Properties

Label 1170.4.a.f.1.1
Level $1170$
Weight $4$
Character 1170.1
Self dual yes
Analytic conductor $69.032$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1170,4,Mod(1,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1170.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1170.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: \(69.0322347067\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 130)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1170.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -8.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -8.00000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +32.0000 q^{11} -13.0000 q^{13} +16.0000 q^{14} +16.0000 q^{16} +86.0000 q^{17} -56.0000 q^{19} +20.0000 q^{20} -64.0000 q^{22} -68.0000 q^{23} +25.0000 q^{25} +26.0000 q^{26} -32.0000 q^{28} +202.000 q^{29} -56.0000 q^{31} -32.0000 q^{32} -172.000 q^{34} -40.0000 q^{35} +66.0000 q^{37} +112.000 q^{38} -40.0000 q^{40} -490.000 q^{41} +460.000 q^{43} +128.000 q^{44} +136.000 q^{46} +24.0000 q^{47} -279.000 q^{49} -50.0000 q^{50} -52.0000 q^{52} +294.000 q^{53} +160.000 q^{55} +64.0000 q^{56} -404.000 q^{58} +480.000 q^{59} -338.000 q^{61} +112.000 q^{62} +64.0000 q^{64} -65.0000 q^{65} +676.000 q^{67} +344.000 q^{68} +80.0000 q^{70} -120.000 q^{71} -210.000 q^{73} -132.000 q^{74} -224.000 q^{76} -256.000 q^{77} +184.000 q^{79} +80.0000 q^{80} +980.000 q^{82} +660.000 q^{83} +430.000 q^{85} -920.000 q^{86} -256.000 q^{88} +286.000 q^{89} +104.000 q^{91} -272.000 q^{92} -48.0000 q^{94} -280.000 q^{95} -1202.00 q^{97} +558.000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −8.00000 −0.431959 −0.215980 0.976398i \(-0.569295\pi\)
−0.215980 + 0.976398i \(0.569295\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) 32.0000 0.877124 0.438562 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 16.0000 0.305441
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 86.0000 1.22694 0.613472 0.789716i \(-0.289772\pi\)
0.613472 + 0.789716i \(0.289772\pi\)
\(18\) 0 0
\(19\) −56.0000 −0.676173 −0.338086 0.941115i \(-0.609780\pi\)
−0.338086 + 0.941115i \(0.609780\pi\)
\(20\) 20.0000 0.223607
\(21\) 0 0
\(22\) −64.0000 −0.620220
\(23\) −68.0000 −0.616477 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 26.0000 0.196116
\(27\) 0 0
\(28\) −32.0000 −0.215980
\(29\) 202.000 1.29346 0.646732 0.762717i \(-0.276135\pi\)
0.646732 + 0.762717i \(0.276135\pi\)
\(30\) 0 0
\(31\) −56.0000 −0.324448 −0.162224 0.986754i \(-0.551867\pi\)
−0.162224 + 0.986754i \(0.551867\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) −172.000 −0.867581
\(35\) −40.0000 −0.193178
\(36\) 0 0
\(37\) 66.0000 0.293252 0.146626 0.989192i \(-0.453159\pi\)
0.146626 + 0.989192i \(0.453159\pi\)
\(38\) 112.000 0.478126
\(39\) 0 0
\(40\) −40.0000 −0.158114
\(41\) −490.000 −1.86647 −0.933233 0.359271i \(-0.883026\pi\)
−0.933233 + 0.359271i \(0.883026\pi\)
\(42\) 0 0
\(43\) 460.000 1.63138 0.815690 0.578489i \(-0.196358\pi\)
0.815690 + 0.578489i \(0.196358\pi\)
\(44\) 128.000 0.438562
\(45\) 0 0
\(46\) 136.000 0.435915
\(47\) 24.0000 0.0744843 0.0372421 0.999306i \(-0.488143\pi\)
0.0372421 + 0.999306i \(0.488143\pi\)
\(48\) 0 0
\(49\) −279.000 −0.813411
\(50\) −50.0000 −0.141421
\(51\) 0 0
\(52\) −52.0000 −0.138675
\(53\) 294.000 0.761962 0.380981 0.924583i \(-0.375586\pi\)
0.380981 + 0.924583i \(0.375586\pi\)
\(54\) 0 0
\(55\) 160.000 0.392262
\(56\) 64.0000 0.152721
\(57\) 0 0
\(58\) −404.000 −0.914617
\(59\) 480.000 1.05916 0.529582 0.848259i \(-0.322349\pi\)
0.529582 + 0.848259i \(0.322349\pi\)
\(60\) 0 0
\(61\) −338.000 −0.709450 −0.354725 0.934971i \(-0.615426\pi\)
−0.354725 + 0.934971i \(0.615426\pi\)
\(62\) 112.000 0.229420
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −65.0000 −0.124035
\(66\) 0 0
\(67\) 676.000 1.23263 0.616317 0.787498i \(-0.288624\pi\)
0.616317 + 0.787498i \(0.288624\pi\)
\(68\) 344.000 0.613472
\(69\) 0 0
\(70\) 80.0000 0.136598
\(71\) −120.000 −0.200583 −0.100291 0.994958i \(-0.531978\pi\)
−0.100291 + 0.994958i \(0.531978\pi\)
\(72\) 0 0
\(73\) −210.000 −0.336694 −0.168347 0.985728i \(-0.553843\pi\)
−0.168347 + 0.985728i \(0.553843\pi\)
\(74\) −132.000 −0.207361
\(75\) 0 0
\(76\) −224.000 −0.338086
\(77\) −256.000 −0.378882
\(78\) 0 0
\(79\) 184.000 0.262046 0.131023 0.991379i \(-0.458174\pi\)
0.131023 + 0.991379i \(0.458174\pi\)
\(80\) 80.0000 0.111803
\(81\) 0 0
\(82\) 980.000 1.31979
