↑

Properties

Label 6034.2.a.d.1.1
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $1$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +4.00000 q^{10} +4.00000 q^{11} -2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +3.00000 q^{18} +4.00000 q^{19} -4.00000 q^{20} -4.00000 q^{22} -8.00000 q^{23} +11.0000 q^{25} +2.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -4.00000 q^{34} -4.00000 q^{35} -3.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} +4.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} +4.00000 q^{44} +12.0000 q^{45} +8.00000 q^{46} +1.00000 q^{49} -11.0000 q^{50} -2.00000 q^{52} -2.00000 q^{53} -16.0000 q^{55} -1.00000 q^{56} +6.00000 q^{58} +8.00000 q^{59} -8.00000 q^{61} +4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +8.00000 q^{65} -12.0000 q^{67} +4.00000 q^{68} +4.00000 q^{70} +8.00000 q^{71} +3.00000 q^{72} +16.0000 q^{73} -6.00000 q^{74} +4.00000 q^{76} +4.00000 q^{77} +16.0000 q^{79} -4.00000 q^{80} +9.00000 q^{81} +6.00000 q^{82} +14.0000 q^{83} -16.0000 q^{85} -4.00000 q^{86} -4.00000 q^{88} -12.0000 q^{90} -2.00000 q^{91} -8.00000 q^{92} -16.0000 q^{95} -2.00000 q^{97} -1.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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
\(3\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.00000 −1.78885 −0.894427 − 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 4.00000 1.26491
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 − 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 3.00000 0.707107
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −8.00000 −1.66812 −0.834058 − 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) −4.00000 −0.676123
\(36\) −3.00000 −0.500000
\(37\) 6.00000 0.986394 0.493197 − 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) −4.00000 −0.648886
\(39\) 0 0
\(40\) 4.00000 0.632456
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 4.00000 0.603023
\(45\) 12.0000 1.78885
\(46\) 8.00000 1.17954
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −11.0000 −1.55563
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −16.0000 −2.15744
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 − 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 4.00000 0.508001
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 3.00000 0.353553
\(73\) 16.0000 1.87266 0.936329 − 0.351123i \(-0.114200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) −6.00000 −0.697486
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 − 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) −4.00000 −0.447214
\(81\) 9.00000 1.00000
\(82\) 6.00000 0.662589
\(83\) 14.0000 1.53670 0.768350 − 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −12.0000 −1.26491
\(91\) −2.00000 −0.209657
\(92\) −8.00000 −0.834058
\(93\) 0 0
\(94\) 0 0
\(95\) −16.0000 −1.64157
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 − 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −1.00000 −0.101015
\(99\) −12.0000 −1.20605
\(100\) 11.0000 1.10000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 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
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 16.0000 1.52554
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 32.0000 2.98402
\(116\) −6.00000 −0.557086
\(117\) 6.00000 0.554700
\(118\) −8.00000 −0.736460
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 8.00000 0.724286
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −24.0000 −2.14663
\(126\) 3.00000 0.267261
\(127\) 8.00000 0.709885 0.354943 − 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −8.00000 −0.701646
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −4.00000 −0.342997
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 − 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) −4.00000 −0.338062
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) −8.00000 −0.668994
\(144\) −3.00000 −0.250000
\(145\) 24.0000 1.99309
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) −18.0000 −1.47462 −0.737309 − 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 − 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) −4.00000 −0.324443
\(153\) −12.0000 −0.970143
\(154\) −4.00000 −0.322329
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 − 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −16.0000 −1.27289
\(159\) 0 0
\(160\) 4.00000 0.316228
\(161\) −8.00000 −0.630488
\(162\) −9.00000 −0.707107
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −14.0000 −1.08661
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 16.0000 1.22714
\(171\) −12.0000 −0.917663
\(172\) 4.00000 0.304997
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 11.0000 0.831522
