Properties

Label 960.4.a.j.1.1
Level $960$
Weight $4$
Character 960.1
Self dual yes
Analytic conductor $56.642$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [960,4,Mod(1,960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(960, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("960.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.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: \(56.6418336055\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 960.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -5.00000 q^{5} +32.0000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -5.00000 q^{5} +32.0000 q^{7} +9.00000 q^{9} +60.0000 q^{11} +34.0000 q^{13} +15.0000 q^{15} +42.0000 q^{17} +76.0000 q^{19} -96.0000 q^{21} +25.0000 q^{25} -27.0000 q^{27} -6.00000 q^{29} -232.000 q^{31} -180.000 q^{33} -160.000 q^{35} -134.000 q^{37} -102.000 q^{39} +234.000 q^{41} +412.000 q^{43} -45.0000 q^{45} -360.000 q^{47} +681.000 q^{49} -126.000 q^{51} -222.000 q^{53} -300.000 q^{55} -228.000 q^{57} -660.000 q^{59} +490.000 q^{61} +288.000 q^{63} -170.000 q^{65} -812.000 q^{67} +120.000 q^{71} +746.000 q^{73} -75.0000 q^{75} +1920.00 q^{77} +152.000 q^{79} +81.0000 q^{81} +804.000 q^{83} -210.000 q^{85} +18.0000 q^{87} -678.000 q^{89} +1088.00 q^{91} +696.000 q^{93} -380.000 q^{95} +194.000 q^{97} +540.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 32.0000 1.72784 0.863919 0.503631i \(-0.168003\pi\)
0.863919 + 0.503631i \(0.168003\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 60.0000 1.64461 0.822304 0.569049i \(-0.192689\pi\)
0.822304 + 0.569049i \(0.192689\pi\)
\(12\) 0 0
\(13\) 34.0000 0.725377 0.362689 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 0 0
\(15\) 15.0000 0.258199
\(16\) 0 0
\(17\) 42.0000 0.599206 0.299603 0.954064i \(-0.403146\pi\)
0.299603 + 0.954064i \(0.403146\pi\)
\(18\) 0 0
\(19\) 76.0000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −96.0000 −0.997567
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −6.00000 −0.0384197 −0.0192099 0.999815i \(-0.506115\pi\)
−0.0192099 + 0.999815i \(0.506115\pi\)
\(30\) 0 0
\(31\) −232.000 −1.34414 −0.672071 0.740486i \(-0.734595\pi\)
−0.672071 + 0.740486i \(0.734595\pi\)
\(32\) 0 0
\(33\) −180.000 −0.949514
\(34\) 0 0
\(35\) −160.000 −0.772712
\(36\) 0 0
\(37\) −134.000 −0.595391 −0.297695 0.954661i \(-0.596218\pi\)
−0.297695 + 0.954661i \(0.596218\pi\)
\(38\) 0 0
\(39\) −102.000 −0.418797
\(40\) 0 0
\(41\) 234.000 0.891333 0.445667 0.895199i \(-0.352967\pi\)
0.445667 + 0.895199i \(0.352967\pi\)
\(42\) 0 0
\(43\) 412.000 1.46115 0.730575 0.682833i \(-0.239252\pi\)
0.730575 + 0.682833i \(0.239252\pi\)
\(44\) 0 0
\(45\) −45.0000 −0.149071
\(46\) 0 0
\(47\) −360.000 −1.11726 −0.558632 0.829416i \(-0.688674\pi\)
−0.558632 + 0.829416i \(0.688674\pi\)
\(48\) 0 0
\(49\) 681.000 1.98542
\(50\) 0 0
\(51\) −126.000 −0.345952
\(52\) 0 0
\(53\) −222.000 −0.575359 −0.287680 0.957727i \(-0.592884\pi\)
−0.287680 + 0.957727i \(0.592884\pi\)
\(54\) 0 0
\(55\) −300.000 −0.735491
\(56\) 0 0
\(57\) −228.000 −0.529813
\(58\) 0 0
\(59\) −660.000 −1.45635 −0.728175 0.685391i \(-0.759631\pi\)
−0.728175 + 0.685391i \(0.759631\pi\)
\(60\) 0 0
\(61\) 490.000 1.02849 0.514246 0.857642i \(-0.328072\pi\)
0.514246 + 0.857642i \(0.328072\pi\)
\(62\) 0 0
\(63\) 288.000 0.575946
\(64\) 0 0
\(65\) −170.000 −0.324399
\(66\) 0 0
\(67\) −812.000 −1.48062 −0.740310 0.672265i \(-0.765321\pi\)
−0.740310 + 0.672265i \(0.765321\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 120.000 0.200583 0.100291 0.994958i \(-0.468022\pi\)
0.100291 + 0.994958i \(0.468022\pi\)
\(72\) 0 0
\(73\) 746.000 1.19606 0.598032 0.801472i \(-0.295949\pi\)
0.598032 + 0.801472i \(0.295949\pi\)
\(74\) 0 0
\(75\) −75.0000 −0.115470
\(76\) 0 0
\(77\) 1920.00 2.84161
\(78\) 0 0
\(79\) 152.000 0.216473 0.108236 0.994125i \(-0.465480\pi\)
0.108236 + 0.994125i \(0.465480\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 804.000 1.06326 0.531629 0.846977i \(-0.321580\pi\)
0.531629 + 0.846977i \(0.321580\pi\)
\(84\) 0 0
\(85\) −210.000 −0.267973
\(86\) 0 0
\(87\) 18.0000 0.0221816
\(88\) 0 0
\(89\) −678.000 −0.807504 −0.403752 0.914868i \(-0.632294\pi\)
