Properties

Label 1232.4.a.e.1.1
Level $1232$
Weight $4$
Character 1232.1
Self dual yes
Analytic conductor $72.690$
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] = [1232,4,Mod(1,1232)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1232, 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("1232.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.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: \(72.6903531271\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1232.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} +7.00000 q^{7} -27.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{5} +7.00000 q^{7} -27.0000 q^{9} -11.0000 q^{11} +26.0000 q^{13} -46.0000 q^{17} +48.0000 q^{19} +128.000 q^{23} -121.000 q^{25} -146.000 q^{29} +128.000 q^{31} +14.0000 q^{35} -26.0000 q^{37} +10.0000 q^{41} -52.0000 q^{43} -54.0000 q^{45} +544.000 q^{47} +49.0000 q^{49} +318.000 q^{53} -22.0000 q^{55} +48.0000 q^{59} +466.000 q^{61} -189.000 q^{63} +52.0000 q^{65} -516.000 q^{67} +392.000 q^{71} +754.000 q^{73} -77.0000 q^{77} +729.000 q^{81} -624.000 q^{83} -92.0000 q^{85} -1590.00 q^{89} +182.000 q^{91} +96.0000 q^{95} +1018.00 q^{97} +297.000 q^{99} +O(q^{100})\)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 2.00000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) −27.0000 −1.00000
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 26.0000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −46.0000 −0.656273 −0.328136 0.944630i \(-0.606421\pi\)
−0.328136 + 0.944630i \(0.606421\pi\)
\(18\) 0 0
\(19\) 48.0000 0.579577 0.289788 0.957091i \(-0.406415\pi\)
0.289788 + 0.957091i \(0.406415\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 128.000 1.16043 0.580214 0.814464i \(-0.302969\pi\)
0.580214 + 0.814464i \(0.302969\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −146.000 −0.934880 −0.467440 0.884025i \(-0.654824\pi\)
−0.467440 + 0.884025i \(0.654824\pi\)
\(30\) 0 0
\(31\) 128.000 0.741596 0.370798 0.928714i \(-0.379084\pi\)
0.370798 + 0.928714i \(0.379084\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 14.0000 0.0676123
\(36\) 0 0
\(37\) −26.0000 −0.115524 −0.0577618 0.998330i \(-0.518396\pi\)
−0.0577618 + 0.998330i \(0.518396\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.0000 0.0380912 0.0190456 0.999819i \(-0.493937\pi\)
0.0190456 + 0.999819i \(0.493937\pi\)
\(42\) 0 0
\(43\) −52.0000 −0.184417 −0.0922084 0.995740i \(-0.529393\pi\)
−0.0922084 + 0.995740i \(0.529393\pi\)
\(44\) 0 0
\(45\) −54.0000 −0.178885
\(46\) 0 0
\(47\) 544.000 1.68831 0.844155 0.536099i \(-0.180103\pi\)
0.844155 + 0.536099i \(0.180103\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 318.000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −22.0000 −0.0539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 48.0000 0.105916 0.0529582 0.998597i \(-0.483135\pi\)
0.0529582 + 0.998597i \(0.483135\pi\)
\(60\) 0 0
\(61\) 466.000 0.978118 0.489059 0.872251i \(-0.337340\pi\)
0.489059 + 0.872251i \(0.337340\pi\)
\(62\) 0 0
\(63\) −189.000 −0.377964
\(64\) 0 0
\(65\) 52.0000 0.0992278
\(66\) 0 0
\(67\) −516.000 −0.940887 −0.470444 0.882430i \(-0.655906\pi\)
−0.470444 + 0.882430i \(0.655906\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 392.000 0.655237 0.327619 0.944810i \(-0.393754\pi\)
0.327619 + 0.944810i \(0.393754\pi\)
\(72\) 0 0
\(73\) 754.000 1.20889 0.604445 0.796647i \(-0.293395\pi\)
0.604445 + 0.796647i \(0.293395\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 729.000 1.00000
\(82\) 0 0
\(83\) −624.000 −0.825216 −0.412608 0.910909i \(-0.635382\pi\)
−0.412608 + 0.910909i \(0.635382\pi\)
\(84\) 0 0
\(85\) −92.0000 −0.117398
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1590.00 −1.89370 −0.946852 0.321669i \(-0.895756\pi\)
−0.946852 + 0.321669i \(0.895756\pi\)
\(90\) 0 0
\(91\) 182.000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 96.0000 0.103678
