Properties

Label 5292.2.j.i.1765.12
Level $5292$
Weight $2$
Character 5292.1765
Analytic conductor $42.257$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5292,2,Mod(1765,5292)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5292.1765");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.j (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(42.2568327497\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 1764)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1765.12
Character \(\chi\) \(=\) 5292.1765
Dual form 5292.2.j.i.3529.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.94623 - 3.37097i) q^{5} +(2.18778 + 3.78935i) q^{11} +(-0.792201 + 1.37213i) q^{13} +5.33356 q^{17} -4.64323 q^{19} +(0.183900 - 0.318523i) q^{23} +(-5.07564 - 8.79126i) q^{25} +(5.08750 + 8.81180i) q^{29} +(1.14776 - 1.98798i) q^{31} +10.8803 q^{37} +(0.690443 - 1.19588i) q^{41} +(3.81699 + 6.61122i) q^{43} +(-3.80432 - 6.58928i) q^{47} +0.925693 q^{53} +17.0317 q^{55} +(-0.460475 + 0.797565i) q^{59} +(-3.27780 - 5.67731i) q^{61} +(3.08361 + 5.34097i) q^{65} +(-7.50420 + 12.9976i) q^{67} +4.91059 q^{71} +7.56707 q^{73} +(-0.987715 - 1.71077i) q^{79} +(0.253011 + 0.438227i) q^{83} +(10.3803 - 17.9793i) q^{85} +12.2197 q^{89} +(-9.03679 + 15.6522i) q^{95} +(4.45315 + 7.71308i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{11} + 8 q^{23} - 12 q^{25} + 32 q^{29} + 24 q^{37} - 32 q^{53} + 36 q^{65} + 12 q^{67} - 48 q^{71} + 12 q^{79} + 12 q^{85} - 32 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.94623 3.37097i 0.870381 1.50754i 0.00877856 0.999961i \(-0.497206\pi\)
0.861603 0.507583i \(-0.169461\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.18778 + 3.78935i 0.659642 + 1.14253i 0.980708 + 0.195476i \(0.0626253\pi\)
−0.321067 + 0.947057i \(0.604041\pi\)
\(12\) 0 0
\(13\) −0.792201 + 1.37213i −0.219717 + 0.380561i −0.954721 0.297501i \(-0.903847\pi\)
0.735004 + 0.678062i \(0.237180\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.33356 1.29358 0.646789 0.762669i \(-0.276111\pi\)
0.646789 + 0.762669i \(0.276111\pi\)
\(18\) 0 0
\(19\) −4.64323 −1.06523 −0.532614 0.846358i \(-0.678790\pi\)
−0.532614 + 0.846358i \(0.678790\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.183900 0.318523i 0.0383457 0.0664167i −0.846216 0.532841i \(-0.821125\pi\)
0.884561 + 0.466424i \(0.154458\pi\)
\(24\) 0 0
\(25\) −5.07564 8.79126i −1.01513 1.75825i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.08750 + 8.81180i 0.944724 + 1.63631i 0.756302 + 0.654222i \(0.227004\pi\)
0.188422 + 0.982088i \(0.439663\pi\)
\(30\) 0 0
\(31\) 1.14776 1.98798i 0.206144 0.357052i −0.744353 0.667787i \(-0.767242\pi\)
0.950497 + 0.310735i \(0.100575\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.8803 1.78872 0.894359 0.447351i \(-0.147632\pi\)
0.894359 + 0.447351i \(0.147632\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.690443 1.19588i 0.107829 0.186766i −0.807061 0.590467i \(-0.798943\pi\)
0.914891 + 0.403702i \(0.132277\pi\)
\(42\) 0 0
\(43\) 3.81699 + 6.61122i 0.582086 + 1.00820i 0.995232 + 0.0975372i \(0.0310965\pi\)
−0.413146 + 0.910665i \(0.635570\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.80432 6.58928i −0.554918 0.961145i −0.997910 0.0646200i \(-0.979416\pi\)
0.442992 0.896525i \(-0.353917\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.925693 0.127154 0.0635769 0.997977i \(-0.479749\pi\)
0.0635769 + 0.997977i \(0.479749\pi\)
\(54\) 0 0
\(55\) 17.0317 2.29656
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.460475 + 0.797565i −0.0599487 + 0.103834i −0.894442 0.447184i \(-0.852427\pi\)
0.834493 + 0.551018i \(0.185760\pi\)
\(60\) 0 0
\(61\) −3.27780 5.67731i −0.419679 0.726905i 0.576228 0.817289i \(-0.304524\pi\)
−0.995907 + 0.0903836i \(0.971191\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.08361 + 5.34097i 0.382475 + 0.662466i
\(66\) 0 0
\(67\) −7.50420 + 12.9976i −0.916783 + 1.58792i −0.112514 + 0.993650i \(0.535890\pi\)
−0.804269 + 0.594265i \(0.797443\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.91059 0.582780 0.291390 0.956604i \(-0.405882\pi\)
0.291390 + 0.956604i \(0.405882\pi\)
\(72\) 0 0
\(73\) 7.56707 0.885658 0.442829 0.896606i \(-0.353975\pi\)
0.442829 + 0.896606i \(0.353975\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.987715 1.71077i −0.111127 0.192477i 0.805098 0.593142i \(-0.202113\pi\)
