Properties

Label 1290.2.a.b.1.1
Level $1290$
Weight $2$
Character 1290.1
Self dual yes
Analytic conductor $10.301$
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] = [1290,2,Mod(1,1290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1290, 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("1290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1290.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: \(10.3007018607\)
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 \(\chi\) \(=\) 1290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -2.00000 q^{19} +1.00000 q^{20} -6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} +1.00000 q^{30} +8.00000 q^{31} -1.00000 q^{32} -6.00000 q^{33} +1.00000 q^{36} -8.00000 q^{37} +2.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -1.00000 q^{43} +6.00000 q^{44} +1.00000 q^{45} +4.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} +8.00000 q^{53} +1.00000 q^{54} +6.00000 q^{55} +2.00000 q^{57} -2.00000 q^{58} +2.00000 q^{59} -1.00000 q^{60} -6.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +6.00000 q^{66} -4.00000 q^{67} +4.00000 q^{69} +12.0000 q^{71} -1.00000 q^{72} +8.00000 q^{74} -1.00000 q^{75} -2.00000 q^{76} +2.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} +1.00000 q^{86} -2.00000 q^{87} -6.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -4.00000 q^{92} -8.00000 q^{93} -12.0000 q^{94} -2.00000 q^{95} +1.00000 q^{96} -2.00000 q^{97} +7.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −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
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 1.00000 0.182574
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −1.00000 −0.176777
\(33\) −6.00000 −1.04447
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 2.00000 0.324443
\(39\) −2.00000 −0.320256
\(40\) −1.00000 −0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499
\(44\) 6.00000 0.904534
\(45\) 1.00000 0.149071
\(46\) 4.00000 0.589768
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 8.00000 1.09888 0.549442 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) 1.00000 0.136083
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) −2.00000 −0.262613
\(59\) 2.00000 0.260378 0.130189 0.991489i \(-0.458442\pi\)
0.130189 + 0.991489i \(0.458442\pi\)
\(60\) −1.00000 −0.129099
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 6.00000 0.738549
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 8.00000 0.929981
\(75\) −1.00000 −0.115470
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) −2.00000 −0.214423
\(88\) −6.00000 −0.639602
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −8.00000 −0.829561
\(94\) −12.0000 −1.23771
\(95\) −2.00000 −0.205196
\(96\) 1.00000 0.102062
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 7.00000 0.707107
\(99\) 6.00000 0.603023
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −8.00000 −0.777029
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) −6.00000 −0.572078
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −2.00000 −0.187317
\(115\) −4.00000 −0.373002
\(116\) 2.00000 0.185695
\(117\) 2.00000 0.184900
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 25.0000 2.27273
\(122\) 6.00000 0.543214
\(123\) 2.00000 0.180334
\(124\) 8.00000 0.718421
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) −2.00000 −0.175412
\(131\) 16.0000 1.39793 0.698963 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) −4.00000 −0.340503
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) −12.0000 −1.00702
\(143\) 12.0000 1.00349
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) 7.00000 0.577350
\(148\) −8.00000 −0.657596
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 1.00000 0.0816497
\(151\) 22.0000 1.79033 0.895167 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) −2.00000 −0.160128
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) −8.00000 −0.634441
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −2.00000 −0.156174
\(165\) −6.00000 −0.467099
\(166\) −12.0000 −0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) −1.00000 −0.0762493
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) −2.00000 −0.150329
