Properties

Label 2736.3.o.q.721.11
Level $2736$
Weight $3$
Character 2736.721
Analytic conductor $74.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,3,Mod(721,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.721");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.o (of order \(2\), degree \(1\), 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: \(74.5506003290\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 264 x^{18} + 28274 x^{16} - 1545308 x^{14} + 45358441 x^{12} - 637328868 x^{10} + 1825819356 x^{8} + 32794262368 x^{6} + 135580415344 x^{4} + \cdots + 194396337216 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{32} \)
Twist minimal: no (minimal twist has level 1368)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 721.11
Root \(0.399553 - 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 2736.721
Dual form 2736.3.o.q.721.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.399553 q^{5} -9.64754 q^{7} +O(q^{10})\) \(q+0.399553 q^{5} -9.64754 q^{7} -9.57683 q^{11} -9.40920i q^{13} +25.3458 q^{17} +(1.88030 - 18.9067i) q^{19} -14.2995 q^{23} -24.8404 q^{25} +10.9418i q^{29} +12.8914i q^{31} -3.85470 q^{35} -3.29545i q^{37} -63.6191i q^{41} +26.8821 q^{43} -18.1542 q^{47} +44.0749 q^{49} +36.7558i q^{53} -3.82645 q^{55} +12.5340i q^{59} +46.8960 q^{61} -3.75947i q^{65} -71.4070i q^{67} -36.3839i q^{71} -60.6094 q^{73} +92.3928 q^{77} +101.769i q^{79} -63.1863 q^{83} +10.1270 q^{85} +107.557i q^{89} +90.7756i q^{91} +(0.751278 - 7.55424i) q^{95} +120.705i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 16 q^{7} + 8 q^{19} + 68 q^{25} + 128 q^{43} + 116 q^{49} - 144 q^{55} - 104 q^{61} - 88 q^{73} - 280 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(5\) 0.399553 0.0799105 0.0399553 0.999201i \(-0.487278\pi\)
0.0399553 + 0.999201i \(0.487278\pi\)
\(6\) 0 0
\(7\) −9.64754 −1.37822 −0.689110 0.724657i \(-0.741998\pi\)
−0.689110 + 0.724657i \(0.741998\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −9.57683 −0.870621 −0.435311 0.900280i \(-0.643361\pi\)
−0.435311 + 0.900280i \(0.643361\pi\)
\(12\) 0 0
\(13\) 9.40920i 0.723785i −0.932220 0.361892i \(-0.882131\pi\)
0.932220 0.361892i \(-0.117869\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 25.3458 1.49093 0.745464 0.666546i \(-0.232228\pi\)
0.745464 + 0.666546i \(0.232228\pi\)
\(18\) 0 0
\(19\) 1.88030 18.9067i 0.0989631 0.995091i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −14.2995 −0.621716 −0.310858 0.950456i \(-0.600616\pi\)
−0.310858 + 0.950456i \(0.600616\pi\)
\(24\) 0 0
\(25\) −24.8404 −0.993614
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.9418i 0.377302i 0.982044 + 0.188651i \(0.0604115\pi\)
−0.982044 + 0.188651i \(0.939588\pi\)
\(30\) 0 0
\(31\) 12.8914i 0.415853i 0.978144 + 0.207926i \(0.0666714\pi\)
−0.978144 + 0.207926i \(0.933329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.85470 −0.110134
\(36\) 0 0
\(37\) 3.29545i 0.0890663i −0.999008 0.0445332i \(-0.985820\pi\)
0.999008 0.0445332i \(-0.0141800\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 63.6191i 1.55168i −0.630927 0.775842i \(-0.717325\pi\)
0.630927 0.775842i \(-0.282675\pi\)
\(42\) 0 0
\(43\) 26.8821 0.625166 0.312583 0.949891i \(-0.398806\pi\)
0.312583 + 0.949891i \(0.398806\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −18.1542 −0.386259 −0.193129 0.981173i \(-0.561864\pi\)
−0.193129 + 0.981173i \(0.561864\pi\)
\(48\) 0 0
\(49\) 44.0749 0.899489
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 36.7558i 0.693506i 0.937956 + 0.346753i \(0.112716\pi\)
−0.937956 + 0.346753i \(0.887284\pi\)
\(54\) 0 0
\(55\) −3.82645 −0.0695718
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.5340i 0.212440i 0.994343 + 0.106220i \(0.0338748\pi\)
−0.994343 + 0.106220i \(0.966125\pi\)
\(60\) 0 0
\(61\) 46.8960 0.768787 0.384394 0.923169i \(-0.374411\pi\)
0.384394 + 0.923169i \(0.374411\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.75947i 0.0578380i
\(66\) 0 0
\(67\) 71.4070i 1.06578i −0.846186 0.532888i \(-0.821107\pi\)
0.846186 0.532888i \(-0.178893\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 36.3839i 0.512449i −0.966617 0.256225i \(-0.917521\pi\)
