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Properties

Label 1960.4.a.e.1.1
Level $1960$
Weight $4$
Character 1960.1
Self dual yes
Analytic conductor $115.644$
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] = [1960,4,Mod(1,1960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1960, 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("1960.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1960.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: \(115.643743611\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1960.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{3} -5.00000 q^{5} -11.0000 q^{9} +36.0000 q^{11} +42.0000 q^{13} +20.0000 q^{15} +110.000 q^{17} +116.000 q^{19} +16.0000 q^{23} +25.0000 q^{25} +152.000 q^{27} +198.000 q^{29} -240.000 q^{31} -144.000 q^{33} -258.000 q^{37} -168.000 q^{39} -442.000 q^{41} -292.000 q^{43} +55.0000 q^{45} -392.000 q^{47} -440.000 q^{51} +142.000 q^{53} -180.000 q^{55} -464.000 q^{57} +348.000 q^{59} +570.000 q^{61} -210.000 q^{65} +692.000 q^{67} -64.0000 q^{69} +168.000 q^{71} +134.000 q^{73} -100.000 q^{75} +784.000 q^{79} -311.000 q^{81} -564.000 q^{83} -550.000 q^{85} -792.000 q^{87} -1034.00 q^{89} +960.000 q^{93} -580.000 q^{95} +382.000 q^{97} -396.000 q^{99} +O(q^{100})\)

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
\(3\) −4.00000 −0.769800 −0.384900 − 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −11.0000 −0.407407
\(10\) 0 0
\(11\) 36.0000 0.986764 0.493382 − 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(12\) 0 0
\(13\) 42.0000 0.896054 0.448027 − 0.894020i \(-0.352127\pi\)
0.448027 + 0.894020i \(0.352127\pi\)
\(14\) 0 0
\(15\) 20.0000 0.344265
\(16\) 0 0
\(17\) 110.000 1.56935 0.784674 − 0.619909i \(-0.212830\pi\)
0.784674 + 0.619909i \(0.212830\pi\)
\(18\) 0 0
\(19\) 116.000 1.40064 0.700322 − 0.713827i \(-0.253040\pi\)
0.700322 + 0.713827i \(0.253040\pi\)
\(20\) 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
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 152.000 1.08342
\(28\) 0 0
\(29\) 198.000 1.26785 0.633925 − 0.773394i \(-0.281443\pi\)
0.633925 + 0.773394i \(0.281443\pi\)
\(30\) 0 0
\(31\) −240.000 −1.39049 −0.695246 − 0.718772i \(-0.744705\pi\)
−0.695246 + 0.718772i \(0.744705\pi\)
\(32\) 0 0
\(33\) −144.000 −0.759612
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −258.000 −1.14635 −0.573175 − 0.819433i \(-0.694288\pi\)
−0.573175 + 0.819433i \(0.694288\pi\)
\(38\) 0 0
\(39\) −168.000 −0.689783
\(40\) 0 0
\(41\) −442.000 −1.68363 −0.841815 − 0.539767i \(-0.818512\pi\)
−0.841815 + 0.539767i \(0.818512\pi\)
\(42\) 0 0
\(43\) −292.000 −1.03557 −0.517786 − 0.855510i \(-0.673244\pi\)
−0.517786 + 0.855510i \(0.673244\pi\)
\(44\) 0 0
\(45\) 55.0000 0.182198
\(46\) 0 0
\(47\) −392.000 −1.21658 −0.608288 − 0.793716i \(-0.708143\pi\)
−0.608288 + 0.793716i \(0.708143\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −440.000 −1.20808
\(52\) 0 0
\(53\) 142.000 0.368023 0.184011 − 0.982924i \(-0.441092\pi\)
0.184011 + 0.982924i \(0.441092\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) 0 0
\(57\) −464.000 −1.07822
\(58\) 0 0
\(59\) 348.000 0.767894 0.383947 − 0.923355i \(-0.374565\pi\)
0.383947 + 0.923355i \(0.374565\pi\)
\(60\) 0 0
\(61\) 570.000 1.19641 0.598205 − 0.801343i \(-0.295881\pi\)
0.598205 + 0.801343i \(0.295881\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −210.000 −0.400728
\(66\) 0 0
\(67\) 692.000 1.26181 0.630905 − 0.775860i \(-0.282684\pi\)
0.630905 + 0.775860i \(0.282684\pi\)
\(68\) 0 0
\(69\) −64.0000 −0.111662
\(70\) 0 0
\(71\) 168.000 0.280816 0.140408 − 0.990094i \(-0.455159\pi\)
0.140408 + 0.990094i \(0.455159\pi\)
\(72\) 0 0
\(73\) 134.000 0.214843 0.107421 − 0.994214i \(-0.465741\pi\)
0.107421 + 0.994214i \(0.465741\pi\)
\(74\) 0 0
\(75\) −100.000 −0.153960
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 784.000 1.11654 0.558271 − 0.829658i \(-0.311465\pi\)
0.558271 + 0.829658i \(0.311465\pi\)
\(80\) 0 0
\(81\) −311.000 −0.426612
\(82\) 0 0
\(83\) −564.000 −0.745868 −0.372934 − 0.927858i \(-0.621648\pi\)
−0.372934 + 0.927858i \(0.621648\pi\)
\(84\) 0 0
\(85\) −550.000 −0.701834
\(86\) 0 0
\(87\) −792.000 −0.975992