\(96\) 0 0
\(97\) 1018.00 1.06559 0.532795 0.846244i \(-0.321142\pi\)
0.532795 + 0.846244i \(0.321142\pi\)
\(98\) 0 0
\(99\) 297.000 0.301511
\(100\) 0 0
\(101\) 474.000 0.466978 0.233489 0.972359i \(-0.424986\pi\)
0.233489 + 0.972359i \(0.424986\pi\)
\(102\) 0 0
\(103\) 984.000 0.941324 0.470662 0.882314i \(-0.344015\pi\)
0.470662 + 0.882314i \(0.344015\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −92.0000 −0.0831213 −0.0415606 0.999136i \(-0.513233\pi\)
−0.0415606 + 0.999136i \(0.513233\pi\)
\(108\) 0 0
\(109\) 1246.00 1.09491 0.547455 0.836835i \(-0.315597\pi\)
0.547455 + 0.836835i \(0.315597\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1630.00 −1.35697 −0.678485 0.734615i \(-0.737363\pi\)
−0.678485 + 0.734615i \(0.737363\pi\)
\(114\) 0 0
\(115\) 256.000 0.207584
\(116\) 0 0
\(117\) −702.000 −0.554700
\(118\) 0 0
\(119\) −322.000 −0.248048
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) −1016.00 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1920.00 1.28054 0.640272 0.768149i \(-0.278822\pi\)
0.640272 + 0.768149i \(0.278822\pi\)
\(132\) 0 0
\(133\) 336.000 0.219059
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1482.00 0.924203 0.462101 0.886827i \(-0.347096\pi\)
0.462101 + 0.886827i \(0.347096\pi\)
\(138\) 0 0
\(139\) 2608.00 1.59142 0.795711 0.605676i \(-0.207097\pi\)
0.795711 + 0.605676i \(0.207097\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −286.000 −0.167248
\(144\) 0 0
\(145\) −292.000 −0.167236
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1310.00 0.720264 0.360132 0.932901i \(-0.382732\pi\)
0.360132 + 0.932901i \(0.382732\pi\)
\(150\) 0 0
\(151\) 192.000 0.103475 0.0517375 0.998661i \(-0.483524\pi\)
0.0517375 + 0.998661i \(0.483524\pi\)
\(152\) 0 0
\(153\) 1242.00 0.656273
\(154\) 0 0
\(155\) 256.000 0.132661
\(156\) 0 0
\(157\) 658.000 0.334485 0.167242 0.985916i \(-0.446514\pi\)
0.167242 + 0.985916i \(0.446514\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 896.000 0.438601
\(162\) 0 0
\(163\) −2236.00 −1.07446 −0.537230 0.843436i \(-0.680529\pi\)
−0.537230 + 0.843436i \(0.680529\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1664.00 0.771043 0.385522 0.922699i \(-0.374022\pi\)
0.385522 + 0.922699i \(0.374022\pi\)
\(168\) 0 0
\(169\) −1521.00 −0.692308
\(170\) 0 0
\(171\) −1296.00 −0.579577
\(172\) 0 0
\(173\) −662.000 −0.290930 −0.145465 0.989363i \(-0.546468\pi\)
−0.145465 + 0.989363i \(0.546468\pi\)
\(174\) 0 0
\(175\) −847.000 −0.365870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2540.00 1.06061 0.530303 0.847808i \(-0.322078\pi\)
0.530303 + 0.847808i \(0.322078\pi\)
\(180\) 0 0
\(181\) 2762.00 1.13424 0.567121 0.823634i \(-0.308057\pi\)
0.567121 + 0.823634i \(0.308057\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −52.0000 −0.0206655
\(186\) 0 0
\(187\) 506.000 0.197874
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 0.00606136 0.00303068 0.999995i \(-0.499035\pi\)
0.00303068 + 0.999995i \(0.499035\pi\)
\(192\) 0 0
\(193\) 5138.00 1.91628 0.958138 0.286306i \(-0.0924275\pi\)
0.958138 + 0.286306i \(0.0924275\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4350.00 1.57322 0.786611 0.617449i \(-0.211834\pi\)
0.786611 + 0.617449i \(0.211834\pi\)
\(198\) 0 0
\(199\) 4040.00 1.43914 0.719568 0.694422i \(-0.244340\pi\)
0.719568 + 0.694422i \(0.244340\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1022.00 −0.353351
\(204\) 0 0
\(205\) 20.0000 0.00681395
\(206\) 0 0
\(207\) −3456.00 −1.16043
\(208\) 0 0
\(209\) −528.000 −0.174749
\(210\) 0 0
\(211\) 1820.00 0.593810 0.296905 0.954907i \(-0.404045\pi\)
0.296905 + 0.954907i \(0.404045\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −104.000 −0.0329895
\(216\) 0 0
\(217\) 896.000 0.280297
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1196.00 −0.364035
\(222\) 0 0
