Properties

Label 3528.2.s.bk.361.1
Level $3528$
Weight $2$
Character 3528.361
Analytic conductor $28.171$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.1712218331\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(-1.63746 - 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 3528.361
Dual form 3528.2.s.bk.3313.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.63746 - 2.83616i) q^{5} +O(q^{10})\) \(q+(-1.63746 - 2.83616i) q^{5} +(1.63746 - 2.83616i) q^{11} -6.27492 q^{13} +(2.00000 - 3.46410i) q^{17} +(-3.13746 - 5.43424i) q^{19} +(2.00000 + 3.46410i) q^{23} +(-2.86254 + 4.95807i) q^{25} -5.27492 q^{29} +(-0.500000 + 0.866025i) q^{31} +(1.13746 + 1.97014i) q^{37} -4.54983 q^{41} +0.274917 q^{43} +(3.00000 + 5.19615i) q^{47} +(4.63746 - 8.03231i) q^{53} -10.7251 q^{55} +(0.637459 - 1.10411i) q^{59} +(5.00000 + 8.66025i) q^{61} +(10.2749 + 17.7967i) q^{65} +(0.137459 - 0.238085i) q^{67} -2.00000 q^{71} +(-2.13746 + 3.70219i) q^{73} +(-5.77492 - 10.0025i) q^{79} +7.27492 q^{83} -13.0997 q^{85} +(5.27492 + 9.13642i) q^{89} +(-10.2749 + 17.7967i) q^{95} -8.72508 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{5} + O(q^{10}) \) \( 4q + q^{5} - q^{11} - 10q^{13} + 8q^{17} - 5q^{19} + 8q^{23} - 19q^{25} - 6q^{29} - 2q^{31} - 3q^{37} + 12q^{41} - 14q^{43} + 12q^{47} + 11q^{53} - 58q^{55} - 5q^{59} + 20q^{61} + 26q^{65} - 7q^{67} - 8q^{71} - q^{73} - 8q^{79} + 14q^{83} + 8q^{85} + 6q^{89} - 26q^{95} - 50q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(5\) −1.63746 2.83616i −0.732294 1.26837i −0.955901 0.293691i \(-0.905116\pi\)
0.223607 0.974679i \(-0.428217\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.63746 2.83616i 0.493712 0.855135i −0.506261 0.862380i \(-0.668973\pi\)
0.999974 + 0.00724520i \(0.00230624\pi\)
\(12\) 0 0
\(13\) −6.27492 −1.74035 −0.870174 0.492744i \(-0.835994\pi\)
−0.870174 + 0.492744i \(0.835994\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0 0
\(19\) −3.13746 5.43424i −0.719782 1.24670i −0.961086 0.276250i \(-0.910908\pi\)
0.241303 0.970450i \(-0.422425\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) −2.86254 + 4.95807i −0.572508 + 0.991613i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.27492 −0.979528 −0.489764 0.871855i \(-0.662917\pi\)
−0.489764 + 0.871855i \(0.662917\pi\)
\(30\) 0 0
\(31\) −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i \(-0.861957\pi\)
0.817625 + 0.575751i \(0.195290\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.13746 + 1.97014i 0.186997 + 0.323888i 0.944248 0.329236i \(-0.106791\pi\)
−0.757251 + 0.653124i \(0.773458\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.54983 −0.710565 −0.355282 0.934759i \(-0.615615\pi\)
−0.355282 + 0.934759i \(0.615615\pi\)
\(42\) 0 0
\(43\) 0.274917 0.0419245 0.0209622 0.999780i \(-0.493327\pi\)
0.0209622 + 0.999780i \(0.493327\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.63746 8.03231i 0.637004 1.10332i −0.349083 0.937092i \(-0.613507\pi\)
0.986087 0.166231i \(-0.0531598\pi\)
\(54\) 0 0
\(55\) −10.7251 −1.44617
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.637459 1.10411i 0.0829900 0.143743i −0.821543 0.570147i \(-0.806886\pi\)
0.904533 + 0.426404i \(0.140220\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.2749 + 17.7967i 1.27445 + 2.20741i
\(66\) 0 0
\(67\) 0.137459 0.238085i 0.0167932 0.0290867i −0.857507 0.514473i \(-0.827988\pi\)
0.874300 + 0.485386i \(0.161321\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −2.13746 + 3.70219i −0.250171 + 0.433308i −0.963573 0.267447i \(-0.913820\pi\)
0.713402 + 0.700755i \(0.247153\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.77492 10.0025i −0.649729 1.12536i −0.983188 0.182599i \(-0.941549\pi\)
