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Properties

Label 1008.4.a.r.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
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)
 
\(f(q)\) \(=\) \(q+12.0000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q+12.0000 q^{5} -7.00000 q^{7} +48.0000 q^{11} +56.0000 q^{13} +114.000 q^{17} -2.00000 q^{19} -120.000 q^{23} +19.0000 q^{25} +54.0000 q^{29} -236.000 q^{31} -84.0000 q^{35} +146.000 q^{37} -126.000 q^{41} +376.000 q^{43} -12.0000 q^{47} +49.0000 q^{49} -174.000 q^{53} +576.000 q^{55} +138.000 q^{59} +380.000 q^{61} +672.000 q^{65} +484.000 q^{67} +576.000 q^{71} -1150.00 q^{73} -336.000 q^{77} -776.000 q^{79} +378.000 q^{83} +1368.00 q^{85} +390.000 q^{89} -392.000 q^{91} -24.0000 q^{95} -1330.00 q^{97} +O(q^{100})\)

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
\(5\) 12.0000 1.07331 0.536656 − 0.843801i \(-0.319687\pi\)
0.536656 + 0.843801i \(0.319687\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 48.0000 1.31569 0.657843 − 0.753155i \(-0.271469\pi\)
0.657843 + 0.753155i \(0.271469\pi\)
\(12\) 0 0
\(13\) 56.0000 1.19474 0.597369 − 0.801966i \(-0.296213\pi\)
0.597369 + 0.801966i \(0.296213\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 114.000 1.62642 0.813208 − 0.581974i \(-0.197719\pi\)
0.813208 + 0.581974i \(0.197719\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.0241490 −0.0120745 − 0.999927i \(-0.503844\pi\)
−0.0120745 + 0.999927i \(0.503844\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −120.000 −1.08790 −0.543951 − 0.839117i \(-0.683072\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(24\) 0 0
\(25\) 19.0000 0.152000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 54.0000 0.345778 0.172889 − 0.984941i \(-0.444690\pi\)
0.172889 + 0.984941i \(0.444690\pi\)
\(30\) 0 0
\(31\) −236.000 −1.36732 −0.683659 − 0.729802i \(-0.739612\pi\)
−0.683659 + 0.729802i \(0.739612\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −84.0000 −0.405674
\(36\) 0 0
\(37\) 146.000 0.648710 0.324355 − 0.945936i \(-0.394853\pi\)
0.324355 + 0.945936i \(0.394853\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −126.000 −0.479949 −0.239974 − 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(42\) 0 0
\(43\) 376.000 1.33348 0.666738 − 0.745292i \(-0.267690\pi\)
0.666738 + 0.745292i \(0.267690\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.0000 −0.0372421 −0.0186211 − 0.999827i \(-0.505928\pi\)
−0.0186211 + 0.999827i \(0.505928\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −174.000 −0.450957 −0.225479 − 0.974248i \(-0.572395\pi\)
−0.225479 + 0.974248i \(0.572395\pi\)
\(54\) 0 0
\(55\) 576.000 1.41214
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 138.000 0.304510 0.152255 − 0.988341i \(-0.451347\pi\)
0.152255 + 0.988341i \(0.451347\pi\)
\(60\) 0 0
\(61\) 380.000 0.797607 0.398803 − 0.917036i \(-0.369426\pi\)
0.398803 + 0.917036i \(0.369426\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 672.000 1.28233
\(66\) 0 0
\(67\) 484.000 0.882537 0.441269 − 0.897375i \(-0.354529\pi\)
0.441269 + 0.897375i \(0.354529\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 576.000 0.962798 0.481399 − 0.876502i \(-0.340129\pi\)
0.481399 + 0.876502i \(0.340129\pi\)
\(72\) 0 0
\(73\) −1150.00 −1.84380 −0.921899 − 0.387429i \(-0.873363\pi\)
−0.921899 + 0.387429i \(0.873363\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −336.000 −0.497283
\(78\) 0 0
\(79\) −776.000 −1.10515 −0.552575 − 0.833463i \(-0.686355\pi\)
−0.552575 + 0.833463i \(0.686355\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 378.000 0.499890 0.249945 − 0.968260i \(-0.419587\pi\)
0.249945 + 0.968260i \(0.419587\pi\)
\(84\) 0 0
\(85\) 1368.00 1.74565
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 390.000 0.464493 0.232247 − 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(90\) 0 0
\(91\) −392.000 −0.451569
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −24.0000 −0.0259195
\(96\) 0 0
\(97\) −1330.00 −1.39218 −0.696088 − 0.717957i \(-0.745078\pi\)