\(88\) 0 0
\(89\) −1034.00 −1.23150 −0.615752 − 0.787940i \(-0.711148\pi\)
−0.615752 + 0.787940i \(0.711148\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 960.000 1.07040
\(94\) 0 0
\(95\) −580.000 −0.626387
\(96\) 0 0
\(97\) 382.000 0.399858 0.199929 − 0.979810i \(-0.435929\pi\)
0.199929 + 0.979810i \(0.435929\pi\)
\(98\) 0 0
\(99\) −396.000 −0.402015
\(100\) 0 0
\(101\) 674.000 0.664015 0.332007 − 0.943277i \(-0.392274\pi\)
0.332007 + 0.943277i \(0.392274\pi\)
\(102\) 0 0
\(103\) 992.000 0.948977 0.474489 − 0.880262i \(-0.342633\pi\)
0.474489 + 0.880262i \(0.342633\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −500.000 −0.451746 −0.225873 − 0.974157i \(-0.572523\pi\)
−0.225873 + 0.974157i \(0.572523\pi\)
\(108\) 0 0
\(109\) 1046.00 0.919162 0.459581 − 0.888136i \(-0.348000\pi\)
0.459581 + 0.888136i \(0.348000\pi\)
\(110\) 0 0
\(111\) 1032.00 0.882460
\(112\) 0 0
\(113\) −558.000 −0.464533 −0.232266 − 0.972652i \(-0.574614\pi\)
−0.232266 + 0.972652i \(0.574614\pi\)
\(114\) 0 0
\(115\) −80.0000 −0.0648699
\(116\) 0 0
\(117\) −462.000 −0.365059
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) 0 0
\(123\) 1768.00 1.29606
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −328.000 −0.229176 −0.114588 − 0.993413i \(-0.536555\pi\)
−0.114588 + 0.993413i \(0.536555\pi\)
\(128\) 0 0
\(129\) 1168.00 0.797183
\(130\) 0 0
\(131\) 212.000 0.141393 0.0706967 − 0.997498i \(-0.477478\pi\)
0.0706967 + 0.997498i \(0.477478\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −760.000 −0.484521
\(136\) 0 0
\(137\) 1434.00 0.894269 0.447135 − 0.894467i \(-0.352444\pi\)
0.447135 + 0.894467i \(0.352444\pi\)
\(138\) 0 0
\(139\) −2196.00 −1.34002 −0.670008 − 0.742354i \(-0.733709\pi\)
−0.670008 + 0.742354i \(0.733709\pi\)
\(140\) 0 0
\(141\) 1568.00 0.936521
\(142\) 0 0
\(143\) 1512.00 0.884194
\(144\) 0 0
\(145\) −990.000 −0.567000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2418.00 −1.32946 −0.664732 − 0.747081i \(-0.731454\pi\)
−0.664732 + 0.747081i \(0.731454\pi\)
\(150\) 0 0
\(151\) 3672.00 1.97896 0.989481 − 0.144666i \(-0.0462108\pi\)
0.989481 + 0.144666i \(0.0462108\pi\)
\(152\) 0 0
\(153\) −1210.00 −0.639364
\(154\) 0 0
\(155\) 1200.00 0.621847
\(156\) 0 0
\(157\) −358.000 −0.181984 −0.0909921 − 0.995852i \(-0.529004\pi\)
−0.0909921 + 0.995852i \(0.529004\pi\)
\(158\) 0 0
\(159\) −568.000 −0.283304
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2564.00 1.23207 0.616037 − 0.787717i \(-0.288737\pi\)
0.616037 + 0.787717i \(0.288737\pi\)
\(164\) 0 0
\(165\) 720.000 0.339709
\(166\) 0 0
\(167\) 3056.00 1.41605 0.708025 − 0.706187i \(-0.249586\pi\)
0.708025 + 0.706187i \(0.249586\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 0 0
\(171\) −1276.00 −0.570633
\(172\) 0 0
\(173\) 234.000 0.102836 0.0514182 − 0.998677i \(-0.483626\pi\)
0.0514182 + 0.998677i \(0.483626\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1392.00 −0.591125
\(178\) 0 0
\(179\) 524.000 0.218802 0.109401 − 0.993998i \(-0.465107\pi\)
0.109401 + 0.993998i \(0.465107\pi\)
\(180\) 0 0
\(181\) 1138.00 0.467331 0.233665 − 0.972317i \(-0.424928\pi\)
0.233665 + 0.972317i \(0.424928\pi\)
\(182\) 0 0
\(183\) −2280.00 −0.920997
\(184\) 0 0
\(185\) 1290.00 0.512663
\(186\) 0 0
\(187\) 3960.00 1.54858
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1520.00 0.575829 0.287915 − 0.957656i \(-0.407038\pi\)
0.287915 + 0.957656i \(0.407038\pi\)
\(192\) 0 0
\(193\) −2142.00 −0.798884 −0.399442 − 0.916759i \(-0.630796\pi\)
−0.399442 + 0.916759i \(0.630796\pi\)
\(194\) 0 0
\(195\) 840.000 0.308480
\(196\) 0 0
\(197\) −2306.00 −0.833988 −0.416994 − 0.908909i \(-0.636916\pi\)
−0.416994 + 0.908909i \(0.636916\pi\)
\(198\) 0 0
\(199\) −3288.00 −1.17126 −0.585628 − 0.810580i \(-0.699152\pi\)
−0.585628 + 0.810580i \(0.699152\pi\)
\(200\) 0 0
\(201\) −2768.00 −0.971342
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2210.00 0.752942
\(206\) 0 0
\(207\) −176.000 −0.0590959
\(208\) 0 0
\(209\) 4176.00 1.38211
\(210\) 0 0
\(211\) −3876.00 −1.26462 −0.632310 − 0.774715i \(-0.717893\pi\)
−0.632310 + 0.774715i \(0.717893\pi\)
\(212\) 0 0
\(213\) −672.000 −0.216172
\(214\) 0 0
\(215\) 1460.00 0.463122