\(223\) 2360.00 0.708687 0.354344 0.935115i \(-0.384704\pi\)
0.354344 + 0.935115i \(0.384704\pi\)
\(224\) 0 0
\(225\) 3267.00 0.968000
\(226\) 0 0
\(227\) 6416.00 1.87597 0.937984 0.346678i \(-0.112690\pi\)
0.937984 + 0.346678i \(0.112690\pi\)
\(228\) 0 0
\(229\) −1558.00 −0.449588 −0.224794 0.974406i \(-0.572171\pi\)
−0.224794 + 0.974406i \(0.572171\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 522.000 0.146770 0.0733849 0.997304i \(-0.476620\pi\)
0.0733849 + 0.997304i \(0.476620\pi\)
\(234\) 0 0
\(235\) 1088.00 0.302014
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2152.00 −0.582432 −0.291216 0.956657i \(-0.594060\pi\)
−0.291216 + 0.956657i \(0.594060\pi\)
\(240\) 0 0
\(241\) −606.000 −0.161975 −0.0809873 0.996715i \(-0.525807\pi\)
−0.0809873 + 0.996715i \(0.525807\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 98.0000 0.0255551
\(246\) 0 0
\(247\) 1248.00 0.321491
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1608.00 0.404367 0.202183 0.979348i \(-0.435196\pi\)
0.202183 + 0.979348i \(0.435196\pi\)
\(252\) 0 0
\(253\) −1408.00 −0.349882
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4446.00 −1.07912 −0.539560 0.841947i \(-0.681409\pi\)
−0.539560 + 0.841947i \(0.681409\pi\)
\(258\) 0 0
\(259\) −182.000 −0.0436638
\(260\) 0 0
\(261\) 3942.00 0.934880
\(262\) 0 0
\(263\) −6600.00 −1.54743 −0.773714 0.633535i \(-0.781603\pi\)
−0.773714 + 0.633535i \(0.781603\pi\)
\(264\) 0 0
\(265\) 636.000 0.147431
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1854.00 −0.420224 −0.210112 0.977677i \(-0.567383\pi\)
−0.210112 + 0.977677i \(0.567383\pi\)
\(270\) 0 0
\(271\) 272.000 0.0609698 0.0304849 0.999535i \(-0.490295\pi\)
0.0304849 + 0.999535i \(0.490295\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1331.00 0.291863
\(276\) 0 0
\(277\) −5010.00 −1.08672 −0.543361 0.839499i \(-0.682848\pi\)
−0.543361 + 0.839499i \(0.682848\pi\)
\(278\) 0 0
\(279\) −3456.00 −0.741596
\(280\) 0 0
\(281\) 314.000 0.0666607 0.0333304 0.999444i \(-0.489389\pi\)
0.0333304 + 0.999444i \(0.489389\pi\)
\(282\) 0 0
\(283\) −3480.00 −0.730970 −0.365485 0.930817i \(-0.619097\pi\)
−0.365485 + 0.930817i \(0.619097\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 70.0000 0.0143971
\(288\) 0 0
\(289\) −2797.00 −0.569306
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4230.00 −0.843410 −0.421705 0.906733i \(-0.638568\pi\)
−0.421705 + 0.906733i \(0.638568\pi\)
\(294\) 0 0
\(295\) 96.0000 0.0189469
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3328.00 0.643690
\(300\) 0 0
\(301\) −364.000 −0.0697030
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 932.000 0.174971
\(306\) 0 0
\(307\) 1552.00 0.288525 0.144263 0.989539i \(-0.453919\pi\)
0.144263 + 0.989539i \(0.453919\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4864.00 0.886856 0.443428 0.896310i \(-0.353762\pi\)
0.443428 + 0.896310i \(0.353762\pi\)
\(312\) 0 0
\(313\) 4786.00 0.864283 0.432142 0.901806i \(-0.357758\pi\)
0.432142 + 0.901806i \(0.357758\pi\)
\(314\) 0 0
\(315\) −378.000 −0.0676123
\(316\) 0 0
\(317\) −1530.00 −0.271083 −0.135542 0.990772i \(-0.543277\pi\)
−0.135542 + 0.990772i \(0.543277\pi\)
\(318\) 0 0
\(319\) 1606.00 0.281877
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2208.00 −0.380360
\(324\) 0 0
\(325\) −3146.00 −0.536950
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3808.00 0.638121
\(330\) 0 0
\(331\) 10844.0 1.80073 0.900363 0.435140i \(-0.143301\pi\)
0.900363 + 0.435140i \(0.143301\pi\)
\(332\) 0 0
\(333\) 702.000 0.115524
\(334\) 0 0
\(335\) −1032.00 −0.168311
\(336\) 0 0
\(337\) 402.000 0.0649802 0.0324901 0.999472i \(-0.489656\pi\)
0.0324901 + 0.999472i \(0.489656\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1408.00 −0.223600
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5980.00 0.925139 0.462569 0.886583i \(-0.346928\pi\)