−0.696088 + 0.717957i \(0.745078\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1500.00 1.47778 0.738889 − 0.673827i \(-0.235351\pi\)
0.738889 + 0.673827i \(0.235351\pi\)
\(102\) 0 0
\(103\) −380.000 −0.363520 −0.181760 − 0.983343i \(-0.558179\pi\)
−0.181760 + 0.983343i \(0.558179\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 636.000 0.574621 0.287310 − 0.957838i \(-0.407239\pi\)
0.287310 + 0.957838i \(0.407239\pi\)
\(108\) 0 0
\(109\) 146.000 0.128296 0.0641480 − 0.997940i \(-0.479567\pi\)
0.0641480 + 0.997940i \(0.479567\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −198.000 −0.164834 −0.0824171 − 0.996598i \(-0.526264\pi\)
−0.0824171 + 0.996598i \(0.526264\pi\)
\(114\) 0 0
\(115\) −1440.00 −1.16766
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −798.000 −0.614727
\(120\) 0 0
\(121\) 973.000 0.731029
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1272.00 −0.910169
\(126\) 0 0
\(127\) 376.000 0.262713 0.131357 − 0.991335i \(-0.458067\pi\)
0.131357 + 0.991335i \(0.458067\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2130.00 1.42060 0.710301 − 0.703898i \(-0.248559\pi\)
0.710301 + 0.703898i \(0.248559\pi\)
\(132\) 0 0
\(133\) 14.0000 0.00912747
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 78.0000 0.0486423 0.0243211 − 0.999704i \(-0.492258\pi\)
0.0243211 + 0.999704i \(0.492258\pi\)
\(138\) 0 0
\(139\) 2338.00 1.42667 0.713333 − 0.700825i \(-0.247185\pi\)
0.713333 + 0.700825i \(0.247185\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2688.00 1.57190
\(144\) 0 0
\(145\) 648.000 0.371127
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1002.00 0.550920 0.275460 − 0.961313i \(-0.411170\pi\)
0.275460 + 0.961313i \(0.411170\pi\)
\(150\) 0 0
\(151\) 2752.00 1.48314 0.741571 − 0.670874i \(-0.234081\pi\)
0.741571 + 0.670874i \(0.234081\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2832.00 −1.46756
\(156\) 0 0
\(157\) −520.000 −0.264335 −0.132167 − 0.991227i \(-0.542194\pi\)
−0.132167 + 0.991227i \(0.542194\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 840.000 0.411188
\(162\) 0 0
\(163\) −1280.00 −0.615076 −0.307538 − 0.951536i \(-0.599505\pi\)
−0.307538 + 0.951536i \(0.599505\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1764.00 0.817380 0.408690 − 0.912673i \(-0.365986\pi\)
0.408690 + 0.912673i \(0.365986\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 768.000 0.337514 0.168757 − 0.985658i \(-0.446025\pi\)
0.168757 + 0.985658i \(0.446025\pi\)
\(174\) 0 0
\(175\) −133.000 −0.0574506
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1812.00 0.756621 0.378311 − 0.925679i \(-0.376505\pi\)
0.378311 + 0.925679i \(0.376505\pi\)
\(180\) 0 0
\(181\) −448.000 −0.183976 −0.0919878 − 0.995760i \(-0.529322\pi\)
−0.0919878 + 0.995760i \(0.529322\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1752.00 0.696268
\(186\) 0 0
\(187\) 5472.00 2.13985
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2136.00 −0.809191 −0.404596 − 0.914496i \(-0.632588\pi\)
−0.404596 + 0.914496i \(0.632588\pi\)
\(192\) 0 0
\(193\) 4430.00 1.65222 0.826110 − 0.563509i \(-0.190549\pi\)
0.826110 + 0.563509i \(0.190549\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −198.000 −0.0716087 −0.0358044 − 0.999359i \(-0.511399\pi\)
−0.0358044 + 0.999359i \(0.511399\pi\)
\(198\) 0 0
\(199\) 2284.00 0.813610 0.406805 − 0.913515i \(-0.366643\pi\)
0.406805 + 0.913515i \(0.366643\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −378.000 −0.130692
\(204\) 0 0
\(205\) −1512.00 −0.515135
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −96.0000 −0.0317725
\(210\) 0 0
\(211\) −4412.00 −1.43950 −0.719750 − 0.694233i \(-0.755744\pi\)
−0.719750 + 0.694233i \(0.755744\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4512.00 1.43124
\(216\) 0 0
\(217\) 1652.00 0.516798
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6384.00 1.94314
\(222\) 0 0
\(223\) −2072.00 −0.622204 −0.311102 − 0.950377i \(-0.600698\pi\)
−0.311102 + 0.950377i \(0.600698\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −366.000 −0.107014 −0.0535072 − 0.998567i \(-0.517040\pi\)
