Properties

Label 1764.2.t.c.1097.8
Level $1764$
Weight $2$
Character 1764.1097
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \( x^{16} - x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1097.8
Root \(-0.991445 - 0.130526i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1097
Dual form 1764.2.t.c.521.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923880 - 1.60021i) q^{5} +O(q^{10})\) \(q+(0.923880 - 1.60021i) q^{5} +(1.73205 - 1.00000i) q^{11} -4.46088i q^{13} +(-1.14805 - 1.98848i) q^{17} +(-1.32565 - 0.765367i) q^{19} +(-7.64564 - 4.41421i) q^{23} +(0.792893 + 1.37333i) q^{25} -1.17157i q^{29} +(-5.07517 + 2.93015i) q^{31} +(-4.12132 + 7.13834i) q^{37} +11.8519 q^{41} +1.17157 q^{43} +(4.01254 - 6.94993i) q^{47} +(3.25397 - 1.87868i) q^{53} -3.69552i q^{55} +(-4.90923 - 8.50303i) q^{59} +(-10.6523 - 6.15013i) q^{61} +(-7.13834 - 4.12132i) q^{65} +(-6.24264 - 10.8126i) q^{67} +13.3137i q^{71} +(2.37676 - 1.37222i) q^{73} +(-5.65685 + 9.79796i) q^{79} +10.4525 q^{83} -4.24264 q^{85} +(7.23252 - 12.5271i) q^{89} +(-2.44949 + 1.41421i) q^{95} -2.74444i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{25} - 32 q^{37} + 64 q^{43} - 32 q^{67}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) 0.923880 1.60021i 0.413171 0.715634i −0.582063 0.813144i \(-0.697754\pi\)
0.995235 + 0.0975096i \(0.0310877\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.73205 1.00000i 0.522233 0.301511i −0.215615 0.976478i \(-0.569176\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(12\) 0 0
\(13\) 4.46088i 1.23723i −0.785695 0.618613i \(-0.787695\pi\)
0.785695 0.618613i \(-0.212305\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.14805 1.98848i −0.278443 0.482278i 0.692555 0.721365i \(-0.256485\pi\)
−0.970998 + 0.239088i \(0.923152\pi\)
\(18\) 0 0
\(19\) −1.32565 0.765367i −0.304126 0.175587i 0.340169 0.940364i \(-0.389516\pi\)
−0.644295 + 0.764777i \(0.722849\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.64564 4.41421i −1.59423 0.920427i −0.992570 0.121672i \(-0.961174\pi\)
−0.601656 0.798755i \(-0.705492\pi\)
\(24\) 0 0
\(25\) 0.792893 + 1.37333i 0.158579 + 0.274666i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.17157i 0.217556i −0.994066 0.108778i \(-0.965306\pi\)
0.994066 0.108778i \(-0.0346937\pi\)
\(30\) 0 0
\(31\) −5.07517 + 2.93015i −0.911528 + 0.526271i −0.880922 0.473261i \(-0.843077\pi\)
−0.0306053 + 0.999532i \(0.509743\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.12132 + 7.13834i −0.677541 + 1.17354i 0.298178 + 0.954510i \(0.403621\pi\)
−0.975719 + 0.219025i \(0.929712\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.8519 1.85096 0.925480 0.378798i \(-0.123662\pi\)
0.925480 + 0.378798i \(0.123662\pi\)
\(42\) 0 0
\(43\) 1.17157 0.178663 0.0893316 0.996002i \(-0.471527\pi\)
0.0893316 + 0.996002i \(0.471527\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.01254 6.94993i 0.585290 1.01375i −0.409550 0.912288i \(-0.634314\pi\)
0.994839 0.101464i \(-0.0323525\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.25397 1.87868i 0.446967 0.258056i −0.259581 0.965721i \(-0.583585\pi\)
0.706548 + 0.707665i \(0.250251\pi\)
\(54\) 0 0
\(55\) 3.69552i 0.498304i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.90923 8.50303i −0.639127 1.10700i −0.985625 0.168949i \(-0.945963\pi\)
0.346498 0.938051i \(-0.387371\pi\)
