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Properties

Label 570.2.a.f.1.1
Level $570$
Weight $2$
Character 570.1
Self dual yes
Analytic conductor $4.551$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(1,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.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: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 570.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +2.00000 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +1.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} -6.00000 q^{29} -1.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -1.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} -2.00000 q^{42} +8.00000 q^{43} +1.00000 q^{45} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -2.00000 q^{56} +1.00000 q^{57} +6.00000 q^{58} -6.00000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -2.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -4.00000 q^{67} -2.00000 q^{70} -1.00000 q^{72} +14.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} -2.00000 q^{78} +2.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{83} +2.00000 q^{84} -8.00000 q^{86} -6.00000 q^{87} -12.0000 q^{89} -1.00000 q^{90} +4.00000 q^{91} +2.00000 q^{93} +1.00000 q^{95} -1.00000 q^{96} -10.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) 2.00000 0.755929 0.377964 − 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 0.229416
\(20\) 1.00000 0.223607
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) 2.00000 0.377964
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 −0.182574
\(31\) 2.00000 0.359211 0.179605 − 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −1.00000 −0.162221
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −2.00000 −0.308607
\(43\) 8.00000 1.21999 0.609994 − 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 1.00000 0.132453
\(58\) 6.00000 0.787839
\(59\) −6.00000 −0.781133 −0.390567 − 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 1.00000 0.129099
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −2.00000 −0.254000
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −2.00000 −0.239046
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −0.117851
\(73\) 14.0000 1.63858 0.819288 − 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 2.00000 0.225018 0.112509 − 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 2.00000 0.218218
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −12.0000 −1.27200 −0.635999 − 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) −1.00000 −0.105409
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) −1.00000 −0.102062
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 − 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −2.00000 −0.196116
\(105\) 2.00000 0.195180
\(106\) −6.00000 −0.582772
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.0000 −1.53252 −0.766261 − 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 2.00000 0.188982
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 2.00000 0.184900
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −11.0000 −1.00000
\(122\) −2.00000 −0.181071
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) 1.00000 0.0894427
\(126\) −2.00000 −0.178174
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) −2.00000 −0.175412
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 4.00000 0.345547
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 0.169031
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −14.0000 −1.15865
\(147\) −3.00000 −0.247436
\(148\) 2.00000 0.164399
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 2.00000 0.160128
\(157\) −4.00000 −0.319235 −0.159617 − 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −2.00000 −0.159111
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −2.00000 −0.154303
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 8.00000 0.609994
\(173\) −18.0000 −1.36851 −0.684257 − 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 6.00000 0.454859
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 12.0000 0.899438
\(179\) 6.00000 0.448461 0.224231 − 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 1.00000 0.0745356
\(181\) −16.0000 −1.18927 −0.594635 − 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −4.00000 −0.296500
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) −2.00000 −0.146647
\(187\) 0 0
\(188\) 0 0
\(189\) 2.00000 0.145479
\(190\) −1.00000 −0.0725476
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.00000 0.143963 0.0719816 − 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 10.0000 0.717958
\(195\) 2.00000 0.143223
\(196\) −3.00000 −0.214286
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 − 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.00000 −0.282138
\(202\) 6.00000 0.422159
\(203\) −12.0000 −0.842235
\(204\) 0 0
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) −2.00000 −0.138013
\(211\) 8.00000 0.550743 0.275371 − 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 0 0
\(215\) 8.00000 0.545595
\(216\) −1.00000 −0.0680414
\(217\) 4.00000 0.271538
\(218\) 16.0000 1.08366
