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Properties

Label 1600.4.a.s.1.1
Level $1600$
Weight $4$
Character 1600.1
Self dual yes
Analytic conductor $94.403$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1600,4,Mod(1,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1600.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.a (trivial)

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: yes
Analytic conductor: \(94.4030560092\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{3} +6.00000 q^{7} -23.0000 q^{9} +32.0000 q^{11} -38.0000 q^{13} -26.0000 q^{17} +100.000 q^{19} -12.0000 q^{21} -78.0000 q^{23} +100.000 q^{27} +50.0000 q^{29} +108.000 q^{31} -64.0000 q^{33} +266.000 q^{37} +76.0000 q^{39} +22.0000 q^{41} -442.000 q^{43} -514.000 q^{47} -307.000 q^{49} +52.0000 q^{51} +2.00000 q^{53} -200.000 q^{57} +500.000 q^{59} +518.000 q^{61} -138.000 q^{63} -126.000 q^{67} +156.000 q^{69} -412.000 q^{71} +878.000 q^{73} +192.000 q^{77} -600.000 q^{79} +421.000 q^{81} -282.000 q^{83} -100.000 q^{87} -150.000 q^{89} -228.000 q^{91} -216.000 q^{93} -386.000 q^{97} -736.000 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −0.384900 −0.192450 − 0.981307i \(-0.561643\pi\)
−0.192450 + 0.981307i \(0.561643\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 6.00000 0.323970 0.161985 − 0.986793i \(-0.448210\pi\)
0.161985 + 0.986793i \(0.448210\pi\)
\(8\) 0 0
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) 32.0000 0.877124 0.438562 − 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 − 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −26.0000 −0.370937 −0.185468 − 0.982650i \(-0.559380\pi\)
−0.185468 + 0.982650i \(0.559380\pi\)
\(18\) 0 0
\(19\) 100.000 1.20745 0.603726 − 0.797192i \(-0.293682\pi\)
0.603726 + 0.797192i \(0.293682\pi\)
\(20\) 0 0
\(21\) −12.0000 −0.124696
\(22\) 0 0
\(23\) −78.0000 −0.707136 −0.353568 − 0.935409i \(-0.615032\pi\)
−0.353568 + 0.935409i \(0.615032\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 100.000 0.712778
\(28\) 0 0
\(29\) 50.0000 0.320164 0.160082 − 0.987104i \(-0.448824\pi\)
0.160082 + 0.987104i \(0.448824\pi\)
\(30\) 0 0
\(31\) 108.000 0.625722 0.312861 − 0.949799i \(-0.398713\pi\)
0.312861 + 0.949799i \(0.398713\pi\)
\(32\) 0 0
\(33\) −64.0000 −0.337605
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 266.000 1.18190 0.590948 − 0.806710i \(-0.298754\pi\)
0.590948 + 0.806710i \(0.298754\pi\)
\(38\) 0 0
\(39\) 76.0000 0.312045
\(40\) 0 0
\(41\) 22.0000 0.0838006 0.0419003 − 0.999122i \(-0.486659\pi\)
0.0419003 + 0.999122i \(0.486659\pi\)
\(42\) 0 0
\(43\) −442.000 −1.56754 −0.783772 − 0.621049i \(-0.786707\pi\)
−0.783772 + 0.621049i \(0.786707\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −514.000 −1.59520 −0.797602 − 0.603184i \(-0.793899\pi\)
−0.797602 + 0.603184i \(0.793899\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 52.0000 0.142774
\(52\) 0 0
\(53\) 2.00000 0.00518342 0.00259171 − 0.999997i \(-0.499175\pi\)
0.00259171 + 0.999997i \(0.499175\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −200.000 −0.464748
\(58\) 0 0
\(59\) 500.000 1.10330 0.551648 − 0.834077i \(-0.313999\pi\)
0.551648 + 0.834077i \(0.313999\pi\)
\(60\) 0 0
\(61\) 518.000 1.08726 0.543632 − 0.839324i \(-0.317049\pi\)
0.543632 + 0.839324i \(0.317049\pi\)
\(62\) 0 0
\(63\) −138.000 −0.275974
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −126.000 −0.229751 −0.114876 − 0.993380i \(-0.536647\pi\)
−0.114876 + 0.993380i \(0.536647\pi\)
\(68\) 0 0
\(69\) 156.000 0.272177
\(70\) 0 0
\(71\) −412.000 −0.688668 −0.344334 − 0.938847i \(-0.611895\pi\)
−0.344334 + 0.938847i \(0.611895\pi\)
\(72\) 0 0
\(73\) 878.000 1.40770 0.703850 − 0.710348i \(-0.251463\pi\)
0.703850 + 0.710348i \(0.251463\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 192.000 0.284161
\(78\) 0 0
\(79\) −600.000 −0.854497 −0.427249 − 0.904134i \(-0.640517\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 0 0
\(83\) −282.000 −0.372934 −0.186467 − 0.982461i \(-0.559704\pi\)
−0.186467 + 0.982461i \(0.559704\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −100.000 −0.123231
\(88\) 0 0
\(89\) −150.000 −0.178651 −0.0893257 − 0.996002i \(-0.528471\pi\)
−0.0893257 + 0.996002i \(0.528471\pi\)
\(90\) 0 0