\(178\) −6.00000 −0.449719
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 1.00000 0.0745356
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 4.00000 0.294884
\(185\) −8.00000 −0.588172
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 2.00000 0.145095
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 26.0000 1.87152 0.935760 0.352636i \(-0.114715\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) 2.00000 0.143592
\(195\) −2.00000 −0.143223
\(196\) −7.00000 −0.500000
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) −6.00000 −0.426401
\(199\) −26.0000 −1.84309 −0.921546 0.388270i \(-0.873073\pi\)
−0.921546 + 0.388270i \(0.873073\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 4.00000 0.282138
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) 0 0
\(205\) −2.00000 −0.139686
\(206\) 16.0000 1.11477
\(207\) −4.00000 −0.278019
\(208\) 2.00000 0.138675
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 8.00000 0.549442
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −1.00000 −0.0681994
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −18.0000 −1.21911
\(219\) 0 0
\(220\) 6.00000 0.404520
\(221\) 0 0
\(222\) −8.00000 −0.536925
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 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 \(0.369623\pi\)
\(228\) 2.00000 0.132453
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −2.00000 −0.130744
\(235\) 12.0000 0.782794
\(236\) 2.00000 0.130189
\(237\) 0 0
\(238\) 0 0
\(239\) −10.0000 −0.646846 −0.323423 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) −25.0000 −1.60706
\(243\) −1.00000 −0.0641500
\(244\) −6.00000 −0.384111
\(245\) −7.00000 −0.447214
\(246\) −2.00000 −0.127515
\(247\) −4.00000 −0.254514
\(248\) −8.00000 −0.508001
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) 26.0000 1.64111 0.820553 0.571571i \(-0.193666\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 2.00000 0.123797
\(262\) −16.0000 −0.988483
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 6.00000 0.369274
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) −26.0000 −1.58525 −0.792624 0.609711i \(-0.791286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 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
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 6.00000 0.361814
\(276\) 4.00000 0.240772
\(277\) −24.0000 −1.44202 −0.721010 0.692925i \(-0.756322\pi\)
−0.721010 + 0.692925i \(0.756322\pi\)
\(278\) −16.0000 −0.959616
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 12.0000 0.714590
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 12.0000 0.712069
\(285\) 2.00000 0.118470
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) −2.00000 −0.117444
\(291\) 2.00000 0.117242
\(292\) 0 0
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) −7.00000 −0.408248
\(295\) 2.00000 0.116445
\(296\) 8.00000 0.464991
\(297\) −6.00000 −0.348155
\(298\) 10.0000 0.579284
\(299\) −8.00000 −0.462652
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) −22.0000 −1.26596
\(303\) 2.00000 0.114897
\(304\) −2.00000 −0.114708
\(305\) −6.00000 −0.343559
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −8.00000 −0.454369
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) 2.00000 0.113228
\(313\) 12.0000 0.678280 0.339140 0.940736i \(-0.389864\pi\)
0.339140 + 0.940736i \(0.389864\pi\)
\(314\) −8.00000 −0.451466
\(315\) 0 0
\(316\) 0 0
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 8.00000 0.448618
\(319\) 12.0000 0.671871
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) 16.0000 0.886158
\(327\) −18.0000 −0.995402
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) 6.00000 0.330289
\(331\) −10.0000 −0.549650 −0.274825 0.961494i \(-0.588620\pi\)
−0.274825 + 0.961494i \(0.588620\pi\)
\(332\) 12.0000 0.658586
\(333\) −8.00000 −0.438397
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 9.00000 0.489535
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 48.0000 2.59935
\(342\) 2.00000 0.108148
\(343\) 0 0
\(344\) 1.00000 0.0539164
\(345\) 4.00000 0.215353
\(346\) 0 0
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) −2.00000 −0.107211
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −6.00000 −0.319801