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) −4.00000 −0.267860 −0.133930 − 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.00000 −0.133631
\(225\) 1.00000 0.0666667
\(226\) 6.00000 0.399114
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 1.00000 0.0662266
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 24.0000 1.57229 0.786146 − 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) 2.00000 0.129914
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 1.00000 0.0645497
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 11.0000 0.707107
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) −3.00000 −0.191663
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) −2.00000 −0.127000
\(249\) 6.00000 0.380235
\(250\) −1.00000 −0.0632456
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −8.00000 −0.498058
\(259\) 4.00000 0.248548
\(260\) 2.00000 0.124035
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) −2.00000 −0.122628
\(267\) −12.0000 −0.734388
\(268\) −4.00000 −0.244339
\(269\) 18.0000 1.09748 0.548740 − 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 20.0000 1.21491 0.607457 − 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) 4.00000 0.242091
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) −28.0000 −1.68236 −0.841178 − 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 4.00000 0.239904
\(279\) 2.00000 0.119737
\(280\) −2.00000 −0.119523
\(281\) 24.0000 1.43172 0.715860 − 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 32.0000 1.90220 0.951101 − 0.308879i \(-0.0999539\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) 0 0
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 6.00000 0.352332
\(291\) −10.0000 −0.586210
\(292\) 14.0000 0.819288
\(293\) −6.00000 −0.350524 −0.175262 − 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 3.00000 0.174964
\(295\) −6.00000 −0.349334
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 16.0000 0.922225
\(302\) 10.0000 0.575435
\(303\) −6.00000 −0.344691
\(304\) 1.00000 0.0573539
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 − 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) −2.00000 −0.113592
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −2.00000 −0.113228
\(313\) −10.0000 −0.565233 −0.282617 − 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 4.00000 0.225733
\(315\) 2.00000 0.112687
\(316\) 2.00000 0.112509
\(317\) −30.0000 −1.68497 −0.842484 − 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) 4.00000 0.221540
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 6.00000 0.329293
\(333\) 2.00000 0.109599
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 2.00000 0.109109
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 9.00000 0.489535
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) −20.0000 −1.07990
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 18.0000 0.966291 0.483145 − 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) −6.00000 −0.321634
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −2.00000 −0.106904
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 12.0000 0.638696 0.319348 − 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) −12.0000 −0.635999
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 24.0000 1.26667 0.633336 − 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 1.00000 0.0526316
\(362\) 16.0000 0.840941
\(363\) −11.0000 −0.577350
\(364\) 4.00000 0.209657
\(365\) 14.0000 0.732793
\(366\) −2.00000 −0.104542
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 12.0000 0.623009
\(372\) 2.00000 0.103695
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) −2.00000 −0.102869
\(379\) 8.00000 0.410932 0.205466 − 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 1.00000 0.0512989
\(381\) −16.0000 −0.819705
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 8.00000 0.406663
\(388\) −10.0000 −0.507673
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −2.00000 −0.101274
\(391\) 0 0
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 2.00000 0.100631
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 − 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 4.00000 0.200502
\(399\) 2.00000 0.100125
\(400\) 1.00000 0.0500000
\(401\) 12.0000 0.599251 0.299626 − 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 4.00000 0.199502
\(403\) 4.00000 0.199254
\(404\) −6.00000 −0.298511
\(405\) 1.00000 0.0496904
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 8.00000 0.394132
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) −2.00000 −0.0980581
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 2.00000 0.0975900
\(421\) 8.00000 0.389896 0.194948 − 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −8.00000 −0.389434
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 0 0
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −4.00000 −0.192006
\(435\) −6.00000 −0.287678
\(436\) −16.0000 −0.766261
\(437\) 0 0
\(438\) −14.0000 −0.668946
\(439\) −22.0000 −1.05000 −0.525001 − 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −30.0000 −1.42534 −0.712672 − 0.701498i \(-0.752515\pi\)
−0.712672 + 0.701498i \(0.752515\pi\)
\(444\) 2.00000 0.0949158