\(91\) −228.000 −0.262647
\(92\) 0 0
\(93\) −216.000 −0.240840
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −386.000 −0.404045 −0.202022 − 0.979381i \(-0.564751\pi\)
−0.202022 + 0.979381i \(0.564751\pi\)
\(98\) 0 0
\(99\) −736.000 −0.747180
\(100\) 0 0
\(101\) −702.000 −0.691600 −0.345800 − 0.938308i \(-0.612392\pi\)
−0.345800 + 0.938308i \(0.612392\pi\)
\(102\) 0 0
\(103\) −598.000 −0.572065 −0.286032 − 0.958220i \(-0.592337\pi\)
−0.286032 + 0.958220i \(0.592337\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1194.00 1.07877 0.539385 − 0.842059i \(-0.318657\pi\)
0.539385 + 0.842059i \(0.318657\pi\)
\(108\) 0 0
\(109\) 550.000 0.483307 0.241653 − 0.970363i \(-0.422310\pi\)
0.241653 + 0.970363i \(0.422310\pi\)
\(110\) 0 0
\(111\) −532.000 −0.454912
\(112\) 0 0
\(113\) −1562.00 −1.30036 −0.650180 − 0.759781i \(-0.725306\pi\)
−0.650180 + 0.759781i \(0.725306\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 874.000 0.690610
\(118\) 0 0
\(119\) −156.000 −0.120172
\(120\) 0 0
\(121\) −307.000 −0.230654
\(122\) 0 0
\(123\) −44.0000 −0.0322548
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1846.00 1.28981 0.644906 − 0.764262i \(-0.276897\pi\)
0.644906 + 0.764262i \(0.276897\pi\)
\(128\) 0 0
\(129\) 884.000 0.603348
\(130\) 0 0
\(131\) −2208.00 −1.47262 −0.736312 − 0.676642i \(-0.763435\pi\)
−0.736312 + 0.676642i \(0.763435\pi\)
\(132\) 0 0
\(133\) 600.000 0.391177
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2334.00 1.45553 0.727763 − 0.685829i \(-0.240560\pi\)
0.727763 + 0.685829i \(0.240560\pi\)
\(138\) 0 0
\(139\) −700.000 −0.427146 −0.213573 − 0.976927i \(-0.568510\pi\)
−0.213573 + 0.976927i \(0.568510\pi\)
\(140\) 0 0
\(141\) 1028.00 0.613994
\(142\) 0 0
\(143\) −1216.00 −0.711098
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 614.000 0.344502
\(148\) 0 0
\(149\) −2050.00 −1.12713 −0.563566 − 0.826071i \(-0.690571\pi\)
−0.563566 + 0.826071i \(0.690571\pi\)
\(150\) 0 0
\(151\) −1852.00 −0.998103 −0.499052 − 0.866572i \(-0.666318\pi\)
−0.499052 + 0.866572i \(0.666318\pi\)
\(152\) 0 0
\(153\) 598.000 0.315983
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2494.00 −1.26779 −0.633894 − 0.773420i \(-0.718545\pi\)
−0.633894 + 0.773420i \(0.718545\pi\)
\(158\) 0 0
\(159\) −4.00000 −0.00199510
\(160\) 0 0
\(161\) −468.000 −0.229090
\(162\) 0 0
\(163\) −2762.00 −1.32722 −0.663609 − 0.748080i \(-0.730976\pi\)
−0.663609 + 0.748080i \(0.730976\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3126.00 1.44849 0.724243 − 0.689545i \(-0.242189\pi\)
0.724243 + 0.689545i \(0.242189\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) −2300.00 −1.02857
\(172\) 0 0
\(173\) −78.0000 −0.0342788 −0.0171394 − 0.999853i \(-0.505456\pi\)
−0.0171394 + 0.999853i \(0.505456\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1000.00 −0.424659
\(178\) 0 0
\(179\) −1300.00 −0.542830 −0.271415 − 0.962462i \(-0.587492\pi\)
−0.271415 + 0.962462i \(0.587492\pi\)
\(180\) 0 0
\(181\) −1742.00 −0.715369 −0.357685 − 0.933842i \(-0.616434\pi\)
−0.357685 + 0.933842i \(0.616434\pi\)
\(182\) 0 0
\(183\) −1036.00 −0.418488
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −832.000 −0.325358
\(188\) 0 0
\(189\) 600.000 0.230918
\(190\) 0 0
\(191\) −3772.00 −1.42897 −0.714483 − 0.699653i \(-0.753338\pi\)
−0.714483 + 0.699653i \(0.753338\pi\)
\(192\) 0 0
\(193\) 358.000 0.133520 0.0667601 − 0.997769i \(-0.478734\pi\)
0.0667601 + 0.997769i \(0.478734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2214.00 −0.800716 −0.400358 − 0.916359i \(-0.631114\pi\)
−0.400358 + 0.916359i \(0.631114\pi\)
\(198\) 0 0
\(199\) 2600.00 0.926176 0.463088 − 0.886312i \(-0.346741\pi\)
0.463088 + 0.886312i \(0.346741\pi\)
\(200\) 0 0
\(201\) 252.000 0.0884314
\(202\) 0 0
\(203\) 300.000 0.103724
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1794.00 0.602375
\(208\) 0 0
\(209\) 3200.00 1.05908
\(210\) 0 0
\(211\) −1168.00 −0.381083 −0.190541 − 0.981679i \(-0.561024\pi\)
−0.190541 + 0.981679i \(0.561024\pi\)
\(212\) 0 0
\(213\) 824.000 0.265068
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 648.000 0.202715
\(218\) 0 0
\(219\) −1756.00 −0.541824
\(220\) 0 0
\(221\) 988.000 0.300724
\(222\) 0 0
\(223\) −6478.00 −1.94529 −0.972643 − 0.232303i \(-0.925374\pi\)
