Properties

Label 1512.2.s.o.1297.4
Level $1512$
Weight $2$
Character 1512.1297
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} + 28 x^{5} + 14 x^{4} - 52 x^{3} + 306 x^{2} + 1052 x + 1051\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.4
Root \(-1.30724 - 1.29485i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.o.865.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70873 - 2.95960i) q^{5} +(-2.27499 + 1.35071i) q^{7} +O(q^{10})\) \(q+(1.70873 - 2.95960i) q^{5} +(-2.27499 + 1.35071i) q^{7} +(-3.01597 - 5.22381i) q^{11} +0.417453 q^{13} +(-1.27499 - 2.20835i) q^{17} +(-1.74274 + 3.01852i) q^{19} +(-4.54822 + 7.87774i) q^{23} +(-3.33949 - 5.78417i) q^{25} +1.67898 q^{29} +(-3.82321 - 6.62200i) q^{31} +(0.110210 + 9.04106i) q^{35} +(-4.69245 + 8.12755i) q^{37} +2.13253 q^{41} -6.03194 q^{43} +(3.94970 - 6.84108i) q^{47} +(3.35119 - 6.14569i) q^{49} +(-0.967751 - 1.67619i) q^{53} -20.6139 q^{55} +(3.91922 + 6.78829i) q^{59} +(-4.67648 + 8.09990i) q^{61} +(0.713312 - 1.23549i) q^{65} +(-0.516281 - 0.894224i) q^{67} +0.650582 q^{71} +(-0.642460 - 1.11277i) q^{73} +(13.9171 + 7.81045i) q^{77} +(8.20665 - 14.2143i) q^{79} -14.1645 q^{83} -8.71446 q^{85} +(6.70841 - 11.6193i) q^{89} +(-0.949702 + 0.563856i) q^{91} +(5.95574 + 10.3157i) q^{95} -2.26507 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 8q + 2q^{5} - 4q^{7} + q^{11} - 20q^{13} + 4q^{17} + q^{19} - 12q^{23} - 14q^{25} - 12q^{29} + 8q^{31} - 9q^{35} + 12q^{41} + 2q^{43} + 9q^{47} + 6q^{49} - 7q^{53} - 36q^{55} + 4q^{59} - 25q^{61} + 28q^{65} - 30q^{67} + 22q^{71} + 4q^{73} + 37q^{77} + 7q^{79} - 58q^{83} + 14q^{85} - 9q^{89} + 15q^{91} + 4q^{95} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 1.70873 2.95960i 0.764166 1.32357i −0.176521 0.984297i \(-0.556484\pi\)
0.940687 0.339277i \(-0.110182\pi\)
\(6\) 0 0
\(7\) −2.27499 + 1.35071i −0.859867 + 0.510519i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.01597 5.22381i −0.909349 1.57504i −0.814971 0.579502i \(-0.803247\pi\)
−0.0943778 0.995536i \(-0.530086\pi\)
\(12\) 0 0
\(13\) 0.417453 0.115781 0.0578903 0.998323i \(-0.481563\pi\)
0.0578903 + 0.998323i \(0.481563\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.27499 2.20835i −0.309231 0.535604i 0.668963 0.743296i \(-0.266738\pi\)
−0.978194 + 0.207691i \(0.933405\pi\)
\(18\) 0 0
\(19\) −1.74274 + 3.01852i −0.399813 + 0.692496i −0.993703 0.112050i \(-0.964258\pi\)
0.593890 + 0.804546i \(0.297592\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.54822 + 7.87774i −0.948369 + 1.64262i −0.199508 + 0.979896i \(0.563934\pi\)
−0.748861 + 0.662727i \(0.769399\pi\)
\(24\) 0 0
\(25\) −3.33949 5.78417i −0.667898 1.15683i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.67898 0.311779 0.155890 0.987774i \(-0.450176\pi\)
0.155890 + 0.987774i \(0.450176\pi\)
\(30\) 0 0
\(31\) −3.82321 6.62200i −0.686669 1.18935i −0.972909 0.231188i \(-0.925739\pi\)
0.286240 0.958158i \(-0.407594\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.110210 + 9.04106i 0.0186290 + 1.52822i
\(36\) 0 0
\(37\) −4.69245 + 8.12755i −0.771433 + 1.33616i 0.165344 + 0.986236i \(0.447127\pi\)
−0.936777 + 0.349926i \(0.886207\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.13253 0.333046 0.166523 0.986038i \(-0.446746\pi\)
0.166523 + 0.986038i \(0.446746\pi\)
\(42\) 0 0
\(43\) −6.03194 −0.919862 −0.459931 0.887955i \(-0.652126\pi\)
−0.459931 + 0.887955i \(0.652126\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.94970 6.84108i 0.576123 0.997875i −0.419795 0.907619i \(-0.637898\pi\)
0.995919 0.0902560i \(-0.0287685\pi\)
\(48\) 0 0
\(49\) 3.35119 6.14569i 0.478741 0.877956i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.967751 1.67619i −0.132931 0.230243i 0.791874 0.610684i \(-0.209105\pi\)
