Properties

Label 576.7.h.b.161.22
Level $576$
Weight $7$
Character 576.161
Analytic conductor $132.511$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,7,Mod(161,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.161");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.h (of order \(2\), degree \(1\), 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: \(132.511152165\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 161.22
Character \(\chi\) \(=\) 576.161
Dual form 576.7.h.b.161.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+89.8672 q^{5} -443.362 q^{7} +O(q^{10})\) \(q+89.8672 q^{5} -443.362 q^{7} -42.6164 q^{11} +1280.86i q^{13} -6980.95i q^{17} +5878.06i q^{19} +4676.83i q^{23} -7548.89 q^{25} -29022.5 q^{29} +35918.8 q^{31} -39843.7 q^{35} -13478.5i q^{37} -94302.7i q^{41} +127117. i q^{43} +23599.2i q^{47} +78921.2 q^{49} +50787.5 q^{53} -3829.81 q^{55} +251523. q^{59} -44183.6i q^{61} +115107. i q^{65} -275182. i q^{67} -202612. i q^{71} +126284. q^{73} +18894.5 q^{77} +132427. q^{79} +336972. q^{83} -627358. i q^{85} +487794. i q^{89} -567885. i q^{91} +528244. i q^{95} -548674. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 169888 q^{25} + 829792 q^{49} - 1493888 q^{73} - 15893248 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(5\) 89.8672 0.718937 0.359469 0.933157i \(-0.382958\pi\)
0.359469 + 0.933157i \(0.382958\pi\)
\(6\) 0 0
\(7\) −443.362 −1.29260 −0.646301 0.763083i \(-0.723685\pi\)
−0.646301 + 0.763083i \(0.723685\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −42.6164 −0.0320183 −0.0160092 0.999872i \(-0.505096\pi\)
−0.0160092 + 0.999872i \(0.505096\pi\)
\(12\) 0 0
\(13\) 1280.86i 0.583004i 0.956570 + 0.291502i \(0.0941549\pi\)
−0.956570 + 0.291502i \(0.905845\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 6980.95i − 1.42091i −0.703741 0.710457i \(-0.748488\pi\)
0.703741 0.710457i \(-0.251512\pi\)
\(18\) 0 0
\(19\) 5878.06i 0.856984i 0.903545 + 0.428492i \(0.140955\pi\)
−0.903545 + 0.428492i \(0.859045\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4676.83i 0.384386i 0.981357 + 0.192193i \(0.0615600\pi\)
−0.981357 + 0.192193i \(0.938440\pi\)
\(24\) 0 0
\(25\) −7548.89 −0.483129
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −29022.5 −1.18998 −0.594991 0.803733i \(-0.702844\pi\)
−0.594991 + 0.803733i \(0.702844\pi\)
\(30\) 0 0
\(31\) 35918.8 1.20569 0.602847 0.797857i \(-0.294033\pi\)
0.602847 + 0.797857i \(0.294033\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −39843.7 −0.929300
\(36\) 0 0
\(37\) − 13478.5i − 0.266095i −0.991110 0.133047i \(-0.957524\pi\)
0.991110 0.133047i \(-0.0424763\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 94302.7i − 1.36827i −0.729354 0.684136i \(-0.760179\pi\)
0.729354 0.684136i \(-0.239821\pi\)
\(42\) 0 0
\(43\) 127117.i 1.59881i 0.600792 + 0.799406i \(0.294852\pi\)
−0.600792 + 0.799406i \(0.705148\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 23599.2i 0.227303i 0.993521 + 0.113651i \(0.0362547\pi\)
−0.993521 + 0.113651i \(0.963745\pi\)
\(48\) 0 0
\(49\) 78921.2 0.670819
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 50787.5 0.341137 0.170569 0.985346i \(-0.445440\pi\)
0.170569 + 0.985346i \(0.445440\pi\)
\(54\) 0 0
\(55\) −3829.81 −0.0230192
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 251523. 1.22468 0.612338 0.790596i \(-0.290229\pi\)
0.612338 + 0.790596i \(0.290229\pi\)
\(60\) 0 0
\(61\) − 44183.6i − 0.194658i −0.995252 0.0973289i \(-0.968970\pi\)
0.995252 0.0973289i \(-0.0310299\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 115107.i 0.419143i
\(66\) 0 0
\(67\) − 275182.i − 0.914945i −0.889224 0.457473i \(-0.848755\pi\)
0.889224 0.457473i \(-0.151245\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 202612.i − 0.566096i −0.959106 0.283048i \(-0.908655\pi\)
0.959106 0.283048i \(-0.0913455\pi\)
\(72\) 0 0
\(73\) 126284. 0.324623 0.162311 0.986740i \(-0.448105\pi\)
0.162311 + 0.986740i \(0.448105\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18894.5 0.0413869
\(78\) 0 0
\(79\) 132427. 0.268594 0.134297 0.990941i \(-0.457122\pi\)