−0.916225 + 0.400665i \(0.868779\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.253011 + 0.438227i 0.0277715 + 0.0481017i 0.879577 0.475756i \(-0.157826\pi\)
−0.851806 + 0.523858i \(0.824492\pi\)
\(84\) 0 0
\(85\) 10.3803 17.9793i 1.12591 1.95013i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.2197 1.29529 0.647645 0.761942i \(-0.275754\pi\)
0.647645 + 0.761942i \(0.275754\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.03679 + 15.6522i −0.927155 + 1.60588i
\(96\) 0 0
\(97\) 4.45315 + 7.71308i 0.452149 + 0.783145i 0.998519 0.0543987i \(-0.0173242\pi\)
−0.546370 + 0.837544i \(0.683991\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.51180 + 9.54672i 0.548445 + 0.949935i 0.998381 + 0.0568740i \(0.0181133\pi\)
−0.449936 + 0.893061i \(0.648553\pi\)
\(102\) 0 0
\(103\) −1.36543 + 2.36499i −0.134540 + 0.233029i −0.925421 0.378939i \(-0.876289\pi\)
0.790882 + 0.611969i \(0.209622\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.7921 1.04331 0.521655 0.853156i \(-0.325315\pi\)
0.521655 + 0.853156i \(0.325315\pi\)
\(108\) 0 0
\(109\) −9.98374 −0.956269 −0.478134 0.878287i \(-0.658687\pi\)
−0.478134 + 0.878287i \(0.658687\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.12019 10.6005i 0.575739 0.997209i −0.420222 0.907421i \(-0.638048\pi\)
0.995961 0.0897875i \(-0.0286188\pi\)
\(114\) 0 0
\(115\) −0.715822 1.23984i −0.0667508 0.115616i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.07280 + 7.05429i −0.370254 + 0.641299i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −20.0511 −1.79343
\(126\) 0 0
\(127\) −13.2005 −1.17135 −0.585677 0.810544i \(-0.699171\pi\)
−0.585677 + 0.810544i \(0.699171\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.54342 4.40532i 0.222219 0.384895i −0.733262 0.679946i \(-0.762003\pi\)
0.955482 + 0.295051i \(0.0953366\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.67208 + 11.5564i 0.570034 + 0.987328i 0.996562 + 0.0828538i \(0.0264034\pi\)
−0.426527 + 0.904475i \(0.640263\pi\)
\(138\) 0 0
\(139\) −4.85642 + 8.41157i −0.411916 + 0.713460i −0.995099 0.0988809i \(-0.968474\pi\)
0.583183 + 0.812341i \(0.301807\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −6.93265 −0.579738
\(144\) 0 0
\(145\) 39.6058 3.28908
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.92116 11.9878i 0.567004 0.982079i −0.429856 0.902897i \(-0.641436\pi\)
0.996860 0.0791820i \(-0.0252308\pi\)
\(150\) 0 0
\(151\) −11.4380 19.8112i −0.930809 1.61221i −0.781942 0.623352i \(-0.785771\pi\)
−0.148867 0.988857i \(-0.547563\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.46762 7.73815i −0.358848 0.621543i
\(156\) 0 0
\(157\) −5.78991 + 10.0284i −0.462085 + 0.800355i −0.999065 0.0432404i \(-0.986232\pi\)
0.536980 + 0.843595i \(0.319565\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3.41155 0.267213 0.133607 0.991034i \(-0.457344\pi\)
0.133607 + 0.991034i \(0.457344\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.69996 8.14057i 0.363694 0.629936i −0.624872 0.780727i \(-0.714849\pi\)
0.988566 + 0.150791i \(0.0481821\pi\)
\(168\) 0 0
\(169\) 5.24484 + 9.08432i 0.403449 + 0.698794i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.20256 5.54700i −0.243486 0.421730i 0.718219 0.695817i \(-0.244958\pi\)
−0.961705 + 0.274087i \(0.911624\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −17.0808 −1.27668 −0.638338 0.769756i \(-0.720378\pi\)
−0.638338 + 0.769756i \(0.720378\pi\)
\(180\) 0 0
\(181\) 1.35988 0.101079 0.0505395 0.998722i \(-0.483906\pi\)
0.0505395 + 0.998722i \(0.483906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 21.1757 36.6773i 1.55687 2.69657i
\(186\) 0 0
\(187\) 11.6687 + 20.2107i 0.853298 + 1.47796i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.94048 15.4854i −0.646911 1.12048i −0.983857 0.178958i \(-0.942727\pi\)
0.336946 0.941524i \(-0.390606\pi\)
\(192\) 0 0
\(193\) 6.50664 11.2698i 0.468358 0.811220i −0.530988 0.847380i \(-0.678179\pi\)
0.999346 + 0.0361591i \(0.0115123\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.36486 −0.453478 −0.226739 0.973956i \(-0.572806\pi\)
−0.226739 + 0.973956i \(0.572806\pi\)
\(198\) 0 0
\(199\) 23.1529 1.64126 0.820631 0.571458i \(-0.193622\pi\)
0.820631 + 0.571458i \(0.193622\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.68753 4.65493i −0.187705 0.325114i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −10.1584 17.5948i −0.702669 1.21706i
\(210\) 0 0
\(211\) −5.67737 + 9.83349i −0.390846 + 0.676965i −0.992561 0.121745i \(-0.961151\pi\)
