Properties

Label 1512.2.s.l.865.1
Level 1512
Weight 2
Character 1512.865
Analytic conductor 12.073
Analytic rank 0
Dimension 6
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.l.1297.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.849814 - 1.47192i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +O(q^{10})\) \(q+(-0.849814 - 1.47192i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +(-2.14400 + 3.71351i) q^{11} +2.69963 q^{13} +(1.64400 - 2.84748i) q^{17} +(1.79418 + 3.10761i) q^{19} +(1.29418 + 2.24159i) q^{23} +(1.05563 - 1.82841i) q^{25} -7.68725 q^{29} +(0.461078 - 0.798611i) q^{31} +(2.10507 + 3.97364i) q^{35} +(5.23236 + 9.06271i) q^{37} +5.76509 q^{41} +11.0865 q^{43} +(2.66071 + 4.60848i) q^{47} +(6.98143 + 0.509538i) q^{49} +(2.23855 - 3.87728i) q^{53} +7.28799 q^{55} +(4.60507 - 7.97622i) q^{59} +(4.08836 + 7.08125i) q^{61} +(-2.29418 - 3.97364i) q^{65} +(1.81708 - 3.14728i) q^{67} -10.1643 q^{71} +(-0.333104 + 0.576953i) q^{73} +(6.02654 - 9.61192i) q^{77} +(4.88255 + 8.45682i) q^{79} -1.25457 q^{83} -5.58836 q^{85} +(-0.800372 - 1.38628i) q^{89} +(-7.13781 - 0.260130i) q^{91} +(3.04944 - 5.28179i) q^{95} +0.823272 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{5} - 4q^{7} + O(q^{10}) \) \( 6q + q^{5} - 4q^{7} - q^{11} + 4q^{13} - 2q^{17} + 5q^{19} + 2q^{23} + 6q^{25} + 2q^{29} - 4q^{31} - 6q^{35} + 8q^{37} - 6q^{43} - 3q^{47} - 12q^{49} + 8q^{53} + 20q^{55} + 9q^{59} + 13q^{61} - 8q^{65} + 16q^{67} - 2q^{71} - 3q^{73} + 7q^{77} + 12q^{79} + 2q^{83} - 22q^{85} - 17q^{89} - 13q^{91} + 28q^{97} + O(q^{100}) \)

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
\(5\) −0.849814 1.47192i −0.380048 0.658263i 0.611020 0.791615i \(-0.290759\pi\)
−0.991069 + 0.133352i \(0.957426\pi\)
\(6\) 0 0
\(7\) −2.64400 0.0963576i −0.999337 0.0364197i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.14400 + 3.71351i −0.646439 + 1.11967i 0.337528 + 0.941315i \(0.390409\pi\)
−0.983967 + 0.178350i \(0.942924\pi\)
\(12\) 0 0
\(13\) 2.69963 0.748742 0.374371 0.927279i \(-0.377859\pi\)
0.374371 + 0.927279i \(0.377859\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.64400 2.84748i 0.398728 0.690616i −0.594842 0.803843i \(-0.702785\pi\)
0.993569 + 0.113226i \(0.0361186\pi\)
\(18\) 0 0
\(19\) 1.79418 + 3.10761i 0.411614 + 0.712936i 0.995066 0.0992114i \(-0.0316320\pi\)
−0.583453 + 0.812147i \(0.698299\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.29418 + 2.24159i 0.269856 + 0.467404i 0.968824 0.247749i \(-0.0796907\pi\)
−0.698969 + 0.715152i \(0.746357\pi\)
\(24\) 0 0
\(25\) 1.05563 1.82841i 0.211126 0.365682i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.68725 −1.42749 −0.713743 0.700408i \(-0.753002\pi\)
−0.713743 + 0.700408i \(0.753002\pi\)
\(30\) 0 0
\(31\) 0.461078 0.798611i 0.0828121 0.143435i −0.821645 0.570000i \(-0.806943\pi\)
0.904457 + 0.426565i \(0.140277\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.10507 + 3.97364i 0.355823 + 0.671668i
\(36\) 0 0
\(37\) 5.23236 + 9.06271i 0.860195 + 1.48990i 0.871741 + 0.489968i \(0.162991\pi\)
−0.0115460 + 0.999933i \(0.503675\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.76509 0.900356 0.450178 0.892939i \(-0.351361\pi\)
0.450178 + 0.892939i \(0.351361\pi\)
\(42\) 0 0
\(43\) 11.0865 1.69068 0.845338 0.534232i \(-0.179399\pi\)
0.845338 + 0.534232i \(0.179399\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.66071 + 4.60848i 0.388104 + 0.672216i 0.992194 0.124700i \(-0.0397968\pi\)
−0.604091 + 0.796916i \(0.706463\pi\)
\(48\) 0 0
\(49\) 6.98143 + 0.509538i 0.997347 + 0.0727912i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.23855 3.87728i 0.307488 0.532586i −0.670324 0.742069i \(-0.733845\pi\)
0.977812 + 0.209483i \(0.0671781\pi\)
\(54\) 0 0