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 12.0000 0.894427
\(181\) −18.0000 −1.33793 −0.668965 − 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 2.00000 0.148250
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) −24.0000 −1.76452
\(186\) 0 0
\(187\) 16.0000 1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 16.0000 1.16076
\(191\) −16.0000 −1.15772 −0.578860 − 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) 10.0000 0.719816 0.359908 − 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 12.0000 0.852803
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −11.0000 −0.777817
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 24.0000 1.67623
\(206\) −8.00000 −0.557386
\(207\) 24.0000 1.66812
\(208\) −2.00000 −0.138675
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) −16.0000 −1.09119
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) −2.00000 −0.135457
\(219\) 0 0
\(220\) −16.0000 −1.07872
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 − 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −33.0000 −2.20000
\(226\) 6.00000 0.399114
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 − 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) −32.0000 −2.11002
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −18.0000 −1.17922 −0.589610 − 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) −6.00000 −0.392232
\(235\) 0 0
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) −4.00000 −0.259281
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −20.0000 −1.28831 −0.644157 − 0.764894i \(-0.722792\pi\)
−0.644157 + 0.764894i \(0.722792\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) −4.00000 −0.255551
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 24.0000 1.51789
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) −3.00000 −0.188982
\(253\) −32.0000 −2.01182
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 8.00000 0.496139
\(261\) 18.0000 1.11417
\(262\) −6.00000 −0.370681
\(263\) −28.0000 −1.72655 −0.863277 − 0.504730i \(-0.831592\pi\)
−0.863277 + 0.504730i \(0.831592\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) −4.00000 −0.245256
\(267\) 0 0
\(268\) −12.0000 −0.733017
\(269\) −2.00000 −0.121942 −0.0609711 − 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 − 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 44.0000 2.65330
\(276\) 0 0
\(277\) −18.0000 −1.08152 −0.540758 − 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 8.00000 0.479808
\(279\) 12.0000 0.718421
\(280\) 4.00000 0.239046
\(281\) −18.0000 −1.07379 −0.536895 − 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 − 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) −6.00000 −0.354169
\(288\) 3.00000 0.176777
\(289\) −1.00000 −0.0588235
\(290\) −24.0000 −1.40933
\(291\) 0 0
\(292\) 16.0000 0.936329
\(293\) 14.0000 0.817889 0.408944 − 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) −32.0000 −1.86311
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 16.0000 0.925304
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) −4.00000 −0.230174
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 32.0000 1.83231
\(306\) 12.0000 0.685994
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 4.00000 0.227921
\(309\) 0 0
\(310\) −16.0000 −0.908739
\(311\) 8.00000 0.453638 0.226819 − 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 16.0000 0.904373 0.452187 − 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) 4.00000 0.225733
\(315\) 12.0000 0.676123
\(316\) 16.0000 0.900070
\(317\) −6.00000 −0.336994 −0.168497 − 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) −4.00000 −0.223607
\(321\) 0 0
\(322\) 8.00000 0.445823
\(323\) 16.0000 0.890264
\(324\) 9.00000 0.500000
\(325\) −22.0000 −1.22034
\(326\) −12.0000 −0.664619
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 14.0000 0.768350
\(333\) −18.0000 −0.986394
\(334\) 0 0
\(335\) 48.0000 2.62252
\(336\) 0 0
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) −16.0000 −0.867722
\(341\) −16.0000 −0.866449
\(342\) 12.0000 0.648886
\(343\) 1.00000 0.0539949
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 0 0
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 − 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −11.0000 −0.587975
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −32.0000 −1.69838
\(356\) 0 0
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −8.00000 −0.422224 −0.211112 − 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) −12.0000 −0.632456
\(361\) −3.00000 −0.157895
\(362\) 18.0000 0.946059
\(363\) 0 0
\(364\) −2.00000 −0.104828
\(365\) −64.0000 −3.34991
\(366\) 0 0
