Properties

Label 1008.4.a.k.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
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] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} -7.00000 q^{7} +12.0000 q^{11} -66.0000 q^{13} +70.0000 q^{17} +92.0000 q^{19} +16.0000 q^{23} -121.000 q^{25} +122.000 q^{29} -64.0000 q^{31} -14.0000 q^{35} -306.000 q^{37} -50.0000 q^{41} -20.0000 q^{43} -176.000 q^{47} +49.0000 q^{49} -526.000 q^{53} +24.0000 q^{55} +540.000 q^{59} -818.000 q^{61} -132.000 q^{65} +228.000 q^{67} +864.000 q^{71} +106.000 q^{73} -84.0000 q^{77} -736.000 q^{79} -588.000 q^{83} +140.000 q^{85} -146.000 q^{89} +462.000 q^{91} +184.000 q^{95} -1214.00 q^{97} +O(q^{100})\)

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
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 12.0000 0.328921 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 0 0
\(13\) −66.0000 −1.40809 −0.704043 0.710158i \(-0.748624\pi\)
−0.704043 + 0.710158i \(0.748624\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 70.0000 0.998676 0.499338 0.866407i \(-0.333577\pi\)
0.499338 + 0.866407i \(0.333577\pi\)
\(18\) 0 0
\(19\) 92.0000 1.11086 0.555428 0.831565i \(-0.312555\pi\)
0.555428 + 0.831565i \(0.312555\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 16.0000 0.145054 0.0725268 0.997366i \(-0.476894\pi\)
0.0725268 + 0.997366i \(0.476894\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 122.000 0.781201 0.390601 0.920560i \(-0.372267\pi\)
0.390601 + 0.920560i \(0.372267\pi\)
\(30\) 0 0
\(31\) −64.0000 −0.370798 −0.185399 0.982663i \(-0.559358\pi\)
−0.185399 + 0.982663i \(0.559358\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14.0000 −0.0676123
\(36\) 0 0
\(37\) −306.000 −1.35962 −0.679812 0.733386i \(-0.737939\pi\)
−0.679812 + 0.733386i \(0.737939\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −50.0000 −0.190456 −0.0952279 0.995455i \(-0.530358\pi\)
−0.0952279 + 0.995455i \(0.530358\pi\)
\(42\) 0 0
\(43\) −20.0000 −0.0709296 −0.0354648 0.999371i \(-0.511291\pi\)
−0.0354648 + 0.999371i \(0.511291\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −176.000 −0.546218 −0.273109 0.961983i \(-0.588052\pi\)
−0.273109 + 0.961983i \(0.588052\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −526.000 −1.36324 −0.681619 0.731707i \(-0.738724\pi\)
−0.681619 + 0.731707i \(0.738724\pi\)
\(54\) 0 0
\(55\) 24.0000 0.0588393
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 540.000 1.19156 0.595780 0.803148i \(-0.296843\pi\)
0.595780 + 0.803148i \(0.296843\pi\)
\(60\) 0 0
\(61\) −818.000 −1.71695 −0.858477 0.512852i \(-0.828589\pi\)
−0.858477 + 0.512852i \(0.828589\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −132.000 −0.251886
\(66\) 0 0
\(67\) 228.000 0.415741 0.207870 0.978156i \(-0.433347\pi\)
0.207870 + 0.978156i \(0.433347\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 864.000 1.44420 0.722098 0.691791i \(-0.243178\pi\)
0.722098 + 0.691791i \(0.243178\pi\)
\(72\) 0 0
\(73\) 106.000 0.169950 0.0849751 0.996383i \(-0.472919\pi\)
0.0849751 + 0.996383i \(0.472919\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −84.0000 −0.124321
\(78\) 0 0
\(79\) −736.000 −1.04818 −0.524092 0.851662i \(-0.675595\pi\)
−0.524092 + 0.851662i \(0.675595\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −588.000 −0.777607 −0.388804 0.921321i \(-0.627112\pi\)
−0.388804 + 0.921321i \(0.627112\pi\)
\(84\) 0 0
\(85\) 140.000 0.178649
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −146.000 −0.173887 −0.0869436 0.996213i \(-0.527710\pi\)
−0.0869436 + 0.996213i \(0.527710\pi\)
\(90\) 0 0
\(91\) 462.000 0.532206
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 184.000 0.198716
\(96\) 0 0
\(97\) −1214.00 −1.27075 −0.635376 0.772203i \(-0.719155\pi\)
−0.635376 + 0.772203i \(0.719155\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −846.000 −0.833467 −0.416733 0.909029i \(-0.636825\pi\)