\(60\) 0 0
\(61\) −10.6523 6.15013i −1.36389 0.787444i −0.373753 0.927528i \(-0.621929\pi\)
−0.990140 + 0.140085i \(0.955263\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.13834 4.12132i −0.885402 0.511187i
\(66\) 0 0
\(67\) −6.24264 10.8126i −0.762660 1.32097i −0.941475 0.337083i \(-0.890560\pi\)
0.178815 0.983883i \(-0.442774\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.3137i 1.58005i 0.613077 + 0.790023i \(0.289932\pi\)
−0.613077 + 0.790023i \(0.710068\pi\)
\(72\) 0 0
\(73\) 2.37676 1.37222i 0.278178 0.160606i −0.354420 0.935086i \(-0.615322\pi\)
0.632598 + 0.774480i \(0.281988\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.65685 + 9.79796i −0.636446 + 1.10236i 0.349761 + 0.936839i \(0.386263\pi\)
−0.986207 + 0.165518i \(0.947071\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.4525 1.14731 0.573656 0.819097i \(-0.305525\pi\)
0.573656 + 0.819097i \(0.305525\pi\)
\(84\) 0 0
\(85\) −4.24264 −0.460179
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.23252 12.5271i 0.766646 1.32787i −0.172726 0.984970i \(-0.555258\pi\)
0.939372 0.342900i \(-0.111409\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.44949 + 1.41421i −0.251312 + 0.145095i
\(96\) 0 0
\(97\) 2.74444i 0.278656i −0.990246 0.139328i \(-0.955506\pi\)
0.990246 0.139328i \(-0.0444942\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.37222 2.37676i −0.136541 0.236496i 0.789644 0.613565i \(-0.210265\pi\)
−0.926185 + 0.377069i \(0.876932\pi\)
\(102\) 0 0
\(103\) 0.549104 + 0.317025i 0.0541048 + 0.0312374i 0.526808 0.849984i \(-0.323389\pi\)
−0.472704 + 0.881221i \(0.656722\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.1097 6.41421i −1.07402 0.620085i −0.144743 0.989469i \(-0.546235\pi\)
−0.929277 + 0.369384i \(0.879569\pi\)
\(108\) 0 0
\(109\) −1.53553 2.65962i −0.147077 0.254746i 0.783069 0.621935i \(-0.213653\pi\)
−0.930146 + 0.367190i \(0.880320\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.4142i 1.26190i −0.775822 0.630952i \(-0.782665\pi\)
0.775822 0.630952i \(-0.217335\pi\)
\(114\) 0 0
\(115\) −14.1273 + 8.15640i −1.31738 + 0.760589i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1689 1.08842
\(126\) 0 0
\(127\) 6.82843 0.605925 0.302962 0.953002i \(-0.402024\pi\)
0.302962 + 0.953002i \(0.402024\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.67459 + 9.82868i −0.495792 + 0.858736i −0.999988 0.00485273i \(-0.998455\pi\)
0.504197 + 0.863589i \(0.331789\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.47871 2.58579i 0.382642 0.220919i −0.296325 0.955087i \(-0.595761\pi\)
0.678967 + 0.734169i \(0.262428\pi\)
\(138\) 0 0
\(139\) 6.49435i 0.550844i −0.961323 0.275422i \(-0.911182\pi\)
0.961323 0.275422i \(-0.0888176\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.46088 7.72648i −0.373038 0.646121i
\(144\) 0 0
\(145\) −1.87476 1.08239i −0.155690 0.0898878i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.12372 3.53553i −0.501675 0.289642i 0.227730 0.973724i \(-0.426870\pi\)
−0.729405 + 0.684082i \(0.760203\pi\)
\(150\) 0 0
\(151\) 9.07107 + 15.7116i 0.738193 + 1.27859i 0.953308 + 0.301999i \(0.0976540\pi\)
−0.215115 + 0.976589i \(0.569013\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.8284i 0.869760i
\(156\) 0 0
\(157\) 9.71496 5.60894i 0.775338 0.447642i −0.0594373 0.998232i \(-0.518931\pi\)