−0.972643 + 0.232303i \(0.925374\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −646.000 −0.188883 −0.0944417 − 0.995530i \(-0.530107\pi\)
−0.0944417 + 0.995530i \(0.530107\pi\)
\(228\) 0 0
\(229\) −3750.00 −1.08213 −0.541063 − 0.840982i \(-0.681978\pi\)
−0.541063 + 0.840982i \(0.681978\pi\)
\(230\) 0 0
\(231\) −384.000 −0.109374
\(232\) 0 0
\(233\) −1482.00 −0.416691 −0.208346 − 0.978055i \(-0.566808\pi\)
−0.208346 + 0.978055i \(0.566808\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1200.00 0.328896
\(238\) 0 0
\(239\) −1400.00 −0.378906 −0.189453 − 0.981890i \(-0.560671\pi\)
−0.189453 + 0.981890i \(0.560671\pi\)
\(240\) 0 0
\(241\) 3022.00 0.807735 0.403867 − 0.914817i \(-0.367666\pi\)
0.403867 + 0.914817i \(0.367666\pi\)
\(242\) 0 0
\(243\) −3542.00 −0.935059
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3800.00 −0.978900
\(248\) 0 0
\(249\) 564.000 0.143542
\(250\) 0 0
\(251\) −1248.00 −0.313837 −0.156918 − 0.987612i \(-0.550156\pi\)
−0.156918 + 0.987612i \(0.550156\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2106.00 −0.511162 −0.255581 − 0.966788i \(-0.582267\pi\)
−0.255581 + 0.966788i \(0.582267\pi\)
\(258\) 0 0
\(259\) 1596.00 0.382898
\(260\) 0 0
\(261\) −1150.00 −0.272733
\(262\) 0 0
\(263\) −3638.00 −0.852961 −0.426480 − 0.904497i \(-0.640247\pi\)
−0.426480 + 0.904497i \(0.640247\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 300.000 0.0687629
\(268\) 0 0
\(269\) 6550.00 1.48461 0.742306 − 0.670061i \(-0.233732\pi\)
0.742306 + 0.670061i \(0.233732\pi\)
\(270\) 0 0
\(271\) 4388.00 0.983587 0.491793 − 0.870712i \(-0.336342\pi\)
0.491793 + 0.870712i \(0.336342\pi\)
\(272\) 0 0
\(273\) 456.000 0.101093
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 546.000 0.118433 0.0592165 − 0.998245i \(-0.481140\pi\)
0.0592165 + 0.998245i \(0.481140\pi\)
\(278\) 0 0
\(279\) −2484.00 −0.533022
\(280\) 0 0
\(281\) −6858.00 −1.45592 −0.727961 − 0.685619i \(-0.759532\pi\)
−0.727961 + 0.685619i \(0.759532\pi\)
\(282\) 0 0
\(283\) −9282.00 −1.94967 −0.974837 − 0.222920i \(-0.928441\pi\)
−0.974837 + 0.222920i \(0.928441\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 132.000 0.0271488
\(288\) 0 0
\(289\) −4237.00 −0.862406
\(290\) 0 0
\(291\) 772.000 0.155517
\(292\) 0 0
\(293\) 4842.00 0.965436 0.482718 − 0.875776i \(-0.339650\pi\)
0.482718 + 0.875776i \(0.339650\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3200.00 0.625195
\(298\) 0 0
\(299\) 2964.00 0.573286
\(300\) 0 0
\(301\) −2652.00 −0.507836
\(302\) 0 0
\(303\) 1404.00 0.266197
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2594.00 0.482239 0.241120 − 0.970495i \(-0.422485\pi\)
0.241120 + 0.970495i \(0.422485\pi\)
\(308\) 0 0
\(309\) 1196.00 0.220188
\(310\) 0 0
\(311\) −7332.00 −1.33685 −0.668424 − 0.743781i \(-0.733031\pi\)
−0.668424 + 0.743781i \(0.733031\pi\)
\(312\) 0 0
\(313\) −1562.00 −0.282075 −0.141037 − 0.990004i \(-0.545044\pi\)
−0.141037 + 0.990004i \(0.545044\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1426.00 0.252657 0.126328 − 0.991988i \(-0.459681\pi\)
0.126328 + 0.991988i \(0.459681\pi\)
\(318\) 0 0
\(319\) 1600.00 0.280824
\(320\) 0 0
\(321\) −2388.00 −0.415219
\(322\) 0 0
\(323\) −2600.00 −0.447888
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1100.00 −0.186025
\(328\) 0 0
\(329\) −3084.00 −0.516798
\(330\) 0 0
\(331\) −4008.00 −0.665558 −0.332779 − 0.943005i \(-0.607986\pi\)
−0.332779 + 0.943005i \(0.607986\pi\)
\(332\) 0 0
\(333\) −6118.00 −1.00680
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −8866.00 −1.43312 −0.716561 − 0.697525i \(-0.754285\pi\)
−0.716561 + 0.697525i \(0.754285\pi\)
\(338\) 0 0
\(339\) 3124.00 0.500509
\(340\) 0 0
\(341\) 3456.00 0.548835
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1714.00 0.265165 0.132583 − 0.991172i \(-0.457673\pi\)
0.132583 + 0.991172i \(0.457673\pi\)
\(348\) 0 0
\(349\) −1150.00 −0.176384 −0.0881921 − 0.996103i \(-0.528109\pi\)
−0.0881921 + 0.996103i \(0.528109\pi\)
\(350\) 0 0
\(351\) −3800.00 −0.577860
\(352\) 0 0
\(353\) 4398.00 0.663122 0.331561 − 0.943434i \(-0.392425\pi\)
0.331561 + 0.943434i \(0.392425\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 312.000 0.0462543
\(358\) 0 0
\(359\) −1800.00 −0.264625 −0.132312 − 0.991208i \(-0.542240\pi\)