\(55\) 7.28799 0.982713
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.60507 7.97622i 0.599530 1.03842i −0.393361 0.919384i \(-0.628688\pi\)
0.992890 0.119032i \(-0.0379790\pi\)
\(60\) 0 0
\(61\) 4.08836 + 7.08125i 0.523461 + 0.906662i 0.999627 + 0.0273061i \(0.00869289\pi\)
−0.476166 + 0.879356i \(0.657974\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.29418 3.97364i −0.284558 0.492869i
\(66\) 0 0
\(67\) 1.81708 3.14728i 0.221992 0.384501i −0.733421 0.679775i \(-0.762077\pi\)
0.955413 + 0.295274i \(0.0954108\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.1643 −1.20629 −0.603143 0.797633i \(-0.706085\pi\)
−0.603143 + 0.797633i \(0.706085\pi\)
\(72\) 0 0
\(73\) −0.333104 + 0.576953i −0.0389868 + 0.0675272i −0.884860 0.465856i \(-0.845746\pi\)
0.845874 + 0.533383i \(0.179080\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.02654 9.61192i 0.686788 1.09538i
\(78\) 0 0
\(79\) 4.88255 + 8.45682i 0.549329 + 0.951466i 0.998321 + 0.0579302i \(0.0184501\pi\)
−0.448991 + 0.893536i \(0.648217\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.25457 −0.137707 −0.0688536 0.997627i \(-0.521934\pi\)
−0.0688536 + 0.997627i \(0.521934\pi\)
\(84\) 0 0
\(85\) −5.58836 −0.606143
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.800372 1.38628i −0.0848392 0.146946i 0.820483 0.571670i \(-0.193704\pi\)
−0.905323 + 0.424724i \(0.860371\pi\)
\(90\) 0 0
\(91\) −7.13781 0.260130i −0.748245 0.0272690i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.04944 5.28179i 0.312866 0.541900i
\(96\) 0 0
\(97\) 0.823272 0.0835906 0.0417953 0.999126i \(-0.486692\pi\)
0.0417953 + 0.999126i \(0.486692\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.26145 + 2.18490i −0.125519 + 0.217405i −0.921936 0.387343i \(-0.873393\pi\)
0.796417 + 0.604748i \(0.206726\pi\)
\(102\) 0 0
\(103\) 6.08836 + 10.5454i 0.599904 + 1.03906i 0.992835 + 0.119497i \(0.0381280\pi\)
−0.392930 + 0.919568i \(0.628539\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.49381 + 11.2476i 0.627780 + 1.08735i 0.987996 + 0.154478i \(0.0493697\pi\)
−0.360216 + 0.932869i \(0.617297\pi\)
\(108\) 0 0
\(109\) 7.51052 13.0086i 0.719377 1.24600i −0.241869 0.970309i \(-0.577761\pi\)
0.961247 0.275689i \(-0.0889061\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.73167 0.727334 0.363667 0.931529i \(-0.381525\pi\)
0.363667 + 0.931529i \(0.381525\pi\)
\(114\) 0 0
\(115\) 2.19963 3.80987i 0.205116 0.355272i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.62110 + 7.37033i −0.423615 + 0.675637i
\(120\) 0 0
\(121\) −3.69344 6.39722i −0.335767 0.581566i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0865 −1.08105
\(126\) 0 0
\(127\) −16.3869 −1.45410 −0.727050 0.686584i \(-0.759109\pi\)
−0.727050 + 0.686584i \(0.759109\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.4091 + 18.0291i 0.909446 + 1.57521i 0.814835 + 0.579693i \(0.196827\pi\)
0.0946111 + 0.995514i \(0.469839\pi\)
\(132\) 0 0
\(133\) −4.44437 8.38940i −0.385376 0.727454i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.81089 + 8.33271i −0.411022 + 0.711911i −0.995002 0.0998569i \(-0.968161\pi\)
0.583980 + 0.811768i \(0.301495\pi\)
\(138\) 0 0
\(139\) 17.2756 1.46530 0.732649 0.680606i \(-0.238284\pi\)
0.732649 + 0.680606i \(0.238284\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.78799 + 10.0251i −0.484016 + 0.838341i
\(144\) 0 0
\(145\) 6.53273 + 11.3150i 0.542514 + 0.939662i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −10.1156 17.5207i −0.828702 1.43535i −0.899057 0.437832i \(-0.855747\pi\)
0.0703552 0.997522i \(-0.477587\pi\)
\(150\) 0 0
\(151\) 0.656376 1.13688i 0.0534151 0.0925177i −0.838082 0.545545i \(-0.816323\pi\)
0.891497 + 0.453027i \(0.149656\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.56732 −0.125890