0.834776 + 0.550590i \(0.185597\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.41421 2.44949i 0.110770 0.191859i −0.805311 0.592852i \(-0.798002\pi\)
0.916081 + 0.400994i \(0.131335\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16.3128 −1.26232 −0.631161 0.775652i \(-0.717421\pi\)
−0.631161 + 0.775652i \(0.717421\pi\)
\(168\) 0 0
\(169\) −6.89949 −0.530730
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.05728 10.4915i 0.460526 0.797655i −0.538461 0.842650i \(-0.680994\pi\)
0.998987 + 0.0449956i \(0.0143274\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.5300 6.65685i 0.861793 0.497557i −0.00281905 0.999996i \(-0.500897\pi\)
0.864612 + 0.502439i \(0.167564\pi\)
\(180\) 0 0
\(181\) 14.4650i 1.07518i −0.843207 0.537589i \(-0.819335\pi\)
0.843207 0.537589i \(-0.180665\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.61521 + 13.1899i 0.559881 + 0.969743i
\(186\) 0 0
\(187\) −3.97696 2.29610i −0.290824 0.167908i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.60181 + 2.65685i 0.332975 + 0.192243i 0.657161 0.753750i \(-0.271757\pi\)
−0.324186 + 0.945993i \(0.605090\pi\)
\(192\) 0 0
\(193\) −0.828427 1.43488i −0.0596315 0.103285i 0.834669 0.550753i \(-0.185659\pi\)
−0.894300 + 0.447468i \(0.852326\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.0711i 0.788781i −0.918943 0.394390i \(-0.870956\pi\)
0.918943 0.394390i \(-0.129044\pi\)
\(198\) 0 0
\(199\) −2.65131 + 1.53073i −0.187946 + 0.108511i −0.591021 0.806656i \(-0.701275\pi\)
0.403074 + 0.915167i \(0.367942\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 10.9497 18.9655i 0.764764 1.32461i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.06147 −0.211766
\(210\) 0 0
\(211\) 26.6274 1.83311 0.916553 0.399912i \(-0.130959\pi\)
0.916553 + 0.399912i \(0.130959\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.08239 1.87476i 0.0738185 0.127857i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.87039 + 5.12132i −0.596687 + 0.344497i
\(222\) 0 0
\(223\) 21.2764i 1.42477i 0.701786 + 0.712387i \(0.252386\pi\)
−0.701786 + 0.712387i \(0.747614\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.93015 5.07517i −0.194481 0.336851i 0.752249 0.658879i \(-0.228969\pi\)
−0.946730 + 0.322028i \(0.895636\pi\)
\(228\) 0 0
\(229\) 11.4289 + 6.59847i 0.755242 + 0.436039i 0.827585 0.561340i \(-0.189714\pi\)
−0.0723426 + 0.997380i \(0.523048\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.0379 + 10.4142i 1.18171 + 0.682258i 0.956408 0.292032i \(-0.0943315\pi\)
0.225297 + 0.974290i \(0.427665\pi\)
\(234\) 0 0
\(235\) −7.41421 12.8418i −0.483650 0.837706i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3.17157i 0.205152i 0.994725 + 0.102576i \(0.0327085\pi\)
−0.994725 + 0.102576i \(0.967292\pi\)
\(240\) 0 0
\(241\) −5.41634 + 3.12713i −0.348897 + 0.201436i −0.664199 0.747555i \(-0.731227\pi\)
0.315302 + 0.948991i \(0.397894\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.41421 + 5.91359i −0.217241 + 0.376273i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.7457 −1.24634 −0.623169 0.782088i \(-0.714155\pi\)
−0.623169 + 0.782088i \(0.714155\pi\)
\(252\) 0 0
\(253\) −17.6569 −1.11008
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.56001 + 11.3623i −0.409202 + 0.708759i −0.994801 0.101842i \(-0.967526\pi\)
0.585598 + 0.810601i \(0.300860\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.22538 + 4.17157i −0.445536 + 0.257230i −0.705943 0.708269i \(-0.749477\pi\)