0.601715 + 0.798711i \(0.294484\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 29.7150 2.02655
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.22525 + 7.31835i −0.284221 + 0.492285i
\(222\) 0 0
\(223\) −13.3206 23.0719i −0.892011 1.54501i −0.837461 0.546498i \(-0.815961\pi\)
−0.0545504 0.998511i \(-0.517373\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.30136 14.3784i −0.550981 0.954326i −0.998204 0.0599042i \(-0.980920\pi\)
0.447224 0.894422i \(-0.352413\pi\)
\(228\) 0 0
\(229\) 7.25072 12.5586i 0.479141 0.829897i −0.520573 0.853817i \(-0.674282\pi\)
0.999714 + 0.0239205i \(0.00761485\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.9804 −1.04691 −0.523456 0.852053i \(-0.675357\pi\)
−0.523456 + 0.852053i \(0.675357\pi\)
\(234\) 0 0
\(235\) −29.6164 −1.93196
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.58994 16.6103i 0.620322 1.07443i −0.369104 0.929388i \(-0.620335\pi\)
0.989426 0.145040i \(-0.0463312\pi\)
\(240\) 0 0
\(241\) −11.6785 20.2277i −0.752276 1.30298i −0.946717 0.322067i \(-0.895623\pi\)
0.194441 0.980914i \(-0.437711\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.67837 6.37112i 0.234049 0.405384i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 30.4619 1.92274 0.961371 0.275257i \(-0.0887631\pi\)
0.961371 + 0.275257i \(0.0887631\pi\)
\(252\) 0 0
\(253\) 1.60933 0.101178
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.40438 + 5.89657i −0.212360 + 0.367818i −0.952453 0.304687i \(-0.901448\pi\)
0.740093 + 0.672505i \(0.234782\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.30000 3.98372i −0.141824 0.245647i 0.786359 0.617769i \(-0.211963\pi\)
−0.928184 + 0.372122i \(0.878630\pi\)
\(264\) 0 0
\(265\) 1.80161 3.12049i 0.110672 0.191690i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.50179 0.518363 0.259182 0.965829i \(-0.416547\pi\)
0.259182 + 0.965829i \(0.416547\pi\)
\(270\) 0 0
\(271\) 6.58381 0.399938 0.199969 0.979802i \(-0.435916\pi\)
0.199969 + 0.979802i \(0.435916\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 22.2088 38.4668i 1.33924 2.31963i
\(276\) 0 0
\(277\) 5.63483 + 9.75982i 0.338564 + 0.586411i 0.984163 0.177266i \(-0.0567254\pi\)
−0.645599 + 0.763677i \(0.723392\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.50741 13.0032i −0.447854 0.775707i 0.550392 0.834907i \(-0.314478\pi\)
−0.998246 + 0.0592000i \(0.981145\pi\)
\(282\) 0 0
\(283\) −7.33657 + 12.7073i −0.436114 + 0.755371i −0.997386 0.0722602i \(-0.976979\pi\)
0.561272 + 0.827631i \(0.310312\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 11.4469 0.673344
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.38981 16.2636i 0.548559 0.950132i −0.449815 0.893122i \(-0.648510\pi\)
0.998374 0.0570099i \(-0.0181567\pi\)
\(294\) 0 0
\(295\) 1.79238 + 3.10449i 0.104356 + 0.180751i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.291371 + 0.504669i 0.0168504 + 0.0291858i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −25.5174 −1.46112
\(306\) 0 0
\(307\) −28.9425 −1.65184 −0.825919 0.563789i \(-0.809343\pi\)
−0.825919 + 0.563789i \(0.809343\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.79681 + 11.7724i −0.385412 + 0.667553i −0.991826 0.127596i \(-0.959274\pi\)
0.606414 + 0.795149i \(0.292607\pi\)
\(312\) 0 0
\(313\) 6.93222 + 12.0070i 0.391832 + 0.678673i 0.992691 0.120682i \(-0.0385080\pi\)
−0.600859 + 0.799355i \(0.705175\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.5428 + 19.9927i 0.648309 + 1.12290i 0.983527 + 0.180764i \(0.0578569\pi\)
−0.335217 + 0.942141i \(0.608810\pi\)
\(318\) 0 0
\(319\) −22.2607 + 38.5566i −1.24636 + 2.15876i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.7649 −1.37796
\(324\) 0 0
\(325\) 16.0837 0.892163
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.82647 + 13.5558i 0.430182 + 0.745097i 0.996889 0.0788227i \(-0.0251161\pi\)
−0.566707 + 0.823920i \(0.691783\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 29.2098 + 50.5929i 1.59590 + 2.76418i
\(336\) 0 0
\(337\) 3.56686 6.17799i 0.194299 0.336537i −0.752371 0.658739i \(-0.771090\pi\)
0.946671 + 0.322203i \(0.104423\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.0442 0.543925
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.77827 4.81211i 0.149146 0.258328i −0.781766 0.623571i \(-0.785681\pi\)
0.930912 + 0.365244i \(0.119014\pi\)
\(348\) 0 0
\(349\) −5.33296 9.23696i −0.285467 0.494443i 0.687256 0.726416i \(-0.258815\pi\)