−0.403752 + 0.914868i \(0.632294\pi\)
\(90\) 0 0
\(91\) 1088.00 1.25333
\(92\) 0 0
\(93\) 696.000 0.776041
\(94\) 0 0
\(95\) −380.000 −0.410391
\(96\) 0 0
\(97\) 194.000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 540.000 0.548202
\(100\) 0 0
\(101\) −798.000 −0.786178 −0.393089 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(102\) 0 0
\(103\) 1088.00 1.04081 0.520407 0.853918i \(-0.325780\pi\)
0.520407 + 0.853918i \(0.325780\pi\)
\(104\) 0 0
\(105\) 480.000 0.446126
\(106\) 0 0
\(107\) −1716.00 −1.55039 −0.775196 0.631721i \(-0.782349\pi\)
−0.775196 + 0.631721i \(0.782349\pi\)
\(108\) 0 0
\(109\) 970.000 0.852378 0.426189 0.904634i \(-0.359856\pi\)
0.426189 + 0.904634i \(0.359856\pi\)
\(110\) 0 0
\(111\) 402.000 0.343749
\(112\) 0 0
\(113\) 426.000 0.354643 0.177322 0.984153i \(-0.443257\pi\)
0.177322 + 0.984153i \(0.443257\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 306.000 0.241792
\(118\) 0 0
\(119\) 1344.00 1.03533
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) −702.000 −0.514611
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 200.000 0.139741 0.0698706 0.997556i \(-0.477741\pi\)
0.0698706 + 0.997556i \(0.477741\pi\)
\(128\) 0 0
\(129\) −1236.00 −0.843595
\(130\) 0 0
\(131\) −60.0000 −0.0400170 −0.0200085 0.999800i \(-0.506369\pi\)
−0.0200085 + 0.999800i \(0.506369\pi\)
\(132\) 0 0
\(133\) 2432.00 1.58557
\(134\) 0 0
\(135\) 135.000 0.0860663
\(136\) 0 0
\(137\) 642.000 0.400363 0.200182 0.979759i \(-0.435847\pi\)
0.200182 + 0.979759i \(0.435847\pi\)
\(138\) 0 0
\(139\) 2836.00 1.73055 0.865275 0.501298i \(-0.167144\pi\)
0.865275 + 0.501298i \(0.167144\pi\)
\(140\) 0 0
\(141\) 1080.00 0.645053
\(142\) 0 0
\(143\) 2040.00 1.19296
\(144\) 0 0
\(145\) 30.0000 0.0171818
\(146\) 0 0
\(147\) −2043.00 −1.14628
\(148\) 0 0
\(149\) 1554.00 0.854420 0.427210 0.904152i \(-0.359496\pi\)
0.427210 + 0.904152i \(0.359496\pi\)
\(150\) 0 0
\(151\) −2272.00 −1.22446 −0.612228 0.790682i \(-0.709726\pi\)
−0.612228 + 0.790682i \(0.709726\pi\)
\(152\) 0 0
\(153\) 378.000 0.199735
\(154\) 0 0
\(155\) 1160.00 0.601119
\(156\) 0 0
\(157\) −1694.00 −0.861120 −0.430560 0.902562i \(-0.641684\pi\)
−0.430560 + 0.902562i \(0.641684\pi\)
\(158\) 0 0
\(159\) 666.000 0.332184
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 52.0000 0.0249874 0.0124937 0.999922i \(-0.496023\pi\)
0.0124937 + 0.999922i \(0.496023\pi\)
\(164\) 0 0
\(165\) 900.000 0.424636
\(166\) 0 0
\(167\) −1200.00 −0.556041 −0.278020 0.960575i \(-0.589678\pi\)
−0.278020 + 0.960575i \(0.589678\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 0 0
\(171\) 684.000 0.305888
\(172\) 0 0
\(173\) −54.0000 −0.0237315 −0.0118657 0.999930i \(-0.503777\pi\)
−0.0118657 + 0.999930i \(0.503777\pi\)
\(174\) 0 0
\(175\) 800.000 0.345568
\(176\) 0 0
\(177\) 1980.00 0.840824
\(178\) 0 0
\(179\) −876.000 −0.365784 −0.182892 0.983133i \(-0.558546\pi\)
−0.182892 + 0.983133i \(0.558546\pi\)
\(180\) 0 0
\(181\) −3854.00 −1.58268 −0.791341 0.611375i \(-0.790617\pi\)
−0.791341 + 0.611375i \(0.790617\pi\)
\(182\) 0 0
\(183\) −1470.00 −0.593801
\(184\) 0 0
\(185\) 670.000 0.266267
\(186\) 0 0
\(187\) 2520.00 0.985458
\(188\) 0 0
\(189\) −864.000 −0.332522
\(190\) 0 0
\(191\) −2784.00 −1.05468 −0.527338 0.849656i \(-0.676810\pi\)
−0.527338 + 0.849656i \(0.676810\pi\)
\(192\) 0 0
\(193\) 914.000 0.340887 0.170443 0.985367i \(-0.445480\pi\)
0.170443 + 0.985367i \(0.445480\pi\)
\(194\) 0 0
\(195\) 510.000 0.187292
\(196\) 0 0
\(197\) 5202.00 1.88136 0.940678 0.339300i \(-0.110190\pi\)
0.940678 + 0.339300i \(0.110190\pi\)
\(198\) 0 0
\(199\) 3152.00 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(200\) 0 0
\(201\) 2436.00 0.854837
\(202\) 0 0
\(203\) −192.000 −0.0663830
\(204\) 0 0
\(205\) −1170.00 −0.398616
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4560.00 1.50920
\(210\) 0 0
\(211\) −740.000 −0.241439 −0.120720 0.992687i \(-0.538520\pi\)
−0.120720 + 0.992687i \(0.538520\pi\)
\(212\) 0 0
\(213\) −360.000 −0.115807
\(214\) 0 0
\(215\) −2060.00 −0.653446
\(216\) 0 0
\(217\) −7424.00 −2.32246
\(218\) 0 0
\(219\) −2238.00 −0.690548
\(220\) 0 0
\(221\) 1428.00 0.434650
\(222\) 0 0