\(83\) 660.000 0.872824 0.436412 0.899747i \(-0.356249\pi\)
0.436412 + 0.899747i \(0.356249\pi\)
\(84\) 0 0
\(85\) 430.000 0.548706
\(86\) −920.000 −1.15356
\(87\) 0 0
\(88\) −256.000 −0.310110
\(89\) 286.000 0.340629 0.170314 0.985390i \(-0.445522\pi\)
0.170314 + 0.985390i \(0.445522\pi\)
\(90\) 0 0
\(91\) 104.000 0.119804
\(92\) −272.000 −0.308239
\(93\) 0 0
\(94\) −48.0000 −0.0526683
\(95\) −280.000 −0.302394
\(96\) 0 0
\(97\) −1202.00 −1.25819 −0.629096 0.777328i \(-0.716575\pi\)
−0.629096 + 0.777328i \(0.716575\pi\)
\(98\) 558.000 0.575168
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) 1066.00 1.05021 0.525104 0.851038i \(-0.324026\pi\)
0.525104 + 0.851038i \(0.324026\pi\)
\(102\) 0 0
\(103\) 556.000 0.531886 0.265943 0.963989i \(-0.414317\pi\)
0.265943 + 0.963989i \(0.414317\pi\)
\(104\) 104.000 0.0980581
\(105\) 0 0
\(106\) −588.000 −0.538789
\(107\) −412.000 −0.372239 −0.186119 0.982527i \(-0.559591\pi\)
−0.186119 + 0.982527i \(0.559591\pi\)
\(108\) 0 0
\(109\) −1814.00 −1.59403 −0.797017 0.603957i \(-0.793590\pi\)
−0.797017 + 0.603957i \(0.793590\pi\)
\(110\) −320.000 −0.277371
\(111\) 0 0
\(112\) −128.000 −0.107990
\(113\) 454.000 0.377953 0.188977 0.981982i \(-0.439483\pi\)
0.188977 + 0.981982i \(0.439483\pi\)
\(114\) 0 0
\(115\) −340.000 −0.275697
\(116\) 808.000 0.646732
\(117\) 0 0
\(118\) −960.000 −0.748942
\(119\) −688.000 −0.529990
\(120\) 0 0
\(121\) −307.000 −0.230654
\(122\) 676.000 0.501657
\(123\) 0 0
\(124\) −224.000 −0.162224
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −508.000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 130.000 0.0877058
\(131\) 1876.00 1.25120 0.625599 0.780145i \(-0.284855\pi\)
0.625599 + 0.780145i \(0.284855\pi\)
\(132\) 0 0
\(133\) 448.000 0.292079
\(134\) −1352.00 −0.871605
\(135\) 0 0
\(136\) −688.000 −0.433791
\(137\) −574.000 −0.357957 −0.178979 0.983853i \(-0.557279\pi\)
−0.178979 + 0.983853i \(0.557279\pi\)
\(138\) 0 0
\(139\) −1852.00 −1.13010 −0.565052 0.825055i \(-0.691144\pi\)
−0.565052 + 0.825055i \(0.691144\pi\)
\(140\) −160.000 −0.0965891
\(141\) 0 0
\(142\) 240.000 0.141833
\(143\) −416.000 −0.243270
\(144\) 0 0
\(145\) 1010.00 0.578455
\(146\) 420.000 0.238078
\(147\) 0 0
\(148\) 264.000 0.146626
\(149\) 2902.00 1.59558 0.797789 0.602937i \(-0.206003\pi\)
0.797789 + 0.602937i \(0.206003\pi\)
\(150\) 0 0
\(151\) 1736.00 0.935587 0.467794 0.883838i \(-0.345049\pi\)
0.467794 + 0.883838i \(0.345049\pi\)
\(152\) 448.000 0.239063
\(153\) 0 0
\(154\) 512.000 0.267910
\(155\) −280.000 −0.145098
\(156\) 0 0
\(157\) 3770.00 1.91643 0.958213 0.286057i \(-0.0923447\pi\)
0.958213 + 0.286057i \(0.0923447\pi\)
\(158\) −368.000 −0.185294
\(159\) 0 0
\(160\) −160.000 −0.0790569
\(161\) 544.000 0.266293
\(162\) 0 0
\(163\) 2028.00 0.974511 0.487255 0.873260i \(-0.337998\pi\)
0.487255 + 0.873260i \(0.337998\pi\)
\(164\) −1960.00 −0.933233
\(165\) 0 0
\(166\) −1320.00 −0.617180
\(167\) 240.000 0.111208 0.0556041 0.998453i \(-0.482292\pi\)
0.0556041 + 0.998453i \(0.482292\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) −860.000 −0.387994
\(171\) 0 0
\(172\) 1840.00 0.815690
\(173\) 1630.00 0.716339 0.358169 0.933657i \(-0.383401\pi\)
0.358169 + 0.933657i \(0.383401\pi\)
\(174\) 0 0
\(175\) −200.000 −0.0863919
\(176\) 512.000 0.219281
\(177\) 0 0
\(178\) −572.000 −0.240861
\(179\) −764.000 −0.319017 −0.159508 0.987197i \(-0.550991\pi\)
−0.159508 + 0.987197i \(0.550991\pi\)
\(180\) 0 0
\(181\) 1790.00 0.735081 0.367540 0.930008i \(-0.380200\pi\)
0.367540 + 0.930008i \(0.380200\pi\)
\(182\) −208.000 −0.0847142
\(183\) 0 0
\(184\) 544.000 0.217958
\(185\) 330.000 0.131146
\(186\) 0 0
\(187\) 2752.00 1.07618
\(188\) 96.0000 0.0372421
\(189\) 0 0
\(190\) 560.000 0.213825
\(191\) −2440.00 −0.924357 −0.462179 0.886787i \(-0.652932\pi\)
−0.462179 + 0.886787i \(0.652932\pi\)
\(192\) 0 0
\(193\) 3102.00 1.15693 0.578463 0.815708i \(-0.303653\pi\)
0.578463 + 0.815708i \(0.303653\pi\)
\(194\) 2404.00 0.889676
\(195\) 0 0
\(196\) −1116.00 −0.406706
\(197\) 1982.00 0.716810 0.358405 0.933566i \(-0.383321\pi\)
0.358405 + 0.933566i \(0.383321\pi\)
\(198\) 0 0
\(199\) −2520.00 −0.897679 −0.448839 0.893612i \(-0.648162\pi\)
−0.448839 + 0.893612i \(0.648162\pi\)
\(200\) −200.000 −0.0707107
\(201\) 0 0
\(202\) −2132.00 −0.742609
\(203\) −1616.00 −0.558724
\(204\) 0 0
\(205\) −2450.00 −0.834709
\(206\) −1112.00 −0.376101
\(207\) 0 0
\(208\) −208.000 −0.0693375
\(209\) −1792.00 −0.593087
