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Properties

Label 1584.4.a.g.1.1
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
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] = [1584,4,Mod(1,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, 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("1584.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1584.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: \(93.4590254491\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 88)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-9.00000 q^{5} -2.00000 q^{7} +O(q^{10})\) \(q-9.00000 q^{5} -2.00000 q^{7} -11.0000 q^{11} +38.0000 q^{17} -44.0000 q^{19} +175.000 q^{23} -44.0000 q^{25} +264.000 q^{29} -159.000 q^{31} +18.0000 q^{35} -173.000 q^{37} +220.000 q^{41} +542.000 q^{43} -264.000 q^{47} -339.000 q^{49} -682.000 q^{53} +99.0000 q^{55} +421.000 q^{59} +308.000 q^{61} -177.000 q^{67} +365.000 q^{71} -528.000 q^{73} +22.0000 q^{77} -686.000 q^{79} +698.000 q^{83} -342.000 q^{85} -967.000 q^{89} +396.000 q^{95} -1127.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −9.00000 −0.804984 −0.402492 − 0.915423i \(-0.631856\pi\)
−0.402492 + 0.915423i \(0.631856\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.107990 −0.0539949 − 0.998541i \(-0.517195\pi\)
−0.0539949 + 0.998541i \(0.517195\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 38.0000 0.542138 0.271069 − 0.962560i \(-0.412623\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(18\) 0 0
\(19\) −44.0000 −0.531279 −0.265639 − 0.964072i \(-0.585583\pi\)
−0.265639 + 0.964072i \(0.585583\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 175.000 1.58652 0.793261 − 0.608881i \(-0.208381\pi\)
0.793261 + 0.608881i \(0.208381\pi\)
\(24\) 0 0
\(25\) −44.0000 −0.352000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 264.000 1.69047 0.845234 − 0.534396i \(-0.179461\pi\)
0.845234 + 0.534396i \(0.179461\pi\)
\(30\) 0 0
\(31\) −159.000 −0.921201 −0.460601 − 0.887607i \(-0.652366\pi\)
−0.460601 + 0.887607i \(0.652366\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 18.0000 0.0869302
\(36\) 0 0
\(37\) −173.000 −0.768676 −0.384338 − 0.923192i \(-0.625570\pi\)
−0.384338 + 0.923192i \(0.625570\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 220.000 0.838006 0.419003 − 0.907985i \(-0.362380\pi\)
0.419003 + 0.907985i \(0.362380\pi\)
\(42\) 0 0
\(43\) 542.000 1.92219 0.961096 − 0.276216i \(-0.0890805\pi\)
0.961096 + 0.276216i \(0.0890805\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −264.000 −0.819327 −0.409663 − 0.912237i \(-0.634354\pi\)
−0.409663 + 0.912237i \(0.634354\pi\)
\(48\) 0 0
\(49\) −339.000 −0.988338
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −682.000 −1.76755 −0.883773 − 0.467916i \(-0.845005\pi\)
−0.883773 + 0.467916i \(0.845005\pi\)
\(54\) 0 0
\(55\) 99.0000 0.242712
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 421.000 0.928975 0.464488 − 0.885580i \(-0.346239\pi\)
0.464488 + 0.885580i \(0.346239\pi\)
\(60\) 0 0
\(61\) 308.000 0.646481 0.323241 − 0.946317i \(-0.395228\pi\)
0.323241 + 0.946317i \(0.395228\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −177.000 −0.322746 −0.161373 − 0.986893i \(-0.551592\pi\)
−0.161373 + 0.986893i \(0.551592\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 365.000 0.610106 0.305053 − 0.952335i \(-0.401326\pi\)
0.305053 + 0.952335i \(0.401326\pi\)
\(72\) 0 0
\(73\) −528.000 −0.846544 −0.423272 − 0.906003i \(-0.639119\pi\)
−0.423272 + 0.906003i \(0.639119\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 22.0000 0.0325602
\(78\) 0 0
\(79\) −686.000 −0.976975 −0.488488 − 0.872571i \(-0.662451\pi\)
−0.488488 + 0.872571i \(0.662451\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 698.000 0.923078 0.461539 − 0.887120i \(-0.347297\pi\)
0.461539 + 0.887120i \(0.347297\pi\)
\(84\) 0 0