\(445\) −12.0000 −0.568855
\(446\) 4.00000 0.189405
\(447\) −6.00000 −0.283790
\(448\) 2.00000 0.0944911
\(449\) 24.0000 1.13263 0.566315 − 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) −10.0000 −0.469841
\(454\) −12.0000 −0.563188
\(455\) 4.00000 0.187523
\(456\) −1.00000 −0.0468293
\(457\) −22.0000 −1.02912 −0.514558 − 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 − 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 − 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −6.00000 −0.278543
\(465\) 2.00000 0.0927478
\(466\) −24.0000 −1.11178
\(467\) 6.00000 0.277647 0.138823 − 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 2.00000 0.0924500
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) −4.00000 −0.184310
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) −2.00000 −0.0918630
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) −24.0000 −1.09773
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 4.00000 0.182384
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −10.0000 −0.454077
\(486\) −1.00000 −0.0453609
\(487\) −16.0000 −0.725029 −0.362515 − 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −4.00000 −0.180886
\(490\) 3.00000 0.135526
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −2.00000 −0.0899843
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) 20.0000 0.895323 0.447661 − 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) −12.0000 −0.535054 −0.267527 − 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) −2.00000 −0.0890871
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −16.0000 −0.709885
\(509\) −6.00000 −0.265945 −0.132973 − 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 28.0000 1.23865
\(512\) −1.00000 −0.0441942
\(513\) 1.00000 0.0441511
\(514\) −6.00000 −0.264649
\(515\) 8.00000 0.352522
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) −4.00000 −0.175750
\(519\) −18.0000 −0.790112
\(520\) −2.00000 −0.0877058
\(521\) 12.0000 0.525730 0.262865 − 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 6.00000 0.262613
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) −6.00000 −0.260378
\(532\) 2.00000 0.0867110
\(533\) 0 0
\(534\) 12.0000 0.519291
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 6.00000 0.258919
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −10.0000 −0.429934 −0.214967 − 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −20.0000 −0.859074
\(543\) −16.0000 −0.686626
\(544\) 0 0
\(545\) −16.0000 −0.685365
\(546\) −4.00000 −0.171184
\(547\) −4.00000 −0.171028 −0.0855138 − 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −12.0000 −0.512615
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 28.0000 1.18961
\(555\) 2.00000 0.0848953
\(556\) −4.00000 −0.169638
\(557\) 6.00000 0.254228 0.127114 − 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 16.0000 0.676728
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) −24.0000 −1.01238
\(563\) −24.0000 −1.01148 −0.505740 − 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) −32.0000 −1.34506
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 − 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) −1.00000 −0.0418854
\(571\) 20.0000 0.836974 0.418487 − 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 − 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 17.0000 0.707107
\(579\) 2.00000 0.0831172
\(580\) −6.00000 −0.249136
\(581\) 12.0000 0.497844
\(582\) 10.0000 0.414513
\(583\) 0 0
\(584\) −14.0000 −0.579324
\(585\) 2.00000 0.0826898
\(586\) 6.00000 0.247858
\(587\) 18.0000 0.742940 0.371470 − 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) −3.00000 −0.123718
\(589\) 2.00000 0.0824086
\(590\) 6.00000 0.247016
\(591\) 18.0000 0.740421
\(592\) 2.00000 0.0821995
\(593\) 36.0000 1.47834 0.739171 − 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −4.00000 −0.163709
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 − 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 26.0000 1.06056 0.530281 − 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −16.0000 −0.652111
\(603\) −4.00000 −0.162893
\(604\) −10.0000 −0.406894
\(605\) −11.0000 −0.447214
\(606\) 6.00000 0.243733
\(607\) 32.0000 1.29884 0.649420 − 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −12.0000 −0.486265
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) 0 0
\(613\) −16.0000 −0.646234 −0.323117 − 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 − 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) −8.00000 −0.321807
\(619\) 20.0000 0.803868 0.401934 − 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 2.00000 0.0803219
\(621\) 0 0
\(622\) 0 0
\(623\) −24.0000 −0.961540
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 0 0
\(630\) −2.00000 −0.0796819
\(631\) 32.0000 1.27390 0.636950 − 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −2.00000 −0.0795557
\(633\) 8.00000 0.317971
\(634\) 30.0000 1.19145
\(635\) −16.0000 −0.634941
\(636\) 6.00000 0.237915
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) −24.0000 −0.947943 −0.473972 − 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 − 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 − 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 4.00000 0.156772