−0.416733 + 0.909029i \(0.636825\pi\)
\(102\) 0 0
\(103\) 168.000 0.160714 0.0803570 0.996766i \(-0.474394\pi\)
0.0803570 + 0.996766i \(0.474394\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −708.000 −0.639672 −0.319836 0.947473i \(-0.603628\pi\)
−0.319836 + 0.947473i \(0.603628\pi\)
\(108\) 0 0
\(109\) 646.000 0.567666 0.283833 0.958874i \(-0.408394\pi\)
0.283833 + 0.958874i \(0.408394\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1938.00 −1.61338 −0.806689 0.590976i \(-0.798743\pi\)
−0.806689 + 0.590976i \(0.798743\pi\)
\(114\) 0 0
\(115\) 32.0000 0.0259480
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −490.000 −0.377464
\(120\) 0 0
\(121\) −1187.00 −0.891811
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) −224.000 −0.156510 −0.0782551 0.996933i \(-0.524935\pi\)
−0.0782551 + 0.996933i \(0.524935\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2588.00 −1.72607 −0.863033 0.505148i \(-0.831438\pi\)
−0.863033 + 0.505148i \(0.831438\pi\)
\(132\) 0 0
\(133\) −644.000 −0.419864
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −490.000 −0.305573 −0.152787 0.988259i \(-0.548825\pi\)
−0.152787 + 0.988259i \(0.548825\pi\)
\(138\) 0 0
\(139\) 1716.00 1.04712 0.523558 0.851990i \(-0.324604\pi\)
0.523558 + 0.851990i \(0.324604\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −792.000 −0.463149
\(144\) 0 0
\(145\) 244.000 0.139745
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2386.00 1.31187 0.655935 0.754817i \(-0.272274\pi\)
0.655935 + 0.754817i \(0.272274\pi\)
\(150\) 0 0
\(151\) 104.000 0.0560490 0.0280245 0.999607i \(-0.491078\pi\)
0.0280245 + 0.999607i \(0.491078\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −128.000 −0.0663304
\(156\) 0 0
\(157\) 1566.00 0.796054 0.398027 0.917374i \(-0.369695\pi\)
0.398027 + 0.917374i \(0.369695\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −112.000 −0.0548251
\(162\) 0 0
\(163\) 1076.00 0.517048 0.258524 0.966005i \(-0.416764\pi\)
0.258524 + 0.966005i \(0.416764\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2760.00 −1.27889 −0.639447 0.768835i \(-0.720837\pi\)
−0.639447 + 0.768835i \(0.720837\pi\)
\(168\) 0 0
\(169\) 2159.00 0.982704
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1558.00 −0.684697 −0.342348 0.939573i \(-0.611222\pi\)
−0.342348 + 0.939573i \(0.611222\pi\)
\(174\) 0 0
\(175\) 847.000 0.365870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3452.00 −1.44142 −0.720711 0.693235i \(-0.756185\pi\)
−0.720711 + 0.693235i \(0.756185\pi\)
\(180\) 0 0
\(181\) −1162.00 −0.477187 −0.238593 0.971120i \(-0.576686\pi\)
−0.238593 + 0.971120i \(0.576686\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −612.000 −0.243217
\(186\) 0 0
\(187\) 840.000 0.328486
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1928.00 0.730394 0.365197 0.930930i \(-0.381002\pi\)
0.365197 + 0.930930i \(0.381002\pi\)
\(192\) 0 0
\(193\) −318.000 −0.118602 −0.0593009 0.998240i \(-0.518887\pi\)
−0.0593009 + 0.998240i \(0.518887\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4062.00 −1.46906 −0.734532 0.678574i \(-0.762598\pi\)
−0.734532 + 0.678574i \(0.762598\pi\)
\(198\) 0 0
\(199\) −5480.00 −1.95209 −0.976047 0.217558i \(-0.930191\pi\)
−0.976047 + 0.217558i \(0.930191\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −854.000 −0.295266
\(204\) 0 0
\(205\) −100.000 −0.0340698
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1104.00 0.365384
\(210\) 0 0
\(211\) −4892.00 −1.59611 −0.798055 0.602585i \(-0.794138\pi\)
−0.798055 + 0.602585i \(0.794138\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −40.0000 −0.0126883
\(216\) 0 0
\(217\) 448.000 0.140148
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4620.00 −1.40622
\(222\) 0 0
\(223\) −4320.00 −1.29726 −0.648629 0.761105i \(-0.724657\pi\)