\(85\) −342.000 −0.436413
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −967.000 −1.15171 −0.575853 − 0.817553i \(-0.695330\pi\)
−0.575853 + 0.817553i \(0.695330\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 396.000 0.427671
\(96\) 0 0
\(97\) −1127.00 −1.17969 −0.589843 − 0.807518i \(-0.700810\pi\)
−0.589843 + 0.807518i \(0.700810\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −510.000 −0.502445 −0.251222 − 0.967929i \(-0.580833\pi\)
−0.251222 + 0.967929i \(0.580833\pi\)
\(102\) 0 0
\(103\) 1056.00 1.01020 0.505101 − 0.863060i \(-0.331455\pi\)
0.505101 + 0.863060i \(0.331455\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1046.00 0.945053 0.472526 − 0.881317i \(-0.343342\pi\)
0.472526 + 0.881317i \(0.343342\pi\)
\(108\) 0 0
\(109\) 250.000 0.219685 0.109842 − 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1401.00 −1.16633 −0.583164 − 0.812355i \(-0.698185\pi\)
−0.583164 + 0.812355i \(0.698185\pi\)
\(114\) 0 0
\(115\) −1575.00 −1.27713
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −76.0000 −0.0585455
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1521.00 1.08834
\(126\) 0 0
\(127\) 132.000 0.0922292 0.0461146 − 0.998936i \(-0.485316\pi\)
0.0461146 + 0.998936i \(0.485316\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2054.00 −1.36991 −0.684957 − 0.728583i \(-0.740179\pi\)
−0.684957 + 0.728583i \(0.740179\pi\)
\(132\) 0 0
\(133\) 88.0000 0.0573727
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −889.000 −0.554397 −0.277199 − 0.960813i \(-0.589406\pi\)
−0.277199 + 0.960813i \(0.589406\pi\)
\(138\) 0 0
\(139\) −2638.00 −1.60973 −0.804864 − 0.593459i \(-0.797762\pi\)
−0.804864 + 0.593459i \(0.797762\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −2376.00 −1.36080
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3338.00 −1.83530 −0.917650 − 0.397390i \(-0.869916\pi\)
−0.917650 + 0.397390i \(0.869916\pi\)
\(150\) 0 0
\(151\) 430.000 0.231741 0.115871 − 0.993264i \(-0.463034\pi\)
0.115871 + 0.993264i \(0.463034\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1431.00 0.741553
\(156\) 0 0
\(157\) −1159.00 −0.589161 −0.294580 − 0.955627i \(-0.595180\pi\)
−0.294580 + 0.955627i \(0.595180\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −350.000 −0.171328
\(162\) 0 0
\(163\) −1012.00 −0.486294 −0.243147 − 0.969989i \(-0.578180\pi\)
−0.243147 + 0.969989i \(0.578180\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1584.00 0.733974 0.366987 − 0.930226i \(-0.380389\pi\)
0.366987 + 0.930226i \(0.380389\pi\)
\(168\) 0 0
\(169\) −2197.00 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −474.000 −0.208310 −0.104155 − 0.994561i \(-0.533214\pi\)
−0.104155 + 0.994561i \(0.533214\pi\)
\(174\) 0 0
\(175\) 88.0000 0.0380124
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1665.00 0.695240 0.347620 − 0.937636i \(-0.386990\pi\)
0.347620 + 0.937636i \(0.386990\pi\)
\(180\) 0 0
\(181\) 2543.00 1.04431 0.522154 − 0.852851i \(-0.325129\pi\)
0.522154 + 0.852851i \(0.325129\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1557.00 0.618773
\(186\) 0 0
\(187\) −418.000 −0.163461
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1631.00 −0.617880 −0.308940 − 0.951082i \(-0.599974\pi\)
−0.308940 + 0.951082i \(0.599974\pi\)
\(192\) 0 0
\(193\) 484.000 0.180513 0.0902567 − 0.995919i \(-0.471231\pi\)
0.0902567 + 0.995919i \(0.471231\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1966.00 −0.711024 −0.355512 − 0.934672i \(-0.615693\pi\)
−0.355512 + 0.934672i \(0.615693\pi\)
\(198\) 0 0
\(199\) −968.000 −0.344823 −0.172411 − 0.985025i \(-0.555156\pi\)
−0.172411 + 0.985025i \(0.555156\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −528.000 −0.182553
\(204\) 0 0
\(205\) −1980.00 −0.674581
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 484.000 0.160187
\(210\) 0 0