0.260407 + 0.965499i \(0.416143\pi\)
\(264\) 0 0
\(265\) 6.94269i 0.426486i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.3659 + 21.4184i 0.753964 + 1.30590i 0.945888 + 0.324493i \(0.105194\pi\)
−0.191924 + 0.981410i \(0.561473\pi\)
\(270\) 0 0
\(271\) 20.5281 + 11.8519i 1.24700 + 0.719953i 0.970509 0.241065i \(-0.0774967\pi\)
0.276486 + 0.961018i \(0.410830\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.74666 + 1.58579i 0.165630 + 0.0956265i
\(276\) 0 0
\(277\) 10.4853 + 18.1610i 0.630000 + 1.09119i 0.987551 + 0.157298i \(0.0502783\pi\)
−0.357552 + 0.933893i \(0.616388\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.48528i 0.386879i −0.981112 0.193440i \(-0.938036\pi\)
0.981112 0.193440i \(-0.0619644\pi\)
\(282\) 0 0
\(283\) 27.7055 15.9958i 1.64692 0.950850i 0.668635 0.743590i \(-0.266879\pi\)
0.978286 0.207260i \(-0.0664547\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.86396 10.1567i 0.344939 0.597452i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.34211 0.487351 0.243676 0.969857i \(-0.421647\pi\)
0.243676 + 0.969857i \(0.421647\pi\)
\(294\) 0 0
\(295\) −18.1421 −1.05628
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −19.6913 + 34.1063i −1.13878 + 1.97242i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −19.6830 + 11.3640i −1.12704 + 0.650699i
\(306\) 0 0
\(307\) 28.5587i 1.62993i 0.579510 + 0.814965i \(0.303244\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −10.9552 18.9750i −0.621215 1.07598i −0.989260 0.146167i \(-0.953306\pi\)
0.368045 0.929808i \(-0.380027\pi\)
\(312\) 0 0
\(313\) −19.6379 11.3379i −1.11000 0.640857i −0.171169 0.985242i \(-0.554754\pi\)
−0.938829 + 0.344385i \(0.888088\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.9947 + 12.1213i 1.17918 + 0.680801i 0.955825 0.293936i \(-0.0949651\pi\)
0.223357 + 0.974737i \(0.428298\pi\)
\(318\) 0 0
\(319\) −1.17157 2.02922i −0.0655955 0.113615i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.51472i 0.195564i
\(324\) 0 0
\(325\) 6.12627 3.53701i 0.339824 0.196198i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.34315 4.05845i 0.128791 0.223072i −0.794417 0.607372i \(-0.792224\pi\)
0.923208 + 0.384300i \(0.125557\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −23.0698 −1.26044
\(336\) 0 0
\(337\) −12.9289 −0.704284 −0.352142 0.935947i \(-0.614547\pi\)
−0.352142 + 0.935947i \(0.614547\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.86030 + 10.1503i −0.317353 + 0.549672i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.48617 4.89949i 0.455562 0.263019i −0.254615 0.967043i \(-0.581949\pi\)
0.710176 + 0.704024i \(0.248615\pi\)
\(348\) 0 0
\(349\) 30.0669i 1.60944i 0.593652 + 0.804722i \(0.297685\pi\)
−0.593652 + 0.804722i \(0.702315\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.2856 + 28.2075i 0.866796 + 1.50133i 0.865253 + 0.501335i \(0.167158\pi\)
0.00154235 + 0.999999i \(0.499509\pi\)
\(354\) 0 0
\(355\) 21.3047 + 12.3003i 1.13074 + 0.652830i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 27.2416 + 15.7279i 1.43775 + 0.830088i 0.997694 0.0678799i \(-0.0216235\pi\)
0.440061 + 0.897968i \(0.354957\pi\)
\(360\) 0 0
\(361\) −8.32843 14.4253i −0.438338 0.759224i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.07107i 0.265432i
\(366\) 0 0
