Properties

Label 1764.2.k.j.1549.1
Level $1764$
Weight $2$
Character 1764.1549
Analytic conductor $14.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1549.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1549
Dual form 1764.2.k.j.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{5} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{11} +3.00000 q^{13} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -4.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{37} +6.00000 q^{41} +11.0000 q^{43} +(-3.00000 + 5.19615i) q^{47} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-2.00000 - 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(3.00000 - 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} +10.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(1.50000 - 2.59808i) q^{79} +2.00000 q^{83} -16.0000 q^{85} +(1.00000 + 1.73205i) q^{95} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} + O(q^{10}) \) \( 2q + 2q^{5} + 2q^{11} + 6q^{13} - 8q^{17} - q^{19} + 8q^{23} + q^{25} - 8q^{29} + 3q^{31} + q^{37} + 12q^{41} + 22q^{43} - 6q^{47} - 12q^{53} + 8q^{55} - 4q^{59} - 6q^{61} + 6q^{65} - 13q^{67} + 20q^{71} - 11q^{73} + 3q^{79} + 4q^{83} - 32q^{85} + 2q^{95} - 20q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.00000 6.92820i −0.970143 1.68034i −0.695113 0.718900i \(-0.744646\pi\)
−0.275029 0.961436i \(-0.588688\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i \(-0.874609\pi\)
0.129307 0.991605i \(-0.458725\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i \(-0.651027\pi\)
0.998793 0.0491146i \(-0.0156400\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −8.00000 13.8564i −0.746004 1.29212i
\(116\) 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
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.00000 1.73205i 0.0873704 0.151330i −0.819028 0.573753i \(-0.805487\pi\)
0.906399 + 0.422423i \(0.138820\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 + 3.46410i 0.170872 + 0.295958i 0.938725 0.344668i \(-0.112008\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i \(-0.141236\pi\)
−0.823359 + 0.567521i \(0.807902\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.00000 + 13.8564i −0.608229 + 1.05348i 0.383304 + 0.923622i \(0.374786\pi\)
−0.991532 + 0.129861i \(0.958547\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) 15.0000 1.11494 0.557471 0.830197i \(-0.311772\pi\)
0.557471 + 0.830197i \(0.311772\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 0 0
\(187\) 8.00000 13.8564i 0.585018 1.01328i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.0000 19.0526i 0.750194 1.29937i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.0000 20.7846i −0.807207 1.39812i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 0 0
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i \(-0.681690\pi\)
0.998886 + 0.0471787i \(0.0150230\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.00000 + 1.73205i 0.0609711 + 0.105605i 0.894900 0.446267i \(-0.147247\pi\)
−0.833929 + 0.551872i \(0.813914\pi\)
\(270\) 0 0
\(271\) −12.0000 + 20.7846i −0.728948 + 1.26258i 0.228380 + 0.973572i \(0.426657\pi\)
−0.957328 + 0.289003i \(0.906676\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i \(-0.996047\pi\)
0.489207 0.872167i \(-0.337286\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 0 0
\(283\) 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i \(0.0243478\pi\)
−0.432360 + 0.901701i \(0.642319\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −23.5000 + 40.7032i −1.38235 + 2.39431i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 + 1.73205i 0.0567048 + 0.0982156i 0.892984 0.450088i \(-0.148607\pi\)
−0.836280 + 0.548303i \(0.815274\pi\)
\(312\) 0 0
\(313\) −8.50000 + 14.7224i −0.480448 + 0.832161i −0.999748 0.0224310i \(-0.992859\pi\)
0.519300 + 0.854592i \(0.326193\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i \(0.402086\pi\)
−0.976764 + 0.214318i \(0.931247\pi\)
\(318\) 0 0
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) 1.50000 + 2.59808i 0.0832050 + 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −26.0000 −1.42053