\(211\) 2948.00 0.961842 0.480921 − 0.876764i \(-0.340302\pi\)
0.480921 + 0.876764i \(0.340302\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4878.00 −1.54733
\(216\) 0 0
\(217\) 318.000 0.0994804
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1995.00 −0.599081 −0.299541 − 0.954084i \(-0.596833\pi\)
−0.299541 + 0.954084i \(0.596833\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6026.00 −1.76194 −0.880968 − 0.473175i \(-0.843108\pi\)
−0.880968 + 0.473175i \(0.843108\pi\)
\(228\) 0 0
\(229\) −4417.00 −1.27460 −0.637300 − 0.770615i \(-0.719949\pi\)
−0.637300 + 0.770615i \(0.719949\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5808.00 −1.63302 −0.816512 − 0.577328i \(-0.804095\pi\)
−0.816512 + 0.577328i \(0.804095\pi\)
\(234\) 0 0
\(235\) 2376.00 0.659545
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 626.000 0.169425 0.0847125 − 0.996405i \(-0.473003\pi\)
0.0847125 + 0.996405i \(0.473003\pi\)
\(240\) 0 0
\(241\) −3520.00 −0.940843 −0.470421 − 0.882442i \(-0.655898\pi\)
−0.470421 + 0.882442i \(0.655898\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3051.00 0.795597
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3921.00 0.986021 0.493011 − 0.870023i \(-0.335896\pi\)
0.493011 + 0.870023i \(0.335896\pi\)
\(252\) 0 0
\(253\) −1925.00 −0.478355
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4598.00 −1.11601 −0.558007 − 0.829837i \(-0.688434\pi\)
−0.558007 + 0.829837i \(0.688434\pi\)
\(258\) 0 0
\(259\) 346.000 0.0830092
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5838.00 −1.36877 −0.684385 − 0.729121i \(-0.739929\pi\)
−0.684385 + 0.729121i \(0.739929\pi\)
\(264\) 0 0
\(265\) 6138.00 1.42285
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5038.00 1.14190 0.570952 − 0.820983i \(-0.306574\pi\)
0.570952 + 0.820983i \(0.306574\pi\)
\(270\) 0 0
\(271\) 8096.00 1.81475 0.907374 − 0.420323i \(-0.138083\pi\)
0.907374 + 0.420323i \(0.138083\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 484.000 0.106132
\(276\) 0 0
\(277\) 7014.00 1.52141 0.760705 − 0.649098i \(-0.224854\pi\)
0.760705 + 0.649098i \(0.224854\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4362.00 0.926032 0.463016 − 0.886350i \(-0.346767\pi\)
0.463016 + 0.886350i \(0.346767\pi\)
\(282\) 0 0
\(283\) −4620.00 −0.970426 −0.485213 − 0.874396i \(-0.661258\pi\)
−0.485213 + 0.874396i \(0.661258\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −440.000 −0.0904961
\(288\) 0 0
\(289\) −3469.00 −0.706086
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7172.00 1.43001 0.715005 − 0.699120i \(-0.246425\pi\)
0.715005 + 0.699120i \(0.246425\pi\)
\(294\) 0 0
\(295\) −3789.00 −0.747811
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −1084.00 −0.207577
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2772.00 −0.520407
\(306\) 0 0
\(307\) −7348.00 −1.36603 −0.683017 − 0.730402i \(-0.739333\pi\)
−0.683017 + 0.730402i \(0.739333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5508.00 −1.00428 −0.502138 − 0.864787i \(-0.667453\pi\)
−0.502138 + 0.864787i \(0.667453\pi\)
\(312\) 0 0
\(313\) −7009.00 −1.26573 −0.632863 − 0.774264i \(-0.718120\pi\)
−0.632863 + 0.774264i \(0.718120\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −853.000 −0.151133 −0.0755666 − 0.997141i \(-0.524077\pi\)
−0.0755666 + 0.997141i \(0.524077\pi\)
\(318\) 0 0
\(319\) −2904.00 −0.509695
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1672.00 −0.288027
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 528.000 0.0884790
\(330\) 0 0
\(331\) −3631.00 −0.602954 −0.301477 − 0.953473i \(-0.597480\pi\)
−0.301477 + 0.953473i \(0.597480\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1593.00 0.259806
\(336\) 0 0
\(337\) 11574.0 1.87085 0.935424 − 0.353527i \(-0.115018\pi\)
0.935424 + 0.353527i \(0.115018\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1749.00 0.277753
\(342\) 0 0