0.333459 0.942765i \(-0.391784\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.27492 0.798526 0.399263 0.916836i \(-0.369266\pi\)
0.399263 + 0.916836i \(0.369266\pi\)
\(84\) 0 0
\(85\) −13.0997 −1.42086
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.27492 + 9.13642i 0.559140 + 0.968459i 0.997568 + 0.0696929i \(0.0222020\pi\)
−0.438428 + 0.898766i \(0.644465\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −10.2749 + 17.7967i −1.05418 + 1.82590i
\(96\) 0 0
\(97\) −8.72508 −0.885898 −0.442949 0.896547i \(-0.646068\pi\)
−0.442949 + 0.896547i \(0.646068\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 5.41238 + 9.37451i 0.533297 + 0.923698i 0.999244 + 0.0388850i \(0.0123806\pi\)
−0.465946 + 0.884813i \(0.654286\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.91238 13.7046i −0.764918 1.32488i −0.940290 0.340375i \(-0.889446\pi\)
0.175372 0.984502i \(-0.443887\pi\)
\(108\) 0 0
\(109\) −8.41238 + 14.5707i −0.805759 + 1.39562i 0.110018 + 0.993930i \(0.464909\pi\)
−0.915777 + 0.401687i \(0.868424\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.54983 0.428012 0.214006 0.976832i \(-0.431349\pi\)
0.214006 + 0.976832i \(0.431349\pi\)
\(114\) 0 0
\(115\) 6.54983 11.3446i 0.610775 1.05789i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.137459 + 0.238085i 0.0124962 + 0.0216441i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.37459 0.212389
\(126\) 0 0
\(127\) −6.45017 −0.572360 −0.286180 0.958176i \(-0.592385\pi\)
−0.286180 + 0.958176i \(0.592385\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.63746 6.30026i −0.317806 0.550457i 0.662224 0.749306i \(-0.269613\pi\)
−0.980030 + 0.198850i \(0.936279\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.725083 1.25588i 0.0619480 0.107297i −0.833388 0.552688i \(-0.813602\pi\)
0.895336 + 0.445391i \(0.146935\pi\)
\(138\) 0 0
\(139\) −8.27492 −0.701869 −0.350935 0.936400i \(-0.614136\pi\)
−0.350935 + 0.936400i \(0.614136\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −10.2749 + 17.7967i −0.859232 + 1.48823i
\(144\) 0 0
\(145\) 8.63746 + 14.9605i 0.717302 + 1.24240i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.27492 12.6005i −0.595984 1.03228i −0.993407 0.114640i \(-0.963429\pi\)
0.397423 0.917636i \(-0.369905\pi\)
\(150\) 0 0
\(151\) −11.1873 + 19.3770i −0.910409 + 1.57687i −0.0969217 + 0.995292i \(0.530900\pi\)
−0.813487 + 0.581583i \(0.802434\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.27492 0.263048
\(156\) 0 0
\(157\) −0.274917 + 0.476171i −0.0219408 + 0.0380026i −0.876787 0.480878i \(-0.840318\pi\)
0.854847 + 0.518881i \(0.173651\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.00000 + 10.3923i 0.469956 + 0.813988i 0.999410 0.0343508i \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 26.3746 2.02881
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.2749 + 19.5287i 0.857216 + 1.48474i 0.874574 + 0.484892i \(0.161141\pi\)
−0.0173577 + 0.999849i \(0.505525\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.27492 + 14.3326i −0.618496 + 1.07127i 0.371264 + 0.928527i \(0.378925\pi\)
−0.989760 + 0.142740i \(0.954409\pi\)
\(180\) 0 0
\(181\) 18.8248 1.39923 0.699616 0.714519i \(-0.253354\pi\)
0.699616 + 0.714519i \(0.253354\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.72508 6.45203i 0.273874 0.474363i
\(186\) 0 0
\(187\) −6.54983 11.3446i −0.478971 0.829603i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.27492 + 3.94027i 0.164607 + 0.285108i 0.936516 0.350626i \(-0.114031\pi\)
−0.771909 + 0.635734i \(0.780698\pi\)
\(192\) 0 0
\(193\) −0.225083 + 0.389855i −0.0162018 + 0.0280624i −0.874013 0.485903i \(-0.838491\pi\)