−0.648629 + 0.761105i \(0.724657\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5516.00 −1.61282 −0.806409 0.591358i \(-0.798592\pi\)
−0.806409 + 0.591358i \(0.798592\pi\)
\(228\) 0 0
\(229\) 1670.00 0.481907 0.240954 0.970537i \(-0.422540\pi\)
0.240954 + 0.970537i \(0.422540\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3926.00 1.10387 0.551933 0.833888i \(-0.313890\pi\)
0.551933 + 0.833888i \(0.313890\pi\)
\(234\) 0 0
\(235\) −352.000 −0.0977104
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3640.00 0.985155 0.492577 0.870269i \(-0.336055\pi\)
0.492577 + 0.870269i \(0.336055\pi\)
\(240\) 0 0
\(241\) 5650.00 1.51016 0.755080 0.655633i \(-0.227598\pi\)
0.755080 + 0.655633i \(0.227598\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 98.0000 0.0255551
\(246\) 0 0
\(247\) −6072.00 −1.56418
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4652.00 1.16985 0.584924 0.811088i \(-0.301124\pi\)
0.584924 + 0.811088i \(0.301124\pi\)
\(252\) 0 0
\(253\) 192.000 0.0477112
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6006.00 1.45776 0.728879 0.684642i \(-0.240042\pi\)
0.728879 + 0.684642i \(0.240042\pi\)
\(258\) 0 0
\(259\) 2142.00 0.513890
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5040.00 1.18167 0.590836 0.806792i \(-0.298798\pi\)
0.590836 + 0.806792i \(0.298798\pi\)
\(264\) 0 0
\(265\) −1052.00 −0.243864
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5478.00 −1.24163 −0.620817 0.783956i \(-0.713199\pi\)
−0.620817 + 0.783956i \(0.713199\pi\)
\(270\) 0 0
\(271\) 2176.00 0.487759 0.243879 0.969806i \(-0.421580\pi\)
0.243879 + 0.969806i \(0.421580\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1452.00 −0.318396
\(276\) 0 0
\(277\) −4658.00 −1.01037 −0.505184 0.863011i \(-0.668575\pi\)
−0.505184 + 0.863011i \(0.668575\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4614.00 0.979531 0.489765 0.871854i \(-0.337082\pi\)
0.489765 + 0.871854i \(0.337082\pi\)
\(282\) 0 0
\(283\) −1244.00 −0.261301 −0.130650 0.991429i \(-0.541707\pi\)
−0.130650 + 0.991429i \(0.541707\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 350.000 0.0719855
\(288\) 0 0
\(289\) −13.0000 −0.00264604
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6354.00 1.26691 0.633455 0.773780i \(-0.281636\pi\)
0.633455 + 0.773780i \(0.281636\pi\)
\(294\) 0 0
\(295\) 1080.00 0.213153
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1056.00 −0.204248
\(300\) 0 0
\(301\) 140.000 0.0268089
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1636.00 −0.307138
\(306\) 0 0
\(307\) 3740.00 0.695287 0.347643 0.937627i \(-0.386982\pi\)
0.347643 + 0.937627i \(0.386982\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2184.00 −0.398210 −0.199105 0.979978i \(-0.563803\pi\)
−0.199105 + 0.979978i \(0.563803\pi\)
\(312\) 0 0
\(313\) 4442.00 0.802162 0.401081 0.916043i \(-0.368635\pi\)
0.401081 + 0.916043i \(0.368635\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4314.00 0.764348 0.382174 0.924090i \(-0.375175\pi\)
0.382174 + 0.924090i \(0.375175\pi\)
\(318\) 0 0
\(319\) 1464.00 0.256954
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6440.00 1.10938
\(324\) 0 0
\(325\) 7986.00 1.36303
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1232.00 0.206451
\(330\) 0 0
\(331\) −7988.00 −1.32647 −0.663233 0.748413i \(-0.730816\pi\)
−0.663233 + 0.748413i \(0.730816\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 456.000 0.0743700
\(336\) 0 0
\(337\) −10606.0 −1.71438 −0.857189 0.515001i \(-0.827791\pi\)
−0.857189 + 0.515001i \(0.827791\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −768.000 −0.121963
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8340.00 −1.29024 −0.645122 0.764080i \(-0.723193\pi\)
−0.645122 + 0.764080i \(0.723193\pi\)
\(348\) 0 0
\(349\) −10498.0 −1.61016 −0.805079 0.593168i \(-0.797877\pi\)