\(343\) 1364.00 0.214720
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1056.00 −0.163369 −0.0816845 − 0.996658i \(-0.526030\pi\)
−0.0816845 + 0.996658i \(0.526030\pi\)
\(348\) 0 0
\(349\) 6810.00 1.04450 0.522251 − 0.852792i \(-0.325093\pi\)
0.522251 + 0.852792i \(0.325093\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9923.00 −1.49617 −0.748085 − 0.663603i \(-0.769026\pi\)
−0.748085 + 0.663603i \(0.769026\pi\)
\(354\) 0 0
\(355\) −3285.00 −0.491126
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2200.00 −0.323431 −0.161715 − 0.986837i \(-0.551703\pi\)
−0.161715 + 0.986837i \(0.551703\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4752.00 0.681455
\(366\) 0 0
\(367\) −8935.00 −1.27085 −0.635427 − 0.772161i \(-0.719176\pi\)
−0.635427 + 0.772161i \(0.719176\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1364.00 0.190877
\(372\) 0 0
\(373\) 9122.00 1.26627 0.633136 − 0.774041i \(-0.281767\pi\)
0.633136 + 0.774041i \(0.281767\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −8963.00 −1.21477 −0.607386 − 0.794407i \(-0.707782\pi\)
−0.607386 + 0.794407i \(0.707782\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1721.00 −0.229606 −0.114803 − 0.993388i \(-0.536624\pi\)
−0.114803 + 0.993388i \(0.536624\pi\)
\(384\) 0 0
\(385\) −198.000 −0.0262104
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7351.00 0.958125 0.479062 − 0.877781i \(-0.340977\pi\)
0.479062 + 0.877781i \(0.340977\pi\)
\(390\) 0 0
\(391\) 6650.00 0.860115
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6174.00 0.786450
\(396\) 0 0
\(397\) −8338.00 −1.05409 −0.527043 − 0.849839i \(-0.676699\pi\)
−0.527043 + 0.849839i \(0.676699\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11814.0 1.47123 0.735615 − 0.677400i \(-0.236893\pi\)
0.735615 + 0.677400i \(0.236893\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1903.00 0.231765
\(408\) 0 0
\(409\) −7278.00 −0.879887 −0.439944 − 0.898025i \(-0.645002\pi\)
−0.439944 + 0.898025i \(0.645002\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −842.000 −0.100320
\(414\) 0 0
\(415\) −6282.00 −0.743063
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3828.00 −0.446325 −0.223162 − 0.974781i \(-0.571638\pi\)
−0.223162 + 0.974781i \(0.571638\pi\)
\(420\) 0 0
\(421\) −15466.0 −1.79042 −0.895210 − 0.445645i \(-0.852974\pi\)
−0.895210 + 0.445645i \(0.852974\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1672.00 −0.190833
\(426\) 0 0
\(427\) −616.000 −0.0698134
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2710.00 −0.302868 −0.151434 − 0.988467i \(-0.548389\pi\)
−0.151434 + 0.988467i \(0.548389\pi\)
\(432\) 0 0
\(433\) −3347.00 −0.371470 −0.185735 − 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7700.00 −0.842885
\(438\) 0 0
\(439\) −2464.00 −0.267882 −0.133941 − 0.990989i \(-0.542763\pi\)
−0.133941 + 0.990989i \(0.542763\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5955.00 −0.638669 −0.319335 − 0.947642i \(-0.603459\pi\)
−0.319335 + 0.947642i \(0.603459\pi\)
\(444\) 0 0
\(445\) 8703.00 0.927105
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13173.0 1.38457 0.692285 − 0.721624i \(-0.256604\pi\)
0.692285 + 0.721624i \(0.256604\pi\)
\(450\) 0 0
\(451\) −2420.00 −0.252668
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6292.00 −0.644042 −0.322021 − 0.946732i \(-0.604362\pi\)
−0.322021 + 0.946732i \(0.604362\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10164.0 −1.02686 −0.513432 − 0.858130i \(-0.671626\pi\)
−0.513432 + 0.858130i \(0.671626\pi\)
\(462\) 0 0
\(463\) −5677.00 −0.569833 −0.284916 − 0.958552i \(-0.591966\pi\)
−0.284916 + 0.958552i \(0.591966\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6675.00 −0.661418 −0.330709 − 0.943733i \(-0.607288\pi\)
−0.330709 + 0.943733i \(0.607288\pi\)
\(468\) 0 0
\(469\) 354.000 0.0348533
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5962.00 −0.579562