\(210\) 0 0
\(211\) 3188.00 1.04015 0.520073 0.854122i \(-0.325905\pi\)
0.520073 + 0.854122i \(0.325905\pi\)
\(212\) 1176.00 0.380981
\(213\) 0 0
\(214\) 824.000 0.263213
\(215\) 2300.00 0.729575
\(216\) 0 0
\(217\) 448.000 0.140148
\(218\) 3628.00 1.12715
\(219\) 0 0
\(220\) 640.000 0.196131
\(221\) −1118.00 −0.340293
\(222\) 0 0
\(223\) 6392.00 1.91946 0.959731 0.280921i \(-0.0906399\pi\)
0.959731 + 0.280921i \(0.0906399\pi\)
\(224\) 256.000 0.0763604
\(225\) 0 0
\(226\) −908.000 −0.267253
\(227\) 5748.00 1.68065 0.840326 0.542081i \(-0.182363\pi\)
0.840326 + 0.542081i \(0.182363\pi\)
\(228\) 0 0
\(229\) 2410.00 0.695447 0.347723 0.937597i \(-0.386955\pi\)
0.347723 + 0.937597i \(0.386955\pi\)
\(230\) 680.000 0.194947
\(231\) 0 0
\(232\) −1616.00 −0.457309
\(233\) 1358.00 0.381826 0.190913 0.981607i \(-0.438855\pi\)
0.190913 + 0.981607i \(0.438855\pi\)
\(234\) 0 0
\(235\) 120.000 0.0333104
\(236\) 1920.00 0.529582
\(237\) 0 0
\(238\) 1376.00 0.374760
\(239\) −3256.00 −0.881226 −0.440613 0.897697i \(-0.645239\pi\)
−0.440613 + 0.897697i \(0.645239\pi\)
\(240\) 0 0
\(241\) 4898.00 1.30916 0.654581 0.755992i \(-0.272845\pi\)
0.654581 + 0.755992i \(0.272845\pi\)
\(242\) 614.000 0.163097
\(243\) 0 0
\(244\) −1352.00 −0.354725
\(245\) −1395.00 −0.363768
\(246\) 0 0
\(247\) 728.000 0.187537
\(248\) 448.000 0.114710
\(249\) 0 0
\(250\) −250.000 −0.0632456
\(251\) 4100.00 1.03103 0.515517 0.856879i \(-0.327600\pi\)
0.515517 + 0.856879i \(0.327600\pi\)
\(252\) 0 0
\(253\) −2176.00 −0.540727
\(254\) 1016.00 0.250982
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 5270.00 1.27912 0.639559 0.768742i \(-0.279117\pi\)
0.639559 + 0.768742i \(0.279117\pi\)
\(258\) 0 0
\(259\) −528.000 −0.126673
\(260\) −260.000 −0.0620174
\(261\) 0 0
\(262\) −3752.00 −0.884730
\(263\) 84.0000 0.0196945 0.00984727 0.999952i \(-0.496865\pi\)
0.00984727 + 0.999952i \(0.496865\pi\)
\(264\) 0 0
\(265\) 1470.00 0.340760
\(266\) −896.000 −0.206531
\(267\) 0 0
\(268\) 2704.00 0.616317
\(269\) 7186.00 1.62877 0.814383 0.580328i \(-0.197075\pi\)
0.814383 + 0.580328i \(0.197075\pi\)
\(270\) 0 0
\(271\) 6368.00 1.42741 0.713706 0.700446i \(-0.247015\pi\)
0.713706 + 0.700446i \(0.247015\pi\)
\(272\) 1376.00 0.306736
\(273\) 0 0
\(274\) 1148.00 0.253114
\(275\) 800.000 0.175425
\(276\) 0 0
\(277\) −5846.00 −1.26806 −0.634029 0.773309i \(-0.718600\pi\)
−0.634029 + 0.773309i \(0.718600\pi\)
\(278\) 3704.00 0.799105
\(279\) 0 0
\(280\) 320.000 0.0682988
\(281\) −4274.00 −0.907350 −0.453675 0.891167i \(-0.649887\pi\)
−0.453675 + 0.891167i \(0.649887\pi\)
\(282\) 0 0
\(283\) 532.000 0.111746 0.0558730 0.998438i \(-0.482206\pi\)
0.0558730 + 0.998438i \(0.482206\pi\)
\(284\) −480.000 −0.100291
\(285\) 0 0
\(286\) 832.000 0.172018
\(287\) 3920.00 0.806238
\(288\) 0 0
\(289\) 2483.00 0.505394
\(290\) −2020.00 −0.409029
\(291\) 0 0
\(292\) −840.000 −0.168347
\(293\) 1374.00 0.273959 0.136979 0.990574i \(-0.456261\pi\)
0.136979 + 0.990574i \(0.456261\pi\)
\(294\) 0 0
\(295\) 2400.00 0.473673
\(296\) −528.000 −0.103680
\(297\) 0 0
\(298\) −5804.00 −1.12824
\(299\) 884.000 0.170980
\(300\) 0 0
\(301\) −3680.00 −0.704690
\(302\) −3472.00 −0.661560
\(303\) 0 0
\(304\) −896.000 −0.169043
\(305\) −1690.00 −0.317276
\(306\) 0 0
\(307\) −8532.00 −1.58615 −0.793073 0.609126i \(-0.791520\pi\)
−0.793073 + 0.609126i \(0.791520\pi\)
\(308\) −1024.00 −0.189441
\(309\) 0 0
\(310\) 560.000 0.102600
\(311\) 10672.0 1.94583 0.972916 0.231160i \(-0.0742521\pi\)
0.972916 + 0.231160i \(0.0742521\pi\)
\(312\) 0 0
\(313\) −7318.00 −1.32153 −0.660763 0.750594i \(-0.729767\pi\)
−0.660763 + 0.750594i \(0.729767\pi\)
\(314\) −7540.00 −1.35512
\(315\) 0 0
\(316\) 736.000 0.131023
\(317\) −5674.00 −1.00531 −0.502656 0.864487i \(-0.667644\pi\)
−0.502656 + 0.864487i \(0.667644\pi\)
\(318\) 0 0
\(319\) 6464.00 1.13453
\(320\) 320.000 0.0559017
\(321\) 0 0
\(322\) −1088.00 −0.188298
\(323\) −4816.00 −0.829627
\(324\) 0 0
\(325\) −325.000 −0.0554700
\(326\) −4056.00 −0.689083
\(327\) 0 0
\(328\) 3920.00 0.659896
\(329\) −192.000 −0.0321742
\(330\) 0 0
\(331\) −3664.00 −0.608434 −0.304217 0.952603i \(-0.598395\pi\)
−0.304217 + 0.952603i \(0.598395\pi\)
\(332\) 2640.00 0.436412
\(333\) 0 0
\(334\) −480.000 −0.0786360
\(335\) 3380.00 0.551251
\(336\) 0 0
\(337\) −494.000 −0.0798513 −0.0399257 0.999203i \(-0.512712\pi\)
−0.0399257 + 0.999203i \(0.512712\pi\)
\(338\) −338.000 −0.0543928
\(339\) 0 0