−0.972722 + 0.231973i \(0.925482\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.42132 11.1221i −0.341772 0.591967i 0.642989 0.765875i \(-0.277694\pi\)
−0.984762 + 0.173908i \(0.944361\pi\)
\(354\) 0 0
\(355\) 9.55715 16.5535i 0.507241 0.878567i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −25.6835 −1.35552 −0.677761 0.735282i \(-0.737050\pi\)
−0.677761 + 0.735282i \(0.737050\pi\)
\(360\) 0 0
\(361\) 2.55954 0.134713
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.7273 25.5084i 0.770861 1.33517i
\(366\) 0 0
\(367\) 8.49197 + 14.7085i 0.443277 + 0.767778i 0.997930 0.0643031i \(-0.0204824\pi\)
−0.554653 + 0.832082i \(0.687149\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 4.38503 7.59509i 0.227048 0.393259i −0.729884 0.683571i \(-0.760426\pi\)
0.956932 + 0.290312i \(0.0937592\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.1213 −0.830288
\(378\) 0 0
\(379\) 11.7002 0.601001 0.300500 0.953782i \(-0.402846\pi\)
0.300500 + 0.953782i \(0.402846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.50360 + 7.80046i −0.230123 + 0.398585i −0.957844 0.287288i \(-0.907246\pi\)
0.727721 + 0.685873i \(0.240580\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.89390 8.47649i −0.248131 0.429775i 0.714876 0.699251i \(-0.246483\pi\)
−0.963007 + 0.269476i \(0.913150\pi\)
\(390\) 0 0
\(391\) 0.980839 1.69886i 0.0496032 0.0859152i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.68929 −0.386890
\(396\) 0 0
\(397\) 13.9186 0.698554 0.349277 0.937020i \(-0.386427\pi\)
0.349277 + 0.937020i \(0.386427\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.7414 + 20.3367i −0.586336 + 1.01556i 0.408371 + 0.912816i \(0.366097\pi\)
−0.994707 + 0.102748i \(0.967236\pi\)
\(402\) 0 0
\(403\) 1.81852 + 3.14976i 0.0905867 + 0.156901i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 23.8038 + 41.2295i 1.17991 + 2.04367i
\(408\) 0 0
\(409\) 6.81225 11.7992i 0.336844 0.583431i −0.646993 0.762496i \(-0.723974\pi\)
0.983837 + 0.179064i \(0.0573071\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.96967 0.0966873
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.97733 6.88894i 0.194305 0.336547i −0.752367 0.658744i \(-0.771088\pi\)
0.946673 + 0.322197i \(0.104421\pi\)
\(420\) 0 0
\(421\) 1.30584 + 2.26178i 0.0636426 + 0.110232i 0.896091 0.443870i \(-0.146395\pi\)
−0.832448 + 0.554102i \(0.813062\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −27.0712 46.8887i −1.31315 2.27444i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.58213 0.0762086 0.0381043 0.999274i \(-0.487868\pi\)
0.0381043 + 0.999274i \(0.487868\pi\)
\(432\) 0 0
\(433\) 5.17110 0.248507 0.124254 0.992250i \(-0.460346\pi\)
0.124254 + 0.992250i \(0.460346\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.853887 + 1.47898i −0.0408470 + 0.0707490i
\(438\) 0 0
\(439\) 12.4806 + 21.6170i 0.595665 + 1.03172i 0.993453 + 0.114244i \(0.0364446\pi\)
−0.397788 + 0.917477i \(0.630222\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.542263 + 0.939227i 0.0257637 + 0.0446240i 0.878620 0.477522i \(-0.158465\pi\)
−0.852856 + 0.522146i \(0.825132\pi\)
\(444\) 0 0
\(445\) 23.7825 41.1924i 1.12740 1.95271i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.23372 −0.199802 −0.0999008 0.994997i \(-0.531853\pi\)
−0.0999008 + 0.994997i \(0.531853\pi\)
\(450\) 0 0
\(451\) 6.04216 0.284514
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.1513 + 31.4390i 0.849083 + 1.47065i 0.882028 + 0.471197i \(0.156178\pi\)
−0.0329453 + 0.999457i \(0.510489\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.71236 + 2.96589i 0.0797524 + 0.138135i 0.903143 0.429340i \(-0.141254\pi\)
−0.823391 + 0.567475i \(0.807920\pi\)
\(462\) 0 0
\(463\) 2.38499 4.13092i 0.110840 0.191980i −0.805269 0.592909i \(-0.797979\pi\)
0.916109 + 0.400929i \(0.131313\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.0979 0.930021 0.465010 0.885305i \(-0.346051\pi\)
0.465010 + 0.885305i \(0.346051\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.7015 + 28.9279i −0.767936 + 1.33010i
\(474\) 0 0
\(475\) 23.5673 + 40.8198i 1.08134 + 1.87294i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.42528 + 14.5930i 0.384961 + 0.666772i 0.991764 0.128080i \(-0.0408816\pi\)
−0.606803 + 0.794852i \(0.707548\pi\)
\(480\) 0 0
\(481\) −8.61941 + 14.9293i −0.393011 + 0.680716i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 34.6675 1.57417