\(474\) 0 0
\(475\) 1936.00 0.187010
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6424.00 0.612777 0.306388 − 0.951907i \(-0.400879\pi\)
0.306388 + 0.951907i \(0.400879\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10143.0 0.949629
\(486\) 0 0
\(487\) 21369.0 1.98834 0.994170 − 0.107822i \(-0.0343876\pi\)
0.994170 + 0.107822i \(0.0343876\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1848.00 0.169856 0.0849278 − 0.996387i \(-0.472934\pi\)
0.0849278 + 0.996387i \(0.472934\pi\)
\(492\) 0 0
\(493\) 10032.0 0.916468
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −730.000 −0.0658853
\(498\) 0 0
\(499\) 19228.0 1.72498 0.862488 − 0.506077i \(-0.168905\pi\)
0.862488 + 0.506077i \(0.168905\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10878.0 0.964266 0.482133 − 0.876098i \(-0.339862\pi\)
0.482133 + 0.876098i \(0.339862\pi\)
\(504\) 0 0
\(505\) 4590.00 0.404460
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10047.0 −0.874903 −0.437451 − 0.899242i \(-0.644119\pi\)
−0.437451 + 0.899242i \(0.644119\pi\)
\(510\) 0 0
\(511\) 1056.00 0.0914182
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9504.00 −0.813197
\(516\) 0 0
\(517\) 2904.00 0.247036
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5827.00 0.489991 0.244996 − 0.969524i \(-0.421213\pi\)
0.244996 + 0.969524i \(0.421213\pi\)
\(522\) 0 0
\(523\) −836.000 −0.0698962 −0.0349481 − 0.999389i \(-0.511127\pi\)
−0.0349481 + 0.999389i \(0.511127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6042.00 −0.499419
\(528\) 0 0
\(529\) 18458.0 1.51705
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −9414.00 −0.760753
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3729.00 0.297995
\(540\) 0 0
\(541\) −7172.00 −0.569960 −0.284980 − 0.958533i \(-0.591987\pi\)
−0.284980 + 0.958533i \(0.591987\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2250.00 −0.176843
\(546\) 0 0
\(547\) 11264.0 0.880464 0.440232 − 0.897884i \(-0.354896\pi\)
0.440232 + 0.897884i \(0.354896\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11616.0 −0.898109
\(552\) 0 0
\(553\) 1372.00 0.105503
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −306.000 −0.0232776 −0.0116388 − 0.999932i \(-0.503705\pi\)
−0.0116388 + 0.999932i \(0.503705\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23804.0 1.78192 0.890958 − 0.454085i \(-0.150034\pi\)
0.890958 + 0.454085i \(0.150034\pi\)
\(564\) 0 0
\(565\) 12609.0 0.938875
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4664.00 0.343629 0.171815 − 0.985129i \(-0.445037\pi\)
0.171815 + 0.985129i \(0.445037\pi\)
\(570\) 0 0
\(571\) −11572.0 −0.848114 −0.424057 − 0.905635i \(-0.639394\pi\)
−0.424057 + 0.905635i \(0.639394\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7700.00 −0.558456
\(576\) 0 0
\(577\) −24407.0 −1.76096 −0.880482 − 0.474079i \(-0.842781\pi\)
−0.880482 + 0.474079i \(0.842781\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1396.00 −0.0996830
\(582\) 0 0
\(583\) 7502.00 0.532935
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18436.0 1.29631 0.648156 − 0.761508i \(-0.275540\pi\)
0.648156 + 0.761508i \(0.275540\pi\)
\(588\) 0 0
\(589\) 6996.00 0.489415
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11044.0 0.764794 0.382397 − 0.923998i \(-0.375099\pi\)
0.382397 + 0.923998i \(0.375099\pi\)
\(594\) 0 0
\(595\) 684.000 0.0471282
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8800.00 0.600264 0.300132 − 0.953898i \(-0.402969\pi\)
0.300132 + 0.953898i \(0.402969\pi\)
\(600\) 0 0
\(601\) −10826.0 −0.734778 −0.367389 − 0.930067i \(-0.619748\pi\)
−0.367389 + 0.930067i \(0.619748\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1089.00 −0.0731804
\(606\) 0 0
\(607\) −4066.00 −0.271884 −0.135942 − 0.990717i \(-0.543406\pi\)
