Properties

Label 576.4.a.n.1.1
Level $576$
Weight $4$
Character 576.1
Self dual yes
Analytic conductor $33.985$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,4,Mod(1,576)]
 
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, 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("576.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(33.9851001633\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} -12.0000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} -12.0000 q^{7} -60.0000 q^{11} +42.0000 q^{13} -10.0000 q^{17} +132.000 q^{19} -48.0000 q^{23} -121.000 q^{25} +226.000 q^{29} +252.000 q^{31} -24.0000 q^{35} +362.000 q^{37} +94.0000 q^{41} -228.000 q^{43} -408.000 q^{47} -199.000 q^{49} +346.000 q^{53} -120.000 q^{55} +300.000 q^{59} +466.000 q^{61} +84.0000 q^{65} +204.000 q^{67} +1056.00 q^{71} +330.000 q^{73} +720.000 q^{77} -612.000 q^{79} -564.000 q^{83} -20.0000 q^{85} +1510.00 q^{89} -504.000 q^{91} +264.000 q^{95} +594.000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 2.00000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) −12.0000 −0.647939 −0.323970 0.946068i \(-0.605018\pi\)
−0.323970 + 0.946068i \(0.605018\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −60.0000 −1.64461 −0.822304 0.569049i \(-0.807311\pi\)
−0.822304 + 0.569049i \(0.807311\pi\)
\(12\) 0 0
\(13\) 42.0000 0.896054 0.448027 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −10.0000 −0.142668 −0.0713340 0.997452i \(-0.522726\pi\)
−0.0713340 + 0.997452i \(0.522726\pi\)
\(18\) 0 0
\(19\) 132.000 1.59384 0.796918 0.604088i \(-0.206462\pi\)
0.796918 + 0.604088i \(0.206462\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −48.0000 −0.435161 −0.217580 0.976042i \(-0.569816\pi\)
−0.217580 + 0.976042i \(0.569816\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 226.000 1.44714 0.723571 0.690249i \(-0.242499\pi\)
0.723571 + 0.690249i \(0.242499\pi\)
\(30\) 0 0
\(31\) 252.000 1.46002 0.730009 0.683438i \(-0.239516\pi\)
0.730009 + 0.683438i \(0.239516\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −24.0000 −0.115907
\(36\) 0 0
\(37\) 362.000 1.60844 0.804222 0.594329i \(-0.202582\pi\)
0.804222 + 0.594329i \(0.202582\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 94.0000 0.358057 0.179028 0.983844i \(-0.442705\pi\)
0.179028 + 0.983844i \(0.442705\pi\)
\(42\) 0 0
\(43\) −228.000 −0.808597 −0.404299 0.914627i \(-0.632484\pi\)
−0.404299 + 0.914627i \(0.632484\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −408.000 −1.26623 −0.633116 0.774057i \(-0.718224\pi\)
−0.633116 + 0.774057i \(0.718224\pi\)
\(48\) 0 0
\(49\) −199.000 −0.580175
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 346.000 0.896731 0.448366 0.893850i \(-0.352006\pi\)
0.448366 + 0.893850i \(0.352006\pi\)
\(54\) 0 0
\(55\) −120.000 −0.294196
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 300.000 0.661978 0.330989 0.943635i \(-0.392618\pi\)
0.330989 + 0.943635i \(0.392618\pi\)
\(60\) 0 0
\(61\) 466.000 0.978118 0.489059 0.872251i \(-0.337340\pi\)
0.489059 + 0.872251i \(0.337340\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 84.0000 0.160291
\(66\) 0 0
\(67\) 204.000 0.371979 0.185989 0.982552i \(-0.440451\pi\)
0.185989 + 0.982552i \(0.440451\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1056.00 1.76513 0.882564 0.470192i \(-0.155815\pi\)
0.882564 + 0.470192i \(0.155815\pi\)
\(72\) 0 0
\(73\) 330.000 0.529090 0.264545 0.964373i \(-0.414778\pi\)
0.264545 + 0.964373i \(0.414778\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 720.000 1.06561
\(78\) 0 0
\(79\) −612.000 −0.871587 −0.435794 0.900047i \(-0.643532\pi\)
−0.435794 + 0.900047i \(0.643532\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −564.000 −0.745868 −0.372934 0.927858i \(-0.621648\pi\)
−0.372934 + 0.927858i \(0.621648\pi\)
\(84\) 0 0
\(85\) −20.0000 −0.0255212
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1510.00 1.79842 0.899212 0.437514i \(-0.144141\pi\)