−0.0535072 + 0.998567i \(0.517040\pi\)
\(228\) 0 0
\(229\) −376.000 −0.108501 −0.0542506 − 0.998527i \(-0.517277\pi\)
−0.0542506 + 0.998527i \(0.517277\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2262.00 0.636002 0.318001 − 0.948090i \(-0.396988\pi\)
0.318001 + 0.948090i \(0.396988\pi\)
\(234\) 0 0
\(235\) −144.000 −0.0399724
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2592.00 0.701517 0.350758 − 0.936466i \(-0.385924\pi\)
0.350758 + 0.936466i \(0.385924\pi\)
\(240\) 0 0
\(241\) 110.000 0.0294013 0.0147007 − 0.999892i \(-0.495320\pi\)
0.0147007 + 0.999892i \(0.495320\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 588.000 0.153330
\(246\) 0 0
\(247\) −112.000 −0.0288518
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1890.00 −0.475282 −0.237641 − 0.971353i \(-0.576374\pi\)
−0.237641 + 0.971353i \(0.576374\pi\)
\(252\) 0 0
\(253\) −5760.00 −1.43134
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2130.00 −0.516987 −0.258494 − 0.966013i \(-0.583226\pi\)
−0.258494 + 0.966013i \(0.583226\pi\)
\(258\) 0 0
\(259\) −1022.00 −0.245189
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4992.00 −1.17042 −0.585209 − 0.810883i \(-0.698988\pi\)
−0.585209 + 0.810883i \(0.698988\pi\)
\(264\) 0 0
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6816.00 −1.54490 −0.772451 − 0.635074i \(-0.780970\pi\)
−0.772451 + 0.635074i \(0.780970\pi\)
\(270\) 0 0
\(271\) −8192.00 −1.83627 −0.918134 − 0.396270i \(-0.870304\pi\)
−0.918134 + 0.396270i \(0.870304\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 912.000 0.199984
\(276\) 0 0
\(277\) 2414.00 0.523622 0.261811 − 0.965119i \(-0.415680\pi\)
0.261811 + 0.965119i \(0.415680\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1962.00 −0.416524 −0.208262 − 0.978073i \(-0.566781\pi\)
−0.208262 + 0.978073i \(0.566781\pi\)
\(282\) 0 0
\(283\) −5402.00 −1.13468 −0.567342 − 0.823482i \(-0.692028\pi\)
−0.567342 + 0.823482i \(0.692028\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 882.000 0.181404
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4788.00 0.954669 0.477334 − 0.878722i \(-0.341603\pi\)
0.477334 + 0.878722i \(0.341603\pi\)
\(294\) 0 0
\(295\) 1656.00 0.326834
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6720.00 −1.29976
\(300\) 0 0
\(301\) −2632.00 −0.504007
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4560.00 0.856081
\(306\) 0 0
\(307\) 574.000 0.106710 0.0533549 − 0.998576i \(-0.483009\pi\)
0.0533549 + 0.998576i \(0.483009\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8808.00 −1.60597 −0.802984 − 0.596001i \(-0.796755\pi\)
−0.802984 + 0.596001i \(0.796755\pi\)
\(312\) 0 0
\(313\) −2770.00 −0.500223 −0.250111 − 0.968217i \(-0.580467\pi\)
−0.250111 + 0.968217i \(0.580467\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7566.00 −1.34053 −0.670266 − 0.742121i \(-0.733820\pi\)
−0.670266 + 0.742121i \(0.733820\pi\)
\(318\) 0 0
\(319\) 2592.00 0.454935
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −228.000 −0.0392763
\(324\) 0 0
\(325\) 1064.00 0.181600
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 84.0000 0.0140762
\(330\) 0 0
\(331\) 11320.0 1.87977 0.939884 − 0.341493i \(-0.110932\pi\)
0.939884 + 0.341493i \(0.110932\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5808.00 0.947239
\(336\) 0 0
\(337\) −4786.00 −0.773620 −0.386810 − 0.922159i \(-0.626423\pi\)
−0.386810 + 0.922159i \(0.626423\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11328.0 −1.79896
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12648.0 1.95672 0.978358 − 0.206921i \(-0.0663443\pi\)
0.978358 + 0.206921i \(0.0663443\pi\)
\(348\) 0 0
\(349\) 9632.00 1.47733 0.738666 − 0.674071i \(-0.235456\pi\)
0.738666 + 0.674071i \(0.235456\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3390.00 0.511137 0.255569 − 0.966791i \(-0.417737\pi\)
0.255569 + 0.966791i \(0.417737\pi\)
\(354\) 0 0
\(355\) 6912.00 1.03338
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10704.0 −1.57364 −0.786818 − 0.617185i \(-0.788273\pi\)