0.966617 0.256225i \(-0.0824787\pi\)
\(72\) 0 0
\(73\) −60.6094 −0.830266 −0.415133 0.909761i \(-0.636265\pi\)
−0.415133 + 0.909761i \(0.636265\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 92.3928 1.19991
\(78\) 0 0
\(79\) 101.769i 1.28821i 0.764936 + 0.644106i \(0.222770\pi\)
−0.764936 + 0.644106i \(0.777230\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −63.1863 −0.761281 −0.380640 0.924723i \(-0.624296\pi\)
−0.380640 + 0.924723i \(0.624296\pi\)
\(84\) 0 0
\(85\) 10.1270 0.119141
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 107.557i 1.20851i 0.796792 + 0.604254i \(0.206529\pi\)
−0.796792 + 0.604254i \(0.793471\pi\)
\(90\) 0 0
\(91\) 90.7756i 0.997534i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.751278 7.55424i 0.00790819 0.0795183i
\(96\) 0 0
\(97\) 120.705i 1.24439i 0.782864 + 0.622193i \(0.213758\pi\)
−0.782864 + 0.622193i \(0.786242\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 122.849 1.21632 0.608162 0.793813i \(-0.291907\pi\)
0.608162 + 0.793813i \(0.291907\pi\)
\(102\) 0 0
\(103\) 43.7202i 0.424468i 0.977219 + 0.212234i \(0.0680739\pi\)
−0.977219 + 0.212234i \(0.931926\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 176.900i 1.65327i 0.562738 + 0.826635i \(0.309748\pi\)
−0.562738 + 0.826635i \(0.690252\pi\)
\(108\) 0 0
\(109\) 141.865i 1.30151i 0.759287 + 0.650756i \(0.225548\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 91.8737i 0.813041i −0.913642 0.406521i \(-0.866742\pi\)
0.913642 0.406521i \(-0.133258\pi\)
\(114\) 0 0
\(115\) −5.71339 −0.0496816
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −244.524 −2.05482
\(120\) 0 0
\(121\) −29.2843 −0.242019
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −19.9139 −0.159311
\(126\) 0 0
\(127\) 200.209i 1.57645i 0.615388 + 0.788225i \(0.288999\pi\)
−0.615388 + 0.788225i \(0.711001\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −193.983 −1.48078 −0.740392 0.672175i \(-0.765360\pi\)
−0.740392 + 0.672175i \(0.765360\pi\)
\(132\) 0 0
\(133\) −18.1402 + 182.403i −0.136393 + 1.37145i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 239.550 1.74854 0.874272 0.485437i \(-0.161339\pi\)
0.874272 + 0.485437i \(0.161339\pi\)
\(138\) 0 0
\(139\) −62.8976 −0.452501 −0.226250 0.974069i \(-0.572647\pi\)
−0.226250 + 0.974069i \(0.572647\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 90.1104i 0.630142i
\(144\) 0 0
\(145\) 4.37181i 0.0301504i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 88.2998 0.592616 0.296308 0.955092i \(-0.404244\pi\)
0.296308 + 0.955092i \(0.404244\pi\)
\(150\) 0 0
\(151\) 206.583i 1.36810i 0.729436 + 0.684049i \(0.239783\pi\)
−0.729436 + 0.684049i \(0.760217\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.15081i 0.0332310i
\(156\) 0 0
\(157\) 26.7209 0.170197 0.0850983 0.996373i \(-0.472880\pi\)
0.0850983 + 0.996373i \(0.472880\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 137.955 0.856861
\(162\) 0 0
\(163\) 97.2877 0.596857 0.298428 0.954432i \(-0.403538\pi\)
0.298428 + 0.954432i \(0.403538\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 223.241i 1.33678i −0.743813 0.668388i \(-0.766985\pi\)
0.743813 0.668388i \(-0.233015\pi\)
\(168\) 0 0
\(169\) 80.4669 0.476135
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 204.170i 1.18018i −0.807339 0.590088i \(-0.799093\pi\)
0.807339 0.590088i \(-0.200907\pi\)
\(174\) 0 0
\(175\) 239.648 1.36942
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 232.055i 1.29640i −0.761471 0.648199i \(-0.775522\pi\)
0.761471 0.648199i \(-0.224478\pi\)
\(180\) 0 0
\(181\) 331.929i 1.83386i 0.399046 + 0.916931i \(0.369341\pi\)
−0.399046 + 0.916931i \(0.630659\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.31671i 0.00711734i
\(186\) 0 0
\(187\) −242.732 −1.29803
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.3760 0.0909740 0.0454870 0.998965i \(-0.485516\pi\)
0.0454870 + 0.998965i \(0.485516\pi\)
\(192\) 0 0
\(193\) 76.4470i 0.396098i −0.980192 0.198049i \(-0.936539\pi\)
0.980192 0.198049i \(-0.0634606\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −160.689 −0.815682 −0.407841 0.913053i \(-0.633718\pi\)