0.899212 + 0.437514i \(0.144141\pi\)
\(90\) 0 0
\(91\) −504.000 −0.580589
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 264.000 0.285114
\(96\) 0 0
\(97\) 594.000 0.621769 0.310884 0.950448i \(-0.399375\pi\)
0.310884 + 0.950448i \(0.399375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 554.000 0.545793 0.272896 0.962043i \(-0.412018\pi\)
0.272896 + 0.962043i \(0.412018\pi\)
\(102\) 0 0
\(103\) −1284.00 −1.22831 −0.614157 0.789184i \(-0.710504\pi\)
−0.614157 + 0.789184i \(0.710504\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1356.00 1.22514 0.612568 0.790418i \(-0.290137\pi\)
0.612568 + 0.790418i \(0.290137\pi\)
\(108\) 0 0
\(109\) −390.000 −0.342708 −0.171354 0.985209i \(-0.554814\pi\)
−0.171354 + 0.985209i \(0.554814\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 766.000 0.637692 0.318846 0.947807i \(-0.396705\pi\)
0.318846 + 0.947807i \(0.396705\pi\)
\(114\) 0 0
\(115\) −96.0000 −0.0778439
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 120.000 0.0924402
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) 2388.00 1.66851 0.834255 0.551379i \(-0.185898\pi\)
0.834255 + 0.551379i \(0.185898\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −396.000 −0.264112 −0.132056 0.991242i \(-0.542158\pi\)
−0.132056 + 0.991242i \(0.542158\pi\)
\(132\) 0 0
\(133\) −1584.00 −1.03271
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 110.000 0.0685981 0.0342990 0.999412i \(-0.489080\pi\)
0.0342990 + 0.999412i \(0.489080\pi\)
\(138\) 0 0
\(139\) −732.000 −0.446672 −0.223336 0.974742i \(-0.571695\pi\)
−0.223336 + 0.974742i \(0.571695\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2520.00 −1.47366
\(144\) 0 0
\(145\) 452.000 0.258873
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1934.00 −1.06335 −0.531676 0.846948i \(-0.678438\pi\)
−0.531676 + 0.846948i \(0.678438\pi\)
\(150\) 0 0
\(151\) 1092.00 0.588515 0.294257 0.955726i \(-0.404928\pi\)
0.294257 + 0.955726i \(0.404928\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 504.000 0.261176
\(156\) 0 0
\(157\) 578.000 0.293818 0.146909 0.989150i \(-0.453068\pi\)
0.146909 + 0.989150i \(0.453068\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 576.000 0.281958
\(162\) 0 0
\(163\) 2532.00 1.21670 0.608348 0.793670i \(-0.291832\pi\)
0.608348 + 0.793670i \(0.291832\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −648.000 −0.300262 −0.150131 0.988666i \(-0.547970\pi\)
−0.150131 + 0.988666i \(0.547970\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3338.00 1.46696 0.733478 0.679713i \(-0.237896\pi\)
0.733478 + 0.679713i \(0.237896\pi\)
\(174\) 0 0
\(175\) 1452.00 0.627205
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3804.00 −1.58840 −0.794202 0.607654i \(-0.792111\pi\)
−0.794202 + 0.607654i \(0.792111\pi\)
\(180\) 0 0
\(181\) −1854.00 −0.761363 −0.380682 0.924706i \(-0.624311\pi\)
−0.380682 + 0.924706i \(0.624311\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 724.000 0.287727
\(186\) 0 0
\(187\) 600.000 0.234633
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1344.00 0.509154 0.254577 0.967052i \(-0.418064\pi\)
0.254577 + 0.967052i \(0.418064\pi\)
\(192\) 0 0
\(193\) −1262.00 −0.470677 −0.235339 0.971913i \(-0.575620\pi\)
−0.235339 + 0.971913i \(0.575620\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4294.00 −1.55297 −0.776484 0.630137i \(-0.782999\pi\)
−0.776484 + 0.630137i \(0.782999\pi\)
\(198\) 0 0
\(199\) −4308.00 −1.53460 −0.767302 0.641286i \(-0.778401\pi\)
−0.767302 + 0.641286i \(0.778401\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2712.00 −0.937661
\(204\) 0 0
\(205\) 188.000 0.0640512
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7920.00 −2.62123
\(210\) 0 0
\(211\) 1212.00 0.395438 0.197719 0.980259i \(-0.436647\pi\)
0.197719 + 0.980259i \(0.436647\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −456.000 −0.144646
\(216\) 0 0
\(217\) −3024.00 −0.946002