0.134297 + 0.990941i \(0.457122\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 336972. 0.589331 0.294666 0.955600i \(-0.404792\pi\)
0.294666 + 0.955600i \(0.404792\pi\)
\(84\) 0 0
\(85\) − 627358.i − 1.02155i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 487794.i 0.691937i 0.938246 + 0.345968i \(0.112450\pi\)
−0.938246 + 0.345968i \(0.887550\pi\)
\(90\) 0 0
\(91\) − 567885.i − 0.753591i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 528244.i 0.616118i
\(96\) 0 0
\(97\) −548674. −0.601173 −0.300586 0.953755i \(-0.597182\pi\)
−0.300586 + 0.953755i \(0.597182\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.96827e6 1.91039 0.955193 0.295985i \(-0.0956479\pi\)
0.955193 + 0.295985i \(0.0956479\pi\)
\(102\) 0 0
\(103\) −610969. −0.559123 −0.279562 0.960128i \(-0.590189\pi\)
−0.279562 + 0.960128i \(0.590189\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −917363. −0.748841 −0.374421 0.927259i \(-0.622158\pi\)
−0.374421 + 0.927259i \(0.622158\pi\)
\(108\) 0 0
\(109\) 1.42620e6i 1.10129i 0.834740 + 0.550645i \(0.185618\pi\)
−0.834740 + 0.550645i \(0.814382\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 1.18126e6i − 0.818671i −0.912384 0.409335i \(-0.865761\pi\)
0.912384 0.409335i \(-0.134239\pi\)
\(114\) 0 0
\(115\) 420293.i 0.276350i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.09509e6i 1.83668i
\(120\) 0 0
\(121\) −1.76974e6 −0.998975
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.08257e6 −1.06628
\(126\) 0 0
\(127\) 3.05167e6 1.48980 0.744898 0.667178i \(-0.232498\pi\)
0.744898 + 0.667178i \(0.232498\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −166786. −0.0741902 −0.0370951 0.999312i \(-0.511810\pi\)
−0.0370951 + 0.999312i \(0.511810\pi\)
\(132\) 0 0
\(133\) − 2.60611e6i − 1.10774i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 2.87781e6i − 1.11918i −0.828769 0.559591i \(-0.810958\pi\)
0.828769 0.559591i \(-0.189042\pi\)
\(138\) 0 0
\(139\) − 2.02839e6i − 0.755278i −0.925953 0.377639i \(-0.876736\pi\)
0.925953 0.377639i \(-0.123264\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 54585.6i − 0.0186668i
\(144\) 0 0
\(145\) −2.60817e6 −0.855522
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.22778e6 1.58037 0.790184 0.612869i \(-0.209985\pi\)
0.790184 + 0.612869i \(0.209985\pi\)
\(150\) 0 0
\(151\) 1.66916e6 0.484805 0.242402 0.970176i \(-0.422065\pi\)
0.242402 + 0.970176i \(0.422065\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.22792e6 0.866818
\(156\) 0 0
\(157\) − 2.48935e6i − 0.643262i −0.946865 0.321631i \(-0.895769\pi\)
0.946865 0.321631i \(-0.104231\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 2.07353e6i − 0.496858i
\(162\) 0 0
\(163\) 953137.i 0.220086i 0.993927 + 0.110043i \(0.0350988\pi\)
−0.993927 + 0.110043i \(0.964901\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.85882e6i 1.25794i 0.777428 + 0.628971i \(0.216524\pi\)
−0.777428 + 0.628971i \(0.783476\pi\)
\(168\) 0 0
\(169\) 3.18621e6 0.660107
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.56280e6 1.07437 0.537187 0.843463i \(-0.319487\pi\)
0.537187 + 0.843463i \(0.319487\pi\)
\(174\) 0 0
\(175\) 3.34689e6 0.624493
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.72771e6 1.52174 0.760872 0.648902i \(-0.224772\pi\)
0.760872 + 0.648902i \(0.224772\pi\)
\(180\) 0 0
\(181\) − 7.28035e6i − 1.22777i −0.789396 0.613885i \(-0.789606\pi\)
0.789396 0.613885i \(-0.210394\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 1.21128e6i − 0.191306i
\(186\) 0 0
\(187\) 297503.i 0.0454953i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.61648e6i 0.519022i 0.965740 + 0.259511i \(0.0835613\pi\)
−0.965740 + 0.259511i \(0.916439\pi\)
\(192\) 0 0
\(193\) 8.22425e6 1.14400 0.571998 0.820255i \(-0.306169\pi\)
0.571998 + 0.820255i \(0.306169\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.09570e7 1.43315 0.716576 0.697509i \(-0.245708\pi\)
0.716576 + 0.697509i \(0.245708\pi\)
\(198\) 0 0
\(199\) 4.36810e6 0.554285 0.277143 0.960829i \(-0.410613\pi\)
0.277143 + 0.960829i \(0.410613\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.28675e7 1.53817
\(204\) 0 0