0.857811 + 0.513966i \(0.171824\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.45017 0.103320 0.0516600 0.998665i \(-0.483549\pi\)
0.0516600 + 0.998665i \(0.483549\pi\)
\(198\) 0 0
\(199\) −2.54983 + 4.41644i −0.180753 + 0.313073i −0.942137 0.335228i \(-0.891187\pi\)
0.761384 + 0.648301i \(0.224520\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 7.45017 + 12.9041i 0.520342 + 0.901259i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −20.5498 −1.42146
\(210\) 0 0
\(211\) −27.6495 −1.90347 −0.951735 0.306921i \(-0.900701\pi\)
−0.951735 + 0.306921i \(0.900701\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.450166 0.779710i −0.0307010 0.0531758i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.5498 + 21.7370i −0.844193 + 1.46219i
\(222\) 0 0
\(223\) 1.27492 0.0853748 0.0426874 0.999088i \(-0.486408\pi\)
0.0426874 + 0.999088i \(0.486408\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.63746 9.76436i 0.374171 0.648084i −0.616031 0.787722i \(-0.711261\pi\)
0.990203 + 0.139638i \(0.0445939\pi\)
\(228\) 0 0
\(229\) 9.13746 + 15.8265i 0.603820 + 1.04585i 0.992237 + 0.124363i \(0.0396889\pi\)
−0.388416 + 0.921484i \(0.626978\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.274917 0.476171i −0.0180104 0.0311950i 0.856880 0.515516i \(-0.172400\pi\)
−0.874890 + 0.484321i \(0.839067\pi\)
\(234\) 0 0
\(235\) 9.82475 17.0170i 0.640896 1.11006i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −15.4502 −0.999388 −0.499694 0.866202i \(-0.666554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(240\) 0 0
\(241\) 4.91238 8.50848i 0.316434 0.548080i −0.663307 0.748347i \(-0.730848\pi\)
0.979741 + 0.200267i \(0.0641811\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 19.6873 + 34.0994i 1.25267 + 2.16969i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.3746 −1.15979 −0.579897 0.814690i \(-0.696907\pi\)
−0.579897 + 0.814690i \(0.696907\pi\)
\(252\) 0 0
\(253\) 13.0997 0.823569
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.54983 9.61260i −0.346189 0.599617i 0.639380 0.768891i \(-0.279191\pi\)
−0.985569 + 0.169274i \(0.945858\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.72508 + 8.18408i −0.291361 + 0.504652i −0.974132 0.225980i \(-0.927441\pi\)
0.682771 + 0.730633i \(0.260775\pi\)
\(264\) 0 0
\(265\) −30.3746 −1.86590
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.3625 + 17.9484i −0.631815 + 1.09434i 0.355365 + 0.934728i \(0.384357\pi\)
−0.987180 + 0.159609i \(0.948977\pi\)
\(270\) 0 0
\(271\) 0.637459 + 1.10411i 0.0387229 + 0.0670699i 0.884737 0.466090i \(-0.154338\pi\)
−0.846014 + 0.533160i \(0.821004\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.37459 + 16.2373i 0.565309 + 0.979144i
\(276\) 0 0
\(277\) 13.4124 23.2309i 0.805872 1.39581i −0.109830 0.993950i \(-0.535030\pi\)
0.915701 0.401860i \(-0.131636\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.5498 1.58383 0.791915 0.610631i \(-0.209084\pi\)
0.791915 + 0.610631i \(0.209084\pi\)
\(282\) 0 0
\(283\) −12.9622 + 22.4512i −0.770523 + 1.33459i 0.166753 + 0.985999i \(0.446672\pi\)
−0.937276 + 0.348587i \(0.886662\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −27.8248 −1.62554 −0.812770 0.582585i \(-0.802041\pi\)
−0.812770 + 0.582585i \(0.802041\pi\)
\(294\) 0 0
\(295\) −4.17525 −0.243092
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.5498 21.7370i −0.725776 1.25708i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 16.3746 28.3616i 0.937606 1.62398i
\(306\) 0 0
\(307\) −11.3746 −0.649182 −0.324591 0.945854i \(-0.605227\pi\)
−0.324591 + 0.945854i \(0.605227\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.27492 3.94027i 0.128999 0.223432i −0.794290 0.607539i \(-0.792157\pi\)
