Properties

Label 1512.2.s.n.865.1
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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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 865.1
Root \(-1.30724 + 1.29485i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.n.1297.1

$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.940687 0.339277i \(-0.889818\pi\)
0.176521 0.984297i \(-0.443516\pi\)
\(6\) 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 0.0943778 0.995536i \(-0.469914\pi\)
0.814971 0.579502i \(-0.196753\pi\)
\(12\) 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 \(-0.733262\pi\)
0.978194 + 0.207691i \(0.0665950\pi\)
\(18\) 0 0
\(19\) −1.74274 3.01852i −0.399813 0.692496i 0.593890 0.804546i \(-0.297592\pi\)
−0.993703 + 0.112050i \(0.964258\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.54822 + 7.87774i 0.948369 + 1.64262i 0.748861 + 0.662727i \(0.230601\pi\)
0.199508 + 0.979896i \(0.436066\pi\)
\(24\) 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 \(-0.549824\pi\)
−0.155890 + 0.987774i \(0.549824\pi\)
\(30\) 0 0
\(31\) −3.82321 + 6.62200i −0.686669 + 1.18935i 0.286240 + 0.958158i \(0.407594\pi\)
−0.972909 + 0.231188i \(0.925739\pi\)
\(32\) 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 −0.936777 0.349926i \(-0.886207\pi\)
0.165344 0.986236i \(-0.447127\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.13253 −0.333046 −0.166523 0.986038i \(-0.553254\pi\)
−0.166523 + 0.986038i \(0.553254\pi\)
\(42\) 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 −0.995919 0.0902560i \(-0.971231\pi\)
0.419795 0.907619i \(-0.362102\pi\)
\(48\) 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 \(-0.790895\pi\)
0.924805 + 0.380441i \(0.124228\pi\)
\(54\) 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 0.489691 + 0.871896i \(0.337110\pi\)
−0.999930 + 0.0118637i \(0.996224\pi\)
\(60\) 0 0
\(61\) −4.67648 8.09990i −0.598762 1.03709i −0.993004 0.118079i \(-0.962326\pi\)
0.394243 0.919006i \(-0.371007\pi\)
\(62\) 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 −0.895838 0.444381i \(-0.853424\pi\)
0.832764 + 0.553628i \(0.186757\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.650582 −0.0772099 −0.0386049 0.999255i \(-0.512291\pi\)
−0.0386049 + 0.999255i \(0.512291\pi\)
\(72\) 0 0
\(73\) −0.642460 + 1.11277i −0.0751942 + 0.130240i −0.901171 0.433464i \(-0.857291\pi\)
0.825976 + 0.563705i \(0.190624\pi\)
\(74\) 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 0.794241 + 0.607603i \(0.207869\pi\)
0.129079 + 0.991634i \(0.458798\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.1645 1.55475 0.777376 0.629036i \(-0.216550\pi\)
0.777376 + 0.629036i \(0.216550\pi\)
\(84\) 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 −0.964448 0.264272i \(-0.914868\pi\)
0.253358 0.967373i \(-0.418465\pi\)
\(90\) 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 \(-0.851593\pi\)
0.835934 + 0.548830i \(0.184926\pi\)
\(102\) 0 0
\(103\) −2.32352 4.02446i −0.228944 0.396542i 0.728552 0.684991i \(-0.240194\pi\)
−0.957495 + 0.288449i \(0.906860\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.50177 + 4.33319i 0.241855 + 0.418905i 0.961243 0.275704i \(-0.0889108\pi\)
−0.719388 + 0.694609i \(0.755577\pi\)
\(108\) 0 0
\(109\) −6.54999 + 11.3449i −0.627375 + 1.08665i 0.360702 + 0.932681i \(0.382537\pi\)
−0.988076 + 0.153964i \(0.950796\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.3169 1.53496 0.767480 0.641072i \(-0.221510\pi\)
0.767480 + 0.641072i \(0.221510\pi\)
\(114\) 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 \(-0.151740\pi\)
−0.841635 + 0.540046i \(0.818407\pi\)
\(132\) 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 −0.398240 0.917281i \(-0.630379\pi\)
0.993509 0.113754i \(-0.0362876\pi\)
\(138\) 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 \(-0.310696\pi\)