\(205\) − 8.47472e6i − 0.983703i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 250501.i − 0.0274392i
\(210\) 0 0
\(211\) − 1.72401e7i − 1.83524i −0.397456 0.917621i \(-0.630107\pi\)
0.397456 0.917621i \(-0.369893\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.14236e7i 1.14945i
\(216\) 0 0
\(217\) −1.59251e7 −1.55848
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.94161e6 0.828398
\(222\) 0 0
\(223\) 1.98062e7 1.78602 0.893008 0.450040i \(-0.148590\pi\)
0.893008 + 0.450040i \(0.148590\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.89837e6 −0.504260 −0.252130 0.967693i \(-0.581131\pi\)
−0.252130 + 0.967693i \(0.581131\pi\)
\(228\) 0 0
\(229\) − 1.06812e7i − 0.889432i −0.895672 0.444716i \(-0.853305\pi\)
0.895672 0.444716i \(-0.146695\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 1.66399e7i − 1.31547i −0.753248 0.657737i \(-0.771514\pi\)
0.753248 0.657737i \(-0.228486\pi\)
\(234\) 0 0
\(235\) 2.12080e6i 0.163416i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.06411e7i 0.779461i 0.920929 + 0.389730i \(0.127432\pi\)
−0.920929 + 0.389730i \(0.872568\pi\)
\(240\) 0 0
\(241\) −2.33513e7 −1.66824 −0.834122 0.551580i \(-0.814025\pi\)
−0.834122 + 0.551580i \(0.814025\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.09243e6 0.482277
\(246\) 0 0
\(247\) −7.52896e6 −0.499625
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.67640e6 0.106012 0.0530062 0.998594i \(-0.483120\pi\)
0.0530062 + 0.998594i \(0.483120\pi\)
\(252\) 0 0
\(253\) − 199309.i − 0.0123074i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 2.40911e7i − 1.41924i −0.704582 0.709622i \(-0.748866\pi\)
0.704582 0.709622i \(-0.251134\pi\)
\(258\) 0 0
\(259\) 5.97586e6i 0.343955i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.53990e7i 1.94591i 0.230985 + 0.972957i \(0.425805\pi\)
−0.230985 + 0.972957i \(0.574195\pi\)
\(264\) 0 0
\(265\) 4.56413e6 0.245256
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.61266e7 1.85597 0.927983 0.372622i \(-0.121541\pi\)
0.927983 + 0.372622i \(0.121541\pi\)
\(270\) 0 0
\(271\) 1.59271e7 0.800253 0.400127 0.916460i \(-0.368966\pi\)
0.400127 + 0.916460i \(0.368966\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 321706. 0.0154690
\(276\) 0 0
\(277\) 1.87252e7i 0.881023i 0.897747 + 0.440511i \(0.145203\pi\)
−0.897747 + 0.440511i \(0.854797\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.09704e7i 0.494427i 0.968961 + 0.247213i \(0.0795149\pi\)
−0.968961 + 0.247213i \(0.920485\pi\)
\(282\) 0 0
\(283\) − 3.72731e7i − 1.64451i −0.569121 0.822254i \(-0.692716\pi\)
0.569121 0.822254i \(-0.307284\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.18103e7i 1.76863i
\(288\) 0 0
\(289\) −2.45961e7 −1.01900
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.07872e7 −0.428852 −0.214426 0.976740i \(-0.568788\pi\)
−0.214426 + 0.976740i \(0.568788\pi\)
\(294\) 0 0
\(295\) 2.26037e7 0.880466
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.99035e6 −0.224098
\(300\) 0 0
\(301\) − 5.63588e7i − 2.06663i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 3.97066e6i − 0.139947i
\(306\) 0 0
\(307\) 2.03376e7i 0.702886i 0.936209 + 0.351443i \(0.114309\pi\)
−0.936209 + 0.351443i \(0.885691\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 2.59570e7i − 0.862924i −0.902131 0.431462i \(-0.857998\pi\)
0.902131 0.431462i \(-0.142002\pi\)
\(312\) 0 0
\(313\) −1.23211e7 −0.401807 −0.200904 0.979611i \(-0.564388\pi\)
−0.200904 + 0.979611i \(0.564388\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.20662e7 1.32055 0.660276 0.751023i \(-0.270439\pi\)
0.660276 + 0.751023i \(0.270439\pi\)
\(318\) 0 0
\(319\) 1.23683e6 0.0381012
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.10344e7 1.21770
\(324\) 0 0
\(325\) − 9.66906e6i − 0.281666i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 1.04630e7i − 0.293812i
\(330\) 0 0
\(331\) − 2.66885e7i − 0.735937i −0.929838 0.367968i \(-0.880053\pi\)
0.929838 0.367968i \(-0.119947\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 2.47298e7i − 0.657788i
\(336\) 0 0
\(337\) 5.77829e7 1.50977 0.754883 0.655860i \(-0.227694\pi\)