−0.407841 + 0.913053i \(0.633718\pi\)
\(198\) 0 0
\(199\) 65.4612 0.328951 0.164475 0.986381i \(-0.447407\pi\)
0.164475 + 0.986381i \(0.447407\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 105.561i 0.520005i
\(204\) 0 0
\(205\) 25.4192i 0.123996i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.0073 + 181.067i −0.0861594 + 0.866347i
\(210\) 0 0
\(211\) 2.14353i 0.0101589i 0.999987 + 0.00507945i \(0.00161685\pi\)
−0.999987 + 0.00507945i \(0.998383\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.7408 0.0499573
\(216\) 0 0
\(217\) 124.371i 0.573136i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 238.483i 1.07911i
\(222\) 0 0
\(223\) 213.813i 0.958801i 0.877596 + 0.479401i \(0.159146\pi\)
−0.877596 + 0.479401i \(0.840854\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 255.635i 1.12615i 0.826407 + 0.563074i \(0.190381\pi\)
−0.826407 + 0.563074i \(0.809619\pi\)
\(228\) 0 0
\(229\) −8.51136 −0.0371675 −0.0185837 0.999827i \(-0.505916\pi\)
−0.0185837 + 0.999827i \(0.505916\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −258.670 −1.11017 −0.555087 0.831793i \(-0.687315\pi\)
−0.555087 + 0.831793i \(0.687315\pi\)
\(234\) 0 0
\(235\) −7.25354 −0.0308661
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −198.289 −0.829659 −0.414830 0.909899i \(-0.636159\pi\)
−0.414830 + 0.909899i \(0.636159\pi\)
\(240\) 0 0
\(241\) 276.361i 1.14673i 0.819301 + 0.573363i \(0.194362\pi\)
−0.819301 + 0.573363i \(0.805638\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 17.6103 0.0718786
\(246\) 0 0
\(247\) −177.897 17.6921i −0.720232 0.0716280i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 36.0391 0.143582 0.0717910 0.997420i \(-0.477129\pi\)
0.0717910 + 0.997420i \(0.477129\pi\)
\(252\) 0 0
\(253\) 136.944 0.541279
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 54.9763i 0.213916i 0.994264 + 0.106958i \(0.0341110\pi\)
−0.994264 + 0.106958i \(0.965889\pi\)
\(258\) 0 0
\(259\) 31.7930i 0.122753i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 412.873 1.56986 0.784930 0.619585i \(-0.212699\pi\)
0.784930 + 0.619585i \(0.212699\pi\)
\(264\) 0 0
\(265\) 14.6859i 0.0554185i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 53.5609i 0.199111i −0.995032 0.0995556i \(-0.968258\pi\)
0.995032 0.0995556i \(-0.0317421\pi\)
\(270\) 0 0
\(271\) −144.211 −0.532144 −0.266072 0.963953i \(-0.585726\pi\)
−0.266072 + 0.963953i \(0.585726\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 237.892 0.865062
\(276\) 0 0
\(277\) −147.518 −0.532555 −0.266278 0.963896i \(-0.585794\pi\)
−0.266278 + 0.963896i \(0.585794\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 174.862i 0.622285i 0.950363 + 0.311143i \(0.100712\pi\)
−0.950363 + 0.311143i \(0.899288\pi\)
\(282\) 0 0
\(283\) 369.648 1.30618 0.653088 0.757282i \(-0.273473\pi\)
0.653088 + 0.757282i \(0.273473\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 613.767i 2.13856i
\(288\) 0 0
\(289\) 353.408 1.22286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 412.246i 1.40698i 0.710703 + 0.703492i \(0.248377\pi\)
−0.710703 + 0.703492i \(0.751623\pi\)
\(294\) 0 0
\(295\) 5.00798i 0.0169762i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 134.547i 0.449988i
\(300\) 0 0
\(301\) −259.346 −0.861615
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 18.7374 0.0614342
\(306\) 0 0
\(307\) 235.408i 0.766801i 0.923582 + 0.383401i \(0.125247\pi\)
−0.923582 + 0.383401i \(0.874753\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −88.0082 −0.282985 −0.141492 0.989939i \(-0.545190\pi\)
−0.141492 + 0.989939i \(0.545190\pi\)
\(312\) 0 0
\(313\) −35.2591 −0.112649 −0.0563244 0.998413i \(-0.517938\pi\)
−0.0563244 + 0.998413i \(0.517938\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 158.913i 0.501304i 0.968077 + 0.250652i \(0.0806449\pi\)
−0.968077 + 0.250652i \(0.919355\pi\)
\(318\) 0 0
\(319\) 104.787i 0.328487i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 47.6576 479.206i 0.147547 1.48361i
\(324\) 0 0
\(325\) 233.728i 0.719163i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 175.143 0.532349
\(330\) 0 0