\(353\) −16.0000 −0.851594 −0.425797 0.904819i \(-0.640006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) 2.00000 0.106299
\(355\) 12.0000 0.636894
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −15.0000 −0.789474
\(362\) 14.0000 0.735824
\(363\) −25.0000 −1.31216
\(364\) 0 0
\(365\) 0 0
\(366\) −6.00000 −0.313625
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −4.00000 −0.208514
\(369\) −2.00000 −0.104116
\(370\) 8.00000 0.415900
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) 36.0000 1.86401 0.932005 0.362446i \(-0.118058\pi\)
0.932005 + 0.362446i \(0.118058\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −12.0000 −0.618853
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −2.00000 −0.102598
\(381\) −8.00000 −0.409852
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) −1.00000 −0.0508329
\(388\) −2.00000 −0.101535
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 2.00000 0.101274
\(391\) 0 0
\(392\) 7.00000 0.353553
\(393\) −16.0000 −0.807093
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 26.0000 1.30326
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) −4.00000 −0.199502
\(403\) 16.0000 0.797017
\(404\) −2.00000 −0.0995037
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −48.0000 −2.37927
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 2.00000 0.0987730
\(411\) −2.00000 −0.0986527
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 4.00000 0.196589
\(415\) 12.0000 0.589057
\(416\) −2.00000 −0.0980581
\(417\) −16.0000 −0.783523
\(418\) 12.0000 0.586939
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 14.0000 0.681509
\(423\) 12.0000 0.583460
\(424\) −8.00000 −0.388514
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 0 0
\(429\) −12.0000 −0.579365
\(430\) 1.00000 0.0482243
\(431\) 10.0000 0.481683 0.240842 0.970564i \(-0.422577\pi\)
0.240842 + 0.970564i \(0.422577\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 18.0000 0.862044
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −6.00000 −0.286039
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −32.0000 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(444\) 8.00000 0.379663
\(445\) 6.00000 0.284427
\(446\) −16.0000 −0.757622
\(447\) 10.0000 0.472984
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −12.0000 −0.565058
\(452\) 6.00000 0.282216
\(453\) −22.0000 −1.03365
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −8.00000 −0.374224 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 22.0000 1.02799
\(459\) 0 0
\(460\) −4.00000 −0.186501
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 2.00000 0.0928477
\(465\) −8.00000 −0.370991
\(466\) 14.0000 0.648537
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) −12.0000 −0.553519
\(471\) −8.00000 −0.368621
\(472\) −2.00000 −0.0920575
\(473\) −6.00000 −0.275880
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 8.00000 0.366295
\(478\) 10.0000 0.457389
\(479\) −30.0000 −1.37073 −0.685367 0.728197i \(-0.740358\pi\)
−0.685367 + 0.728197i \(0.740358\pi\)
\(480\) 1.00000 0.0456435
\(481\) −16.0000 −0.729537
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −2.00000 −0.0908153
\(486\) 1.00000 0.0453609
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 6.00000 0.271607
\(489\) 16.0000 0.723545
\(490\) 7.00000 0.316228
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 2.00000 0.0901670
\(493\) 0 0
\(494\) 4.00000 0.179969
\(495\) 6.00000 0.269680
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) 26.0000 1.16392 0.581960 0.813217i \(-0.302286\pi\)
0.581960 + 0.813217i \(0.302286\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0 0
\(502\) −26.0000 −1.16044
\(503\) −32.0000 −1.42681 −0.713405 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) 24.0000 1.06693
\(507\) 9.00000 0.399704
\(508\) 8.00000 0.354943
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) 18.0000 0.793946
\(515\) −16.0000 −0.705044
\(516\) 1.00000 0.0440225
\(517\) 72.0000 3.16656
\(518\) 0 0
\(519\) 0 0
\(520\) −2.00000 −0.0877058
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 28.0000 1.22435 0.612177 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 16.0000 0.698963