−0.924805 + 0.380441i \(0.875772\pi\)
\(54\) 0 0
\(55\) −20.6139 −2.77957
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.91922 + 6.78829i 0.510239 + 0.883760i 0.999930 + 0.0118637i \(0.00377642\pi\)
−0.489691 + 0.871896i \(0.662890\pi\)
\(60\) 0 0
\(61\) −4.67648 + 8.09990i −0.598762 + 1.03709i 0.394243 + 0.919006i \(0.371007\pi\)
−0.993004 + 0.118079i \(0.962326\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.713312 1.23549i 0.0884755 0.153244i
\(66\) 0 0
\(67\) −0.516281 0.894224i −0.0630737 0.109247i 0.832764 0.553628i \(-0.186757\pi\)
−0.895838 + 0.444381i \(0.853424\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.650582 0.0772099 0.0386049 0.999255i \(-0.487709\pi\)
0.0386049 + 0.999255i \(0.487709\pi\)
\(72\) 0 0
\(73\) −0.642460 1.11277i −0.0751942 0.130240i 0.825976 0.563705i \(-0.190624\pi\)
−0.901171 + 0.433464i \(0.857291\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.9171 + 7.81045i 1.58601 + 0.890083i
\(78\) 0 0
\(79\) 8.20665 14.2143i 0.923320 1.59924i 0.129079 0.991634i \(-0.458798\pi\)
0.794241 0.607603i \(-0.207869\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.1645 −1.55475 −0.777376 0.629036i \(-0.783450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(84\) 0 0
\(85\) −8.71446 −0.945216
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.70841 11.6193i 0.711090 1.23164i −0.253358 0.967373i \(-0.581535\pi\)
0.964448 0.264272i \(-0.0851317\pi\)
\(90\) 0 0
\(91\) −0.949702 + 0.563856i −0.0995558 + 0.0591082i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.95574 + 10.3157i 0.611046 + 1.05836i
\(96\) 0 0
\(97\) −2.26507 −0.229983 −0.114991 0.993366i \(-0.536684\pi\)
−0.114991 + 0.993366i \(0.536684\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.576193 + 0.997996i 0.0573334 + 0.0993043i 0.893268 0.449525i \(-0.148407\pi\)
−0.835934 + 0.548830i \(0.815074\pi\)
\(102\) 0 0
\(103\) −2.32352 + 4.02446i −0.228944 + 0.396542i −0.957495 0.288449i \(-0.906860\pi\)
0.728552 + 0.684991i \(0.240194\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.50177 + 4.33319i −0.241855 + 0.418905i −0.961243 0.275704i \(-0.911089\pi\)
0.719388 + 0.694609i \(0.244423\pi\)
\(108\) 0 0
\(109\) −6.54999 11.3449i −0.627375 1.08665i −0.988076 0.153964i \(-0.950796\pi\)
0.360702 0.932681i \(-0.382537\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.3169 −1.53496 −0.767480 0.641072i \(-0.778490\pi\)
−0.767480 + 0.641072i \(0.778490\pi\)
\(114\) 0 0
\(115\) 15.5433 + 26.9218i 1.44942 + 2.51047i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.88344 + 3.30185i 0.539334 + 0.302680i
\(120\) 0 0
\(121\) −12.6921 + 21.9834i −1.15383 + 1.99849i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.73785 −0.513209
\(126\) 0 0
\(127\) 14.5373 1.28997 0.644987 0.764193i \(-0.276863\pi\)
0.644987 + 0.764193i \(0.276863\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.536523 + 0.929286i −0.0468763 + 0.0811921i −0.888512 0.458854i \(-0.848260\pi\)
0.841635 + 0.540046i \(0.181593\pi\)
\(132\) 0 0
\(133\) −0.112405 9.22105i −0.00974671 0.799566i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.96744 12.0680i −0.595268 1.03104i −0.993509 0.113754i \(-0.963712\pi\)
0.398240 0.917281i \(-0.369621\pi\)
\(138\) 0 0
\(139\) 0.811516 0.0688319 0.0344160 0.999408i \(-0.489043\pi\)
0.0344160 + 0.999408i \(0.489043\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.25902 2.18069i −0.105285 0.182359i
\(144\) 0 0
\(145\) 2.86892 4.96912i 0.238251 0.412663i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.33667 9.24339i 0.437197 0.757248i −0.560275 0.828307i \(-0.689304\pi\)
0.997472 + 0.0710588i \(0.0226378\pi\)
\(150\) 0 0
\(151\) −8.69245 15.0558i −0.707381 1.22522i −0.965825 0.259194i \(-0.916543\pi\)