0.923289 + 0.384106i \(0.125490\pi\)
\(312\) 0 0
\(313\) −9.77492 16.9307i −0.552511 0.956977i −0.998093 0.0617357i \(-0.980336\pi\)
0.445582 0.895241i \(-0.352997\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.9124 24.0969i −0.781397 1.35342i −0.931128 0.364692i \(-0.881174\pi\)
0.149731 0.988727i \(-0.452159\pi\)
\(318\) 0 0
\(319\) −8.63746 + 14.9605i −0.483605 + 0.837628i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −25.0997 −1.39658
\(324\) 0 0
\(325\) 17.9622 31.1115i 0.996364 1.72575i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.587624 1.01779i −0.0322987 0.0559431i 0.849424 0.527711i \(-0.176949\pi\)
−0.881723 + 0.471768i \(0.843616\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.900331 −0.0491903
\(336\) 0 0
\(337\) −24.0997 −1.31279 −0.656396 0.754416i \(-0.727920\pi\)
−0.656396 + 0.754416i \(0.727920\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.63746 + 2.83616i 0.0886734 + 0.153587i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.0997 26.1534i 0.810593 1.40399i −0.101857 0.994799i \(-0.532478\pi\)
0.912450 0.409189i \(-0.134188\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.2749 17.7967i 0.546879 0.947222i −0.451607 0.892217i \(-0.649149\pi\)
0.998486 0.0550049i \(-0.0175174\pi\)
\(354\) 0 0
\(355\) 3.27492 + 5.67232i 0.173815 + 0.301056i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.82475 17.0170i −0.518531 0.898121i −0.999768 0.0215311i \(-0.993146\pi\)
0.481238 0.876590i \(-0.340187\pi\)
\(360\) 0 0
\(361\) −10.1873 + 17.6449i −0.536173 + 0.928679i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) 11.0498 19.1389i 0.576797 0.999041i −0.419047 0.907964i \(-0.637636\pi\)
0.995844 0.0910767i \(-0.0290308\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.13746 + 5.43424i 0.162451 + 0.281374i 0.935747 0.352671i \(-0.114727\pi\)
−0.773296 + 0.634045i \(0.781393\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 33.0997 1.70472
\(378\) 0 0
\(379\) 13.1752 0.676767 0.338384 0.941008i \(-0.390120\pi\)
0.338384 + 0.941008i \(0.390120\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.27492 9.13642i −0.269536 0.466849i 0.699206 0.714920i \(-0.253537\pi\)
−0.968742 + 0.248070i \(0.920204\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 + 1.73205i −0.0507020 + 0.0878185i −0.890263 0.455448i \(-0.849479\pi\)
0.839561 + 0.543266i \(0.182813\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −18.9124 + 32.7572i −0.951585 + 1.64819i
\(396\) 0 0
\(397\) −1.68729 2.92248i −0.0846828 0.146675i 0.820573 0.571541i \(-0.193654\pi\)
−0.905256 + 0.424867i \(0.860321\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) 0 0
\(403\) 3.13746 5.43424i 0.156288 0.270699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.45017 0.369291
\(408\) 0 0
\(409\) 5.22508 9.05011i 0.258364 0.447499i −0.707440 0.706773i \(-0.750150\pi\)
0.965804 + 0.259274i \(0.0834834\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −11.9124 20.6328i −0.584756 1.01283i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28.5498 1.39475 0.697375 0.716706i \(-0.254351\pi\)
0.697375 + 0.716706i \(0.254351\pi\)
\(420\) 0 0
\(421\) 8.82475 0.430092 0.215046 0.976604i \(-0.431010\pi\)
0.215046 + 0.976604i \(0.431010\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.4502 + 19.8323i 0.555415 + 0.962006i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.82475 + 15.2849i −0.425073 + 0.736249i −0.996427 0.0844552i \(-0.973085\pi\)
0.571354 + 0.820704i \(0.306418\pi\)
\(432\) 0 0
\(433\) −3.17525 −0.152593 −0.0762963 0.997085i \(-0.524310\pi\)
−0.0762963 + 0.997085i \(0.524310\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.5498 21.7370i 0.600340 1.03982i