\(486\) 0 0
\(487\) 23.9831 1.08678 0.543389 0.839481i \(-0.317141\pi\)
0.543389 + 0.839481i \(0.317141\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.07281 1.85816i 0.0484153 0.0838577i −0.840802 0.541342i \(-0.817916\pi\)
0.889217 + 0.457485i \(0.151250\pi\)
\(492\) 0 0
\(493\) 27.1345 + 46.9983i 1.22207 + 2.11670i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 13.8577 24.0023i 0.620357 1.07449i −0.369062 0.929405i \(-0.620321\pi\)
0.989419 0.145085i \(-0.0463455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.4265 −0.999949 −0.499974 0.866040i \(-0.666657\pi\)
−0.499974 + 0.866040i \(0.666657\pi\)
\(504\) 0 0
\(505\) 42.9090 1.90943
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.6844 25.4342i 0.650876 1.12735i −0.332034 0.943267i \(-0.607735\pi\)
0.982911 0.184083i \(-0.0589316\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.31488 + 9.20563i 0.234201 + 0.405649i
\(516\) 0 0
\(517\) 16.6461 28.8318i 0.732093 1.26802i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16.5078 −0.723219 −0.361610 0.932330i \(-0.617773\pi\)
−0.361610 + 0.932330i \(0.617773\pi\)
\(522\) 0 0
\(523\) −44.6952 −1.95439 −0.977193 0.212352i \(-0.931888\pi\)
−0.977193 + 0.212352i \(0.931888\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.12166 10.6030i 0.266664 0.461875i
\(528\) 0 0
\(529\) 11.4324 + 19.8014i 0.497059 + 0.860932i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.09394 + 1.89476i 0.0473838 + 0.0820711i
\(534\) 0 0
\(535\) 21.0039 36.3798i 0.908078 1.57284i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −20.0737 −0.863037 −0.431519 0.902104i \(-0.642022\pi\)
−0.431519 + 0.902104i \(0.642022\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −19.4307 + 33.6549i −0.832319 + 1.44162i
\(546\) 0 0
\(547\) 6.35012 + 10.9987i 0.271512 + 0.470272i 0.969249 0.246082i \(-0.0791432\pi\)
−0.697738 + 0.716353i \(0.745810\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −23.6224 40.9152i −1.00635 1.74305i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.6949 −0.622642 −0.311321 0.950305i \(-0.600771\pi\)
−0.311321 + 0.950305i \(0.600771\pi\)
\(558\) 0 0
\(559\) −12.0953 −0.511576
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.3930 23.1974i 0.564448 0.977653i −0.432653 0.901561i \(-0.642422\pi\)
0.997101 0.0760922i \(-0.0242443\pi\)
\(564\) 0 0
\(565\) −23.8226 41.2620i −1.00222 1.73590i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.24168 + 5.61475i 0.135898 + 0.235383i 0.925940 0.377670i \(-0.123275\pi\)
−0.790042 + 0.613053i \(0.789941\pi\)
\(570\) 0 0
\(571\) −7.81632 + 13.5383i −0.327103 + 0.566559i −0.981936 0.189215i \(-0.939406\pi\)
0.654833 + 0.755774i \(0.272739\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.73363 −0.155703
\(576\) 0 0
\(577\) −29.1600 −1.21395 −0.606974 0.794722i \(-0.707617\pi\)
−0.606974 + 0.794722i \(0.707617\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.02522 + 3.50778i 0.0838759 + 0.145277i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.33110 + 4.03758i 0.0962146 + 0.166649i 0.910115 0.414356i \(-0.135993\pi\)
−0.813900 + 0.581005i \(0.802660\pi\)
\(588\) 0 0
\(589\) −5.32932 + 9.23065i −0.219591 + 0.380342i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −31.6644 −1.30030 −0.650150 0.759805i \(-0.725294\pi\)
−0.650150 + 0.759805i \(0.725294\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.15268 + 8.92470i −0.210533 + 0.364653i −0.951881 0.306467i \(-0.900853\pi\)
0.741349 + 0.671120i \(0.234187\pi\)
\(600\) 0 0
\(601\) −4.64993 8.05391i −0.189674 0.328526i 0.755467 0.655186i \(-0.227410\pi\)
−0.945142 + 0.326661i \(0.894077\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 15.8532 + 27.4586i 0.644525 + 1.11635i
\(606\) 0 0
\(607\) −10.2484 + 17.7507i −0.415969 + 0.720480i −0.995530 0.0944495i \(-0.969891\pi\)
0.579561 + 0.814929i \(0.303224\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0551 0.487699
\(612\) 0 0
\(613\) −14.3448 −0.579381 −0.289691 0.957120i \(-0.593552\pi\)
−0.289691 + 0.957120i \(0.593552\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.47499 11.2150i 0.260673 0.451499i −0.705748 0.708463i \(-0.749389\pi\)
0.966421 + 0.256964i \(0.0827221\pi\)
\(618\) 0 0
\(619\) 17.6990 + 30.6556i 0.711383 + 1.23215i 0.964338 + 0.264674i \(0.0852642\pi\)
−0.252955 + 0.967478i \(0.581402\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −13.6460 + 23.6355i −0.545839 + 0.945422i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 58.0310 2.31385