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −536.000 −0.165386
\(220\) 0 0
\(221\) 4620.00 1.40622
\(222\) 0 0
\(223\) 5688.00 1.70806 0.854028 − 0.520226i \(-0.174152\pi\)
0.854028 + 0.520226i \(0.174152\pi\)
\(224\) 0 0
\(225\) −275.000 −0.0814815
\(226\) 0 0
\(227\) 2796.00 0.817520 0.408760 − 0.912642i \(-0.365961\pi\)
0.408760 + 0.912642i \(0.365961\pi\)
\(228\) 0 0
\(229\) −4446.00 −1.28297 −0.641485 − 0.767136i \(-0.721681\pi\)
−0.641485 + 0.767136i \(0.721681\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2522.00 0.709106 0.354553 − 0.935036i \(-0.384633\pi\)
0.354553 + 0.935036i \(0.384633\pi\)
\(234\) 0 0
\(235\) 1960.00 0.544069
\(236\) 0 0
\(237\) −3136.00 −0.859515
\(238\) 0 0
\(239\) 816.000 0.220848 0.110424 − 0.993885i \(-0.464779\pi\)
0.110424 + 0.993885i \(0.464779\pi\)
\(240\) 0 0
\(241\) 5422.00 1.44922 0.724609 − 0.689160i \(-0.242020\pi\)
0.724609 + 0.689160i \(0.242020\pi\)
\(242\) 0 0
\(243\) −2860.00 −0.755017
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4872.00 1.25505
\(248\) 0 0
\(249\) 2256.00 0.574169
\(250\) 0 0
\(251\) 5900.00 1.48368 0.741842 − 0.670575i \(-0.233952\pi\)
0.741842 + 0.670575i \(0.233952\pi\)
\(252\) 0 0
\(253\) 576.000 0.143134
\(254\) 0 0
\(255\) 2200.00 0.540272
\(256\) 0 0
\(257\) −5250.00 −1.27426 −0.637132 − 0.770754i \(-0.719880\pi\)
−0.637132 + 0.770754i \(0.719880\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2178.00 −0.516532
\(262\) 0 0
\(263\) 6240.00 1.46302 0.731511 − 0.681829i \(-0.238815\pi\)
0.731511 + 0.681829i \(0.238815\pi\)
\(264\) 0 0
\(265\) −710.000 −0.164585
\(266\) 0 0
\(267\) 4136.00 0.948012
\(268\) 0 0
\(269\) 714.000 0.161834 0.0809170 − 0.996721i \(-0.474215\pi\)
0.0809170 + 0.996721i \(0.474215\pi\)
\(270\) 0 0
\(271\) −2144.00 −0.480586 −0.240293 − 0.970700i \(-0.577243\pi\)
−0.240293 + 0.970700i \(0.577243\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 900.000 0.197353
\(276\) 0 0
\(277\) −4466.00 −0.968722 −0.484361 − 0.874868i \(-0.660948\pi\)
−0.484361 + 0.874868i \(0.660948\pi\)
\(278\) 0 0
\(279\) 2640.00 0.566497
\(280\) 0 0
\(281\) −5302.00 −1.12559 −0.562795 − 0.826596i \(-0.690274\pi\)
−0.562795 + 0.826596i \(0.690274\pi\)
\(282\) 0 0
\(283\) 6932.00 1.45606 0.728029 − 0.685546i \(-0.240436\pi\)
0.728029 + 0.685546i \(0.240436\pi\)
\(284\) 0 0
\(285\) 2320.00 0.482193
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7187.00 1.46285
\(290\) 0 0
\(291\) −1528.00 −0.307811
\(292\) 0 0
\(293\) 4034.00 0.804330 0.402165 − 0.915567i \(-0.368258\pi\)
0.402165 + 0.915567i \(0.368258\pi\)
\(294\) 0 0
\(295\) −1740.00 −0.343413
\(296\) 0 0
\(297\) 5472.00 1.06908
\(298\) 0 0
\(299\) 672.000 0.129976
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2696.00 −0.511159
\(304\) 0 0
\(305\) −2850.00 −0.535051
\(306\) 0 0
\(307\) 3836.00 0.713134 0.356567 − 0.934270i \(-0.383947\pi\)
0.356567 + 0.934270i \(0.383947\pi\)
\(308\) 0 0
\(309\) −3968.00 −0.730523
\(310\) 0 0
\(311\) −664.000 −0.121067 −0.0605337 − 0.998166i \(-0.519280\pi\)
−0.0605337 + 0.998166i \(0.519280\pi\)
\(312\) 0 0
\(313\) −2986.00 −0.539229 −0.269615 − 0.962968i \(-0.586896\pi\)
−0.269615 + 0.962968i \(0.586896\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2726.00 0.482989 0.241494 − 0.970402i \(-0.422362\pi\)
0.241494 + 0.970402i \(0.422362\pi\)
\(318\) 0 0
\(319\) 7128.00 1.25107
\(320\) 0 0
\(321\) 2000.00 0.347754
\(322\) 0 0
\(323\) 12760.0 2.19810
\(324\) 0 0
\(325\) 1050.00 0.179211
\(326\) 0 0
\(327\) −4184.00 −0.707571
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −9212.00 −1.52972 −0.764860 − 0.644197i \(-0.777192\pi\)
−0.764860 + 0.644197i \(0.777192\pi\)
\(332\) 0 0
\(333\) 2838.00 0.467031
\(334\) 0 0
\(335\) −3460.00 −0.564298
\(336\) 0 0
\(337\) −3278.00 −0.529864 −0.264932 − 0.964267i \(-0.585349\pi\)
−0.264932 + 0.964267i \(0.585349\pi\)
\(338\) 0 0
\(339\) 2232.00 0.357598
\(340\) 0 0
\(341\) −8640.00 −1.37209
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 320.000 0.0499369
\(346\) 0 0
\(347\) 4956.00 0.766721 0.383360 − 0.923599i \(-0.374767\pi\)
0.383360 + 0.923599i \(0.374767\pi\)
\(348\) 0 0
\(349\) −4678.00 −0.717500 −0.358750 − 0.933434i \(-0.616797\pi\)
−0.358750 + 0.933434i \(0.616797\pi\)