−0.786818 + 0.617185i \(0.788273\pi\)
\(360\) 0 0
\(361\) −6855.00 −0.999417
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −13800.0 −1.97897
\(366\) 0 0
\(367\) 8584.00 1.22093 0.610465 − 0.792043i \(-0.290983\pi\)
0.610465 + 0.792043i \(0.290983\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1218.00 0.170446
\(372\) 0 0
\(373\) −2122.00 −0.294566 −0.147283 − 0.989094i \(-0.547053\pi\)
−0.147283 + 0.989094i \(0.547053\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3024.00 0.413114
\(378\) 0 0
\(379\) 4912.00 0.665732 0.332866 − 0.942974i \(-0.391984\pi\)
0.332866 + 0.942974i \(0.391984\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9060.00 1.20873 0.604366 − 0.796707i \(-0.293426\pi\)
0.604366 + 0.796707i \(0.293426\pi\)
\(384\) 0 0
\(385\) −4032.00 −0.533740
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8994.00 −1.17227 −0.586136 − 0.810213i \(-0.699352\pi\)
−0.586136 + 0.810213i \(0.699352\pi\)
\(390\) 0 0
\(391\) −13680.0 −1.76938
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9312.00 −1.18617
\(396\) 0 0
\(397\) −12976.0 −1.64042 −0.820210 − 0.572062i \(-0.806143\pi\)
−0.820210 + 0.572062i \(0.806143\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3522.00 0.438604 0.219302 − 0.975657i \(-0.429622\pi\)
0.219302 + 0.975657i \(0.429622\pi\)
\(402\) 0 0
\(403\) −13216.0 −1.63359
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7008.00 0.853498
\(408\) 0 0
\(409\) 12710.0 1.53660 0.768300 − 0.640090i \(-0.221103\pi\)
0.768300 + 0.640090i \(0.221103\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −966.000 −0.115094
\(414\) 0 0
\(415\) 4536.00 0.536539
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1638.00 0.190982 0.0954911 − 0.995430i \(-0.469558\pi\)
0.0954911 + 0.995430i \(0.469558\pi\)
\(420\) 0 0
\(421\) −12850.0 −1.48758 −0.743789 − 0.668414i \(-0.766973\pi\)
−0.743789 + 0.668414i \(0.766973\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2166.00 0.247215
\(426\) 0 0
\(427\) −2660.00 −0.301467
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8016.00 −0.895863 −0.447932 − 0.894068i \(-0.647839\pi\)
−0.447932 + 0.894068i \(0.647839\pi\)
\(432\) 0 0
\(433\) 2198.00 0.243947 0.121974 − 0.992533i \(-0.461078\pi\)
0.121974 + 0.992533i \(0.461078\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 240.000 0.0262718
\(438\) 0 0
\(439\) 376.000 0.0408781 0.0204391 − 0.999791i \(-0.493494\pi\)
0.0204391 + 0.999791i \(0.493494\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7188.00 0.770908 0.385454 − 0.922727i \(-0.374045\pi\)
0.385454 + 0.922727i \(0.374045\pi\)
\(444\) 0 0
\(445\) 4680.00 0.498547
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14670.0 1.54192 0.770958 − 0.636886i \(-0.219778\pi\)
0.770958 + 0.636886i \(0.219778\pi\)
\(450\) 0 0
\(451\) −6048.00 −0.631462
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4704.00 −0.484675
\(456\) 0 0
\(457\) −5146.00 −0.526739 −0.263370 − 0.964695i \(-0.584834\pi\)
−0.263370 + 0.964695i \(0.584834\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1512.00 0.152757 0.0763784 − 0.997079i \(-0.475664\pi\)
0.0763784 + 0.997079i \(0.475664\pi\)
\(462\) 0 0
\(463\) −7184.00 −0.721099 −0.360549 − 0.932740i \(-0.617411\pi\)
−0.360549 + 0.932740i \(0.617411\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16518.0 −1.63675 −0.818375 − 0.574685i \(-0.805125\pi\)
−0.818375 + 0.574685i \(0.805125\pi\)
\(468\) 0 0
\(469\) −3388.00 −0.333568
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18048.0 1.75444
\(474\) 0 0
\(475\) −38.0000 −0.00367065
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10092.0 0.962662 0.481331 − 0.876539i \(-0.340153\pi\)
0.481331 + 0.876539i \(0.340153\pi\)
\(480\) 0 0
\(481\) 8176.00 0.775038
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15960.0 −1.49424
\(486\) 0 0
\(487\) −7832.00 −0.728751 −0.364376 − 0.931252i \(-0.618718\pi\)
−0.364376 + 0.931252i \(0.618718\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6732.00 −0.618759 −0.309380 − 0.950939i \(-0.600121\pi\)