−0.805079 + 0.593168i \(0.797877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7878.00 1.18783 0.593914 0.804528i \(-0.297582\pi\)
0.593914 + 0.804528i \(0.297582\pi\)
\(354\) 0 0
\(355\) 1728.00 0.258346
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11856.0 1.74300 0.871498 0.490399i \(-0.163149\pi\)
0.871498 + 0.490399i \(0.163149\pi\)
\(360\) 0 0
\(361\) 1605.00 0.233999
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 212.000 0.0304016
\(366\) 0 0
\(367\) 5488.00 0.780576 0.390288 0.920693i \(-0.372375\pi\)
0.390288 + 0.920693i \(0.372375\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3682.00 0.515256
\(372\) 0 0
\(373\) −7570.00 −1.05083 −0.525415 0.850846i \(-0.676090\pi\)
−0.525415 + 0.850846i \(0.676090\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8052.00 −1.10000
\(378\) 0 0
\(379\) 13596.0 1.84269 0.921345 0.388746i \(-0.127092\pi\)
0.921345 + 0.388746i \(0.127092\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8592.00 −1.14629 −0.573147 0.819452i \(-0.694278\pi\)
−0.573147 + 0.819452i \(0.694278\pi\)
\(384\) 0 0
\(385\) −168.000 −0.0222392
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 610.000 0.0795070 0.0397535 0.999210i \(-0.487343\pi\)
0.0397535 + 0.999210i \(0.487343\pi\)
\(390\) 0 0
\(391\) 1120.00 0.144861
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1472.00 −0.187505
\(396\) 0 0
\(397\) 910.000 0.115042 0.0575209 0.998344i \(-0.481680\pi\)
0.0575209 + 0.998344i \(0.481680\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8094.00 1.00797 0.503984 0.863713i \(-0.331867\pi\)
0.503984 + 0.863713i \(0.331867\pi\)
\(402\) 0 0
\(403\) 4224.00 0.522115
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3672.00 −0.447210
\(408\) 0 0
\(409\) 10122.0 1.22372 0.611859 0.790967i \(-0.290422\pi\)
0.611859 + 0.790967i \(0.290422\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3780.00 −0.450367
\(414\) 0 0
\(415\) −1176.00 −0.139103
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4228.00 0.492963 0.246481 0.969148i \(-0.420726\pi\)
0.246481 + 0.969148i \(0.420726\pi\)
\(420\) 0 0
\(421\) −9218.00 −1.06712 −0.533560 0.845762i \(-0.679146\pi\)
−0.533560 + 0.845762i \(0.679146\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8470.00 −0.966718
\(426\) 0 0
\(427\) 5726.00 0.648947
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9192.00 1.02729 0.513646 0.858002i \(-0.328294\pi\)
0.513646 + 0.858002i \(0.328294\pi\)
\(432\) 0 0
\(433\) −3614.00 −0.401103 −0.200552 0.979683i \(-0.564273\pi\)
−0.200552 + 0.979683i \(0.564273\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1472.00 0.161133
\(438\) 0 0
\(439\) 4344.00 0.472273 0.236136 0.971720i \(-0.424119\pi\)
0.236136 + 0.971720i \(0.424119\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10876.0 1.16644 0.583222 0.812313i \(-0.301792\pi\)
0.583222 + 0.812313i \(0.301792\pi\)
\(444\) 0 0
\(445\) −292.000 −0.0311059
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 15550.0 1.63441 0.817205 0.576347i \(-0.195522\pi\)
0.817205 + 0.576347i \(0.195522\pi\)
\(450\) 0 0
\(451\) −600.000 −0.0626450
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 924.000 0.0952039
\(456\) 0 0
\(457\) 7834.00 0.801880 0.400940 0.916104i \(-0.368684\pi\)
0.400940 + 0.916104i \(0.368684\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15990.0 −1.61546 −0.807732 0.589550i \(-0.799305\pi\)
−0.807732 + 0.589550i \(0.799305\pi\)
\(462\) 0 0
\(463\) 12448.0 1.24948 0.624738 0.780834i \(-0.285206\pi\)
0.624738 + 0.780834i \(0.285206\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13860.0 1.37337 0.686686 0.726955i \(-0.259065\pi\)
0.686686 + 0.726955i \(0.259065\pi\)
\(468\) 0 0
\(469\) −1596.00 −0.157135
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −240.000 −0.0233303
\(474\) 0 0
\(475\) −11132.0 −1.07531
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14368.0 −1.37054 −0.685272 0.728287i \(-0.740317\pi\)
