Properties

Label 1008.4.bt.b.593.7
Level $1008$
Weight $4$
Character 1008.593
Analytic conductor $59.474$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
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: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.7
Root \(-8.00527 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.b.17.7

$q$-expansion

\(f(q)\) \(=\) \(q+(4.36813 - 7.56582i) q^{5} +(-14.4904 + 11.5338i) q^{7} +O(q^{10})\) \(q+(4.36813 - 7.56582i) q^{5} +(-14.4904 + 11.5338i) q^{7} +(7.60916 - 4.39315i) q^{11} -11.8322i q^{13} +(-22.2920 - 38.6108i) q^{17} +(-10.0856 - 5.82291i) q^{19} +(123.521 + 71.3151i) q^{23} +(24.3389 + 42.1563i) q^{25} -234.018i q^{29} +(-252.809 + 145.960i) q^{31} +(23.9672 + 160.013i) q^{35} +(44.4515 - 76.9923i) q^{37} -145.961 q^{41} -144.633 q^{43} +(-120.183 + 208.164i) q^{47} +(76.9412 - 334.259i) q^{49} +(-263.538 + 152.154i) q^{53} -76.7594i q^{55} +(3.54196 + 6.13486i) q^{59} +(-149.810 - 86.4927i) q^{61} +(-89.5199 - 51.6844i) q^{65} +(-243.280 - 421.373i) q^{67} +653.710i q^{71} +(-99.0378 + 57.1795i) q^{73} +(-59.5896 + 151.421i) q^{77} +(147.307 - 255.144i) q^{79} -877.193 q^{83} -389.496 q^{85} +(-710.379 + 1230.41i) q^{89} +(136.470 + 171.452i) q^{91} +(-88.1102 + 50.8704i) q^{95} +738.981i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 72q^{19} - 212q^{25} + 708q^{31} + 76q^{37} - 1408q^{43} + 400q^{49} - 1632q^{61} + 1528q^{67} - 2700q^{73} + 364q^{79} + 7392q^{85} - 2472q^{91} + O(q^{100}) \)

Character values

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

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

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
\(5\) 4.36813 7.56582i 0.390697 0.676707i −0.601844 0.798613i \(-0.705567\pi\)
0.992542 + 0.121906i \(0.0389006\pi\)
\(6\) 0 0
\(7\) −14.4904 + 11.5338i −0.782406 + 0.622769i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 7.60916 4.39315i 0.208568 0.120417i −0.392078 0.919932i \(-0.628244\pi\)
0.600646 + 0.799515i \(0.294910\pi\)
\(12\) 0 0
\(13\) 11.8322i 0.252435i −0.992003 0.126217i \(-0.959716\pi\)
0.992003 0.126217i \(-0.0402837\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −22.2920 38.6108i −0.318035 0.550853i 0.662043 0.749466i \(-0.269690\pi\)
−0.980078 + 0.198613i \(0.936356\pi\)
\(18\) 0 0
\(19\) −10.0856 5.82291i −0.121778 0.0703088i 0.437873 0.899037i \(-0.355732\pi\)
−0.559652 + 0.828728i \(0.689065\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 123.521 + 71.3151i 1.11982 + 0.646531i 0.941356 0.337414i \(-0.109552\pi\)
0.178469 + 0.983946i \(0.442886\pi\)
\(24\) 0 0
\(25\) 24.3389 + 42.1563i 0.194711 + 0.337250i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 234.018i 1.49848i −0.662298 0.749241i \(-0.730419\pi\)
0.662298 0.749241i \(-0.269581\pi\)
\(30\) 0 0
\(31\) −252.809 + 145.960i −1.46471 + 0.845649i −0.999223 0.0394074i \(-0.987453\pi\)
−0.465484 + 0.885056i \(0.654120\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 23.9672 + 160.013i 0.115748 + 0.772774i
\(36\) 0 0
\(37\) 44.4515 76.9923i 0.197508 0.342093i −0.750212 0.661197i \(-0.770049\pi\)
0.947720 + 0.319104i \(0.103382\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −145.961 −0.555984 −0.277992 0.960583i \(-0.589669\pi\)
−0.277992 + 0.960583i \(0.589669\pi\)
\(42\) 0 0
\(43\) −144.633 −0.512938 −0.256469 0.966552i \(-0.582559\pi\)
−0.256469 + 0.966552i \(0.582559\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −120.183 + 208.164i −0.372991 + 0.646039i −0.990024 0.140898i \(-0.955001\pi\)
0.617033 + 0.786937i \(0.288334\pi\)
\(48\) 0 0
\(49\) 76.9412 334.259i 0.224318 0.974516i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −263.538 + 152.154i −0.683015 + 0.394339i −0.800990 0.598678i \(-0.795693\pi\)