−0.135942 + 0.990717i \(0.543406\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 4752.00 0.313102 0.156551 − 0.987670i \(-0.449962\pi\)
0.156551 + 0.987670i \(0.449962\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3806.00 0.248337 0.124168 − 0.992261i \(-0.460374\pi\)
0.124168 + 0.992261i \(0.460374\pi\)
\(618\) 0 0
\(619\) 5185.00 0.336676 0.168338 − 0.985729i \(-0.446160\pi\)
0.168338 + 0.985729i \(0.446160\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1934.00 0.124373
\(624\) 0 0
\(625\) −8189.00 −0.524096
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6574.00 −0.416729
\(630\) 0 0
\(631\) 13049.0 0.823253 0.411626 − 0.911353i \(-0.364961\pi\)
0.411626 + 0.911353i \(0.364961\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1188.00 −0.0742431
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9959.00 −0.613661 −0.306831 − 0.951764i \(-0.599269\pi\)
−0.306831 + 0.951764i \(0.599269\pi\)
\(642\) 0 0
\(643\) −12197.0 −0.748060 −0.374030 − 0.927417i \(-0.622024\pi\)
−0.374030 + 0.927417i \(0.622024\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5759.00 −0.349938 −0.174969 − 0.984574i \(-0.555982\pi\)
−0.174969 + 0.984574i \(0.555982\pi\)
\(648\) 0 0
\(649\) −4631.00 −0.280097
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25209.0 1.51073 0.755363 − 0.655306i \(-0.227460\pi\)
0.755363 + 0.655306i \(0.227460\pi\)
\(654\) 0 0
\(655\) 18486.0 1.10276
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4062.00 −0.240111 −0.120055 − 0.992767i \(-0.538307\pi\)
−0.120055 + 0.992767i \(0.538307\pi\)
\(660\) 0 0
\(661\) 31173.0 1.83433 0.917163 − 0.398513i \(-0.130474\pi\)
0.917163 + 0.398513i \(0.130474\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −792.000 −0.0461841
\(666\) 0 0
\(667\) 46200.0 2.68197
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3388.00 −0.194921
\(672\) 0 0
\(673\) −26690.0 −1.52871 −0.764357 − 0.644794i \(-0.776943\pi\)
−0.764357 + 0.644794i \(0.776943\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7398.00 0.419983 0.209991 − 0.977703i \(-0.432656\pi\)
0.209991 + 0.977703i \(0.432656\pi\)
\(678\) 0 0
\(679\) 2254.00 0.127394
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 27960.0 1.56641 0.783206 − 0.621762i \(-0.213583\pi\)
0.783206 + 0.621762i \(0.213583\pi\)
\(684\) 0 0
\(685\) 8001.00 0.446281
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −19465.0 −1.07161 −0.535806 − 0.844341i \(-0.679992\pi\)
−0.535806 + 0.844341i \(0.679992\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 23742.0 1.29581
\(696\) 0 0
\(697\) 8360.00 0.454315
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −13518.0 −0.728342 −0.364171 − 0.931332i \(-0.618648\pi\)
−0.364171 + 0.931332i \(0.618648\pi\)
\(702\) 0 0
\(703\) 7612.00 0.408381
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1020.00 0.0542589
\(708\) 0 0
\(709\) 14727.0 0.780090 0.390045 − 0.920796i \(-0.372459\pi\)
0.390045 + 0.920796i \(0.372459\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −27825.0 −1.46151
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 15711.0 0.814912 0.407456 − 0.913225i \(-0.366416\pi\)
0.407456 + 0.913225i \(0.366416\pi\)
\(720\) 0 0
\(721\) −2112.00 −0.109092
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −11616.0 −0.595045
\(726\) 0 0
\(727\) −12099.0 −0.617231 −0.308616 − 0.951187i \(-0.599866\pi\)
−0.308616 + 0.951187i \(0.599866\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20596.0 1.04209
\(732\) 0 0
\(733\) 9812.00 0.494426 0.247213 − 0.968961i \(-0.420485\pi\)
0.247213 + 0.968961i \(0.420485\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1947.00 0.0973116
\(738\) 0 0
\(739\) 11854.0 0.590063 0.295031 − 0.955488i \(-0.404670\pi\)
0.295031 + 0.955488i \(0.404670\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18788.0 0.927678 0.463839 − 0.885919i \(-0.346472\pi\)
0.463839 + 0.885919i \(0.346472\pi\)
\(744\) 0 0