−0.685272 + 0.728287i \(0.740317\pi\)
\(480\) 0 0
\(481\) 20196.0 1.91447
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2428.00 −0.227319
\(486\) 0 0
\(487\) 17240.0 1.60415 0.802073 0.597226i \(-0.203731\pi\)
0.802073 + 0.597226i \(0.203731\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18156.0 1.66878 0.834388 0.551178i \(-0.185821\pi\)
0.834388 + 0.551178i \(0.185821\pi\)
\(492\) 0 0
\(493\) 8540.00 0.780167
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6048.00 −0.545855
\(498\) 0 0
\(499\) −1084.00 −0.0972475 −0.0486238 0.998817i \(-0.515484\pi\)
−0.0486238 + 0.998817i \(0.515484\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1048.00 −0.0928986 −0.0464493 0.998921i \(-0.514791\pi\)
−0.0464493 + 0.998921i \(0.514791\pi\)
\(504\) 0 0
\(505\) −1692.00 −0.149095
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5046.00 −0.439411 −0.219705 0.975566i \(-0.570510\pi\)
−0.219705 + 0.975566i \(0.570510\pi\)
\(510\) 0 0
\(511\) −742.000 −0.0642351
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 336.000 0.0287494
\(516\) 0 0
\(517\) −2112.00 −0.179663
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3390.00 0.285064 0.142532 0.989790i \(-0.454476\pi\)
0.142532 + 0.989790i \(0.454476\pi\)
\(522\) 0 0
\(523\) −13052.0 −1.09125 −0.545625 0.838029i \(-0.683708\pi\)
−0.545625 + 0.838029i \(0.683708\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4480.00 −0.370307
\(528\) 0 0
\(529\) −11911.0 −0.978959
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3300.00 0.268178
\(534\) 0 0
\(535\) −1416.00 −0.114428
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 588.000 0.0469888
\(540\) 0 0
\(541\) 16966.0 1.34829 0.674145 0.738599i \(-0.264512\pi\)
0.674145 + 0.738599i \(0.264512\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1292.00 0.101547
\(546\) 0 0
\(547\) 11348.0 0.887030 0.443515 0.896267i \(-0.353731\pi\)
0.443515 + 0.896267i \(0.353731\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11224.0 0.867801
\(552\) 0 0
\(553\) 5152.00 0.396176
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16118.0 −1.22611 −0.613053 0.790041i \(-0.710059\pi\)
−0.613053 + 0.790041i \(0.710059\pi\)
\(558\) 0 0
\(559\) 1320.00 0.0998749
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15244.0 −1.14113 −0.570567 0.821251i \(-0.693276\pi\)
−0.570567 + 0.821251i \(0.693276\pi\)
\(564\) 0 0
\(565\) −3876.00 −0.288610
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18918.0 1.39382 0.696910 0.717158i \(-0.254558\pi\)
0.696910 + 0.717158i \(0.254558\pi\)
\(570\) 0 0
\(571\) 19372.0 1.41978 0.709889 0.704314i \(-0.248745\pi\)
0.709889 + 0.704314i \(0.248745\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1936.00 −0.140412
\(576\) 0 0
\(577\) −7230.00 −0.521644 −0.260822 0.965387i \(-0.583994\pi\)
−0.260822 + 0.965387i \(0.583994\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4116.00 0.293908
\(582\) 0 0
\(583\) −6312.00 −0.448399
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7396.00 −0.520044 −0.260022 0.965603i \(-0.583730\pi\)
−0.260022 + 0.965603i \(0.583730\pi\)
\(588\) 0 0
\(589\) −5888.00 −0.411903
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −714.000 −0.0494443 −0.0247221 0.999694i \(-0.507870\pi\)
−0.0247221 + 0.999694i \(0.507870\pi\)
\(594\) 0 0
\(595\) −980.000 −0.0675228
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11536.0 −0.786892 −0.393446 0.919348i \(-0.628717\pi\)
−0.393446 + 0.919348i \(0.628717\pi\)
\(600\) 0 0
\(601\) 4138.00 0.280853 0.140426 0.990091i \(-0.455153\pi\)
0.140426 + 0.990091i \(0.455153\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2374.00 −0.159532
\(606\) 0 0
\(607\) 6848.00 0.457911 0.228955 0.973437i \(-0.426469\pi\)
0.228955 + 0.973437i \(0.426469\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11616.0 0.769121
\(612\) 0 0