0.117975 + 0.993017i \(0.462360\pi\)
\(54\) 0 0
\(55\) 76.7594i 0.188186i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.54196 + 6.13486i 0.00781566 + 0.0135371i 0.869907 0.493216i \(-0.164179\pi\)
−0.862091 + 0.506753i \(0.830846\pi\)
\(60\) 0 0
\(61\) −149.810 86.4927i −0.314445 0.181545i 0.334469 0.942407i \(-0.391443\pi\)
−0.648914 + 0.760862i \(0.724777\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −89.5199 51.6844i −0.170824 0.0986255i
\(66\) 0 0
\(67\) −243.280 421.373i −0.443603 0.768342i 0.554351 0.832283i \(-0.312966\pi\)
−0.997954 + 0.0639408i \(0.979633\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 653.710i 1.09269i 0.837560 + 0.546345i \(0.183981\pi\)
−0.837560 + 0.546345i \(0.816019\pi\)
\(72\) 0 0
\(73\) −99.0378 + 57.1795i −0.158788 + 0.0916761i −0.577288 0.816540i \(-0.695889\pi\)
0.418501 + 0.908217i \(0.362556\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −59.5896 + 151.421i −0.0881931 + 0.224104i
\(78\) 0 0
\(79\) 147.307 255.144i 0.209789 0.363366i −0.741859 0.670556i \(-0.766055\pi\)
0.951648 + 0.307190i \(0.0993888\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −877.193 −1.16005 −0.580027 0.814597i \(-0.696958\pi\)
−0.580027 + 0.814597i \(0.696958\pi\)
\(84\) 0 0
\(85\) −389.496 −0.497021
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −710.379 + 1230.41i −0.846068 + 1.46543i 0.0386225 + 0.999254i \(0.487703\pi\)
−0.884691 + 0.466179i \(0.845630\pi\)
\(90\) 0 0
\(91\) 136.470 + 171.452i 0.157208 + 0.197506i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −88.1102 + 50.8704i −0.0951570 + 0.0549389i
\(96\) 0 0
\(97\) 738.981i 0.773527i 0.922179 + 0.386764i \(0.126407\pi\)
−0.922179 + 0.386764i \(0.873593\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 831.442 + 1440.10i 0.819125 + 1.41877i 0.906328 + 0.422575i \(0.138874\pi\)
−0.0872031 + 0.996191i \(0.527793\pi\)
\(102\) 0 0
\(103\) 394.807 + 227.942i 0.377684 + 0.218056i 0.676810 0.736158i \(-0.263362\pi\)
−0.299126 + 0.954214i \(0.596695\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1279.07 738.474i −1.15563 0.667205i −0.205380 0.978682i \(-0.565843\pi\)
−0.950254 + 0.311477i \(0.899176\pi\)
\(108\) 0 0
\(109\) −784.202 1358.28i −0.689110 1.19357i −0.972126 0.234458i \(-0.924668\pi\)
0.283016 0.959115i \(-0.408665\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1077.27i 0.896820i 0.893828 + 0.448410i \(0.148010\pi\)
−0.893828 + 0.448410i \(0.851990\pi\)
\(114\) 0 0
\(115\) 1079.11 623.026i 0.875025 0.505196i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 768.349 + 302.373i 0.591886 + 0.232928i
\(120\) 0 0
\(121\) −626.900 + 1085.82i −0.471000 + 0.815795i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1517.29 1.08569
\(126\) 0 0
\(127\) −1518.00 −1.06063 −0.530317 0.847799i \(-0.677927\pi\)
−0.530317 + 0.847799i \(0.677927\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 201.672 349.306i 0.134505 0.232969i −0.790903 0.611941i \(-0.790389\pi\)
0.925408 + 0.378972i \(0.123722\pi\)
\(132\) 0 0
\(133\) 213.304 31.9493i 0.139066 0.0208298i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −467.650 + 269.998i −0.291636 + 0.168376i −0.638679 0.769473i \(-0.720519\pi\)
0.347044 + 0.937849i \(0.387186\pi\)
\(138\) 0 0
\(139\) 2042.22i 1.24618i −0.782151 0.623089i \(-0.785877\pi\)
0.782151 0.623089i \(-0.214123\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −51.9805 90.0328i −0.0303974 0.0526498i
\(144\) 0 0
\(145\) −1770.53 1022.22i −1.01403 0.585452i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 180.517 + 104.222i 0.0992521 + 0.0573032i 0.548804 0.835951i \(-0.315083\pi\)
−0.449552 + 0.893254i \(0.648416\pi\)
\(150\) 0 0
\(151\) −230.045 398.449i −0.123979 0.214737i 0.797355 0.603511i \(-0.206232\pi\)