\(223\) −520.000 −0.156151 −0.0780757 0.996947i \(-0.524878\pi\)
−0.0780757 + 0.996947i \(0.524878\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 0 0
\(227\) −396.000 −0.115786 −0.0578930 0.998323i \(-0.518438\pi\)
−0.0578930 + 0.998323i \(0.518438\pi\)
\(228\) 0 0
\(229\) 1330.00 0.383794 0.191897 0.981415i \(-0.438536\pi\)
0.191897 + 0.981415i \(0.438536\pi\)
\(230\) 0 0
\(231\) −5760.00 −1.64061
\(232\) 0 0
\(233\) 4866.00 1.36816 0.684082 0.729405i \(-0.260203\pi\)
0.684082 + 0.729405i \(0.260203\pi\)
\(234\) 0 0
\(235\) 1800.00 0.499656
\(236\) 0 0
\(237\) −456.000 −0.124981
\(238\) 0 0
\(239\) −1824.00 −0.493660 −0.246830 0.969059i \(-0.579389\pi\)
−0.246830 + 0.969059i \(0.579389\pi\)
\(240\) 0 0
\(241\) 6482.00 1.73254 0.866270 0.499575i \(-0.166511\pi\)
0.866270 + 0.499575i \(0.166511\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) −3405.00 −0.887908
\(246\) 0 0
\(247\) 2584.00 0.665652
\(248\) 0 0
\(249\) −2412.00 −0.613873
\(250\) 0 0
\(251\) −1476.00 −0.371172 −0.185586 0.982628i \(-0.559418\pi\)
−0.185586 + 0.982628i \(0.559418\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 630.000 0.154714
\(256\) 0 0
\(257\) 4314.00 1.04708 0.523541 0.852001i \(-0.324611\pi\)
0.523541 + 0.852001i \(0.324611\pi\)
\(258\) 0 0
\(259\) −4288.00 −1.02874
\(260\) 0 0
\(261\) −54.0000 −0.0128066
\(262\) 0 0
\(263\) −5280.00 −1.23794 −0.618971 0.785414i \(-0.712450\pi\)
−0.618971 + 0.785414i \(0.712450\pi\)
\(264\) 0 0
\(265\) 1110.00 0.257309
\(266\) 0 0
\(267\) 2034.00 0.466213
\(268\) 0 0
\(269\) −5526.00 −1.25251 −0.626257 0.779617i \(-0.715414\pi\)
−0.626257 + 0.779617i \(0.715414\pi\)
\(270\) 0 0
\(271\) 2024.00 0.453687 0.226844 0.973931i \(-0.427159\pi\)
0.226844 + 0.973931i \(0.427159\pi\)
\(272\) 0 0
\(273\) −3264.00 −0.723613
\(274\) 0 0
\(275\) 1500.00 0.328921
\(276\) 0 0
\(277\) −2054.00 −0.445534 −0.222767 0.974872i \(-0.571509\pi\)
−0.222767 + 0.974872i \(0.571509\pi\)
\(278\) 0 0
\(279\) −2088.00 −0.448048
\(280\) 0 0
\(281\) −7302.00 −1.55018 −0.775090 0.631850i \(-0.782296\pi\)
−0.775090 + 0.631850i \(0.782296\pi\)
\(282\) 0 0
\(283\) 3724.00 0.782222 0.391111 0.920344i \(-0.372091\pi\)
0.391111 + 0.920344i \(0.372091\pi\)
\(284\) 0 0
\(285\) 1140.00 0.236940
\(286\) 0 0
\(287\) 7488.00 1.54008
\(288\) 0 0
\(289\) −3149.00 −0.640953
\(290\) 0 0
\(291\) −582.000 −0.117242
\(292\) 0 0
\(293\) 7218.00 1.43918 0.719591 0.694399i \(-0.244330\pi\)
0.719591 + 0.694399i \(0.244330\pi\)
\(294\) 0 0
\(295\) 3300.00 0.651300
\(296\) 0 0
\(297\) −1620.00 −0.316505
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 13184.0 2.52463
\(302\) 0 0
\(303\) 2394.00 0.453900
\(304\) 0 0
\(305\) −2450.00 −0.459956
\(306\) 0 0
\(307\) −2540.00 −0.472200 −0.236100 0.971729i \(-0.575869\pi\)
−0.236100 + 0.971729i \(0.575869\pi\)
\(308\) 0 0
\(309\) −3264.00 −0.600914
\(310\) 0 0
\(311\) 1560.00 0.284436 0.142218 0.989835i \(-0.454577\pi\)
0.142218 + 0.989835i \(0.454577\pi\)
\(312\) 0 0
\(313\) −934.000 −0.168667 −0.0843335 0.996438i \(-0.526876\pi\)
−0.0843335 + 0.996438i \(0.526876\pi\)
\(314\) 0 0
\(315\) −1440.00 −0.257571
\(316\) 0 0
\(317\) 1674.00 0.296597 0.148298 0.988943i \(-0.452620\pi\)
0.148298 + 0.988943i \(0.452620\pi\)
\(318\) 0 0
\(319\) −360.000 −0.0631854
\(320\) 0 0
\(321\) 5148.00 0.895119
\(322\) 0 0
\(323\) 3192.00 0.549869
\(324\) 0 0
\(325\) 850.000 0.145075
\(326\) 0 0
\(327\) −2910.00 −0.492120
\(328\) 0 0
\(329\) −11520.0 −1.93045
\(330\) 0 0
\(331\) 3988.00 0.662237 0.331118 0.943589i \(-0.392574\pi\)
0.331118 + 0.943589i \(0.392574\pi\)
\(332\) 0 0
\(333\) −1206.00 −0.198464
\(334\) 0 0
\(335\) 4060.00 0.662154
\(336\) 0 0
\(337\) 2.00000 0.000323285 0 0.000161642 1.00000i \(-0.499949\pi\)
0.000161642 1.00000i \(0.499949\pi\)
\(338\) 0 0
\(339\) −1278.00 −0.204753
\(340\) 0 0
\(341\) −13920.0 −2.21059
\(342\) 0 0
\(343\) 10816.0 1.70265
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1764.00 −0.272901 −0.136450 0.990647i \(-0.543569\pi\)
−0.136450 + 0.990647i \(0.543569\pi\)
\(348\) 0 0
\(349\) −4310.00 −0.661057 −0.330529 0.943796i \(-0.607227\pi\)
−0.330529 + 0.943796i \(0.607227\pi\)
\(350\) 0 0
\(351\) −918.000 −0.139599
\(352\) 0 0