\(340\) 1720.00 0.274353
\(341\) −1792.00 −0.284581
\(342\) 0 0
\(343\) 4976.00 0.783320
\(344\) −3680.00 −0.576780
\(345\) 0 0
\(346\) −3260.00 −0.506528
\(347\) 7988.00 1.23579 0.617894 0.786262i \(-0.287986\pi\)
0.617894 + 0.786262i \(0.287986\pi\)
\(348\) 0 0
\(349\) 2138.00 0.327921 0.163961 0.986467i \(-0.447573\pi\)
0.163961 + 0.986467i \(0.447573\pi\)
\(350\) 400.000 0.0610883
\(351\) 0 0
\(352\) −1024.00 −0.155055
\(353\) −3582.00 −0.540087 −0.270043 0.962848i \(-0.587038\pi\)
−0.270043 + 0.962848i \(0.587038\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 1144.00 0.170314
\(357\) 0 0
\(358\) 1528.00 0.225579
\(359\) −9456.00 −1.39016 −0.695082 0.718931i \(-0.744632\pi\)
−0.695082 + 0.718931i \(0.744632\pi\)
\(360\) 0 0
\(361\) −3723.00 −0.542790
\(362\) −3580.00 −0.519781
\(363\) 0 0
\(364\) 416.000 0.0599020
\(365\) −1050.00 −0.150574
\(366\) 0 0
\(367\) 1220.00 0.173524 0.0867622 0.996229i \(-0.472348\pi\)
0.0867622 + 0.996229i \(0.472348\pi\)
\(368\) −1088.00 −0.154119
\(369\) 0 0
\(370\) −660.000 −0.0927345
\(371\) −2352.00 −0.329137
\(372\) 0 0
\(373\) 7778.00 1.07970 0.539852 0.841760i \(-0.318480\pi\)
0.539852 + 0.841760i \(0.318480\pi\)
\(374\) −5504.00 −0.760976
\(375\) 0 0
\(376\) −192.000 −0.0263342
\(377\) −2626.00 −0.358742
\(378\) 0 0
\(379\) −1856.00 −0.251547 −0.125774 0.992059i \(-0.540141\pi\)
−0.125774 + 0.992059i \(0.540141\pi\)
\(380\) −1120.00 −0.151197
\(381\) 0 0
\(382\) 4880.00 0.653619
\(383\) 8624.00 1.15056 0.575282 0.817955i \(-0.304892\pi\)
0.575282 + 0.817955i \(0.304892\pi\)
\(384\) 0 0
\(385\) −1280.00 −0.169441
\(386\) −6204.00 −0.818071
\(387\) 0 0
\(388\) −4808.00 −0.629096
\(389\) −350.000 −0.0456188 −0.0228094 0.999740i \(-0.507261\pi\)
−0.0228094 + 0.999740i \(0.507261\pi\)
\(390\) 0 0
\(391\) −5848.00 −0.756384
\(392\) 2232.00 0.287584
\(393\) 0 0
\(394\) −3964.00 −0.506862
\(395\) 920.000 0.117190
\(396\) 0 0
\(397\) −5334.00 −0.674322 −0.337161 0.941447i \(-0.609467\pi\)
−0.337161 + 0.941447i \(0.609467\pi\)
\(398\) 5040.00 0.634755
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) −10554.0 −1.31432 −0.657159 0.753752i \(-0.728242\pi\)
−0.657159 + 0.753752i \(0.728242\pi\)
\(402\) 0 0
\(403\) 728.000 0.0899858
\(404\) 4264.00 0.525104
\(405\) 0 0
\(406\) 3232.00 0.395078
\(407\) 2112.00 0.257219
\(408\) 0 0
\(409\) −2814.00 −0.340204 −0.170102 0.985426i \(-0.554410\pi\)
−0.170102 + 0.985426i \(0.554410\pi\)
\(410\) 4900.00 0.590229
\(411\) 0 0
\(412\) 2224.00 0.265943
\(413\) −3840.00 −0.457516
\(414\) 0 0
\(415\) 3300.00 0.390339
\(416\) 416.000 0.0490290
\(417\) 0 0
\(418\) 3584.00 0.419376
\(419\) −764.000 −0.0890784 −0.0445392 0.999008i \(-0.514182\pi\)
−0.0445392 + 0.999008i \(0.514182\pi\)
\(420\) 0 0
\(421\) 5330.00 0.617027 0.308513 0.951220i \(-0.400169\pi\)
0.308513 + 0.951220i \(0.400169\pi\)
\(422\) −6376.00 −0.735495
\(423\) 0 0
\(424\) −2352.00 −0.269394
\(425\) 2150.00 0.245389
\(426\) 0 0
\(427\) 2704.00 0.306454
\(428\) −1648.00 −0.186119
\(429\) 0 0
\(430\) −4600.00 −0.515888
\(431\) 11072.0 1.23740 0.618700 0.785627i \(-0.287660\pi\)
0.618700 + 0.785627i \(0.287660\pi\)
\(432\) 0 0
\(433\) 7426.00 0.824182 0.412091 0.911143i \(-0.364799\pi\)
0.412091 + 0.911143i \(0.364799\pi\)
\(434\) −896.000 −0.0990999
\(435\) 0 0
\(436\) −7256.00 −0.797017
\(437\) 3808.00 0.416845
\(438\) 0 0
\(439\) 3392.00 0.368773 0.184386 0.982854i \(-0.440970\pi\)
0.184386 + 0.982854i \(0.440970\pi\)
\(440\) −1280.00 −0.138685
\(441\) 0 0
\(442\) 2236.00 0.240624
\(443\) 13972.0 1.49849 0.749244 0.662295i \(-0.230417\pi\)
0.749244 + 0.662295i \(0.230417\pi\)
\(444\) 0 0
\(445\) 1430.00 0.152334
\(446\) −12784.0 −1.35726
\(447\) 0 0
\(448\) −512.000 −0.0539949
\(449\) −16986.0 −1.78534 −0.892671 0.450708i \(-0.851172\pi\)
−0.892671 + 0.450708i \(0.851172\pi\)
\(450\) 0 0
\(451\) −15680.0 −1.63712
\(452\) 1816.00 0.188977
\(453\) 0 0
\(454\) −11496.0 −1.18840
\(455\) 520.000 0.0535780
\(456\) 0 0
\(457\) 1910.00 0.195506 0.0977528 0.995211i \(-0.468835\pi\)
0.0977528 + 0.995211i \(0.468835\pi\)
\(458\) −4820.00 −0.491755
\(459\) 0 0
\(460\) −1360.00 −0.137849
\(461\) −9834.00 −0.993525 −0.496763 0.867887i \(-0.665478\pi\)
−0.496763 + 0.867887i \(0.665478\pi\)
\(462\) 0 0
\(463\) −13072.0 −1.31211 −0.656055 0.754713i \(-0.727776\pi\)
−0.656055 + 0.754713i \(0.727776\pi\)
\(464\) 3232.00 0.323366
\(465\) 0 0
\(466\) −2716.00 −0.269992
\(467\) −19860.0 −1.96790 −0.983952 0.178433i \(-0.942897\pi\)