−0.921333 + 0.388774i \(0.872899\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2550.28i 1.32157i
\(156\) 0 0
\(157\) −2330.15 + 1345.31i −1.18450 + 0.683869i −0.957050 0.289921i \(-0.906371\pi\)
−0.227446 + 0.973791i \(0.573037\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2612.40 + 391.293i −1.27880 + 0.191542i
\(162\) 0 0
\(163\) −1137.44 + 1970.10i −0.546571 + 0.946689i 0.451935 + 0.892051i \(0.350734\pi\)
−0.998506 + 0.0546381i \(0.982599\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3214.68 −1.48958 −0.744789 0.667300i \(-0.767450\pi\)
−0.744789 + 0.667300i \(0.767450\pi\)
\(168\) 0 0
\(169\) 2057.00 0.936277
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1782.11 + 3086.71i −0.783187 + 1.35652i 0.146889 + 0.989153i \(0.453074\pi\)
−0.930076 + 0.367367i \(0.880259\pi\)
\(174\) 0 0
\(175\) −838.903 330.138i −0.362372 0.142606i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −302.852 + 174.852i −0.126459 + 0.0730113i −0.561895 0.827208i \(-0.689928\pi\)
0.435436 + 0.900220i \(0.356594\pi\)
\(180\) 0 0
\(181\) 1664.25i 0.683439i −0.939802 0.341720i \(-0.888991\pi\)
0.939802 0.341720i \(-0.111009\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −388.340 672.624i −0.154331 0.267310i
\(186\) 0 0
\(187\) −339.246 195.864i −0.132664 0.0765935i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −213.721 123.392i −0.0809650 0.0467452i 0.458971 0.888451i \(-0.348218\pi\)
−0.539936 + 0.841706i \(0.681552\pi\)
\(192\) 0 0
\(193\) −1274.22 2207.01i −0.475235 0.823130i 0.524363 0.851495i \(-0.324303\pi\)
−0.999598 + 0.0283643i \(0.990970\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4579.00i 1.65604i −0.560697 0.828021i \(-0.689467\pi\)
0.560697 0.828021i \(-0.310533\pi\)
\(198\) 0 0
\(199\) −2151.47 + 1242.15i −0.766402 + 0.442482i −0.831590 0.555391i \(-0.812569\pi\)
0.0651876 + 0.997873i \(0.479235\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2699.12 + 3391.00i 0.933207 + 1.17242i
\(204\) 0 0
\(205\) −637.578 + 1104.32i −0.217221 + 0.376238i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −102.324 −0.0338655
\(210\) 0 0
\(211\) −5736.87 −1.87177 −0.935883 0.352311i \(-0.885396\pi\)
−0.935883 + 0.352311i \(0.885396\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −631.775 + 1094.27i −0.200403 + 0.347109i
\(216\) 0 0
\(217\) 1979.83 5030.87i 0.619352 1.57381i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −456.849 + 263.762i −0.139054 + 0.0802830i
\(222\) 0 0
\(223\) 5391.46i 1.61901i −0.587115 0.809504i \(-0.699736\pi\)
0.587115 0.809504i \(-0.300264\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 747.447 + 1294.62i 0.218545 + 0.378532i 0.954364 0.298647i \(-0.0965355\pi\)
−0.735818 + 0.677179i \(0.763202\pi\)
\(228\) 0 0
\(229\) 693.480 + 400.381i 0.200115 + 0.115537i 0.596709 0.802457i \(-0.296475\pi\)
−0.396594 + 0.917994i \(0.629808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2273.75 1312.75i −0.639305 0.369103i 0.145042 0.989426i \(-0.453668\pi\)
−0.784347 + 0.620323i \(0.787002\pi\)
\(234\) 0 0
\(235\) 1049.95 + 1818.57i 0.291453 + 0.504811i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6283.85i 1.70070i 0.526214 + 0.850352i \(0.323611\pi\)
−0.526214 + 0.850352i \(0.676389\pi\)
\(240\) 0 0
\(241\) −811.225 + 468.361i −0.216828 + 0.125186i −0.604481 0.796620i \(-0.706619\pi\)
0.387653 + 0.921806i \(0.373286\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2192.85 2042.21i −0.571822 0.532539i
\(246\) 0 0
\(247\) −68.8976 + 119.334i −0.0177484 + 0.0307411i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2831.45 −0.712031 −0.356015 0.934480i \(-0.615865\pi\)
−0.356015 + 0.934480i \(0.615865\pi\)
\(252\) 0 0
\(253\) 1253.19 0.311413
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2844.65 + 4927.08i −0.690445 + 1.19589i 0.281247 + 0.959636i \(0.409252\pi\)
