Properties

Label 252.4.t.a.17.7
Level $252$
Weight $4$
Character 252.17
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 17.7
Root \(-8.00527 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 252.17
Dual form 252.4.t.a.89.7

$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

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

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
\(5\) 4.36813 + 7.56582i 0.390697 + 0.676707i 0.992542 0.121906i \(-0.0389006\pi\)
−0.601844 + 0.798613i \(0.705567\pi\)
\(6\) 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 \(-0.371756\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(12\) 0 0
\(13\) 11.8322i 0.252435i 0.992003 + 0.126217i \(0.0402837\pi\)
−0.992003 + 0.126217i \(0.959716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −22.2920 + 38.6108i −0.318035 + 0.550853i −0.980078 0.198613i \(-0.936356\pi\)
0.662043 + 0.749466i \(0.269690\pi\)
\(18\) 0 0
\(19\) 10.0856 5.82291i 0.121778 0.0703088i −0.437873 0.899037i \(-0.644268\pi\)
0.559652 + 0.828728i \(0.310935\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −123.521 + 71.3151i −1.11982 + 0.646531i −0.941356 0.337414i \(-0.890448\pi\)
−0.178469 + 0.983946i \(0.557114\pi\)
\(24\) 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 \(0.269581\pi\)
−0.662298 + 0.749241i \(0.730419\pi\)
\(30\) 0 0
\(31\) 252.809 + 145.960i 1.46471 + 0.845649i 0.999223 0.0394074i \(-0.0125470\pi\)
0.465484 + 0.885056i \(0.345880\pi\)
\(32\) 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 0.947720 0.319104i \(-0.103382\pi\)
−0.750212 + 0.661197i \(0.770049\pi\)
\(38\) 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 \(-0.417441\pi\)
0.256469 + 0.966552i \(0.417441\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 120.183 + 208.164i 0.372991 + 0.646039i 0.990024 0.140898i \(-0.0449990\pi\)
−0.617033 + 0.786937i \(0.711666\pi\)
\(48\) 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 0.117975 0.993017i \(-0.462360\pi\)
−0.800990 + 0.598678i \(0.795693\pi\)
\(54\) 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 \(-0.835821\pi\)
0.862091 + 0.506753i \(0.169154\pi\)
\(60\) 0 0
\(61\) −149.810 + 86.4927i −0.314445 + 0.181545i −0.648914 0.760862i \(-0.724777\pi\)
0.334469 + 0.942407i \(0.391443\pi\)
\(62\) 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 \(-0.687034\pi\)
0.997954 + 0.0639408i \(0.0203669\pi\)
\(68\) 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 0.418501 0.908217i \(-0.362556\pi\)
−0.577288 + 0.816540i \(0.695889\pi\)
\(74\) 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 \(-0.233945\pi\)
−0.951648 + 0.307190i \(0.900611\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 877.193 1.16005 0.580027 0.814597i \(-0.303042\pi\)
0.580027 + 0.814597i \(0.303042\pi\)
\(84\) 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 −0.884691 0.466179i \(-0.845630\pi\)
0.0386225 0.999254i \(-0.487703\pi\)
\(90\) 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 \(-0.873593\pi\)
0.922179 0.386764i \(-0.126407\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 831.442 1440.10i 0.819125 1.41877i −0.0872031 0.996191i \(-0.527793\pi\)
0.906328 0.422575i \(-0.138874\pi\)
\(102\) 0 0
\(103\) −394.807 + 227.942i −0.377684 + 0.218056i −0.676810 0.736158i \(-0.736638\pi\)
0.299126 + 0.954214i \(0.403305\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1279.07 738.474i 1.15563 0.667205i 0.205380 0.978682i \(-0.434157\pi\)
0.950254 + 0.311477i \(0.100824\pi\)
\(108\) 0 0
\(109\) −784.202 + 1358.28i −0.689110 + 1.19357i 0.283016 + 0.959115i \(0.408665\pi\)
−0.972126 + 0.234458i \(0.924668\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1077.27i 0.896820i −0.893828 0.448410i \(-0.851990\pi\)
0.893828 0.448410i \(-0.148010\pi\)
\(114\) 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 \(-0.322073\pi\)
0.530317 + 0.847799i \(0.322073\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −201.672 349.306i −0.134505 0.232969i 0.790903 0.611941i \(-0.209611\pi\)
−0.925408 + 0.378972i \(0.876278\pi\)