−0.983952 + 0.178433i \(0.942897\pi\)
\(468\) 0 0
\(469\) −5408.00 −0.532448
\(470\) −240.000 −0.0235540
\(471\) 0 0
\(472\) −3840.00 −0.374471
\(473\) 14720.0 1.43092
\(474\) 0 0
\(475\) −1400.00 −0.135235
\(476\) −2752.00 −0.264995
\(477\) 0 0
\(478\) 6512.00 0.623121
\(479\) 3672.00 0.350267 0.175134 0.984545i \(-0.443964\pi\)
0.175134 + 0.984545i \(0.443964\pi\)
\(480\) 0 0
\(481\) −858.000 −0.0813335
\(482\) −9796.00 −0.925717
\(483\) 0 0
\(484\) −1228.00 −0.115327
\(485\) −6010.00 −0.562680
\(486\) 0 0
\(487\) 3488.00 0.324551 0.162276 0.986745i \(-0.448117\pi\)
0.162276 + 0.986745i \(0.448117\pi\)
\(488\) 2704.00 0.250829
\(489\) 0 0
\(490\) 2790.00 0.257223
\(491\) 5260.00 0.483463 0.241732 0.970343i \(-0.422285\pi\)
0.241732 + 0.970343i \(0.422285\pi\)
\(492\) 0 0
\(493\) 17372.0 1.58701
\(494\) −1456.00 −0.132608
\(495\) 0 0
\(496\) −896.000 −0.0811121
\(497\) 960.000 0.0866436
\(498\) 0 0
\(499\) −8048.00 −0.722000 −0.361000 0.932566i \(-0.617565\pi\)
−0.361000 + 0.932566i \(0.617565\pi\)
\(500\) 500.000 0.0447214
\(501\) 0 0
\(502\) −8200.00 −0.729052
\(503\) 732.000 0.0648872 0.0324436 0.999474i \(-0.489671\pi\)
0.0324436 + 0.999474i \(0.489671\pi\)
\(504\) 0 0
\(505\) 5330.00 0.469667
\(506\) 4352.00 0.382352
\(507\) 0 0
\(508\) −2032.00 −0.177471
\(509\) −13826.0 −1.20398 −0.601991 0.798503i \(-0.705626\pi\)
−0.601991 + 0.798503i \(0.705626\pi\)
\(510\) 0 0
\(511\) 1680.00 0.145438
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −10540.0 −0.904474
\(515\) 2780.00 0.237867
\(516\) 0 0
\(517\) 768.000 0.0653319
\(518\) 1056.00 0.0895714
\(519\) 0 0
\(520\) 520.000 0.0438529
\(521\) 1926.00 0.161957 0.0809785 0.996716i \(-0.474195\pi\)
0.0809785 + 0.996716i \(0.474195\pi\)
\(522\) 0 0
\(523\) 4892.00 0.409010 0.204505 0.978866i \(-0.434442\pi\)
0.204505 + 0.978866i \(0.434442\pi\)
\(524\) 7504.00 0.625599
\(525\) 0 0
\(526\) −168.000 −0.0139261
\(527\) −4816.00 −0.398080
\(528\) 0 0
\(529\) −7543.00 −0.619956
\(530\) −2940.00 −0.240954
\(531\) 0 0
\(532\) 1792.00 0.146040
\(533\) 6370.00 0.517665
\(534\) 0 0
\(535\) −2060.00 −0.166470
\(536\) −5408.00 −0.435802
\(537\) 0 0
\(538\) −14372.0 −1.15171
\(539\) −8928.00 −0.713462
\(540\) 0 0
\(541\) 15042.0 1.19539 0.597695 0.801724i \(-0.296083\pi\)
0.597695 + 0.801724i \(0.296083\pi\)
\(542\) −12736.0 −1.00933
\(543\) 0 0
\(544\) −2752.00 −0.216895
\(545\) −9070.00 −0.712874
\(546\) 0 0
\(547\) −996.000 −0.0778535 −0.0389268 0.999242i \(-0.512394\pi\)
−0.0389268 + 0.999242i \(0.512394\pi\)
\(548\) −2296.00 −0.178979
\(549\) 0 0
\(550\) −1600.00 −0.124044
\(551\) −11312.0 −0.874605
\(552\) 0 0
\(553\) −1472.00 −0.113193
\(554\) 11692.0 0.896652
\(555\) 0 0
\(556\) −7408.00 −0.565052
\(557\) −15626.0 −1.18868 −0.594340 0.804214i \(-0.702587\pi\)
−0.594340 + 0.804214i \(0.702587\pi\)
\(558\) 0 0
\(559\) −5980.00 −0.452463
\(560\) −640.000 −0.0482945
\(561\) 0 0
\(562\) 8548.00 0.641594
\(563\) 20892.0 1.56393 0.781965 0.623322i \(-0.214217\pi\)
0.781965 + 0.623322i \(0.214217\pi\)
\(564\) 0 0
\(565\) 2270.00 0.169026
\(566\) −1064.00 −0.0790164
\(567\) 0 0
\(568\) 960.000 0.0709167
\(569\) −1994.00 −0.146912 −0.0734559 0.997298i \(-0.523403\pi\)
−0.0734559 + 0.997298i \(0.523403\pi\)
\(570\) 0 0
\(571\) −24292.0 −1.78037 −0.890183 0.455604i \(-0.849423\pi\)
−0.890183 + 0.455604i \(0.849423\pi\)
\(572\) −1664.00 −0.121635
\(573\) 0 0
\(574\) −7840.00 −0.570096
\(575\) −1700.00 −0.123295
\(576\) 0 0
\(577\) −17914.0 −1.29249 −0.646247 0.763128i \(-0.723663\pi\)
−0.646247 + 0.763128i \(0.723663\pi\)
\(578\) −4966.00 −0.357367
\(579\) 0 0
\(580\) 4040.00 0.289227
\(581\) −5280.00 −0.377025
\(582\) 0 0
\(583\) 9408.00 0.668335
\(584\) 1680.00 0.119039
\(585\) 0 0
\(586\) −2748.00 −0.193718
\(587\) 996.000 0.0700329 0.0350165 0.999387i \(-0.488852\pi\)
0.0350165 + 0.999387i \(0.488852\pi\)
\(588\) 0 0
\(589\) 3136.00 0.219383
\(590\) −4800.00 −0.334937
\(591\) 0 0
\(592\) 1056.00 0.0733131
\(593\) −20014.0 −1.38596 −0.692982 0.720955i \(-0.743703\pi\)
−0.692982 + 0.720955i \(0.743703\pi\)
\(594\) 0 0
\(595\) −3440.00 −0.237019
\(596\) 11608.0 0.797789
\(597\) 0 0
\(598\) −1768.00 −0.120901
\(599\) −12312.0 −0.839824 −0.419912 0.907565i \(-0.637939\pi\)
−0.419912 + 0.907565i \(0.637939\pi\)
\(600\) 0 0
\(601\) −19110.0 −1.29703 −0.648513 0.761203i \(-0.724609\pi\)
−0.648513 + 0.761203i \(0.724609\pi\)
\(602\) 7360.00 0.498291
\(603\) 0 0