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) −6.00000 −0.261116
\(529\) −7.00000 −0.304348
\(530\) −8.00000 −0.347498
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −4.00000 −0.172613
\(538\) 26.0000 1.12094
\(539\) −42.0000 −1.80907
\(540\) −1.00000 −0.0430331
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) −20.0000 −0.859074
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 2.00000 0.0854358
\(549\) −6.00000 −0.256074
\(550\) −6.00000 −0.255841
\(551\) −4.00000 −0.170406
\(552\) −4.00000 −0.170251
\(553\) 0 0
\(554\) 24.0000 1.01966
\(555\) 8.00000 0.339581
\(556\) 16.0000 0.678551
\(557\) −4.00000 −0.169485 −0.0847427 0.996403i \(-0.527007\pi\)
−0.0847427 + 0.996403i \(0.527007\pi\)
\(558\) −8.00000 −0.338667
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 2.00000 0.0843649
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −12.0000 −0.505291
\(565\) 6.00000 0.252422
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −2.00000 −0.0837708
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 12.0000 0.501745
\(573\) 0 0
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) 17.0000 0.707107
\(579\) −26.0000 −1.08052
\(580\) 2.00000 0.0830455
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) 48.0000 1.98796
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 12.0000 0.495715
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 7.00000 0.288675
\(589\) −16.0000 −0.659269
\(590\) −2.00000 −0.0823387
\(591\) 12.0000 0.493614
\(592\) −8.00000 −0.328798
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 6.00000 0.246183
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 26.0000 1.06411
\(598\) 8.00000 0.327144
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 1.00000 0.0408248
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 22.0000 0.895167
\(605\) 25.0000 1.01639
\(606\) −2.00000 −0.0812444
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) 18.0000 0.727013 0.363507 0.931592i \(-0.381579\pi\)
0.363507 + 0.931592i \(0.381579\pi\)
\(614\) −4.00000 −0.161427
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) −16.0000 −0.643614
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) 8.00000 0.321288
\(621\) 4.00000 0.160514
\(622\) −6.00000 −0.240578
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) 1.00000 0.0400000
\(626\) −12.0000 −0.479616
\(627\) 12.0000 0.479234
\(628\) 8.00000 0.319235
\(629\) 0 0
\(630\) 0 0
\(631\) −46.0000 −1.83123 −0.915616 0.402055i \(-0.868296\pi\)
−0.915616 + 0.402055i \(0.868296\pi\)
\(632\) 0 0
\(633\) 14.0000 0.556450
\(634\) −12.0000 −0.476581
\(635\) 8.00000 0.317470
\(636\) −8.00000 −0.317221
\(637\) −14.0000 −0.554700
\(638\) −12.0000 −0.475085
\(639\) 12.0000 0.474713
\(640\) −1.00000 −0.0395285
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 1.00000 0.0393750
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 12.0000 0.471041
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 18.0000 0.703856
\(655\) 16.0000 0.625172
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) −6.00000 −0.233550
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) −8.00000 −0.309761
\(668\) 0 0
\(669\) −16.0000 −0.618596
\(670\) 4.00000 0.154533
\(671\) −36.0000 −1.38976
\(672\) 0 0
\(673\) −32.0000 −1.23351 −0.616755 0.787155i \(-0.711553\pi\)
−0.616755 + 0.787155i \(0.711553\pi\)
\(674\) 14.0000 0.539260
\(675\) −1.00000 −0.0384900
\(676\) −9.00000 −0.346154
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 6.00000 0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) −48.0000 −1.83801
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) −1.00000 −0.0381246
\(689\) 16.0000 0.609551
\(690\) −4.00000 −0.152277
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 16.0000 0.606915
\(696\) 2.00000 0.0758098
\(697\) 0 0
\(698\) 6.00000 0.227103
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 2.00000 0.0754851
\(703\) 16.0000 0.603451
\(704\) 6.00000 0.226134
\(705\) −12.0000 −0.451946
\(706\) 16.0000 0.602168
\(707\) 0 0
\(708\) −2.00000 −0.0751646
\(709\) −2.00000 −0.0751116 −0.0375558 0.999295i \(-0.511957\pi\)
−0.0375558 + 0.999295i \(0.511957\pi\)
\(710\) −12.0000 −0.450352
\(711\) 0 0