0.462569 + 0.886583i \(0.346928\pi\)
\(348\) 0 0
\(349\) −3094.00 −0.474550 −0.237275 0.971442i \(-0.576254\pi\)
−0.237275 + 0.971442i \(0.576254\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4494.00 −0.677596 −0.338798 0.940859i \(-0.610020\pi\)
−0.338798 + 0.940859i \(0.610020\pi\)
\(354\) 0 0
\(355\) 784.000 0.117212
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2752.00 0.404582 0.202291 0.979325i \(-0.435161\pi\)
0.202291 + 0.979325i \(0.435161\pi\)
\(360\) 0 0
\(361\) −4555.00 −0.664091
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1508.00 0.216253
\(366\) 0 0
\(367\) 2024.00 0.287880 0.143940 0.989586i \(-0.454023\pi\)
0.143940 + 0.989586i \(0.454023\pi\)
\(368\) 0 0
\(369\) −270.000 −0.0380912
\(370\) 0 0
\(371\) 2226.00 0.311504
\(372\) 0 0
\(373\) 5246.00 0.728224 0.364112 0.931355i \(-0.381373\pi\)
0.364112 + 0.931355i \(0.381373\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3796.00 −0.518578
\(378\) 0 0
\(379\) −3892.00 −0.527490 −0.263745 0.964592i \(-0.584958\pi\)
−0.263745 + 0.964592i \(0.584958\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6752.00 −0.900812 −0.450406 0.892824i \(-0.648721\pi\)
−0.450406 + 0.892824i \(0.648721\pi\)
\(384\) 0 0
\(385\) −154.000 −0.0203859
\(386\) 0 0
\(387\) 1404.00 0.184417
\(388\) 0 0
\(389\) 12486.0 1.62742 0.813709 0.581273i \(-0.197445\pi\)
0.813709 + 0.581273i \(0.197445\pi\)
\(390\) 0 0
\(391\) −5888.00 −0.761557
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1938.00 0.245001 0.122501 0.992468i \(-0.460909\pi\)
0.122501 + 0.992468i \(0.460909\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4530.00 0.564133 0.282067 0.959395i \(-0.408980\pi\)
0.282067 + 0.959395i \(0.408980\pi\)
\(402\) 0 0
\(403\) 3328.00 0.411363
\(404\) 0 0
\(405\) 1458.00 0.178885
\(406\) 0 0
\(407\) 286.000 0.0348317
\(408\) 0 0
\(409\) −13718.0 −1.65846 −0.829232 0.558905i \(-0.811222\pi\)
−0.829232 + 0.558905i \(0.811222\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 336.000 0.0400326
\(414\) 0 0
\(415\) −1248.00 −0.147619
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −15280.0 −1.78157 −0.890784 0.454427i \(-0.849844\pi\)
−0.890784 + 0.454427i \(0.849844\pi\)
\(420\) 0 0
\(421\) 478.000 0.0553356 0.0276678 0.999617i \(-0.491192\pi\)
0.0276678 + 0.999617i \(0.491192\pi\)
\(422\) 0 0
\(423\) −14688.0 −1.68831
\(424\) 0 0
\(425\) 5566.00 0.635272
\(426\) 0 0
\(427\) 3262.00 0.369694
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6280.00 −0.701849 −0.350925 0.936404i \(-0.614133\pi\)
−0.350925 + 0.936404i \(0.614133\pi\)
\(432\) 0 0
\(433\) 13802.0 1.53183 0.765914 0.642943i \(-0.222287\pi\)
0.765914 + 0.642943i \(0.222287\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6144.00 0.672557
\(438\) 0 0
\(439\) −8728.00 −0.948895 −0.474447 0.880284i \(-0.657352\pi\)
−0.474447 + 0.880284i \(0.657352\pi\)
\(440\) 0 0
\(441\) −1323.00 −0.142857
\(442\) 0 0
\(443\) 3540.00 0.379662 0.189831 0.981817i \(-0.439206\pi\)
0.189831 + 0.981817i \(0.439206\pi\)
\(444\) 0 0
\(445\) −3180.00 −0.338756
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4194.00 0.440818 0.220409 0.975408i \(-0.429261\pi\)
0.220409 + 0.975408i \(0.429261\pi\)
\(450\) 0 0
\(451\) −110.000 −0.0114849
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 364.000 0.0375046
\(456\) 0 0
\(457\) −14134.0 −1.44674 −0.723370 0.690460i \(-0.757408\pi\)
−0.723370 + 0.690460i \(0.757408\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 234.000 0.0236409 0.0118205 0.999930i \(-0.496237\pi\)
0.0118205 + 0.999930i \(0.496237\pi\)
\(462\) 0 0
\(463\) −13696.0 −1.37475 −0.687373 0.726305i \(-0.741236\pi\)
−0.687373 + 0.726305i \(0.741236\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16104.0 −1.59573 −0.797863 0.602839i \(-0.794036\pi\)
−0.797863 + 0.602839i \(0.794036\pi\)
\(468\) 0 0
\(469\) −3612.00 −0.355622