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −420.000 −0.127838
\(222\) 0 0
\(223\) −2172.00 −0.652233 −0.326116 0.945330i \(-0.605740\pi\)
−0.326116 + 0.945330i \(0.605740\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3948.00 1.15435 0.577176 0.816620i \(-0.304155\pi\)
0.577176 + 0.816620i \(0.304155\pi\)
\(228\) 0 0
\(229\) 3522.00 1.01633 0.508167 0.861259i \(-0.330323\pi\)
0.508167 + 0.861259i \(0.330323\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2774.00 0.779960 0.389980 0.920823i \(-0.372482\pi\)
0.389980 + 0.920823i \(0.372482\pi\)
\(234\) 0 0
\(235\) −816.000 −0.226511
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2784.00 0.753481 0.376741 0.926319i \(-0.377045\pi\)
0.376741 + 0.926319i \(0.377045\pi\)
\(240\) 0 0
\(241\) −4686.00 −1.25250 −0.626249 0.779623i \(-0.715410\pi\)
−0.626249 + 0.779623i \(0.715410\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −398.000 −0.103785
\(246\) 0 0
\(247\) 5544.00 1.42816
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2484.00 0.624656 0.312328 0.949974i \(-0.398891\pi\)
0.312328 + 0.949974i \(0.398891\pi\)
\(252\) 0 0
\(253\) 2880.00 0.715668
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6658.00 −1.61601 −0.808005 0.589175i \(-0.799453\pi\)
−0.808005 + 0.589175i \(0.799453\pi\)
\(258\) 0 0
\(259\) −4344.00 −1.04217
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2904.00 0.680868 0.340434 0.940268i \(-0.389426\pi\)
0.340434 + 0.940268i \(0.389426\pi\)
\(264\) 0 0
\(265\) 692.000 0.160412
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1006.00 −0.228018 −0.114009 0.993480i \(-0.536369\pi\)
−0.114009 + 0.993480i \(0.536369\pi\)
\(270\) 0 0
\(271\) −876.000 −0.196359 −0.0981794 0.995169i \(-0.531302\pi\)
−0.0981794 + 0.995169i \(0.531302\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7260.00 1.59198
\(276\) 0 0
\(277\) −2718.00 −0.589562 −0.294781 0.955565i \(-0.595247\pi\)
−0.294781 + 0.955565i \(0.595247\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5354.00 −1.13663 −0.568315 0.822811i \(-0.692404\pi\)
−0.568315 + 0.822811i \(0.692404\pi\)
\(282\) 0 0
\(283\) −780.000 −0.163838 −0.0819191 0.996639i \(-0.526105\pi\)
−0.0819191 + 0.996639i \(0.526105\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1128.00 −0.231999
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3350.00 −0.667949 −0.333975 0.942582i \(-0.608390\pi\)
−0.333975 + 0.942582i \(0.608390\pi\)
\(294\) 0 0
\(295\) 600.000 0.118418
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2016.00 −0.389927
\(300\) 0 0
\(301\) 2736.00 0.523922
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 932.000 0.174971
\(306\) 0 0
\(307\) −9636.00 −1.79139 −0.895693 0.444673i \(-0.853320\pi\)
−0.895693 + 0.444673i \(0.853320\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7560.00 −1.37842 −0.689209 0.724562i \(-0.742042\pi\)
−0.689209 + 0.724562i \(0.742042\pi\)
\(312\) 0 0
\(313\) −3526.00 −0.636745 −0.318373 0.947966i \(-0.603136\pi\)
−0.318373 + 0.947966i \(0.603136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7634.00 1.35258 0.676290 0.736635i \(-0.263586\pi\)
0.676290 + 0.736635i \(0.263586\pi\)
\(318\) 0 0
\(319\) −13560.0 −2.37998
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1320.00 −0.227389
\(324\) 0 0
\(325\) −5082.00 −0.867380
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4896.00 0.820441
\(330\) 0 0
\(331\) 7572.00 1.25739 0.628693 0.777654i \(-0.283590\pi\)
0.628693 + 0.777654i \(0.283590\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 408.000 0.0665416
\(336\) 0 0
\(337\) 162.000 0.0261861 0.0130930 0.999914i \(-0.495832\pi\)
0.0130930 + 0.999914i \(0.495832\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −15120.0 −2.40116
\(342\) 0 0
\(343\) 6504.00 1.02386
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6636.00 −1.02663 −0.513313 0.858202i \(-0.671582\pi\)
−0.513313 + 0.858202i \(0.671582\pi\)
\(348\) 0 0
\(349\) −4430.00 −0.679463 −0.339731 0.940523i \(-0.610336\pi\)