0.754883 + 0.655860i \(0.227694\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.53073e6 −0.0386043
\(342\) 0 0
\(343\) 1.71704e7 0.425500
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.65007e7 1.59161 0.795807 0.605550i \(-0.207047\pi\)
0.795807 + 0.605550i \(0.207047\pi\)
\(348\) 0 0
\(349\) − 1.59885e7i − 0.376124i −0.982157 0.188062i \(-0.939779\pi\)
0.982157 0.188062i \(-0.0602207\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.58567e7i 0.587826i 0.955832 + 0.293913i \(0.0949576\pi\)
−0.955832 + 0.293913i \(0.905042\pi\)
\(354\) 0 0
\(355\) − 1.82082e7i − 0.406987i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) − 3.71990e6i − 0.0803986i −0.999192 0.0401993i \(-0.987201\pi\)
0.999192 0.0401993i \(-0.0127993\pi\)
\(360\) 0 0
\(361\) 1.24943e7 0.265578
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.13488e7 0.233384
\(366\) 0 0
\(367\) −5.46513e7 −1.10561 −0.552805 0.833311i \(-0.686443\pi\)
−0.552805 + 0.833311i \(0.686443\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.25173e7 −0.440955
\(372\) 0 0
\(373\) 8.17609e6i 0.157550i 0.996892 + 0.0787752i \(0.0251009\pi\)
−0.996892 + 0.0787752i \(0.974899\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 3.71737e7i − 0.693763i
\(378\) 0 0
\(379\) 5.26957e7i 0.967960i 0.875079 + 0.483980i \(0.160809\pi\)
−0.875079 + 0.483980i \(0.839191\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.02655e7i 0.716700i 0.933587 + 0.358350i \(0.116660\pi\)
−0.933587 + 0.358350i \(0.883340\pi\)
\(384\) 0 0
\(385\) 1.69800e6 0.0297546
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.13341e7 −0.192548 −0.0962742 0.995355i \(-0.530693\pi\)
−0.0962742 + 0.995355i \(0.530693\pi\)
\(390\) 0 0
\(391\) 3.26487e7 0.546180
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.19009e7 0.193102
\(396\) 0 0
\(397\) 5.76000e7i 0.920558i 0.887774 + 0.460279i \(0.152251\pi\)
−0.887774 + 0.460279i \(0.847749\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 1.31623e7i − 0.204126i −0.994778 0.102063i \(-0.967456\pi\)
0.994778 0.102063i \(-0.0325443\pi\)
\(402\) 0 0
\(403\) 4.60069e7i 0.702924i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 574405.i 0.00851991i
\(408\) 0 0
\(409\) 2.37357e7 0.346922 0.173461 0.984841i \(-0.444505\pi\)
0.173461 + 0.984841i \(0.444505\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.11516e8 −1.58302
\(414\) 0 0
\(415\) 3.02827e7 0.423692
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.19810e8 −1.62874 −0.814371 0.580345i \(-0.802918\pi\)
−0.814371 + 0.580345i \(0.802918\pi\)
\(420\) 0 0
\(421\) − 3.41749e7i − 0.457995i −0.973427 0.228998i \(-0.926455\pi\)
0.973427 0.228998i \(-0.0735448\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.26984e7i 0.686485i
\(426\) 0 0
\(427\) 1.95894e7i 0.251615i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 1.31163e8i − 1.63825i −0.573617 0.819123i \(-0.694460\pi\)
0.573617 0.819123i \(-0.305540\pi\)
\(432\) 0 0
\(433\) −5.36200e7 −0.660485 −0.330243 0.943896i \(-0.607131\pi\)
−0.330243 + 0.943896i \(0.607131\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.74906e7 −0.329413
\(438\) 0 0
\(439\) 569641. 0.00673299 0.00336649 0.999994i \(-0.498928\pi\)
0.00336649 + 0.999994i \(0.498928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.19062e7 −1.05714 −0.528571 0.848889i \(-0.677272\pi\)
−0.528571 + 0.848889i \(0.677272\pi\)
\(444\) 0 0
\(445\) 4.38367e7i 0.497459i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.65056e6i 0.106614i 0.998578 + 0.0533069i \(0.0169762\pi\)
−0.998578 + 0.0533069i \(0.983024\pi\)
\(450\) 0 0
\(451\) 4.01884e6i 0.0438098i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 5.10342e7i − 0.541785i
\(456\) 0 0
\(457\) −7.77393e7 −0.814502 −0.407251 0.913316i \(-0.633513\pi\)
−0.407251 + 0.913316i \(0.633513\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.29523e7 −0.540483 −0.270241 0.962793i \(-0.587104\pi\)
−0.270241 + 0.962793i \(0.587104\pi\)
\(462\) 0 0
\(463\) −1.91760e8 −1.93204 −0.966019 0.258472i \(-0.916781\pi\)
−0.966019 + 0.258472i \(0.916781\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.45026e8 −1.42396 −0.711978 0.702202i \(-0.752200\pi\)