\(331\) 137.393i 0.415083i 0.978226 + 0.207542i \(0.0665462\pi\)
−0.978226 + 0.207542i \(0.933454\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 28.5309i 0.0851668i
\(336\) 0 0
\(337\) 13.6995i 0.0406513i 0.999793 + 0.0203257i \(0.00647030\pi\)
−0.999793 + 0.0203257i \(0.993530\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 123.459i 0.362050i
\(342\) 0 0
\(343\) 47.5147 0.138527
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −349.872 −1.00828 −0.504138 0.863623i \(-0.668190\pi\)
−0.504138 + 0.863623i \(0.668190\pi\)
\(348\) 0 0
\(349\) −123.670 −0.354355 −0.177178 0.984179i \(-0.556697\pi\)
−0.177178 + 0.984179i \(0.556697\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −450.273 −1.27556 −0.637781 0.770218i \(-0.720147\pi\)
−0.637781 + 0.770218i \(0.720147\pi\)
\(354\) 0 0
\(355\) 14.5373i 0.0409501i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 329.805 0.918677 0.459339 0.888261i \(-0.348086\pi\)
0.459339 + 0.888261i \(0.348086\pi\)
\(360\) 0 0
\(361\) −353.929 71.1006i −0.980413 0.196955i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −24.2167 −0.0663470
\(366\) 0 0
\(367\) 413.600 1.12697 0.563487 0.826125i \(-0.309459\pi\)
0.563487 + 0.826125i \(0.309459\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 354.603i 0.955804i
\(372\) 0 0
\(373\) 499.071i 1.33799i 0.743266 + 0.668996i \(0.233276\pi\)
−0.743266 + 0.668996i \(0.766724\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 102.953 0.273086
\(378\) 0 0
\(379\) 288.611i 0.761506i 0.924677 + 0.380753i \(0.124335\pi\)
−0.924677 + 0.380753i \(0.875665\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 208.950i 0.545561i 0.962076 + 0.272781i \(0.0879433\pi\)
−0.962076 + 0.272781i \(0.912057\pi\)
\(384\) 0 0
\(385\) 36.9158 0.0958852
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −206.027 −0.529633 −0.264816 0.964299i \(-0.585311\pi\)
−0.264816 + 0.964299i \(0.585311\pi\)
\(390\) 0 0
\(391\) −362.431 −0.926933
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 40.6620i 0.102942i
\(396\) 0 0
\(397\) 565.530 1.42451 0.712255 0.701921i \(-0.247674\pi\)
0.712255 + 0.701921i \(0.247674\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 590.729i 1.47314i −0.676362 0.736569i \(-0.736444\pi\)
0.676362 0.736569i \(-0.263556\pi\)
\(402\) 0 0
\(403\) 121.298 0.300988
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 31.5600i 0.0775430i
\(408\) 0 0
\(409\) 618.496i 1.51221i −0.654448 0.756107i \(-0.727099\pi\)
0.654448 0.756107i \(-0.272901\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 120.922i 0.292789i
\(414\) 0 0
\(415\) −25.2463 −0.0608344
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 387.207 0.924122 0.462061 0.886848i \(-0.347110\pi\)
0.462061 + 0.886848i \(0.347110\pi\)
\(420\) 0 0
\(421\) 624.939i 1.48442i 0.670170 + 0.742208i \(0.266221\pi\)
−0.670170 + 0.742208i \(0.733779\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −629.598 −1.48141
\(426\) 0 0
\(427\) −452.431 −1.05956
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 737.075i 1.71015i −0.518503 0.855076i \(-0.673511\pi\)
0.518503 0.855076i \(-0.326489\pi\)
\(432\) 0 0
\(433\) 75.9481i 0.175400i 0.996147 + 0.0876999i \(0.0279517\pi\)
−0.996147 + 0.0876999i \(0.972048\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −26.8873 + 270.356i −0.0615269 + 0.618664i
\(438\) 0 0
\(439\) 230.299i 0.524599i 0.964986 + 0.262300i \(0.0844809\pi\)
−0.964986 + 0.262300i \(0.915519\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 771.602 1.74177 0.870883 0.491490i \(-0.163548\pi\)
0.870883 + 0.491490i \(0.163548\pi\)
\(444\) 0 0
\(445\) 42.9748i 0.0965725i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 624.898i 1.39175i −0.718161 0.695877i \(-0.755016\pi\)
0.718161 0.695877i \(-0.244984\pi\)
\(450\) 0 0
\(451\) 609.269i 1.35093i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 36.2696i 0.0797135i
\(456\) 0 0
\(457\) 202.318 0.442709 0.221355 0.975193i \(-0.428952\pi\)
0.221355 + 0.975193i \(0.428952\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −760.243 −1.64912 −0.824558 0.565777i \(-0.808576\pi\)
−0.824558 + 0.565777i \(0.808576\pi\)