−0.132312 + 0.991208i \(0.542240\pi\)
\(360\) 0 0
\(361\) 3141.00 0.457938
\(362\) 0 0
\(363\) 614.000 0.0887786
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −5874.00 −0.835478 −0.417739 − 0.908567i \(-0.637177\pi\)
−0.417739 + 0.908567i \(0.637177\pi\)
\(368\) 0 0
\(369\) −506.000 −0.0713857
\(370\) 0 0
\(371\) 12.0000 0.00167927
\(372\) 0 0
\(373\) −2078.00 −0.288458 −0.144229 − 0.989544i \(-0.546070\pi\)
−0.144229 + 0.989544i \(0.546070\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1900.00 −0.259562
\(378\) 0 0
\(379\) 7900.00 1.07070 0.535351 − 0.844630i \(-0.320179\pi\)
0.535351 + 0.844630i \(0.320179\pi\)
\(380\) 0 0
\(381\) −3692.00 −0.496449
\(382\) 0 0
\(383\) −7518.00 −1.00301 −0.501504 − 0.865155i \(-0.667220\pi\)
−0.501504 + 0.865155i \(0.667220\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10166.0 1.33531
\(388\) 0 0
\(389\) 1950.00 0.254162 0.127081 − 0.991892i \(-0.459439\pi\)
0.127081 + 0.991892i \(0.459439\pi\)
\(390\) 0 0
\(391\) 2028.00 0.262303
\(392\) 0 0
\(393\) 4416.00 0.566814
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 13786.0 1.74282 0.871410 − 0.490555i \(-0.163206\pi\)
0.871410 + 0.490555i \(0.163206\pi\)
\(398\) 0 0
\(399\) −1200.00 −0.150564
\(400\) 0 0
\(401\) 6402.00 0.797258 0.398629 − 0.917112i \(-0.369486\pi\)
0.398629 + 0.917112i \(0.369486\pi\)
\(402\) 0 0
\(403\) −4104.00 −0.507282
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8512.00 1.03667
\(408\) 0 0
\(409\) 11150.0 1.34800 0.674000 − 0.738731i \(-0.264575\pi\)
0.674000 + 0.738731i \(0.264575\pi\)
\(410\) 0 0
\(411\) −4668.00 −0.560232
\(412\) 0 0
\(413\) 3000.00 0.357434
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1400.00 0.164408
\(418\) 0 0
\(419\) −13700.0 −1.59735 −0.798674 − 0.601764i \(-0.794465\pi\)
−0.798674 + 0.601764i \(0.794465\pi\)
\(420\) 0 0
\(421\) 5438.00 0.629529 0.314765 − 0.949170i \(-0.398074\pi\)
0.314765 + 0.949170i \(0.398074\pi\)
\(422\) 0 0
\(423\) 11822.0 1.35888
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3108.00 0.352240
\(428\) 0 0
\(429\) 2432.00 0.273702
\(430\) 0 0
\(431\) −7692.00 −0.859653 −0.429827 − 0.902911i \(-0.641425\pi\)
−0.429827 + 0.902911i \(0.641425\pi\)
\(432\) 0 0
\(433\) 1118.00 0.124082 0.0620412 − 0.998074i \(-0.480239\pi\)
0.0620412 + 0.998074i \(0.480239\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7800.00 −0.853832
\(438\) 0 0
\(439\) 2600.00 0.282668 0.141334 − 0.989962i \(-0.454861\pi\)
0.141334 + 0.989962i \(0.454861\pi\)
\(440\) 0 0
\(441\) 7061.00 0.762445
\(442\) 0 0
\(443\) 11958.0 1.28249 0.641243 − 0.767337i \(-0.278419\pi\)
0.641243 + 0.767337i \(0.278419\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4100.00 0.433833
\(448\) 0 0
\(449\) −17050.0 −1.79207 −0.896035 − 0.443984i \(-0.853565\pi\)
−0.896035 + 0.443984i \(0.853565\pi\)
\(450\) 0 0
\(451\) 704.000 0.0735035
\(452\) 0 0
\(453\) 3704.00 0.384170
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9494.00 0.971796 0.485898 − 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(458\) 0 0
\(459\) −2600.00 −0.264396
\(460\) 0 0
\(461\) 11418.0 1.15356 0.576778 − 0.816901i \(-0.304310\pi\)
0.576778 + 0.816901i \(0.304310\pi\)
\(462\) 0 0
\(463\) 7962.00 0.799191 0.399596 − 0.916692i \(-0.369151\pi\)
0.399596 + 0.916692i \(0.369151\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6526.00 −0.646654 −0.323327 − 0.946287i \(-0.604801\pi\)
−0.323327 + 0.946287i \(0.604801\pi\)
\(468\) 0 0
\(469\) −756.000 −0.0744325
\(470\) 0 0
\(471\) 4988.00 0.487972
\(472\) 0 0
\(473\) −14144.0 −1.37493
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −46.0000 −0.00441550
\(478\) 0 0
\(479\) −17400.0 −1.65976 −0.829881 − 0.557940i \(-0.811592\pi\)
−0.829881 + 0.557940i \(0.811592\pi\)
\(480\) 0 0
\(481\) −10108.0 −0.958181
\(482\) 0 0
\(483\) 936.000 0.0881770
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1166.00 0.108494 0.0542469 − 0.998528i \(-0.482724\pi\)
0.0542469 + 0.998528i \(0.482724\pi\)
\(488\) 0 0
\(489\) 5524.00 0.510846
\(490\) 0 0
\(491\) 7072.00 0.650010 0.325005 − 0.945712i \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(492\) 0 0
\(493\) −1300.00 −0.118761
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2472.00 −0.223107
\(498\) 0 0