\(367\) −24.1834 + 13.9623i −1.26237 + 0.728827i −0.973532 0.228553i \(-0.926601\pi\)
−0.288833 + 0.957379i \(0.593267\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 7.31371 12.6677i 0.378689 0.655909i −0.612182 0.790717i \(-0.709708\pi\)
0.990872 + 0.134807i \(0.0430415\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.22625 −0.269166
\(378\) 0 0
\(379\) 20.2843 1.04193 0.520967 0.853577i \(-0.325572\pi\)
0.520967 + 0.853577i \(0.325572\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.06147 5.30262i 0.156434 0.270951i −0.777146 0.629320i \(-0.783334\pi\)
0.933580 + 0.358369i \(0.116667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.91359 + 3.41421i −0.299831 + 0.173107i −0.642367 0.766397i \(-0.722047\pi\)
0.342536 + 0.939505i \(0.388714\pi\)
\(390\) 0 0
\(391\) 20.2710i 1.02515i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10.4525 + 18.1043i 0.525923 + 0.910925i
\(396\) 0 0
\(397\) 6.90282 + 3.98535i 0.346443 + 0.200019i 0.663117 0.748515i \(-0.269233\pi\)
−0.316675 + 0.948534i \(0.602566\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.4728 + 11.2426i 0.972426 + 0.561431i 0.899975 0.435941i \(-0.143584\pi\)
0.0724514 + 0.997372i \(0.476918\pi\)
\(402\) 0 0
\(403\) 13.0711 + 22.6398i 0.651116 + 1.12777i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.4853i 0.817145i
\(408\) 0 0
\(409\) 24.7796 14.3065i 1.22527 0.707413i 0.259237 0.965814i \(-0.416529\pi\)
0.966038 + 0.258401i \(0.0831956\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 9.65685 16.7262i 0.474036 0.821055i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14.5194 −0.709321 −0.354661 0.934995i \(-0.615404\pi\)
−0.354661 + 0.934995i \(0.615404\pi\)
\(420\) 0 0
\(421\) −7.31371 −0.356448 −0.178224 0.983990i \(-0.557035\pi\)
−0.178224 + 0.983990i \(0.557035\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.82056 3.15331i 0.0883103 0.152958i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.25460 + 5.34315i −0.445778 + 0.257370i −0.706046 0.708166i \(-0.749523\pi\)
0.260267 + 0.965537i \(0.416189\pi\)
\(432\) 0 0
\(433\) 19.6913i 0.946303i −0.880981 0.473152i \(-0.843116\pi\)
0.880981 0.473152i \(-0.156884\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.75699 + 11.7034i 0.323230 + 0.559852i
\(438\) 0 0
\(439\) −16.2295 9.37011i −0.774592 0.447211i 0.0599181 0.998203i \(-0.480916\pi\)
−0.834510 + 0.550992i \(0.814249\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.79050 + 3.34315i 0.275115 + 0.158838i 0.631210 0.775612i \(-0.282559\pi\)
−0.356095 + 0.934450i \(0.615892\pi\)
\(444\) 0 0
\(445\) −13.3640 23.1471i −0.633513 1.09728i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.5563i 0.922921i −0.887161 0.461461i \(-0.847326\pi\)
0.887161 0.461461i \(-0.152674\pi\)
\(450\) 0 0
\(451\) 20.5281 11.8519i 0.966632 0.558085i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −28.1647 −1.31176 −0.655881 0.754864i \(-0.727703\pi\)
−0.655881 + 0.754864i \(0.727703\pi\)
\(462\) 0 0
\(463\) 2.82843 0.131448 0.0657241 0.997838i \(-0.479064\pi\)
0.0657241 + 0.997838i \(0.479064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.6089 + 32.2316i −0.861118 + 1.49150i 0.00973373 + 0.999953i \(0.496902\pi\)
−0.870851 + 0.491547i \(0.836432\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.02922 1.17157i 0.0933038 0.0538690i
\(474\) 0 0