\(630\) 0 0
\(631\) 33.1936 1.32141 0.660707 0.750644i \(-0.270256\pi\)
0.660707 + 0.750644i \(0.270256\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −25.6912 + 44.4985i −1.01952 + 1.76587i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.119634 0.207213i −0.00472528 0.00818442i 0.863653 0.504087i \(-0.168171\pi\)
−0.868378 + 0.495902i \(0.834837\pi\)
\(642\) 0 0
\(643\) −4.57211 + 7.91913i −0.180307 + 0.312300i −0.941985 0.335655i \(-0.891042\pi\)
0.761678 + 0.647955i \(0.224376\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.31214 −0.248156 −0.124078 0.992272i \(-0.539597\pi\)
−0.124078 + 0.992272i \(0.539597\pi\)
\(648\) 0 0
\(649\) −4.02968 −0.158179
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.27888 + 3.94713i −0.0891793 + 0.154463i −0.907164 0.420776i \(-0.861758\pi\)
0.817985 + 0.575239i \(0.195091\pi\)
\(654\) 0 0
\(655\) −9.90015 17.1476i −0.386831 0.670011i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 16.4631 + 28.5149i 0.641311 + 1.11078i 0.985140 + 0.171751i \(0.0549425\pi\)
−0.343829 + 0.939032i \(0.611724\pi\)
\(660\) 0 0
\(661\) −0.270668 + 0.468811i −0.0105278 + 0.0182346i −0.871241 0.490855i \(-0.836684\pi\)
0.860714 + 0.509090i \(0.170018\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.74235 0.144905
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 14.3422 24.8415i 0.553676 0.958994i
\(672\) 0 0
\(673\) −11.8205 20.4737i −0.455647 0.789204i 0.543078 0.839682i \(-0.317259\pi\)
−0.998725 + 0.0504780i \(0.983926\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.36494 2.36415i −0.0524591 0.0908618i 0.838603 0.544742i \(-0.183373\pi\)
−0.891062 + 0.453881i \(0.850039\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 31.9279 1.22169 0.610844 0.791751i \(-0.290830\pi\)
0.610844 + 0.791751i \(0.290830\pi\)
\(684\) 0 0
\(685\) 51.9417 1.98459
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.733335 + 1.27017i −0.0279378 + 0.0483897i
\(690\) 0 0
\(691\) 1.19103 + 2.06292i 0.0453089 + 0.0784773i 0.887790 0.460248i \(-0.152239\pi\)
−0.842482 + 0.538725i \(0.818906\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18.9034 + 32.7417i 0.717048 + 1.24196i
\(696\) 0 0
\(697\) 3.68252 6.37831i 0.139485 0.241596i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −50.3767 −1.90270 −0.951350 0.308111i \(-0.900303\pi\)
−0.951350 + 0.308111i \(0.900303\pi\)
\(702\) 0 0
\(703\) −50.5199 −1.90539
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −20.1600 34.9182i −0.757126 1.31138i −0.944310 0.329056i \(-0.893269\pi\)
0.187184 0.982325i \(-0.440064\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.422146 0.731178i −0.0158095 0.0273828i
\(714\) 0 0
\(715\) −13.4926 + 23.3698i −0.504593 + 0.873981i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34.0893 1.27132 0.635658 0.771971i \(-0.280729\pi\)
0.635658 + 0.771971i \(0.280729\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 51.6446 89.4510i 1.91803 3.32213i
\(726\) 0 0
\(727\) 10.9453 + 18.9578i 0.405938 + 0.703105i 0.994430 0.105398i \(-0.0336117\pi\)
−0.588492 + 0.808503i \(0.700278\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20.3581 + 35.2613i 0.752973 + 1.30419i
\(732\) 0 0
\(733\) 4.34416 7.52430i 0.160455 0.277916i −0.774577 0.632480i \(-0.782037\pi\)
0.935032 + 0.354563i \(0.115370\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −65.6702 −2.41899
\(738\) 0 0
\(739\) 6.69385 0.246237 0.123119 0.992392i \(-0.460710\pi\)
0.123119 + 0.992392i \(0.460710\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21.5001 + 37.2392i −0.788761 + 1.36617i 0.137965 + 0.990437i \(0.455944\pi\)
−0.926726 + 0.375737i \(0.877389\pi\)
\(744\) 0 0
\(745\) −26.9404 46.6621i −0.987019 1.70957i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.36369 14.4863i 0.305196 0.528614i −0.672109 0.740452i \(-0.734612\pi\)
0.977305 + 0.211838i \(0.0679448\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −89.0438 −3.24064
\(756\) 0 0
\(757\) −4.68561 −0.170301 −0.0851507 0.996368i \(-0.527137\pi\)
−0.0851507 + 0.996368i \(0.527137\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −25.8242 + 44.7288i −0.936127 + 1.62142i −0.163514 + 0.986541i \(0.552283\pi\)
−0.772613 + 0.634878i \(0.781050\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.729576 1.26366i −0.0263435 0.0456282i
\(768\) 0 0