\(499\) 100.000 0.00897117 0.00448559 − 0.999990i \(-0.498572\pi\)
0.00448559 + 0.999990i \(0.498572\pi\)
\(500\) 0 0
\(501\) −6252.00 −0.557522
\(502\) 0 0
\(503\) 2602.00 0.230651 0.115325 − 0.993328i \(-0.463209\pi\)
0.115325 + 0.993328i \(0.463209\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1506.00 0.131921
\(508\) 0 0
\(509\) −11150.0 −0.970953 −0.485476 − 0.874250i \(-0.661354\pi\)
−0.485476 + 0.874250i \(0.661354\pi\)
\(510\) 0 0
\(511\) 5268.00 0.456052
\(512\) 0 0
\(513\) 10000.0 0.860645
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −16448.0 −1.39919
\(518\) 0 0
\(519\) 156.000 0.0131939
\(520\) 0 0
\(521\) −3638.00 −0.305919 −0.152959 − 0.988232i \(-0.548880\pi\)
−0.152959 + 0.988232i \(0.548880\pi\)
\(522\) 0 0
\(523\) 2078.00 0.173737 0.0868686 − 0.996220i \(-0.472314\pi\)
0.0868686 + 0.996220i \(0.472314\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2808.00 −0.232103
\(528\) 0 0
\(529\) −6083.00 −0.499959
\(530\) 0 0
\(531\) −11500.0 −0.939845
\(532\) 0 0
\(533\) −836.000 −0.0679384
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2600.00 0.208935
\(538\) 0 0
\(539\) −9824.00 −0.785064
\(540\) 0 0
\(541\) −5622.00 −0.446781 −0.223391 − 0.974729i \(-0.571713\pi\)
−0.223391 + 0.974729i \(0.571713\pi\)
\(542\) 0 0
\(543\) 3484.00 0.275346
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16486.0 −1.28865 −0.644324 − 0.764753i \(-0.722861\pi\)
−0.644324 + 0.764753i \(0.722861\pi\)
\(548\) 0 0
\(549\) −11914.0 −0.926188
\(550\) 0 0
\(551\) 5000.00 0.386583
\(552\) 0 0
\(553\) −3600.00 −0.276831
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11706.0 0.890483 0.445242 − 0.895410i \(-0.353118\pi\)
0.445242 + 0.895410i \(0.353118\pi\)
\(558\) 0 0
\(559\) 16796.0 1.27083
\(560\) 0 0
\(561\) 1664.00 0.125230
\(562\) 0 0
\(563\) 25038.0 1.87429 0.937146 − 0.348939i \(-0.113458\pi\)
0.937146 + 0.348939i \(0.113458\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2526.00 0.187094
\(568\) 0 0
\(569\) 17550.0 1.29303 0.646515 − 0.762901i \(-0.276226\pi\)
0.646515 + 0.762901i \(0.276226\pi\)
\(570\) 0 0
\(571\) 10712.0 0.785084 0.392542 − 0.919734i \(-0.371596\pi\)
0.392542 + 0.919734i \(0.371596\pi\)
\(572\) 0 0
\(573\) 7544.00 0.550009
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 13654.0 0.985136 0.492568 − 0.870274i \(-0.336058\pi\)
0.492568 + 0.870274i \(0.336058\pi\)
\(578\) 0 0
\(579\) −716.000 −0.0513920
\(580\) 0 0
\(581\) −1692.00 −0.120819
\(582\) 0 0
\(583\) 64.0000 0.00454650
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14166.0 −0.996071 −0.498035 − 0.867157i \(-0.665945\pi\)
−0.498035 + 0.867157i \(0.665945\pi\)
\(588\) 0 0
\(589\) 10800.0 0.755528
\(590\) 0 0
\(591\) 4428.00 0.308196
\(592\) 0 0
\(593\) −17842.0 −1.23555 −0.617777 − 0.786354i \(-0.711966\pi\)
−0.617777 + 0.786354i \(0.711966\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5200.00 −0.356485
\(598\) 0 0
\(599\) 17600.0 1.20053 0.600264 − 0.799802i \(-0.295062\pi\)
0.600264 + 0.799802i \(0.295062\pi\)
\(600\) 0 0
\(601\) 27302.0 1.85303 0.926516 − 0.376256i \(-0.122789\pi\)
0.926516 + 0.376256i \(0.122789\pi\)
\(602\) 0 0
\(603\) 2898.00 0.195714
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −3794.00 −0.253696 −0.126848 − 0.991922i \(-0.540486\pi\)
−0.126848 + 0.991922i \(0.540486\pi\)
\(608\) 0 0
\(609\) −600.000 −0.0399232
\(610\) 0 0
\(611\) 19532.0 1.29326
\(612\) 0 0
\(613\) −13238.0 −0.872231 −0.436116 − 0.899891i \(-0.643646\pi\)
−0.436116 + 0.899891i \(0.643646\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11574.0 0.755189 0.377595 − 0.925971i \(-0.376751\pi\)
0.377595 + 0.925971i \(0.376751\pi\)
\(618\) 0 0
\(619\) 8300.00 0.538942 0.269471 − 0.963008i \(-0.413151\pi\)
0.269471 + 0.963008i \(0.413151\pi\)
\(620\) 0 0
\(621\) −7800.00 −0.504031
\(622\) 0 0
\(623\) −900.000 −0.0578776
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −6400.00 −0.407642
\(628\) 0 0
\(629\) −6916.00 −0.438409
\(630\) 0 0
\(631\) 7508.00 0.473675 0.236837 − 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(632\) 0 0
\(633\) 2336.00 0.146679
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 11666.0 0.725626
\(638\) 0 0
\(639\) 9476.00 0.586643
\(640\) 0 0
\(641\) −27378.0 −1.68700 −0.843499 − 0.537130i \(-0.819508\pi\)