\(132\) 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 0.347044 0.937849i \(-0.387186\pi\)
−0.638679 + 0.769473i \(0.720519\pi\)
\(138\) 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 −0.449552 0.893254i \(-0.648416\pi\)
0.548804 + 0.835951i \(0.315083\pi\)
\(150\) 0 0
\(151\) 230.045 398.449i 0.123979 0.214737i −0.797355 0.603511i \(-0.793768\pi\)
0.921333 + 0.388774i \(0.127101\pi\)
\(152\) 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 −0.227446 0.973791i \(-0.573037\pi\)
−0.957050 + 0.289921i \(0.906371\pi\)
\(158\) 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 0.998506 + 0.0546381i \(0.0174005\pi\)
−0.451935 + 0.892051i \(0.649266\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3214.68 1.48958 0.744789 0.667300i \(-0.232550\pi\)
0.744789 + 0.667300i \(0.232550\pi\)
\(168\) 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 −0.930076 0.367367i \(-0.880259\pi\)
0.146889 0.989153i \(-0.453074\pi\)
\(174\) 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 \(-0.310072\pi\)
−0.435436 + 0.900220i \(0.643406\pi\)
\(180\) 0 0
\(181\) 1664.25i 0.683439i 0.939802 + 0.341720i \(0.111009\pi\)
−0.939802 + 0.341720i \(0.888991\pi\)
\(182\) 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 \(-0.651782\pi\)
0.539936 + 0.841706i \(0.318448\pi\)
\(192\) 0 0
\(193\) −1274.22 + 2207.01i −0.475235 + 0.823130i −0.999598 0.0283643i \(-0.990970\pi\)
0.524363 + 0.851495i \(0.324303\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4579.00i 1.65604i 0.560697 + 0.828021i \(0.310533\pi\)
−0.560697 + 0.828021i \(0.689467\pi\)
\(198\) 0 0
\(199\) 2151.47 + 1242.15i 0.766402 + 0.442482i 0.831590 0.555391i \(-0.187431\pi\)
−0.0651876 + 0.997873i \(0.520765\pi\)
\(200\) 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 \(-0.114604\pi\)
0.935883 + 0.352311i \(0.114604\pi\)
\(212\) 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 \(-0.903465\pi\)
0.735818 + 0.677179i \(0.236798\pi\)
\(228\) 0 0
\(229\) 693.480 400.381i 0.200115 0.115537i −0.396594 0.917994i \(-0.629808\pi\)
0.596709 + 0.802457i \(0.296475\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2273.75 + 1312.75i −0.639305 + 0.369103i −0.784347 0.620323i \(-0.787002\pi\)
0.145042 + 0.989426i \(0.453668\pi\)
\(234\) 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 0.387653 0.921806i \(-0.373286\pi\)
−0.604481 + 0.796620i \(0.706619\pi\)
\(242\) 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 \(-0.384135\pi\)
0.356015 + 0.934480i \(0.384135\pi\)
\(252\) 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 −0.971692 0.236251i \(-0.924081\pi\)
0.281247 0.959636i \(-0.409252\pi\)
\(258\) 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 \(-0.489446\pi\)
−0.848974 + 0.528435i \(0.822779\pi\)
\(264\) 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 −0.564453 0.825465i \(-0.690913\pi\)
0.997100 + 0.0760977i \(0.0242461\pi\)
\(270\) 0 0
\(271\) −6193.16 + 3575.62i −1.38822 + 0.801489i −0.993115 0.117147i \(-0.962625\pi\)
−0.395105 + 0.918636i \(0.629292\pi\)
\(272\) 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 −0.398834 0.917023i \(-0.630585\pi\)
0.993582 0.113111i \(-0.0360815\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5525.72i 1.17308i 0.809919 + 0.586542i \(0.199511\pi\)
−0.809919 + 0.586542i \(0.800489\pi\)
\(282\) 0 0
\(283\) 217.828 + 125.763i 0.0457545 + 0.0264164i 0.522703 0.852515i \(-0.324924\pi\)
−0.476948 + 0.878931i \(0.658257\pi\)
\(284\) 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 −0.425980 0.904733i \(-0.640071\pi\)
0.996511 0.0834566i \(-0.0265960\pi\)
\(312\) 0 0
\(313\) −1843.53 + 1064.36i −0.332915 + 0.192208i −0.657134 0.753773i \(-0.728232\pi\)
0.324220 + 0.945982i \(0.394898\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4547.45 2625.47i 0.805710 0.465177i −0.0397541 0.999209i \(-0.512657\pi\)
0.845464 + 0.534033i \(0.179324\pi\)
\(318\) 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 −0.956464 0.291852i \(-0.905729\pi\)
0.225481 0.974248i \(-0.427605\pi\)