\(613\) −12722.0 −0.838233 −0.419116 0.907932i \(-0.637660\pi\)
−0.419116 + 0.907932i \(0.637660\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24726.0 1.61334 0.806670 0.591002i \(-0.201267\pi\)
0.806670 + 0.591002i \(0.201267\pi\)
\(618\) 0 0
\(619\) −23964.0 −1.55605 −0.778025 0.628234i \(-0.783778\pi\)
−0.778025 + 0.628234i \(0.783778\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1022.00 0.0657232
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21420.0 −1.35782
\(630\) 0 0
\(631\) 17224.0 1.08665 0.543325 0.839522i \(-0.317165\pi\)
0.543325 + 0.839522i \(0.317165\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −448.000 −0.0279974
\(636\) 0 0
\(637\) −3234.00 −0.201155
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18190.0 1.12085 0.560423 0.828207i \(-0.310639\pi\)
0.560423 + 0.828207i \(0.310639\pi\)
\(642\) 0 0
\(643\) −14116.0 −0.865755 −0.432878 0.901453i \(-0.642502\pi\)
−0.432878 + 0.901453i \(0.642502\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4056.00 0.246457 0.123229 0.992378i \(-0.460675\pi\)
0.123229 + 0.992378i \(0.460675\pi\)
\(648\) 0 0
\(649\) 6480.00 0.391930
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16490.0 0.988214 0.494107 0.869401i \(-0.335495\pi\)
0.494107 + 0.869401i \(0.335495\pi\)
\(654\) 0 0
\(655\) −5176.00 −0.308768
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4988.00 −0.294848 −0.147424 0.989073i \(-0.547098\pi\)
−0.147424 + 0.989073i \(0.547098\pi\)
\(660\) 0 0
\(661\) 4982.00 0.293158 0.146579 0.989199i \(-0.453174\pi\)
0.146579 + 0.989199i \(0.453174\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1288.00 −0.0751075
\(666\) 0 0
\(667\) 1952.00 0.113316
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9816.00 −0.564743
\(672\) 0 0
\(673\) −16190.0 −0.927309 −0.463654 0.886016i \(-0.653462\pi\)
−0.463654 + 0.886016i \(0.653462\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23202.0 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(678\) 0 0
\(679\) 8498.00 0.480299
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13452.0 0.753626 0.376813 0.926289i \(-0.377020\pi\)
0.376813 + 0.926289i \(0.377020\pi\)
\(684\) 0 0
\(685\) −980.000 −0.0546626
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 34716.0 1.91956
\(690\) 0 0
\(691\) −31220.0 −1.71876 −0.859381 0.511336i \(-0.829151\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3432.00 0.187314
\(696\) 0 0
\(697\) −3500.00 −0.190204
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −33542.0 −1.80722 −0.903612 0.428352i \(-0.859094\pi\)
−0.903612 + 0.428352i \(0.859094\pi\)
\(702\) 0 0
\(703\) −28152.0 −1.51035
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5922.00 0.315021
\(708\) 0 0
\(709\) −28562.0 −1.51293 −0.756466 0.654033i \(-0.773076\pi\)
−0.756466 + 0.654033i \(0.773076\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1024.00 −0.0537856
\(714\) 0 0
\(715\) −1584.00 −0.0828507
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1248.00 0.0647323 0.0323662 0.999476i \(-0.489696\pi\)
0.0323662 + 0.999476i \(0.489696\pi\)
\(720\) 0 0
\(721\) −1176.00 −0.0607441
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −14762.0 −0.756203
\(726\) 0 0
\(727\) 4216.00 0.215079 0.107540 0.994201i \(-0.465703\pi\)
0.107540 + 0.994201i \(0.465703\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1400.00 −0.0708357
\(732\) 0 0
\(733\) 12670.0 0.638441 0.319220 0.947680i \(-0.396579\pi\)
0.319220 + 0.947680i \(0.396579\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2736.00 0.136746
\(738\) 0 0
\(739\) −25996.0 −1.29402 −0.647008 0.762483i \(-0.723980\pi\)
−0.647008 + 0.762483i \(0.723980\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24368.0 −1.20320 −0.601598 0.798799i \(-0.705469\pi\)
−0.601598 + 0.798799i \(0.705469\pi\)
\(744\) 0 0
\(745\) 4772.00 0.234675