\(475\) 2.42742i 0.111378i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.4860 21.6263i −0.570499 0.988133i −0.996515 0.0834170i \(-0.973417\pi\)
0.426016 0.904716i \(-0.359917\pi\)
\(480\) 0 0
\(481\) 31.8433 + 18.3847i 1.45193 + 0.838272i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.39167 2.53553i −0.199416 0.115133i
\(486\) 0 0
\(487\) 9.89949 + 17.1464i 0.448589 + 0.776979i 0.998294 0.0583797i \(-0.0185934\pi\)
−0.549706 + 0.835359i \(0.685260\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.5147i 0.790428i 0.918589 + 0.395214i \(0.129330\pi\)
−0.918589 + 0.395214i \(0.870670\pi\)
\(492\) 0 0
\(493\) −2.32965 + 1.34502i −0.104922 + 0.0605769i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.07107 1.85514i 0.0479476 0.0830476i −0.841056 0.540949i \(-0.818065\pi\)
0.889003 + 0.457901i \(0.151399\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.2459 −0.546016 −0.273008 0.962012i \(-0.588019\pi\)
−0.273008 + 0.962012i \(0.588019\pi\)
\(504\) 0 0
\(505\) −5.07107 −0.225660
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.67878 4.63979i 0.118735 0.205655i −0.800532 0.599291i \(-0.795449\pi\)
0.919267 + 0.393635i \(0.128783\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.01461 0.585786i 0.0447091 0.0258128i
\(516\) 0 0
\(517\) 16.0502i 0.705886i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.99789 13.8528i −0.350394 0.606900i 0.635925 0.771751i \(-0.280619\pi\)
−0.986318 + 0.164851i \(0.947286\pi\)
\(522\) 0 0
\(523\) 25.2816 + 14.5964i 1.10549 + 0.638254i 0.937657 0.347561i \(-0.112990\pi\)
0.167832 + 0.985816i \(0.446323\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.6531 + 6.72792i 0.507617 + 0.293073i
\(528\) 0 0
\(529\) 27.4706 + 47.5804i 1.19437 + 2.06871i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 52.8701i 2.29006i
\(534\) 0 0
\(535\) −20.5281 + 11.8519i −0.887508 + 0.512403i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9.82843 + 17.0233i −0.422557 + 0.731890i −0.996189 0.0872230i \(-0.972201\pi\)
0.573632 + 0.819113i \(0.305534\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.67459 −0.243073
\(546\) 0 0
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.896683 + 1.55310i −0.0382000 + 0.0661643i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.55860 4.36396i 0.320268 0.184907i −0.331244 0.943545i \(-0.607468\pi\)
0.651512 + 0.758638i \(0.274135\pi\)
\(558\) 0 0
\(559\) 5.22625i 0.221047i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21.4077 + 37.0793i 0.902229 + 1.56271i 0.824595 + 0.565724i \(0.191403\pi\)
0.0776342 + 0.996982i \(0.475263\pi\)
\(564\) 0 0
\(565\) −21.4655 12.3931i −0.903061 0.521382i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14.2767 8.24264i −0.598509 0.345549i 0.169946 0.985453i \(-0.445641\pi\)
−0.768455 + 0.639904i \(0.778974\pi\)
\(570\) 0 0
\(571\) −21.3137 36.9164i −0.891951 1.54490i −0.837533 0.546386i \(-0.816003\pi\)
−0.0544175 0.998518i \(-0.517330\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.0000i 0.583840i
\(576\) 0 0
\(577\) 12.7545 7.36384i 0.530979 0.306561i −0.210436 0.977608i \(-0.567488\pi\)
0.741415 + 0.671047i \(0.234155\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.75736 6.50794i 0.155614 0.269531i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.9414 0.657971 0.328986 0.944335i \(-0.393293\pi\)
0.328986 + 0.944335i \(0.393293\pi\)