\(156\) 0 0
\(157\) −10.6483 + 18.4434i −0.849829 + 1.47195i 0.0315316 + 0.999503i \(0.489962\pi\)
−0.881361 + 0.472444i \(0.843372\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.20582 6.05146i −0.252654 0.476922i
\(162\) 0 0
\(163\) −3.57165 6.18629i −0.279754 0.484547i 0.691570 0.722310i \(-0.256919\pi\)
−0.971323 + 0.237762i \(0.923586\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.49814 −0.580224 −0.290112 0.956993i \(-0.593692\pi\)
−0.290112 + 0.956993i \(0.593692\pi\)
\(168\) 0 0
\(169\) −5.71201 −0.439385
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.967268 + 1.67536i 0.0735400 + 0.127375i 0.900450 0.434959i \(-0.143237\pi\)
−0.826910 + 0.562334i \(0.809904\pi\)
\(174\) 0 0
\(175\) −2.96727 + 4.73259i −0.224304 + 0.357750i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −5.61491 + 9.72530i −0.419678 + 0.726903i −0.995907 0.0903850i \(-0.971190\pi\)
0.576229 + 0.817288i \(0.304524\pi\)
\(180\) 0 0
\(181\) 14.8974 1.10731 0.553657 0.832745i \(-0.313232\pi\)
0.553657 + 0.832745i \(0.313232\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.89307 15.4032i 0.653831 1.13247i
\(186\) 0 0
\(187\) 7.04944 + 12.2100i 0.515506 + 0.892883i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.20946 5.55895i −0.232228 0.402231i 0.726235 0.687446i \(-0.241268\pi\)
−0.958464 + 0.285215i \(0.907935\pi\)
\(192\) 0 0
\(193\) 6.07165 10.5164i 0.437047 0.756988i −0.560413 0.828213i \(-0.689358\pi\)
0.997460 + 0.0712253i \(0.0226909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.6538 1.32903 0.664515 0.747275i \(-0.268638\pi\)
0.664515 + 0.747275i \(0.268638\pi\)
\(198\) 0 0
\(199\) 4.66435 8.07889i 0.330647 0.572697i −0.651992 0.758226i \(-0.726066\pi\)
0.982639 + 0.185529i \(0.0593998\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 20.3251 + 0.740725i 1.42654 + 0.0519887i
\(204\) 0 0
\(205\) −4.89926 8.48576i −0.342179 0.592671i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −15.3869 −1.06433
\(210\) 0 0
\(211\) −2.71201 −0.186702 −0.0933512 0.995633i \(-0.529758\pi\)
−0.0933512 + 0.995633i \(0.529758\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.42147 16.3185i −0.642539 1.11291i
\(216\) 0 0
\(217\) −1.29604 + 2.06710i −0.0879810 + 0.140324i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.43818 7.68715i 0.298544 0.517094i
\(222\) 0 0
\(223\) −16.0741 −1.07640 −0.538202 0.842816i \(-0.680896\pi\)
−0.538202 + 0.842816i \(0.680896\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.25890 + 10.8407i −0.415418 + 0.719525i −0.995472 0.0950529i \(-0.969698\pi\)
0.580054 + 0.814578i \(0.303031\pi\)
\(228\) 0 0
\(229\) −8.65816 14.9964i −0.572147 0.990988i −0.996345 0.0854185i \(-0.972777\pi\)
0.424198 0.905569i \(-0.360556\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.67673 9.83238i −0.371895 0.644141i 0.617962 0.786208i \(-0.287958\pi\)
−0.989857 + 0.142067i \(0.954625\pi\)
\(234\) 0 0
\(235\) 4.52221 7.83270i 0.294997 0.510949i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.341076 0.0220624 0.0110312 0.999939i \(-0.496489\pi\)
0.0110312 + 0.999939i \(0.496489\pi\)
\(240\) 0 0
\(241\) −10.8214 + 18.7432i −0.697068 + 1.20736i 0.272410 + 0.962181i \(0.412179\pi\)
−0.969478 + 0.245177i \(0.921154\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.18292 10.7091i −0.331124 0.684181i
\(246\) 0 0
\(247\) 4.84362 + 8.38940i 0.308192 + 0.533805i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 26.8850 1.69697 0.848484 0.529222i \(-0.177516\pi\)
0.848484 + 0.529222i \(0.177516\pi\)
\(252\) 0 0
\(253\) −11.0989 −0.697781
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.57784 + 4.46496i 0.160801 + 0.278516i 0.935156 0.354235i \(-0.115259\pi\)
−0.774355 + 0.632752i \(0.781925\pi\)
\(258\) 0 0