−0.997472 + 0.0710588i \(0.977362\pi\)
\(150\) 0 0
\(151\) −8.69245 + 15.0558i −0.707381 + 1.22522i 0.258444 + 0.966026i \(0.416790\pi\)
−0.965825 + 0.259194i \(0.916543\pi\)
\(152\) 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 0.125183 + 0.992134i \(0.460048\pi\)
−0.921804 + 0.387655i \(0.873285\pi\)
\(158\) 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 0.874691 0.484681i \(-0.161064\pi\)
−0.857092 + 0.515164i \(0.827731\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.15946 −0.167104 −0.0835520 0.996503i \(-0.526626\pi\)
−0.0835520 + 0.996503i \(0.526626\pi\)
\(168\) 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 −0.993750 0.111631i \(-0.964393\pi\)
0.400200 0.916428i \(-0.368941\pi\)
\(174\) 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 \(-0.726975\pi\)
0.982105 + 0.188332i \(0.0603080\pi\)
\(180\) 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 \(-0.213265\pi\)
−0.929697 + 0.368324i \(0.879932\pi\)
\(192\) 0 0
\(193\) −2.93373 + 5.08138i −0.211175 + 0.365765i −0.952082 0.305841i \(-0.901062\pi\)
0.740908 + 0.671607i \(0.234396\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.711544 −0.0506954 −0.0253477 0.999679i \(-0.508069\pi\)
−0.0253477 + 0.999679i \(0.508069\pi\)
\(198\) 0 0
\(199\) −5.11448 + 8.85855i −0.362556 + 0.627966i −0.988381 0.151998i \(-0.951429\pi\)
0.625825 + 0.779964i \(0.284763\pi\)
\(200\) 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 \(-0.711413\pi\)
0.990136 + 0.140112i \(0.0447464\pi\)
\(228\) 0 0
\(229\) −10.5132 18.2093i −0.694729 1.20331i −0.970272 0.242017i \(-0.922191\pi\)
0.275544 0.961289i \(-0.411142\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.80901 11.7936i −0.446073 0.772621i 0.552053 0.833809i \(-0.313845\pi\)
−0.998126 + 0.0611876i \(0.980511\pi\)
\(234\) 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 \(-0.723082\pi\)
−0.644854 + 0.764305i \(0.723082\pi\)
\(240\) 0 0
\(241\) 6.39940 11.0841i 0.412222 0.713989i −0.582911 0.812536i \(-0.698086\pi\)
0.995132 + 0.0985472i \(0.0314195\pi\)
\(242\) 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 \(-0.550765\pi\)
−0.158807 + 0.987310i \(0.550765\pi\)
\(252\) 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 \(-0.0617176\pi\)
−0.657496 + 0.753458i \(0.728384\pi\)
\(258\) 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 \(-0.925741\pi\)
0.686664 + 0.726975i \(0.259074\pi\)
\(264\) 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 \(-0.947193\pi\)
0.636148 + 0.771567i \(0.280527\pi\)
\(270\) 0 0
\(271\) 0.142148 + 0.246207i 0.00863486 + 0.0149560i 0.870311 0.492503i \(-0.163918\pi\)
−0.861676 + 0.507459i \(0.830585\pi\)
\(272\) 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 −0.101209 0.994865i \(-0.532271\pi\)
0.912183 0.409783i \(-0.134396\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.6145 0.931482 0.465741 0.884921i \(-0.345788\pi\)
0.465741 + 0.884921i \(0.345788\pi\)
\(282\) 0 0
\(283\) 16.0504 27.8001i 0.954098 1.65255i 0.217679 0.976020i \(-0.430151\pi\)
0.736419 0.676526i \(-0.236515\pi\)
\(284\) 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 \(-0.657922\pi\)
−0.476022 + 0.879433i \(0.657922\pi\)
\(294\) 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 0.310817 + 0.950470i \(0.399397\pi\)
−0.978539 + 0.206060i \(0.933936\pi\)
\(312\) 0 0
\(313\) −2.08255 3.60708i −0.117713 0.203884i 0.801148 0.598466i \(-0.204223\pi\)
−0.918861 + 0.394582i \(0.870889\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.82321 4.88994i −0.158567 0.274647i 0.775785 0.630997i \(-0.217354\pi\)
−0.934352 + 0.356351i \(0.884021\pi\)
\(318\) 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 0.958160 0.286233i \(-0.0924032\pi\)
−0.726965 + 0.686674i \(0.759070\pi\)
\(332\) 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 \(-0.751101\pi\)