\(367\) −4.00000 −0.208798 −0.104399 − 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −8.00000 −0.417029
\(369\) 18.0000 0.937043
\(370\) 24.0000 1.24770
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 − 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −16.0000 −0.827340
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 − 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −16.0000 −0.820783
\(381\) 0 0
\(382\) 16.0000 0.818631
\(383\) 12.0000 0.613171 0.306586 − 0.951843i \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) 0 0
\(385\) −16.0000 −0.815436
\(386\) −10.0000 −0.508987
\(387\) −12.0000 −0.609994
\(388\) −2.00000 −0.101535
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −32.0000 −1.61831
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 18.0000 0.906827
\(395\) −64.0000 −3.22019
\(396\) −12.0000 −0.603023
\(397\) 16.0000 0.803017 0.401508 − 0.915855i \(-0.368486\pi\)
0.401508 + 0.915855i \(0.368486\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) −18.0000 −0.898877 −0.449439 − 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 10.0000 0.497519
\(405\) −36.0000 −1.78885
\(406\) 6.00000 0.297775
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 − 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) −24.0000 −1.18528
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 8.00000 0.393654
\(414\) −24.0000 −1.17954
\(415\) −56.0000 −2.74893
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) −16.0000 −0.782586
\(419\) −18.0000 −0.879358 −0.439679 − 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 − 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 8.00000 0.389434
\(423\) 0 0
\(424\) 2.00000 0.0971286
\(425\) 44.0000 2.13431
\(426\) 0 0
\(427\) −8.00000 −0.387147
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 16.0000 0.771589
\(431\) 1.00000 0.0481683
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 − 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 4.00000 0.192006
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −32.0000 −1.53077
\(438\) 0 0
\(439\) 26.0000 1.24091 0.620456 − 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 16.0000 0.762770
\(441\) −3.00000 −0.142857
\(442\) 8.00000 0.380521
\(443\) −20.0000 −0.950229 −0.475114 − 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.00000 −0.284108
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 30.0000 1.41579 0.707894 − 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 33.0000 1.55563
\(451\) −24.0000 −1.13012
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) 0 0
\(455\) 8.00000 0.375046
\(456\) 0 0
\(457\) −30.0000 −1.40334 −0.701670 − 0.712502i \(-0.747562\pi\)
−0.701670 + 0.712502i \(0.747562\pi\)
\(458\) 20.0000 0.934539
\(459\) 0 0
\(460\) 32.0000 1.49201
\(461\) −12.0000 −0.558896 −0.279448 − 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 − 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 8.00000 0.370196 0.185098 − 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 6.00000 0.277350
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) −8.00000 −0.368230
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 44.0000 2.01886
\(476\) 4.00000 0.183340
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 38.0000 1.73626 0.868132 − 0.496333i \(-0.165321\pi\)
0.868132 + 0.496333i \(0.165321\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 20.0000 0.910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 8.00000 0.363261
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 − 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 8.00000 0.362143
\(489\) 0 0
\(490\) 4.00000 0.180702
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −24.0000 −1.08091
\(494\) 8.00000 0.359937
\(495\) 48.0000 2.15744
\(496\) −4.00000 −0.179605
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 − 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −24.0000 −1.07331
\(501\) 0 0
\(502\) 6.00000 0.267793
\(503\) −30.0000 −1.33763 −0.668817 − 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 3.00000 0.133631
\(505\) −40.0000 −1.77998
\(506\) 32.0000 1.42257
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 16.0000 0.707798
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) −32.0000 −1.41009
\(516\) 0 0
\(517\) 0 0
\(518\) −6.00000 −0.263625
\(519\) 0 0
\(520\) −8.00000 −0.350823
\(521\) 14.0000 0.613351 0.306676 − 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) −18.0000 −0.787839
\(523\) 28.0000 1.22435 0.612177 − 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 28.0000 1.22086
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −8.00000 −0.347498
\(531\) −24.0000 −1.04151
\(532\) 4.00000 0.173422