−0.711978 + 0.702202i \(0.752200\pi\)
\(468\) 0 0
\(469\) 1.22005e8i 1.18266i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 5.41725e6i − 0.0511912i
\(474\) 0 0
\(475\) − 4.43728e7i − 0.414034i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.36591e8i 1.24284i 0.783478 + 0.621419i \(0.213444\pi\)
−0.783478 + 0.621419i \(0.786556\pi\)
\(480\) 0 0
\(481\) 1.72641e7 0.155134
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.93078e7 −0.432206
\(486\) 0 0
\(487\) −7.85713e7 −0.680263 −0.340132 0.940378i \(-0.610472\pi\)
−0.340132 + 0.940378i \(0.610472\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.72964e8 1.46121 0.730604 0.682802i \(-0.239239\pi\)
0.730604 + 0.682802i \(0.239239\pi\)
\(492\) 0 0
\(493\) 2.02604e8i 1.69086i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.98305e7i 0.731736i
\(498\) 0 0
\(499\) 7.93484e7i 0.638611i 0.947652 + 0.319306i \(0.103450\pi\)
−0.947652 + 0.319306i \(0.896550\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 2.23058e8i − 1.75273i −0.481648 0.876365i \(-0.659962\pi\)
0.481648 0.876365i \(-0.340038\pi\)
\(504\) 0 0
\(505\) 1.76883e8 1.37345
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.75511e8 −1.33092 −0.665458 0.746436i \(-0.731764\pi\)
−0.665458 + 0.746436i \(0.731764\pi\)
\(510\) 0 0
\(511\) −5.59895e7 −0.419608
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.49061e7 −0.401975
\(516\) 0 0
\(517\) − 1.00571e6i − 0.00727784i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.60442e8i 1.84161i 0.390025 + 0.920804i \(0.372466\pi\)
−0.390025 + 0.920804i \(0.627534\pi\)
\(522\) 0 0
\(523\) − 1.43273e8i − 1.00152i −0.865586 0.500760i \(-0.833054\pi\)
0.865586 0.500760i \(-0.166946\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 2.50748e8i − 1.71319i
\(528\) 0 0
\(529\) 1.26163e8 0.852247
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.20788e8 0.797708
\(534\) 0 0
\(535\) −8.24408e7 −0.538370
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.36334e6 −0.0214785
\(540\) 0 0
\(541\) − 4.45953e7i − 0.281642i −0.990035 0.140821i \(-0.955026\pi\)
0.990035 0.140821i \(-0.0449742\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.28169e8i 0.791758i
\(546\) 0 0
\(547\) 1.65329e8i 1.01016i 0.863074 + 0.505078i \(0.168536\pi\)
−0.863074 + 0.505078i \(0.831464\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 1.70596e8i − 1.01980i
\(552\) 0 0
\(553\) −5.87133e7 −0.347185
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.28148e8 −1.32024 −0.660118 0.751162i \(-0.729494\pi\)
−0.660118 + 0.751162i \(0.729494\pi\)
\(558\) 0 0
\(559\) −1.62819e8 −0.932113
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.27992e8 −0.717229 −0.358615 0.933486i \(-0.616751\pi\)
−0.358615 + 0.933486i \(0.616751\pi\)
\(564\) 0 0
\(565\) − 1.06156e8i − 0.588573i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.89105e7i 0.428349i 0.976795 + 0.214175i \(0.0687062\pi\)
−0.976795 + 0.214175i \(0.931294\pi\)
\(570\) 0 0
\(571\) − 4.95304e7i − 0.266050i −0.991113 0.133025i \(-0.957531\pi\)
0.991113 0.133025i \(-0.0424691\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 3.53048e7i − 0.185708i
\(576\) 0 0
\(577\) 1.02547e8 0.533821 0.266910 0.963721i \(-0.413997\pi\)
0.266910 + 0.963721i \(0.413997\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.49401e8 −0.761770
\(582\) 0 0
\(583\) −2.16438e6 −0.0109226
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.04244e8 −0.515389 −0.257694 0.966226i \(-0.582963\pi\)
−0.257694 + 0.966226i \(0.582963\pi\)
\(588\) 0 0
\(589\) 2.11133e8i 1.03326i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 8.76870e7i − 0.420505i −0.977647 0.210252i \(-0.932571\pi\)
0.977647 0.210252i \(-0.0674286\pi\)
\(594\) 0 0
\(595\) 2.78147e8i 1.32046i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 1.02978e8i − 0.479142i −0.970879 0.239571i \(-0.922993\pi\)
0.970879 0.239571i \(-0.0770068\pi\)
\(600\) 0 0
\(601\) 2.53945e8 1.16981 0.584907 0.811100i \(-0.301131\pi\)
0.584907 + 0.811100i \(0.301131\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.59042e8 −0.718200
\(606\) 0 0
\(607\) 3.34354e8 1.49500 0.747500 0.664262i \(-0.231254\pi\)