−0.971692 + 0.236251i \(0.924081\pi\)
\(258\) 0 0
\(259\) 243.898 + 1628.34i 0.0585138 + 0.390657i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3479.60 2008.95i 0.815823 0.471016i −0.0331509 0.999450i \(-0.510554\pi\)
0.848974 + 0.528435i \(0.177221\pi\)
\(264\) 0 0
\(265\) 2658.51i 0.616268i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1908.81 + 3306.16i 0.432648 + 0.749368i 0.997100 0.0760977i \(-0.0242461\pi\)
−0.564453 + 0.825465i \(0.690913\pi\)
\(270\) 0 0
\(271\) 6193.16 + 3575.62i 1.38822 + 0.801489i 0.993115 0.117147i \(-0.0373747\pi\)
0.395105 + 0.918636i \(0.370708\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 370.398 + 213.849i 0.0812212 + 0.0468931i
\(276\) 0 0
\(277\) 2741.91 + 4749.12i 0.594748 + 1.03013i 0.993582 + 0.113111i \(0.0360815\pi\)
−0.398834 + 0.917023i \(0.630585\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5525.72i 1.17308i −0.809919 0.586542i \(-0.800489\pi\)
0.809919 0.586542i \(-0.199511\pi\)
\(282\) 0 0
\(283\) −217.828 + 125.763i −0.0457545 + 0.0264164i −0.522703 0.852515i \(-0.675076\pi\)
0.476948 + 0.878931i \(0.341743\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2115.03 1683.49i 0.435005 0.346249i
\(288\) 0 0
\(289\) 1462.64 2533.36i 0.297707 0.515645i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9296.44 1.85360 0.926798 0.375560i \(-0.122550\pi\)
0.926798 + 0.375560i \(0.122550\pi\)
\(294\) 0 0
\(295\) 61.8869 0.0122142
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 843.811 1461.52i 0.163207 0.282683i
\(300\) 0 0
\(301\) 2095.78 1668.17i 0.401326 0.319442i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1308.78 + 755.622i −0.245706 + 0.141858i
\(306\) 0 0
\(307\) 1498.96i 0.278666i 0.990246 + 0.139333i \(0.0444958\pi\)
−0.990246 + 0.139333i \(0.955504\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3129.10 5419.77i −0.570531 0.988189i −0.996511 0.0834566i \(-0.973404\pi\)
0.425980 0.904733i \(-0.359929\pi\)
\(312\) 0 0
\(313\) −1843.53 1064.36i −0.332915 0.192208i 0.324220 0.945982i \(-0.394898\pi\)
−0.657134 + 0.753773i \(0.728232\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4547.45 + 2625.47i 0.805710 + 0.465177i 0.845464 0.534033i \(-0.179324\pi\)
−0.0397541 + 0.999209i \(0.512657\pi\)
\(318\) 0 0
\(319\) −1028.07 1780.68i −0.180442 0.312535i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 519.216i 0.0894427i
\(324\) 0 0
\(325\) 498.799 287.982i 0.0851336 0.0491519i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −659.426 4402.55i −0.110503 0.737752i
\(330\) 0 0
\(331\) 4401.99 7624.47i 0.730983 1.26610i −0.225481 0.974248i \(-0.572395\pi\)
0.956464 0.291852i \(-0.0942714\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4250.71 −0.693257
\(336\) 0 0
\(337\) −1428.63 −0.230927 −0.115463 0.993312i \(-0.536835\pi\)
−0.115463 + 0.993312i \(0.536835\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1282.45 + 2221.26i −0.203661 + 0.352751i
\(342\) 0 0
\(343\) 2740.38 + 5730.96i 0.431390 + 0.902166i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7896.72 4559.17i 1.22167 0.705329i 0.256393 0.966573i \(-0.417466\pi\)
0.965273 + 0.261244i \(0.0841327\pi\)
\(348\) 0 0
\(349\) 11899.1i 1.82506i 0.409011 + 0.912530i \(0.365874\pi\)
−0.409011 + 0.912530i \(0.634126\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4578.82 + 7930.75i 0.690385 + 1.19578i 0.971712 + 0.236170i \(0.0758923\pi\)
−0.281327 + 0.959612i \(0.590774\pi\)
\(354\) 0 0
\(355\) 4945.85 + 2855.49i 0.739432 + 0.426911i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6729.83 3885.47i −0.989379 0.571218i −0.0842902 0.996441i \(-0.526862\pi\)
−0.905089 + 0.425223i \(0.860196\pi\)
\(360\) 0 0