\(259\) −12.9611 24.4660i −0.805362 1.52024i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.70396 + 16.8077i −0.598372 + 1.03641i 0.394690 + 0.918814i \(0.370852\pi\)
−0.993062 + 0.117596i \(0.962481\pi\)
\(264\) 0 0
\(265\) −7.60940 −0.467442
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.9549 + 20.7065i −0.728902 + 1.26250i 0.228445 + 0.973557i \(0.426636\pi\)
−0.957347 + 0.288939i \(0.906697\pi\)
\(270\) 0 0
\(271\) −9.34727 16.1899i −0.567806 0.983469i −0.996783 0.0801532i \(-0.974459\pi\)
0.428977 0.903316i \(-0.358874\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.52654 + 7.84020i 0.272961 + 0.472782i
\(276\) 0 0
\(277\) 8.33310 14.4334i 0.500688 0.867217i −0.499312 0.866422i \(-0.666414\pi\)
1.00000 0.000794246i \(-0.000252817\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.45744 0.206253 0.103127 0.994668i \(-0.467115\pi\)
0.103127 + 0.994668i \(0.467115\pi\)
\(282\) 0 0
\(283\) −9.23236 + 15.9909i −0.548807 + 0.950561i 0.449550 + 0.893255i \(0.351584\pi\)
−0.998357 + 0.0573061i \(0.981749\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −15.2429 0.555510i −0.899759 0.0327907i
\(288\) 0 0
\(289\) 3.09455 + 5.35992i 0.182033 + 0.315290i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 26.7156 1.56074 0.780370 0.625318i \(-0.215031\pi\)
0.780370 + 0.625318i \(0.215031\pi\)
\(294\) 0 0
\(295\) −15.6538 −0.911401
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.49381 + 6.05146i 0.202052 + 0.349965i
\(300\) 0 0
\(301\) −29.3127 1.06827i −1.68955 0.0615740i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.94870 12.0355i 0.397881 0.689151i
\(306\) 0 0
\(307\) −33.0370 −1.88552 −0.942760 0.333471i \(-0.891780\pi\)
−0.942760 + 0.333471i \(0.891780\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.07784 12.2592i 0.401348 0.695155i −0.592541 0.805540i \(-0.701875\pi\)
0.993889 + 0.110386i \(0.0352086\pi\)
\(312\) 0 0
\(313\) 4.64468 + 8.04483i 0.262533 + 0.454721i 0.966914 0.255101i \(-0.0821088\pi\)
−0.704381 + 0.709822i \(0.748775\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.25959 + 7.37783i 0.239242 + 0.414380i 0.960497 0.278290i \(-0.0897676\pi\)
−0.721255 + 0.692670i \(0.756434\pi\)
\(318\) 0 0
\(319\) 16.4814 28.5467i 0.922783 1.59831i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11.7985 0.656487
\(324\) 0 0
\(325\) 2.84981 4.93602i 0.158079 0.273801i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.59084 12.4412i −0.363365 0.685904i
\(330\) 0 0
\(331\) −3.42580 5.93366i −0.188299 0.326143i 0.756384 0.654128i \(-0.226964\pi\)
−0.944683 + 0.327984i \(0.893631\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.17673 −0.337471
\(336\) 0 0
\(337\) −34.5068 −1.87971 −0.939853 0.341580i \(-0.889038\pi\)
−0.939853 + 0.341580i \(0.889038\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.97710 + 3.42444i 0.107066 + 0.185444i
\(342\) 0 0
\(343\) −18.4098 2.01993i −0.994035 0.109066i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.3090 19.5878i 0.607101 1.05153i −0.384615 0.923077i \(-0.625666\pi\)
0.991716 0.128452i \(-0.0410009\pi\)
\(348\) 0 0
\(349\) 21.6080 1.15665 0.578326 0.815806i \(-0.303706\pi\)
0.578326 + 0.815806i \(0.303706\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.94870 + 13.7675i −0.423067 + 0.732773i −0.996238 0.0866629i \(-0.972380\pi\)
0.573171 + 0.819436i \(0.305713\pi\)
\(354\) 0 0
\(355\) 8.63781 + 14.9611i 0.458447 + 0.794054i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.55563 + 6.15854i 0.187659 + 0.325035i 0.944469 0.328600i \(-0.106577\pi\)
−0.756810 + 0.653635i \(0.773243\pi\)
\(360\) 0 0
\(361\) 3.06182 5.30323i 0.161149 0.279117i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.13231 0.0592676
\(366\) 0 0