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 32.0000 1.38348
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 2.00000 0.0862261
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 20.0000 0.859074
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 − 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −18.0000 −0.768922
\(549\) 24.0000 1.02430
\(550\) −44.0000 −1.87617
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 16.0000 0.680389
\(554\) 18.0000 0.764747
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) −12.0000 −0.508001
\(559\) −8.00000 −0.338364
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 18.0000 0.759284
\(563\) 36.0000 1.51722 0.758610 − 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) 24.0000 1.00969
\(566\) −4.00000 −0.168133
\(567\) 9.00000 0.377964
\(568\) −8.00000 −0.335673
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 − 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) −8.00000 −0.334497
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −88.0000 −3.66985
\(576\) −3.00000 −0.125000
\(577\) −32.0000 −1.33218 −0.666089 − 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 24.0000 0.996546
\(581\) 14.0000 0.580818
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) −16.0000 −0.662085
\(585\) −24.0000 −0.992278
\(586\) −14.0000 −0.578335
\(587\) 10.0000 0.412744 0.206372 − 0.978474i \(-0.433834\pi\)
0.206372 + 0.978474i \(0.433834\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 32.0000 1.31742
\(591\) 0 0
\(592\) 6.00000 0.246598
\(593\) −6.00000 −0.246390 −0.123195 − 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −16.0000 −0.654289
\(599\) 40.0000 1.63436 0.817178 − 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) −4.00000 −0.163163 −0.0815817 − 0.996667i \(-0.525997\pi\)
−0.0815817 + 0.996667i \(0.525997\pi\)
\(602\) −4.00000 −0.163028
\(603\) 36.0000 1.46603
\(604\) 4.00000 0.162758
\(605\) −20.0000 −0.813116
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 − 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −32.0000 −1.29564
\(611\) 0 0
\(612\) −12.0000 −0.485071
\(613\) 34.0000 1.37325 0.686624 − 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) 8.00000 0.322854
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) −2.00000 −0.0805170 −0.0402585 − 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) −18.0000 −0.723481 −0.361741 − 0.932279i \(-0.617817\pi\)
−0.361741 + 0.932279i \(0.617817\pi\)
\(620\) 16.0000 0.642575
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 24.0000 0.956943
\(630\) −12.0000 −0.478091
\(631\) −12.0000 −0.477712 −0.238856 − 0.971055i \(-0.576772\pi\)
−0.238856 + 0.971055i \(0.576772\pi\)
\(632\) −16.0000 −0.636446
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) −32.0000 −1.26988
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 24.0000 0.950169
\(639\) −24.0000 −0.949425
\(640\) 4.00000 0.158114
\(641\) −26.0000 −1.02694 −0.513469 − 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) 40.0000 1.57745 0.788723 − 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) −16.0000 −0.629512
\(647\) 18.0000 0.707653 0.353827 − 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) −9.00000 −0.353553
\(649\) 32.0000 1.25611
\(650\) 22.0000 0.862911
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) −2.00000 −0.0782660 −0.0391330 − 0.999234i \(-0.512460\pi\)
−0.0391330 + 0.999234i \(0.512460\pi\)
\(654\) 0 0
\(655\) −24.0000 −0.937758
\(656\) −6.00000 −0.234261
\(657\) −48.0000 −1.87266
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 − 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 40.0000 1.55582 0.777910 − 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) −14.0000 −0.543305
\(665\) −16.0000 −0.620453
\(666\) 18.0000 0.697486
\(667\) 48.0000 1.85857
\(668\) 0 0
\(669\) 0 0
\(670\) −48.0000 −1.85440
\(671\) −32.0000 −1.23535
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 − 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 6.00000 0.231111
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −12.0000 −0.461197 −0.230599 − 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) 16.0000 0.613572
\(681\) 0 0
\(682\) 16.0000 0.612672
\(683\) −44.0000 −1.68361 −0.841807 − 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) −12.0000 −0.458831
\(685\) 72.0000 2.75098
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) 34.0000 1.29342 0.646710 − 0.762736i \(-0.276144\pi\)
0.646710 + 0.762736i \(0.276144\pi\)
\(692\) 0 0
\(693\) −12.0000 −0.455842
\(694\) 4.00000 0.151838
\(695\) 32.0000 1.21383
\(696\) 0 0
\(697\) −24.0000 −0.909065
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) 11.0000 0.415761