\(769\) 15.3910 26.6580i 0.555014 0.961313i −0.442888 0.896577i \(-0.646046\pi\)
0.997902 0.0647361i \(-0.0206205\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −27.0517 −0.972982 −0.486491 0.873686i \(-0.661723\pi\)
−0.486491 + 0.873686i \(0.661723\pi\)
\(774\) 0 0
\(775\) −23.3025 −0.837050
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.20588 + 5.55275i −0.114863 + 0.198948i
\(780\) 0 0
\(781\) 10.7433 + 18.6080i 0.384426 + 0.665845i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 22.5370 + 39.0352i 0.804380 + 1.39323i
\(786\) 0 0
\(787\) 17.5997 30.4837i 0.627363 1.08662i −0.360716 0.932676i \(-0.617468\pi\)
0.988079 0.153949i \(-0.0491992\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 10.3867 0.368842
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.8268 41.2692i 0.843988 1.46183i −0.0425084 0.999096i \(-0.513535\pi\)
0.886497 0.462735i \(-0.153132\pi\)
\(798\) 0 0
\(799\) −20.2906 35.1443i −0.717829 1.24332i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16.5551 + 28.6743i 0.584217 + 1.01189i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −19.7542 −0.694521 −0.347261 0.937769i \(-0.612888\pi\)
−0.347261 + 0.937769i \(0.612888\pi\)
\(810\) 0 0
\(811\) −49.2424 −1.72913 −0.864567 0.502518i \(-0.832407\pi\)
−0.864567 + 0.502518i \(0.832407\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.63967 11.5002i 0.232577 0.402836i
\(816\) 0 0
\(817\) −17.7231 30.6974i −0.620054 1.07397i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5.00013 + 8.66048i 0.174506 + 0.302253i 0.939990 0.341202i \(-0.110834\pi\)
−0.765484 + 0.643455i \(0.777501\pi\)
\(822\) 0 0
\(823\) 17.5138 30.3348i 0.610493 1.05741i −0.380664 0.924713i \(-0.624305\pi\)
0.991157 0.132692i \(-0.0423621\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.7079 0.789631 0.394816 0.918760i \(-0.370808\pi\)
0.394816 + 0.918760i \(0.370808\pi\)
\(828\) 0 0
\(829\) −12.4417 −0.432117 −0.216058 0.976380i \(-0.569320\pi\)
−0.216058 + 0.976380i \(0.569320\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −18.2944 31.6869i −0.633105 1.09657i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 13.8249 + 23.9455i 0.477290 + 0.826690i 0.999661 0.0260281i \(-0.00828595\pi\)
−0.522372 + 0.852718i \(0.674953\pi\)
\(840\) 0 0
\(841\) −37.2652 + 64.5453i −1.28501 + 2.22570i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 40.8307 1.40462
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.00089 3.46564i 0.0685896 0.118801i
\(852\) 0 0
\(853\) −22.0459 38.1847i −0.754839 1.30742i −0.945454 0.325754i \(-0.894382\pi\)
0.190616 0.981665i \(-0.438952\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −13.3838 23.1814i −0.457182 0.791862i 0.541629 0.840618i \(-0.317808\pi\)
−0.998811 + 0.0487557i \(0.984474\pi\)
\(858\) 0 0
\(859\) 10.0951 17.4852i 0.344439 0.596587i −0.640812 0.767698i \(-0.721402\pi\)
0.985252 + 0.171111i \(0.0547357\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.49075 −0.323069 −0.161534 0.986867i \(-0.551644\pi\)
−0.161534 + 0.986867i \(0.551644\pi\)
\(864\) 0 0
\(865\) −24.9317 −0.847703
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.32182 7.48560i 0.146608 0.253932i
\(870\) 0 0
\(871\) −11.8897 20.5935i −0.402866 0.697784i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −14.6227 + 25.3273i −0.493774 + 0.855242i −0.999974 0.00717380i \(-0.997716\pi\)
0.506200 + 0.862416i \(0.331050\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −37.2768 −1.25589 −0.627944 0.778259i \(-0.716103\pi\)
−0.627944 + 0.778259i \(0.716103\pi\)
\(882\) 0 0
\(883\) −56.9436 −1.91630 −0.958152 0.286260i \(-0.907588\pi\)
−0.958152 + 0.286260i \(0.907588\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.96127 + 8.59316i −0.166583 + 0.288530i −0.937216 0.348749i \(-0.886607\pi\)
0.770633 + 0.637279i \(0.219940\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 17.6643 + 30.5955i 0.591114 + 1.02384i
\(894\) 0 0
\(895\) −33.2431 + 57.5787i −1.11119 + 1.92465i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 23.3569 0.778997
\(900\) 0 0
\(901\) 4.93724 0.164483
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.64664 4.58412i 0.0879774 0.152381i
\(906\) 0 0
\(907\) 12.2887 + 21.2847i 0.408040 + 0.706747i 0.994670 0.103109i \(-0.0328789\pi\)
−0.586630 + 0.809855i \(0.699546\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −9.73496 16.8614i −0.322534 0.558645i 0.658476 0.752601i \(-0.271201\pi\)
