1.00000i \(-0.500003\pi\)
0.866021 + 0.500008i \(0.166670\pi\)
\(432\) 0 0
\(433\) 11833.0i 1.31330i 0.754194 + 0.656651i \(0.228028\pi\)
−0.754194 + 0.656651i \(0.771972\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3756.14 6505.83i −0.411169 0.712165i
\(438\) 0 0
\(439\) 7376.74 + 4258.96i 0.801988 + 0.463028i 0.844166 0.536082i \(-0.180096\pi\)
−0.0421781 + 0.999110i \(0.513430\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7190.84 + 4151.64i 0.771213 + 0.445260i 0.833307 0.552810i \(-0.186445\pi\)
−0.0620942 + 0.998070i \(0.519778\pi\)
\(444\) 0 0
\(445\) −2010.44 3482.19i −0.214166 0.370947i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14235.2i 1.49622i 0.663575 + 0.748110i \(0.269039\pi\)
−0.663575 + 0.748110i \(0.730961\pi\)
\(450\) 0 0
\(451\) −5822.08 + 3361.38i −0.607873 + 0.350956i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1499.88 + 464.865i −0.154539 + 0.0478972i
\(456\) 0 0
\(457\) 3046.98 5277.52i 0.311885 0.540201i −0.666885 0.745160i \(-0.732373\pi\)
0.978770 + 0.204959i \(0.0657062\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −13335.2 −1.34725 −0.673625 0.739073i \(-0.735264\pi\)
−0.673625 + 0.739073i \(0.735264\pi\)
\(462\) 0 0
\(463\) −6596.99 −0.662178 −0.331089 0.943600i \(-0.607416\pi\)
−0.331089 + 0.943600i \(0.607416\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2176.35 + 3769.54i −0.215652 + 0.373519i −0.953474 0.301475i \(-0.902521\pi\)
0.737822 + 0.674995i \(0.235854\pi\)
\(468\) 0 0
\(469\) −2469.35 560.114i −0.243122 0.0551464i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11873.4 6855.10i 1.15420 0.666380i
\(474\) 0 0
\(475\) 6063.59i 0.585719i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −159.875 276.912i −0.0152503 0.0264143i 0.858300 0.513149i \(-0.171521\pi\)
−0.873550 + 0.486735i \(0.838188\pi\)
\(480\) 0 0
\(481\) −3175.94 1833.63i −0.301061 0.173818i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3866.71 + 2232.45i 0.362017 + 0.209011i
\(486\) 0 0
\(487\) −2919.49 5056.70i −0.271652 0.470515i 0.697633 0.716455i \(-0.254237\pi\)
−0.969285 + 0.245940i \(0.920903\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12442.2i 1.14360i 0.820392 + 0.571801i \(0.193755\pi\)
−0.820392 + 0.571801i \(0.806245\pi\)
\(492\) 0 0
\(493\) −12483.9 + 7207.58i −1.14046 + 0.658444i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8220.92 + 7607.31i 0.741969 + 0.686589i
\(498\) 0 0
\(499\) −8348.40 + 14459.9i −0.748949 + 1.29722i 0.199378 + 0.979923i \(0.436108\pi\)
−0.948327 + 0.317295i \(0.897225\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4435.36 0.393167 0.196583 0.980487i \(-0.437015\pi\)
0.196583 + 0.980487i \(0.437015\pi\)
\(504\) 0 0
\(505\) −9009.57 −0.793902
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11207.4 + 19411.8i −0.975951 + 1.69040i −0.299190 + 0.954193i \(0.596717\pi\)
−0.676761 + 0.736203i \(0.736617\pi\)
\(510\) 0 0
\(511\) 198.581 875.476i 0.0171912 0.0757901i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5501.05 + 3176.03i −0.470689 + 0.271753i
\(516\) 0 0
\(517\) 12688.2i 1.07936i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9561.15 + 16560.4i 0.803996 + 1.39256i 0.916967 + 0.398963i \(0.130630\pi\)