−0.339731 + 0.940523i \(0.610336\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8402.00 −1.26684 −0.633418 0.773810i \(-0.718349\pi\)
−0.633418 + 0.773810i \(0.718349\pi\)
\(354\) 0 0
\(355\) 2112.00 0.315756
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11520.0 1.69360 0.846800 0.531912i \(-0.178526\pi\)
0.846800 + 0.531912i \(0.178526\pi\)
\(360\) 0 0
\(361\) 10565.0 1.54031
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 660.000 0.0946465
\(366\) 0 0
\(367\) 7404.00 1.05309 0.526547 0.850146i \(-0.323486\pi\)
0.526547 + 0.850146i \(0.323486\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4152.00 −0.581027
\(372\) 0 0
\(373\) −1910.00 −0.265137 −0.132568 0.991174i \(-0.542322\pi\)
−0.132568 + 0.991174i \(0.542322\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9492.00 1.29672
\(378\) 0 0
\(379\) 10332.0 1.40031 0.700157 0.713989i \(-0.253113\pi\)
0.700157 + 0.713989i \(0.253113\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6624.00 0.883735 0.441868 0.897080i \(-0.354316\pi\)
0.441868 + 0.897080i \(0.354316\pi\)
\(384\) 0 0
\(385\) 1440.00 0.190621
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10210.0 1.33076 0.665382 0.746503i \(-0.268268\pi\)
0.665382 + 0.746503i \(0.268268\pi\)
\(390\) 0 0
\(391\) 480.000 0.0620835
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1224.00 −0.155914
\(396\) 0 0
\(397\) 4066.00 0.514022 0.257011 0.966408i \(-0.417262\pi\)
0.257011 + 0.966408i \(0.417262\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5510.00 0.686175 0.343088 0.939303i \(-0.388527\pi\)
0.343088 + 0.939303i \(0.388527\pi\)
\(402\) 0 0
\(403\) 10584.0 1.30825
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21720.0 −2.64526
\(408\) 0 0
\(409\) 15450.0 1.86786 0.933928 0.357460i \(-0.116357\pi\)
0.933928 + 0.357460i \(0.116357\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3600.00 −0.428921
\(414\) 0 0
\(415\) −1128.00 −0.133425
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3084.00 0.359578 0.179789 0.983705i \(-0.442458\pi\)
0.179789 + 0.983705i \(0.442458\pi\)
\(420\) 0 0
\(421\) −10446.0 −1.20928 −0.604640 0.796499i \(-0.706683\pi\)
−0.604640 + 0.796499i \(0.706683\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1210.00 0.138103
\(426\) 0 0
\(427\) −5592.00 −0.633761
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2184.00 −0.244083 −0.122041 0.992525i \(-0.538944\pi\)
−0.122041 + 0.992525i \(0.538944\pi\)
\(432\) 0 0
\(433\) −110.000 −0.0122085 −0.00610423 0.999981i \(-0.501943\pi\)
−0.00610423 + 0.999981i \(0.501943\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6336.00 −0.693574
\(438\) 0 0
\(439\) 2412.00 0.262229 0.131114 0.991367i \(-0.458144\pi\)
0.131114 + 0.991367i \(0.458144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6540.00 −0.701410 −0.350705 0.936486i \(-0.614058\pi\)
−0.350705 + 0.936486i \(0.614058\pi\)
\(444\) 0 0
\(445\) 3020.00 0.321712
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9670.00 1.01638 0.508191 0.861244i \(-0.330314\pi\)
0.508191 + 0.861244i \(0.330314\pi\)
\(450\) 0 0
\(451\) −5640.00 −0.588863
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1008.00 −0.103859
\(456\) 0 0
\(457\) −6774.00 −0.693379 −0.346690 0.937980i \(-0.612694\pi\)
−0.346690 + 0.937980i \(0.612694\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14602.0 1.47523 0.737617 0.675219i \(-0.235951\pi\)
0.737617 + 0.675219i \(0.235951\pi\)
\(462\) 0 0
\(463\) 13620.0 1.36712 0.683558 0.729896i \(-0.260431\pi\)
0.683558 + 0.729896i \(0.260431\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8508.00 0.843048 0.421524 0.906817i \(-0.361495\pi\)
0.421524 + 0.906817i \(0.361495\pi\)
\(468\) 0 0
\(469\) −2448.00 −0.241019
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 13680.0 1.32982
\(474\) 0 0
\(475\) −15972.0 −1.54283
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6312.00 0.602093 0.301047 0.953609i \(-0.402664\pi\)