\(367\) −1.51052 + 2.61630i −0.0788485 + 0.136570i −0.902753 0.430158i \(-0.858458\pi\)
0.823905 + 0.566728i \(0.191791\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.29232 + 10.0358i −0.326681 + 0.521034i
\(372\) 0 0
\(373\) −5.73167 9.92755i −0.296775 0.514029i 0.678621 0.734488i \(-0.262578\pi\)
−0.975396 + 0.220459i \(0.929244\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −20.7527 −1.06882
\(378\) 0 0
\(379\) −26.9432 −1.38398 −0.691990 0.721908i \(-0.743266\pi\)
−0.691990 + 0.721908i \(0.743266\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.4567 31.9679i −0.943092 1.63348i −0.759527 0.650475i \(-0.774570\pi\)
−0.183564 0.983008i \(-0.558764\pi\)
\(384\) 0 0
\(385\) −19.2694 0.702253i −0.982061 0.0357901i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.12797 3.68576i 0.107893 0.186875i −0.807024 0.590519i \(-0.798923\pi\)
0.914916 + 0.403644i \(0.132256\pi\)
\(390\) 0 0
\(391\) 8.51052 0.430396
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.29851 14.3734i 0.417543 0.723207i
\(396\) 0 0
\(397\) 6.33929 + 10.9800i 0.318160 + 0.551069i 0.980104 0.198484i \(-0.0636017\pi\)
−0.661944 + 0.749553i \(0.730268\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.64764 + 9.78200i 0.282030 + 0.488490i 0.971885 0.235458i \(-0.0756590\pi\)
−0.689855 + 0.723948i \(0.742326\pi\)
\(402\) 0 0
\(403\) 1.24474 2.15595i 0.0620049 0.107396i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −44.8726 −2.22425
\(408\) 0 0
\(409\) 19.1458 33.1615i 0.946698 1.63973i 0.194382 0.980926i \(-0.437730\pi\)
0.752316 0.658803i \(-0.228937\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12.9444 + 20.6454i −0.636951 + 1.01589i
\(414\) 0 0
\(415\) 1.06615 + 1.84663i 0.0523354 + 0.0906475i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17.3535 0.847772 0.423886 0.905716i \(-0.360666\pi\)
0.423886 + 0.905716i \(0.360666\pi\)
\(420\) 0 0
\(421\) 0.185389 0.00903532 0.00451766 0.999990i \(-0.498562\pi\)
0.00451766 + 0.999990i \(0.498562\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.47091 6.01179i −0.168364 0.291615i
\(426\) 0 0
\(427\) −10.1273 19.1168i −0.490094 0.925125i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.08768 12.2762i 0.341401 0.591324i −0.643292 0.765621i \(-0.722432\pi\)
0.984693 + 0.174297i \(0.0557652\pi\)
\(432\) 0 0
\(433\) 13.2101 0.634839 0.317420 0.948285i \(-0.397184\pi\)
0.317420 + 0.948285i \(0.397184\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.64400 + 8.04364i −0.222152 + 0.384779i
\(438\) 0 0
\(439\) 6.38874 + 11.0656i 0.304918 + 0.528133i 0.977243 0.212123i \(-0.0680377\pi\)
−0.672325 + 0.740256i \(0.734704\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.3986 + 19.7429i 0.541562 + 0.938013i 0.998815 + 0.0486764i \(0.0155003\pi\)
−0.457252 + 0.889337i \(0.651166\pi\)
\(444\) 0 0
\(445\) −1.36033 + 2.35617i −0.0644860 + 0.111693i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 36.7330 1.73354 0.866770 0.498708i \(-0.166192\pi\)
0.866770 + 0.498708i \(0.166192\pi\)
\(450\) 0 0
\(451\) −12.3603 + 21.4087i −0.582025 + 1.00810i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.68292 + 10.7273i 0.266419 + 0.502906i
\(456\) 0 0
\(457\) −11.7589 20.3670i −0.550058 0.952729i −0.998270 0.0588013i \(-0.981272\pi\)
0.448211 0.893928i \(-0.352061\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.76509 −0.361656 −0.180828 0.983515i \(-0.557878\pi\)
−0.180828 + 0.983515i \(0.557878\pi\)
\(462\) 0 0
\(463\) −11.5549 −0.537004 −0.268502 0.963279i \(-0.586529\pi\)
−0.268502 + 0.963279i \(0.586529\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.1774 24.5560i −0.656053 1.13632i −0.981629 0.190801i \(-0.938892\pi\)
0.325576 0.945516i \(-0.394442\pi\)
\(468\) 0 0
\(469\) −5.10762 + 8.14630i −0.235848 + 0.376161i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23.7694 + 41.1698i −1.09292 + 1.89299i