0.965025 + 0.262157i \(0.0844339\pi\)
\(348\) 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 −0.309579 0.950874i \(-0.600188\pi\)
0.978270 0.207333i \(-0.0664784\pi\)
\(354\) 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 −0.988414 0.151779i \(-0.951500\pi\)
0.362763 0.931882i \(-0.381834\pi\)
\(360\) 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 −0.207578 0.978218i \(-0.566558\pi\)
0.950951 0.309341i \(-0.100109\pi\)
\(368\) 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 0.996521 0.0833468i \(-0.0265609\pi\)
−0.570441 + 0.821339i \(0.693228\pi\)
\(374\) 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 −0.766139 0.642675i \(-0.777824\pi\)
−0.173504 0.984833i \(-0.555509\pi\)
\(384\) 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 −0.495442 0.868641i \(-0.664994\pi\)
0.999986 0.00525463i \(-0.00167261\pi\)
\(390\) 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 −0.982795 0.184700i \(-0.940869\pi\)
0.331443 0.943475i \(-0.392465\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.2506 26.4148i −0.761578 1.31909i −0.942037 0.335509i \(-0.891092\pi\)
0.180459 0.983583i \(-0.442242\pi\)
\(402\) 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 −0.760168 0.649726i \(-0.774884\pi\)
0.942764 + 0.333462i \(0.108217\pi\)
\(410\) 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 \(-0.318711\pi\)
0.539241 + 0.842152i \(0.318711\pi\)
\(420\) 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 \(-0.799879\pi\)
0.913700 + 0.406389i \(0.133212\pi\)
\(432\) 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 0.891840 0.452351i \(-0.149415\pi\)
−0.837667 + 0.546181i \(0.816081\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.95932 12.0539i −0.330647 0.572698i 0.651992 0.758226i \(-0.273934\pi\)
−0.982639 + 0.185528i \(0.940600\pi\)
\(444\) 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 \(-0.662141\pi\)
−0.487636 + 0.873047i \(0.662141\pi\)
\(450\) 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 0.684567 0.728950i \(-0.259991\pi\)
−0.973573 + 0.228377i \(0.926658\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 24.4304 1.13784 0.568918 0.822394i \(-0.307362\pi\)
0.568918 + 0.822394i \(0.307362\pi\)
\(462\) 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 \(-0.0677098\pi\)
−0.671562 + 0.740948i \(0.734377\pi\)
\(468\) 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 −0.0126417 0.999920i \(-0.504024\pi\)
0.872277 0.489012i \(-0.162643\pi\)
\(480\) 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 −0.992679 0.120780i \(-0.961460\pi\)
0.600938 + 0.799295i \(0.294794\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10.1837 −0.459584 −0.229792 0.973240i \(-0.573805\pi\)
−0.229792 + 0.973240i \(0.573805\pi\)
\(492\) 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 0.997394 + 0.0721540i \(0.0229873\pi\)
−0.436210 + 0.899845i \(0.643679\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −32.2887 −1.43968 −0.719841 0.694139i \(-0.755785\pi\)
−0.719841 + 0.694139i \(0.755785\pi\)
\(504\) 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 0.996006 + 0.0892808i \(0.0284568\pi\)
−0.420684 + 0.907207i \(0.638210\pi\)
\(510\) 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 \(-0.765622\pi\)
0.952066 + 0.305893i \(0.0989551\pi\)
\(522\) 0 0
\(523\) −8.48372 14.6942i −0.370967 0.642534i 0.618747 0.785590i \(-0.287640\pi\)
−0.989715 + 0.143056i \(0.954307\pi\)
\(524\) 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 0.923506 0.383585i \(-0.125311\pi\)
−0.793947 + 0.607987i \(0.791977\pi\)
\(542\) 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 \(-0.864794\pi\)
0.812461 + 0.583015i \(0.198127\pi\)
\(558\) 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 \(-0.695776\pi\)
0.995821 + 0.0913216i \(0.0291091\pi\)