\(438\) 0 0
\(439\) 8.63746 + 14.9605i 0.412243 + 0.714027i 0.995135 0.0985236i \(-0.0314120\pi\)
−0.582891 + 0.812550i \(0.698079\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.18729 5.52055i −0.151433 0.262289i 0.780322 0.625378i \(-0.215055\pi\)
−0.931754 + 0.363089i \(0.881722\pi\)
\(444\) 0 0
\(445\) 17.2749 29.9210i 0.818910 1.41839i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.5498 −0.969807 −0.484903 0.874568i \(-0.661145\pi\)
−0.484903 + 0.874568i \(0.661145\pi\)
\(450\) 0 0
\(451\) −7.45017 + 12.9041i −0.350815 + 0.607629i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.3248 31.7394i −0.857196 1.48471i −0.874593 0.484858i \(-0.838871\pi\)
0.0173972 0.999849i \(-0.494462\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.64950 −0.169974 −0.0849872 0.996382i \(-0.527085\pi\)
−0.0849872 + 0.996382i \(0.527085\pi\)
\(462\) 0 0
\(463\) 13.1752 0.612306 0.306153 0.951982i \(-0.400958\pi\)
0.306153 + 0.951982i \(0.400958\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.2749 35.1172i −0.938211 1.62503i −0.768805 0.639483i \(-0.779148\pi\)
−0.169406 0.985546i \(-0.554185\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.450166 0.779710i 0.0206986 0.0358511i
\(474\) 0 0
\(475\) 35.9244 1.64833
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.72508 4.71998i 0.124512 0.215661i −0.797030 0.603940i \(-0.793597\pi\)
0.921542 + 0.388278i \(0.126930\pi\)
\(480\) 0 0
\(481\) −7.13746 12.3624i −0.325440 0.563679i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14.2870 + 24.7457i 0.648738 + 1.12365i
\(486\) 0 0
\(487\) −0.500000 + 0.866025i −0.0226572 + 0.0392434i −0.877132 0.480250i \(-0.840546\pi\)
0.854475 + 0.519493i \(0.173879\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −36.9244 −1.66638 −0.833188 0.552990i \(-0.813487\pi\)
−0.833188 + 0.552990i \(0.813487\pi\)
\(492\) 0 0
\(493\) −10.5498 + 18.2728i −0.475141 + 0.822968i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −16.1375 27.9509i −0.722412 1.25125i −0.960030 0.279896i \(-0.909700\pi\)
0.237619 0.971359i \(-0.423633\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −37.6495 −1.67871 −0.839354 0.543585i \(-0.817067\pi\)
−0.839354 + 0.543585i \(0.817067\pi\)
\(504\) 0 0
\(505\) −19.6495 −0.874391
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.63746 + 9.76436i 0.249876 + 0.432798i 0.963491 0.267740i \(-0.0862768\pi\)
−0.713615 + 0.700538i \(0.752943\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.7251 30.7007i 0.781060 1.35284i
\(516\) 0 0
\(517\) 19.6495 0.864184
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.27492 12.6005i 0.318720 0.552039i −0.661501 0.749944i \(-0.730080\pi\)
0.980221 + 0.197905i \(0.0634137\pi\)
\(522\) 0 0
\(523\) −8.86254 15.3504i −0.387532 0.671225i 0.604585 0.796541i \(-0.293339\pi\)
−0.992117 + 0.125316i \(0.960006\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 + 3.46410i 0.0871214 + 0.150899i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.5498 1.23663
\(534\) 0 0
\(535\) −25.9124 + 44.8816i −1.12029 + 1.94040i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4.13746 + 7.16629i 0.177883 + 0.308103i 0.941155 0.337974i \(-0.109742\pi\)
−0.763272 + 0.646077i \(0.776408\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 55.0997 2.36021
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.5498 + 28.6652i 0.705047 + 1.22118i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.9124 + 25.8290i −0.631858 + 1.09441i 0.355314 + 0.934747i \(0.384374\pi\)
−0.987172 + 0.159663i \(0.948959\pi\)
\(558\) 0 0
\(559\) −1.72508 −0.0729632