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4956.00 0.241773
\(750\) 0 0
\(751\) −17600.0 −0.855171 −0.427585 0.903975i \(-0.640636\pi\)
−0.427585 + 0.903975i \(0.640636\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 208.000 0.0100264
\(756\) 0 0
\(757\) 17182.0 0.824954 0.412477 0.910968i \(-0.364664\pi\)
0.412477 + 0.910968i \(0.364664\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7038.00 0.335253 0.167626 0.985851i \(-0.446390\pi\)
0.167626 + 0.985851i \(0.446390\pi\)
\(762\) 0 0
\(763\) −4522.00 −0.214558
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −35640.0 −1.67782
\(768\) 0 0
\(769\) −18254.0 −0.855990 −0.427995 0.903781i \(-0.640780\pi\)
−0.427995 + 0.903781i \(0.640780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2990.00 −0.139124 −0.0695620 0.997578i \(-0.522160\pi\)
−0.0695620 + 0.997578i \(0.522160\pi\)
\(774\) 0 0
\(775\) 7744.00 0.358933
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4600.00 −0.211569
\(780\) 0 0
\(781\) 10368.0 0.475027
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3132.00 0.142402
\(786\) 0 0
\(787\) −10804.0 −0.489353 −0.244677 0.969605i \(-0.578682\pi\)
−0.244677 + 0.969605i \(0.578682\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 13566.0 0.609800
\(792\) 0 0
\(793\) 53988.0 2.41762
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11238.0 −0.499461 −0.249730 0.968315i \(-0.580342\pi\)
−0.249730 + 0.968315i \(0.580342\pi\)
\(798\) 0 0
\(799\) −12320.0 −0.545495
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1272.00 0.0559003
\(804\) 0 0
\(805\) −224.000 −0.00980741
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −35034.0 −1.52253 −0.761267 0.648439i \(-0.775422\pi\)
−0.761267 + 0.648439i \(0.775422\pi\)
\(810\) 0 0
\(811\) 9252.00 0.400594 0.200297 0.979735i \(-0.435809\pi\)
0.200297 + 0.979735i \(0.435809\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2152.00 0.0924924
\(816\) 0 0
\(817\) −1840.00 −0.0787925
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18318.0 −0.778688 −0.389344 0.921092i \(-0.627298\pi\)
−0.389344 + 0.921092i \(0.627298\pi\)
\(822\) 0 0
\(823\) −30200.0 −1.27911 −0.639554 0.768746i \(-0.720881\pi\)
−0.639554 + 0.768746i \(0.720881\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9612.00 0.404162 0.202081 0.979369i \(-0.435230\pi\)
0.202081 + 0.979369i \(0.435230\pi\)
\(828\) 0 0
\(829\) 3806.00 0.159455 0.0797273 0.996817i \(-0.474595\pi\)
0.0797273 + 0.996817i \(0.474595\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3430.00 0.142668
\(834\) 0 0
\(835\) −5520.00 −0.228775
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −19176.0 −0.789069 −0.394535 0.918881i \(-0.629094\pi\)
−0.394535 + 0.918881i \(0.629094\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4318.00 0.175791
\(846\) 0 0
\(847\) 8309.00 0.337073
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4896.00 −0.197218
\(852\) 0 0
\(853\) −38234.0 −1.53471 −0.767355 0.641223i \(-0.778427\pi\)
−0.767355 + 0.641223i \(0.778427\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −34818.0 −1.38782 −0.693909 0.720063i \(-0.744113\pi\)
−0.693909 + 0.720063i \(0.744113\pi\)
\(858\) 0 0
\(859\) 15764.0 0.626148 0.313074 0.949729i \(-0.398641\pi\)
0.313074 + 0.949729i \(0.398641\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1832.00 −0.0722619 −0.0361309 0.999347i \(-0.511503\pi\)
−0.0361309 + 0.999347i \(0.511503\pi\)
\(864\) 0 0
\(865\) −3116.00 −0.122482
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8832.00 −0.344770
\(870\) 0 0
\(871\) −15048.0 −0.585398
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3444.00 0.133061
\(876\) 0 0
\(877\) 18374.0 0.707464 0.353732 0.935347i \(-0.384912\pi\)
0.353732 + 0.935347i \(0.384912\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −40490.0 −1.54840 −0.774201 0.632939i \(-0.781848\pi\)
−0.774201 + 0.632939i \(0.781848\pi\)