\(350\) 0 0
\(351\) 6384.00 0.970805
\(352\) 0 0
\(353\) −1890.00 −0.284970 −0.142485 − 0.989797i \(-0.545509\pi\)
−0.142485 + 0.989797i \(0.545509\pi\)
\(354\) 0 0
\(355\) −840.000 −0.125585
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6472.00 −0.951474 −0.475737 − 0.879588i \(-0.657819\pi\)
−0.475737 + 0.879588i \(0.657819\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) 0 0
\(363\) 140.000 0.0202427
\(364\) 0 0
\(365\) −670.000 −0.0960806
\(366\) 0 0
\(367\) −1960.00 −0.278777 −0.139389 − 0.990238i \(-0.544514\pi\)
−0.139389 + 0.990238i \(0.544514\pi\)
\(368\) 0 0
\(369\) 4862.00 0.685923
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 8750.00 1.21463 0.607316 − 0.794460i \(-0.292246\pi\)
0.607316 + 0.794460i \(0.292246\pi\)
\(374\) 0 0
\(375\) 500.000 0.0688530
\(376\) 0 0
\(377\) 8316.00 1.13606
\(378\) 0 0
\(379\) −380.000 −0.0515021 −0.0257510 − 0.999668i \(-0.508198\pi\)
−0.0257510 + 0.999668i \(0.508198\pi\)
\(380\) 0 0
\(381\) 1312.00 0.176419
\(382\) 0 0
\(383\) 9688.00 1.29252 0.646258 − 0.763119i \(-0.276333\pi\)
0.646258 + 0.763119i \(0.276333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3212.00 0.421900
\(388\) 0 0
\(389\) 3870.00 0.504413 0.252207 − 0.967673i \(-0.418844\pi\)
0.252207 + 0.967673i \(0.418844\pi\)
\(390\) 0 0
\(391\) 1760.00 0.227639
\(392\) 0 0
\(393\) −848.000 −0.108845
\(394\) 0 0
\(395\) −3920.00 −0.499333
\(396\) 0 0
\(397\) −1622.00 −0.205053 −0.102526 − 0.994730i \(-0.532693\pi\)
−0.102526 + 0.994730i \(0.532693\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9906.00 1.23362 0.616811 − 0.787112i \(-0.288424\pi\)
0.616811 + 0.787112i \(0.288424\pi\)
\(402\) 0 0
\(403\) −10080.0 −1.24596
\(404\) 0 0
\(405\) 1555.00 0.190787
\(406\) 0 0
\(407\) −9288.00 −1.13118
\(408\) 0 0
\(409\) 4214.00 0.509459 0.254730 − 0.967012i \(-0.418014\pi\)
0.254730 + 0.967012i \(0.418014\pi\)
\(410\) 0 0
\(411\) −5736.00 −0.688409
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2820.00 0.333562
\(416\) 0 0
\(417\) 8784.00 1.03155
\(418\) 0 0
\(419\) 7012.00 0.817562 0.408781 − 0.912632i \(-0.365954\pi\)
0.408781 + 0.912632i \(0.365954\pi\)
\(420\) 0 0
\(421\) −1602.00 −0.185455 −0.0927277 − 0.995692i \(-0.529559\pi\)
−0.0927277 + 0.995692i \(0.529559\pi\)
\(422\) 0 0
\(423\) 4312.00 0.495642
\(424\) 0 0
\(425\) 2750.00 0.313870
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −6048.00 −0.680653
\(430\) 0 0
\(431\) −3584.00 −0.400546 −0.200273 − 0.979740i \(-0.564183\pi\)
−0.200273 + 0.979740i \(0.564183\pi\)
\(432\) 0 0
\(433\) 3470.00 0.385121 0.192561 − 0.981285i \(-0.438321\pi\)
0.192561 + 0.981285i \(0.438321\pi\)
\(434\) 0 0
\(435\) 3960.00 0.436477
\(436\) 0 0
\(437\) 1856.00 0.203168
\(438\) 0 0
\(439\) 3416.00 0.371382 0.185691 − 0.982608i \(-0.440548\pi\)
0.185691 + 0.982608i \(0.440548\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9708.00 1.04118 0.520588 − 0.853808i \(-0.325713\pi\)
0.520588 + 0.853808i \(0.325713\pi\)
\(444\) 0 0
\(445\) 5170.00 0.550745
\(446\) 0 0
\(447\) 9672.00 1.02342
\(448\) 0 0
\(449\) −10366.0 −1.08954 −0.544768 − 0.838587i \(-0.683382\pi\)
−0.544768 + 0.838587i \(0.683382\pi\)
\(450\) 0 0
\(451\) −15912.0 −1.66135
\(452\) 0 0
\(453\) −14688.0 −1.52340
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16742.0 −1.71369 −0.856847 − 0.515572i \(-0.827580\pi\)
−0.856847 + 0.515572i \(0.827580\pi\)
\(458\) 0 0
\(459\) 16720.0 1.70027
\(460\) 0 0
\(461\) 1258.00 0.127095 0.0635476 − 0.997979i \(-0.479759\pi\)
0.0635476 + 0.997979i \(0.479759\pi\)
\(462\) 0 0
\(463\) 13528.0 1.35788 0.678941 − 0.734193i \(-0.262439\pi\)
0.678941 + 0.734193i \(0.262439\pi\)
\(464\) 0 0
\(465\) −4800.00 −0.478698
\(466\) 0 0
\(467\) −6916.00 −0.685298 −0.342649 − 0.939463i \(-0.611324\pi\)
−0.342649 + 0.939463i \(0.611324\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1432.00 0.140091
\(472\) 0 0
\(473\) −10512.0 −1.02187
\(474\) 0 0
\(475\) 2900.00 0.280129
\(476\) 0 0
\(477\) −1562.00 −0.149935
\(478\) 0 0
\(479\) −1728.00 −0.164832 −0.0824158 − 0.996598i \(-0.526264\pi\)
−0.0824158 + 0.996598i \(0.526264\pi\)
\(480\) 0 0
\(481\) −10836.0 −1.02719
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1910.00 −0.178822