−0.309380 + 0.950939i \(0.600121\pi\)
\(492\) 0 0
\(493\) 6156.00 0.562378
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4032.00 −0.363903
\(498\) 0 0
\(499\) −18668.0 −1.67474 −0.837369 − 0.546638i \(-0.815907\pi\)
−0.837369 + 0.546638i \(0.815907\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6048.00 −0.536117 −0.268059 − 0.963403i \(-0.586382\pi\)
−0.268059 + 0.963403i \(0.586382\pi\)
\(504\) 0 0
\(505\) 18000.0 1.58612
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11328.0 −0.986453 −0.493227 − 0.869901i \(-0.664183\pi\)
−0.493227 + 0.869901i \(0.664183\pi\)
\(510\) 0 0
\(511\) 8050.00 0.696890
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4560.00 −0.390170
\(516\) 0 0
\(517\) −576.000 −0.0489989
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4146.00 0.348636 0.174318 − 0.984689i \(-0.444228\pi\)
0.174318 + 0.984689i \(0.444228\pi\)
\(522\) 0 0
\(523\) 1006.00 0.0841096 0.0420548 − 0.999115i \(-0.486610\pi\)
0.0420548 + 0.999115i \(0.486610\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26904.0 −2.22383
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7056.00 −0.573413
\(534\) 0 0
\(535\) 7632.00 0.616748
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2352.00 0.187955
\(540\) 0 0
\(541\) −14722.0 −1.16996 −0.584980 − 0.811048i \(-0.698898\pi\)
−0.584980 + 0.811048i \(0.698898\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1752.00 0.137702
\(546\) 0 0
\(547\) 13480.0 1.05368 0.526840 − 0.849964i \(-0.323377\pi\)
0.526840 + 0.849964i \(0.323377\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −108.000 −0.00835019
\(552\) 0 0
\(553\) 5432.00 0.417707
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6222.00 −0.473312 −0.236656 − 0.971594i \(-0.576051\pi\)
−0.236656 + 0.971594i \(0.576051\pi\)
\(558\) 0 0
\(559\) 21056.0 1.59316
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4926.00 0.368750 0.184375 − 0.982856i \(-0.440974\pi\)
0.184375 + 0.982856i \(0.440974\pi\)
\(564\) 0 0
\(565\) −2376.00 −0.176919
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22182.0 −1.63430 −0.817151 − 0.576424i \(-0.804448\pi\)
−0.817151 + 0.576424i \(0.804448\pi\)
\(570\) 0 0
\(571\) −3296.00 −0.241564 −0.120782 − 0.992679i \(-0.538540\pi\)
−0.120782 + 0.992679i \(0.538540\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2280.00 −0.165361
\(576\) 0 0
\(577\) −24334.0 −1.75570 −0.877849 − 0.478938i \(-0.841022\pi\)
−0.877849 + 0.478938i \(0.841022\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2646.00 −0.188941
\(582\) 0 0
\(583\) −8352.00 −0.593318
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1638.00 0.115175 0.0575873 − 0.998340i \(-0.481659\pi\)
0.0575873 + 0.998340i \(0.481659\pi\)
\(588\) 0 0
\(589\) 472.000 0.0330194
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7446.00 0.515633 0.257817 − 0.966194i \(-0.416997\pi\)
0.257817 + 0.966194i \(0.416997\pi\)
\(594\) 0 0
\(595\) −9576.00 −0.659794
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6504.00 −0.443650 −0.221825 − 0.975087i \(-0.571201\pi\)
−0.221825 + 0.975087i \(0.571201\pi\)
\(600\) 0 0
\(601\) 16058.0 1.08988 0.544941 − 0.838474i \(-0.316552\pi\)
0.544941 + 0.838474i \(0.316552\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11676.0 0.784623
\(606\) 0 0
\(607\) −10208.0 −0.682586 −0.341293 − 0.939957i \(-0.610865\pi\)
−0.341293 + 0.939957i \(0.610865\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −672.000 −0.0444946
\(612\) 0 0
\(613\) −14974.0 −0.986614 −0.493307 − 0.869855i \(-0.664212\pi\)
−0.493307 + 0.869855i \(0.664212\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7254.00 −0.473314 −0.236657 − 0.971593i \(-0.576052\pi\)
−0.236657 + 0.971593i \(0.576052\pi\)
\(618\) 0 0
\(619\) −12458.0 −0.808933 −0.404466 − 0.914553i \(-0.632543\pi\)
−0.404466 + 0.914553i \(0.632543\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2730.00 −0.175562
\(624\) 0 0
\(625\) −17639.0 −1.12890
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16644.0 1.05507
\(630\) 0 0