\(353\) 138.000 0.0208074 0.0104037 0.999946i \(-0.496688\pi\)
0.0104037 + 0.999946i \(0.496688\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 0 0
\(357\) −4032.00 −0.597748
\(358\) 0 0
\(359\) −11976.0 −1.76064 −0.880319 0.474382i \(-0.842672\pi\)
−0.880319 + 0.474382i \(0.842672\pi\)
\(360\) 0 0
\(361\) −1083.00 −0.157895
\(362\) 0 0
\(363\) −6807.00 −0.984228
\(364\) 0 0
\(365\) −3730.00 −0.534896
\(366\) 0 0
\(367\) 9704.00 1.38023 0.690115 0.723699i \(-0.257560\pi\)
0.690115 + 0.723699i \(0.257560\pi\)
\(368\) 0 0
\(369\) 2106.00 0.297111
\(370\) 0 0
\(371\) −7104.00 −0.994128
\(372\) 0 0
\(373\) 8122.00 1.12746 0.563728 0.825960i \(-0.309367\pi\)
0.563728 + 0.825960i \(0.309367\pi\)
\(374\) 0 0
\(375\) 375.000 0.0516398
\(376\) 0 0
\(377\) −204.000 −0.0278688
\(378\) 0 0
\(379\) −3404.00 −0.461350 −0.230675 0.973031i \(-0.574093\pi\)
−0.230675 + 0.973031i \(0.574093\pi\)
\(380\) 0 0
\(381\) −600.000 −0.0806796
\(382\) 0 0
\(383\) −2520.00 −0.336204 −0.168102 0.985770i \(-0.553764\pi\)
−0.168102 + 0.985770i \(0.553764\pi\)
\(384\) 0 0
\(385\) −9600.00 −1.27081
\(386\) 0 0
\(387\) 3708.00 0.487050
\(388\) 0 0
\(389\) −1566.00 −0.204111 −0.102056 0.994779i \(-0.532542\pi\)
−0.102056 + 0.994779i \(0.532542\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 180.000 0.0231038
\(394\) 0 0
\(395\) −760.000 −0.0968095
\(396\) 0 0
\(397\) 4354.00 0.550431 0.275215 0.961383i \(-0.411251\pi\)
0.275215 + 0.961383i \(0.411251\pi\)
\(398\) 0 0
\(399\) −7296.00 −0.915431
\(400\) 0 0
\(401\) −8046.00 −1.00199 −0.500995 0.865450i \(-0.667033\pi\)
−0.500995 + 0.865450i \(0.667033\pi\)
\(402\) 0 0
\(403\) −7888.00 −0.975011
\(404\) 0 0
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) −8040.00 −0.979184
\(408\) 0 0
\(409\) −2806.00 −0.339237 −0.169618 0.985510i \(-0.554253\pi\)
−0.169618 + 0.985510i \(0.554253\pi\)
\(410\) 0 0
\(411\) −1926.00 −0.231150
\(412\) 0 0
\(413\) −21120.0 −2.51634
\(414\) 0 0
\(415\) −4020.00 −0.475504
\(416\) 0 0
\(417\) −8508.00 −0.999133
\(418\) 0 0
\(419\) −11580.0 −1.35017 −0.675084 0.737741i \(-0.735892\pi\)
−0.675084 + 0.737741i \(0.735892\pi\)
\(420\) 0 0
\(421\) 370.000 0.0428330 0.0214165 0.999771i \(-0.493182\pi\)
0.0214165 + 0.999771i \(0.493182\pi\)
\(422\) 0 0
\(423\) −3240.00 −0.372421
\(424\) 0 0
\(425\) 1050.00 0.119841
\(426\) 0 0
\(427\) 15680.0 1.77707
\(428\) 0 0
\(429\) −6120.00 −0.688756
\(430\) 0 0
\(431\) 5040.00 0.563267 0.281634 0.959522i \(-0.409124\pi\)
0.281634 + 0.959522i \(0.409124\pi\)
\(432\) 0 0
\(433\) −3742.00 −0.415310 −0.207655 0.978202i \(-0.566583\pi\)
−0.207655 + 0.978202i \(0.566583\pi\)
\(434\) 0 0
\(435\) −90.0000 −0.00991993
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −6208.00 −0.674924 −0.337462 0.941339i \(-0.609568\pi\)
−0.337462 + 0.941339i \(0.609568\pi\)
\(440\) 0 0
\(441\) 6129.00 0.661808
\(442\) 0 0
\(443\) 15564.0 1.66923 0.834614 0.550835i \(-0.185691\pi\)
0.834614 + 0.550835i \(0.185691\pi\)
\(444\) 0 0
\(445\) 3390.00 0.361127
\(446\) 0 0
\(447\) −4662.00 −0.493300
\(448\) 0 0
\(449\) −15774.0 −1.65795 −0.828977 0.559283i \(-0.811076\pi\)
−0.828977 + 0.559283i \(0.811076\pi\)
\(450\) 0 0
\(451\) 14040.0 1.46589
\(452\) 0 0
\(453\) 6816.00 0.706940
\(454\) 0 0
\(455\) −5440.00 −0.560508
\(456\) 0 0
\(457\) 9722.00 0.995133 0.497567 0.867426i \(-0.334227\pi\)
0.497567 + 0.867426i \(0.334227\pi\)
\(458\) 0 0
\(459\) −1134.00 −0.115317
\(460\) 0 0
\(461\) 10890.0 1.10021 0.550106 0.835095i \(-0.314587\pi\)
0.550106 + 0.835095i \(0.314587\pi\)
\(462\) 0 0
\(463\) 15128.0 1.51848 0.759242 0.650809i \(-0.225570\pi\)
0.759242 + 0.650809i \(0.225570\pi\)
\(464\) 0 0
\(465\) −3480.00 −0.347056
\(466\) 0 0
\(467\) −10668.0 −1.05708 −0.528540 0.848909i \(-0.677260\pi\)
−0.528540 + 0.848909i \(0.677260\pi\)
\(468\) 0 0
\(469\) −25984.0 −2.55827
\(470\) 0 0
\(471\) 5082.00 0.497168
\(472\) 0 0
\(473\) 24720.0 2.40302
\(474\) 0 0
\(475\) 1900.00 0.183533
\(476\) 0 0
\(477\) −1998.00 −0.191786
\(478\) 0 0
\(479\) 15264.0 1.45601 0.728006 0.685571i \(-0.240447\pi\)
0.728006 + 0.685571i \(0.240447\pi\)
\(480\) 0 0
\(481\) −4556.00 −0.431883
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −970.000 −0.0908153