\(486\) 0 0
\(487\) 16656.0 1.54981 0.774903 − 0.632080i \(-0.217799\pi\)
0.774903 + 0.632080i \(0.217799\pi\)
\(488\) 0 0
\(489\) −10256.0 −0.948451
\(490\) 0 0
\(491\) −1084.00 −0.0996339 −0.0498169 − 0.998758i \(-0.515864\pi\)
−0.0498169 + 0.998758i \(0.515864\pi\)
\(492\) 0 0
\(493\) 21780.0 1.98970
\(494\) 0 0
\(495\) 1980.00 0.179787
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5804.00 0.520687 0.260343 − 0.965516i \(-0.416164\pi\)
0.260343 + 0.965516i \(0.416164\pi\)
\(500\) 0 0
\(501\) −12224.0 −1.09008
\(502\) 0 0
\(503\) −10512.0 −0.931823 −0.465911 − 0.884831i \(-0.654273\pi\)
−0.465911 + 0.884831i \(0.654273\pi\)
\(504\) 0 0
\(505\) −3370.00 −0.296956
\(506\) 0 0
\(507\) 1732.00 0.151718
\(508\) 0 0
\(509\) 4314.00 0.375667 0.187834 − 0.982201i \(-0.439853\pi\)
0.187834 + 0.982201i \(0.439853\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 17632.0 1.51749
\(514\) 0 0
\(515\) −4960.00 −0.424396
\(516\) 0 0
\(517\) −14112.0 −1.20047
\(518\) 0 0
\(519\) −936.000 −0.0791635
\(520\) 0 0
\(521\) 1190.00 0.100067 0.0500334 − 0.998748i \(-0.484067\pi\)
0.0500334 + 0.998748i \(0.484067\pi\)
\(522\) 0 0
\(523\) 3780.00 0.316038 0.158019 − 0.987436i \(-0.449489\pi\)
0.158019 + 0.987436i \(0.449489\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26400.0 −2.18217
\(528\) 0 0
\(529\) −11911.0 −0.978959
\(530\) 0 0
\(531\) −3828.00 −0.312846
\(532\) 0 0
\(533\) −18564.0 −1.50862
\(534\) 0 0
\(535\) 2500.00 0.202027
\(536\) 0 0
\(537\) −2096.00 −0.168434
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11002.0 −0.874331 −0.437165 − 0.899381i \(-0.644018\pi\)
−0.437165 + 0.899381i \(0.644018\pi\)
\(542\) 0 0
\(543\) −4552.00 −0.359751
\(544\) 0 0
\(545\) −5230.00 −0.411062
\(546\) 0 0
\(547\) 5908.00 0.461806 0.230903 − 0.972977i \(-0.425832\pi\)
0.230903 + 0.972977i \(0.425832\pi\)
\(548\) 0 0
\(549\) −6270.00 −0.487426
\(550\) 0 0
\(551\) 22968.0 1.77581
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −5160.00 −0.394648
\(556\) 0 0
\(557\) 14806.0 1.12630 0.563151 − 0.826354i \(-0.309589\pi\)
0.563151 + 0.826354i \(0.309589\pi\)
\(558\) 0 0
\(559\) −12264.0 −0.927928
\(560\) 0 0
\(561\) −15840.0 −1.19210
\(562\) 0 0
\(563\) 684.000 0.0512028 0.0256014 − 0.999672i \(-0.491850\pi\)
0.0256014 + 0.999672i \(0.491850\pi\)
\(564\) 0 0
\(565\) 2790.00 0.207745
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2582.00 −0.190234 −0.0951169 − 0.995466i \(-0.530323\pi\)
−0.0951169 + 0.995466i \(0.530323\pi\)
\(570\) 0 0
\(571\) −2540.00 −0.186157 −0.0930785 − 0.995659i \(-0.529671\pi\)
−0.0930785 + 0.995659i \(0.529671\pi\)
\(572\) 0 0
\(573\) −6080.00 −0.443273
\(574\) 0 0
\(575\) 400.000 0.0290107
\(576\) 0 0
\(577\) −22786.0 −1.64401 −0.822005 − 0.569480i \(-0.807144\pi\)
−0.822005 + 0.569480i \(0.807144\pi\)
\(578\) 0 0
\(579\) 8568.00 0.614981
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 5112.00 0.363152
\(584\) 0 0
\(585\) 2310.00 0.163259
\(586\) 0 0
\(587\) −7884.00 −0.554357 −0.277178 − 0.960818i \(-0.589399\pi\)
−0.277178 + 0.960818i \(0.589399\pi\)
\(588\) 0 0
\(589\) −27840.0 −1.94758
\(590\) 0 0
\(591\) 9224.00 0.642005
\(592\) 0 0
\(593\) 21902.0 1.51671 0.758354 − 0.651843i \(-0.226004\pi\)
0.758354 + 0.651843i \(0.226004\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 13152.0 0.901634
\(598\) 0 0
\(599\) 15080.0 1.02863 0.514317 − 0.857600i \(-0.328045\pi\)
0.514317 + 0.857600i \(0.328045\pi\)
\(600\) 0 0
\(601\) 19702.0 1.33721 0.668603 − 0.743619i \(-0.266892\pi\)
0.668603 + 0.743619i \(0.266892\pi\)
\(602\) 0 0
\(603\) −7612.00 −0.514071
\(604\) 0 0
\(605\) 175.000 0.0117599
\(606\) 0 0
\(607\) −7320.00 −0.489472 −0.244736 − 0.969590i \(-0.578701\pi\)
−0.244736 + 0.969590i \(0.578701\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16464.0 −1.09012
\(612\) 0 0
\(613\) 24350.0 1.60438 0.802192 − 0.597066i \(-0.203667\pi\)
0.802192 + 0.597066i \(0.203667\pi\)
\(614\) 0 0
\(615\) −8840.00 −0.579615
\(616\) 0 0
\(617\) 19546.0 1.27535 0.637676 − 0.770305i \(-0.279896\pi\)
0.637676 + 0.770305i \(0.279896\pi\)
\(618\) 0 0
\(619\) −3476.00 −0.225706 −0.112853 − 0.993612i \(-0.535999\pi\)
−0.112853 + 0.993612i \(0.535999\pi\)