\(631\) −28352.0 −1.78871 −0.894354 − 0.447359i \(-0.852365\pi\)
−0.894354 + 0.447359i \(0.852365\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4512.00 0.281974
\(636\) 0 0
\(637\) 2744.00 0.170677
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −27390.0 −1.68774 −0.843869 − 0.536549i \(-0.819728\pi\)
−0.843869 + 0.536549i \(0.819728\pi\)
\(642\) 0 0
\(643\) 21490.0 1.31801 0.659007 − 0.752137i \(-0.270977\pi\)
0.659007 + 0.752137i \(0.270977\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17652.0 1.07260 0.536300 − 0.844028i \(-0.319822\pi\)
0.536300 + 0.844028i \(0.319822\pi\)
\(648\) 0 0
\(649\) 6624.00 0.400639
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4782.00 0.286576 0.143288 − 0.989681i \(-0.454232\pi\)
0.143288 + 0.989681i \(0.454232\pi\)
\(654\) 0 0
\(655\) 25560.0 1.52475
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −27144.0 −1.60452 −0.802261 − 0.596973i \(-0.796370\pi\)
−0.802261 + 0.596973i \(0.796370\pi\)
\(660\) 0 0
\(661\) −11860.0 −0.697883 −0.348941 − 0.937145i \(-0.613459\pi\)
−0.348941 + 0.937145i \(0.613459\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 168.000 0.00979663
\(666\) 0 0
\(667\) −6480.00 −0.376172
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 18240.0 1.04940
\(672\) 0 0
\(673\) 5546.00 0.317656 0.158828 − 0.987306i \(-0.449228\pi\)
0.158828 + 0.987306i \(0.449228\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14880.0 0.844734 0.422367 − 0.906425i \(-0.361199\pi\)
0.422367 + 0.906425i \(0.361199\pi\)
\(678\) 0 0
\(679\) 9310.00 0.526193
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20964.0 1.17447 0.587237 − 0.809415i \(-0.300216\pi\)
0.587237 + 0.809415i \(0.300216\pi\)
\(684\) 0 0
\(685\) 936.000 0.0522084
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9744.00 −0.538776
\(690\) 0 0
\(691\) −13106.0 −0.721528 −0.360764 − 0.932657i \(-0.617484\pi\)
−0.360764 + 0.932657i \(0.617484\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 28056.0 1.53126
\(696\) 0 0
\(697\) −14364.0 −0.780596
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4590.00 0.247307 0.123653 − 0.992325i \(-0.460539\pi\)
0.123653 + 0.992325i \(0.460539\pi\)
\(702\) 0 0
\(703\) −292.000 −0.0156657
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10500.0 −0.558548
\(708\) 0 0
\(709\) −862.000 −0.0456602 −0.0228301 − 0.999739i \(-0.507268\pi\)
−0.0228301 + 0.999739i \(0.507268\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 28320.0 1.48751
\(714\) 0 0
\(715\) 32256.0 1.68714
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3540.00 −0.183616 −0.0918079 − 0.995777i \(-0.529265\pi\)
−0.0918079 + 0.995777i \(0.529265\pi\)
\(720\) 0 0
\(721\) 2660.00 0.137397
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1026.00 0.0525582
\(726\) 0 0
\(727\) 4228.00 0.215692 0.107846 − 0.994168i \(-0.465605\pi\)
0.107846 + 0.994168i \(0.465605\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 42864.0 2.16879
\(732\) 0 0
\(733\) 5420.00 0.273114 0.136557 − 0.990632i \(-0.456396\pi\)
0.136557 + 0.990632i \(0.456396\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 23232.0 1.16114
\(738\) 0 0
\(739\) −1280.00 −0.0637152 −0.0318576 − 0.999492i \(-0.510142\pi\)
−0.0318576 + 0.999492i \(0.510142\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −35712.0 −1.76332 −0.881660 − 0.471886i \(-0.843573\pi\)
−0.881660 + 0.471886i \(0.843573\pi\)
\(744\) 0 0
\(745\) 12024.0 0.591309
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4452.00 −0.217186
\(750\) 0 0
\(751\) −24464.0 −1.18869 −0.594344 − 0.804211i \(-0.702588\pi\)
−0.594344 + 0.804211i \(0.702588\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 33024.0 1.59188
\(756\) 0 0
\(757\) 30242.0 1.45200 0.726000 − 0.687695i \(-0.241377\pi\)
0.726000 + 0.687695i \(0.241377\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2154.00 0.102605 0.0513025 − 0.998683i \(-0.483663\pi\)
0.0513025 + 0.998683i \(0.483663\pi\)
\(762\) 0 0
\(763\) −1022.00 −0.0484913
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7728.00 0.363810