−0.112971 + 0.993598i \(0.536037\pi\)
\(522\) 0 0
\(523\) 18873.4 + 10896.5i 1.57796 + 0.911037i 0.995143 + 0.0984349i \(0.0313836\pi\)
0.582819 + 0.812602i \(0.301950\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 808.028 + 466.515i 0.0667899 + 0.0385612i
\(528\) 0 0
\(529\) −4005.72 6938.12i −0.329229 0.570241i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2103.84i 0.170970i
\(534\) 0 0
\(535\) −1745.87 + 1007.98i −0.141085 + 0.0814554i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6152.57 + 8972.12i 0.491670 + 0.716988i
\(540\) 0 0
\(541\) 101.107 175.122i 0.00803498 0.0139170i −0.861980 0.506942i \(-0.830776\pi\)
0.870015 + 0.493025i \(0.164109\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1986.38 0.156123
\(546\) 0 0
\(547\) 1510.85 0.118097 0.0590486 0.998255i \(-0.481193\pi\)
0.0590486 + 0.998255i \(0.481193\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6585.16 11405.8i 0.509142 0.881859i
\(552\) 0 0
\(553\) 4557.49 + 14704.6i 0.350459 + 1.13075i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3266.16 1885.72i 0.248459 0.143448i −0.370599 0.928793i \(-0.620848\pi\)
0.619058 + 0.785345i \(0.287514\pi\)
\(558\) 0 0
\(559\) 4290.51i 0.324632i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3916.56 6783.67i −0.293185 0.507811i 0.681376 0.731933i \(-0.261382\pi\)
−0.974561 + 0.224122i \(0.928049\pi\)
\(564\) 0 0
\(565\) −16766.4 9680.07i −1.24844 0.720785i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4941.75 + 2853.12i 0.364093 + 0.210209i 0.670875 0.741571i \(-0.265919\pi\)
−0.306782 + 0.951780i \(0.599252\pi\)
\(570\) 0 0
\(571\) −3568.83 6181.40i −0.261560 0.453036i 0.705096 0.709111i \(-0.250904\pi\)
−0.966657 + 0.256076i \(0.917570\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3354.18i 0.243268i
\(576\) 0 0
\(577\) −6579.24 + 3798.52i −0.474692 + 0.274064i −0.718202 0.695835i \(-0.755035\pi\)
0.243510 + 0.969898i \(0.421701\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 468.367 506.145i 0.0334443 0.0361419i
\(582\) 0 0
\(583\) 2231.66 3865.36i 0.158535 0.274591i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8212.13 0.577429 0.288714 0.957415i \(-0.406772\pi\)
0.288714 + 0.957415i \(0.406772\pi\)
\(588\) 0 0
\(589\) −852.457 −0.0596348
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9490.08 16437.3i 0.657186 1.13828i −0.324155 0.946004i \(-0.605080\pi\)
0.981341 0.192275i \(-0.0615866\pi\)
\(594\) 0 0
\(595\) −13705.1 + 14810.5i −0.944291 + 1.02046i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −17794.3 + 10273.5i −1.21378 + 0.700776i −0.963580 0.267419i \(-0.913829\pi\)
−0.250199 + 0.968195i \(0.580496\pi\)
\(600\) 0 0
\(601\) 15444.1i 1.04821i 0.851652 + 0.524107i \(0.175601\pi\)
−0.851652 + 0.524107i \(0.824399\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1388.16 + 2404.37i 0.0932840 + 0.161573i
\(606\) 0 0
\(607\) 1320.67 + 762.488i 0.0883102 + 0.0509859i 0.543505 0.839406i \(-0.317097\pi\)
−0.455195 + 0.890392i \(0.650430\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3438.71 1985.34i −0.227685 0.131454i
\(612\) 0 0