\(462\) 0 0
\(463\) −698.217 −1.50803 −0.754014 0.656858i \(-0.771885\pi\)
−0.754014 + 0.656858i \(0.771885\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 348.694 0.746669 0.373334 0.927697i \(-0.378214\pi\)
0.373334 + 0.927697i \(0.378214\pi\)
\(468\) 0 0
\(469\) 688.902i 1.46887i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −257.446 −0.544282
\(474\) 0 0
\(475\) −46.7073 + 469.650i −0.0983311 + 0.988737i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 771.639 1.61094 0.805469 0.592638i \(-0.201914\pi\)
0.805469 + 0.592638i \(0.201914\pi\)
\(480\) 0 0
\(481\) −31.0076 −0.0644649
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 48.2282i 0.0994395i
\(486\) 0 0
\(487\) 388.393i 0.797522i −0.917055 0.398761i \(-0.869440\pi\)
0.917055 0.398761i \(-0.130560\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −93.7707 −0.190979 −0.0954896 0.995430i \(-0.530442\pi\)
−0.0954896 + 0.995430i \(0.530442\pi\)
\(492\) 0 0
\(493\) 277.327i 0.562530i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 351.015i 0.706267i
\(498\) 0 0
\(499\) 805.601 1.61443 0.807216 0.590256i \(-0.200973\pi\)
0.807216 + 0.590256i \(0.200973\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 47.6059 0.0946438 0.0473219 0.998880i \(-0.484931\pi\)
0.0473219 + 0.998880i \(0.484931\pi\)
\(504\) 0 0
\(505\) 49.0845 0.0971971
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 503.616i 0.989423i 0.869057 + 0.494712i \(0.164726\pi\)
−0.869057 + 0.494712i \(0.835274\pi\)
\(510\) 0 0
\(511\) 584.731 1.14429
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.4685i 0.0339194i
\(516\) 0 0
\(517\) 173.859 0.336285
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 295.180i 0.566565i 0.959037 + 0.283283i \(0.0914234\pi\)
−0.959037 + 0.283283i \(0.908577\pi\)
\(522\) 0 0
\(523\) 276.982i 0.529602i 0.964303 + 0.264801i \(0.0853063\pi\)
−0.964303 + 0.264801i \(0.914694\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 326.743i 0.620006i
\(528\) 0 0
\(529\) −324.525 −0.613470
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −598.605 −1.12309
\(534\) 0 0
\(535\) 70.6808i 0.132114i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −422.098 −0.783114
\(540\) 0 0
\(541\) −290.663 −0.537270 −0.268635 0.963242i \(-0.586573\pi\)
−0.268635 + 0.963242i \(0.586573\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 56.6825i 0.104005i
\(546\) 0 0
\(547\) 462.255i 0.845073i −0.906346 0.422536i \(-0.861140\pi\)
0.906346 0.422536i \(-0.138860\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 206.873 + 20.5738i 0.375450 + 0.0373390i
\(552\) 0 0
\(553\) 981.817i 1.77544i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −262.668 −0.471576 −0.235788 0.971805i \(-0.575767\pi\)
−0.235788 + 0.971805i \(0.575767\pi\)
\(558\) 0 0
\(559\) 252.939i 0.452485i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 778.649i 1.38303i 0.722360 + 0.691517i \(0.243057\pi\)
−0.722360 + 0.691517i \(0.756943\pi\)
\(564\) 0 0
\(565\) 36.7084i 0.0649706i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 211.390i 0.371511i 0.982596 + 0.185756i \(0.0594733\pi\)
−0.982596 + 0.185756i \(0.940527\pi\)
\(570\) 0 0
\(571\) 414.687 0.726246 0.363123 0.931741i \(-0.381710\pi\)
0.363123 + 0.931741i \(0.381710\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 355.204 0.617746
\(576\) 0 0
\(577\) −930.861 −1.61328 −0.806639 0.591045i \(-0.798716\pi\)
−0.806639 + 0.591045i \(0.798716\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 609.592 1.04921
\(582\) 0 0
\(583\) 352.005i 0.603781i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 423.095 0.720776 0.360388 0.932803i \(-0.382644\pi\)
0.360388 + 0.932803i \(0.382644\pi\)
\(588\) 0 0
\(589\) 243.735 + 24.2397i 0.413811 + 0.0411541i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −531.055 −0.895540 −0.447770 0.894149i \(-0.647782\pi\)
−0.447770 + 0.894149i \(0.647782\pi\)
\(594\) 0 0
\(595\) −97.7003 −0.164202
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 97.5458i 0.162848i −0.996680 0.0814239i \(-0.974053\pi\)
0.996680 0.0814239i \(-0.0259467\pi\)
\(600\) 0 0