\(768\) 0 0
\(769\) 10262.0 0.481219 0.240609 − 0.970622i \(-0.422653\pi\)
0.240609 + 0.970622i \(0.422653\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9084.00 −0.422676 −0.211338 − 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(774\) 0 0
\(775\) −4484.00 −0.207832
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 252.000 0.0115903
\(780\) 0 0
\(781\) 27648.0 1.26674
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6240.00 −0.283714
\(786\) 0 0
\(787\) 19798.0 0.896725 0.448362 − 0.893852i \(-0.352007\pi\)
0.448362 + 0.893852i \(0.352007\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1386.00 0.0623015
\(792\) 0 0
\(793\) 21280.0 0.952932
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30240.0 −1.34398 −0.671992 − 0.740558i \(-0.734561\pi\)
−0.671992 + 0.740558i \(0.734561\pi\)
\(798\) 0 0
\(799\) −1368.00 −0.0605712
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −55200.0 −2.42586
\(804\) 0 0
\(805\) 10080.0 0.441333
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2346.00 0.101954 0.0509771 − 0.998700i \(-0.483766\pi\)
0.0509771 + 0.998700i \(0.483766\pi\)
\(810\) 0 0
\(811\) 29806.0 1.29054 0.645271 − 0.763953i \(-0.276744\pi\)
0.645271 + 0.763953i \(0.276744\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −15360.0 −0.660169
\(816\) 0 0
\(817\) −752.000 −0.0322021
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1506.00 0.0640192 0.0320096 − 0.999488i \(-0.489809\pi\)
0.0320096 + 0.999488i \(0.489809\pi\)
\(822\) 0 0
\(823\) 20392.0 0.863694 0.431847 − 0.901947i \(-0.357862\pi\)
0.431847 + 0.901947i \(0.357862\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36108.0 1.51826 0.759128 − 0.650941i \(-0.225626\pi\)
0.759128 + 0.650941i \(0.225626\pi\)
\(828\) 0 0
\(829\) −13876.0 −0.581343 −0.290672 − 0.956823i \(-0.593879\pi\)
−0.290672 + 0.956823i \(0.593879\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5586.00 0.232345
\(834\) 0 0
\(835\) 21168.0 0.877304
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 23436.0 0.964363 0.482182 − 0.876071i \(-0.339845\pi\)
0.482182 + 0.876071i \(0.339845\pi\)
\(840\) 0 0
\(841\) −21473.0 −0.880438
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 11268.0 0.458735
\(846\) 0 0
\(847\) −6811.00 −0.276303
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −17520.0 −0.705732
\(852\) 0 0
\(853\) 8120.00 0.325936 0.162968 − 0.986631i \(-0.447893\pi\)
0.162968 + 0.986631i \(0.447893\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 50010.0 1.99336 0.996680 − 0.0814218i \(-0.0259461\pi\)
0.996680 + 0.0814218i \(0.0259461\pi\)
\(858\) 0 0
\(859\) −34526.0 −1.37138 −0.685688 − 0.727896i \(-0.740499\pi\)
−0.685688 + 0.727896i \(0.740499\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −17256.0 −0.680650 −0.340325 − 0.940308i \(-0.610537\pi\)
−0.340325 + 0.940308i \(0.610537\pi\)
\(864\) 0 0
\(865\) 9216.00 0.362258
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −37248.0 −1.45403
\(870\) 0 0
\(871\) 27104.0 1.05440
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8904.00 0.344012
\(876\) 0 0
\(877\) 8714.00 0.335520 0.167760 − 0.985828i \(-0.446347\pi\)
0.167760 + 0.985828i \(0.446347\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 22806.0 0.872138 0.436069 − 0.899913i \(-0.356370\pi\)
0.436069 + 0.899913i \(0.356370\pi\)
\(882\) 0 0
\(883\) −40196.0 −1.53194 −0.765970 − 0.642876i \(-0.777741\pi\)
−0.765970 + 0.642876i \(0.777741\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 40812.0 1.54491 0.772454 − 0.635071i \(-0.219029\pi\)
0.772454 + 0.635071i \(0.219029\pi\)
\(888\) 0 0
\(889\) −2632.00 −0.0992963
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 24.0000 0.000899361 0
\(894\) 0 0
\(895\) 21744.0 0.812091
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −12744.0 −0.472788
\(900\) 0 0
\(901\) −19836.0 −0.733444
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5376.00 −0.197463
\(906\) 0 0
\(907\) 13588.0 0.497444 0.248722 − 0.968575i \(-0.419989\pi\)