\(620\) 0 0
\(621\) 2432.00 0.157154
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −16704.0 −1.06394
\(628\) 0 0
\(629\) −28380.0 −1.79902
\(630\) 0 0
\(631\) 21880.0 1.38039 0.690197 − 0.723621i \(-0.257524\pi\)
0.690197 + 0.723621i \(0.257524\pi\)
\(632\) 0 0
\(633\) 15504.0 0.973505
\(634\) 0 0
\(635\) 1640.00 0.102490
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1848.00 −0.114406
\(640\) 0 0
\(641\) 20994.0 1.29362 0.646812 − 0.762649i \(-0.276102\pi\)
0.646812 + 0.762649i \(0.276102\pi\)
\(642\) 0 0
\(643\) 18204.0 1.11648 0.558239 − 0.829680i \(-0.311477\pi\)
0.558239 + 0.829680i \(0.311477\pi\)
\(644\) 0 0
\(645\) −5840.00 −0.356511
\(646\) 0 0
\(647\) 2064.00 0.125416 0.0627080 − 0.998032i \(-0.480026\pi\)
0.0627080 + 0.998032i \(0.480026\pi\)
\(648\) 0 0
\(649\) 12528.0 0.757730
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9942.00 0.595805 0.297902 − 0.954596i \(-0.403713\pi\)
0.297902 + 0.954596i \(0.403713\pi\)
\(654\) 0 0
\(655\) −1060.00 −0.0632330
\(656\) 0 0
\(657\) −1474.00 −0.0875285
\(658\) 0 0
\(659\) 24236.0 1.43263 0.716313 − 0.697779i \(-0.245828\pi\)
0.716313 + 0.697779i \(0.245828\pi\)
\(660\) 0 0
\(661\) −17614.0 −1.03647 −0.518234 − 0.855239i \(-0.673410\pi\)
−0.518234 + 0.855239i \(0.673410\pi\)
\(662\) 0 0
\(663\) −18480.0 −1.08251
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3168.00 0.183906
\(668\) 0 0
\(669\) −22752.0 −1.31486
\(670\) 0 0
\(671\) 20520.0 1.18057
\(672\) 0 0
\(673\) 13058.0 0.747918 0.373959 − 0.927445i \(-0.378000\pi\)
0.373959 + 0.927445i \(0.378000\pi\)
\(674\) 0 0
\(675\) 3800.00 0.216685
\(676\) 0 0
\(677\) 33186.0 1.88396 0.941980 − 0.335668i \(-0.108962\pi\)
0.941980 + 0.335668i \(0.108962\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11184.0 −0.629327
\(682\) 0 0
\(683\) −31716.0 −1.77684 −0.888418 − 0.459035i \(-0.848195\pi\)
−0.888418 + 0.459035i \(0.848195\pi\)
\(684\) 0 0
\(685\) −7170.00 −0.399929
\(686\) 0 0
\(687\) 17784.0 0.987630
\(688\) 0 0
\(689\) 5964.00 0.329768
\(690\) 0 0
\(691\) 2084.00 0.114731 0.0573655 − 0.998353i \(-0.481730\pi\)
0.0573655 + 0.998353i \(0.481730\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10980.0 0.599274
\(696\) 0 0
\(697\) −48620.0 −2.64220
\(698\) 0 0
\(699\) −10088.0 −0.545870
\(700\) 0 0
\(701\) −7418.00 −0.399678 −0.199839 − 0.979829i \(-0.564042\pi\)
−0.199839 + 0.979829i \(0.564042\pi\)
\(702\) 0 0
\(703\) −29928.0 −1.60563
\(704\) 0 0
\(705\) −7840.00 −0.418825
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −18242.0 −0.966280 −0.483140 − 0.875543i \(-0.660504\pi\)
−0.483140 + 0.875543i \(0.660504\pi\)
\(710\) 0 0
\(711\) −8624.00 −0.454888
\(712\) 0 0
\(713\) −3840.00 −0.201696
\(714\) 0 0
\(715\) −7560.00 −0.395424
\(716\) 0 0
\(717\) −3264.00 −0.170009
\(718\) 0 0
\(719\) −3024.00 −0.156851 −0.0784257 − 0.996920i \(-0.524989\pi\)
−0.0784257 + 0.996920i \(0.524989\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −21688.0 −1.11561
\(724\) 0 0
\(725\) 4950.00 0.253570
\(726\) 0 0
\(727\) 26176.0 1.33537 0.667685 − 0.744444i \(-0.267285\pi\)
0.667685 + 0.744444i \(0.267285\pi\)
\(728\) 0 0
\(729\) 19837.0 1.00782
\(730\) 0 0
\(731\) −32120.0 −1.62517
\(732\) 0 0
\(733\) 17818.0 0.897848 0.448924 − 0.893570i \(-0.351807\pi\)
0.448924 + 0.893570i \(0.351807\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24912.0 1.24511
\(738\) 0 0
\(739\) −22052.0 −1.09769 −0.548847 − 0.835923i \(-0.684933\pi\)
−0.548847 + 0.835923i \(0.684933\pi\)
\(740\) 0 0
\(741\) −19488.0 −0.966140
\(742\) 0 0
\(743\) 15840.0 0.782117 0.391059 − 0.920366i \(-0.372109\pi\)
0.391059 + 0.920366i \(0.372109\pi\)
\(744\) 0 0
\(745\) 12090.0 0.594555
\(746\) 0 0
\(747\) 6204.00 0.303872
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 21024.0 1.02154 0.510770 − 0.859717i \(-0.329360\pi\)
0.510770 + 0.859717i \(0.329360\pi\)
\(752\) 0 0
\(753\) −23600.0 −1.14214
\(754\) 0 0
\(755\) −18360.0 −0.885018
\(756\) 0 0
\(757\) −38034.0 −1.82612 −0.913058 − 0.407831i \(-0.866285\pi\)
−0.913058 + 0.407831i \(0.866285\pi\)
\(758\) 0 0
\(759\) −2304.00 −0.110184
\(760\) 0 0
\(761\) −37802.0 −1.80069 −0.900343 − 0.435182i \(-0.856684\pi\)