\(882\) 0 0
\(883\) 548.000 0.0208852 0.0104426 0.999945i \(-0.496676\pi\)
0.0104426 + 0.999945i \(0.496676\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1272.00 −0.0481506 −0.0240753 0.999710i \(-0.507664\pi\)
−0.0240753 + 0.999710i \(0.507664\pi\)
\(888\) 0 0
\(889\) 1568.00 0.0591553
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −16192.0 −0.606769
\(894\) 0 0
\(895\) −6904.00 −0.257849
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7808.00 −0.289668
\(900\) 0 0
\(901\) −36820.0 −1.36143
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2324.00 −0.0853617
\(906\) 0 0
\(907\) 15100.0 0.552797 0.276399 0.961043i \(-0.410859\pi\)
0.276399 + 0.961043i \(0.410859\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 53192.0 1.93450 0.967250 0.253825i \(-0.0816889\pi\)
0.967250 + 0.253825i \(0.0816889\pi\)
\(912\) 0 0
\(913\) −7056.00 −0.255772
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18116.0 0.652392
\(918\) 0 0
\(919\) 53624.0 1.92480 0.962401 0.271634i \(-0.0875639\pi\)
0.962401 + 0.271634i \(0.0875639\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −57024.0 −2.03355
\(924\) 0 0
\(925\) 37026.0 1.31612
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28966.0 1.02297 0.511487 0.859291i \(-0.329095\pi\)
0.511487 + 0.859291i \(0.329095\pi\)
\(930\) 0 0
\(931\) 4508.00 0.158694
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1680.00 0.0587614
\(936\) 0 0
\(937\) 50874.0 1.77373 0.886863 0.462033i \(-0.152880\pi\)
0.886863 + 0.462033i \(0.152880\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −16566.0 −0.573896 −0.286948 0.957946i \(-0.592641\pi\)
−0.286948 + 0.957946i \(0.592641\pi\)
\(942\) 0 0
\(943\) −800.000 −0.0276263
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −38428.0 −1.31863 −0.659315 0.751867i \(-0.729154\pi\)
−0.659315 + 0.751867i \(0.729154\pi\)
\(948\) 0 0
\(949\) −6996.00 −0.239304
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −746.000 −0.0253571 −0.0126785 0.999920i \(-0.504036\pi\)
−0.0126785 + 0.999920i \(0.504036\pi\)
\(954\) 0 0
\(955\) 3856.00 0.130657
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 3430.00 0.115496
\(960\) 0 0
\(961\) −25695.0 −0.862509
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −636.000 −0.0212161
\(966\) 0 0
\(967\) −9432.00 −0.313664 −0.156832 0.987625i \(-0.550128\pi\)
−0.156832 + 0.987625i \(0.550128\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3452.00 0.114089 0.0570443 0.998372i \(-0.481832\pi\)
0.0570443 + 0.998372i \(0.481832\pi\)
\(972\) 0 0
\(973\) −12012.0 −0.395773
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18078.0 0.591982 0.295991 0.955191i \(-0.404350\pi\)
0.295991 + 0.955191i \(0.404350\pi\)
\(978\) 0 0
\(979\) −1752.00 −0.0571953
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 792.000 0.0256977 0.0128489 0.999917i \(-0.495910\pi\)
0.0128489 + 0.999917i \(0.495910\pi\)
\(984\) 0 0
\(985\) −8124.00 −0.262794
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −320.000 −0.0102886
\(990\) 0 0
\(991\) 14976.0 0.480049 0.240024 0.970767i \(-0.422845\pi\)
0.240024 + 0.970767i \(0.422845\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −10960.0 −0.349201
\(996\) 0 0
\(997\) −17114.0 −0.543637 −0.271818 0.962349i \(-0.587625\pi\)
−0.271818 + 0.962349i \(0.587625\pi\)
\(998\) 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 1008.4.a.k.1.1 1
3.2 odd 2 336.4.a.i.1.1 1
4.3 odd 2 504.4.a.d.1.1 1
12.11 even 2 168.4.a.b.1.1 1
21.20 even 2 2352.4.a.k.1.1 1
24.5 odd 2 1344.4.a.h.1.1 1
24.11 even 2 1344.4.a.u.1.1 1
84.83 odd 2 1176.4.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.b.1.1 1 12.11 even 2
336.4.a.i.1.1 1 3.2 odd 2
504.4.a.d.1.1 1 4.3 odd 2
1008.4.a.k.1.1 1 1.1 even 1 trivial
1176.4.a.l.1.1 1 84.83 odd 2
1344.4.a.h.1.1 1 24.5 odd 2
1344.4.a.u.1.1 1 24.11 even 2
2352.4.a.k.1.1 1 21.20 even 2