\(336\) 0 0
\(337\) 21.0000 1.14394 0.571971 0.820274i \(-0.306179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) 10.0000 17.3205i 0.530745 0.919277i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −22.0000 −1.15153
\(366\) 0 0
\(367\) 2.50000 + 4.33013i 0.130499 + 0.226031i 0.923869 0.382709i \(-0.125009\pi\)
−0.793370 + 0.608740i \(0.791675\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 2.50000 4.33013i 0.129445 0.224205i −0.794017 0.607896i \(-0.792014\pi\)
0.923462 + 0.383691i \(0.125347\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i \(-0.579593\pi\)
0.962818 0.270151i \(-0.0870736\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i \(-0.0850816\pi\)
−0.710980 + 0.703213i \(0.751748\pi\)
\(390\) 0 0
\(391\) −64.0000 −3.23662
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.00000 5.19615i −0.150946 0.261447i
\(396\) 0 0
\(397\) 1.50000 2.59808i 0.0752828 0.130394i −0.825926 0.563778i \(-0.809347\pi\)
0.901209 + 0.433384i \(0.142681\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) 4.50000 + 7.79423i 0.224161 + 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) −9.50000 16.4545i −0.469745 0.813622i 0.529657 0.848212i \(-0.322321\pi\)
−0.999402 + 0.0345902i \(0.988987\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.00000 3.46410i 0.0981761 0.170046i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) 25.0000 1.20142 0.600712 0.799466i \(-0.294884\pi\)
0.600712 + 0.799466i \(0.294884\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.00000 + 6.92820i 0.191346 + 0.331421i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6.50000 + 11.2583i −0.304057 + 0.526642i −0.977051 0.213006i \(-0.931675\pi\)
0.672994 + 0.739648i \(0.265008\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) −11.0000 −0.511213 −0.255607 0.966781i \(-0.582275\pi\)
−0.255607 + 0.966781i \(0.582275\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.0000 + 29.4449i −0.786666 + 1.36255i 0.141332 + 0.989962i \(0.454861\pi\)
−0.927999 + 0.372584i \(0.878472\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11.0000 + 19.0526i 0.505781 + 0.876038i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 0 0
\(481\) 1.50000 2.59808i 0.0683941 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.0000 + 17.3205i −0.454077 + 0.786484i
\(486\) 0 0
\(487\) 9.50000 + 16.4545i 0.430486 + 0.745624i 0.996915 0.0784867i \(-0.0250088\pi\)
−0.566429 + 0.824110i \(0.691675\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 16.0000 + 27.7128i 0.720604 + 1.24812i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.5000 25.1147i 0.649109 1.12429i −0.334227 0.942493i \(-0.608475\pi\)
0.983336 0.181797i \(-0.0581915\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.0000 19.0526i −0.484718 0.839556i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) 0 0
\(523\) −15.5000 + 26.8468i −0.677768 + 1.17393i 0.297884 + 0.954602i \(0.403719\pi\)
−0.975652 + 0.219326i \(0.929614\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.50000 12.9904i 0.322450 0.558500i −0.658543 0.752543i \(-0.728827\pi\)
0.980993 + 0.194043i \(0.0621602\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 22.0000 0.942376
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 3.46410i 0.0852029 0.147576i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.0000 + 19.0526i 0.466085 + 0.807283i 0.999250 0.0387286i \(-0.0123308\pi\)
−0.533165 + 0.846011i \(0.678997\pi\)
\(558\) 0 0
\(559\) 33.0000 1.39575
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.0000 + 39.8372i 0.969334 + 1.67894i 0.697489 + 0.716596i \(0.254301\pi\)
0.271846 + 0.962341i \(0.412366\pi\)
\(564\) 0 0
\(565\) 14.0000 24.2487i 0.588984 1.02015i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 10.5000 + 18.1865i 0.439411 + 0.761083i 0.997644 0.0686016i \(-0.0218537\pi\)
−0.558233 + 0.829684i \(0.688520\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) −20.5000 35.5070i −0.853426 1.47818i −0.878097 0.478482i \(-0.841187\pi\)