0.258444 0.966026i \(-0.416790\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −26.1313 −2.09892
\(156\) 0 0
\(157\) −9.98164 17.2887i −0.796622 1.37979i −0.921804 0.387655i \(-0.873285\pi\)
0.125183 0.992134i \(-0.460048\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.293354 24.0651i −0.0231195 1.89660i
\(162\) 0 0
\(163\) 0.224695 0.389183i 0.0175995 0.0304832i −0.857092 0.515164i \(-0.827731\pi\)
0.874691 + 0.484681i \(0.161064\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.15946 0.167104 0.0835520 0.996503i \(-0.473374\pi\)
0.0835520 + 0.996503i \(0.473374\pi\)
\(168\) 0 0
\(169\) −12.8257 −0.986595
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.80693 13.5220i 0.593550 1.02806i −0.400200 0.916428i \(-0.631059\pi\)
0.993750 0.111631i \(-0.0356074\pi\)
\(174\) 0 0
\(175\) 15.4100 + 8.64827i 1.16489 + 0.653748i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.38771 7.59974i −0.327953 0.568031i 0.654153 0.756363i \(-0.273025\pi\)
−0.982105 + 0.188332i \(0.939692\pi\)
\(180\) 0 0
\(181\) 14.7464 1.09609 0.548045 0.836449i \(-0.315372\pi\)
0.548045 + 0.836449i \(0.315372\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 16.0362 + 27.7755i 1.17901 + 2.04210i
\(186\) 0 0
\(187\) −7.69068 + 13.3206i −0.562398 + 0.974102i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.01597 3.49176i 0.145870 0.252655i −0.783827 0.620979i \(-0.786735\pi\)
0.929697 + 0.368324i \(0.120068\pi\)
\(192\) 0 0
\(193\) −2.93373 5.08138i −0.211175 0.365765i 0.740908 0.671607i \(-0.234396\pi\)
−0.952082 + 0.305841i \(0.901062\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.711544 0.0506954 0.0253477 0.999679i \(-0.491931\pi\)
0.0253477 + 0.999679i \(0.491931\pi\)
\(198\) 0 0
\(199\) −5.11448 8.85855i −0.362556 0.627966i 0.625825 0.779964i \(-0.284763\pi\)
−0.988381 + 0.151998i \(0.951429\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.81967 + 2.26781i −0.268089 + 0.159169i
\(204\) 0 0
\(205\) 3.64392 6.31145i 0.254502 0.440811i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 21.0242 1.45428
\(210\) 0 0
\(211\) 20.5500 1.41472 0.707360 0.706854i \(-0.249886\pi\)
0.707360 + 0.706854i \(0.249886\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.3069 + 17.8521i −0.702927 + 1.21750i
\(216\) 0 0
\(217\) 17.6421 + 9.90096i 1.19763 + 0.672121i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.532249 0.921883i −0.0358030 0.0620125i
\(222\) 0 0
\(223\) −17.8633 −1.19622 −0.598108 0.801416i \(-0.704081\pi\)
−0.598108 + 0.801416i \(0.704081\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.63077 9.75277i −0.373727 0.647314i 0.616409 0.787426i \(-0.288587\pi\)
−0.990136 + 0.140112i \(0.955254\pi\)
\(228\) 0 0
\(229\) −10.5132 + 18.2093i −0.694729 + 1.20331i 0.275544 + 0.961289i \(0.411142\pi\)
−0.970272 + 0.242017i \(0.922191\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.80901 11.7936i 0.446073 0.772621i −0.552053 0.833809i \(-0.686155\pi\)
0.998126 + 0.0611876i \(0.0194888\pi\)
\(234\) 0 0
\(235\) −13.4979 23.3791i −0.880507 1.52508i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.9384 1.28971 0.644854 0.764305i \(-0.276918\pi\)
0.644854 + 0.764305i \(0.276918\pi\)
\(240\) 0 0
\(241\) 6.39940 + 11.0841i 0.412222 + 0.713989i 0.995132 0.0985472i \(-0.0314195\pi\)
−0.582911 + 0.812536i \(0.698086\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −12.4625 20.4195i −0.796203 1.30455i
\(246\) 0 0
\(247\) −0.727513 + 1.26009i −0.0462906 + 0.0801776i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.03194 0.317613 0.158807 0.987310i \(-0.449235\pi\)
0.158807 + 0.987310i \(0.449235\pi\)
\(252\) 0 0
\(253\) 54.8691 3.44959
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.19037 + 8.98998i −0.323766 + 0.560779i −0.981262 0.192679i \(-0.938282\pi\)