\(701\) −22.0000 −0.830929 −0.415464 − 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) 24.0000 0.905177
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 10.0000 0.376089
\(708\) 0 0
\(709\) −46.0000 −1.72757 −0.863783 − 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) 32.0000 1.20094
\(711\) −48.0000 −1.80014
\(712\) 0 0
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 32.0000 1.19673
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) 8.00000 0.298557
\(719\) −18.0000 −0.671287 −0.335643 − 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 12.0000 0.447214
\(721\) 8.00000 0.297936
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) −18.0000 −0.668965
\(725\) −66.0000 −2.45118
\(726\) 0 0
\(727\) −20.0000 −0.741759 −0.370879 − 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(728\) 2.00000 0.0741249
\(729\) −27.0000 −1.00000
\(730\) 64.0000 2.36875
\(731\) 16.0000 0.591781
\(732\) 0 0
\(733\) 44.0000 1.62518 0.812589 − 0.582838i \(-0.198058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(734\) 4.00000 0.147643
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) −48.0000 −1.76810
\(738\) −18.0000 −0.662589
\(739\) −12.0000 −0.441427 −0.220714 − 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) −24.0000 −0.882258
\(741\) 0 0
\(742\) 2.00000 0.0734223
\(743\) −8.00000 −0.293492 −0.146746 − 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) 72.0000 2.63788
\(746\) 10.0000 0.366126
\(747\) −42.0000 −1.53670
\(748\) 16.0000 0.585018
\(749\) −8.00000 −0.292314
\(750\) 0 0
\(751\) −52.0000 −1.89751 −0.948753 − 0.316017i \(-0.897654\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −12.0000 −0.437014
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 − 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 16.0000 0.580381
\(761\) −38.0000 −1.37750 −0.688749 − 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 0 0
\(763\) 2.00000 0.0724049
\(764\) −16.0000 −0.578860
\(765\) 48.0000 1.73544
\(766\) −12.0000 −0.433578
\(767\) −16.0000 −0.577727
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 − 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 16.0000 0.576600
\(771\) 0 0
\(772\) 10.0000 0.359908
\(773\) −52.0000 −1.87031 −0.935155 − 0.354239i \(-0.884740\pi\)
−0.935155 + 0.354239i \(0.884740\pi\)
\(774\) 12.0000 0.431331
\(775\) −44.0000 −1.58053
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) 32.0000 1.14432
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 16.0000 0.571064
\(786\) 0 0
\(787\) 14.0000 0.499046 0.249523 − 0.968369i \(-0.419726\pi\)
0.249523 + 0.968369i \(0.419726\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) 64.0000 2.27702
\(791\) −6.00000 −0.213335
\(792\) 12.0000 0.426401
\(793\) 16.0000 0.568177
\(794\) −16.0000 −0.567819
\(795\) 0 0
\(796\) −20.0000 −0.708881
\(797\) −36.0000 −1.27519 −0.637593 − 0.770374i \(-0.720070\pi\)
−0.637593 + 0.770374i \(0.720070\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −11.0000 −0.388909
\(801\) 0 0
\(802\) 18.0000 0.635602
\(803\) 64.0000 2.25851
\(804\) 0 0
\(805\) 32.0000 1.12785
\(806\) −8.00000 −0.281788
\(807\) 0 0
\(808\) −10.0000 −0.351799
\(809\) −46.0000 −1.61727 −0.808637 − 0.588308i \(-0.799794\pi\)
−0.808637 + 0.588308i \(0.799794\pi\)
\(810\) 36.0000 1.26491
\(811\) −40.0000 −1.40459 −0.702295 − 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) −6.00000 −0.210559
\(813\) 0 0
\(814\) −24.0000 −0.841200
\(815\) −48.0000 −1.68137
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) 4.00000 0.139857
\(819\) 6.00000 0.209657
\(820\) 24.0000 0.838116
\(821\) −10.0000 −0.349002 −0.174501 − 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 − 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −8.00000 −0.278693
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) −28.0000 −0.973655 −0.486828 − 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 24.0000 0.834058
\(829\) −14.0000 −0.486240 −0.243120 − 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 56.0000 1.94379
\(831\) 0 0
\(832\) −2.00000 −0.0693375
\(833\) 4.00000 0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) 16.0000 0.553372
\(837\) 0 0
\(838\) 18.0000 0.621800
\(839\) 40.0000 1.38095 0.690477 − 0.723355i \(-0.257401\pi\)
0.690477 + 0.723355i \(0.257401\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 22.0000 0.758170
\(843\) 0 0
\(844\) −8.00000 −0.275371
\(845\) 36.0000 1.23844
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) −2.00000 −0.0686803
\(849\) 0 0
\(850\) −44.0000 −1.50919
\(851\) −48.0000 −1.64542
\(852\) 0 0
\(853\) 34.0000 1.16414 0.582069 − 0.813139i \(-0.302243\pi\)
0.582069 + 0.813139i \(0.302243\pi\)