0.301047 + 0.953609i \(0.402664\pi\)
\(480\) 0 0
\(481\) 15204.0 1.44125
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1188.00 0.111225
\(486\) 0 0
\(487\) −10572.0 −0.983702 −0.491851 0.870679i \(-0.663680\pi\)
−0.491851 + 0.870679i \(0.663680\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4332.00 0.398168 0.199084 0.979982i \(-0.436203\pi\)
0.199084 + 0.979982i \(0.436203\pi\)
\(492\) 0 0
\(493\) −2260.00 −0.206461
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −12672.0 −1.14370
\(498\) 0 0
\(499\) −3684.00 −0.330498 −0.165249 0.986252i \(-0.552843\pi\)
−0.165249 + 0.986252i \(0.552843\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11184.0 −0.991391 −0.495696 0.868496i \(-0.665087\pi\)
−0.495696 + 0.868496i \(0.665087\pi\)
\(504\) 0 0
\(505\) 1108.00 0.0976344
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12946.0 1.12735 0.563675 0.825997i \(-0.309387\pi\)
0.563675 + 0.825997i \(0.309387\pi\)
\(510\) 0 0
\(511\) −3960.00 −0.342818
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2568.00 −0.219727
\(516\) 0 0
\(517\) 24480.0 2.08245
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17150.0 1.44214 0.721070 0.692862i \(-0.243651\pi\)
0.721070 + 0.692862i \(0.243651\pi\)
\(522\) 0 0
\(523\) 7884.00 0.659165 0.329582 0.944127i \(-0.393092\pi\)
0.329582 + 0.944127i \(0.393092\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2520.00 −0.208298
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3948.00 0.320838
\(534\) 0 0
\(535\) 2712.00 0.219159
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11940.0 0.954160
\(540\) 0 0
\(541\) −5910.00 −0.469669 −0.234834 0.972035i \(-0.575455\pi\)
−0.234834 + 0.972035i \(0.575455\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −780.000 −0.0613056
\(546\) 0 0
\(547\) −972.000 −0.0759775 −0.0379888 0.999278i \(-0.512095\pi\)
−0.0379888 + 0.999278i \(0.512095\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 29832.0 2.30651
\(552\) 0 0
\(553\) 7344.00 0.564735
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2458.00 0.186982 0.0934908 0.995620i \(-0.470197\pi\)
0.0934908 + 0.995620i \(0.470197\pi\)
\(558\) 0 0
\(559\) −9576.00 −0.724547
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11316.0 −0.847092 −0.423546 0.905875i \(-0.639215\pi\)
−0.423546 + 0.905875i \(0.639215\pi\)
\(564\) 0 0
\(565\) 1532.00 0.114074
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1810.00 −0.133355 −0.0666776 0.997775i \(-0.521240\pi\)
−0.0666776 + 0.997775i \(0.521240\pi\)
\(570\) 0 0
\(571\) 10500.0 0.769547 0.384773 0.923011i \(-0.374280\pi\)
0.384773 + 0.923011i \(0.374280\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5808.00 0.421235
\(576\) 0 0
\(577\) −19438.0 −1.40245 −0.701226 0.712939i \(-0.747363\pi\)
−0.701226 + 0.712939i \(0.747363\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6768.00 0.483277
\(582\) 0 0
\(583\) −20760.0 −1.47477
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15084.0 1.06062 0.530309 0.847804i \(-0.322076\pi\)
0.530309 + 0.847804i \(0.322076\pi\)
\(588\) 0 0
\(589\) 33264.0 2.32703
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5794.00 −0.401233 −0.200616 0.979670i \(-0.564294\pi\)
−0.200616 + 0.979670i \(0.564294\pi\)
\(594\) 0 0
\(595\) 240.000 0.0165362
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 25152.0 1.71566 0.857832 0.513930i \(-0.171811\pi\)
0.857832 + 0.513930i \(0.171811\pi\)
\(600\) 0 0
\(601\) −11846.0 −0.804007 −0.402004 0.915638i \(-0.631686\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4538.00 0.304952
\(606\) 0 0
\(607\) −8940.00 −0.597798 −0.298899 0.954285i \(-0.596619\pi\)
−0.298899 + 0.954285i \(0.596619\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17136.0 −1.13461
\(612\) 0 0
\(613\) 4570.00 0.301110 0.150555 0.988602i \(-0.451894\pi\)
0.150555 + 0.988602i \(0.451894\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17786.0 −1.16051 −0.580257 0.814433i \(-0.697048\pi\)