\(474\) 0 0
\(475\) 7.57598 0.347610
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.1804 26.2932i 0.693609 1.20137i −0.277039 0.960859i \(-0.589353\pi\)
0.970647 0.240507i \(-0.0773137\pi\)
\(480\) 0 0
\(481\) 14.1254 + 24.4660i 0.644064 + 1.11555i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.699628 1.21179i −0.0317685 0.0550246i
\(486\) 0 0
\(487\) 9.02221 15.6269i 0.408835 0.708124i −0.585924 0.810366i \(-0.699268\pi\)
0.994760 + 0.102242i \(0.0326017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −39.0865 −1.76395 −0.881975 0.471297i \(-0.843786\pi\)
−0.881975 + 0.471297i \(0.843786\pi\)
\(492\) 0 0
\(493\) −12.6378 + 21.8893i −0.569178 + 0.985846i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 26.8745 + 0.979412i 1.20549 + 0.0439326i
\(498\) 0 0
\(499\) 12.8862 + 22.3195i 0.576865 + 0.999159i 0.995836 + 0.0911600i \(0.0290575\pi\)
−0.418971 + 0.907999i \(0.637609\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.90978 −0.0851527 −0.0425764 0.999093i \(-0.513557\pi\)
−0.0425764 + 0.999093i \(0.513557\pi\)
\(504\) 0 0
\(505\) 4.28799 0.190813
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.2553 + 31.6190i 0.809150 + 1.40149i 0.913453 + 0.406944i \(0.133405\pi\)
−0.104303 + 0.994546i \(0.533261\pi\)
\(510\) 0 0
\(511\) 0.936319 1.49336i 0.0414203 0.0660625i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.3480 17.9232i 0.455985 0.789790i
\(516\) 0 0
\(517\) −22.8182 −1.00354
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −19.2095 + 33.2718i −0.841582 + 1.45766i 0.0469753 + 0.998896i \(0.485042\pi\)
−0.888557 + 0.458766i \(0.848292\pi\)
\(522\) 0 0
\(523\) 2.82946 + 4.90077i 0.123724 + 0.214296i 0.921233 0.389010i \(-0.127183\pi\)
−0.797510 + 0.603306i \(0.793850\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.51602 2.62583i −0.0660389 0.114383i
\(528\) 0 0
\(529\) 8.15019 14.1165i 0.354356 0.613762i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 15.5636 0.674135
\(534\) 0 0
\(535\) 11.0371 19.1168i 0.477174 0.826489i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.8603 + 24.8332i −0.726226 + 1.06964i
\(540\) 0 0
\(541\) 12.2324 + 21.1871i 0.525910 + 0.910903i 0.999544 + 0.0301816i \(0.00960856\pi\)
−0.473634 + 0.880722i \(0.657058\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −25.5302 −1.09359
\(546\) 0 0
\(547\) 13.5636 0.579938 0.289969 0.957036i \(-0.406355\pi\)
0.289969 + 0.957036i \(0.406355\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.7923 23.8890i −0.587573 1.01771i
\(552\) 0 0
\(553\) −12.0946 22.8303i −0.514313 0.970842i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.50619 6.07290i 0.148562 0.257317i −0.782134 0.623110i \(-0.785869\pi\)
0.930696 + 0.365793i \(0.119202\pi\)
\(558\) 0 0
\(559\) 29.9294 1.26588
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.6731 21.9504i 0.534107 0.925100i −0.465099 0.885259i \(-0.653981\pi\)
0.999206 0.0398417i \(-0.0126854\pi\)
\(564\) 0 0
\(565\) −6.57048 11.3804i −0.276422 0.478777i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.11559 + 3.66432i 0.0886903 + 0.153616i 0.906958 0.421222i \(-0.138399\pi\)
−0.818267 + 0.574838i \(0.805065\pi\)
\(570\) 0 0
\(571\) 3.87890 6.71846i 0.162327 0.281159i −0.773376 0.633948i \(-0.781433\pi\)
0.935703 + 0.352789i \(0.114767\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.46472 0.227895
\(576\) 0 0
\(577\) 7.17123 12.4209i 0.298542 0.517090i −0.677261 0.735743i \(-0.736833\pi\)
0.975803 + 0.218653i \(0.0701663\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.31708 + 0.120887i 0.137616 + 0.00501526i
\(582\) 0 0
\(583\) 9.59888 + 16.6258i 0.397545 + 0.688568i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 28.1062 1.16007 0.580033 0.814593i \(-0.303040\pi\)