0.0246713 0.999696i \(-0.492146\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.0000 1.32078 0.660391 0.750922i \(-0.270391\pi\)
0.660391 + 0.750922i \(0.270391\pi\)
\(588\) 0 0
\(589\) −3.00000 −0.123613
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) 1.00000 0.0407909 0.0203954 0.999792i \(-0.493507\pi\)
0.0203954 + 0.999792i \(0.493507\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) −1.50000 + 2.59808i −0.0608831 + 0.105453i −0.894860 0.446346i \(-0.852725\pi\)
0.833977 + 0.551799i \(0.186058\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 + 15.5885i −0.364101 + 0.630641i
\(612\) 0 0
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) −5.50000 9.52628i −0.221064 0.382893i 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.00000 5.19615i 0.119051 0.206203i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.0000 34.6410i −0.789953 1.36824i −0.925995 0.377535i \(-0.876772\pi\)
0.136043 0.990703i \(-0.456562\pi\)
\(642\) 0 0
\(643\) −35.0000 −1.38027 −0.690133 0.723683i \(-0.742448\pi\)
−0.690133 + 0.723683i \(0.742448\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3.00000 5.19615i −0.117942 0.204282i 0.801010 0.598651i \(-0.204296\pi\)
−0.918952 + 0.394369i \(0.870963\pi\)
\(648\) 0 0
\(649\) 4.00000 6.92820i 0.157014 0.271956i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 0 0
\(655\) −2.00000 3.46410i −0.0781465 0.135354i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −14.5000 25.1147i −0.563985 0.976850i −0.997143 0.0755324i \(-0.975934\pi\)
0.433159 0.901318i \(-0.357399\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −16.0000 + 27.7128i −0.619522 + 1.07304i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.0000 + 31.1769i 0.688751 + 1.19295i 0.972242 + 0.233977i \(0.0751739\pi\)
−0.283491 + 0.958975i \(0.591493\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −21.5000 + 37.2391i −0.817899 + 1.41664i 0.0893292 + 0.996002i \(0.471528\pi\)
−0.907228 + 0.420640i \(0.861806\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.00000 8.66025i 0.189661 0.328502i
\(696\) 0 0
\(697\) −24.0000 41.5692i −0.909065 1.57455i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.00000 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 0 0
\(703\) 0.500000 + 0.866025i 0.0188579 + 0.0326628i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −44.0000 76.2102i −1.62740 2.81874i
\(732\) 0 0
\(733\) 22.5000 38.9711i 0.831056 1.43943i −0.0661448 0.997810i \(-0.521070\pi\)
0.897201 0.441622i \(-0.145597\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.0000 22.5167i 0.478861 0.829412i
\(738\) 0 0
\(739\) 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 0.660356 0.330178 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(744\) 0 0
\(745\) 12.0000 + 20.7846i 0.439646 + 0.761489i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i \(-0.921574\pi\)
0.696122 + 0.717923i \(0.254907\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i \(-0.879652\pi\)
0.784373 + 0.620289i \(0.212985\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 10.3923i −0.216647 0.375244i
\(768\) 0 0
\(769\) −31.0000 −1.11789 −0.558944 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11.0000 19.0526i −0.395643 0.685273i 0.597540 0.801839i \(-0.296145\pi\)
−0.993183 + 0.116566i \(0.962811\pi\)
\(774\) 0 0
\(775\) −1.50000 + 2.59808i −0.0538816 + 0.0933257i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 10.0000 + 17.3205i 0.357828 + 0.619777i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) 12.0000 + 20.7846i 0.427754 + 0.740891i 0.996673 0.0815020i \(-0.0259717\pi\)
−0.568919 + 0.822393i \(0.692638\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.00000 + 15.5885i −0.319599 + 0.553562i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −48.0000 −1.70025 −0.850124 0.526583i \(-0.823473\pi\)
−0.850124 + 0.526583i \(0.823473\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11.0000 19.0526i 0.388182 0.672350i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0