−0.580257 + 0.814433i \(0.697048\pi\)
\(618\) 0 0
\(619\) −15804.0 −1.02620 −0.513099 0.858330i \(-0.671503\pi\)
−0.513099 + 0.858330i \(0.671503\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18120.0 −1.16527
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3620.00 −0.229474
\(630\) 0 0
\(631\) 18468.0 1.16513 0.582567 0.812783i \(-0.302048\pi\)
0.582567 + 0.812783i \(0.302048\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4776.00 0.298472
\(636\) 0 0
\(637\) −8358.00 −0.519868
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7814.00 0.481489 0.240744 0.970589i \(-0.422608\pi\)
0.240744 + 0.970589i \(0.422608\pi\)
\(642\) 0 0
\(643\) 5364.00 0.328982 0.164491 0.986379i \(-0.447402\pi\)
0.164491 + 0.986379i \(0.447402\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3936.00 −0.239166 −0.119583 0.992824i \(-0.538156\pi\)
−0.119583 + 0.992824i \(0.538156\pi\)
\(648\) 0 0
\(649\) −18000.0 −1.08869
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7610.00 0.456053 0.228026 0.973655i \(-0.426773\pi\)
0.228026 + 0.973655i \(0.426773\pi\)
\(654\) 0 0
\(655\) −792.000 −0.0472458
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13620.0 0.805098 0.402549 0.915398i \(-0.368124\pi\)
0.402549 + 0.915398i \(0.368124\pi\)
\(660\) 0 0
\(661\) −8710.00 −0.512526 −0.256263 0.966607i \(-0.582491\pi\)
−0.256263 + 0.966607i \(0.582491\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3168.00 −0.184736
\(666\) 0 0
\(667\) −10848.0 −0.629739
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −27960.0 −1.60862
\(672\) 0 0
\(673\) −12094.0 −0.692703 −0.346352 0.938105i \(-0.612580\pi\)
−0.346352 + 0.938105i \(0.612580\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16466.0 0.934771 0.467385 0.884054i \(-0.345196\pi\)
0.467385 + 0.884054i \(0.345196\pi\)
\(678\) 0 0
\(679\) −7128.00 −0.402868
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16428.0 −0.920351 −0.460176 0.887828i \(-0.652214\pi\)
−0.460176 + 0.887828i \(0.652214\pi\)
\(684\) 0 0
\(685\) 220.000 0.0122712
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 14532.0 0.803520
\(690\) 0 0
\(691\) 13332.0 0.733970 0.366985 0.930227i \(-0.380390\pi\)
0.366985 + 0.930227i \(0.380390\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1464.00 −0.0799031
\(696\) 0 0
\(697\) −940.000 −0.0510833
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19118.0 −1.03007 −0.515033 0.857170i \(-0.672221\pi\)
−0.515033 + 0.857170i \(0.672221\pi\)
\(702\) 0 0
\(703\) 47784.0 2.56360
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6648.00 −0.353640
\(708\) 0 0
\(709\) −798.000 −0.0422701 −0.0211351 0.999777i \(-0.506728\pi\)
−0.0211351 + 0.999777i \(0.506728\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −12096.0 −0.635342
\(714\) 0 0
\(715\) −5040.00 −0.263616
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8856.00 −0.459351 −0.229675 0.973267i \(-0.573766\pi\)
−0.229675 + 0.973267i \(0.573766\pi\)
\(720\) 0 0
\(721\) 15408.0 0.795872
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −27346.0 −1.40083
\(726\) 0 0
\(727\) 13764.0 0.702171 0.351086 0.936343i \(-0.385813\pi\)
0.351086 + 0.936343i \(0.385813\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2280.00 0.115361
\(732\) 0 0
\(733\) 20538.0 1.03491 0.517455 0.855711i \(-0.326880\pi\)
0.517455 + 0.855711i \(0.326880\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12240.0 −0.611759
\(738\) 0 0
\(739\) 15900.0 0.791463 0.395731 0.918366i \(-0.370491\pi\)
0.395731 + 0.918366i \(0.370491\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20856.0 −1.02979 −0.514894 0.857254i \(-0.672169\pi\)
−0.514894 + 0.857254i \(0.672169\pi\)
\(744\) 0 0
\(745\) −3868.00 −0.190218
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16272.0 −0.793813
\(750\) 0 0
\(751\) 10332.0 0.502024 0.251012 0.967984i \(-0.419237\pi\)
0.251012 + 0.967984i \(0.419237\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2184.00 0.105277