\(361\) −3361.69 5822.61i −0.490113 0.848901i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 999.070i 0.143270i
\(366\) 0 0
\(367\) 5456.63 3150.39i 0.776114 0.448090i −0.0589371 0.998262i \(-0.518771\pi\)
0.835051 + 0.550172i \(0.185438\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2063.85 5244.37i 0.288813 0.733893i
\(372\) 0 0
\(373\) −5051.76 + 8749.90i −0.701260 + 1.21462i 0.266764 + 0.963762i \(0.414046\pi\)
−0.968024 + 0.250857i \(0.919288\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2768.93 −0.378269
\(378\) 0 0
\(379\) −1122.50 −0.152134 −0.0760671 0.997103i \(-0.524236\pi\)
−0.0760671 + 0.997103i \(0.524236\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5313.98 9204.08i 0.708960 1.22795i −0.256283 0.966602i \(-0.582498\pi\)
0.965243 0.261353i \(-0.0841686\pi\)
\(384\) 0 0
\(385\) 885.330 + 1112.27i 0.117196 + 0.147238i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11571.8 6680.96i 1.50826 0.870792i 0.508301 0.861179i \(-0.330274\pi\)
0.999954 0.00961230i \(-0.00305974\pi\)
\(390\) 0 0
\(391\) 6359.01i 0.822478i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1286.91 2229.00i −0.163928 0.283932i
\(396\) 0 0
\(397\) −2304.31 1330.40i −0.291310 0.168188i 0.347222 0.937783i \(-0.387125\pi\)
−0.638533 + 0.769595i \(0.720458\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5288.60 3053.37i −0.658603 0.380245i 0.133141 0.991097i \(-0.457494\pi\)
−0.791745 + 0.610852i \(0.790827\pi\)
\(402\) 0 0
\(403\) 1727.02 + 2991.28i 0.213471 + 0.369743i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 781.129i 0.0951330i
\(408\) 0 0
\(409\) −1998.03 + 1153.56i −0.241556 + 0.139462i −0.615892 0.787831i \(-0.711204\pi\)
0.374336 + 0.927293i \(0.377871\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −122.083 48.0439i −0.0145455 0.00572418i
\(414\) 0 0
\(415\) −3831.69 + 6636.69i −0.453230 + 0.785017i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11116.9 −1.29617 −0.648083 0.761570i \(-0.724429\pi\)
−0.648083 + 0.761570i \(0.724429\pi\)
\(420\) 0 0
\(421\) 4188.14 0.484840 0.242420 0.970171i \(-0.422059\pi\)
0.242420 + 0.970171i \(0.422059\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1085.12 1879.49i 0.123850 0.214515i
\(426\) 0 0
\(427\) 3168.39 474.571i 0.359085 0.0537847i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4253.15 2455.56i 0.475329 0.274432i −0.243139 0.969992i \(-0.578177\pi\)
0.718468 + 0.695560i \(0.244844\pi\)
\(432\) 0 0
\(433\) 14412.6i 1.59960i −0.600268 0.799799i \(-0.704939\pi\)
0.600268 0.799799i \(-0.295061\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −830.522 1438.51i −0.0909137 0.157467i
\(438\) 0 0
\(439\) −7721.97 4458.28i −0.839520 0.484697i 0.0175809 0.999845i \(-0.494404\pi\)
−0.857101 + 0.515148i \(0.827737\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1022.14 590.133i −0.109624 0.0632913i 0.444186 0.895935i \(-0.353493\pi\)
−0.553809 + 0.832643i \(0.686826\pi\)
\(444\) 0 0
\(445\) 6206.05 + 10749.2i 0.661113 + 1.14508i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12536.1i 1.31763i −0.752307 0.658813i \(-0.771059\pi\)
0.752307 0.658813i \(-0.228941\pi\)
\(450\) 0 0
\(451\) −1110.64 + 641.230i −0.115960 + 0.0669498i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1893.30 283.583i 0.195075 0.0292189i
\(456\) 0 0
\(457\) 5051.92 8750.18i 0.517109 0.895659i −0.482694 0.875789i \(-0.660342\pi\)
0.999803 0.0198696i \(-0.00632509\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 418.675 0.0422985 0.0211493 0.999776i \(-0.493267\pi\)
0.0211493 + 0.999776i \(0.493267\pi\)
\(462\) 0 0
\(463\) 2178.42 0.218661 0.109330 0.994005i \(-0.465129\pi\)
0.109330 + 0.994005i \(0.465129\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1929.85 3342.59i 0.191226 0.331213i −0.754431 0.656380i \(-0.772087\pi\)