\(564\) 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 0.955580 + 0.294731i \(0.0952300\pi\)
−0.222546 + 0.974922i \(0.571437\pi\)
\(570\) 0 0
\(571\) −5.21049 + 9.02484i −0.218052 + 0.377678i −0.954212 0.299130i \(-0.903304\pi\)
0.736160 + 0.676807i \(0.236637\pi\)
\(572\) 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 −0.168649 0.985676i \(-0.553940\pi\)
0.937945 0.346784i \(-0.112726\pi\)
\(578\) 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 \(-0.314896\pi\)
0.549296 + 0.835628i \(0.314896\pi\)
\(588\) 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 \(-0.133959\pi\)
−0.810171 + 0.586193i \(0.800626\pi\)
\(594\) 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 −0.343196 0.939264i \(-0.611509\pi\)
0.985024 0.172416i \(-0.0551572\pi\)
\(600\) 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 0.922032 0.387114i \(-0.126528\pi\)
−0.796267 + 0.604946i \(0.793195\pi\)
\(608\) 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 −0.694213 0.719769i \(-0.744248\pi\)
0.970445 + 0.241322i \(0.0775809\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.8071 0.636371 0.318186 0.948028i \(-0.396927\pi\)
0.318186 + 0.948028i \(0.396927\pi\)
\(618\) 0 0
\(619\) −17.6961 + 30.6505i −0.711266 + 1.23195i 0.253116 + 0.967436i \(0.418545\pi\)
−0.964382 + 0.264513i \(0.914789\pi\)
\(620\) 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 \(-0.859555\pi\)
0.821947 + 0.569565i \(0.192888\pi\)
\(642\) 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 \(-0.763954\pi\)
0.953655 + 0.300901i \(0.0972874\pi\)
\(648\) 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 \(-0.0828081\pi\)
−0.705939 + 0.708273i \(0.749475\pi\)
\(654\) 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 \(-0.681590\pi\)
−0.540036 + 0.841642i \(0.681590\pi\)
\(660\) 0 0
\(661\) 7.65561 13.2599i 0.297769 0.515751i −0.677856 0.735194i \(-0.737091\pi\)
0.975625 + 0.219444i \(0.0704242\pi\)
\(662\) 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 \(-0.141119\pi\)
−0.823150 + 0.567824i \(0.807786\pi\)
\(678\) 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 \(-0.977302\pi\)
0.560430 + 0.828201i \(0.310636\pi\)
\(684\) 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 0.554001 0.832516i \(-0.313100\pi\)
−0.997980 + 0.0635214i \(0.979767\pi\)
\(692\) 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 \(-0.448589\pi\)
0.160810 + 0.986985i \(0.448589\pi\)
\(702\) 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 0.553681 0.832729i \(-0.313223\pi\)
−0.998005 + 0.0631380i \(0.979889\pi\)
\(710\) 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 \(-0.107784\pi\)
−0.759285 + 0.650759i \(0.774451\pi\)
\(720\) 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 0.676962 0.736018i \(-0.263296\pi\)
−0.975891 + 0.218258i \(0.929963\pi\)
\(734\) 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 −0.961406 0.275134i \(-0.911278\pi\)
0.718976 + 0.695035i \(0.244611\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 30.9733 1.13630 0.568149 0.822925i \(-0.307660\pi\)
0.568149 + 0.822925i \(0.307660\pi\)
\(744\) 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 −0.808585 0.588379i \(-0.799766\pi\)
−0.105258 0.994445i \(-0.533567\pi\)
\(752\) 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 \(-0.187871\pi\)
−0.897387 + 0.441244i \(0.854537\pi\)
\(762\) 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 \(-0.866943\pi\)
0.808506 + 0.588487i \(0.200276\pi\)
\(774\) 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 −0.964315 0.264757i \(-0.914708\pi\)
0.711444 + 0.702743i \(0.248042\pi\)
\(788\) 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 \(-0.530982\pi\)
−0.0971791 + 0.995267i \(0.530982\pi\)
\(798\) 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
\(804\) 0 0
\(805\) −71.7244 + 40.2525i −2.52795 + 1.41871i