\(601\) 660.902i 1.09967i −0.835273 0.549835i \(-0.814690\pi\)
0.835273 0.549835i \(-0.185310\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.7006 −0.0193398
\(606\) 0 0
\(607\) 982.250i 1.61820i −0.587668 0.809102i \(-0.699954\pi\)
0.587668 0.809102i \(-0.300046\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 170.816i 0.279568i
\(612\) 0 0
\(613\) 584.604 0.953676 0.476838 0.878991i \(-0.341783\pi\)
0.476838 + 0.878991i \(0.341783\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 517.294 0.838402 0.419201 0.907893i \(-0.362310\pi\)
0.419201 + 0.907893i \(0.362310\pi\)
\(618\) 0 0
\(619\) −311.076 −0.502547 −0.251273 0.967916i \(-0.580849\pi\)
−0.251273 + 0.967916i \(0.580849\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1037.66i 1.66559i
\(624\) 0 0
\(625\) 613.052 0.980884
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 83.5258i 0.132791i
\(630\) 0 0
\(631\) 316.443 0.501494 0.250747 0.968053i \(-0.419324\pi\)
0.250747 + 0.968053i \(0.419324\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 79.9941i 0.125975i
\(636\) 0 0
\(637\) 414.710i 0.651036i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 269.856i 0.420992i −0.977595 0.210496i \(-0.932492\pi\)
0.977595 0.210496i \(-0.0675078\pi\)
\(642\) 0 0
\(643\) −1088.71 −1.69317 −0.846585 0.532253i \(-0.821345\pi\)
−0.846585 + 0.532253i \(0.821345\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1130.62 −1.74748 −0.873742 0.486390i \(-0.838313\pi\)
−0.873742 + 0.486390i \(0.838313\pi\)
\(648\) 0 0
\(649\) 120.036i 0.184955i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 737.823 1.12990 0.564949 0.825126i \(-0.308896\pi\)
0.564949 + 0.825126i \(0.308896\pi\)
\(654\) 0 0
\(655\) −77.5063 −0.118330
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 837.755i 1.27125i 0.771997 + 0.635626i \(0.219258\pi\)
−0.771997 + 0.635626i \(0.780742\pi\)
\(660\) 0 0
\(661\) 365.664i 0.553198i 0.960985 + 0.276599i \(0.0892074\pi\)
−0.960985 + 0.276599i \(0.910793\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.24799 + 72.8798i −0.0108992 + 0.109594i
\(666\) 0 0
\(667\) 156.461i 0.234575i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −449.115 −0.669323
\(672\) 0 0
\(673\) 463.801i 0.689154i −0.938758 0.344577i \(-0.888022\pi\)
0.938758 0.344577i \(-0.111978\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 174.869i 0.258299i −0.991625 0.129150i \(-0.958775\pi\)
0.991625 0.129150i \(-0.0412247\pi\)
\(678\) 0 0
\(679\) 1164.51i 1.71504i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 813.802i 1.19151i −0.803166 0.595755i \(-0.796853\pi\)
0.803166 0.595755i \(-0.203147\pi\)
\(684\) 0 0
\(685\) 95.7130 0.139727
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 345.843 0.501949
\(690\) 0 0
\(691\) −132.179 −0.191286 −0.0956430 0.995416i \(-0.530491\pi\)
−0.0956430 + 0.995416i \(0.530491\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25.1309 −0.0361596
\(696\) 0 0
\(697\) 1612.47i 2.31345i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 567.236 0.809182 0.404591 0.914498i \(-0.367414\pi\)
0.404591 + 0.914498i \(0.367414\pi\)
\(702\) 0 0
\(703\) −62.3063 6.19644i −0.0886291 0.00881428i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1185.19 −1.67636
\(708\) 0 0
\(709\) 1074.59 1.51564 0.757818 0.652466i \(-0.226265\pi\)
0.757818 + 0.652466i \(0.226265\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 184.341i 0.258542i
\(714\) 0 0
\(715\) 36.0038i 0.0503550i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −24.8511 −0.0345634 −0.0172817 0.999851i \(-0.505501\pi\)
−0.0172817 + 0.999851i \(0.505501\pi\)
\(720\) 0 0
\(721\) 421.792i 0.585010i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 271.797i 0.374893i
\(726\) 0 0
\(727\) −23.9916 −0.0330008 −0.0165004 0.999864i \(-0.505252\pi\)
−0.0165004 + 0.999864i \(0.505252\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 681.348 0.932076
\(732\) 0 0
\(733\) −1111.45 −1.51631 −0.758153 0.652077i \(-0.773898\pi\)
−0.758153 + 0.652077i \(0.773898\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 683.853i 0.927887i
\(738\) 0 0
\(739\) 125.652 0.170030 0.0850151 0.996380i \(-0.472906\pi\)