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 572.000 0.0556038
\(474\) 0 0
\(475\) −5808.00 −0.561030
\(476\) 0 0
\(477\) −8586.00 −0.824163
\(478\) 0 0
\(479\) 11272.0 1.07522 0.537610 0.843193i \(-0.319327\pi\)
0.537610 + 0.843193i \(0.319327\pi\)
\(480\) 0 0
\(481\) −676.000 −0.0640810
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2036.00 0.190619
\(486\) 0 0
\(487\) 304.000 0.0282866 0.0141433 0.999900i \(-0.495498\pi\)
0.0141433 + 0.999900i \(0.495498\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10572.0 −0.971706 −0.485853 0.874041i \(-0.661491\pi\)
−0.485853 + 0.874041i \(0.661491\pi\)
\(492\) 0 0
\(493\) 6716.00 0.613536
\(494\) 0 0
\(495\) 594.000 0.0539360
\(496\) 0 0
\(497\) 2744.00 0.247656
\(498\) 0 0
\(499\) 15004.0 1.34603 0.673017 0.739627i \(-0.264998\pi\)
0.673017 + 0.739627i \(0.264998\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16872.0 −1.49560 −0.747799 0.663926i \(-0.768889\pi\)
−0.747799 + 0.663926i \(0.768889\pi\)
\(504\) 0 0
\(505\) 948.000 0.0835355
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 818.000 0.0712322 0.0356161 0.999366i \(-0.488661\pi\)
0.0356161 + 0.999366i \(0.488661\pi\)
\(510\) 0 0
\(511\) 5278.00 0.456918
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1968.00 0.168389
\(516\) 0 0
\(517\) −5984.00 −0.509045
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2270.00 −0.190884 −0.0954419 0.995435i \(-0.530426\pi\)
−0.0954419 + 0.995435i \(0.530426\pi\)
\(522\) 0 0
\(523\) −12776.0 −1.06817 −0.534087 0.845429i \(-0.679345\pi\)
−0.534087 + 0.845429i \(0.679345\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5888.00 −0.486689
\(528\) 0 0
\(529\) 4217.00 0.346593
\(530\) 0 0
\(531\) −1296.00 −0.105916
\(532\) 0 0
\(533\) 260.000 0.0211292
\(534\) 0 0
\(535\) −184.000 −0.0148692
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −539.000 −0.0430730
\(540\) 0 0
\(541\) −23050.0 −1.83179 −0.915894 0.401421i \(-0.868516\pi\)
−0.915894 + 0.401421i \(0.868516\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2492.00 0.195863
\(546\) 0 0
\(547\) 6564.00 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 0 0
\(549\) −12582.0 −0.978118
\(550\) 0 0
\(551\) −7008.00 −0.541835
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4522.00 −0.343992 −0.171996 0.985098i \(-0.555022\pi\)
−0.171996 + 0.985098i \(0.555022\pi\)
\(558\) 0 0
\(559\) −1352.00 −0.102296
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20440.0 1.53009 0.765047 0.643974i \(-0.222716\pi\)
0.765047 + 0.643974i \(0.222716\pi\)
\(564\) 0 0
\(565\) −3260.00 −0.242742
\(566\) 0 0
\(567\) 5103.00 0.377964
\(568\) 0 0
\(569\) −16518.0 −1.21700 −0.608498 0.793556i \(-0.708228\pi\)
−0.608498 + 0.793556i \(0.708228\pi\)
\(570\) 0 0
\(571\) 8828.00 0.647006 0.323503 0.946227i \(-0.395139\pi\)
0.323503 + 0.946227i \(0.395139\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −15488.0 −1.12329
\(576\) 0 0
\(577\) −15550.0 −1.12193 −0.560966 0.827839i \(-0.689570\pi\)
−0.560966 + 0.827839i \(0.689570\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4368.00 −0.311902
\(582\) 0 0
\(583\) −3498.00 −0.248495
\(584\) 0 0
\(585\) −1404.00 −0.0992278
\(586\) 0 0
\(587\) 4536.00 0.318945 0.159473 0.987202i \(-0.449021\pi\)
0.159473 + 0.987202i \(0.449021\pi\)
\(588\) 0 0
\(589\) 6144.00 0.429812
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11142.0 −0.771580 −0.385790 0.922587i \(-0.626071\pi\)
−0.385790 + 0.922587i \(0.626071\pi\)
\(594\) 0 0
\(595\) −644.000 −0.0443721
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16248.0 1.10831 0.554153 0.832415i \(-0.313042\pi\)
0.554153 + 0.832415i \(0.313042\pi\)
\(600\) 0 0
\(601\) −9646.00 −0.654690 −0.327345 0.944905i \(-0.606154\pi\)
−0.327345 + 0.944905i \(0.606154\pi\)
\(602\) 0 0
\(603\) 13932.0 0.940887
\(604\) 0 0
\(605\) 242.000 0.0162623
\(606\) 0 0