\(613\) 8883.48 + 15386.6i 0.585319 + 1.01380i 0.994836 + 0.101499i \(0.0323639\pi\)
−0.409517 + 0.912302i \(0.634303\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21575.8i 1.40779i 0.710302 + 0.703897i \(0.248558\pi\)
−0.710302 + 0.703897i \(0.751442\pi\)
\(618\) 0 0
\(619\) 7448.71 4300.51i 0.483665 0.279244i −0.238277 0.971197i \(-0.576583\pi\)
0.721943 + 0.691953i \(0.243249\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2580.81 + 8326.94i 0.165968 + 0.535493i
\(624\) 0 0
\(625\) 3206.82 5554.37i 0.205236 0.355480i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −47126.2 −2.98736
\(630\) 0 0
\(631\) −5922.32 −0.373635 −0.186817 0.982395i \(-0.559817\pi\)
−0.186817 + 0.982395i \(0.559817\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7157.05 12396.4i 0.447274 0.774701i
\(636\) 0 0
\(637\) 3394.29 263.567i 0.211125 0.0163939i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19398.9 11199.9i 1.19533 0.690127i 0.235823 0.971796i \(-0.424221\pi\)
0.959512 + 0.281669i \(0.0908881\pi\)
\(642\) 0 0
\(643\) 19715.7i 1.20919i −0.796533 0.604595i \(-0.793335\pi\)
0.796533 0.604595i \(-0.206665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3763.68 6518.89i −0.228695 0.396111i 0.728727 0.684805i \(-0.240113\pi\)
−0.957422 + 0.288693i \(0.906779\pi\)
\(648\) 0 0
\(649\) −14252.9 8228.94i −0.862060 0.497711i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −14524.4 8385.65i −0.870417 0.502536i −0.00293044 0.999996i \(-0.500933\pi\)
−0.867487 + 0.497460i \(0.834266\pi\)
\(654\) 0 0
\(655\) 5066.36 + 8775.19i 0.302227 + 0.523473i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 20834.0i 1.23153i 0.787930 + 0.615765i \(0.211153\pi\)
−0.787930 + 0.615765i \(0.788847\pi\)
\(660\) 0 0
\(661\) 22838.3 13185.7i 1.34388 0.775892i 0.356509 0.934292i \(-0.383967\pi\)
0.987375 + 0.158400i \(0.0506334\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4078.21 17979.4i 0.237814 1.04844i
\(666\) 0 0
\(667\) −3642.69 + 6309.33i −0.211463 + 0.366264i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −862.959 −0.0496485
\(672\) 0 0
\(673\) −18150.5 −1.03960 −0.519800 0.854288i \(-0.673993\pi\)
−0.519800 + 0.854288i \(0.673993\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11357.7 19672.2i 0.644776 1.11679i −0.339577 0.940578i \(-0.610284\pi\)
0.984353 0.176207i \(-0.0563829\pi\)
\(678\) 0 0
\(679\) −7105.08 6574.76i −0.401573 0.371600i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11788.2 6805.92i 0.660414 0.381290i −0.132021 0.991247i \(-0.542146\pi\)
0.792435 + 0.609957i \(0.208813\pi\)
\(684\) 0 0
\(685\) 27060.1i 1.50936i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −698.383 1209.63i −0.0386158 0.0668845i
\(690\) 0 0
\(691\) 24565.6 + 14182.9i 1.35241 + 0.780817i 0.988587 0.150650i \(-0.0481367\pi\)
0.363827 + 0.931467i \(0.381470\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4496.47 2596.04i −0.245411 0.141688i
\(696\) 0 0
\(697\) 13517.7 + 23413.3i 0.734604 + 1.27237i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9203.01i 0.495853i −0.968779 0.247927i \(-0.920251\pi\)
0.968779 0.247927i \(-0.0797492\pi\)
\(702\) 0 0