\(712\) −6.00000 −0.224860
\(713\) −32.0000 −1.19841
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 4.00000 0.149487
\(717\) 10.0000 0.373457
\(718\) 18.0000 0.671754
\(719\) −34.0000 −1.26799 −0.633993 0.773339i \(-0.718585\pi\)
−0.633993 + 0.773339i \(0.718585\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 2.00000 0.0743808
\(724\) −14.0000 −0.520306
\(725\) 2.00000 0.0742781
\(726\) 25.0000 0.927837
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 6.00000 0.221766
\(733\) −8.00000 −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) 0 0
\(735\) 7.00000 0.258199
\(736\) 4.00000 0.147442
\(737\) −24.0000 −0.884051
\(738\) 2.00000 0.0736210
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) −8.00000 −0.294086
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 32.0000 1.17397 0.586983 0.809599i \(-0.300316\pi\)
0.586983 + 0.809599i \(0.300316\pi\)
\(744\) 8.00000 0.293294
\(745\) −10.0000 −0.366372
\(746\) −36.0000 −1.31805
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) 12.0000 0.437595
\(753\) −26.0000 −0.947493
\(754\) −4.00000 −0.145671
\(755\) 22.0000 0.800662
\(756\) 0 0
\(757\) 20.0000 0.726912 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(758\) 20.0000 0.726433
\(759\) 24.0000 0.871145
\(760\) 2.00000 0.0725476
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 4.00000 0.144432
\(768\) −1.00000 −0.0360844
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 26.0000 0.935760
\(773\) −26.0000 −0.935155 −0.467578 0.883952i \(-0.654873\pi\)
−0.467578 + 0.883952i \(0.654873\pi\)
\(774\) 1.00000 0.0359443
\(775\) 8.00000 0.287368
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 4.00000 0.143315
\(780\) −2.00000 −0.0716115
\(781\) 72.0000 2.57636
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) −7.00000 −0.250000
\(785\) 8.00000 0.285532
\(786\) 16.0000 0.570701
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) −12.0000 −0.427482
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) −6.00000 −0.213201
\(793\) −12.0000 −0.426132
\(794\) −22.0000 −0.780751
\(795\) −8.00000 −0.283731
\(796\) −26.0000 −0.921546
\(797\) 48.0000 1.70025 0.850124 0.526583i \(-0.176527\pi\)
0.850124 + 0.526583i \(0.176527\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 6.00000 0.212000
\(802\) −10.0000 −0.353112
\(803\) 0 0
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 26.0000 0.915243
\(808\) 2.00000 0.0703598
\(809\) 38.0000 1.33601 0.668004 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 48.0000 1.68240
\(815\) −16.0000 −0.560456
\(816\) 0 0
\(817\) 2.00000 0.0699711
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) −2.00000 −0.0698430
\(821\) −38.0000 −1.32621 −0.663105 0.748527i \(-0.730762\pi\)
−0.663105 + 0.748527i \(0.730762\pi\)
\(822\) 2.00000 0.0697580
\(823\) −56.0000 −1.95204 −0.976019 0.217687i \(-0.930149\pi\)
−0.976019 + 0.217687i \(0.930149\pi\)
\(824\) 16.0000 0.557386
\(825\) −6.00000 −0.208893
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −4.00000 −0.139010
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −12.0000 −0.416526
\(831\) 24.0000 0.832551
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) 16.0000 0.554035
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) −8.00000 −0.276520
\(838\) −24.0000 −0.829066
\(839\) −48.0000 −1.65714 −0.828572 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −10.0000 −0.344623
\(843\) 2.00000 0.0688837
\(844\) −14.0000 −0.481900
\(845\) −9.00000 −0.309609
\(846\) −12.0000 −0.412568
\(847\) 0 0
\(848\) 8.00000 0.274721
\(849\) 4.00000 0.137280
\(850\) 0 0
\(851\) 32.0000 1.09695
\(852\) −12.0000 −0.411113
\(853\) −2.00000 −0.0684787 −0.0342393 0.999414i \(-0.510901\pi\)
−0.0342393 + 0.999414i \(0.510901\pi\)
\(854\) 0 0
\(855\) −2.00000 −0.0683986
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 12.0000 0.409673
\(859\) 42.0000 1.43302 0.716511 0.697576i \(-0.245738\pi\)
0.716511 + 0.697576i \(0.245738\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 0 0
\(862\) −10.0000 −0.340601
\(863\) 40.0000 1.36162 0.680808 0.732462i \(-0.261629\pi\)
0.680808 + 0.732462i \(0.261629\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 0 0
\(867\) 17.0000 0.577350