\(607\) −4064.00 −0.271751 −0.135875 0.990726i \(-0.543385\pi\)
−0.135875 + 0.990726i \(0.543385\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14144.0 0.936506
\(612\) 0 0
\(613\) −15098.0 −0.994784 −0.497392 0.867526i \(-0.665709\pi\)
−0.497392 + 0.867526i \(0.665709\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4470.00 −0.291662 −0.145831 0.989310i \(-0.546586\pi\)
−0.145831 + 0.989310i \(0.546586\pi\)
\(618\) 0 0
\(619\) 21184.0 1.37554 0.687768 0.725931i \(-0.258591\pi\)
0.687768 + 0.725931i \(0.258591\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −11130.0 −0.715753
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1196.00 0.0758150
\(630\) 0 0
\(631\) 8760.00 0.552663 0.276331 0.961062i \(-0.410881\pi\)
0.276331 + 0.961062i \(0.410881\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2032.00 −0.126988
\(636\) 0 0
\(637\) 1274.00 0.0792429
\(638\) 0 0
\(639\) −10584.0 −0.655237
\(640\) 0 0
\(641\) −3582.00 −0.220718 −0.110359 0.993892i \(-0.535200\pi\)
−0.110359 + 0.993892i \(0.535200\pi\)
\(642\) 0 0
\(643\) 23168.0 1.42093 0.710464 0.703734i \(-0.248485\pi\)
0.710464 + 0.703734i \(0.248485\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30216.0 −1.83603 −0.918017 0.396542i \(-0.870210\pi\)
−0.918017 + 0.396542i \(0.870210\pi\)
\(648\) 0 0
\(649\) −528.000 −0.0319350
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8158.00 0.488893 0.244447 0.969663i \(-0.421394\pi\)
0.244447 + 0.969663i \(0.421394\pi\)
\(654\) 0 0
\(655\) 3840.00 0.229071
\(656\) 0 0
\(657\) −20358.0 −1.20889
\(658\) 0 0
\(659\) −11932.0 −0.705318 −0.352659 0.935752i \(-0.614722\pi\)
−0.352659 + 0.935752i \(0.614722\pi\)
\(660\) 0 0
\(661\) 26882.0 1.58183 0.790914 0.611927i \(-0.209605\pi\)
0.790914 + 0.611927i \(0.209605\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 672.000 0.0391865
\(666\) 0 0
\(667\) −18688.0 −1.08486
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5126.00 −0.294914
\(672\) 0 0
\(673\) 13090.0 0.749751 0.374875 0.927075i \(-0.377685\pi\)
0.374875 + 0.927075i \(0.377685\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33790.0 −1.91825 −0.959125 0.282983i \(-0.908676\pi\)
−0.959125 + 0.282983i \(0.908676\pi\)
\(678\) 0 0
\(679\) 7126.00 0.402755
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24588.0 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 2964.00 0.165326
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8268.00 0.457164
\(690\) 0 0
\(691\) 1128.00 0.0621001 0.0310500 0.999518i \(-0.490115\pi\)
0.0310500 + 0.999518i \(0.490115\pi\)
\(692\) 0 0
\(693\) 2079.00 0.113961
\(694\) 0 0
\(695\) 5216.00 0.284682
\(696\) 0 0
\(697\) −460.000 −0.0249982
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18786.0 −1.01218 −0.506089 0.862481i \(-0.668909\pi\)
−0.506089 + 0.862481i \(0.668909\pi\)
\(702\) 0 0
\(703\) −1248.00 −0.0669548
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3318.00 0.176501
\(708\) 0 0
\(709\) 12102.0 0.641044 0.320522 0.947241i \(-0.396142\pi\)
0.320522 + 0.947241i \(0.396142\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16384.0 0.860569
\(714\) 0 0
\(715\) −572.000 −0.0299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18112.0 −0.939449 −0.469724 0.882813i \(-0.655647\pi\)
−0.469724 + 0.882813i \(0.655647\pi\)
\(720\) 0 0
\(721\) 6888.00 0.355787
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 17666.0 0.904964
\(726\) 0 0
\(727\) −12728.0 −0.649320 −0.324660 0.945831i \(-0.605250\pi\)
−0.324660 + 0.945831i \(0.605250\pi\)
\(728\) 0 0
\(729\) −19683.0 −1.00000
\(730\) 0 0
\(731\) 2392.00 0.121028
\(732\) 0 0
\(733\) 17138.0 0.863583 0.431792 0.901973i \(-0.357882\pi\)
0.431792 + 0.901973i \(0.357882\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5676.00 0.283688
\(738\) 0 0
\(739\) 8340.00 0.415145 0.207572 0.978220i \(-0.433444\pi\)