0.945657 + 0.325166i \(0.105420\pi\)
\(468\) 0 0
\(469\) 8385.26 + 3299.90i 0.825577 + 0.324894i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1100.54 + 635.394i −0.106982 + 0.0617663i
\(474\) 0 0
\(475\) 566.894i 0.0547597i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8106.86 + 14041.5i 0.773302 + 1.33940i 0.935744 + 0.352680i \(0.114730\pi\)
−0.162442 + 0.986718i \(0.551937\pi\)
\(480\) 0 0
\(481\) −910.985 525.957i −0.0863562 0.0498578i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5591.00 + 3227.96i 0.523452 + 0.302215i
\(486\) 0 0
\(487\) 9902.83 + 17152.2i 0.921437 + 1.59598i 0.797193 + 0.603725i \(0.206317\pi\)
0.124244 + 0.992252i \(0.460349\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11104.5i 1.02065i −0.859983 0.510323i \(-0.829526\pi\)
0.859983 0.510323i \(-0.170474\pi\)
\(492\) 0 0
\(493\) −9035.61 + 5216.71i −0.825443 + 0.476570i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7539.78 9472.49i −0.680494 0.854928i
\(498\) 0 0
\(499\) 435.024 753.483i 0.0390267 0.0675963i −0.845852 0.533417i \(-0.820908\pi\)
0.884879 + 0.465821i \(0.154241\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12435.5 1.10233 0.551166 0.834396i \(-0.314183\pi\)
0.551166 + 0.834396i \(0.314183\pi\)
\(504\) 0 0
\(505\) 14527.4 1.28012
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9850.04 17060.8i 0.857751 1.48567i −0.0163174 0.999867i \(-0.505194\pi\)
0.874069 0.485802i \(-0.161472\pi\)
\(510\) 0 0
\(511\) 775.595 1970.84i 0.0671434 0.170616i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3449.13 1991.36i 0.295120 0.170388i
\(516\) 0 0
\(517\) 2111.94i 0.179657i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4813.26 8336.82i −0.404747 0.701042i 0.589545 0.807735i \(-0.299307\pi\)
−0.994292 + 0.106694i \(0.965974\pi\)
\(522\) 0 0
\(523\) −1451.42 837.977i −0.121350 0.0700615i 0.438096 0.898928i \(-0.355653\pi\)
−0.559446 + 0.828867i \(0.688986\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11271.2 + 6507.45i 0.931656 + 0.537892i
\(528\) 0 0
\(529\) 4088.17 + 7080.92i 0.336005 + 0.581978i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1727.04i 0.140350i
\(534\) 0 0
\(535\) −11174.3 + 6451.50i −0.903006 + 0.521351i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −882.992 2881.44i −0.0705624 0.230265i
\(540\) 0 0
\(541\) 4323.06 7487.76i 0.343554 0.595054i −0.641536 0.767093i \(-0.721702\pi\)
0.985090 + 0.172040i \(0.0550357\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −13702.0 −1.07693
\(546\) 0 0
\(547\) −183.297 −0.0143276 −0.00716382 0.999974i \(-0.502280\pi\)
−0.00716382 + 0.999974i \(0.502280\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1362.66 + 2360.20i −0.105356 + 0.182483i
\(552\) 0 0
\(553\) 808.250 + 5396.14i 0.0621524 + 0.414950i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18922.7 10925.0i 1.43946 0.831072i 0.441647 0.897189i \(-0.354394\pi\)
0.997812 + 0.0661167i \(0.0210610\pi\)
\(558\) 0 0
\(559\) 1711.32i 0.129483i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7624.11 + 13205.3i 0.570724 + 0.988523i 0.996492 + 0.0836908i \(0.0266708\pi\)
−0.425767 + 0.904833i \(0.639996\pi\)
\(564\) 0 0
\(565\) 8150.40 + 4705.64i 0.606885 + 0.350385i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10861.9 6271.10i −0.800269 0.462035i 0.0432965 0.999062i \(-0.486214\pi\)
−0.843565 + 0.537027i \(0.819547\pi\)
\(570\) 0 0
\(571\) 5721.40 + 9909.76i 0.419323 + 0.726288i 0.995871 0.0907745i \(-0.0289343\pi\)
−0.576549 + 0.817063i \(0.695601\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6942.93i 0.503548i
\(576\) 0 0
\(577\) 9599.35 5542.18i 0.692593 0.399869i −0.111990 0.993709i \(-0.535722\pi\)
0.804583 + 0.593841i \(0.202389\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12710.8 10117.4i 0.907633 0.722445i