\(868\) 0 0
\(869\) 0 0
\(870\) 2.00000 0.0678064
\(871\) −8.00000 −0.271070
\(872\) −18.0000 −0.609557
\(873\) −2.00000 −0.0676897
\(874\) −8.00000 −0.270604
\(875\) 0 0
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 0 0
\(879\) 12.0000 0.404750
\(880\) 6.00000 0.202260
\(881\) −10.0000 −0.336909 −0.168454 0.985709i \(-0.553878\pi\)
−0.168454 + 0.985709i \(0.553878\pi\)
\(882\) 7.00000 0.235702
\(883\) −12.0000 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 0 0
\(885\) −2.00000 −0.0672293
\(886\) 32.0000 1.07506
\(887\) 8.00000 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) −8.00000 −0.268462
\(889\) 0 0
\(890\) −6.00000 −0.201120
\(891\) 6.00000 0.201008
\(892\) 16.0000 0.535720
\(893\) −24.0000 −0.803129
\(894\) −10.0000 −0.334450
\(895\) 4.00000 0.133705
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) −2.00000 −0.0667409
\(899\) 16.0000 0.533630
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 12.0000 0.399556
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) −14.0000 −0.465376
\(906\) 22.0000 0.730901
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 12.0000 0.398234
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 2.00000 0.0662266
\(913\) 72.0000 2.38285
\(914\) 8.00000 0.264616
\(915\) 6.00000 0.198354
\(916\) −22.0000 −0.726900
\(917\) 0 0
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 4.00000 0.131876
\(921\) −4.00000 −0.131804
\(922\) 10.0000 0.329332
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) −8.00000 −0.263038
\(926\) 20.0000 0.657241
\(927\) −16.0000 −0.525509
\(928\) −2.00000 −0.0656532
\(929\) −42.0000 −1.37798 −0.688988 0.724773i \(-0.741945\pi\)
−0.688988 + 0.724773i \(0.741945\pi\)
\(930\) 8.00000 0.262330
\(931\) 14.0000 0.458831
\(932\) −14.0000 −0.458585
\(933\) −6.00000 −0.196431
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) −44.0000 −1.43742 −0.718709 0.695311i \(-0.755266\pi\)
−0.718709 + 0.695311i \(0.755266\pi\)
\(938\) 0 0
\(939\) −12.0000 −0.391605
\(940\) 12.0000 0.391397
\(941\) 54.0000 1.76035 0.880175 0.474650i \(-0.157425\pi\)
0.880175 + 0.474650i \(0.157425\pi\)
\(942\) 8.00000 0.260654
\(943\) 8.00000 0.260516
\(944\) 2.00000 0.0650945
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) −24.0000 −0.779895 −0.389948 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.00000 0.0648886
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −18.0000 −0.583077 −0.291539 0.956559i \(-0.594167\pi\)
−0.291539 + 0.956559i \(0.594167\pi\)
\(954\) −8.00000 −0.259010
\(955\) 0 0
\(956\) −10.0000 −0.323423
\(957\) −12.0000 −0.387905
\(958\) 30.0000 0.969256
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) 33.0000 1.06452
\(962\) 16.0000 0.515861
\(963\) 0 0
\(964\) −2.00000 −0.0644157
\(965\) 26.0000 0.836970
\(966\) 0 0
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) −25.0000 −0.803530
\(969\) 0 0
\(970\) 2.00000 0.0642161
\(971\) −42.0000 −1.34784 −0.673922 0.738802i \(-0.735392\pi\)
−0.673922 + 0.738802i \(0.735392\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 0 0
\(975\) −2.00000 −0.0640513
\(976\) −6.00000 −0.192055
\(977\) −60.0000 −1.91957 −0.959785 0.280736i \(-0.909421\pi\)
−0.959785 + 0.280736i \(0.909421\pi\)
\(978\) −16.0000 −0.511624
\(979\) 36.0000 1.15056
\(980\) −7.00000 −0.223607
\(981\) 18.0000 0.574696
\(982\) −12.0000 −0.382935
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) −2.00000 −0.0637577
\(985\) −12.0000 −0.382352
\(986\) 0 0
\(987\) 0 0
\(988\) −4.00000 −0.127257
\(989\) 4.00000 0.127193
\(990\) −6.00000 −0.190693
\(991\) −50.0000 −1.58830 −0.794151 0.607720i \(-0.792084\pi\)
−0.794151 + 0.607720i \(0.792084\pi\)
\(992\) −8.00000 −0.254000
\(993\) 10.0000 0.317340
\(994\) 0 0
\(995\) −26.0000 −0.824255
\(996\) −12.0000 −0.380235
\(997\) 8.00000 0.253363 0.126681 0.991943i \(-0.459567\pi\)
0.126681 + 0.991943i \(0.459567\pi\)
\(998\) −26.0000 −0.823016
\(999\) 8.00000 0.253109
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 1290.2.a.b.1.1 1
3.2 odd 2 3870.2.a.p.1.1 1
5.4 even 2 6450.2.a.bk.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1290.2.a.b.1.1 1 1.1 even 1 trivial
3870.2.a.p.1.1 1 3.2 odd 2
6450.2.a.bk.1.1 1 5.4 even 2