\(486\) 0 0
\(487\) −5776.00 −0.537445 −0.268722 0.963218i \(-0.586601\pi\)
−0.268722 + 0.963218i \(0.586601\pi\)
\(488\) 0 0
\(489\) −156.000 −0.0144265
\(490\) 0 0
\(491\) −14244.0 −1.30921 −0.654606 0.755971i \(-0.727165\pi\)
−0.654606 + 0.755971i \(0.727165\pi\)
\(492\) 0 0
\(493\) −252.000 −0.0230213
\(494\) 0 0
\(495\) −2700.00 −0.245164
\(496\) 0 0
\(497\) 3840.00 0.346575
\(498\) 0 0
\(499\) 17116.0 1.53551 0.767753 0.640746i \(-0.221375\pi\)
0.767753 + 0.640746i \(0.221375\pi\)
\(500\) 0 0
\(501\) 3600.00 0.321030
\(502\) 0 0
\(503\) −16848.0 −1.49347 −0.746735 0.665122i \(-0.768380\pi\)
−0.746735 + 0.665122i \(0.768380\pi\)
\(504\) 0 0
\(505\) 3990.00 0.351589
\(506\) 0 0
\(507\) 3123.00 0.273565
\(508\) 0 0
\(509\) 3834.00 0.333868 0.166934 0.985968i \(-0.446613\pi\)
0.166934 + 0.985968i \(0.446613\pi\)
\(510\) 0 0
\(511\) 23872.0 2.06660
\(512\) 0 0
\(513\) −2052.00 −0.176604
\(514\) 0 0
\(515\) −5440.00 −0.465466
\(516\) 0 0
\(517\) −21600.0 −1.83746
\(518\) 0 0
\(519\) 162.000 0.0137014
\(520\) 0 0
\(521\) −18822.0 −1.58274 −0.791369 0.611338i \(-0.790631\pi\)
−0.791369 + 0.611338i \(0.790631\pi\)
\(522\) 0 0
\(523\) 15340.0 1.28255 0.641273 0.767313i \(-0.278407\pi\)
0.641273 + 0.767313i \(0.278407\pi\)
\(524\) 0 0
\(525\) −2400.00 −0.199513
\(526\) 0 0
\(527\) −9744.00 −0.805418
\(528\) 0 0
\(529\) −12167.0 −1.00000
\(530\) 0 0
\(531\) −5940.00 −0.485450
\(532\) 0 0
\(533\) 7956.00 0.646553
\(534\) 0 0
\(535\) 8580.00 0.693357
\(536\) 0 0
\(537\) 2628.00 0.211185
\(538\) 0 0
\(539\) 40860.0 3.26524
\(540\) 0 0
\(541\) −18950.0 −1.50596 −0.752980 0.658044i \(-0.771384\pi\)
−0.752980 + 0.658044i \(0.771384\pi\)
\(542\) 0 0
\(543\) 11562.0 0.913762
\(544\) 0 0
\(545\) −4850.00 −0.381195
\(546\) 0 0
\(547\) 10036.0 0.784476 0.392238 0.919864i \(-0.371701\pi\)
0.392238 + 0.919864i \(0.371701\pi\)
\(548\) 0 0
\(549\) 4410.00 0.342831
\(550\) 0 0
\(551\) −456.000 −0.0352564
\(552\) 0 0
\(553\) 4864.00 0.374030
\(554\) 0 0
\(555\) −2010.00 −0.153729
\(556\) 0 0
\(557\) −10326.0 −0.785506 −0.392753 0.919644i \(-0.628477\pi\)
−0.392753 + 0.919644i \(0.628477\pi\)
\(558\) 0 0
\(559\) 14008.0 1.05988
\(560\) 0 0
\(561\) −7560.00 −0.568954
\(562\) 0 0
\(563\) −4524.00 −0.338657 −0.169328 0.985560i \(-0.554160\pi\)
−0.169328 + 0.985560i \(0.554160\pi\)
\(564\) 0 0
\(565\) −2130.00 −0.158601
\(566\) 0 0
\(567\) 2592.00 0.191982
\(568\) 0 0
\(569\) 16362.0 1.20550 0.602751 0.797929i \(-0.294071\pi\)
0.602751 + 0.797929i \(0.294071\pi\)
\(570\) 0 0
\(571\) −6620.00 −0.485181 −0.242591 0.970129i \(-0.577997\pi\)
−0.242591 + 0.970129i \(0.577997\pi\)
\(572\) 0 0
\(573\) 8352.00 0.608918
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8834.00 0.637373 0.318687 0.947860i \(-0.396758\pi\)
0.318687 + 0.947860i \(0.396758\pi\)
\(578\) 0 0
\(579\) −2742.00 −0.196811
\(580\) 0 0
\(581\) 25728.0 1.83714
\(582\) 0 0
\(583\) −13320.0 −0.946240
\(584\) 0 0
\(585\) −1530.00 −0.108133
\(586\) 0 0
\(587\) −3636.00 −0.255662 −0.127831 0.991796i \(-0.540802\pi\)
−0.127831 + 0.991796i \(0.540802\pi\)
\(588\) 0 0
\(589\) −17632.0 −1.23347
\(590\) 0 0
\(591\) −15606.0 −1.08620
\(592\) 0 0
\(593\) 6570.00 0.454971 0.227485 0.973782i \(-0.426950\pi\)
0.227485 + 0.973782i \(0.426950\pi\)
\(594\) 0 0
\(595\) −6720.00 −0.463014
\(596\) 0 0
\(597\) −9456.00 −0.648255
\(598\) 0 0
\(599\) 16584.0 1.13123 0.565613 0.824671i \(-0.308640\pi\)
0.565613 + 0.824671i \(0.308640\pi\)
\(600\) 0 0
\(601\) −502.000 −0.0340716 −0.0170358 0.999855i \(-0.505423\pi\)
−0.0170358 + 0.999855i \(0.505423\pi\)
\(602\) 0 0
\(603\) −7308.00 −0.493540
\(604\) 0 0
\(605\) −11345.0 −0.762380
\(606\) 0 0
\(607\) −18568.0 −1.24160 −0.620801 0.783969i \(-0.713192\pi\)
−0.620801 + 0.783969i \(0.713192\pi\)
\(608\) 0 0
\(609\) 576.000 0.0383263
\(610\) 0 0
\(611\) −12240.0 −0.810438
\(612\) 0 0
\(613\) 13114.0 0.864061 0.432031 0.901859i \(-0.357797\pi\)
0.432031 + 0.901859i \(0.357797\pi\)
\(614\) 0 0
\(615\) 3510.00 0.230141
\(616\) 0 0
\(617\) 5250.00 0.342556 0.171278 0.985223i \(-0.445210\pi\)
0.171278 + 0.985223i \(0.445210\pi\)
\(618\) 0 0
\(619\) 10804.0 0.701534 0.350767 0.936463i \(-0.385921\pi\)