−0.843499 + 0.537130i \(0.819508\pi\)
\(642\) 0 0
\(643\) −1842.00 −0.112973 −0.0564863 − 0.998403i \(-0.517990\pi\)
−0.0564863 + 0.998403i \(0.517990\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10114.0 −0.614563 −0.307282 − 0.951619i \(-0.599419\pi\)
−0.307282 + 0.951619i \(0.599419\pi\)
\(648\) 0 0
\(649\) 16000.0 0.967727
\(650\) 0 0
\(651\) −1296.00 −0.0780250
\(652\) 0 0
\(653\) 10402.0 0.623372 0.311686 − 0.950185i \(-0.399106\pi\)
0.311686 + 0.950185i \(0.399106\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −20194.0 −1.19915
\(658\) 0 0
\(659\) 7100.00 0.419692 0.209846 − 0.977734i \(-0.432704\pi\)
0.209846 + 0.977734i \(0.432704\pi\)
\(660\) 0 0
\(661\) 7118.00 0.418847 0.209424 − 0.977825i \(-0.432841\pi\)
0.209424 + 0.977825i \(0.432841\pi\)
\(662\) 0 0
\(663\) −1976.00 −0.115749
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3900.00 −0.226400
\(668\) 0 0
\(669\) 12956.0 0.748741
\(670\) 0 0
\(671\) 16576.0 0.953665
\(672\) 0 0
\(673\) 31278.0 1.79150 0.895749 − 0.444560i \(-0.146640\pi\)
0.895749 + 0.444560i \(0.146640\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30054.0 −1.70616 −0.853079 − 0.521782i \(-0.825268\pi\)
−0.853079 + 0.521782i \(0.825268\pi\)
\(678\) 0 0
\(679\) −2316.00 −0.130898
\(680\) 0 0
\(681\) 1292.00 0.0727012
\(682\) 0 0
\(683\) 4518.00 0.253113 0.126557 − 0.991959i \(-0.459607\pi\)
0.126557 + 0.991959i \(0.459607\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7500.00 0.416511
\(688\) 0 0
\(689\) −76.0000 −0.00420228
\(690\) 0 0
\(691\) 29272.0 1.61152 0.805759 − 0.592243i \(-0.201758\pi\)
0.805759 + 0.592243i \(0.201758\pi\)
\(692\) 0 0
\(693\) −4416.00 −0.242063
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −572.000 −0.0310847
\(698\) 0 0
\(699\) 2964.00 0.160385
\(700\) 0 0
\(701\) 5798.00 0.312393 0.156196 − 0.987726i \(-0.450077\pi\)
0.156196 + 0.987726i \(0.450077\pi\)
\(702\) 0 0
\(703\) 26600.0 1.42708
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4212.00 −0.224057
\(708\) 0 0
\(709\) −8950.00 −0.474082 −0.237041 − 0.971500i \(-0.576178\pi\)
−0.237041 + 0.971500i \(0.576178\pi\)
\(710\) 0 0
\(711\) 13800.0 0.727905
\(712\) 0 0
\(713\) −8424.00 −0.442470
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2800.00 0.145841
\(718\) 0 0
\(719\) −7800.00 −0.404577 −0.202289 − 0.979326i \(-0.564838\pi\)
−0.202289 + 0.979326i \(0.564838\pi\)
\(720\) 0 0
\(721\) −3588.00 −0.185332
\(722\) 0 0
\(723\) −6044.00 −0.310897
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −8554.00 −0.436383 −0.218191 − 0.975906i \(-0.570016\pi\)
−0.218191 + 0.975906i \(0.570016\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) 11492.0 0.581460
\(732\) 0 0
\(733\) 2882.00 0.145224 0.0726119 − 0.997360i \(-0.476867\pi\)
0.0726119 + 0.997360i \(0.476867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4032.00 −0.201521
\(738\) 0 0
\(739\) 18700.0 0.930840 0.465420 − 0.885090i \(-0.345903\pi\)
0.465420 + 0.885090i \(0.345903\pi\)
\(740\) 0 0
\(741\) 7600.00 0.376779
\(742\) 0 0
\(743\) 12242.0 0.604462 0.302231 − 0.953235i \(-0.402269\pi\)
0.302231 + 0.953235i \(0.402269\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6486.00 0.317685
\(748\) 0 0
\(749\) 7164.00 0.349488
\(750\) 0 0
\(751\) 31148.0 1.51346 0.756729 − 0.653729i \(-0.226796\pi\)
0.756729 + 0.653729i \(0.226796\pi\)
\(752\) 0 0
\(753\) 2496.00 0.120796
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −7694.00 −0.369410 −0.184705 − 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(758\) 0 0
\(759\) 4992.00 0.238733
\(760\) 0 0
\(761\) −4518.00 −0.215213 −0.107607 − 0.994194i \(-0.534319\pi\)
−0.107607 + 0.994194i \(0.534319\pi\)
\(762\) 0 0
\(763\) 3300.00 0.156577
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19000.0 −0.894459
\(768\) 0 0
\(769\) −39550.0 −1.85463 −0.927314 − 0.374283i \(-0.877889\pi\)
−0.927314 + 0.374283i \(0.877889\pi\)
\(770\) 0 0
\(771\) 4212.00 0.196746
\(772\) 0 0
\(773\) 22122.0 1.02933 0.514666 − 0.857391i \(-0.327916\pi\)
0.514666 + 0.857391i \(0.327916\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −3192.00 −0.147378
\(778\) 0 0
\(779\) 2200.00 0.101185
\(780\) 0 0
\(781\) −13184.0 −0.604047
\(782\) 0 0
\(783\) 5000.00 0.228206