0.657496 + 0.753458i \(0.271616\pi\)
\(258\) 0 0
\(259\) −0.302656 24.8282i −0.0188061 1.54275i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.64215 + 8.04044i 0.286247 + 0.495795i 0.972911 0.231181i \(-0.0742588\pi\)
−0.686664 + 0.726975i \(0.740926\pi\)
\(264\) 0 0
\(265\) −6.61448 −0.406325
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.74243 + 9.94618i 0.350122 + 0.606430i 0.986271 0.165137i \(-0.0528067\pi\)
−0.636148 + 0.771567i \(0.719473\pi\)
\(270\) 0 0
\(271\) 0.142148 0.246207i 0.00863486 0.0149560i −0.861676 0.507459i \(-0.830585\pi\)
0.870311 + 0.492503i \(0.163918\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −20.1436 + 34.8897i −1.21471 + 2.10393i
\(276\) 0 0
\(277\) 13.4973 + 23.3780i 0.810974 + 1.40465i 0.912183 + 0.409783i \(0.134396\pi\)
−0.101209 + 0.994865i \(0.532271\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.6145 −0.931482 −0.465741 0.884921i \(-0.654212\pi\)
−0.465741 + 0.884921i \(0.654212\pi\)
\(282\) 0 0
\(283\) 16.0504 + 27.8001i 0.954098 + 1.65255i 0.736419 + 0.676526i \(0.236515\pi\)
0.217679 + 0.976020i \(0.430151\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.85150 + 2.88043i −0.286375 + 0.170026i
\(288\) 0 0
\(289\) 5.24879 9.09116i 0.308752 0.534774i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.2964 0.952045 0.476022 0.879433i \(-0.342078\pi\)
0.476022 + 0.879433i \(0.342078\pi\)
\(294\) 0 0
\(295\) 26.7875 1.55963
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.89867 + 3.28859i −0.109803 + 0.190184i
\(300\) 0 0
\(301\) 13.7226 8.14737i 0.790958 0.469607i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 15.9816 + 27.6810i 0.915106 + 1.58501i
\(306\) 0 0
\(307\) −0.673971 −0.0384656 −0.0192328 0.999815i \(-0.506122\pi\)
−0.0192328 + 0.999815i \(0.506122\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 11.7754 + 20.3956i 0.667723 + 1.15653i 0.978539 + 0.206060i \(0.0660642\pi\)
−0.310817 + 0.950470i \(0.600603\pi\)
\(312\) 0 0
\(313\) −2.08255 + 3.60708i −0.117713 + 0.203884i −0.918861 0.394582i \(-0.870889\pi\)
0.801148 + 0.598466i \(0.204223\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.82321 4.88994i 0.158567 0.274647i −0.775785 0.630997i \(-0.782646\pi\)
0.934352 + 0.356351i \(0.115979\pi\)
\(318\) 0 0
\(319\) −5.06376 8.77069i −0.283516 0.491064i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.88794 0.494538
\(324\) 0 0
\(325\) −1.39408 2.41462i −0.0773296 0.133939i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.254750 + 20.8983i 0.0140448 + 1.15216i
\(330\) 0 0
\(331\) 4.20622 7.28539i 0.231195 0.400441i −0.726965 0.686674i \(-0.759070\pi\)
0.958160 + 0.286233i \(0.0924032\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.52873 −0.192795
\(336\) 0 0
\(337\) 11.0390 0.601333 0.300667 0.953729i \(-0.402791\pi\)
0.300667 + 0.953729i \(0.402791\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −23.0614 + 39.9435i −1.24884 + 2.16306i
\(342\) 0 0
\(343\) 0.677101 + 18.5079i 0.0365600 + 0.999331i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.75902 8.24287i −0.255478 0.442501i 0.709547 0.704658i \(-0.248899\pi\)
−0.965025 + 0.262157i \(0.915566\pi\)
\(348\) 0 0
\(349\) 15.7053 0.840685 0.420342 0.907366i \(-0.361910\pi\)
0.420342 + 0.907366i \(0.361910\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.5636 21.7607i −0.668691 1.15821i −0.978270 0.207333i \(-0.933522\pi\)
0.309579 0.950874i \(-0.399812\pi\)
\(354\) 0 0
\(355\) 1.11167 1.92546i 0.0590011 0.102193i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.8544 20.5324i 0.625652 1.08366i −0.362763 0.931882i \(-0.618166\pi\)
0.988414 0.151779i \(-0.0485003\pi\)
\(360\) 0 0
\(361\) 3.42569 + 5.93347i 0.180299 + 0.312288i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.39115 −0.229843