0.580033 + 0.814593i \(0.303040\pi\)
\(588\) 0 0
\(589\) 3.30903 0.136346
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.2262 33.3007i −0.789524 1.36750i −0.926259 0.376888i \(-0.876994\pi\)
0.136735 0.990608i \(-0.456339\pi\)
\(594\) 0 0
\(595\) 14.7756 + 0.538481i 0.605741 + 0.0220756i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.46796 + 2.54258i −0.0599791 + 0.103887i −0.894456 0.447156i \(-0.852437\pi\)
0.834477 + 0.551043i \(0.185770\pi\)
\(600\) 0 0
\(601\) −6.00728 −0.245042 −0.122521 0.992466i \(-0.539098\pi\)
−0.122521 + 0.992466i \(0.539098\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.27747 + 10.8729i −0.255216 + 0.442046i
\(606\) 0 0
\(607\) 12.2324 + 21.1871i 0.496496 + 0.859957i 0.999992 0.00404115i \(-0.00128634\pi\)
−0.503496 + 0.863998i \(0.667953\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.18292 + 12.4412i 0.290590 + 0.503316i
\(612\) 0 0
\(613\) −5.33675 + 9.24351i −0.215549 + 0.373342i −0.953442 0.301575i \(-0.902487\pi\)
0.737893 + 0.674918i \(0.235821\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.71339 0.230012 0.115006 0.993365i \(-0.463311\pi\)
0.115006 + 0.993365i \(0.463311\pi\)
\(618\) 0 0
\(619\) −4.79163 + 8.29935i −0.192592 + 0.333579i −0.946108 0.323850i \(-0.895023\pi\)
0.753516 + 0.657429i \(0.228356\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.98260 + 3.74245i 0.0794312 + 0.149938i
\(624\) 0 0
\(625\) 4.99312 + 8.64834i 0.199725 + 0.345934i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 34.4079 1.37193
\(630\) 0 0
\(631\) −21.4523 −0.854004 −0.427002 0.904251i \(-0.640430\pi\)
−0.427002 + 0.904251i \(0.640430\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13.9258 + 24.1202i 0.552628 + 0.957181i
\(636\) 0 0
\(637\) 18.8473 + 1.37556i 0.746756 + 0.0545018i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.8356 18.7678i 0.427979 0.741282i −0.568714 0.822535i \(-0.692559\pi\)
0.996693 + 0.0812531i \(0.0258922\pi\)
\(642\) 0 0
\(643\) −1.62907 −0.0642442 −0.0321221 0.999484i \(-0.510227\pi\)
−0.0321221 + 0.999484i \(0.510227\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.48260 4.29999i 0.0976011 0.169050i −0.813090 0.582138i \(-0.802216\pi\)
0.910691 + 0.413088i \(0.135550\pi\)
\(648\) 0 0
\(649\) 19.7465 + 34.2020i 0.775119 + 1.34255i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.7520 34.2115i −0.772956 1.33880i −0.935936 0.352170i \(-0.885444\pi\)
0.162980 0.986629i \(-0.447890\pi\)
\(654\) 0 0
\(655\) 17.6916 30.6427i 0.691267 1.19731i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0901 1.40587 0.702935 0.711254i \(-0.251873\pi\)
0.702935 + 0.711254i \(0.251873\pi\)
\(660\) 0 0
\(661\) −7.66071 + 13.2687i −0.297967 + 0.516094i −0.975671 0.219241i \(-0.929642\pi\)
0.677704 + 0.735335i \(0.262975\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.57165 + 13.6712i −0.332394 + 0.530146i
\(666\) 0 0
\(667\) −9.94870 17.2317i −0.385215 0.667212i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −35.0617 −1.35354
\(672\) 0 0
\(673\) −45.4807 −1.75315 −0.876575 0.481265i \(-0.840178\pi\)
−0.876575 + 0.481265i \(0.840178\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.1662 + 17.6084i 0.390719 + 0.676745i 0.992545 0.121882i \(-0.0388930\pi\)
−0.601825 + 0.798628i \(0.705560\pi\)
\(678\) 0 0
\(679\) −2.17673 0.0793285i −0.0835352 0.00304435i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.0007 19.0538i 0.420930 0.729072i −0.575101 0.818082i \(-0.695037\pi\)
0.996031 + 0.0890109i \(0.0283706\pi\)
\(684\) 0 0
\(685\) 16.3535 0.624833
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.04325 10.4672i 0.230230 0.398769i
\(690\) 0 0
\(691\) 5.53892 + 9.59369i 0.210711 + 0.364961i 0.951937 0.306294i \(-0.0990889\pi\)