\(652\) −4.00000 −0.156652
\(653\) −18.0000 −0.704394 −0.352197 − 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 16.0000 0.625650
\(655\) 0 0
\(656\) 0 0
\(657\) 14.0000 0.546192
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 − 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) 32.0000 1.24466 0.622328 − 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) −20.0000 −0.777322
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 2.00000 0.0775567
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 0 0
\(669\) −4.00000 −0.154649
\(670\) 4.00000 0.154533
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) 14.0000 0.539660 0.269830 − 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −2.00000 −0.0770371
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −30.0000 −1.15299 −0.576497 − 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 6.00000 0.230429
\(679\) −20.0000 −0.767530
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 − 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 1.00000 0.0382360
\(685\) −12.0000 −0.458496
\(686\) 20.0000 0.763604
\(687\) −10.0000 −0.381524
\(688\) 8.00000 0.304997
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) −4.00000 −0.151729
\(696\) 6.00000 0.227429
\(697\) 0 0
\(698\) 10.0000 0.378506
\(699\) 24.0000 0.907763
\(700\) 2.00000 0.0755929
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 2.00000 0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) −12.0000 −0.451306
\(708\) −6.00000 −0.225494
\(709\) −10.0000 −0.375558 −0.187779 − 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) 2.00000 0.0750059
\(712\) 12.0000 0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) 24.0000 0.896296
\(718\) −24.0000 −0.895672
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 1.00000 0.0372678
\(721\) 16.0000 0.595871
\(722\) −1.00000 −0.0372161
\(723\) −22.0000 −0.818189
\(724\) −16.0000 −0.594635
\(725\) −6.00000 −0.222834
\(726\) 11.0000 0.408248
\(727\) −34.0000 −1.26099 −0.630495 − 0.776193i \(-0.717148\pi\)
−0.630495 + 0.776193i \(0.717148\pi\)
\(728\) −4.00000 −0.148250
\(729\) 1.00000 0.0370370
\(730\) −14.0000 −0.518163
\(731\) 0 0
\(732\) 2.00000 0.0739221
\(733\) 32.0000 1.18195 0.590973 − 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) 10.0000 0.369107
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 2.00000 0.0735215
\(741\) 2.00000 0.0734718
\(742\) −12.0000 −0.440534
\(743\) −48.0000 −1.76095 −0.880475 − 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) −2.00000 −0.0733236
\(745\) −6.00000 −0.219823
\(746\) −14.0000 −0.512576
\(747\) 6.00000 0.219529
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −22.0000 −0.802791 −0.401396 − 0.915905i \(-0.631475\pi\)
−0.401396 + 0.915905i \(0.631475\pi\)
\(752\) 0 0
\(753\) 12.0000 0.437304
\(754\) 12.0000 0.437014
\(755\) −10.0000 −0.363937
\(756\) 2.00000 0.0727393
\(757\) 32.0000 1.16306 0.581530 − 0.813525i \(-0.302454\pi\)
0.581530 + 0.813525i \(0.302454\pi\)
\(758\) −8.00000 −0.290573
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) 6.00000 0.217500 0.108750 − 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 16.0000 0.579619
\(763\) −32.0000 −1.15848
\(764\) 0 0
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) −12.0000 −0.433295
\(768\) 1.00000 0.0360844
\(769\) −34.0000 −1.22607 −0.613036 − 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 2.00000 0.0719816
\(773\) −18.0000 −0.647415 −0.323708 − 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) −8.00000 −0.287554
\(775\) 2.00000 0.0718421
\(776\) 10.0000 0.358979
\(777\) 4.00000 0.143499
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) −3.00000 −0.107143
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) 44.0000 1.56843 0.784215 − 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) 18.0000 0.641223
\(789\) −24.0000 −0.854423
\(790\) −2.00000 −0.0711568
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) −8.00000 −0.283909
\(795\) 6.00000 0.212798
\(796\) −4.00000 −0.141776
\(797\) 42.0000 1.48772 0.743858 − 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) −12.0000 −0.423999
\(802\) −12.0000 −0.423735
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) 18.0000 0.633630
\(808\) 6.00000 0.211079
\(809\) 54.0000 1.89854 0.949269 − 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −12.0000 −0.421117
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) −4.00000 −0.140114
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 22.0000 0.769212
\(819\) 4.00000 0.139771
\(820\) 0 0
\(821\) 42.0000 1.46581 0.732905 − 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 12.0000 0.418548
\(823\) −22.0000 −0.766872 −0.383436 − 0.923567i \(-0.625259\pi\)
−0.383436 + 0.923567i \(0.625259\pi\)
\(824\) −8.00000 −0.278693
\(825\) 0 0
\(826\) 12.0000 0.417533
\(827\) 48.0000 1.66912 0.834562 − 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 0 0
\(829\) 8.00000 0.277851 0.138926 − 0.990303i \(-0.455635\pi\)
0.138926 + 0.990303i \(0.455635\pi\)
\(830\) −6.00000 −0.208263
\(831\) −28.0000 −0.971309