\(582\) 0 0
\(583\) −1336.87 + 2315.53i −0.0949700 + 0.164493i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1493.49 0.105014 0.0525068 0.998621i \(-0.483279\pi\)
0.0525068 + 0.998621i \(0.483279\pi\)
\(588\) 0 0
\(589\) 3399.64 0.237826
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2832.72 + 4906.42i −0.196165 + 0.339768i −0.947282 0.320401i \(-0.896182\pi\)
0.751117 + 0.660170i \(0.229516\pi\)
\(594\) 0 0
\(595\) 5643.95 4492.39i 0.388873 0.309529i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4487.18 + 2590.68i −0.306079 + 0.176715i −0.645171 0.764039i \(-0.723214\pi\)
0.339091 + 0.940753i \(0.389880\pi\)
\(600\) 0 0
\(601\) 13911.4i 0.944186i −0.881549 0.472093i \(-0.843499\pi\)
0.881549 0.472093i \(-0.156501\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5476.76 + 9486.03i 0.368036 + 0.637458i
\(606\) 0 0
\(607\) −6537.98 3774.70i −0.437180 0.252406i 0.265221 0.964188i \(-0.414555\pi\)
−0.702401 + 0.711782i \(0.747889\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2463.03 + 1422.03i 0.163083 + 0.0941557i
\(612\) 0 0
\(613\) 6443.77 + 11160.9i 0.424570 + 0.735377i 0.996380 0.0850093i \(-0.0270920\pi\)
−0.571810 + 0.820386i \(0.693759\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22388.7i 1.46084i 0.683000 + 0.730419i \(0.260675\pi\)
−0.683000 + 0.730419i \(0.739325\pi\)
\(618\) 0 0
\(619\) −4791.17 + 2766.18i −0.311104 + 0.179616i −0.647420 0.762133i \(-0.724152\pi\)
0.336316 + 0.941749i \(0.390819\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3897.73 26022.5i −0.250657 1.67347i
\(624\) 0 0
\(625\) 3585.37 6210.04i 0.229463 0.397442i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3963.65 −0.251257
\(630\) 0 0
\(631\) 24188.4 1.52603 0.763015 0.646381i \(-0.223718\pi\)
0.763015 + 0.646381i \(0.223718\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6630.81 + 11484.9i −0.414387 + 0.717739i
\(636\) 0 0
\(637\) −3955.00 910.380i −0.246002 0.0566257i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7955.44 + 4593.08i −0.490205 + 0.283020i −0.724659 0.689107i \(-0.758003\pi\)
0.234455 + 0.972127i \(0.424670\pi\)
\(642\) 0 0
\(643\) 21051.2i 1.29110i 0.763718 + 0.645550i \(0.223372\pi\)
−0.763718 + 0.645550i \(0.776628\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1834.16 3176.85i −0.111450 0.193037i 0.804905 0.593403i \(-0.202216\pi\)
−0.916355 + 0.400367i \(0.868883\pi\)
\(648\) 0 0
\(649\) 53.9027 + 31.1207i 0.00326019 + 0.00188227i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6653.57 + 3841.44i 0.398736 + 0.230210i 0.685938 0.727660i \(-0.259392\pi\)
−0.287203 + 0.957870i \(0.592725\pi\)
\(654\) 0 0
\(655\) −1761.85 3051.62i −0.105101 0.182041i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 529.107i 0.0312763i 0.999878 + 0.0156382i \(0.00497798\pi\)
−0.999878 + 0.0156382i \(0.995022\pi\)
\(660\) 0 0
\(661\) −11918.0 + 6880.84i −0.701294 + 0.404892i −0.807829 0.589417i \(-0.799358\pi\)
0.106535 + 0.994309i \(0.466024\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 690.017 1753.38i 0.0402372 0.102245i
\(666\) 0 0
\(667\) 16689.0 28906.1i 0.968815 1.67804i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1519.90 −0.0874443
\(672\) 0 0
\(673\) −31045.7 −1.77819 −0.889095 0.457722i \(-0.848666\pi\)
−0.889095 + 0.457722i \(0.848666\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2924.24 5064.94i 0.166009 0.287535i −0.771004 0.636830i \(-0.780245\pi\)
0.937013 + 0.349295i \(0.113579\pi\)
\(678\) 0 0
\(679\) −8523.29 10708.1i −0.481729 0.605213i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11813.9 6820.78i 0.661856 0.382123i −0.131127 0.991366i \(-0.541860\pi\)
0.792984 + 0.609242i \(0.208526\pi\)
\(684\) 0 0