\(745\) 30042.0 1.47739
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2092.00 −0.102056
\(750\) 0 0
\(751\) 16559.0 0.804589 0.402295 − 0.915510i \(-0.368213\pi\)
0.402295 + 0.915510i \(0.368213\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3870.00 −0.186548
\(756\) 0 0
\(757\) 26610.0 1.27762 0.638809 − 0.769365i \(-0.279427\pi\)
0.638809 + 0.769365i \(0.279427\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7040.00 −0.335348 −0.167674 − 0.985843i \(-0.553626\pi\)
−0.167674 + 0.985843i \(0.553626\pi\)
\(762\) 0 0
\(763\) −500.000 −0.0237237
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −18128.0 −0.850081 −0.425041 − 0.905174i \(-0.639740\pi\)
−0.425041 + 0.905174i \(0.639740\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9570.00 −0.445290 −0.222645 − 0.974900i \(-0.571469\pi\)
−0.222645 + 0.974900i \(0.571469\pi\)
\(774\) 0 0
\(775\) 6996.00 0.324263
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9680.00 −0.445214
\(780\) 0 0
\(781\) −4015.00 −0.183954
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10431.0 0.474265
\(786\) 0 0
\(787\) 16280.0 0.737382 0.368691 − 0.929552i \(-0.379806\pi\)
0.368691 + 0.929552i \(0.379806\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2802.00 0.125952
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 603.000 0.0267997 0.0133998 − 0.999910i \(-0.495735\pi\)
0.0133998 + 0.999910i \(0.495735\pi\)
\(798\) 0 0
\(799\) −10032.0 −0.444189
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5808.00 0.255243
\(804\) 0 0
\(805\) 3150.00 0.137917
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −23276.0 −1.01155 −0.505773 − 0.862667i \(-0.668793\pi\)
−0.505773 + 0.862667i \(0.668793\pi\)
\(810\) 0 0
\(811\) 45662.0 1.97708 0.988539 − 0.150968i \(-0.0482390\pi\)
0.988539 + 0.150968i \(0.0482390\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9108.00 0.391459
\(816\) 0 0
\(817\) −23848.0 −1.02122
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33222.0 −1.41225 −0.706124 − 0.708088i \(-0.749558\pi\)
−0.706124 + 0.708088i \(0.749558\pi\)
\(822\) 0 0
\(823\) 3569.00 0.151163 0.0755817 − 0.997140i \(-0.475919\pi\)
0.0755817 + 0.997140i \(0.475919\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −41008.0 −1.72429 −0.862145 − 0.506662i \(-0.830879\pi\)
−0.862145 + 0.506662i \(0.830879\pi\)
\(828\) 0 0
\(829\) −17839.0 −0.747375 −0.373688 − 0.927555i \(-0.621907\pi\)
−0.373688 + 0.927555i \(0.621907\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −12882.0 −0.535816
\(834\) 0 0
\(835\) −14256.0 −0.590837
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 20731.0 0.853056 0.426528 − 0.904474i \(-0.359737\pi\)
0.426528 + 0.904474i \(0.359737\pi\)
\(840\) 0 0
\(841\) 45307.0 1.85768
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 19773.0 0.804984
\(846\) 0 0
\(847\) −242.000 −0.00981726
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −30275.0 −1.21952
\(852\) 0 0
\(853\) 9102.00 0.365354 0.182677 − 0.983173i \(-0.441524\pi\)
0.182677 + 0.983173i \(0.441524\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −12936.0 −0.515619 −0.257809 − 0.966196i \(-0.583001\pi\)
−0.257809 + 0.966196i \(0.583001\pi\)
\(858\) 0 0
\(859\) −15113.0 −0.600290 −0.300145 − 0.953894i \(-0.597035\pi\)
−0.300145 + 0.953894i \(0.597035\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29216.0 1.15240 0.576202 − 0.817308i \(-0.304534\pi\)
0.576202 + 0.817308i \(0.304534\pi\)
\(864\) 0 0
\(865\) 4266.00 0.167686
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7546.00 0.294569
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3042.00 −0.117530
\(876\) 0 0
\(877\) 29304.0 1.12831 0.564154 − 0.825670i \(-0.309202\pi\)
0.564154 + 0.825670i \(0.309202\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23715.0 0.906900 0.453450 − 0.891282i \(-0.350193\pi\)
0.453450 + 0.891282i \(0.350193\pi\)