0.248722 + 0.968575i \(0.419989\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −47304.0 −1.72036 −0.860182 − 0.509987i \(-0.829650\pi\)
−0.860182 + 0.509987i \(0.829650\pi\)
\(912\) 0 0
\(913\) 18144.0 0.657699
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −14910.0 −0.536937
\(918\) 0 0
\(919\) −1784.00 −0.0640356 −0.0320178 − 0.999487i \(-0.510193\pi\)
−0.0320178 + 0.999487i \(0.510193\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 32256.0 1.15029
\(924\) 0 0
\(925\) 2774.00 0.0986038
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 35922.0 1.26864 0.634318 − 0.773072i \(-0.281281\pi\)
0.634318 + 0.773072i \(0.281281\pi\)
\(930\) 0 0
\(931\) −98.0000 −0.00344986
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 65664.0 2.29673
\(936\) 0 0
\(937\) −26782.0 −0.933756 −0.466878 − 0.884322i \(-0.654621\pi\)
−0.466878 + 0.884322i \(0.654621\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4044.00 −0.140096 −0.0700482 − 0.997544i \(-0.522315\pi\)
−0.0700482 + 0.997544i \(0.522315\pi\)
\(942\) 0 0
\(943\) 15120.0 0.522137
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2136.00 −0.0732953 −0.0366477 − 0.999328i \(-0.511668\pi\)
−0.0366477 + 0.999328i \(0.511668\pi\)
\(948\) 0 0
\(949\) −64400.0 −2.20286
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 15174.0 0.515776 0.257888 − 0.966175i \(-0.416974\pi\)
0.257888 + 0.966175i \(0.416974\pi\)
\(954\) 0 0
\(955\) −25632.0 −0.868515
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −546.000 −0.0183850
\(960\) 0 0
\(961\) 25905.0 0.869558
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 53160.0 1.77335
\(966\) 0 0
\(967\) −25832.0 −0.859050 −0.429525 − 0.903055i \(-0.641319\pi\)
−0.429525 + 0.903055i \(0.641319\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −37686.0 −1.24552 −0.622761 − 0.782412i \(-0.713989\pi\)
−0.622761 + 0.782412i \(0.713989\pi\)
\(972\) 0 0
\(973\) −16366.0 −0.539229
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 54006.0 1.76848 0.884240 − 0.467033i \(-0.154677\pi\)
0.884240 + 0.467033i \(0.154677\pi\)
\(978\) 0 0
\(979\) 18720.0 0.611127
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33276.0 1.07969 0.539847 − 0.841763i \(-0.318482\pi\)
0.539847 + 0.841763i \(0.318482\pi\)
\(984\) 0 0
\(985\) −2376.00 −0.0768585
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −45120.0 −1.45069
\(990\) 0 0
\(991\) 3760.00 0.120525 0.0602625 − 0.998183i \(-0.480806\pi\)
0.0602625 + 0.998183i \(0.480806\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 27408.0 0.873258
\(996\) 0 0
\(997\) 36524.0 1.16021 0.580104 − 0.814543i \(-0.303012\pi\)
0.580104 + 0.814543i \(0.303012\pi\)
\(998\) 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.r.1.1 1
3.2 odd 2 112.4.a.e.1.1 1
4.3 odd 2 126.4.a.d.1.1 1
12.11 even 2 14.4.a.b.1.1 ✓ 1
21.20 even 2 784.4.a.h.1.1 1
24.5 odd 2 448.4.a.g.1.1 1
24.11 even 2 448.4.a.k.1.1 1
28.3 even 6 882.4.g.v.667.1 2
28.11 odd 6 882.4.g.p.667.1 2
28.19 even 6 882.4.g.v.361.1 2
28.23 odd 6 882.4.g.p.361.1 2
28.27 even 2 882.4.a.b.1.1 1
60.23 odd 4 350.4.c.g.99.1 2
60.47 odd 4 350.4.c.g.99.2 2
60.59 even 2 350.4.a.f.1.1 1
84.11 even 6 98.4.c.c.79.1 2
84.23 even 6 98.4.c.c.67.1 2
84.47 odd 6 98.4.c.b.67.1 2
84.59 odd 6 98.4.c.b.79.1 2
84.83 odd 2 98.4.a.e.1.1 1
132.131 odd 2 1694.4.a.b.1.1 1
156.155 even 2 2366.4.a.c.1.1 1
420.419 odd 2 2450.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.a.b.1.1 ✓ 1 12.11 even 2
98.4.a.e.1.1 1 84.83 odd 2
98.4.c.b.67.1 2 84.47 odd 6
98.4.c.b.79.1 2 84.59 odd 6
98.4.c.c.67.1 2 84.23 even 6
98.4.c.c.79.1 2 84.11 even 6
112.4.a.e.1.1 1 3.2 odd 2
126.4.a.d.1.1 1 4.3 odd 2
350.4.a.f.1.1 1 60.59 even 2
350.4.c.g.99.1 2 60.23 odd 4
350.4.c.g.99.2 2 60.47 odd 4
448.4.a.g.1.1 1 24.5 odd 2
448.4.a.k.1.1 1 24.11 even 2
784.4.a.h.1.1 1 21.20 even 2
882.4.a.b.1.1 1 28.27 even 2
882.4.g.p.361.1 2 28.23 odd 6
882.4.g.p.667.1 2 28.11 odd 6
882.4.g.v.361.1 2 28.19 even 6
882.4.g.v.667.1 2 28.3 even 6
1008.4.a.r.1.1 1 1.1 even 1 trivial
1694.4.a.b.1.1 1 132.131 odd 2
2366.4.a.c.1.1 1 156.155 even 2
2450.4.a.i.1.1 1 420.419 odd 2