\(685\) 4717.54i 0.263136i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1800.31 + 3118.23i 0.0995447 + 0.172417i
\(690\) 0 0
\(691\) −12034.8 6948.27i −0.662552 0.382525i 0.130696 0.991422i \(-0.458279\pi\)
−0.793249 + 0.608898i \(0.791612\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15451.1 8920.68i −0.843298 0.486879i
\(696\) 0 0
\(697\) 3253.76 + 5635.69i 0.176822 + 0.306265i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30902.8i 1.66503i 0.554005 + 0.832513i \(0.313099\pi\)
−0.554005 + 0.832513i \(0.686901\pi\)
\(702\) 0 0
\(703\) −896.638 + 517.674i −0.0481044 + 0.0277731i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −28657.8 11277.9i −1.52445 0.599926i
\(708\) 0 0
\(709\) 2160.65 3742.35i 0.114450 0.198233i −0.803110 0.595831i \(-0.796823\pi\)
0.917560 + 0.397598i \(0.130156\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −41636.5 −2.18695
\(714\) 0 0
\(715\) −908.229 −0.0475047
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16131.0 + 27939.7i −0.836696 + 1.44920i 0.0559456 + 0.998434i \(0.482183\pi\)
−0.892642 + 0.450767i \(0.851151\pi\)
\(720\) 0 0
\(721\) −8349.93 + 1250.68i −0.431301 + 0.0646014i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9865.30 5695.74i 0.505363 0.291771i
\(726\) 0 0
\(727\) 12056.4i 0.615056i −0.951539 0.307528i \(-0.900498\pi\)
0.951539 0.307528i \(-0.0995017\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3224.15 + 5584.40i 0.163132 + 0.282553i
\(732\) 0 0
\(733\) −22122.9 12772.7i −1.11477 0.643615i −0.174712 0.984620i \(-0.555899\pi\)
−0.940061 + 0.341005i \(0.889233\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3702.31 2137.53i −0.185043 0.106834i
\(738\) 0 0
\(739\) −12402.9 21482.4i −0.617384 1.06934i −0.989961 0.141340i \(-0.954859\pi\)
0.372577 0.928001i \(-0.378474\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 23318.4i 1.15137i −0.817671 0.575686i \(-0.804735\pi\)
0.817671 0.575686i \(-0.195265\pi\)
\(744\) 0 0
\(745\) 1577.05 910.508i 0.0775550 0.0447764i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 27051.7 4051.88i 1.31969 0.197667i
\(750\) 0 0
\(751\) −155.921 + 270.063i −0.00757607 + 0.0131221i −0.869789 0.493425i \(-0.835745\pi\)
0.862213 + 0.506547i \(0.169078\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4019.46 −0.193752
\(756\) 0 0
\(757\) −26444.1 −1.26965 −0.634825 0.772656i \(-0.718928\pi\)
−0.634825 + 0.772656i \(0.718928\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10265.6 + 17780.5i −0.488997 + 0.846968i −0.999920 0.0126584i \(-0.995971\pi\)
0.510922 + 0.859627i \(0.329304\pi\)
\(762\) 0 0
\(763\) 27029.5 + 10637.1i 1.28248 + 0.504703i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 72.5886 41.9090i 0.00341724 0.00197294i
\(768\) 0 0
\(769\) 19950.3i 0.935533i −0.883852 0.467767i \(-0.845059\pi\)
0.883852 0.467767i \(-0.154941\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19809.6 + 34311.3i 0.921737 + 1.59650i 0.796726 + 0.604340i \(0.206563\pi\)
0.125011 + 0.992155i \(0.460103\pi\)
\(774\) 0 0
\(775\) −12306.2 7105.00i −0.570390 0.329315i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1472.10 + 849.920i 0.0677068 + 0.0390906i
\(780\) 0 0
\(781\) 2871.84 + 4974.18i 0.131578 + 0.227900i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 23506.0i 1.06874i
\(786\) 0 0
\(787\) −28877.8 + 16672.6i −1.30798 + 0.755163i −0.981759 0.190130i \(-0.939109\pi\)
−0.326222 + 0.945293i \(0.605776\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12425.0 15610.0i −0.558512 0.701678i
\(792\) 0 0
\(793\) −1023.39 + 1772.57i −0.0458283 + 0.0793769i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15138.0 −0.672793 −0.336397 0.941720i \(-0.609208\pi\)
−0.336397 + 0.941720i \(0.609208\pi\)
\(798\) 0 0
\(799\) 10716.5 0.474496
\(800\) 0 0
\(801\) 0 0