0.747500 + 0.664262i \(0.231254\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.02273e7 −0.132518
\(612\) 0 0
\(613\) 3.24904e7i 0.141050i 0.997510 + 0.0705251i \(0.0224675\pi\)
−0.997510 + 0.0705251i \(0.977533\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 2.64427e8i − 1.12577i −0.826535 0.562885i \(-0.809691\pi\)
0.826535 0.562885i \(-0.190309\pi\)
\(618\) 0 0
\(619\) 3.99576e7i 0.168472i 0.996446 + 0.0842359i \(0.0268449\pi\)
−0.996446 + 0.0842359i \(0.973155\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 2.16270e8i − 0.894399i
\(624\) 0 0
\(625\) −6.92035e7 −0.283458
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.40928e7 −0.378098
\(630\) 0 0
\(631\) −4.60716e8 −1.83377 −0.916886 0.399148i \(-0.869306\pi\)
−0.916886 + 0.399148i \(0.869306\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.74245e8 1.07107
\(636\) 0 0
\(637\) 1.01087e8i 0.391090i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.20142e7i 0.273429i 0.990611 + 0.136714i \(0.0436543\pi\)
−0.990611 + 0.136714i \(0.956346\pi\)
\(642\) 0 0
\(643\) 4.30921e8i 1.62093i 0.585786 + 0.810466i \(0.300786\pi\)
−0.585786 + 0.810466i \(0.699214\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.79530e8i 1.40131i 0.713502 + 0.700653i \(0.247108\pi\)
−0.713502 + 0.700653i \(0.752892\pi\)
\(648\) 0 0
\(649\) −1.07190e7 −0.0392121
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.45700e7 −0.160067 −0.0800337 0.996792i \(-0.525503\pi\)
−0.0800337 + 0.996792i \(0.525503\pi\)
\(654\) 0 0
\(655\) −1.49886e7 −0.0533381
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.65766e8 −1.62746 −0.813731 0.581241i \(-0.802567\pi\)
−0.813731 + 0.581241i \(0.802567\pi\)
\(660\) 0 0
\(661\) 5.06364e8i 1.75331i 0.481121 + 0.876654i \(0.340230\pi\)
−0.481121 + 0.876654i \(0.659770\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 2.34204e8i − 0.796395i
\(666\) 0 0
\(667\) − 1.35733e8i − 0.457412i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.88295e6i 0.00623262i
\(672\) 0 0
\(673\) −3.72114e7 −0.122076 −0.0610381 0.998135i \(-0.519441\pi\)
−0.0610381 + 0.998135i \(0.519441\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.38536e8 −1.73560 −0.867798 0.496917i \(-0.834465\pi\)
−0.867798 + 0.496917i \(0.834465\pi\)
\(678\) 0 0
\(679\) 2.43261e8 0.777077
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.97430e8 0.619656 0.309828 0.950793i \(-0.399729\pi\)
0.309828 + 0.950793i \(0.399729\pi\)
\(684\) 0 0
\(685\) − 2.58621e8i − 0.804622i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.50516e7i 0.198884i
\(690\) 0 0
\(691\) − 3.11370e8i − 0.943720i −0.881673 0.471860i \(-0.843583\pi\)
0.881673 0.471860i \(-0.156417\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 1.82286e8i − 0.542998i
\(696\) 0 0
\(697\) −6.58323e8 −1.94420
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.34596e8 1.84223 0.921113 0.389295i \(-0.127281\pi\)
0.921113 + 0.389295i \(0.127281\pi\)
\(702\) 0 0
\(703\) 7.92274e7 0.228039
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.72658e8 −2.46937
\(708\) 0 0
\(709\) − 4.45746e8i − 1.25069i −0.780350 0.625344i \(-0.784959\pi\)
0.780350 0.625344i \(-0.215041\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.67986e8i 0.463452i
\(714\) 0 0
\(715\) − 4.90545e6i − 0.0134203i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 1.71293e8i − 0.460842i −0.973091 0.230421i \(-0.925990\pi\)
0.973091 0.230421i \(-0.0740103\pi\)
\(720\) 0 0
\(721\) 2.70881e8 0.722724
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.19087e8 0.574914
\(726\) 0 0
\(727\) 7.16750e7 0.186537 0.0932683 0.995641i \(-0.470269\pi\)
0.0932683 + 0.995641i \(0.470269\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.87395e8 2.27177
\(732\) 0 0
\(733\) − 4.52426e8i − 1.14878i −0.818583 0.574388i \(-0.805240\pi\)
0.818583 0.574388i \(-0.194760\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.17272e7i 0.0292950i
\(738\) 0 0
\(739\) − 2.11428e8i − 0.523878i −0.965084 0.261939i \(-0.915638\pi\)
0.965084 0.261939i \(-0.0843619\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.92654e8i 0.957291i 0.878008 + 0.478645i \(0.158872\pi\)