−0.900343 + 0.435182i \(0.856684\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 6050.00 0.285932
\(766\) 0 0
\(767\) 14616.0 0.688075
\(768\) 0 0
\(769\) −15042.0 −0.705369 −0.352684 − 0.935742i \(-0.614731\pi\)
−0.352684 + 0.935742i \(0.614731\pi\)
\(770\) 0 0
\(771\) 21000.0 0.980929
\(772\) 0 0
\(773\) −5950.00 −0.276852 −0.138426 − 0.990373i \(-0.544204\pi\)
−0.138426 + 0.990373i \(0.544204\pi\)
\(774\) 0 0
\(775\) −6000.00 −0.278099
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −51272.0 −2.35816
\(780\) 0 0
\(781\) 6048.00 0.277099
\(782\) 0 0
\(783\) 30096.0 1.37362
\(784\) 0 0
\(785\) 1790.00 0.0813858
\(786\) 0 0
\(787\) −23364.0 −1.05824 −0.529121 − 0.848546i \(-0.677478\pi\)
−0.529121 + 0.848546i \(0.677478\pi\)
\(788\) 0 0
\(789\) −24960.0 −1.12624
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 23940.0 1.07205
\(794\) 0 0
\(795\) 2840.00 0.126697
\(796\) 0 0
\(797\) −19846.0 −0.882034 −0.441017 − 0.897499i \(-0.645382\pi\)
−0.441017 + 0.897499i \(0.645382\pi\)
\(798\) 0 0
\(799\) −43120.0 −1.90923
\(800\) 0 0
\(801\) 11374.0 0.501724
\(802\) 0 0
\(803\) 4824.00 0.211999
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2856.00 −0.124580
\(808\) 0 0
\(809\) 24762.0 1.07613 0.538063 − 0.842905i \(-0.319156\pi\)
0.538063 + 0.842905i \(0.319156\pi\)
\(810\) 0 0
\(811\) −16644.0 −0.720653 −0.360327 − 0.932826i \(-0.617335\pi\)
−0.360327 + 0.932826i \(0.617335\pi\)
\(812\) 0 0
\(813\) 8576.00 0.369955
\(814\) 0 0
\(815\) −12820.0 −0.551000
\(816\) 0 0
\(817\) −33872.0 −1.45047
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3182.00 0.135265 0.0676325 − 0.997710i \(-0.478455\pi\)
0.0676325 + 0.997710i \(0.478455\pi\)
\(822\) 0 0
\(823\) −7504.00 −0.317829 −0.158914 − 0.987292i \(-0.550799\pi\)
−0.158914 + 0.987292i \(0.550799\pi\)
\(824\) 0 0
\(825\) −3600.00 −0.151922
\(826\) 0 0
\(827\) 12604.0 0.529969 0.264984 − 0.964253i \(-0.414633\pi\)
0.264984 + 0.964253i \(0.414633\pi\)
\(828\) 0 0
\(829\) −12230.0 −0.512383 −0.256191 − 0.966626i \(-0.582468\pi\)
−0.256191 + 0.966626i \(0.582468\pi\)
\(830\) 0 0
\(831\) 17864.0 0.745722
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −15280.0 −0.633277
\(836\) 0 0
\(837\) −36480.0 −1.50649
\(838\) 0 0
\(839\) −9656.00 −0.397333 −0.198666 − 0.980067i \(-0.563661\pi\)
−0.198666 + 0.980067i \(0.563661\pi\)
\(840\) 0 0
\(841\) 14815.0 0.607446
\(842\) 0 0
\(843\) 21208.0 0.866480
\(844\) 0 0
\(845\) 2165.00 0.0881400
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −27728.0 −1.12087
\(850\) 0 0
\(851\) −4128.00 −0.166282
\(852\) 0 0
\(853\) −5806.00 −0.233052 −0.116526 − 0.993188i \(-0.537176\pi\)
−0.116526 + 0.993188i \(0.537176\pi\)
\(854\) 0 0
\(855\) 6380.00 0.255195
\(856\) 0 0
\(857\) 39094.0 1.55826 0.779128 − 0.626865i \(-0.215662\pi\)
0.779128 + 0.626865i \(0.215662\pi\)
\(858\) 0 0
\(859\) 18876.0 0.749756 0.374878 − 0.927074i \(-0.377685\pi\)
0.374878 + 0.927074i \(0.377685\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 32296.0 1.27389 0.636946 − 0.770909i \(-0.280197\pi\)
0.636946 + 0.770909i \(0.280197\pi\)
\(864\) 0 0
\(865\) −1170.00 −0.0459898
\(866\) 0 0
\(867\) −28748.0 −1.12611
\(868\) 0 0
\(869\) 28224.0 1.10176
\(870\) 0 0
\(871\) 29064.0 1.13065
\(872\) 0 0
\(873\) −4202.00 −0.162905
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −9578.00 −0.368787 −0.184393 − 0.982853i \(-0.559032\pi\)
−0.184393 + 0.982853i \(0.559032\pi\)
\(878\) 0 0
\(879\) −16136.0 −0.619174
\(880\) 0 0
\(881\) 41710.0 1.59506 0.797529 − 0.603281i \(-0.206140\pi\)
0.797529 + 0.603281i \(0.206140\pi\)
\(882\) 0 0
\(883\) 2260.00 0.0861326 0.0430663 − 0.999072i \(-0.486287\pi\)
0.0430663 + 0.999072i \(0.486287\pi\)
\(884\) 0 0
\(885\) 6960.00 0.264359
\(886\) 0 0
\(887\) 33696.0 1.27554 0.637768 − 0.770228i \(-0.279858\pi\)
0.637768 + 0.770228i \(0.279858\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −11196.0 −0.420965
\(892\) 0 0
\(893\) −45472.0 −1.70399
\(894\) 0 0
\(895\) −2620.00 −0.0978513
\(896\) 0 0
\(897\) −2688.00 −0.100055
\(898\) 0 0
\(899\) −47520.0 −1.76294
\(900\) 0 0
\(901\) 15620.0 0.577556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5690.00 −0.208997
\(906\) 0 0
\(907\) 7756.00 0.283940 0.141970 − 0.989871i \(-0.454656\pi\)