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 16634.0 0.753416 0.376708 − 0.926332i \(-0.377056\pi\)
0.376708 + 0.926332i \(0.377056\pi\)
\(788\) 0 0
\(789\) 7276.00 0.328305
\(790\) 0 0
\(791\) −9372.00 −0.421277
\(792\) 0 0
\(793\) −19684.0 −0.881462
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 27586.0 1.22603 0.613015 − 0.790071i \(-0.289956\pi\)
0.613015 + 0.790071i \(0.289956\pi\)
\(798\) 0 0
\(799\) 13364.0 0.591720
\(800\) 0 0
\(801\) 3450.00 0.152184
\(802\) 0 0
\(803\) 28096.0 1.23473
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −13100.0 −0.571427
\(808\) 0 0
\(809\) 3850.00 0.167316 0.0836581 − 0.996495i \(-0.473340\pi\)
0.0836581 + 0.996495i \(0.473340\pi\)
\(810\) 0 0
\(811\) 10032.0 0.434366 0.217183 − 0.976131i \(-0.430313\pi\)
0.217183 + 0.976131i \(0.430313\pi\)
\(812\) 0 0
\(813\) −8776.00 −0.378583
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −44200.0 −1.89273
\(818\) 0 0
\(819\) 5244.00 0.223736
\(820\) 0 0
\(821\) −20562.0 −0.874079 −0.437039 − 0.899442i \(-0.643973\pi\)
−0.437039 + 0.899442i \(0.643973\pi\)
\(822\) 0 0
\(823\) 10322.0 0.437184 0.218592 − 0.975816i \(-0.429854\pi\)
0.218592 + 0.975816i \(0.429854\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8846.00 −0.371954 −0.185977 − 0.982554i \(-0.559545\pi\)
−0.185977 + 0.982554i \(0.559545\pi\)
\(828\) 0 0
\(829\) 25350.0 1.06205 0.531026 − 0.847355i \(-0.321806\pi\)
0.531026 + 0.847355i \(0.321806\pi\)
\(830\) 0 0
\(831\) −1092.00 −0.0455849
\(832\) 0 0
\(833\) 7982.00 0.332005
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 10800.0 0.446001
\(838\) 0 0
\(839\) −46000.0 −1.89284 −0.946422 − 0.322932i \(-0.895331\pi\)
−0.946422 + 0.322932i \(0.895331\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 0 0
\(843\) 13716.0 0.560385
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1842.00 −0.0747248
\(848\) 0 0
\(849\) 18564.0 0.750430
\(850\) 0 0
\(851\) −20748.0 −0.835761
\(852\) 0 0
\(853\) −16998.0 −0.682298 −0.341149 − 0.940009i \(-0.610816\pi\)
−0.341149 + 0.940009i \(0.610816\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 26494.0 1.05603 0.528015 − 0.849235i \(-0.322936\pi\)
0.528015 + 0.849235i \(0.322936\pi\)
\(858\) 0 0
\(859\) −21500.0 −0.853982 −0.426991 − 0.904256i \(-0.640426\pi\)
−0.426991 + 0.904256i \(0.640426\pi\)
\(860\) 0 0
\(861\) −264.000 −0.0104496
\(862\) 0 0
\(863\) 25762.0 1.01616 0.508082 − 0.861309i \(-0.330355\pi\)
0.508082 + 0.861309i \(0.330355\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8474.00 0.331940
\(868\) 0 0
\(869\) −19200.0 −0.749500
\(870\) 0 0
\(871\) 4788.00 0.186263
\(872\) 0 0
\(873\) 8878.00 0.344186
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30546.0 1.17613 0.588064 − 0.808814i \(-0.299890\pi\)
0.588064 + 0.808814i \(0.299890\pi\)
\(878\) 0 0
\(879\) −9684.00 −0.371596
\(880\) 0 0
\(881\) 32942.0 1.25976 0.629878 − 0.776694i \(-0.283105\pi\)
0.629878 + 0.776694i \(0.283105\pi\)
\(882\) 0 0
\(883\) 27118.0 1.03351 0.516757 − 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −38634.0 −1.46246 −0.731230 − 0.682131i \(-0.761054\pi\)
−0.731230 + 0.682131i \(0.761054\pi\)
\(888\) 0 0
\(889\) 11076.0 0.417860
\(890\) 0 0
\(891\) 13472.0 0.506542
\(892\) 0 0
\(893\) −51400.0 −1.92613
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5928.00 −0.220658
\(898\) 0 0
\(899\) 5400.00 0.200334
\(900\) 0 0
\(901\) −52.0000 −0.00192272
\(902\) 0 0
\(903\) 5304.00 0.195466
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1794.00 0.0656767 0.0328384 − 0.999461i \(-0.489545\pi\)
0.0328384 + 0.999461i \(0.489545\pi\)
\(908\) 0 0
\(909\) 16146.0 0.589141
\(910\) 0 0
\(911\) −41732.0 −1.51772 −0.758860 − 0.651254i \(-0.774243\pi\)
−0.758860 + 0.651254i \(0.774243\pi\)
\(912\) 0 0
\(913\) −9024.00 −0.327109
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −13248.0 −0.477086
\(918\) 0 0
\(919\) −29200.0 −1.04812 −0.524058 − 0.851682i \(-0.675583\pi\)
−0.524058 + 0.851682i \(0.675583\pi\)
\(920\) 0 0
\(921\) −5188.00 −0.185614
\(922\) 0 0
\(923\) 15656.0 0.558314
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 13754.0 0.487315
\(928\) 0 0
\(929\) −48650.0 −1.71814 −0.859071 − 0.511856i \(-0.828958\pi\)
−0.859071 + 0.511856i \(0.828958\pi\)
\(930\) 0 0
\(931\) −30700.0 −1.08072
\(932\) 0 0
\(933\) 14664.0 0.514553