0.0850151 + 0.996380i \(0.472906\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 181.459i 0.244225i −0.992516 0.122113i \(-0.961033\pi\)
0.992516 0.122113i \(-0.0389669\pi\)
\(744\) 0 0
\(745\) 35.2804 0.0473563
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1706.65i 2.27857i
\(750\) 0 0
\(751\) 366.770i 0.488376i 0.969728 + 0.244188i \(0.0785214\pi\)
−0.969728 + 0.244188i \(0.921479\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 82.5407i 0.109325i
\(756\) 0 0
\(757\) −1200.98 −1.58650 −0.793249 0.608897i \(-0.791612\pi\)
−0.793249 + 0.608897i \(0.791612\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 75.2919 0.0989381 0.0494690 0.998776i \(-0.484247\pi\)
0.0494690 + 0.998776i \(0.484247\pi\)
\(762\) 0 0
\(763\) 1368.65i 1.79377i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 117.935 0.153761
\(768\) 0 0
\(769\) −1293.99 −1.68269 −0.841345 0.540498i \(-0.818236\pi\)
−0.841345 + 0.540498i \(0.818236\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 121.722i 0.157466i 0.996896 + 0.0787332i \(0.0250875\pi\)
−0.996896 + 0.0787332i \(0.974912\pi\)
\(774\) 0 0
\(775\) 320.228i 0.413197i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1202.83 119.623i −1.54407 0.153560i
\(780\) 0 0
\(781\) 348.442i 0.446149i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.6764 0.0136005
\(786\) 0 0
\(787\) 913.776i 1.16109i −0.814229 0.580544i \(-0.802840\pi\)
0.814229 0.580544i \(-0.197160\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 886.354i 1.12055i
\(792\) 0 0
\(793\) 441.254i 0.556437i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 758.213i 0.951334i 0.879625 + 0.475667i \(0.157793\pi\)
−0.879625 + 0.475667i \(0.842207\pi\)
\(798\) 0 0
\(799\) −460.131 −0.575884
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 580.446 0.722847
\(804\) 0 0
\(805\) 55.1201 0.0684722
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 226.582 0.280077 0.140039 0.990146i \(-0.455277\pi\)
0.140039 + 0.990146i \(0.455277\pi\)
\(810\) 0 0
\(811\) 268.988i 0.331675i 0.986153 + 0.165837i \(0.0530326\pi\)
−0.986153 + 0.165837i \(0.946967\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 38.8716 0.0476952
\(816\) 0 0
\(817\) 50.5464 508.253i 0.0618683 0.622097i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1008.05 −1.22783 −0.613915 0.789372i \(-0.710406\pi\)
−0.613915 + 0.789372i \(0.710406\pi\)
\(822\) 0 0
\(823\) 747.774 0.908595 0.454298 0.890850i \(-0.349890\pi\)
0.454298 + 0.890850i \(0.349890\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 363.466i 0.439499i −0.975556 0.219750i \(-0.929476\pi\)
0.975556 0.219750i \(-0.0705240\pi\)
\(828\) 0 0
\(829\) 42.7417i 0.0515582i 0.999668 + 0.0257791i \(0.00820665\pi\)
−0.999668 + 0.0257791i \(0.991793\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1117.11 1.34107
\(834\) 0 0
\(835\) 89.1967i 0.106822i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 769.521i 0.917189i −0.888646 0.458594i \(-0.848353\pi\)
0.888646 0.458594i \(-0.151647\pi\)
\(840\) 0 0
\(841\) 721.278 0.857643
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 32.1508 0.0380482
\(846\) 0 0
\(847\) 282.521 0.333555
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 47.1232i 0.0553739i
\(852\) 0 0
\(853\) 296.927 0.348097 0.174049 0.984737i \(-0.444315\pi\)
0.174049 + 0.984737i \(0.444315\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 993.109i 1.15882i 0.815036 + 0.579410i \(0.196717\pi\)
−0.815036 + 0.579410i \(0.803283\pi\)
\(858\) 0 0
\(859\) 761.846 0.886899 0.443449 0.896299i \(-0.353755\pi\)
0.443449 + 0.896299i \(0.353755\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 886.359i 1.02707i 0.858070 + 0.513533i \(0.171664\pi\)
−0.858070 + 0.513533i \(0.828336\pi\)
\(864\) 0 0
\(865\) 81.5768i 0.0943085i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 974.622i 1.12154i
\(870\) 0 0
\(871\) −671.883 −0.771393
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 192.120 0.219565
\(876\) 0 0
\(877\) 775.062i 0.883765i −0.897073 0.441883i \(-0.854311\pi\)
0.897073 0.441883i \(-0.145689\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 286.737 0.325468 0.162734 0.986670i \(-0.447969\pi\)