0.207572 + 0.978220i \(0.433444\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8304.00 −0.410019 −0.205010 0.978760i \(-0.565723\pi\)
−0.205010 + 0.978760i \(0.565723\pi\)
\(744\) 0 0
\(745\) 2620.00 0.128845
\(746\) 0 0
\(747\) 16848.0 0.825216
\(748\) 0 0
\(749\) −644.000 −0.0314169
\(750\) 0 0
\(751\) −2152.00 −0.104564 −0.0522820 0.998632i \(-0.516649\pi\)
−0.0522820 + 0.998632i \(0.516649\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 384.000 0.0185102
\(756\) 0 0
\(757\) −25594.0 −1.22884 −0.614419 0.788980i \(-0.710609\pi\)
−0.614419 + 0.788980i \(0.710609\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17190.0 −0.818840 −0.409420 0.912346i \(-0.634269\pi\)
−0.409420 + 0.912346i \(0.634269\pi\)
\(762\) 0 0
\(763\) 8722.00 0.413837
\(764\) 0 0
\(765\) 2484.00 0.117398
\(766\) 0 0
\(767\) 1248.00 0.0587518
\(768\) 0 0
\(769\) −15086.0 −0.707432 −0.353716 0.935353i \(-0.615082\pi\)
−0.353716 + 0.935353i \(0.615082\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14178.0 0.659699 0.329849 0.944034i \(-0.393002\pi\)
0.329849 + 0.944034i \(0.393002\pi\)
\(774\) 0 0
\(775\) −15488.0 −0.717865
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 480.000 0.0220767
\(780\) 0 0
\(781\) −4312.00 −0.197561
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1316.00 0.0598345
\(786\) 0 0
\(787\) 18304.0 0.829056 0.414528 0.910037i \(-0.363947\pi\)
0.414528 + 0.910037i \(0.363947\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −11410.0 −0.512886
\(792\) 0 0
\(793\) 12116.0 0.542562
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38206.0 −1.69803 −0.849013 0.528373i \(-0.822802\pi\)
−0.849013 + 0.528373i \(0.822802\pi\)
\(798\) 0 0
\(799\) −25024.0 −1.10799
\(800\) 0 0
\(801\) 42930.0 1.89370
\(802\) 0 0
\(803\) −8294.00 −0.364494
\(804\) 0 0
\(805\) 1792.00 0.0784593
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7146.00 0.310556 0.155278 0.987871i \(-0.450373\pi\)
0.155278 + 0.987871i \(0.450373\pi\)
\(810\) 0 0
\(811\) 21256.0 0.920344 0.460172 0.887830i \(-0.347788\pi\)
0.460172 + 0.887830i \(0.347788\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4472.00 −0.192205
\(816\) 0 0
\(817\) −2496.00 −0.106884
\(818\) 0 0
\(819\) −4914.00 −0.209657
\(820\) 0 0
\(821\) 38670.0 1.64384 0.821920 0.569603i \(-0.192903\pi\)
0.821920 + 0.569603i \(0.192903\pi\)
\(822\) 0 0
\(823\) 21112.0 0.894190 0.447095 0.894487i \(-0.352459\pi\)
0.447095 + 0.894487i \(0.352459\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3172.00 0.133375 0.0666876 0.997774i \(-0.478757\pi\)
0.0666876 + 0.997774i \(0.478757\pi\)
\(828\) 0 0
\(829\) 30346.0 1.27136 0.635682 0.771951i \(-0.280719\pi\)
0.635682 + 0.771951i \(0.280719\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2254.00 −0.0937533
\(834\) 0 0
\(835\) 3328.00 0.137928
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9480.00 0.390091 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(840\) 0 0
\(841\) −3073.00 −0.125999
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3042.00 −0.123844
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3328.00 −0.134057
\(852\) 0 0
\(853\) −24958.0 −1.00181 −0.500906 0.865502i \(-0.667000\pi\)
−0.500906 + 0.865502i \(0.667000\pi\)
\(854\) 0 0
\(855\) −2592.00 −0.103678
\(856\) 0 0
\(857\) −26806.0 −1.06847 −0.534233 0.845337i \(-0.679400\pi\)
−0.534233 + 0.845337i \(0.679400\pi\)
\(858\) 0 0
\(859\) −23128.0 −0.918646 −0.459323 0.888269i \(-0.651908\pi\)
−0.459323 + 0.888269i \(0.651908\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −12496.0 −0.492895 −0.246448 0.969156i \(-0.579263\pi\)
−0.246448 + 0.969156i \(0.579263\pi\)
\(864\) 0 0
\(865\) −1324.00 −0.0520432
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −13416.0 −0.521910
\(872\) 0 0
\(873\) −27486.0 −1.06559
\(874\) 0 0
\(875\) −3444.00 −0.133061
\(876\) 0 0
\(877\) 30478.0 1.17351 0.586755 0.809764i \(-0.300405\pi\)