\(756\) 0 0
\(757\) −13806.0 −0.662863 −0.331432 0.943479i \(-0.607532\pi\)
−0.331432 + 0.943479i \(0.607532\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15554.0 −0.740909 −0.370455 0.928851i \(-0.620798\pi\)
−0.370455 + 0.928851i \(0.620798\pi\)
\(762\) 0 0
\(763\) 4680.00 0.222054
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12600.0 0.593168
\(768\) 0 0
\(769\) 13106.0 0.614583 0.307292 0.951615i \(-0.400577\pi\)
0.307292 + 0.951615i \(0.400577\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18874.0 0.878203 0.439101 0.898438i \(-0.355297\pi\)
0.439101 + 0.898438i \(0.355297\pi\)
\(774\) 0 0
\(775\) −30492.0 −1.41330
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12408.0 0.570684
\(780\) 0 0
\(781\) −63360.0 −2.90294
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1156.00 0.0525598
\(786\) 0 0
\(787\) 15444.0 0.699516 0.349758 0.936840i \(-0.386264\pi\)
0.349758 + 0.936840i \(0.386264\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9192.00 −0.413186
\(792\) 0 0
\(793\) 19572.0 0.876447
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −39286.0 −1.74602 −0.873012 0.487698i \(-0.837837\pi\)
−0.873012 + 0.487698i \(0.837837\pi\)
\(798\) 0 0
\(799\) 4080.00 0.180651
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19800.0 −0.870145
\(804\) 0 0
\(805\) 1152.00 0.0504381
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −20018.0 −0.869957 −0.434979 0.900441i \(-0.643244\pi\)
−0.434979 + 0.900441i \(0.643244\pi\)
\(810\) 0 0
\(811\) −8388.00 −0.363184 −0.181592 0.983374i \(-0.558125\pi\)
−0.181592 + 0.983374i \(0.558125\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 5064.00 0.217649
\(816\) 0 0
\(817\) −30096.0 −1.28877
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −37942.0 −1.61289 −0.806446 0.591307i \(-0.798612\pi\)
−0.806446 + 0.591307i \(0.798612\pi\)
\(822\) 0 0
\(823\) −11628.0 −0.492499 −0.246249 0.969206i \(-0.579198\pi\)
−0.246249 + 0.969206i \(0.579198\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32388.0 −1.36184 −0.680920 0.732358i \(-0.738420\pi\)
−0.680920 + 0.732358i \(0.738420\pi\)
\(828\) 0 0
\(829\) −9846.00 −0.412504 −0.206252 0.978499i \(-0.566127\pi\)
−0.206252 + 0.978499i \(0.566127\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1990.00 0.0827724
\(834\) 0 0
\(835\) −1296.00 −0.0537125
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16848.0 0.693275 0.346637 0.937999i \(-0.387323\pi\)
0.346637 + 0.937999i \(0.387323\pi\)
\(840\) 0 0
\(841\) 26687.0 1.09422
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −866.000 −0.0352560
\(846\) 0 0
\(847\) −27228.0 −1.10456
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −17376.0 −0.699931
\(852\) 0 0
\(853\) −18214.0 −0.731108 −0.365554 0.930790i \(-0.619121\pi\)
−0.365554 + 0.930790i \(0.619121\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2446.00 0.0974956 0.0487478 0.998811i \(-0.484477\pi\)
0.0487478 + 0.998811i \(0.484477\pi\)
\(858\) 0 0
\(859\) −26244.0 −1.04241 −0.521207 0.853430i \(-0.674518\pi\)
−0.521207 + 0.853430i \(0.674518\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25248.0 0.995889 0.497944 0.867209i \(-0.334088\pi\)
0.497944 + 0.867209i \(0.334088\pi\)
\(864\) 0 0
\(865\) 6676.00 0.262417
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 36720.0 1.43342
\(870\) 0 0
\(871\) 8568.00 0.333313
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5904.00 0.228105
\(876\) 0 0
\(877\) 34.0000 0.00130912 0.000654560 1.00000i \(-0.499792\pi\)
0.000654560 1.00000i \(0.499792\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 19022.0 0.727432 0.363716 0.931510i \(-0.381508\pi\)
0.363716 + 0.931510i \(0.381508\pi\)
\(882\) 0 0
\(883\) 12852.0 0.489812 0.244906 0.969547i \(-0.421243\pi\)
0.244906 + 0.969547i \(0.421243\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 40104.0 1.51811 0.759053 0.651028i \(-0.225662\pi\)
0.759053 + 0.651028i \(0.225662\pi\)