−0.878008 + 0.478645i \(0.841128\pi\)
\(744\) 0 0
\(745\) 4.69806e8 1.13619
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.06724e8 0.967953
\(750\) 0 0
\(751\) −1.33542e8 −0.315282 −0.157641 0.987496i \(-0.550389\pi\)
−0.157641 + 0.987496i \(0.550389\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.50003e8 0.348544
\(756\) 0 0
\(757\) 5.62083e8i 1.29572i 0.761758 + 0.647862i \(0.224337\pi\)
−0.761758 + 0.647862i \(0.775663\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.74241e8i 1.75680i 0.477926 + 0.878400i \(0.341389\pi\)
−0.477926 + 0.878400i \(0.658611\pi\)
\(762\) 0 0
\(763\) − 6.32324e8i − 1.42353i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.22165e8i 0.713991i
\(768\) 0 0
\(769\) −3.80577e8 −0.836880 −0.418440 0.908245i \(-0.637423\pi\)
−0.418440 + 0.908245i \(0.637423\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.34339e8 0.290846 0.145423 0.989370i \(-0.453546\pi\)
0.145423 + 0.989370i \(0.453546\pi\)
\(774\) 0 0
\(775\) −2.71147e8 −0.582505
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.54317e8 1.17259
\(780\) 0 0
\(781\) 8.63458e6i 0.0181254i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 2.23711e8i − 0.462465i
\(786\) 0 0
\(787\) 3.53435e8i 0.725079i 0.931968 + 0.362540i \(0.118090\pi\)
−0.931968 + 0.362540i \(0.881910\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.23725e8i 1.05822i
\(792\) 0 0
\(793\) 5.65930e7 0.113486
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.95605e8 0.781424 0.390712 0.920513i \(-0.372229\pi\)
0.390712 + 0.920513i \(0.372229\pi\)
\(798\) 0 0
\(799\) 1.64745e8 0.322977
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.38176e6 −0.0103939
\(804\) 0 0
\(805\) − 1.86342e8i − 0.357210i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 3.17458e8i − 0.599572i −0.954007 0.299786i \(-0.903085\pi\)
0.954007 0.299786i \(-0.0969152\pi\)
\(810\) 0 0
\(811\) − 9.33047e8i − 1.74921i −0.484839 0.874603i \(-0.661122\pi\)
0.484839 0.874603i \(-0.338878\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8.56557e7i 0.158228i
\(816\) 0 0
\(817\) −7.47199e8 −1.37016
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5.78907e8 1.04611 0.523057 0.852298i \(-0.324791\pi\)
0.523057 + 0.852298i \(0.324791\pi\)
\(822\) 0 0
\(823\) 2.89598e8 0.519512 0.259756 0.965674i \(-0.416358\pi\)
0.259756 + 0.965674i \(0.416358\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.87138e8 0.330861 0.165431 0.986221i \(-0.447099\pi\)
0.165431 + 0.986221i \(0.447099\pi\)
\(828\) 0 0
\(829\) − 3.96994e8i − 0.696820i −0.937342 0.348410i \(-0.886722\pi\)
0.937342 0.348410i \(-0.113278\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 5.50945e8i − 0.953176i
\(834\) 0 0
\(835\) 5.26516e8i 0.904382i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.23895e8i 0.209782i 0.994484 + 0.104891i \(0.0334493\pi\)
−0.994484 + 0.104891i \(0.966551\pi\)
\(840\) 0 0
\(841\) 2.47480e8 0.416056
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.86336e8 0.474576
\(846\) 0 0
\(847\) 7.84638e8 1.29128
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6.30366e7 0.102283
\(852\) 0 0
\(853\) − 7.14278e8i − 1.15085i −0.817853 0.575427i \(-0.804836\pi\)
0.817853 0.575427i \(-0.195164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 1.13028e9i − 1.79574i −0.440258 0.897871i \(-0.645113\pi\)
0.440258 0.897871i \(-0.354887\pi\)
\(858\) 0 0
\(859\) − 4.88951e8i − 0.771411i −0.922622 0.385705i \(-0.873958\pi\)
0.922622 0.385705i \(-0.126042\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.12311e8i 0.330324i 0.986266 + 0.165162i \(0.0528147\pi\)
−0.986266 + 0.165162i \(0.947185\pi\)
\(864\) 0 0
\(865\) 4.99914e8 0.772408
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.64357e6 −0.00859992
\(870\) 0 0
\(871\) 3.52469e8 0.533416
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.23334e8 1.37827
\(876\) 0 0
\(877\) − 6.59326e8i − 0.977465i −0.872434 0.488733i \(-0.837459\pi\)
0.872434 0.488733i \(-0.162541\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.67349e8i 0.390976i 0.980706 + 0.195488i \(0.0626291\pi\)
−0.980706 + 0.195488i \(0.937371\pi\)