\(366\) 0 0
\(367\) 14.2410 + 24.6661i 0.743373 + 1.28756i 0.950951 + 0.309341i \(0.100109\pi\)
−0.207578 + 0.978218i \(0.566558\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.46567 + 2.50618i 0.231846 + 0.130114i
\(372\) 0 0
\(373\) 8.22897 14.2530i 0.426080 0.737992i −0.570441 0.821339i \(-0.693228\pi\)
0.996521 + 0.0833468i \(0.0265609\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.700896 0.0360980
\(378\) 0 0
\(379\) −16.4934 −0.847210 −0.423605 0.905847i \(-0.639235\pi\)
−0.423605 + 0.905847i \(0.639235\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.3892 31.8510i 0.939642 1.62751i 0.173504 0.984833i \(-0.444491\pi\)
0.766139 0.642675i \(-0.222176\pi\)
\(384\) 0 0
\(385\) 46.8964 27.8433i 2.39006 1.41902i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.95116 17.2359i −0.504544 0.873895i −0.999986 0.00525463i \(-0.998327\pi\)
0.495442 0.868641i \(-0.335006\pi\)
\(390\) 0 0
\(391\) 23.1958 1.17306
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −28.0458 48.5768i −1.41114 2.44416i
\(396\) 0 0
\(397\) −12.9781 + 22.4787i −0.651352 + 1.12818i 0.331443 + 0.943475i \(0.392465\pi\)
−0.982795 + 0.184700i \(0.940869\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.2506 26.4148i 0.761578 1.31909i −0.180459 0.983583i \(-0.557758\pi\)
0.942037 0.335509i \(-0.108908\pi\)
\(402\) 0 0
\(403\) −1.59601 2.76437i −0.0795029 0.137703i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 56.6091 2.80601
\(408\) 0 0
\(409\) 3.69276 + 6.39604i 0.182595 + 0.316264i 0.942764 0.333462i \(-0.108217\pi\)
−0.760168 + 0.649726i \(0.774884\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −18.0852 10.1496i −0.889914 0.499429i
\(414\) 0 0
\(415\) −24.2032 + 41.9212i −1.18809 + 2.05783i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.0760 −1.07848 −0.539241 0.842152i \(-0.681289\pi\)
−0.539241 + 0.842152i \(0.681289\pi\)
\(420\) 0 0
\(421\) −11.9952 −0.584611 −0.292306 0.956325i \(-0.594422\pi\)
−0.292306 + 0.956325i \(0.594422\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8.51566 + 14.7495i −0.413070 + 0.715458i
\(426\) 0 0
\(427\) −0.301626 24.7438i −0.0145967 1.19743i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.17793 3.77229i −0.104907 0.181705i 0.808793 0.588093i \(-0.200121\pi\)
−0.913700 + 0.406389i \(0.866788\pi\)
\(432\) 0 0
\(433\) −10.6024 −0.509519 −0.254759 0.967004i \(-0.581996\pi\)
−0.254759 + 0.967004i \(0.581996\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.8528 27.4578i −0.758340 1.31348i
\(438\) 0 0
\(439\) 1.13504 1.96595i 0.0541725 0.0938295i −0.837667 0.546181i \(-0.816081\pi\)
0.891840 + 0.452351i \(0.149415\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.95932 12.0539i 0.330647 0.572698i −0.651992 0.758226i \(-0.726066\pi\)
0.982639 + 0.185528i \(0.0593997\pi\)
\(444\) 0 0
\(445\) −22.9257 39.7085i −1.08678 1.88236i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.6657 0.975272 0.487636 0.873047i \(-0.337859\pi\)
0.487636 + 0.873047i \(0.337859\pi\)
\(450\) 0 0
\(451\) −6.43165 11.1400i −0.302855 0.524560i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.0460077 + 3.77421i 0.00215687 + 0.176938i
\(456\) 0 0
\(457\) −6.17825 + 10.7010i −0.289006 + 0.500573i −0.973573 0.228377i \(-0.926658\pi\)
0.684567 + 0.728950i \(0.259991\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −24.4304 −1.13784 −0.568918 0.822394i \(-0.692638\pi\)
−0.568918 + 0.822394i \(0.692638\pi\)
\(462\) 0 0
\(463\) 36.7458 1.70772 0.853860 0.520502i \(-0.174255\pi\)
0.853860 + 0.520502i \(0.174255\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.61052 + 11.4498i −0.305898 + 0.529832i −0.977461 0.211116i \(-0.932290\pi\)
0.671562 + 0.740948i \(0.265623\pi\)
\(468\) 0 0