\(604\) 6944.00 0.467794
\(605\) −1535.00 −0.103151
\(606\) 0 0
\(607\) 25452.0 1.70192 0.850959 0.525231i \(-0.176021\pi\)
0.850959 + 0.525231i \(0.176021\pi\)
\(608\) 1792.00 0.119532
\(609\) 0 0
\(610\) 3380.00 0.224348
\(611\) −312.000 −0.0206582
\(612\) 0 0
\(613\) −4142.00 −0.272910 −0.136455 0.990646i \(-0.543571\pi\)
−0.136455 + 0.990646i \(0.543571\pi\)
\(614\) 17064.0 1.12157
\(615\) 0 0
\(616\) 2048.00 0.133955
\(617\) −1382.00 −0.0901738 −0.0450869 0.998983i \(-0.514356\pi\)
−0.0450869 + 0.998983i \(0.514356\pi\)
\(618\) 0 0
\(619\) 5456.00 0.354273 0.177137 0.984186i \(-0.443317\pi\)
0.177137 + 0.984186i \(0.443317\pi\)
\(620\) −1120.00 −0.0725488
\(621\) 0 0
\(622\) −21344.0 −1.37591
\(623\) −2288.00 −0.147138
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 14636.0 0.934460
\(627\) 0 0
\(628\) 15080.0 0.958213
\(629\) 5676.00 0.359804
\(630\) 0 0
\(631\) 13960.0 0.880727 0.440364 0.897820i \(-0.354850\pi\)
0.440364 + 0.897820i \(0.354850\pi\)
\(632\) −1472.00 −0.0926472
\(633\) 0 0
\(634\) 11348.0 0.710862
\(635\) −2540.00 −0.158735
\(636\) 0 0
\(637\) 3627.00 0.225600
\(638\) −12928.0 −0.802233
\(639\) 0 0
\(640\) −640.000 −0.0395285
\(641\) −9138.00 −0.563072 −0.281536 0.959551i \(-0.590844\pi\)
−0.281536 + 0.959551i \(0.590844\pi\)
\(642\) 0 0
\(643\) 20852.0 1.27888 0.639442 0.768839i \(-0.279165\pi\)
0.639442 + 0.768839i \(0.279165\pi\)
\(644\) 2176.00 0.133147
\(645\) 0 0
\(646\) 9632.00 0.586635
\(647\) −25524.0 −1.55093 −0.775465 0.631390i \(-0.782485\pi\)
−0.775465 + 0.631390i \(0.782485\pi\)
\(648\) 0 0
\(649\) 15360.0 0.929018
\(650\) 650.000 0.0392232
\(651\) 0 0
\(652\) 8112.00 0.487255
\(653\) 30518.0 1.82888 0.914442 0.404716i \(-0.132630\pi\)
0.914442 + 0.404716i \(0.132630\pi\)
\(654\) 0 0
\(655\) 9380.00 0.559553
\(656\) −7840.00 −0.466617
\(657\) 0 0
\(658\) 384.000 0.0227506
\(659\) −30012.0 −1.77405 −0.887027 0.461718i \(-0.847233\pi\)
−0.887027 + 0.461718i \(0.847233\pi\)
\(660\) 0 0
\(661\) 1610.00 0.0947379 0.0473689 0.998877i \(-0.484916\pi\)
0.0473689 + 0.998877i \(0.484916\pi\)
\(662\) 7328.00 0.430228
\(663\) 0 0
\(664\) −5280.00 −0.308590
\(665\) 2240.00 0.130622
\(666\) 0 0
\(667\) −13736.0 −0.797391
\(668\) 960.000 0.0556041
\(669\) 0 0
\(670\) −6760.00 −0.389793
\(671\) −10816.0 −0.622276
\(672\) 0 0
\(673\) 17066.0 0.977483 0.488741 0.872429i \(-0.337456\pi\)
0.488741 + 0.872429i \(0.337456\pi\)
\(674\) 988.000 0.0564634
\(675\) 0 0
\(676\) 676.000 0.0384615
\(677\) −27698.0 −1.57241 −0.786204 0.617967i \(-0.787957\pi\)
−0.786204 + 0.617967i \(0.787957\pi\)
\(678\) 0 0
\(679\) 9616.00 0.543488
\(680\) −3440.00 −0.193997
\(681\) 0 0
\(682\) 3584.00 0.201229
\(683\) 25932.0 1.45280 0.726399 0.687274i \(-0.241193\pi\)
0.726399 + 0.687274i \(0.241193\pi\)
\(684\) 0 0
\(685\) −2870.00 −0.160083
\(686\) −9952.00 −0.553891
\(687\) 0 0
\(688\) 7360.00 0.407845
\(689\) −3822.00 −0.211330
\(690\) 0 0
\(691\) −19848.0 −1.09270 −0.546348 0.837558i \(-0.683983\pi\)
−0.546348 + 0.837558i \(0.683983\pi\)
\(692\) 6520.00 0.358169
\(693\) 0 0
\(694\) −15976.0 −0.873834
\(695\) −9260.00 −0.505398
\(696\) 0 0
\(697\) −42140.0 −2.29005
\(698\) −4276.00 −0.231875
\(699\) 0 0
\(700\) −800.000 −0.0431959
\(701\) −29758.0 −1.60334 −0.801672 0.597764i \(-0.796056\pi\)
−0.801672 + 0.597764i \(0.796056\pi\)
\(702\) 0 0
\(703\) −3696.00 −0.198289
\(704\) 2048.00 0.109640
\(705\) 0 0
\(706\) 7164.00 0.381899
\(707\) −8528.00 −0.453647
\(708\) 0 0
\(709\) 23722.0 1.25656 0.628278 0.777989i \(-0.283760\pi\)
0.628278 + 0.777989i \(0.283760\pi\)
\(710\) 1200.00 0.0634299
\(711\) 0 0
\(712\) −2288.00 −0.120430
\(713\) 3808.00 0.200015
\(714\) 0 0
\(715\) −2080.00 −0.108794
\(716\) −3056.00 −0.159508
\(717\) 0 0
\(718\) 18912.0 0.982994
\(719\) 18168.0 0.942353 0.471177 0.882039i \(-0.343829\pi\)
0.471177 + 0.882039i \(0.343829\pi\)
\(720\) 0 0
\(721\) −4448.00 −0.229753
\(722\) 7446.00 0.383811
\(723\) 0 0
\(724\) 7160.00 0.367540
\(725\) 5050.00 0.258693
\(726\) 0 0
\(727\) −10708.0 −0.546269 −0.273135 0.961976i \(-0.588060\pi\)
−0.273135 + 0.961976i \(0.588060\pi\)
\(728\) −832.000 −0.0423571
\(729\) 0 0
\(730\) 2100.00 0.106472
\(731\) 39560.0 2.00161
\(732\) 0 0
\(733\) −27894.0 −1.40558 −0.702789 0.711399i \(-0.748062\pi\)
−0.702789 + 0.711399i \(0.748062\pi\)
\(734\) −2440.00 −0.122700
\(735\) 0 0
\(736\) 2176.00 0.108979
\(737\) 21632.0 1.08117
\(738\) 0 0
\(739\) −26512.0 −1.31970 −0.659851 0.751397i \(-0.729381\pi\)