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) −12.0000 −0.414533
\(839\) −24.0000 −0.828572 −0.414286 − 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) −2.00000 −0.0690066
\(841\) 7.00000 0.241379
\(842\) −8.00000 −0.275698
\(843\) 24.0000 0.826604
\(844\) 8.00000 0.275371
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −22.0000 −0.755929
\(848\) 6.00000 0.206041
\(849\) 32.0000 1.09824
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 44.0000 1.50653 0.753266 − 0.657716i \(-0.228477\pi\)
0.753266 + 0.657716i \(0.228477\pi\)
\(854\) −4.00000 −0.136877
\(855\) 1.00000 0.0341993
\(856\) 0 0
\(857\) −18.0000 −0.614868 −0.307434 − 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 − 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −18.0000 −0.612018
\(866\) −2.00000 −0.0679628
\(867\) −17.0000 −0.577350
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 6.00000 0.203419
\(871\) −8.00000 −0.271070
\(872\) 16.0000 0.541828
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 2.00000 0.0676123
\(876\) 14.0000 0.473016
\(877\) 38.0000 1.28317 0.641584 − 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 22.0000 0.742464
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 − 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 3.00000 0.101015
\(883\) −16.0000 −0.538443 −0.269221 − 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) 0 0
\(885\) −6.00000 −0.201688
\(886\) 30.0000 1.00787
\(887\) −48.0000 −1.61168 −0.805841 − 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −32.0000 −1.07325
\(890\) 12.0000 0.402241
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) 6.00000 0.200558
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −24.0000 −0.800890
\(899\) −12.0000 −0.400222
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) 6.00000 0.199557
\(905\) −16.0000 −0.531858
\(906\) 10.0000 0.332228
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 12.0000 0.398234
\(909\) −6.00000 −0.199007
\(910\) −4.00000 −0.132599
\(911\) 60.0000 1.98789 0.993944 − 0.109885i \(-0.0350482\pi\)
0.993944 + 0.109885i \(0.0350482\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) 22.0000 0.727695
\(915\) 2.00000 0.0661180
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 0 0
\(919\) −40.0000 −1.31948 −0.659739 − 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −30.0000 −0.987997
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) −26.0000 −0.854413
\(927\) 8.00000 0.262754
\(928\) 6.00000 0.196960
\(929\) −6.00000 −0.196854 −0.0984268 − 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) −2.00000 −0.0655826
\(931\) −3.00000 −0.0983210
\(932\) 24.0000 0.786146
\(933\) 0 0
\(934\) −6.00000 −0.196326
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 26.0000 0.849383 0.424691 − 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 8.00000 0.261209
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 − 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 4.00000 0.130327
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 2.00000 0.0650600
\(946\) 0 0
\(947\) −18.0000 −0.584921 −0.292461 − 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 2.00000 0.0649570
\(949\) 28.0000 0.908918
\(950\) −1.00000 −0.0324443
\(951\) −30.0000 −0.972817
\(952\) 0 0
\(953\) 30.0000 0.971795 0.485898 − 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) 0 0
\(959\) −24.0000 −0.775000
\(960\) 1.00000 0.0322749
\(961\) −27.0000 −0.870968
\(962\) −4.00000 −0.128965
\(963\) 0 0
\(964\) −22.0000 −0.708572
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 26.0000 0.836104 0.418052 − 0.908423i \(-0.362713\pi\)
0.418052 + 0.908423i \(0.362713\pi\)
\(968\) 11.0000 0.353553
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) −42.0000 −1.34784 −0.673922 − 0.738802i \(-0.735392\pi\)
−0.673922 + 0.738802i \(0.735392\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.00000 −0.256468
\(974\) 16.0000 0.512673
\(975\) 2.00000 0.0640513
\(976\) 2.00000 0.0640184
\(977\) −42.0000 −1.34370 −0.671850 − 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 4.00000 0.127906
\(979\) 0 0
\(980\) −3.00000 −0.0958315
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) 24.0000 0.765481 0.382741 − 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) 18.0000 0.573528
\(986\) 0 0
\(987\) 0 0
\(988\) 2.00000 0.0636285
\(989\) 0 0
\(990\) 0 0
\(991\) −58.0000 −1.84243 −0.921215 − 0.389053i \(-0.872802\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −4.00000 −0.126809
\(996\) 6.00000 0.190117
\(997\) 44.0000 1.39349 0.696747 − 0.717317i \(-0.254630\pi\)
0.696747 + 0.717317i \(0.254630\pi\)
\(998\) −20.0000 −0.633089
\(999\) 2.00000 0.0632772
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 570.2.a.f.1.1 ✓ 1
3.2 odd 2 1710.2.a.o.1.1 1
4.3 odd 2 4560.2.a.m.1.1 1
5.2 odd 4 2850.2.d.d.799.1 2
5.3 odd 4 2850.2.d.d.799.2 2
5.4 even 2 2850.2.a.q.1.1 1
15.14 odd 2 8550.2.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.f.1.1 ✓ 1 1.1 even 1 trivial
1710.2.a.o.1.1 1 3.2 odd 2
2850.2.a.q.1.1 1 5.4 even 2
2850.2.d.d.799.1 2 5.2 odd 4
2850.2.d.d.799.2 2 5.3 odd 4
4560.2.a.m.1.1 1 4.3 odd 2
8550.2.a.e.1.1 1 15.14 odd 2