Properties

Label 252.4.t.a.89.3
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 89.3
Root \(-1.35249 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.89
Dual form 252.4.t.a.17.3

$q$-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 −0.991350 0.131243i \(-0.958103\pi\)
0.609335 + 0.792913i \(0.291436\pi\)
\(6\) 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 −0.0738410 0.997270i \(-0.523526\pi\)
0.826741 + 0.562583i \(0.190192\pi\)
\(12\) 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 \(-0.802851\pi\)
−0.0956180 0.995418i \(-0.530483\pi\)
\(18\) 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 0.225118 0.974332i \(-0.427723\pi\)
−0.731237 + 0.682123i \(0.761057\pi\)
\(24\) 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 \(-0.882150\pi\)
0.932242 0.361836i \(-0.117850\pi\)
\(30\) 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 \(-0.632272\pi\)
−0.403688 + 0.914897i \(0.632272\pi\)
\(42\) 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 \(-0.620155\pi\)
0.989343 0.145601i \(-0.0465117\pi\)
\(48\) 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 −0.333692 0.942682i \(-0.608294\pi\)
0.649541 + 0.760327i \(0.274961\pi\)
\(54\) 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 \(-0.972643\pi\)
0.423816 0.905748i \(-0.360690\pi\)
\(60\) 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 \(0.168674\pi\)
−0.862855 + 0.505451i \(0.831326\pi\)
\(72\) 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 \(-0.492162\pi\)
0.0246209 + 0.999697i \(0.492162\pi\)
\(84\) 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 −0.971461 0.237198i \(-0.923771\pi\)
0.691150 + 0.722711i \(0.257104\pi\)
\(90\) 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 \(0.00723329\pi\)
−0.480193 + 0.877163i \(0.659433\pi\)
\(102\) 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 0.589480 0.807783i \(-0.299333\pi\)
−0.404821 + 0.914396i \(0.632666\pi\)
\(108\) 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 \(0.392391\pi\)
−0.331661 + 0.943398i \(0.607609\pi\)
\(114\) 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 −0.597604 0.801791i \(-0.703881\pi\)
0.993174 + 0.116645i \(0.0372138\pi\)
\(132\) 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 \(0.783488\pi\)
−0.933406 + 0.358821i \(0.883179\pi\)
\(138\) 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 0.774710 0.632317i \(-0.217896\pi\)
−0.160247 + 0.987077i \(0.551229\pi\)
\(150\) 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 \(-0.707777\pi\)
−0.607374 + 0.794416i \(0.707777\pi\)
\(168\) 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 \(-0.636039\pi\)
0.995375 0.0960706i \(-0.0306275\pi\)
\(174\) 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 \(-0.333047\pi\)
1.00000 0.000899820i \(-0.000286422\pi\)
\(180\) 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 −0.257161 0.966369i \(-0.582787\pi\)
−0.965480 + 0.260477i \(0.916120\pi\)
\(192\) 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 \(0.214579\pi\)
−0.781256 + 0.624210i \(0.785421\pi\)
\(198\) 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 \(-0.970529\pi\)
0.417792 0.908543i \(-0.362804\pi\)
\(228\) 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 −0.292384 0.956301i \(-0.594448\pi\)
−0.974373 + 0.224939i \(0.927782\pi\)
\(234\) 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 \(-0.934460\pi\)
0.978878 0.204447i \(-0.0655396\pi\)
\(240\) 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 \(-0.661456\pi\)
−0.485757 + 0.874094i \(0.661456\pi\)
\(252\) 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 \(-0.583574\pi\)
0.966121 0.258089i \(-0.0830929\pi\)
\(258\) 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 −0.386287 0.922379i \(-0.626243\pi\)
0.605660 + 0.795724i \(0.292909\pi\)
\(264\) 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 0.706962 0.707251i \(-0.250065\pi\)
−0.965979 + 0.258622i \(0.916732\pi\)
\(270\) 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 \(0.297241\pi\)
−0.594776 + 0.803892i \(0.702759\pi\)
\(282\) 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 \(-0.663333\pi\)
−0.490904 + 0.871214i \(0.663333\pi\)
\(294\) 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 0.951620 0.307276i \(-0.0994175\pi\)
−0.741919 + 0.670490i \(0.766084\pi\)
\(312\) 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 0.976541 0.215330i \(-0.0690828\pi\)
0.301789 + 0.953375i \(0.402416\pi\)
\(318\) 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 −0.311120 0.950370i \(-0.600704\pi\)