−0.981010 + 0.193957i \(0.937868\pi\)
\(912\) 0 0
\(913\) −1.10707 + 1.91749i −0.0366385 + 0.0634598i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −13.2398 −0.436742 −0.218371 0.975866i \(-0.570074\pi\)
−0.218371 + 0.975866i \(0.570074\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.89017 + 6.73798i −0.128047 + 0.221783i
\(924\) 0 0
\(925\) −55.2247 95.6519i −1.81578 3.14502i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15.8682 + 27.4845i 0.520618 + 0.901737i 0.999713 + 0.0239734i \(0.00763170\pi\)
−0.479095 + 0.877763i \(0.659035\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 90.8398 2.97078
\(936\) 0 0
\(937\) −13.5019 −0.441087 −0.220543 0.975377i \(-0.570783\pi\)
−0.220543 + 0.975377i \(0.570783\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −19.8286 + 34.3441i −0.646394 + 1.11959i 0.337584 + 0.941295i \(0.390390\pi\)
−0.983978 + 0.178291i \(0.942943\pi\)
\(942\) 0 0
\(943\) −0.253944 0.439845i −0.00826957 0.0143233i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −30.5172 52.8573i −0.991675 1.71763i −0.607350 0.794434i \(-0.707768\pi\)
−0.384325 0.923198i \(-0.625566\pi\)
\(948\) 0 0
\(949\) −5.99464 + 10.3830i −0.194594 + 0.337047i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.22726 −0.169328 −0.0846638 0.996410i \(-0.526982\pi\)
−0.0846638 + 0.996410i \(0.526982\pi\)
\(954\) 0 0
\(955\) −69.6010 −2.25224
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 12.8653 + 22.2833i 0.415009 + 0.718817i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −25.3269 43.8674i −0.815301 1.41214i
\(966\) 0 0
\(967\) 10.2035 17.6729i 0.328121 0.568323i −0.654018 0.756479i \(-0.726918\pi\)
0.982139 + 0.188156i \(0.0602511\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.17880 −0.0378296 −0.0189148 0.999821i \(-0.506021\pi\)
−0.0189148 + 0.999821i \(0.506021\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.10487 7.10984i 0.131326 0.227464i −0.792862 0.609402i \(-0.791410\pi\)
0.924188 + 0.381938i \(0.124743\pi\)
\(978\) 0 0
\(979\) 26.7342 + 46.3049i 0.854427 + 1.47991i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −0.753481 1.30507i −0.0240323 0.0416252i 0.853759 0.520668i \(-0.174317\pi\)
−0.877791 + 0.479043i \(0.840984\pi\)
\(984\) 0 0
\(985\) −12.3875 + 21.4558i −0.394698 + 0.683638i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.80777 0.0892820
\(990\) 0 0
\(991\) 32.4459 1.03068 0.515339 0.856987i \(-0.327666\pi\)
0.515339 + 0.856987i \(0.327666\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 45.0608 78.0476i 1.42852 2.47428i
\(996\) 0 0
\(997\) 6.26198 + 10.8461i 0.198319 + 0.343498i 0.947983 0.318320i \(-0.103119\pi\)
−0.749665 + 0.661818i \(0.769785\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5292.2.j.i.1765.12 24
3.2 odd 2 1764.2.j.i.589.10 yes 24
7.2 even 3 5292.2.l.j.361.1 24
7.3 odd 6 5292.2.i.j.1549.1 24
7.4 even 3 5292.2.i.j.1549.12 24
7.5 odd 6 5292.2.l.j.361.12 24
7.6 odd 2 inner 5292.2.j.i.1765.1 24
9.2 odd 6 1764.2.j.i.1177.10 yes 24
9.7 even 3 inner 5292.2.j.i.3529.12 24
21.2 odd 6 1764.2.l.j.949.2 24
21.5 even 6 1764.2.l.j.949.11 24
21.11 odd 6 1764.2.i.j.373.7 24
21.17 even 6 1764.2.i.j.373.6 24
21.20 even 2 1764.2.j.i.589.3 24
63.2 odd 6 1764.2.i.j.1537.7 24
63.11 odd 6 1764.2.l.j.961.2 24
63.16 even 3 5292.2.i.j.2125.12 24
63.20 even 6 1764.2.j.i.1177.3 yes 24
63.25 even 3 5292.2.l.j.3313.1 24
63.34 odd 6 inner 5292.2.j.i.3529.1 24
63.38 even 6 1764.2.l.j.961.11 24
63.47 even 6 1764.2.i.j.1537.6 24
63.52 odd 6 5292.2.l.j.3313.12 24
63.61 odd 6 5292.2.i.j.2125.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1764.2.i.j.373.6 24 21.17 even 6
1764.2.i.j.373.7 24 21.11 odd 6
1764.2.i.j.1537.6 24 63.47 even 6
1764.2.i.j.1537.7 24 63.2 odd 6
1764.2.j.i.589.3 24 21.20 even 2
1764.2.j.i.589.10 yes 24 3.2 odd 2
1764.2.j.i.1177.3 yes 24 63.20 even 6
1764.2.j.i.1177.10 yes 24 9.2 odd 6
1764.2.l.j.949.2 24 21.2 odd 6
1764.2.l.j.949.11 24 21.5 even 6
1764.2.l.j.961.2 24 63.11 odd 6
1764.2.l.j.961.11 24 63.38 even 6
5292.2.i.j.1549.1 24 7.3 odd 6
5292.2.i.j.1549.12 24 7.4 even 3
5292.2.i.j.2125.1 24 63.61 odd 6
5292.2.i.j.2125.12 24 63.16 even 3
5292.2.j.i.1765.1 24 7.6 odd 2 inner
5292.2.j.i.1765.12 24 1.1 even 1 trivial
5292.2.j.i.3529.1 24 63.34 odd 6 inner
5292.2.j.i.3529.12 24 9.7 even 3 inner
5292.2.l.j.361.1 24 7.2 even 3
5292.2.l.j.361.12 24 7.5 odd 6
5292.2.l.j.3313.1 24 63.25 even 3
5292.2.l.j.3313.12 24 63.52 odd 6