0.350767 + 0.936463i \(0.385921\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21696.0 −1.39524
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −13680.0 −0.871334
\(628\) 0 0
\(629\) −5628.00 −0.356762
\(630\) 0 0
\(631\) −27088.0 −1.70896 −0.854482 0.519481i \(-0.826125\pi\)
−0.854482 + 0.519481i \(0.826125\pi\)
\(632\) 0 0
\(633\) 2220.00 0.139395
\(634\) 0 0
\(635\) −1000.00 −0.0624942
\(636\) 0 0
\(637\) 23154.0 1.44018
\(638\) 0 0
\(639\) 1080.00 0.0668609
\(640\) 0 0
\(641\) 18930.0 1.16644 0.583222 0.812313i \(-0.301792\pi\)
0.583222 + 0.812313i \(0.301792\pi\)
\(642\) 0 0
\(643\) −20108.0 −1.23325 −0.616627 0.787256i \(-0.711501\pi\)
−0.616627 + 0.787256i \(0.711501\pi\)
\(644\) 0 0
\(645\) 6180.00 0.377267
\(646\) 0 0
\(647\) −7152.00 −0.434581 −0.217291 0.976107i \(-0.569722\pi\)
−0.217291 + 0.976107i \(0.569722\pi\)
\(648\) 0 0
\(649\) −39600.0 −2.39512
\(650\) 0 0
\(651\) 22272.0 1.34087
\(652\) 0 0
\(653\) 31626.0 1.89528 0.947642 0.319333i \(-0.103459\pi\)
0.947642 + 0.319333i \(0.103459\pi\)
\(654\) 0 0
\(655\) 300.000 0.0178961
\(656\) 0 0
\(657\) 6714.00 0.398688
\(658\) 0 0
\(659\) −28092.0 −1.66056 −0.830280 0.557347i \(-0.811819\pi\)
−0.830280 + 0.557347i \(0.811819\pi\)
\(660\) 0 0
\(661\) 13186.0 0.775909 0.387955 0.921678i \(-0.373182\pi\)
0.387955 + 0.921678i \(0.373182\pi\)
\(662\) 0 0
\(663\) −4284.00 −0.250945
\(664\) 0 0
\(665\) −12160.0 −0.709090
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1560.00 0.0901541
\(670\) 0 0
\(671\) 29400.0 1.69147
\(672\) 0 0
\(673\) 5138.00 0.294287 0.147144 0.989115i \(-0.452992\pi\)
0.147144 + 0.989115i \(0.452992\pi\)
\(674\) 0 0
\(675\) −675.000 −0.0384900
\(676\) 0 0
\(677\) −6078.00 −0.345047 −0.172523 0.985005i \(-0.555192\pi\)
−0.172523 + 0.985005i \(0.555192\pi\)
\(678\) 0 0
\(679\) 6208.00 0.350871
\(680\) 0 0
\(681\) 1188.00 0.0668491
\(682\) 0 0
\(683\) −32244.0 −1.80642 −0.903208 0.429203i \(-0.858795\pi\)
−0.903208 + 0.429203i \(0.858795\pi\)
\(684\) 0 0
\(685\) −3210.00 −0.179048
\(686\) 0 0
\(687\) −3990.00 −0.221584
\(688\) 0 0
\(689\) −7548.00 −0.417353
\(690\) 0 0
\(691\) −4484.00 −0.246859 −0.123429 0.992353i \(-0.539389\pi\)
−0.123429 + 0.992353i \(0.539389\pi\)
\(692\) 0 0
\(693\) 17280.0 0.947205
\(694\) 0 0
\(695\) −14180.0 −0.773925
\(696\) 0 0
\(697\) 9828.00 0.534092
\(698\) 0 0
\(699\) −14598.0 −0.789910
\(700\) 0 0
\(701\) 30426.0 1.63934 0.819668 0.572839i \(-0.194158\pi\)
0.819668 + 0.572839i \(0.194158\pi\)
\(702\) 0 0
\(703\) −10184.0 −0.546368
\(704\) 0 0
\(705\) −5400.00 −0.288476
\(706\) 0 0
\(707\) −25536.0 −1.35839
\(708\) 0 0
\(709\) −13262.0 −0.702489 −0.351245 0.936284i \(-0.614241\pi\)
−0.351245 + 0.936284i \(0.614241\pi\)
\(710\) 0 0
\(711\) 1368.00 0.0721575
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −10200.0 −0.533508
\(716\) 0 0
\(717\) 5472.00 0.285015
\(718\) 0 0
\(719\) 13920.0 0.722014 0.361007 0.932563i \(-0.382433\pi\)
0.361007 + 0.932563i \(0.382433\pi\)
\(720\) 0 0
\(721\) 34816.0 1.79836
\(722\) 0 0
\(723\) −19446.0 −1.00028
\(724\) 0 0
\(725\) −150.000 −0.00768395
\(726\) 0 0
\(727\) −9376.00 −0.478317 −0.239159 0.970981i \(-0.576872\pi\)
−0.239159 + 0.970981i \(0.576872\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 17304.0 0.875529
\(732\) 0 0
\(733\) −6014.00 −0.303045 −0.151523 0.988454i \(-0.548418\pi\)
−0.151523 + 0.988454i \(0.548418\pi\)
\(734\) 0 0
\(735\) 10215.0 0.512634
\(736\) 0 0
\(737\) −48720.0 −2.43504
\(738\) 0 0
\(739\) 7468.00 0.371739 0.185869 0.982574i \(-0.440490\pi\)
0.185869 + 0.982574i \(0.440490\pi\)
\(740\) 0 0
\(741\) −7752.00 −0.384314
\(742\) 0 0
\(743\) 31248.0 1.54290 0.771452 0.636287i \(-0.219531\pi\)
0.771452 + 0.636287i \(0.219531\pi\)
\(744\) 0 0
\(745\) −7770.00 −0.382108
\(746\) 0 0
\(747\) 7236.00 0.354420
\(748\) 0 0
\(749\) −54912.0 −2.67883
\(750\) 0 0
\(751\) 32840.0 1.59567 0.797835 0.602875i \(-0.205978\pi\)
0.797835 + 0.602875i \(0.205978\pi\)
\(752\) 0 0
\(753\) 4428.00 0.214297
\(754\) 0 0
\(755\) 11360.0 0.547593
\(756\) 0 0
\(757\) 19066.0 0.915410 0.457705 0.889104i \(-0.348672\pi\)
0.457705 + 0.889104i \(0.348672\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6858.00 0.326678 0.163339 0.986570i \(-0.447773\pi\)