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 11334.0 0.395161 0.197580 − 0.980287i \(-0.436692\pi\)
0.197580 + 0.980287i \(0.436692\pi\)
\(938\) 0 0
\(939\) 3124.00 0.108571
\(940\) 0 0
\(941\) 31178.0 1.08010 0.540050 − 0.841633i \(-0.318405\pi\)
0.540050 + 0.841633i \(0.318405\pi\)
\(942\) 0 0
\(943\) −1716.00 −0.0592584
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4686.00 −0.160797 −0.0803984 − 0.996763i \(-0.525619\pi\)
−0.0803984 + 0.996763i \(0.525619\pi\)
\(948\) 0 0
\(949\) −33364.0 −1.14124
\(950\) 0 0
\(951\) −2852.00 −0.0972476
\(952\) 0 0
\(953\) 598.000 0.0203265 0.0101632 − 0.999948i \(-0.496765\pi\)
0.0101632 + 0.999948i \(0.496765\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −3200.00 −0.108089
\(958\) 0 0
\(959\) 14004.0 0.471546
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) 0 0
\(963\) −27462.0 −0.918952
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41726.0 1.38761 0.693804 − 0.720163i \(-0.255933\pi\)
0.693804 + 0.720163i \(0.255933\pi\)
\(968\) 0 0
\(969\) 5200.00 0.172392
\(970\) 0 0
\(971\) 24312.0 0.803511 0.401756 − 0.915747i \(-0.368400\pi\)
0.401756 + 0.915747i \(0.368400\pi\)
\(972\) 0 0
\(973\) −4200.00 −0.138382
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −40946.0 −1.34082 −0.670409 − 0.741992i \(-0.733881\pi\)
−0.670409 + 0.741992i \(0.733881\pi\)
\(978\) 0 0
\(979\) −4800.00 −0.156699
\(980\) 0 0
\(981\) −12650.0 −0.411706
\(982\) 0 0
\(983\) 42282.0 1.37191 0.685954 − 0.727645i \(-0.259385\pi\)
0.685954 + 0.727645i \(0.259385\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6168.00 0.198916
\(988\) 0 0
\(989\) 34476.0 1.10847
\(990\) 0 0
\(991\) −1172.00 −0.0375679 −0.0187840 − 0.999824i \(-0.505979\pi\)
−0.0187840 + 0.999824i \(0.505979\pi\)
\(992\) 0 0
\(993\) 8016.00 0.256173
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −31614.0 −1.00424 −0.502119 − 0.864798i \(-0.667446\pi\)
−0.502119 + 0.864798i \(0.667446\pi\)
\(998\) 0 0
\(999\) 26600.0 0.842429
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 1600.4.a.s.1.1 1
4.3 odd 2 1600.4.a.bi.1.1 1
5.4 even 2 320.4.a.h.1.1 1
8.3 odd 2 25.4.a.c.1.1 1
8.5 even 2 400.4.a.m.1.1 1
20.19 odd 2 320.4.a.g.1.1 1
24.11 even 2 225.4.a.b.1.1 1
40.3 even 4 25.4.b.a.24.1 2
40.13 odd 4 400.4.c.k.49.2 2
40.19 odd 2 5.4.a.a.1.1 ✓ 1
40.27 even 4 25.4.b.a.24.2 2
40.29 even 2 80.4.a.d.1.1 1
40.37 odd 4 400.4.c.k.49.1 2
56.27 even 2 1225.4.a.k.1.1 1
80.19 odd 4 1280.4.d.e.641.1 2
80.29 even 4 1280.4.d.l.641.2 2
80.59 odd 4 1280.4.d.e.641.2 2
80.69 even 4 1280.4.d.l.641.1 2
120.29 odd 2 720.4.a.u.1.1 1
120.59 even 2 45.4.a.d.1.1 1
120.83 odd 4 225.4.b.c.199.2 2
120.107 odd 4 225.4.b.c.199.1 2
280.19 even 6 245.4.e.g.116.1 2
280.59 even 6 245.4.e.g.226.1 2
280.139 even 2 245.4.a.a.1.1 1
280.179 odd 6 245.4.e.f.226.1 2
280.219 odd 6 245.4.e.f.116.1 2
360.59 even 6 405.4.e.c.136.1 2
360.139 odd 6 405.4.e.l.136.1 2
360.259 odd 6 405.4.e.l.271.1 2
360.299 even 6 405.4.e.c.271.1 2
440.219 even 2 605.4.a.d.1.1 1
520.259 odd 2 845.4.a.b.1.1 1
680.339 odd 2 1445.4.a.a.1.1 1
760.379 even 2 1805.4.a.h.1.1 1
840.419 odd 2 2205.4.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.4.a.a.1.1 ✓ 1 40.19 odd 2
25.4.a.c.1.1 1 8.3 odd 2
25.4.b.a.24.1 2 40.3 even 4
25.4.b.a.24.2 2 40.27 even 4
45.4.a.d.1.1 1 120.59 even 2
80.4.a.d.1.1 1 40.29 even 2
225.4.a.b.1.1 1 24.11 even 2
225.4.b.c.199.1 2 120.107 odd 4
225.4.b.c.199.2 2 120.83 odd 4
245.4.a.a.1.1 1 280.139 even 2
245.4.e.f.116.1 2 280.219 odd 6
245.4.e.f.226.1 2 280.179 odd 6
245.4.e.g.116.1 2 280.19 even 6
245.4.e.g.226.1 2 280.59 even 6
320.4.a.g.1.1 1 20.19 odd 2
320.4.a.h.1.1 1 5.4 even 2
400.4.a.m.1.1 1 8.5 even 2
400.4.c.k.49.1 2 40.37 odd 4
400.4.c.k.49.2 2 40.13 odd 4
405.4.e.c.136.1 2 360.59 even 6
405.4.e.c.271.1 2 360.299 even 6
405.4.e.l.136.1 2 360.139 odd 6
405.4.e.l.271.1 2 360.259 odd 6
605.4.a.d.1.1 1 440.219 even 2
720.4.a.u.1.1 1 120.29 odd 2
845.4.a.b.1.1 1 520.259 odd 2
1225.4.a.k.1.1 1 56.27 even 2
1280.4.d.e.641.1 2 80.19 odd 4
1280.4.d.e.641.2 2 80.59 odd 4
1280.4.d.l.641.1 2 80.69 even 4
1280.4.d.l.641.2 2 80.29 even 4
1445.4.a.a.1.1 1 680.339 odd 2
1600.4.a.s.1.1 1 1.1 even 1 trivial
1600.4.a.bi.1.1 1 4.3 odd 2
1805.4.a.h.1.1 1 760.379 even 2
2205.4.a.q.1.1 1 840.419 odd 2