\(854\) 8.00000 0.273754
\(855\) 48.0000 1.64157
\(856\) 8.00000 0.273434
\(857\) −24.0000 −0.819824 −0.409912 − 0.912125i \(-0.634441\pi\)
−0.409912 + 0.912125i \(0.634441\pi\)
\(858\) 0 0
\(859\) −26.0000 −0.887109 −0.443554 − 0.896248i \(-0.646283\pi\)
−0.443554 + 0.896248i \(0.646283\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −1.00000 −0.0340601
\(863\) 12.0000 0.408485 0.204242 − 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 22.0000 0.747590
\(867\) 0 0
\(868\) −4.00000 −0.135769
\(869\) 64.0000 2.17105
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) −2.00000 −0.0677285
\(873\) 6.00000 0.203069
\(874\) 32.0000 1.08242
\(875\) −24.0000 −0.811348
\(876\) 0 0
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −26.0000 −0.877457
\(879\) 0 0
\(880\) −16.0000 −0.539360
\(881\) 38.0000 1.28025 0.640126 − 0.768270i \(-0.278882\pi\)
0.640126 + 0.768270i \(0.278882\pi\)
\(882\) 3.00000 0.101015
\(883\) 32.0000 1.07689 0.538443 − 0.842662i \(-0.319013\pi\)
0.538443 + 0.842662i \(0.319013\pi\)
\(884\) −8.00000 −0.269069
\(885\) 0 0
\(886\) 20.0000 0.671913
\(887\) 46.0000 1.54453 0.772264 − 0.635301i \(-0.219124\pi\)
0.772264 + 0.635301i \(0.219124\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 36.0000 1.20605
\(892\) 6.00000 0.200895
\(893\) 0 0
\(894\) 0 0
\(895\) −48.0000 −1.60446
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −30.0000 −1.00111
\(899\) 24.0000 0.800445
\(900\) −33.0000 −1.10000
\(901\) −8.00000 −0.266519
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 72.0000 2.39336
\(906\) 0 0
\(907\) 4.00000 0.132818 0.0664089 − 0.997792i \(-0.478846\pi\)
0.0664089 + 0.997792i \(0.478846\pi\)
\(908\) 0 0
\(909\) −30.0000 −0.995037
\(910\) −8.00000 −0.265197
\(911\) −40.0000 −1.32526 −0.662630 − 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 0 0
\(913\) 56.0000 1.85333
\(914\) 30.0000 0.992312
\(915\) 0 0
\(916\) −20.0000 −0.660819
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) −56.0000 −1.84727 −0.923635 − 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) −32.0000 −1.05501
\(921\) 0 0
\(922\) 12.0000 0.395199
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 66.0000 2.17007
\(926\) −20.0000 −0.657241
\(927\) −24.0000 −0.788263
\(928\) 6.00000 0.196960
\(929\) 36.0000 1.18112 0.590561 − 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) 0 0
\(931\) 4.00000 0.131095
\(932\) −18.0000 −0.589610
\(933\) 0 0
\(934\) −8.00000 −0.261768
\(935\) −64.0000 −2.09302
\(936\) −6.00000 −0.196116
\(937\) 46.0000 1.50275 0.751377 − 0.659873i \(-0.229390\pi\)
0.751377 + 0.659873i \(0.229390\pi\)
\(938\) 12.0000 0.391814
\(939\) 0 0
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 48.0000 1.56310
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) 4.00000 0.129983 0.0649913 − 0.997886i \(-0.479298\pi\)
0.0649913 + 0.997886i \(0.479298\pi\)
\(948\) 0 0
\(949\) −32.0000 −1.03876
\(950\) −44.0000 −1.42755
\(951\) 0 0
\(952\) −4.00000 −0.129641
\(953\) −22.0000 −0.712650 −0.356325 − 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) −6.00000 −0.194257
\(955\) 64.0000 2.07099
\(956\) 0 0
\(957\) 0 0
\(958\) −38.0000 −1.22772
\(959\) −18.0000 −0.581250
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 12.0000 0.386896
\(963\) 24.0000 0.773389
\(964\) −20.0000 −0.644157
\(965\) −40.0000 −1.28765
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 − 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) −5.00000 −0.160706
\(969\) 0 0
\(970\) −8.00000 −0.256865
\(971\) −44.0000 −1.41203 −0.706014 − 0.708198i \(-0.749508\pi\)
−0.706014 + 0.708198i \(0.749508\pi\)
\(972\) 0 0
\(973\) −8.00000 −0.256468
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) −34.0000 −1.08776 −0.543878 − 0.839164i \(-0.683045\pi\)
−0.543878 + 0.839164i \(0.683045\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −4.00000 −0.127775
\(981\) −6.00000 −0.191565
\(982\) −12.0000 −0.382935
\(983\) −18.0000 −0.574111 −0.287055 − 0.957914i \(-0.592676\pi\)
−0.287055 + 0.957914i \(0.592676\pi\)
\(984\) 0 0
\(985\) 72.0000 2.29411
\(986\) 24.0000 0.764316
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) −32.0000 −1.01754
\(990\) −48.0000 −1.52554
\(991\) −32.0000 −1.01651 −0.508257 − 0.861206i \(-0.669710\pi\)
−0.508257 + 0.861206i \(0.669710\pi\)
\(992\) 4.00000 0.127000
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 80.0000 2.53617
\(996\) 0 0
\(997\) 28.0000 0.886769 0.443384 − 0.896332i \(-0.353778\pi\)
0.443384 + 0.896332i \(0.353778\pi\)
\(998\) 20.0000 0.633089
\(999\) 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 6034.2.a.d.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.d.1.1 ✓ 1 1.1 even 1 trivial