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.63746 + 13.2285i −0.321881 + 0.557513i −0.980876 0.194633i \(-0.937648\pi\)
0.658996 + 0.752147i \(0.270982\pi\)
\(564\) 0 0
\(565\) −7.45017 12.9041i −0.313431 0.542878i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.72508 + 9.91613i 0.240008 + 0.415706i 0.960716 0.277532i \(-0.0895166\pi\)
−0.720708 + 0.693238i \(0.756183\pi\)
\(570\) 0 0
\(571\) −4.13746 + 7.16629i −0.173147 + 0.299900i −0.939519 0.342498i \(-0.888727\pi\)
0.766371 + 0.642398i \(0.222060\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −22.9003 −0.955010
\(576\) 0 0
\(577\) −12.5000 + 21.6506i −0.520382 + 0.901328i 0.479337 + 0.877631i \(0.340877\pi\)
−0.999719 + 0.0236970i \(0.992456\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −15.1873 26.3052i −0.628993 1.08945i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.27492 0.382817 0.191408 0.981510i \(-0.438695\pi\)
0.191408 + 0.981510i \(0.438695\pi\)
\(588\) 0 0
\(589\) 6.27492 0.258553
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.274917 + 0.476171i 0.0112895 + 0.0195540i 0.871615 0.490191i \(-0.163073\pi\)
−0.860325 + 0.509745i \(0.829740\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11.2749 19.5287i 0.460681 0.797922i −0.538314 0.842744i \(-0.680939\pi\)
0.998995 + 0.0448219i \(0.0142720\pi\)
\(600\) 0 0
\(601\) −4.09967 −0.167229 −0.0836145 0.996498i \(-0.526646\pi\)
−0.0836145 + 0.996498i \(0.526646\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.450166 0.779710i 0.0183018 0.0316997i
\(606\) 0 0
\(607\) −3.50000 6.06218i −0.142061 0.246056i 0.786212 0.617957i \(-0.212039\pi\)
−0.928272 + 0.371901i \(0.878706\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.8248 32.6054i −0.761568 1.31907i
\(612\) 0 0
\(613\) 4.27492 7.40437i 0.172662 0.299060i −0.766688 0.642020i \(-0.778096\pi\)
0.939350 + 0.342961i \(0.111430\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 14.4124 24.9630i 0.579282 1.00335i −0.416280 0.909237i \(-0.636666\pi\)
0.995562 0.0941097i \(-0.0300004\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 10.4244 + 18.0556i 0.416977 + 0.722225i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.09967 0.362828
\(630\) 0 0
\(631\) 19.8248 0.789211 0.394605 0.918851i \(-0.370881\pi\)
0.394605 + 0.918851i \(0.370881\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.5619 + 18.2937i 0.419135 + 0.725964i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.82475 + 3.16056i −0.0720734 + 0.124835i −0.899810 0.436282i \(-0.856295\pi\)
0.827736 + 0.561117i \(0.189628\pi\)
\(642\) 0 0
\(643\) −5.37459 −0.211953 −0.105976 0.994369i \(-0.533797\pi\)
−0.105976 + 0.994369i \(0.533797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.0000 29.4449i 0.668339 1.15760i −0.310029 0.950727i \(-0.600339\pi\)
0.978368 0.206870i \(-0.0663277\pi\)
\(648\) 0 0
\(649\) −2.08762 3.61587i −0.0819464 0.141935i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.46221 5.99672i −0.135487 0.234670i 0.790297 0.612725i \(-0.209926\pi\)
−0.925783 + 0.378055i \(0.876593\pi\)
\(654\) 0 0
\(655\) −11.9124 + 20.6328i −0.465455 + 0.806192i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 42.1993 1.64385 0.821926 0.569594i \(-0.192899\pi\)
0.821926 + 0.569594i \(0.192899\pi\)
\(660\) 0 0
\(661\) 3.58762 6.21395i 0.139542 0.241695i −0.787781 0.615955i \(-0.788770\pi\)
0.927323 + 0.374261i \(0.122104\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −10.5498 18.2728i −0.408491 0.707528i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 32.7492 1.26427
\(672\) 0 0
\(673\) 41.5498 1.60163 0.800814 0.598913i \(-0.204400\pi\)
0.800814 + 0.598913i \(0.204400\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.63746 + 11.4964i 0.255098 + 0.441843i 0.964922 0.262536i \(-0.0845588\pi\)