\(888\) 0 0
\(889\) −28656.0 −1.08109
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −53856.0 −2.01817
\(894\) 0 0
\(895\) −7608.00 −0.284142
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 56952.0 2.11285
\(900\) 0 0
\(901\) −3460.00 −0.127935
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3708.00 −0.136197
\(906\) 0 0
\(907\) 42540.0 1.55735 0.778676 0.627427i \(-0.215892\pi\)
0.778676 + 0.627427i \(0.215892\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −18528.0 −0.673831 −0.336915 0.941535i \(-0.609384\pi\)
−0.336915 + 0.941535i \(0.609384\pi\)
\(912\) 0 0
\(913\) 33840.0 1.22666
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4752.00 0.171129
\(918\) 0 0
\(919\) −15756.0 −0.565552 −0.282776 0.959186i \(-0.591255\pi\)
−0.282776 + 0.959186i \(0.591255\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 44352.0 1.58165
\(924\) 0 0
\(925\) −43802.0 −1.55697
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15542.0 0.548887 0.274444 0.961603i \(-0.411506\pi\)
0.274444 + 0.961603i \(0.411506\pi\)
\(930\) 0 0
\(931\) −26268.0 −0.924703
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1200.00 0.0419724
\(936\) 0 0
\(937\) −29702.0 −1.03556 −0.517781 0.855513i \(-0.673242\pi\)
−0.517781 + 0.855513i \(0.673242\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2890.00 0.100118 0.0500591 0.998746i \(-0.484059\pi\)
0.0500591 + 0.998746i \(0.484059\pi\)
\(942\) 0 0
\(943\) −4512.00 −0.155812
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9180.00 −0.315005 −0.157503 0.987519i \(-0.550344\pi\)
−0.157503 + 0.987519i \(0.550344\pi\)
\(948\) 0 0
\(949\) 13860.0 0.474093
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −37906.0 −1.28845 −0.644227 0.764835i \(-0.722821\pi\)
−0.644227 + 0.764835i \(0.722821\pi\)
\(954\) 0 0
\(955\) 2688.00 0.0910802
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1320.00 −0.0444474
\(960\) 0 0
\(961\) 33713.0 1.13165
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2524.00 −0.0841973
\(966\) 0 0
\(967\) 41916.0 1.39393 0.696964 0.717106i \(-0.254534\pi\)
0.696964 + 0.717106i \(0.254534\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7764.00 0.256600 0.128300 0.991735i \(-0.459048\pi\)
0.128300 + 0.991735i \(0.459048\pi\)
\(972\) 0 0
\(973\) 8784.00 0.289416
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32666.0 −1.06968 −0.534840 0.844953i \(-0.679628\pi\)
−0.534840 + 0.844953i \(0.679628\pi\)
\(978\) 0 0
\(979\) −90600.0 −2.95770
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −53016.0 −1.72019 −0.860096 0.510133i \(-0.829596\pi\)
−0.860096 + 0.510133i \(0.829596\pi\)
\(984\) 0 0
\(985\) −8588.00 −0.277803
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 10944.0 0.351870
\(990\) 0 0
\(991\) −17844.0 −0.571981 −0.285991 0.958232i \(-0.592323\pi\)
−0.285991 + 0.958232i \(0.592323\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8616.00 −0.274518
\(996\) 0 0
\(997\) 55834.0 1.77360 0.886801 0.462152i \(-0.152923\pi\)
0.886801 + 0.462152i \(0.152923\pi\)
\(998\) 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 576.4.a.n.1.1 1
3.2 odd 2 192.4.a.j.1.1 1
4.3 odd 2 576.4.a.o.1.1 1
8.3 odd 2 288.4.a.f.1.1 1
8.5 even 2 288.4.a.e.1.1 1
12.11 even 2 192.4.a.d.1.1 1
24.5 odd 2 96.4.a.b.1.1 1
24.11 even 2 96.4.a.e.1.1 yes 1
48.5 odd 4 768.4.d.m.385.1 2
48.11 even 4 768.4.d.d.385.2 2
48.29 odd 4 768.4.d.m.385.2 2
48.35 even 4 768.4.d.d.385.1 2
120.29 odd 2 2400.4.a.t.1.1 1
120.59 even 2 2400.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.4.a.b.1.1 1 24.5 odd 2
96.4.a.e.1.1 yes 1 24.11 even 2
192.4.a.d.1.1 1 12.11 even 2
192.4.a.j.1.1 1 3.2 odd 2
288.4.a.e.1.1 1 8.5 even 2
288.4.a.f.1.1 1 8.3 odd 2
576.4.a.n.1.1 1 1.1 even 1 trivial
576.4.a.o.1.1 1 4.3 odd 2
768.4.d.d.385.1 2 48.35 even 4
768.4.d.d.385.2 2 48.11 even 4
768.4.d.m.385.1 2 48.5 odd 4
768.4.d.m.385.2 2 48.29 odd 4
2400.4.a.c.1.1 1 120.59 even 2
2400.4.a.t.1.1 1 120.29 odd 2