0.586755 + 0.809764i \(0.300405\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25506.0 0.975390 0.487695 0.873014i \(-0.337838\pi\)
0.487695 + 0.873014i \(0.337838\pi\)
\(882\) 0 0
\(883\) 13244.0 0.504752 0.252376 0.967629i \(-0.418788\pi\)
0.252376 + 0.967629i \(0.418788\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −25456.0 −0.963618 −0.481809 0.876276i \(-0.660020\pi\)
−0.481809 + 0.876276i \(0.660020\pi\)
\(888\) 0 0
\(889\) −7112.00 −0.268311
\(890\) 0 0
\(891\) −8019.00 −0.301511
\(892\) 0 0
\(893\) 26112.0 0.978505
\(894\) 0 0
\(895\) 5080.00 0.189727
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −18688.0 −0.693303
\(900\) 0 0
\(901\) −14628.0 −0.540876
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5524.00 0.202899
\(906\) 0 0
\(907\) 51652.0 1.89093 0.945467 0.325719i \(-0.105606\pi\)
0.945467 + 0.325719i \(0.105606\pi\)
\(908\) 0 0
\(909\) −12798.0 −0.466978
\(910\) 0 0
\(911\) 46392.0 1.68720 0.843598 0.536975i \(-0.180433\pi\)
0.843598 + 0.536975i \(0.180433\pi\)
\(912\) 0 0
\(913\) 6864.00 0.248812
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 13440.0 0.484000
\(918\) 0 0
\(919\) −17832.0 −0.640069 −0.320034 0.947406i \(-0.603695\pi\)
−0.320034 + 0.947406i \(0.603695\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10192.0 0.363460
\(924\) 0 0
\(925\) 3146.00 0.111827
\(926\) 0 0
\(927\) −26568.0 −0.941324
\(928\) 0 0
\(929\) −41334.0 −1.45977 −0.729884 0.683571i \(-0.760426\pi\)
−0.729884 + 0.683571i \(0.760426\pi\)
\(930\) 0 0
\(931\) 2352.00 0.0827967
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1012.00 0.0353967
\(936\) 0 0
\(937\) 23058.0 0.803919 0.401959 0.915657i \(-0.368329\pi\)
0.401959 + 0.915657i \(0.368329\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −11678.0 −0.404561 −0.202281 0.979328i \(-0.564835\pi\)
−0.202281 + 0.979328i \(0.564835\pi\)
\(942\) 0 0
\(943\) 1280.00 0.0442021
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36436.0 1.25028 0.625138 0.780514i \(-0.285043\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(948\) 0 0
\(949\) 19604.0 0.670572
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 21098.0 0.717137 0.358568 0.933503i \(-0.383265\pi\)
0.358568 + 0.933503i \(0.383265\pi\)
\(954\) 0 0
\(955\) 32.0000 0.00108429
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 10374.0 0.349316
\(960\) 0 0
\(961\) −13407.0 −0.450035
\(962\) 0 0
\(963\) 2484.00 0.0831213
\(964\) 0 0
\(965\) 10276.0 0.342794
\(966\) 0 0
\(967\) −7184.00 −0.238906 −0.119453 0.992840i \(-0.538114\pi\)
−0.119453 + 0.992840i \(0.538114\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40048.0 1.32359 0.661793 0.749687i \(-0.269796\pi\)
0.661793 + 0.749687i \(0.269796\pi\)
\(972\) 0 0
\(973\) 18256.0 0.601501
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 51938.0 1.70076 0.850381 0.526168i \(-0.176372\pi\)
0.850381 + 0.526168i \(0.176372\pi\)
\(978\) 0 0
\(979\) 17490.0 0.570973
\(980\) 0 0
\(981\) −33642.0 −1.09491
\(982\) 0 0
\(983\) 28968.0 0.939914 0.469957 0.882689i \(-0.344269\pi\)
0.469957 + 0.882689i \(0.344269\pi\)
\(984\) 0 0
\(985\) 8700.00 0.281426
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6656.00 −0.214003
\(990\) 0 0
\(991\) −37504.0 −1.20217 −0.601087 0.799184i \(-0.705265\pi\)
−0.601087 + 0.799184i \(0.705265\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8080.00 0.257440
\(996\) 0 0
\(997\) 20298.0 0.644778 0.322389 0.946607i \(-0.395514\pi\)
0.322389 + 0.946607i \(0.395514\pi\)
\(998\) 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 1232.4.a.e.1.1 1
4.3 odd 2 154.4.a.b.1.1 1
12.11 even 2 1386.4.a.j.1.1 1
28.27 even 2 1078.4.a.b.1.1 1
44.43 even 2 1694.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.b.1.1 1 4.3 odd 2
1078.4.a.b.1.1 1 28.27 even 2
1232.4.a.e.1.1 1 1.1 even 1 trivial
1386.4.a.j.1.1 1 12.11 even 2
1694.4.a.f.1.1 1 44.43 even 2