−0.659851 + 0.751397i \(0.729381\pi\)
\(740\) 1320.00 0.0655732
\(741\) 0 0
\(742\) 4704.00 0.232735
\(743\) −24024.0 −1.18621 −0.593106 0.805125i \(-0.702098\pi\)
−0.593106 + 0.805125i \(0.702098\pi\)
\(744\) 0 0
\(745\) 14510.0 0.713564
\(746\) −15556.0 −0.763466
\(747\) 0 0
\(748\) 11008.0 0.538091
\(749\) 3296.00 0.160792
\(750\) 0 0
\(751\) −16976.0 −0.824851 −0.412425 0.910991i \(-0.635318\pi\)
−0.412425 + 0.910991i \(0.635318\pi\)
\(752\) 384.000 0.0186211
\(753\) 0 0
\(754\) 5252.00 0.253669
\(755\) 8680.00 0.418407
\(756\) 0 0
\(757\) −23894.0 −1.14722 −0.573608 0.819130i \(-0.694457\pi\)
−0.573608 + 0.819130i \(0.694457\pi\)
\(758\) 3712.00 0.177871
\(759\) 0 0
\(760\) 2240.00 0.106912
\(761\) 14254.0 0.678984 0.339492 0.940609i \(-0.389745\pi\)
0.339492 + 0.940609i \(0.389745\pi\)
\(762\) 0 0
\(763\) 14512.0 0.688558
\(764\) −9760.00 −0.462179
\(765\) 0 0
\(766\) −17248.0 −0.813571
\(767\) −6240.00 −0.293759
\(768\) 0 0
\(769\) −40670.0 −1.90715 −0.953575 0.301157i \(-0.902627\pi\)
−0.953575 + 0.301157i \(0.902627\pi\)
\(770\) 2560.00 0.119813
\(771\) 0 0
\(772\) 12408.0 0.578463
\(773\) 7102.00 0.330454 0.165227 0.986256i \(-0.447164\pi\)
0.165227 + 0.986256i \(0.447164\pi\)
\(774\) 0 0
\(775\) −1400.00 −0.0648897
\(776\) 9616.00 0.444838
\(777\) 0 0
\(778\) 700.000 0.0322573
\(779\) 27440.0 1.26205
\(780\) 0 0
\(781\) −3840.00 −0.175936
\(782\) 11696.0 0.534844
\(783\) 0 0
\(784\) −4464.00 −0.203353
\(785\) 18850.0 0.857051
\(786\) 0 0
\(787\) 29564.0 1.33906 0.669532 0.742784i \(-0.266495\pi\)
0.669532 + 0.742784i \(0.266495\pi\)
\(788\) 7928.00 0.358405
\(789\) 0 0
\(790\) −1840.00 −0.0828662
\(791\) −3632.00 −0.163260
\(792\) 0 0
\(793\) 4394.00 0.196766
\(794\) 10668.0 0.476818
\(795\) 0 0
\(796\) −10080.0 −0.448839
\(797\) 44814.0 1.99171 0.995855 0.0909519i \(-0.0289910\pi\)
0.995855 + 0.0909519i \(0.0289910\pi\)
\(798\) 0 0
\(799\) 2064.00 0.0913881
\(800\) −800.000 −0.0353553
\(801\) 0 0
\(802\) 21108.0 0.929363
\(803\) −6720.00 −0.295322
\(804\) 0 0
\(805\) 2720.00 0.119090
\(806\) −1456.00 −0.0636295
\(807\) 0 0
\(808\) −8528.00 −0.371304
\(809\) 34326.0 1.49177 0.745883 0.666078i \(-0.232028\pi\)
0.745883 + 0.666078i \(0.232028\pi\)
\(810\) 0 0
\(811\) −13768.0 −0.596128 −0.298064 0.954546i \(-0.596341\pi\)
−0.298064 + 0.954546i \(0.596341\pi\)
\(812\) −6464.00 −0.279362
\(813\) 0 0
\(814\) −4224.00 −0.181881
\(815\) 10140.0 0.435814
\(816\) 0 0
\(817\) −25760.0 −1.10309
\(818\) 5628.00 0.240560
\(819\) 0 0
\(820\) −9800.00 −0.417355
\(821\) 41550.0 1.76627 0.883133 0.469122i \(-0.155430\pi\)
0.883133 + 0.469122i \(0.155430\pi\)
\(822\) 0 0
\(823\) 3412.00 0.144514 0.0722569 0.997386i \(-0.476980\pi\)
0.0722569 + 0.997386i \(0.476980\pi\)
\(824\) −4448.00 −0.188050
\(825\) 0 0
\(826\) 7680.00 0.323513
\(827\) 11300.0 0.475138 0.237569 0.971371i \(-0.423649\pi\)
0.237569 + 0.971371i \(0.423649\pi\)
\(828\) 0 0
\(829\) 26798.0 1.12272 0.561359 0.827572i \(-0.310279\pi\)
0.561359 + 0.827572i \(0.310279\pi\)
\(830\) −6600.00 −0.276011
\(831\) 0 0
\(832\) −832.000 −0.0346688
\(833\) −23994.0 −0.998011
\(834\) 0 0
\(835\) 1200.00 0.0497338
\(836\) −7168.00 −0.296544
\(837\) 0 0
\(838\) 1528.00 0.0629879
\(839\) −30744.0 −1.26508 −0.632539 0.774528i \(-0.717987\pi\)
−0.632539 + 0.774528i \(0.717987\pi\)
\(840\) 0 0
\(841\) 16415.0 0.673049
\(842\) −10660.0 −0.436304
\(843\) 0 0
\(844\) 12752.0 0.520073
\(845\) 845.000 0.0344010
\(846\) 0 0
\(847\) 2456.00 0.0996330
\(848\) 4704.00 0.190491
\(849\) 0 0
\(850\) −4300.00 −0.173516
\(851\) −4488.00 −0.180783
\(852\) 0 0
\(853\) 11522.0 0.462492 0.231246 0.972895i \(-0.425720\pi\)
0.231246 + 0.972895i \(0.425720\pi\)
\(854\) −5408.00 −0.216695
\(855\) 0 0
\(856\) 3296.00 0.131606
\(857\) 10198.0 0.406484 0.203242 0.979129i \(-0.434852\pi\)
0.203242 + 0.979129i \(0.434852\pi\)
\(858\) 0 0
\(859\) −11300.0 −0.448837 −0.224419 0.974493i \(-0.572048\pi\)
−0.224419 + 0.974493i \(0.572048\pi\)
\(860\) 9200.00 0.364788
\(861\) 0 0
\(862\) −22144.0 −0.874974
\(863\) −35832.0 −1.41337 −0.706683 0.707530i \(-0.749809\pi\)
−0.706683 + 0.707530i \(0.749809\pi\)
\(864\) 0 0
\(865\) 8150.00 0.320356
\(866\) −14852.0 −0.582785
\(867\) 0 0
\(868\) 1792.00 0.0700742
\(869\) 5888.00 0.229847
\(870\) 0 0
\(871\) −8788.00 −0.341871
\(872\) 14512.0 0.563576
\(873\) 0 0
\(874\) −7616.00 −0.294754
\(875\) −1000.00 −0.0386356
\(876\) 0 0
\(877\) −14518.0 −0.558994 −0.279497 0.960147i \(-0.590168\pi\)