\(588\) 0 0
\(589\) 8.97056 0.369626
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.04473 3.54158i 0.0839671 0.145435i −0.820983 0.570952i \(-0.806574\pi\)
0.904951 + 0.425517i \(0.139908\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.5300 + 6.65685i −0.471103 + 0.271992i −0.716702 0.697380i \(-0.754349\pi\)
0.245598 + 0.969372i \(0.421016\pi\)
\(600\) 0 0
\(601\) 42.0501i 1.71526i 0.514267 + 0.857630i \(0.328064\pi\)
−0.514267 + 0.857630i \(0.671936\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.46716 + 11.2014i 0.262927 + 0.455403i
\(606\) 0 0
\(607\) −0.776550 0.448342i −0.0315192 0.0181976i 0.484158 0.874981i \(-0.339126\pi\)
−0.515677 + 0.856783i \(0.672459\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −31.0028 17.8995i −1.25424 0.724136i
\(612\) 0 0
\(613\) 1.39340 + 2.41344i 0.0562788 + 0.0974778i 0.892792 0.450469i \(-0.148743\pi\)
−0.836513 + 0.547946i \(0.815410\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 33.4558i 1.34688i 0.739241 + 0.673441i \(0.235184\pi\)
−0.739241 + 0.673441i \(0.764816\pi\)
\(618\) 0 0
\(619\) −21.8538 + 12.6173i −0.878378 + 0.507132i −0.870123 0.492834i \(-0.835961\pi\)
−0.00825456 + 0.999966i \(0.502628\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 7.27817 12.6062i 0.291127 0.504247i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 18.9259 0.754626
\(630\) 0 0
\(631\) 4.48528 0.178556 0.0892781 0.996007i \(-0.471544\pi\)
0.0892781 + 0.996007i \(0.471544\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.30864 10.9269i 0.250351 0.433620i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.7775 13.7279i 0.939153 0.542220i 0.0494584 0.998776i \(-0.484250\pi\)
0.889695 + 0.456556i \(0.150917\pi\)
\(642\) 0 0
\(643\) 47.1451i 1.85922i −0.368546 0.929610i \(-0.620144\pi\)
0.368546 0.929610i \(-0.379856\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.1606 31.4550i −0.713965 1.23662i −0.963357 0.268222i \(-0.913564\pi\)
0.249392 0.968403i \(-0.419769\pi\)
\(648\) 0 0
\(649\) −17.0061 9.81845i −0.667546 0.385408i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 29.5680 + 17.0711i 1.15708 + 0.668043i 0.950603 0.310408i \(-0.100466\pi\)
0.206480 + 0.978451i \(0.433799\pi\)
\(654\) 0 0
\(655\) 10.4853 + 18.1610i 0.409694 + 0.709611i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 30.9706i 1.20644i 0.797574 + 0.603221i \(0.206116\pi\)
−0.797574 + 0.603221i \(0.793884\pi\)
\(660\) 0 0
\(661\) 0.890273 0.514000i 0.0346276 0.0199923i −0.482586 0.875848i \(-0.660303\pi\)
0.517214 + 0.855856i \(0.326969\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.17157 + 8.95743i −0.200244 + 0.346833i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.6005 −0.949693
\(672\) 0 0
\(673\) −28.0416 −1.08093 −0.540463 0.841368i \(-0.681751\pi\)
−0.540463 + 0.841368i \(0.681751\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5.02928 8.71096i 0.193291 0.334790i −0.753048 0.657966i \(-0.771417\pi\)
0.946339 + 0.323176i \(0.104751\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.2838 6.51472i 0.431764 0.249279i −0.268334 0.963326i \(-0.586473\pi\)
0.700098 + 0.714047i \(0.253140\pi\)
\(684\) 0 0
\(685\) 9.55582i 0.365109i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −8.38057 14.5156i −0.319274 0.553000i
\(690\) 0 0
\(691\) −27.9330 16.1271i −1.06262 0.613504i −0.136464 0.990645i \(-0.543574\pi\)