\(703\) 37288.1 21528.3i 2.00049 1.15499i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19049.8 + 4321.00i 1.01336 + 0.229856i
\(708\) 0 0
\(709\) 10975.7 19010.4i 0.581383 1.00698i −0.413933 0.910307i \(-0.635845\pi\)
0.995316 0.0966770i \(-0.0308214\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 471.552 0.0247682
\(714\) 0 0
\(715\) −2689.19 −0.140657
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5090.07 + 8816.26i −0.264016 + 0.457289i −0.967305 0.253615i \(-0.918381\pi\)
0.703289 + 0.710904i \(0.251714\pi\)
\(720\) 0 0
\(721\) 13154.6 4077.09i 0.679479 0.210594i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5092.62 + 2940.22i −0.260876 + 0.150617i
\(726\) 0 0
\(727\) 19192.2i 0.979093i 0.871977 + 0.489546i \(0.162838\pi\)
−0.871977 + 0.489546i \(0.837162\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −27567.6 47748.5i −1.39484 2.41593i
\(732\) 0 0
\(733\) 30916.5 + 17849.6i 1.55788 + 0.899442i 0.997460 + 0.0712328i \(0.0226933\pi\)
0.560419 + 0.828209i \(0.310640\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3755.40 2168.18i −0.187696 0.108366i
\(738\) 0 0
\(739\) −13871.9 24026.9i −0.690511 1.19600i −0.971671 0.236339i \(-0.924052\pi\)
0.281160 0.959661i \(-0.409281\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 25212.0i 1.24487i −0.782671 0.622435i \(-0.786143\pi\)
0.782671 0.622435i \(-0.213857\pi\)
\(744\) 0 0
\(745\) −9546.43 + 5511.63i −0.469469 + 0.271048i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4174.89 1293.94i 0.203668 0.0631238i
\(750\) 0 0
\(751\) −6479.18 + 11222.3i −0.314818 + 0.545282i −0.979399 0.201935i \(-0.935277\pi\)
0.664580 + 0.747217i \(0.268610\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24814.7 −1.19616
\(756\) 0 0
\(757\) −1671.41 −0.0802488 −0.0401244 0.999195i \(-0.512775\pi\)
−0.0401244 + 0.999195i \(0.512775\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13983.9 24220.9i 0.666120 1.15375i −0.312861 0.949799i \(-0.601287\pi\)
0.978980 0.203954i \(-0.0653794\pi\)
\(762\) 0 0
\(763\) −4199.99 952.669i −0.199279 0.0452017i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4460.35 + 2575.19i −0.209979 + 0.121231i
\(768\) 0 0
\(769\) 22787.5i 1.06858i −0.845301 0.534290i \(-0.820579\pi\)
0.845301 0.534290i \(-0.179421\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 754.803 + 1307.36i 0.0351208 + 0.0608310i 0.883052 0.469276i \(-0.155485\pi\)
−0.847931 + 0.530107i \(0.822152\pi\)
\(774\) 0 0
\(775\) 329.623 + 190.308i 0.0152779 + 0.00882072i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −21391.4 12350.4i −0.983861 0.568032i
\(780\) 0 0
\(781\) 9590.96 + 16612.0i 0.439426 + 0.761108i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10084.0i 0.458490i
\(786\) 0 0
\(787\) −4781.43 + 2760.56i −0.216569 + 0.125036i −0.604360 0.796711i \(-0.706571\pi\)
0.387792 + 0.921747i \(0.373238\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 30808.2 + 28508.7i 1.38485 + 1.28148i
\(792\) 0 0
\(793\) −135.028 + 233.876i −0.00604665 + 0.0104731i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −32608.8 −1.44926 −0.724631 0.689137i \(-0.757990\pi\)
−0.724631 + 0.689137i \(0.757990\pi\)
\(798\) 0 0
\(799\) −51025.3 −2.25926
\(800\) 0 0
\(801\) 0 0
\(802\) 0