0.163339 + 0.986570i \(0.447773\pi\)
\(762\) 0 0
\(763\) 31040.0 1.47277
\(764\) 0 0
\(765\) −1890.00 −0.0893243
\(766\) 0 0
\(767\) −22440.0 −1.05640
\(768\) 0 0
\(769\) 22178.0 1.04000 0.519999 0.854167i \(-0.325932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(770\) 0 0
\(771\) −12942.0 −0.604533
\(772\) 0 0
\(773\) −14286.0 −0.664724 −0.332362 0.943152i \(-0.607846\pi\)
−0.332362 + 0.943152i \(0.607846\pi\)
\(774\) 0 0
\(775\) −5800.00 −0.268829
\(776\) 0 0
\(777\) 12864.0 0.593943
\(778\) 0 0
\(779\) 17784.0 0.817943
\(780\) 0 0
\(781\) 7200.00 0.329880
\(782\) 0 0
\(783\) 162.000 0.00739388
\(784\) 0 0
\(785\) 8470.00 0.385105
\(786\) 0 0
\(787\) 18868.0 0.854602 0.427301 0.904109i \(-0.359465\pi\)
0.427301 + 0.904109i \(0.359465\pi\)
\(788\) 0 0
\(789\) 15840.0 0.714726
\(790\) 0 0
\(791\) 13632.0 0.612766
\(792\) 0 0
\(793\) 16660.0 0.746045
\(794\) 0 0
\(795\) −3330.00 −0.148557
\(796\) 0 0
\(797\) 21690.0 0.963989 0.481994 0.876174i \(-0.339913\pi\)
0.481994 + 0.876174i \(0.339913\pi\)
\(798\) 0 0
\(799\) −15120.0 −0.669471
\(800\) 0 0
\(801\) −6102.00 −0.269168
\(802\) 0 0
\(803\) 44760.0 1.96706
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 16578.0 0.723139
\(808\) 0 0
\(809\) −24726.0 −1.07456 −0.537281 0.843404i \(-0.680548\pi\)
−0.537281 + 0.843404i \(0.680548\pi\)
\(810\) 0 0
\(811\) 2644.00 0.114480 0.0572401 0.998360i \(-0.481770\pi\)
0.0572401 + 0.998360i \(0.481770\pi\)
\(812\) 0 0
\(813\) −6072.00 −0.261936
\(814\) 0 0
\(815\) −260.000 −0.0111747
\(816\) 0 0
\(817\) 31312.0 1.34084
\(818\) 0 0
\(819\) 9792.00 0.417778
\(820\) 0 0
\(821\) 37842.0 1.60864 0.804321 0.594195i \(-0.202529\pi\)
0.804321 + 0.594195i \(0.202529\pi\)
\(822\) 0 0
\(823\) −880.000 −0.0372720 −0.0186360 0.999826i \(-0.505932\pi\)
−0.0186360 + 0.999826i \(0.505932\pi\)
\(824\) 0 0
\(825\) −4500.00 −0.189903
\(826\) 0 0
\(827\) 12876.0 0.541406 0.270703 0.962663i \(-0.412744\pi\)
0.270703 + 0.962663i \(0.412744\pi\)
\(828\) 0 0
\(829\) 25498.0 1.06825 0.534127 0.845404i \(-0.320641\pi\)
0.534127 + 0.845404i \(0.320641\pi\)
\(830\) 0 0
\(831\) 6162.00 0.257229
\(832\) 0 0
\(833\) 28602.0 1.18968
\(834\) 0 0
\(835\) 6000.00 0.248669
\(836\) 0 0
\(837\) 6264.00 0.258680
\(838\) 0 0
\(839\) −40584.0 −1.66998 −0.834991 0.550263i \(-0.814527\pi\)
−0.834991 + 0.550263i \(0.814527\pi\)
\(840\) 0 0
\(841\) −24353.0 −0.998524
\(842\) 0 0
\(843\) 21906.0 0.894997
\(844\) 0 0
\(845\) 5205.00 0.211902
\(846\) 0 0
\(847\) 72608.0 2.94550
\(848\) 0 0
\(849\) −11172.0 −0.451616
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 25738.0 1.03312 0.516561 0.856251i \(-0.327212\pi\)
0.516561 + 0.856251i \(0.327212\pi\)
\(854\) 0 0
\(855\) −3420.00 −0.136797
\(856\) 0 0
\(857\) 13314.0 0.530686 0.265343 0.964154i \(-0.414515\pi\)
0.265343 + 0.964154i \(0.414515\pi\)
\(858\) 0 0
\(859\) −24524.0 −0.974096 −0.487048 0.873375i \(-0.661926\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(860\) 0 0
\(861\) −22464.0 −0.889165
\(862\) 0 0
\(863\) 5592.00 0.220572 0.110286 0.993900i \(-0.464823\pi\)
0.110286 + 0.993900i \(0.464823\pi\)
\(864\) 0 0
\(865\) 270.000 0.0106130
\(866\) 0 0
\(867\) 9447.00 0.370054
\(868\) 0 0
\(869\) 9120.00 0.356012
\(870\) 0 0
\(871\) −27608.0 −1.07401
\(872\) 0 0
\(873\) 1746.00 0.0676897
\(874\) 0 0
\(875\) −4000.00 −0.154542
\(876\) 0 0
\(877\) 14386.0 0.553912 0.276956 0.960883i \(-0.410674\pi\)
0.276956 + 0.960883i \(0.410674\pi\)
\(878\) 0 0
\(879\) −21654.0 −0.830912
\(880\) 0 0
\(881\) 47106.0 1.80141 0.900705 0.434432i \(-0.143051\pi\)
0.900705 + 0.434432i \(0.143051\pi\)
\(882\) 0 0
\(883\) −51548.0 −1.96458 −0.982292 0.187354i \(-0.940009\pi\)
−0.982292 + 0.187354i \(0.940009\pi\)
\(884\) 0 0
\(885\) −9900.00 −0.376028
\(886\) 0 0
\(887\) 34080.0 1.29007 0.645036 0.764152i \(-0.276842\pi\)
0.645036 + 0.764152i \(0.276842\pi\)
\(888\) 0 0
\(889\) 6400.00 0.241450
\(890\) 0 0
\(891\) 4860.00 0.182734
\(892\) 0 0
\(893\) −27360.0 −1.02527
\(894\) 0 0
\(895\) 4380.00 0.163584
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1392.00 0.0516416
\(900\) 0 0
\(901\) −9324.00 −0.344759