\(882\) 0 0
\(883\) −6028.00 −0.229738 −0.114869 − 0.993381i \(-0.536645\pi\)
−0.114869 + 0.993381i \(0.536645\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 18786.0 0.711130 0.355565 − 0.934652i \(-0.384288\pi\)
0.355565 + 0.934652i \(0.384288\pi\)
\(888\) 0 0
\(889\) −264.000 −0.00995982
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11616.0 0.435291
\(894\) 0 0
\(895\) −14985.0 −0.559657
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −41976.0 −1.55726
\(900\) 0 0
\(901\) −25916.0 −0.958254
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −22887.0 −0.840652
\(906\) 0 0
\(907\) 2156.00 0.0789292 0.0394646 − 0.999221i \(-0.487435\pi\)
0.0394646 + 0.999221i \(0.487435\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −51732.0 −1.88140 −0.940701 − 0.339236i \(-0.889831\pi\)
−0.940701 + 0.339236i \(0.889831\pi\)
\(912\) 0 0
\(913\) −7678.00 −0.278318
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4108.00 0.147937
\(918\) 0 0
\(919\) 18254.0 0.655216 0.327608 − 0.944814i \(-0.393757\pi\)
0.327608 + 0.944814i \(0.393757\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 7612.00 0.270574
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −5610.00 −0.198125 −0.0990625 − 0.995081i \(-0.531584\pi\)
−0.0990625 + 0.995081i \(0.531584\pi\)
\(930\) 0 0
\(931\) 14916.0 0.525083
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3762.00 0.131583
\(936\) 0 0
\(937\) −37180.0 −1.29628 −0.648142 − 0.761520i \(-0.724454\pi\)
−0.648142 + 0.761520i \(0.724454\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 31278.0 1.08356 0.541782 − 0.840519i \(-0.317750\pi\)
0.541782 + 0.840519i \(0.317750\pi\)
\(942\) 0 0
\(943\) 38500.0 1.32951
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −47475.0 −1.62907 −0.814535 − 0.580114i \(-0.803008\pi\)
−0.814535 + 0.580114i \(0.803008\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20462.0 −0.695519 −0.347759 − 0.937584i \(-0.613057\pi\)
−0.347759 + 0.937584i \(0.613057\pi\)
\(954\) 0 0
\(955\) 14679.0 0.497384
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1778.00 0.0598693
\(960\) 0 0
\(961\) −4510.00 −0.151388
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4356.00 −0.145310
\(966\) 0 0
\(967\) −52360.0 −1.74125 −0.870623 − 0.491952i \(-0.836284\pi\)
−0.870623 + 0.491952i \(0.836284\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 56247.0 1.85896 0.929481 − 0.368870i \(-0.120255\pi\)
0.929481 + 0.368870i \(0.120255\pi\)
\(972\) 0 0
\(973\) 5276.00 0.173834
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18155.0 0.594503 0.297252 − 0.954799i \(-0.403930\pi\)
0.297252 + 0.954799i \(0.403930\pi\)
\(978\) 0 0
\(979\) 10637.0 0.347252
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1191.00 0.0386439 0.0193220 − 0.999813i \(-0.493849\pi\)
0.0193220 + 0.999813i \(0.493849\pi\)
\(984\) 0 0
\(985\) 17694.0 0.572363
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 94850.0 3.04960
\(990\) 0 0
\(991\) −28864.0 −0.925222 −0.462611 − 0.886561i \(-0.653087\pi\)
−0.462611 + 0.886561i \(0.653087\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8712.00 0.277577
\(996\) 0 0
\(997\) 51610.0 1.63942 0.819712 − 0.572776i \(-0.194134\pi\)
0.819712 + 0.572776i \(0.194134\pi\)
\(998\) 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 1584.4.a.g.1.1 1
3.2 odd 2 176.4.a.a.1.1 1
4.3 odd 2 792.4.a.b.1.1 1
12.11 even 2 88.4.a.b.1.1 ✓ 1
24.5 odd 2 704.4.a.k.1.1 1
24.11 even 2 704.4.a.a.1.1 1
33.32 even 2 1936.4.a.b.1.1 1
60.59 even 2 2200.4.a.a.1.1 1
132.131 odd 2 968.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.4.a.b.1.1 ✓ 1 12.11 even 2
176.4.a.a.1.1 1 3.2 odd 2
704.4.a.a.1.1 1 24.11 even 2
704.4.a.k.1.1 1 24.5 odd 2
792.4.a.b.1.1 1 4.3 odd 2
968.4.a.e.1.1 1 132.131 odd 2
1584.4.a.g.1.1 1 1.1 even 1 trivial
1936.4.a.b.1.1 1 33.32 even 2
2200.4.a.a.1.1 1 60.59 even 2