−0.741227 + 0.671255i \(0.765756\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.6811 25.4283i −0.556884 0.964552i
\(696\) 0 0
\(697\) 9.47779 16.4160i 0.358997 0.621801i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.19420 0.0451044 0.0225522 0.999746i \(-0.492821\pi\)
0.0225522 + 0.999746i \(0.492821\pi\)
\(702\) 0 0
\(703\) −18.7756 + 32.5203i −0.708136 + 1.22653i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.54580 5.65531i 0.133354 0.212690i
\(708\) 0 0
\(709\) −2.41232 4.17827i −0.0905968 0.156918i 0.817166 0.576403i \(-0.195544\pi\)
−0.907762 + 0.419485i \(0.862211\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.38688 0.0893892
\(714\) 0 0
\(715\) 19.6749 0.735798
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13.7120 23.7499i −0.511372 0.885722i −0.999913 0.0131810i \(-0.995804\pi\)
0.488542 0.872541i \(-0.337529\pi\)
\(720\) 0 0
\(721\) −15.0815 28.4685i −0.561664 1.06022i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.11491 + 14.0554i −0.301380 + 0.522006i
\(726\) 0 0
\(727\) 36.0704 1.33778 0.668889 0.743363i \(-0.266770\pi\)
0.668889 + 0.743363i \(0.266770\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18.2262 31.5687i 0.674119 1.16761i
\(732\) 0 0
\(733\) 13.6156 + 23.5829i 0.502903 + 0.871054i 0.999994 + 0.00335589i \(0.00106821\pi\)
−0.497091 + 0.867698i \(0.665598\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.79163 + 13.4955i 0.287009 + 0.497113i
\(738\) 0 0
\(739\) 19.9141 34.4922i 0.732552 1.26882i −0.223237 0.974764i \(-0.571662\pi\)
0.955789 0.294053i \(-0.0950044\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −43.3869 −1.59171 −0.795855 0.605487i \(-0.792978\pi\)
−0.795855 + 0.605487i \(0.792978\pi\)
\(744\) 0 0
\(745\) −17.1927 + 29.7787i −0.629894 + 1.09101i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16.0858 30.3644i −0.587763 1.10949i
\(750\) 0 0
\(751\) 5.47710 + 9.48662i 0.199862 + 0.346172i 0.948484 0.316826i \(-0.102617\pi\)
−0.748621 + 0.662998i \(0.769284\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.23119 −0.0812013
\(756\) 0 0
\(757\) 37.5933 1.36635 0.683176 0.730254i \(-0.260598\pi\)
0.683176 + 0.730254i \(0.260598\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.1366 + 41.8059i 0.874952 + 1.51546i 0.856813 + 0.515626i \(0.172441\pi\)
0.0181389 + 0.999835i \(0.494226\pi\)
\(762\) 0 0
\(763\) −21.1113 + 33.6710i −0.764279 + 1.21897i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.4320 21.5328i 0.448893 0.777506i
\(768\) 0 0
\(769\) 49.0022 1.76706 0.883532 0.468371i \(-0.155159\pi\)
0.883532 + 0.468371i \(0.155159\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −10.8949 + 18.8706i −0.391863 + 0.678727i −0.992695 0.120648i \(-0.961503\pi\)
0.600832 + 0.799375i \(0.294836\pi\)
\(774\) 0 0
\(775\) −0.973458 1.68608i −0.0349676 0.0605657i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.3436 + 17.9157i 0.370599 + 0.641896i
\(780\) 0 0
\(781\) 21.7923 37.7454i 0.779791 1.35064i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 36.1964 1.29190
\(786\) 0 0
\(787\) −2.98948 + 5.17793i −0.106563 + 0.184573i −0.914376 0.404866i \(-0.867318\pi\)
0.807812 + 0.589440i \(0.200651\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20.4425 0.745005i −0.726852 0.0264893i
\(792\) 0 0
\(793\) 11.0371 + 19.1168i 0.391938 + 0.678856i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.6401 −0.660265 −0.330133 0.943935i \(-0.607093\pi\)
−0.330133 + 0.943935i \(0.607093\pi\)
\(798\) 0 0
\(799\) 17.4968 0.618991
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.42835 2.47397i −0.0504052 0.0873044i
\(804\) 0 0
\(805\) −6.18292 + 9.86132i −0.217919 + 0.347566i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18.2367 +