\(332\) 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 \(-0.582534\pi\)
−0.965273 + 0.261244i \(0.915867\pi\)
\(348\) 0 0
\(349\) 11899.1i 1.82506i −0.409011 0.912530i \(-0.634126\pi\)
0.409011 0.912530i \(-0.365874\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4578.82 7930.75i 0.690385 1.19578i −0.281327 0.959612i \(-0.590774\pi\)
0.971712 0.236170i \(-0.0758923\pi\)
\(354\) 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 \(-0.473138\pi\)
0.905089 + 0.425223i \(0.139804\pi\)
\(360\) 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 \(-0.481229\pi\)
−0.835051 + 0.550172i \(0.814562\pi\)
\(368\) 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 −0.968024 0.250857i \(-0.919288\pi\)
0.266764 0.963762i \(-0.414046\pi\)
\(374\) 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 \(-0.475764\pi\)
0.0760671 + 0.997103i \(0.475764\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5313.98 9204.08i −0.708960 1.22795i −0.965243 0.261353i \(-0.915831\pi\)
0.256283 0.966602i \(-0.417502\pi\)
\(384\) 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 0.999954 + 0.00961230i \(0.00305974\pi\)
0.508301 + 0.861179i \(0.330274\pi\)
\(390\) 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 −0.638533 0.769595i \(-0.720458\pi\)
0.347222 + 0.937783i \(0.387125\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5288.60 + 3053.37i −0.658603 + 0.380245i −0.791745 0.610852i \(-0.790827\pi\)
0.133141 + 0.991097i \(0.457494\pi\)
\(402\) 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 0.374336 0.927293i \(-0.377871\pi\)
−0.615892 + 0.787831i \(0.711204\pi\)
\(410\) 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 \(-0.275571\pi\)
0.648083 + 0.761570i \(0.275571\pi\)
\(420\) 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 \(-0.421823\pi\)
−0.718468 + 0.695560i \(0.755156\pi\)
\(432\) 0 0
\(433\) 14412.6i 1.59960i 0.600268 + 0.799799i \(0.295061\pi\)
−0.600268 + 0.799799i \(0.704939\pi\)
\(434\) 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 \(-0.505596\pi\)
0.857101 + 0.515148i \(0.172263\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1022.14 590.133i 0.109624 0.0632913i −0.444186 0.895935i \(-0.646507\pi\)
0.553809 + 0.832643i \(0.313174\pi\)
\(444\) 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 \(0.228941\pi\)
−0.752307 + 0.658813i \(0.771059\pi\)
\(450\) 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 0.999803 + 0.0198696i \(0.00632509\pi\)
−0.482694 + 0.875789i \(0.660342\pi\)
\(458\) 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 \(-0.534871\pi\)
−0.109330 + 0.994005i \(0.534871\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1929.85 3342.59i −0.191226 0.331213i 0.754431 0.656380i \(-0.227913\pi\)
−0.945657 + 0.325166i \(0.894580\pi\)
\(468\) 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 0.162442 + 0.986718i \(0.448063\pi\)
−0.935744 + 0.352680i \(0.885270\pi\)
\(480\) 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 −0.124244 + 0.992252i \(0.539651\pi\)
−0.797193 + 0.603725i \(0.793683\pi\)
\(488\) 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 \(-0.179092\pi\)
−0.884879 + 0.465821i \(0.845759\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12435.5 −1.10233 −0.551166 0.834396i \(-0.685817\pi\)
−0.551166 + 0.834396i \(0.685817\pi\)
\(504\) 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 0.874069 + 0.485802i \(0.161472\pi\)
−0.0163174 + 0.999867i \(0.505194\pi\)
\(510\) 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 −0.994292 0.106694i \(-0.965974\pi\)
0.589545 + 0.807735i \(0.299307\pi\)
\(522\) 0 0
\(523\) 1451.42 837.977i 0.121350 0.0700615i −0.438096 0.898928i \(-0.644347\pi\)
0.559446 + 0.828867i \(0.311014\pi\)
\(524\) 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 0.985090 0.172040i \(-0.0550357\pi\)
−0.641536 + 0.767093i \(0.721702\pi\)
\(542\) 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 \(-0.497720\pi\)
0.00716382 + 0.999974i \(0.497720\pi\)
\(548\) 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 0.997812 0.0661167i \(-0.0210610\pi\)