0.162734 + 0.986670i \(0.447969\pi\)
\(882\) 0 0
\(883\) −771.537 −0.873768 −0.436884 0.899518i \(-0.643918\pi\)
−0.436884 + 0.899518i \(0.643918\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 361.445i 0.407492i 0.979024 + 0.203746i \(0.0653117\pi\)
−0.979024 + 0.203746i \(0.934688\pi\)
\(888\) 0 0
\(889\) 1931.52i 2.17269i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −34.1352 + 343.236i −0.0382254 + 0.384363i
\(894\) 0 0
\(895\) 92.7183i 0.103596i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −141.055 −0.156902
\(900\) 0 0
\(901\) 931.605i 1.03397i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 132.623i 0.146545i
\(906\) 0 0
\(907\) 665.325i 0.733544i −0.930311 0.366772i \(-0.880463\pi\)
0.930311 0.366772i \(-0.119537\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1312.71i 1.44095i −0.693480 0.720475i \(-0.743924\pi\)
0.693480 0.720475i \(-0.256076\pi\)
\(912\) 0 0
\(913\) 605.125 0.662787
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1871.46 2.04085
\(918\) 0 0
\(919\) −760.325 −0.827340 −0.413670 0.910427i \(-0.635753\pi\)
−0.413670 + 0.910427i \(0.635753\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −342.343 −0.370903
\(924\) 0 0
\(925\) 81.8603i 0.0884976i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −319.967 −0.344421 −0.172210 0.985060i \(-0.555091\pi\)
−0.172210 + 0.985060i \(0.555091\pi\)
\(930\) 0 0
\(931\) 82.8741 833.313i 0.0890162 0.895073i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −96.9843 −0.103727
\(936\) 0 0
\(937\) −85.7418 −0.0915067 −0.0457534 0.998953i \(-0.514569\pi\)
−0.0457534 + 0.998953i \(0.514569\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1308.42i 1.39046i 0.718788 + 0.695229i \(0.244697\pi\)
−0.718788 + 0.695229i \(0.755303\pi\)
\(942\) 0 0
\(943\) 909.718i 0.964707i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1165.13 −1.23034 −0.615170 0.788395i \(-0.710913\pi\)
−0.615170 + 0.788395i \(0.710913\pi\)
\(948\) 0 0
\(949\) 570.286i 0.600934i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 541.282i 0.567977i −0.958828 0.283989i \(-0.908342\pi\)
0.958828 0.283989i \(-0.0916578\pi\)
\(954\) 0 0
\(955\) 6.94264 0.00726979
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2311.07 −2.40988
\(960\) 0 0
\(961\) 794.811 0.827067
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 30.5446i 0.0316524i
\(966\) 0 0
\(967\) 1366.36 1.41298 0.706492 0.707721i \(-0.250276\pi\)
0.706492 + 0.707721i \(0.250276\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 433.446i 0.446391i 0.974774 + 0.223195i \(0.0716488\pi\)
−0.974774 + 0.223195i \(0.928351\pi\)
\(972\) 0 0
\(973\) 606.807 0.623646
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1597.95i 1.63557i −0.575523 0.817786i \(-0.695201\pi\)
0.575523 0.817786i \(-0.304799\pi\)
\(978\) 0 0
\(979\) 1030.06i 1.05215i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1405.05i 1.42934i 0.699459 + 0.714672i \(0.253424\pi\)
−0.699459 + 0.714672i \(0.746576\pi\)
\(984\) 0 0
\(985\) −64.2039 −0.0651816
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −384.400 −0.388675
\(990\) 0 0
\(991\) 185.937i 0.187626i 0.995590 + 0.0938131i \(0.0299056\pi\)
−0.995590 + 0.0938131i \(0.970094\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 26.1552 0.0262866
\(996\) 0 0
\(997\) 644.432 0.646371 0.323186 0.946336i \(-0.395246\pi\)
0.323186 + 0.946336i \(0.395246\pi\)
\(998\) 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 2736.3.o.q.721.11 20
3.2 odd 2 inner 2736.3.o.q.721.9 20
4.3 odd 2 1368.3.o.d.721.11 yes 20
12.11 even 2 1368.3.o.d.721.9 20
19.18 odd 2 inner 2736.3.o.q.721.12 20
57.56 even 2 inner 2736.3.o.q.721.10 20
76.75 even 2 1368.3.o.d.721.12 yes 20
228.227 odd 2 1368.3.o.d.721.10 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.3.o.d.721.9 20 12.11 even 2
1368.3.o.d.721.10 yes 20 228.227 odd 2
1368.3.o.d.721.11 yes 20 4.3 odd 2
1368.3.o.d.721.12 yes 20 76.75 even 2
2736.3.o.q.721.9 20 3.2 odd 2 inner
2736.3.o.q.721.10 20 57.56 even 2 inner
2736.3.o.q.721.11 20 1.1 even 1 trivial
2736.3.o.q.721.12 20 19.18 odd 2 inner