−0.709824 + 0.704379i \(0.751226\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.08762 10.5441i 0.232936 0.403458i −0.725735 0.687975i \(-0.758500\pi\)
0.958671 + 0.284517i \(0.0918332\pi\)
\(684\) 0 0
\(685\) −4.74917 −0.181457
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −29.0997 + 50.4021i −1.10861 + 1.92017i
\(690\) 0 0
\(691\) −5.41238 9.37451i −0.205896 0.356623i 0.744522 0.667598i \(-0.232678\pi\)
−0.950418 + 0.310975i \(0.899344\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 13.5498 + 23.4690i 0.513975 + 0.890230i
\(696\) 0 0
\(697\) −9.09967 + 15.7611i −0.344675 + 0.596994i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.9244 0.488149 0.244074 0.969757i \(-0.421516\pi\)
0.244074 + 0.969757i \(0.421516\pi\)
\(702\) 0 0
\(703\) 7.13746 12.3624i 0.269194 0.466258i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 14.0997 + 24.4213i 0.529524 + 0.917163i 0.999407 + 0.0344340i \(0.0109628\pi\)
−0.469883 + 0.882729i \(0.655704\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 67.2990 2.51684
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.0997 24.4213i −0.525829 0.910762i −0.999547 0.0300860i \(-0.990422\pi\)
0.473718 0.880676i \(-0.342911\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.0997 26.1534i 0.560788 0.971313i
\(726\) 0 0
\(727\) −31.5498 −1.17012 −0.585059 0.810991i \(-0.698929\pi\)
−0.585059 + 0.810991i \(0.698929\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.549834 0.952341i 0.0203364 0.0352236i
\(732\) 0 0
\(733\) 2.96221 + 5.13070i 0.109412 + 0.189507i 0.915532 0.402245i \(-0.131770\pi\)
−0.806120 + 0.591752i \(0.798437\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.450166 0.779710i −0.0165821 0.0287210i
\(738\) 0 0
\(739\) −0.687293 + 1.19043i −0.0252825 + 0.0437905i −0.878390 0.477945i \(-0.841382\pi\)
0.853107 + 0.521735i \(0.174715\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.1993 1.62152 0.810758 0.585381i \(-0.199055\pi\)
0.810758 + 0.585381i \(0.199055\pi\)
\(744\) 0 0
\(745\) −23.8248 + 41.2657i −0.872871 + 1.51186i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 5.22508 + 9.05011i 0.190666 + 0.330243i 0.945471 0.325706i \(-0.105602\pi\)
−0.754805 + 0.655949i \(0.772269\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 73.2749 2.66675
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 12.5498 + 21.7370i 0.454931 + 0.787964i 0.998684 0.0512814i \(-0.0163305\pi\)
−0.543753 + 0.839245i \(0.682997\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.00000 + 6.92820i −0.144432 + 0.250163i
\(768\) 0 0
\(769\) 32.6495 1.17737 0.588686 0.808362i \(-0.299646\pi\)
0.588686 + 0.808362i \(0.299646\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.54983 + 2.68439i −0.0557437 + 0.0965509i −0.892551 0.450947i \(-0.851086\pi\)
0.836807 + 0.547498i \(0.184420\pi\)
\(774\) 0 0
\(775\) −2.86254 4.95807i −0.102826 0.178099i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14.2749 + 24.7249i 0.511452 + 0.885861i
\(780\) 0 0
\(781\) −3.27492 + 5.67232i −0.117186 + 0.202972i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.80066 0.0642684
\(786\) 0 0
\(787\) 1.27492 2.20822i 0.0454459 0.0787146i −0.842408 0.538841i \(-0.818862\pi\)
0.887854 + 0.460126i \(0.152196\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −31.3746 54.3424i −1.11414 1.92975i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −31.4743 −1.11488 −0.557438 0.830219i \(-0.688215\pi\)
−0.557438 + 0.830219i \(0.688215\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.00000 + 12.1244i 0.247025 + 0.427859i
\(804\) 0 0
\(805\) 0 0
\(806\) 0