0.441647 + 0.897189i \(0.354394\pi\)
\(558\) 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 0.425767 + 0.904833i \(0.360004\pi\)
−0.996492 + 0.0836908i \(0.973329\pi\)
\(564\) 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 −0.843565 0.537027i \(-0.819547\pi\)
0.0432965 + 0.999062i \(0.486214\pi\)
\(570\) 0 0
\(571\) −5721.40 + 9909.76i −0.419323 + 0.726288i −0.995871 0.0907745i \(-0.971066\pi\)
0.576549 + 0.817063i \(0.304399\pi\)
\(572\) 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 0.804583 0.593841i \(-0.202389\pi\)
−0.111990 + 0.993709i \(0.535722\pi\)
\(578\) 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 \(-0.516721\pi\)
−0.0525068 + 0.998621i \(0.516721\pi\)
\(588\) 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 0.751117 0.660170i \(-0.229516\pi\)
−0.947282 + 0.320401i \(0.896182\pi\)
\(594\) 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 \(-0.276786\pi\)
−0.339091 + 0.940753i \(0.610120\pi\)
\(600\) 0 0
\(601\) 13911.4i 0.944186i 0.881549 + 0.472093i \(0.156501\pi\)
−0.881549 + 0.472093i \(0.843499\pi\)
\(602\) 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 \(-0.585445\pi\)
0.702401 + 0.711782i \(0.252111\pi\)
\(608\) 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 −0.571810 0.820386i \(-0.693759\pi\)
0.996380 + 0.0850093i \(0.0270920\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22388.7i 1.46084i −0.683000 0.730419i \(-0.739325\pi\)
0.683000 0.730419i \(-0.260675\pi\)
\(618\) 0 0
\(619\) 4791.17 + 2766.18i 0.311104 + 0.179616i 0.647420 0.762133i \(-0.275848\pi\)
−0.336316 + 0.941749i \(0.609181\pi\)
\(620\) 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 \(-0.776282\pi\)
−0.763015 + 0.646381i \(0.776282\pi\)
\(632\) 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 0.234455 0.972127i \(-0.424670\pi\)
−0.724659 + 0.689107i \(0.758003\pi\)
\(642\) 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 \(-0.797784\pi\)
0.916355 + 0.400367i \(0.131117\pi\)
\(648\) 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 −0.287203 0.957870i \(-0.592725\pi\)
0.685938 + 0.727660i \(0.259392\pi\)
\(654\) 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 0.106535 0.994309i \(-0.466024\pi\)
−0.807829 + 0.589417i \(0.799358\pi\)
\(662\) 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 0.937013 0.349295i \(-0.113579\pi\)
−0.771004 + 0.636830i \(0.780245\pi\)
\(678\) 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 \(-0.458140\pi\)
−0.792984 + 0.609242i \(0.791474\pi\)
\(684\) 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 \(-0.541721\pi\)
0.793249 + 0.608898i \(0.208388\pi\)
\(692\) 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 \(-0.686901\pi\)
0.554005 0.832513i \(-0.313099\pi\)
\(702\) 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 0.917560 0.397598i \(-0.130156\pi\)
−0.803110 + 0.595831i \(0.796823\pi\)
\(710\) 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 0.892642 + 0.450767i \(0.148849\pi\)
−0.0559456 + 0.998434i \(0.517817\pi\)
\(720\) 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 −0.940061 0.341005i \(-0.889233\pi\)
−0.174712 + 0.984620i \(0.555899\pi\)
\(734\) 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 −0.372577 0.928001i \(-0.621526\pi\)
0.989961 0.141340i \(-0.0451410\pi\)
\(740\) 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 \(-0.164255\pi\)
−0.862213 + 0.506547i \(0.830922\pi\)
\(752\) 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 0.510922 0.859627i \(-0.329304\pi\)
−0.999920 + 0.0126584i \(0.995971\pi\)
\(762\) 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 \(0.154941\pi\)
−0.883852 + 0.467767i \(0.845059\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19809.6 34311.3i 0.921737 1.59650i 0.125011 0.992155i \(-0.460103\pi\)
0.796726 0.604340i \(-0.206563\pi\)
\(774\) 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 \(-0.0608910\pi\)
0.326222 + 0.945293i \(0.394224\pi\)
\(788\) 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
\(802\)