−0.279497 + 0.960147i \(0.590168\pi\)
\(878\) −6784.00 −0.260762
\(879\) 0 0
\(880\) 2560.00 0.0980654
\(881\) 23214.0 0.887741 0.443870 0.896091i \(-0.353605\pi\)
0.443870 + 0.896091i \(0.353605\pi\)
\(882\) 0 0
\(883\) 45044.0 1.71671 0.858353 0.513060i \(-0.171488\pi\)
0.858353 + 0.513060i \(0.171488\pi\)
\(884\) −4472.00 −0.170147
\(885\) 0 0
\(886\) −27944.0 −1.05959
\(887\) −28164.0 −1.06613 −0.533063 0.846075i \(-0.678959\pi\)
−0.533063 + 0.846075i \(0.678959\pi\)
\(888\) 0 0
\(889\) 4064.00 0.153321
\(890\) −2860.00 −0.107716
\(891\) 0 0
\(892\) 25568.0 0.959731
\(893\) −1344.00 −0.0503642
\(894\) 0 0
\(895\) −3820.00 −0.142669
\(896\) 1024.00 0.0381802
\(897\) 0 0
\(898\) 33972.0 1.26243
\(899\) −11312.0 −0.419662
\(900\) 0 0
\(901\) 25284.0 0.934886
\(902\) 31360.0 1.15762
\(903\) 0 0
\(904\) −3632.00 −0.133627
\(905\) 8950.00 0.328738
\(906\) 0 0
\(907\) 43612.0 1.59660 0.798298 0.602263i \(-0.205734\pi\)
0.798298 + 0.602263i \(0.205734\pi\)
\(908\) 22992.0 0.840326
\(909\) 0 0
\(910\) −1040.00 −0.0378853
\(911\) −4056.00 −0.147510 −0.0737548 0.997276i \(-0.523498\pi\)
−0.0737548 + 0.997276i \(0.523498\pi\)
\(912\) 0 0
\(913\) 21120.0 0.765575
\(914\) −3820.00 −0.138243
\(915\) 0 0
\(916\) 9640.00 0.347723
\(917\) −15008.0 −0.540467
\(918\) 0 0
\(919\) 25976.0 0.932393 0.466197 0.884681i \(-0.345624\pi\)
0.466197 + 0.884681i \(0.345624\pi\)
\(920\) 2720.00 0.0974736
\(921\) 0 0
\(922\) 19668.0 0.702528
\(923\) 1560.00 0.0556317
\(924\) 0 0
\(925\) 1650.00 0.0586504
\(926\) 26144.0 0.927803
\(927\) 0 0
\(928\) −6464.00 −0.228654
\(929\) −46346.0 −1.63677 −0.818387 0.574668i \(-0.805131\pi\)
−0.818387 + 0.574668i \(0.805131\pi\)
\(930\) 0 0
\(931\) 15624.0 0.550006
\(932\) 5432.00 0.190913
\(933\) 0 0
\(934\) 39720.0 1.39152
\(935\) 13760.0 0.481284
\(936\) 0 0
\(937\) −22694.0 −0.791228 −0.395614 0.918417i \(-0.629468\pi\)
−0.395614 + 0.918417i \(0.629468\pi\)
\(938\) 10816.0 0.376498
\(939\) 0 0
\(940\) 480.000 0.0166552
\(941\) −4690.00 −0.162476 −0.0812378 0.996695i \(-0.525887\pi\)
−0.0812378 + 0.996695i \(0.525887\pi\)
\(942\) 0 0
\(943\) 33320.0 1.15063
\(944\) 7680.00 0.264791
\(945\) 0 0
\(946\) −29440.0 −1.01181
\(947\) 38476.0 1.32028 0.660138 0.751144i \(-0.270498\pi\)
0.660138 + 0.751144i \(0.270498\pi\)
\(948\) 0 0
\(949\) 2730.00 0.0933820
\(950\) 2800.00 0.0956253
\(951\) 0 0
\(952\) 5504.00 0.187380
\(953\) 11046.0 0.375462 0.187731 0.982221i \(-0.439887\pi\)
0.187731 + 0.982221i \(0.439887\pi\)
\(954\) 0 0
\(955\) −12200.0 −0.413385
\(956\) −13024.0 −0.440613
\(957\) 0 0
\(958\) −7344.00 −0.247676
\(959\) 4592.00 0.154623
\(960\) 0 0
\(961\) −26655.0 −0.894733
\(962\) 1716.00 0.0575115
\(963\) 0 0
\(964\) 19592.0 0.654581
\(965\) 15510.0 0.517393
\(966\) 0 0
\(967\) −3784.00 −0.125838 −0.0629189 0.998019i \(-0.520041\pi\)
−0.0629189 + 0.998019i \(0.520041\pi\)
\(968\) 2456.00 0.0815484
\(969\) 0 0
\(970\) 12020.0 0.397875
\(971\) 19620.0 0.648441 0.324220 0.945982i \(-0.394898\pi\)
0.324220 + 0.945982i \(0.394898\pi\)
\(972\) 0 0
\(973\) 14816.0 0.488159
\(974\) −6976.00 −0.229492
\(975\) 0 0
\(976\) −5408.00 −0.177363
\(977\) −7350.00 −0.240683 −0.120342 0.992733i \(-0.538399\pi\)
−0.120342 + 0.992733i \(0.538399\pi\)
\(978\) 0 0
\(979\) 9152.00 0.298773
\(980\) −5580.00 −0.181884
\(981\) 0 0
\(982\) −10520.0 −0.341860
\(983\) 22008.0 0.714086 0.357043 0.934088i \(-0.383785\pi\)
0.357043 + 0.934088i \(0.383785\pi\)
\(984\) 0 0
\(985\) 9910.00 0.320567
\(986\) −34744.0 −1.12218
\(987\) 0 0
\(988\) 2912.00 0.0937683
\(989\) −31280.0 −1.00571
\(990\) 0 0
\(991\) −44720.0 −1.43348 −0.716739 0.697341i \(-0.754366\pi\)
−0.716739 + 0.697341i \(0.754366\pi\)
\(992\) 1792.00 0.0573549
\(993\) 0 0
\(994\) −1920.00 −0.0612663
\(995\) −12600.0 −0.401454
\(996\) 0 0
\(997\) −42110.0 −1.33765 −0.668825 0.743420i \(-0.733202\pi\)
−0.668825 + 0.743420i \(0.733202\pi\)
\(998\) 16096.0 0.510531
\(999\) 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 1170.4.a.f.1.1 1
3.2 odd 2 130.4.a.b.1.1 1
12.11 even 2 1040.4.a.e.1.1 1
15.2 even 4 650.4.b.a.599.2 2
15.8 even 4 650.4.b.a.599.1 2
15.14 odd 2 650.4.a.e.1.1 1
39.38 odd 2 1690.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.4.a.b.1.1 1 3.2 odd 2
650.4.a.e.1.1 1 15.14 odd 2
650.4.b.a.599.1 2 15.8 even 4
650.4.b.a.599.2 2 15.2 even 4
1040.4.a.e.1.1 1 12.11 even 2
1170.4.a.f.1.1 1 1.1 even 1 trivial
1690.4.a.c.1.1 1 39.38 odd 2