\(882\) 0 0
\(883\) 1.01615e9i 1.47596i 0.674824 + 0.737979i \(0.264220\pi\)
−0.674824 + 0.737979i \(0.735780\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5.93480e8i 0.850423i 0.905094 + 0.425212i \(0.139800\pi\)
−0.905094 + 0.425212i \(0.860200\pi\)
\(888\) 0 0
\(889\) −1.35300e9 −1.92571
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.38718e8 −0.194795
\(894\) 0 0
\(895\) 7.84335e8 1.09404
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.04245e9 −1.43475
\(900\) 0 0
\(901\) − 3.54545e8i − 0.484727i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 6.54265e8i − 0.882689i
\(906\) 0 0
\(907\) − 4.02396e8i − 0.539302i −0.962958 0.269651i \(-0.913092\pi\)
0.962958 0.269651i \(-0.0869083\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.06320e9i 1.40624i 0.711072 + 0.703119i \(0.248210\pi\)
−0.711072 + 0.703119i \(0.751790\pi\)
\(912\) 0 0
\(913\) −1.43605e7 −0.0188694
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7.39468e7 0.0958984
\(918\) 0 0
\(919\) 6.18958e8 0.797471 0.398735 0.917066i \(-0.369449\pi\)
0.398735 + 0.917066i \(0.369449\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.59517e8 0.330036
\(924\) 0 0
\(925\) 1.01748e8i 0.128558i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 9.86097e8i − 1.22991i −0.788563 0.614954i \(-0.789175\pi\)
0.788563 0.614954i \(-0.210825\pi\)
\(930\) 0 0
\(931\) 4.63903e8i 0.574882i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.67357e7i 0.0327083i
\(936\) 0 0
\(937\) −8.48195e7 −0.103104 −0.0515522 0.998670i \(-0.516417\pi\)
−0.0515522 + 0.998670i \(0.516417\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.05514e9 1.26632 0.633158 0.774023i \(-0.281758\pi\)
0.633158 + 0.774023i \(0.281758\pi\)
\(942\) 0 0
\(943\) 4.41037e8 0.525945
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.06273e8 −0.596122 −0.298061 0.954547i \(-0.596340\pi\)
−0.298061 + 0.954547i \(0.596340\pi\)
\(948\) 0 0
\(949\) 1.61752e8i 0.189256i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.12053e7i 0.105376i 0.998611 + 0.0526880i \(0.0167789\pi\)
−0.998611 + 0.0526880i \(0.983221\pi\)
\(954\) 0 0
\(955\) 3.25003e8i 0.373144i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.27591e9i 1.44666i
\(960\) 0 0
\(961\) 4.02658e8 0.453697
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 7.39090e8 0.822461
\(966\) 0 0
\(967\) 1.98020e8 0.218992 0.109496 0.993987i \(-0.465076\pi\)
0.109496 + 0.993987i \(0.465076\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.67278e9 1.82718 0.913592 0.406633i \(-0.133297\pi\)
0.913592 + 0.406633i \(0.133297\pi\)
\(972\) 0 0
\(973\) 8.99312e8i 0.976274i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 1.70123e8i − 0.182422i −0.995832 0.0912112i \(-0.970926\pi\)
0.995832 0.0912112i \(-0.0290738\pi\)
\(978\) 0 0
\(979\) − 2.07880e7i − 0.0221547i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.02146e8i 0.212816i 0.994323 + 0.106408i \(0.0339349\pi\)
−0.994323 + 0.106408i \(0.966065\pi\)
\(984\) 0 0
\(985\) 9.84674e8 1.03035
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.94503e8 −0.614561
\(990\) 0 0
\(991\) −1.58498e9 −1.62856 −0.814280 0.580473i \(-0.802868\pi\)
−0.814280 + 0.580473i \(0.802868\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.92549e8 0.398496
\(996\) 0 0
\(997\) − 1.57004e9i − 1.58425i −0.610358 0.792126i \(-0.708974\pi\)
0.610358 0.792126i \(-0.291026\pi\)
\(998\) 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 576.7.h.b.161.22 yes 32
3.2 odd 2 inner 576.7.h.b.161.10 yes 32
4.3 odd 2 inner 576.7.h.b.161.24 yes 32
8.3 odd 2 inner 576.7.h.b.161.12 yes 32
8.5 even 2 inner 576.7.h.b.161.11 yes 32
12.11 even 2 inner 576.7.h.b.161.9 32
24.5 odd 2 inner 576.7.h.b.161.23 yes 32
24.11 even 2 inner 576.7.h.b.161.21 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.7.h.b.161.9 32 12.11 even 2 inner
576.7.h.b.161.10 yes 32 3.2 odd 2 inner
576.7.h.b.161.11 yes 32 8.5 even 2 inner
576.7.h.b.161.12 yes 32 8.3 odd 2 inner
576.7.h.b.161.21 yes 32 24.11 even 2 inner
576.7.h.b.161.22 yes 32 1.1 even 1 trivial
576.7.h.b.161.23 yes 32 24.5 odd 2 inner
576.7.h.b.161.24 yes 32 4.3 odd 2 inner