0.141970 + 0.989871i \(0.454656\pi\)
\(908\) 0 0
\(909\) −7414.00 −0.270525
\(910\) 0 0
\(911\) −5312.00 −0.193188 −0.0965941 − 0.995324i \(-0.530795\pi\)
−0.0965941 + 0.995324i \(0.530795\pi\)
\(912\) 0 0
\(913\) −20304.0 −0.735996
\(914\) 0 0
\(915\) 11400.0 0.411882
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −23576.0 −0.846246 −0.423123 − 0.906072i \(-0.639066\pi\)
−0.423123 + 0.906072i \(0.639066\pi\)
\(920\) 0 0
\(921\) −15344.0 −0.548971
\(922\) 0 0
\(923\) 7056.00 0.251626
\(924\) 0 0
\(925\) −6450.00 −0.229270
\(926\) 0 0
\(927\) −10912.0 −0.386620
\(928\) 0 0
\(929\) 19038.0 0.672354 0.336177 − 0.941799i \(-0.390866\pi\)
0.336177 + 0.941799i \(0.390866\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2656.00 0.0931978
\(934\) 0 0
\(935\) −19800.0 −0.692545
\(936\) 0 0
\(937\) −20570.0 −0.717175 −0.358587 − 0.933496i \(-0.616741\pi\)
−0.358587 + 0.933496i \(0.616741\pi\)
\(938\) 0 0
\(939\) 11944.0 0.415099
\(940\) 0 0
\(941\) 21386.0 0.740875 0.370438 − 0.928857i \(-0.379208\pi\)
0.370438 + 0.928857i \(0.379208\pi\)
\(942\) 0 0
\(943\) −7072.00 −0.244216
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 38020.0 1.30463 0.652315 − 0.757948i \(-0.273798\pi\)
0.652315 + 0.757948i \(0.273798\pi\)
\(948\) 0 0
\(949\) 5628.00 0.192511
\(950\) 0 0
\(951\) −10904.0 −0.371805
\(952\) 0 0
\(953\) 20202.0 0.686681 0.343340 − 0.939211i \(-0.388442\pi\)
0.343340 + 0.939211i \(0.388442\pi\)
\(954\) 0 0
\(955\) −7600.00 −0.257519
\(956\) 0 0
\(957\) −28512.0 −0.963074
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 27809.0 0.933470
\(962\) 0 0
\(963\) 5500.00 0.184045
\(964\) 0 0
\(965\) 10710.0 0.357272
\(966\) 0 0
\(967\) 29840.0 0.992337 0.496168 − 0.868226i \(-0.334740\pi\)
0.496168 + 0.868226i \(0.334740\pi\)
\(968\) 0 0
\(969\) −51040.0 −1.69210
\(970\) 0 0
\(971\) 12476.0 0.412332 0.206166 − 0.978517i \(-0.433901\pi\)
0.206166 + 0.978517i \(0.433901\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −4200.00 −0.137957
\(976\) 0 0
\(977\) −36974.0 −1.21075 −0.605375 − 0.795940i \(-0.706977\pi\)
−0.605375 + 0.795940i \(0.706977\pi\)
\(978\) 0 0
\(979\) −37224.0 −1.21520
\(980\) 0 0
\(981\) −11506.0 −0.374473
\(982\) 0 0
\(983\) 16368.0 0.531087 0.265543 − 0.964099i \(-0.414449\pi\)
0.265543 + 0.964099i \(0.414449\pi\)
\(984\) 0 0
\(985\) 11530.0 0.372971
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4672.00 −0.150213
\(990\) 0 0
\(991\) −49552.0 −1.58837 −0.794183 − 0.607678i \(-0.792101\pi\)
−0.794183 + 0.607678i \(0.792101\pi\)
\(992\) 0 0
\(993\) 36848.0 1.17758
\(994\) 0 0
\(995\) 16440.0 0.523802
\(996\) 0 0
\(997\) −24414.0 −0.775526 −0.387763 − 0.921759i \(-0.626752\pi\)
−0.387763 + 0.921759i \(0.626752\pi\)
\(998\) 0 0
\(999\) −39216.0 −1.24198
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 1960.4.a.e.1.1 1
7.6 odd 2 40.4.a.b.1.1 ✓ 1
21.20 even 2 360.4.a.f.1.1 1
28.27 even 2 80.4.a.b.1.1 1
35.13 even 4 200.4.c.f.49.2 2
35.27 even 4 200.4.c.f.49.1 2
35.34 odd 2 200.4.a.d.1.1 1
56.13 odd 2 320.4.a.e.1.1 1
56.27 even 2 320.4.a.j.1.1 1
84.83 odd 2 720.4.a.d.1.1 1
105.62 odd 4 1800.4.f.d.649.2 2
105.83 odd 4 1800.4.f.d.649.1 2
105.104 even 2 1800.4.a.h.1.1 1
112.13 odd 4 1280.4.d.d.641.2 2
112.27 even 4 1280.4.d.m.641.2 2
112.69 odd 4 1280.4.d.d.641.1 2
112.83 even 4 1280.4.d.m.641.1 2
140.27 odd 4 400.4.c.h.49.2 2
140.83 odd 4 400.4.c.h.49.1 2
140.139 even 2 400.4.a.p.1.1 1
280.69 odd 2 1600.4.a.bk.1.1 1
280.139 even 2 1600.4.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.b.1.1 ✓ 1 7.6 odd 2
80.4.a.b.1.1 1 28.27 even 2
200.4.a.d.1.1 1 35.34 odd 2
200.4.c.f.49.1 2 35.27 even 4
200.4.c.f.49.2 2 35.13 even 4
320.4.a.e.1.1 1 56.13 odd 2
320.4.a.j.1.1 1 56.27 even 2
360.4.a.f.1.1 1 21.20 even 2
400.4.a.p.1.1 1 140.139 even 2
400.4.c.h.49.1 2 140.83 odd 4
400.4.c.h.49.2 2 140.27 odd 4
720.4.a.d.1.1 1 84.83 odd 2
1280.4.d.d.641.1 2 112.69 odd 4
1280.4.d.d.641.2 2 112.13 odd 4
1280.4.d.m.641.1 2 112.83 even 4
1280.4.d.m.641.2 2 112.27 even 4
1600.4.a.q.1.1 1 280.139 even 2
1600.4.a.bk.1.1 1 280.69 odd 2
1800.4.a.h.1.1 1 105.104 even 2
1800.4.f.d.649.1 2 105.83 odd 4
1800.4.f.d.649.2 2 105.62 odd 4
1960.4.a.e.1.1 1 1.1 even 1 trivial