\(469\) 2.38237 + 1.33701i 0.110008 + 0.0617374i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18.1921 + 31.5097i 0.836475 + 1.44882i
\(474\) 0 0
\(475\) 23.2795 1.06814
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −18.8140 32.5869i −0.859635 1.48893i −0.872277 0.489012i \(-0.837357\pi\)
0.0126417 0.999920i \(-0.495976\pi\)
\(480\) 0 0
\(481\) −1.95887 + 3.39287i −0.0893170 + 0.154702i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.87038 + 6.70369i −0.175745 + 0.304399i
\(486\) 0 0
\(487\) −8.64497 14.9735i −0.391741 0.678515i 0.600938 0.799295i \(-0.294794\pi\)
−0.992679 + 0.120780i \(0.961460\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.1837 0.459584 0.229792 0.973240i \(-0.426195\pi\)
0.229792 + 0.973240i \(0.426195\pi\)
\(492\) 0 0
\(493\) −2.14069 3.70779i −0.0964119 0.166990i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.48007 + 0.878745i −0.0663902 + 0.0394171i
\(498\) 0 0
\(499\) 12.5359 21.7128i 0.561184 0.971999i −0.436210 0.899845i \(-0.643679\pi\)
0.997394 0.0721540i \(-0.0229873\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 32.2887 1.43968 0.719841 0.694139i \(-0.244215\pi\)
0.719841 + 0.694139i \(0.244215\pi\)
\(504\) 0 0
\(505\) 3.93823 0.175249
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −12.9799 + 22.4818i −0.575323 + 0.996488i 0.420684 + 0.907207i \(0.361790\pi\)
−0.996006 + 0.0892808i \(0.971543\pi\)
\(510\) 0 0
\(511\) 2.96462 + 1.66378i 0.131147 + 0.0736011i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.94053 + 13.7534i 0.349902 + 0.606047i
\(516\) 0 0
\(517\) −47.6487 −2.09559
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.81894 8.34664i −0.211121 0.365673i 0.740944 0.671566i \(-0.234378\pi\)
−0.952066 + 0.305893i \(0.901045\pi\)
\(522\) 0 0
\(523\) −8.48372 + 14.6942i −0.370967 + 0.642534i −0.989715 0.143056i \(-0.954307\pi\)
0.618747 + 0.785590i \(0.287640\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.74913 + 16.8860i −0.424679 + 0.735566i
\(528\) 0 0
\(529\) −29.8726 51.7408i −1.29881 2.24960i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.890232 0.0385602
\(534\) 0 0
\(535\) 8.54967 + 14.8085i 0.369635 + 0.640226i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −42.2110 + 1.02926i −1.81816 + 0.0443332i
\(540\) 0 0
\(541\) 3.01346 5.21947i 0.129559 0.224403i −0.793947 0.607987i \(-0.791977\pi\)
0.923506 + 0.383585i \(0.125311\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −44.7685 −1.91767
\(546\) 0 0
\(547\) −12.6423 −0.540544 −0.270272 0.962784i \(-0.587114\pi\)
−0.270272 + 0.962784i \(0.587114\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.92604 + 5.06805i −0.124653 + 0.215906i
\(552\) 0 0
\(553\) 0.529317 + 43.4223i 0.0225089 + 1.84650i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.32883 + 4.03365i 0.0986756 + 0.170911i 0.911137 0.412104i \(-0.135206\pi\)
−0.812461 + 0.583015i \(0.801873\pi\)
\(558\) 0 0
\(559\) −2.51805 −0.106502
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.93770 17.2126i −0.418824 0.725424i 0.576998 0.816746i \(-0.304224\pi\)
−0.995821 + 0.0913216i \(0.970891\pi\)
\(564\) 0 0
\(565\) −27.8810 + 48.2914i −1.17296 + 2.03163i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.4856 + 30.2860i −0.733035 + 1.26965i 0.222546 + 0.974922i \(0.428563\pi\)
−0.955580 + 0.294731i \(0.904770\pi\)
\(570\) 0 0
\(571\) −5.21049 9.02484i −0.218052 0.377678i 0.736160 0.676807i \(-0.236637\pi\)
−0.954212 + 0.299130i \(0.903304\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 60.7549 2.53366
\(576\) 0 0
\(577\) 18.4791 + 32.0068i 0.769296 + 1.33246i 0.937945 + 0.346784i \(0.112726\pi\)
−0.168649 + 0.985676i \(0.553940\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.2241 19.1320i 1.33688 0.793731i