0.667485 + 0.744623i \(0.267371\pi\)
\(348\) 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 \(-0.953692\pi\)
0.369171 0.929361i \(-0.379642\pi\)
\(354\) 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 0.500543 0.865712i \(-0.333134\pi\)
−0.499457 + 0.866339i \(0.666467\pi\)
\(360\) 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 \(0.344016\pi\)
−0.999437 + 0.0335545i \(0.989317\pi\)
\(384\) 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 0.247262 0.968949i \(-0.420469\pi\)
0.962765 + 0.270339i \(0.0871359\pi\)
\(390\) 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 0.509926 0.860218i \(-0.329673\pi\)
−0.490008 + 0.871718i \(0.663006\pi\)
\(402\) 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 \(-0.766341\pi\)
−0.742460 + 0.669890i \(0.766341\pi\)
\(420\) 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 −0.866021 0.500008i \(-0.833330\pi\)
9.69024e−6 1.00000i \(0.499997\pi\)
\(432\) 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 0.0620942 0.998070i \(-0.480222\pi\)
−0.833307 + 0.552810i \(0.813555\pi\)
\(444\) 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 \(-0.730961\pi\)
0.663575 0.748110i \(-0.269039\pi\)
\(450\) 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 \(-0.264736\pi\)
0.673625 + 0.739073i \(0.264736\pi\)
\(462\) 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 −0.737822 0.674995i \(-0.764146\pi\)
0.953474 + 0.301475i \(0.0974791\pi\)
\(468\) 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 0.873550 0.486735i \(-0.161812\pi\)
−0.858300 + 0.513149i \(0.828479\pi\)
\(480\) 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 \(-0.806245\pi\)
0.820392 0.571801i \(-0.193755\pi\)
\(492\) 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 \(-0.562985\pi\)
−0.196583 + 0.980487i \(0.562985\pi\)
\(504\) 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 \(-0.403283\pi\)
0.676761 0.736203i \(-0.263383\pi\)
\(510\) 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 \(-0.869370\pi\)
0.112971 0.993598i \(-0.463963\pi\)
\(522\) 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 −0.619058 0.785345i \(-0.712486\pi\)
0.370599 + 0.928793i \(0.379152\pi\)
\(558\) 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 0.974561 0.224122i \(-0.0719515\pi\)
−0.681376 + 0.731933i \(0.738618\pi\)
\(564\) 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 0.306782 0.951780i \(-0.400748\pi\)
−0.670875 + 0.741571i \(0.734081\pi\)
\(570\) 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 \(-0.593228\pi\)
−0.288714 + 0.957415i \(0.593228\pi\)
\(588\) 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 \(0.394920\pi\)
−0.981341 + 0.192275i \(0.938413\pi\)
\(594\) 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 0.250199 0.968195i \(-0.419504\pi\)
0.963580 + 0.267419i \(0.0861707\pi\)
\(600\) 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 \(-0.751442\pi\)
0.710302 0.703897i \(-0.248558\pi\)
\(618\) 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 −0.959512 0.281669i \(-0.909112\pi\)
−0.235823 + 0.971796i \(0.575779\pi\)
\(642\) 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 0.957422 0.288693i \(-0.0932208\pi\)
−0.728727 + 0.684805i \(0.759887\pi\)
\(648\) 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 0.867487 0.497460i \(-0.165734\pi\)
0.00293044 + 0.999996i \(0.499067\pi\)
\(654\) 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 \(-0.788847\pi\)
0.787930 0.615765i \(-0.211153\pi\)
\(660\) 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 \(0.389716\pi\)
−0.984353 + 0.176207i \(0.943617\pi\)
\(678\) 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 −0.792435 0.609957i \(-0.791187\pi\)
0.132021 + 0.991247i \(0.457854\pi\)
\(684\) 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 \(0.0797492\pi\)
−0.968779 + 0.247927i \(0.920251\pi\)
\(702\) 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 −0.703289 0.710904i \(-0.748286\pi\)
0.967305 + 0.253615i \(0.0816195\pi\)
\(720\) 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 \(0.213857\pi\)
−0.782671 + 0.622435i \(0.786143\pi\)
\(744\) 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 \(0.398713\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(762\) 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 0.847931 0.530107i \(-0.177848\pi\)
−0.883052 + 0.469276i \(0.844515\pi\)
\(774\) 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 \(-0.242010\pi\)
0.724631 + 0.689137i \(0.242010\pi\)
\(798\) 0 0
\(799\) −51025.3 −2.25926
\(800\) 0 0
\(801\) 0 0
\(802\)