\(902\) 0 0
\(903\) −39552.0 −1.45759
\(904\) 0 0
\(905\) 19270.0 0.707797
\(906\) 0 0
\(907\) −25748.0 −0.942611 −0.471306 0.881970i \(-0.656217\pi\)
−0.471306 + 0.881970i \(0.656217\pi\)
\(908\) 0 0
\(909\) −7182.00 −0.262059
\(910\) 0 0
\(911\) −24768.0 −0.900769 −0.450384 0.892835i \(-0.648713\pi\)
−0.450384 + 0.892835i \(0.648713\pi\)
\(912\) 0 0
\(913\) 48240.0 1.74864
\(914\) 0 0
\(915\) 7350.00 0.265556
\(916\) 0 0
\(917\) −1920.00 −0.0691428
\(918\) 0 0
\(919\) −31264.0 −1.12220 −0.561101 0.827747i \(-0.689622\pi\)
−0.561101 + 0.827747i \(0.689622\pi\)
\(920\) 0 0
\(921\) 7620.00 0.272625
\(922\) 0 0
\(923\) 4080.00 0.145498
\(924\) 0 0
\(925\) −3350.00 −0.119078
\(926\) 0 0
\(927\) 9792.00 0.346938
\(928\) 0 0
\(929\) −6174.00 −0.218043 −0.109022 0.994039i \(-0.534772\pi\)
−0.109022 + 0.994039i \(0.534772\pi\)
\(930\) 0 0
\(931\) 51756.0 1.82195
\(932\) 0 0
\(933\) −4680.00 −0.164219
\(934\) 0 0
\(935\) −12600.0 −0.440710
\(936\) 0 0
\(937\) 28922.0 1.00837 0.504184 0.863596i \(-0.331793\pi\)
0.504184 + 0.863596i \(0.331793\pi\)
\(938\) 0 0
\(939\) 2802.00 0.0973800
\(940\) 0 0
\(941\) −29238.0 −1.01289 −0.506446 0.862272i \(-0.669041\pi\)
−0.506446 + 0.862272i \(0.669041\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 4320.00 0.148709
\(946\) 0 0
\(947\) 2868.00 0.0984134 0.0492067 0.998789i \(-0.484331\pi\)
0.0492067 + 0.998789i \(0.484331\pi\)
\(948\) 0 0
\(949\) 25364.0 0.867598
\(950\) 0 0
\(951\) −5022.00 −0.171240
\(952\) 0 0
\(953\) 24018.0 0.816390 0.408195 0.912895i \(-0.366158\pi\)
0.408195 + 0.912895i \(0.366158\pi\)
\(954\) 0 0
\(955\) 13920.0 0.471666
\(956\) 0 0
\(957\) 1080.00 0.0364801
\(958\) 0 0
\(959\) 20544.0 0.691763
\(960\) 0 0
\(961\) 24033.0 0.806720
\(962\) 0 0
\(963\) −15444.0 −0.516797
\(964\) 0 0
\(965\) −4570.00 −0.152449
\(966\) 0 0
\(967\) 25712.0 0.855059 0.427530 0.904001i \(-0.359384\pi\)
0.427530 + 0.904001i \(0.359384\pi\)
\(968\) 0 0
\(969\) −9576.00 −0.317467
\(970\) 0 0
\(971\) 12396.0 0.409688 0.204844 0.978795i \(-0.434331\pi\)
0.204844 + 0.978795i \(0.434331\pi\)
\(972\) 0 0
\(973\) 90752.0 2.99011
\(974\) 0 0
\(975\) −2550.00 −0.0837593
\(976\) 0 0
\(977\) −46614.0 −1.52642 −0.763211 0.646150i \(-0.776378\pi\)
−0.763211 + 0.646150i \(0.776378\pi\)
\(978\) 0 0
\(979\) −40680.0 −1.32803
\(980\) 0 0
\(981\) 8730.00 0.284126
\(982\) 0 0
\(983\) −672.000 −0.0218041 −0.0109021 0.999941i \(-0.503470\pi\)
−0.0109021 + 0.999941i \(0.503470\pi\)
\(984\) 0 0
\(985\) −26010.0 −0.841368
\(986\) 0 0
\(987\) 34560.0 1.11455
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −38776.0 −1.24295 −0.621473 0.783435i \(-0.713466\pi\)
−0.621473 + 0.783435i \(0.713466\pi\)
\(992\) 0 0
\(993\) −11964.0 −0.382342
\(994\) 0 0
\(995\) −15760.0 −0.502136
\(996\) 0 0
\(997\) −30422.0 −0.966374 −0.483187 0.875517i \(-0.660521\pi\)
−0.483187 + 0.875517i \(0.660521\pi\)
\(998\) 0 0
\(999\) 3618.00 0.114583
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 960.4.a.j.1.1 1
4.3 odd 2 960.4.a.s.1.1 1
8.3 odd 2 240.4.a.c.1.1 1
8.5 even 2 30.4.a.a.1.1 1
24.5 odd 2 90.4.a.d.1.1 1
24.11 even 2 720.4.a.b.1.1 1
40.3 even 4 1200.4.f.u.49.1 2
40.13 odd 4 150.4.c.a.49.2 2
40.19 odd 2 1200.4.a.bk.1.1 1
40.27 even 4 1200.4.f.u.49.2 2
40.29 even 2 150.4.a.e.1.1 1
40.37 odd 4 150.4.c.a.49.1 2
56.13 odd 2 1470.4.a.a.1.1 1
72.5 odd 6 810.4.e.e.541.1 2
72.13 even 6 810.4.e.m.541.1 2
72.29 odd 6 810.4.e.e.271.1 2
72.61 even 6 810.4.e.m.271.1 2
120.29 odd 2 450.4.a.b.1.1 1
120.53 even 4 450.4.c.k.199.1 2
120.77 even 4 450.4.c.k.199.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.4.a.a.1.1 1 8.5 even 2
90.4.a.d.1.1 1 24.5 odd 2
150.4.a.e.1.1 1 40.29 even 2
150.4.c.a.49.1 2 40.37 odd 4
150.4.c.a.49.2 2 40.13 odd 4
240.4.a.c.1.1 1 8.3 odd 2
450.4.a.b.1.1 1 120.29 odd 2
450.4.c.k.199.1 2 120.53 even 4
450.4.c.k.199.2 2 120.77 even 4
720.4.a.b.1.1 1 24.11 even 2
810.4.e.e.271.1 2 72.29 odd 6
810.4.e.e.541.1 2 72.5 odd 6
810.4.e.m.271.1 2 72.61 even 6
810.4.e.m.541.1 2 72.13 even 6
960.4.a.j.1.1 1 1.1 even 1 trivial
960.4.a.s.1.1 1 4.3 odd 2
1200.4.a.bk.1.1 1 40.19 odd 2
1200.4.f.u.49.1 2 40.3 even 4
1200.4.f.u.49.2 2 40.27 even 4
1470.4.a.a.1.1 1 56.13 odd 2