−0.926156 + 0.377141i \(0.876907\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.3923 6.00000i −0.394203 0.227593i
\(696\) 0 0
\(697\) −13.6066 23.5673i −0.515387 0.892676i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 35.4558i 1.33915i 0.742745 + 0.669574i \(0.233523\pi\)
−0.742745 + 0.669574i \(0.766477\pi\)
\(702\) 0 0
\(703\) 10.9269 6.30864i 0.412116 0.237935i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −11.4350 + 19.8061i −0.429452 + 0.743832i −0.996825 0.0796290i \(-0.974626\pi\)
0.567373 + 0.823461i \(0.307960\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 51.7373 1.93758
\(714\) 0 0
\(715\) −16.4853 −0.616515
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.2513 22.9520i 0.494192 0.855965i −0.505786 0.862659i \(-0.668797\pi\)
0.999978 + 0.00669409i \(0.00213081\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.60896 0.928932i 0.0597552 0.0344997i
\(726\) 0 0
\(727\) 25.3434i 0.939933i 0.882684 + 0.469967i \(0.155734\pi\)
−0.882684 + 0.469967i \(0.844266\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.34502 2.32965i −0.0497475 0.0861653i
\(732\) 0 0
\(733\) −1.37276 0.792563i −0.0507040 0.0292740i 0.474434 0.880291i \(-0.342653\pi\)
−0.525138 + 0.851017i \(0.675986\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.6251 12.4853i −0.796572 0.459901i
\(738\) 0 0
\(739\) −26.7279 46.2941i −0.983203 1.70296i −0.649667 0.760219i \(-0.725091\pi\)
−0.333536 0.942737i \(-0.608242\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32.3431i 1.18655i −0.804998 0.593277i \(-0.797834\pi\)
0.804998 0.593277i \(-0.202166\pi\)
\(744\) 0 0
\(745\) −11.3152 + 6.53281i −0.414556 + 0.239344i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10.1421 + 17.5667i −0.370092 + 0.641018i −0.989579 0.143989i \(-0.954007\pi\)
0.619488 + 0.785006i \(0.287340\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 33.5223 1.22000
\(756\) 0 0
\(757\) 37.8995 1.37748 0.688740 0.725008i \(-0.258164\pi\)
0.688740 + 0.725008i \(0.258164\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.28692 12.6213i 0.264151 0.457522i −0.703190 0.711002i \(-0.748242\pi\)
0.967341 + 0.253480i \(0.0815751\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −37.9310 + 21.8995i −1.36961 + 0.790745i
\(768\) 0 0
\(769\) 13.5684i 0.489288i −0.969613 0.244644i \(-0.921329\pi\)
0.969613 0.244644i \(-0.0786710\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.11874 15.7941i −0.327978 0.568075i 0.654132 0.756380i \(-0.273034\pi\)
−0.982111 + 0.188305i \(0.939701\pi\)
\(774\) 0 0
\(775\) −8.04814 4.64659i −0.289098 0.166911i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −15.7116 9.07107i −0.562925 0.325005i
\(780\) 0 0
\(781\) 13.3137 + 23.0600i 0.476402 + 0.825152i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20.7279i 0.739811i
\(786\) 0 0
\(787\) 3.10620 1.79337i 0.110724 0.0639266i −0.443615 0.896217i \(-0.646304\pi\)
0.554339 + 0.832291i \(0.312971\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −27.4350 + 47.5189i −0.974246 + 1.68744i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30.4064 1.07705 0.538526 0.842609i \(-0.318982\pi\)
0.538526 + 0.842609i \(0.318982\pi\)
\(798\) 0 0
\(799\) −18.4264 −0.651879
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.74444 4.75351i 0.0968493 0.167748i
\(804\) 0 0
\(805\) 0 0