\(582\) 0 0
\(583\) −5.83741 + 10.1107i −0.241761 + 0.418742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −26.6168 −1.09859 −0.549296 0.835628i \(-0.685104\pi\)
−0.549296 + 0.835628i \(0.685104\pi\)
\(588\) 0 0
\(589\) 26.6515 1.09816
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.49781 + 4.32633i −0.102573 + 0.177661i −0.912744 0.408532i \(-0.866041\pi\)
0.810171 + 0.586193i \(0.199374\pi\)
\(594\) 0 0
\(595\) 19.8253 11.7707i 0.812759 0.482550i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.7084 27.2078i −0.641828 1.11168i −0.985024 0.172416i \(-0.944843\pi\)
0.343196 0.939264i \(-0.388491\pi\)
\(600\) 0 0
\(601\) −19.5402 −0.797061 −0.398530 0.917155i \(-0.630480\pi\)
−0.398530 + 0.917155i \(0.630480\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 43.3748 + 75.1273i 1.76344 + 3.05436i
\(606\) 0 0
\(607\) 3.09852 5.36679i 0.125765 0.217831i −0.796267 0.604946i \(-0.793195\pi\)
0.922032 + 0.387114i \(0.126528\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.64881 2.85583i 0.0667039 0.115534i
\(612\) 0 0
\(613\) 6.83918 + 11.8458i 0.276232 + 0.478448i 0.970445 0.241322i \(-0.0775809\pi\)
−0.694213 + 0.719769i \(0.744248\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.8071 −0.636371 −0.318186 0.948028i \(-0.603073\pi\)
−0.318186 + 0.948028i \(0.603073\pi\)
\(618\) 0 0
\(619\) −17.6961 30.6505i −0.711266 1.23195i −0.964382 0.264513i \(-0.914789\pi\)
0.253116 0.967436i \(-0.418545\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.432683 + 35.4950i 0.0173351 + 1.42208i
\(624\) 0 0
\(625\) 6.89305 11.9391i 0.275722 0.477565i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 23.9313 0.954205
\(630\) 0 0
\(631\) 14.9994 0.597116 0.298558 0.954392i \(-0.403494\pi\)
0.298558 + 0.954392i \(0.403494\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 24.8402 43.0245i 0.985754 1.70738i
\(636\) 0 0
\(637\) 1.39896 2.56554i 0.0554289 0.101650i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.08327 + 3.60832i 0.0822840 + 0.142520i 0.904231 0.427044i \(-0.140445\pi\)
−0.821947 + 0.569565i \(0.807112\pi\)
\(642\) 0 0
\(643\) −35.1973 −1.38804 −0.694022 0.719954i \(-0.744163\pi\)
−0.694022 + 0.719954i \(0.744163\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.50031 9.52682i −0.216240 0.374538i 0.737416 0.675439i \(-0.236046\pi\)
−0.953655 + 0.300901i \(0.902713\pi\)
\(648\) 0 0
\(649\) 23.6405 40.9465i 0.927971 1.60729i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.65454 + 11.5260i −0.260412 + 0.451048i −0.966352 0.257225i \(-0.917192\pi\)
0.705939 + 0.708273i \(0.250525\pi\)
\(654\) 0 0
\(655\) 1.83354 + 3.17579i 0.0716425 + 0.124088i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 27.7265 1.08007 0.540036 0.841642i \(-0.318410\pi\)
0.540036 + 0.841642i \(0.318410\pi\)
\(660\) 0 0
\(661\) 7.65561 + 13.2599i 0.297769 + 0.515751i 0.975625 0.219444i \(-0.0704242\pi\)
−0.677856 + 0.735194i \(0.737091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −27.4827 15.4236i −1.06573 0.598101i
\(666\) 0 0
\(667\) −7.63638 + 13.2266i −0.295682 + 0.512136i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 56.4164 2.17793
\(672\) 0 0
\(673\) −28.8109 −1.11058 −0.555289 0.831657i \(-0.687392\pi\)
−0.555289 + 0.831657i \(0.687392\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.08608 + 3.61320i −0.0801747 + 0.138867i −0.903325 0.428957i \(-0.858881\pi\)
0.823150 + 0.567824i \(0.192214\pi\)
\(678\) 0 0
\(679\) 5.15301 3.05944i 0.197754 0.117410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.4214 + 19.7825i 0.437028 + 0.756955i 0.997459 0.0712463i \(-0.0226976\pi\)
−0.560430 + 0.828201i \(0.689364\pi\)
\(684\) 0 0
\(685\) −47.6218 −1.81953
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.403990 0.699732i −0.0153908 0.0266576i
\(690\) 0 0
\(691\) −11.6708 + 20.2145i −0.443979 + 0.768994i −0.997980 0.0635214i \(-0.979767\pi\)
0.554001 + 0.832516i \(0.313100\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.38666 2.40176i 0.0525990 0.0911041i
\(696\) 0 0
\(697\) −2.71896 4.70939i −0.102988 0.178381i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.51536 −0.321621 −0.160810 0.986985i \(-0.551411\pi\)
−0.160810 + 0.986985i \(0.551411\pi\)
\(702\) 0 0
\(703\) −16.3555 28.3285i −0.616858 1.06843i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.65883 1.49217i −0.0999958 0.0561187i
\(708\) 0 0
\(709\) −11.8310 + 20.4919i −0.444323 + 0.769591i −0.998005 0.0631380i \(-0.979889\pi\)
0.553681 + 0.832729i \(0.313223\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 69.5552 2.60486
\(714\) 0 0
\(715\) −8.60531 −0.321820
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.93197 + 8.54241i −0.183931 + 0.318578i −0.943216 0.332180i \(-0.892216\pi\)
0.759285 + 0.650759i \(0.225549\pi\)
\(720\) 0 0
\(721\) −0.149864 12.2940i −0.00558123 0.457853i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.60695 9.71152i −0.208237 0.360677i
\(726\) 0 0
\(727\) 6.37428 0.236409 0.118205 0.992989i \(-0.462286\pi\)
0.118205 + 0.992989i \(0.462286\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.69068 + 13.3206i 0.284450 + 0.492682i
\(732\) 0 0
\(733\) −8.09319 + 14.0178i −0.298929 + 0.517760i −0.975891 0.218258i \(-0.929963\pi\)
0.676962 + 0.736018i \(0.263296\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.11417 + 5.39391i −0.114712 + 0.198687i
\(738\) 0 0
\(739\) −6.59036 11.4148i −0.242430 0.419901i 0.718976 0.695035i \(-0.244611\pi\)
−0.961406 + 0.275134i \(0.911278\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.9733 −1.13630 −0.568149 0.822925i \(-0.692340\pi\)
−0.568149 + 0.822925i \(0.692340\pi\)
\(744\) 0 0
\(745\) −18.2378 31.5888i −0.668182 1.15733i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.161361 13.2371i −0.00589599 0.483674i
\(750\) 0 0
\(751\) −25.0433 + 43.3763i −0.913844 + 1.58282i −0.105258 + 0.994445i \(0.533567\pi\)
−0.808585 + 0.588379i \(0.799766\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −59.4120 −2.16223
\(756\) 0 0
\(757\) 19.8647 0.721996 0.360998 0.932567i \(-0.382436\pi\)
0.360998 + 0.932567i \(0.382436\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.83627 3.18051i 0.0665646 0.115293i −0.830822 0.556538i \(-0.812129\pi\)
0.897387 + 0.441244i \(0.145463\pi\)
\(762\) 0 0
\(763\) 30.2248 + 16.9625i 1.09421 + 0.614083i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.63609 + 2.83379i 0.0590758 + 0.102322i
\(768\) 0 0
\(769\) −16.4494 −0.593180 −0.296590 0.955005i \(-0.595850\pi\)
−0.296590 + 0.955005i \(0.595850\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.93020 + 5.07525i 0.105392 + 0.182544i 0.913898 0.405943i \(-0.133057\pi\)
−0.808506 + 0.588487i \(0.799724\pi\)
\(774\) 0 0
\(775\) −25.5352 + 44.2282i −0.917250 + 1.58872i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.71646 + 6.43710i −0.133156 + 0.230633i
\(780\) 0 0
\(781\) −1.96213 3.39852i −0.0702107 0.121608i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −68.2236 −2.43500
\(786\) 0 0
\(787\) −7.09393 12.2870i −0.252871 0.437986i 0.711444 0.702743i \(-0.248042\pi\)
−0.964315 + 0.264757i \(0.914708\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 37.1207 22.0393i 1.31986 0.783627i
\(792\) 0 0
\(793\) −1.95221 + 3.38132i −0.0693249 + 0.120074i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.48696 0.194358 0.0971791 0.995267i \(-0.469018\pi\)
0.0971791 + 0.995267i \(0.469018\pi\)
\(798\) 0 0
\(799\) −20.1434 −0.712621
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.87528 + 6.71218i −0.136756 + 0.236868i