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Properties

Label 4018.2.a.d.1.1
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $1$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, 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("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -6.00000 q^{11} -2.00000 q^{12} +4.00000 q^{13} -4.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +2.00000 q^{20} +6.00000 q^{22} +2.00000 q^{24} -1.00000 q^{25} -4.00000 q^{26} +4.00000 q^{27} +4.00000 q^{30} -1.00000 q^{32} +12.0000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} +2.00000 q^{38} -8.00000 q^{39} -2.00000 q^{40} +1.00000 q^{41} +4.00000 q^{43} -6.00000 q^{44} +2.00000 q^{45} -8.00000 q^{47} -2.00000 q^{48} +1.00000 q^{50} -4.00000 q^{51} +4.00000 q^{52} -4.00000 q^{53} -4.00000 q^{54} -12.0000 q^{55} +4.00000 q^{57} +8.00000 q^{59} -4.00000 q^{60} -10.0000 q^{61} +1.00000 q^{64} +8.00000 q^{65} -12.0000 q^{66} -14.0000 q^{67} +2.00000 q^{68} -12.0000 q^{71} -1.00000 q^{72} +6.00000 q^{73} -10.0000 q^{74} +2.00000 q^{75} -2.00000 q^{76} +8.00000 q^{78} +2.00000 q^{80} -11.0000 q^{81} -1.00000 q^{82} -4.00000 q^{83} +4.00000 q^{85} -4.00000 q^{86} +6.00000 q^{88} +14.0000 q^{89} -2.00000 q^{90} +8.00000 q^{94} -4.00000 q^{95} +2.00000 q^{96} +10.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −1.15470 −0.577350 − 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) −6.00000 −1.80907 −0.904534 − 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) −2.00000 −0.577350
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.00000 0.408248
\(25\) −1.00000 −0.200000
\(26\) −4.00000 −0.784465
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 4.00000 0.730297
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 12.0000 2.08893
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000 1.64399 0.821995 − 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 2.00000 0.324443
\(39\) −8.00000 −1.28103
\(40\) −2.00000 −0.316228
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −6.00000 −0.904534
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 − 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −2.00000 −0.288675
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) −4.00000 −0.560112
\(52\) 4.00000 0.554700
\(53\) −4.00000 −0.549442 −0.274721 − 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) −4.00000 −0.544331
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) −4.00000 −0.516398
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.00000 0.992278
\(66\) −12.0000 −1.47710
\(67\) −14.0000 −1.71037 −0.855186 − 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.00000 0.702247 0.351123 − 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −10.0000 −1.16248
\(75\) 2.00000 0.230940
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.00000 0.223607
\(81\) −11.0000 −1.22222
\(82\) −1.00000 −0.110432
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 6.00000 0.639602
\(89\) 14.0000 1.48400 0.741999 − 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −4.00000 −0.410391
\(96\) 2.00000 0.204124
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) −1.00000 −0.100000
\(101\) −12.0000 −1.19404 −0.597022 − 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 4.00000 0.396059
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 4.00000 0.384900
\(109\) 4.00000 0.383131 0.191565 − 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 12.0000 1.14416
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 − 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 0 0
\(117\) 4.00000 0.369800
\(118\) −8.00000 −0.736460
\(119\) 0 0
\(120\) 4.00000 0.365148
\(121\) 25.0000 2.27273
\(122\) 10.0000 0.905357
\(123\) −2.00000 −0.180334
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.00000 −0.704361
\(130\) −8.00000 −0.701646
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 12.0000 1.04447
\(133\) 0 0
\(134\) 14.0000 1.20942
\(135\) 8.00000 0.688530
\(136\) −2.00000 −0.171499
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 − 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) 16.0000 1.34744
\(142\) 12.0000 1.00702
\(143\) −24.0000 −2.00698
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −20.0000 −1.63846 −0.819232 − 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) −2.00000 −0.163299
\(151\) 4.00000 0.325515 0.162758 − 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 2.00000 0.162221
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) −8.00000 −0.640513
\(157\) −12.0000 −0.957704 −0.478852 − 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 0 0
\(159\) 8.00000 0.634441
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 1.00000 0.0780869
\(165\) 24.0000 1.86840
\(166\) 4.00000 0.310460
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −4.00000 −0.306786
\(171\) −2.00000 −0.152944
\(172\) 4.00000 0.304997
\(173\) −18.0000 −1.36851 −0.684257 − 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.00000 −0.452267
\(177\) −16.0000 −1.20263
\(178\) −14.0000 −1.04934
\(179\) 6.00000 0.448461 0.224231 − 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 2.00000 0.149071
\(181\) 24.0000 1.78391 0.891953 − 0.452128i \(-0.149335\pi\)
0.891953 + 0.452128i \(0.149335\pi\)
\(182\) 0 0
\(183\) 20.0000 1.47844
\(184\) 0 0
\(185\) 20.0000 1.47043
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) −2.00000 −0.144338
\(193\) −26.0000 −1.87152 −0.935760 − 0.352636i \(-0.885285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) −10.0000 −0.717958
\(195\) −16.0000 −1.14578
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 6.00000 0.426401
\(199\) −16.0000 −1.13421 −0.567105 − 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 1.00000 0.0707107
\(201\) 28.0000 1.97497
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) 2.00000 0.139686
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 − 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) −4.00000 −0.274721
\(213\) 24.0000 1.64445
\(214\) −12.0000 −0.820303
\(215\) 8.00000 0.545595
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −4.00000 −0.270914
\(219\) −12.0000 −0.810885
\(220\) −12.0000 −0.809040
\(221\) 8.00000 0.538138
\(222\) 20.0000 1.34231
\(223\) −24.0000 −1.60716 −0.803579 − 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 14.0000 0.931266
\(227\) −10.0000 −0.663723 −0.331862 − 0.943328i \(-0.607677\pi\)
−0.331862 + 0.943328i \(0.607677\pi\)
\(228\) 4.00000 0.264906
\(229\) 16.0000 1.05731 0.528655 − 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −4.00000 −0.261488
\(235\) −16.0000 −1.04372
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 − 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) −4.00000 −0.258199
\(241\) 2.00000 0.128831 0.0644157 − 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −25.0000 −1.60706
\(243\) 10.0000 0.641500
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) −8.00000 −0.509028
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) 12.0000 0.758947
\(251\) −16.0000 −1.00991 −0.504956 − 0.863145i \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −8.00000 −0.500979
\(256\) 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
\(259\) 0 0
\(260\) 8.00000 0.496139
\(261\) 0 0
\(262\) 0 0
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) −12.0000 −0.738549
\(265\) −8.00000 −0.491436
\(266\) 0 0
\(267\) −28.0000 −1.71357
\(268\) −14.0000 −0.855186
\(269\) 26.0000 1.58525 0.792624 − 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) −8.00000 −0.486864
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 8.00000 0.479808
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 − 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −16.0000 −0.952786
\(283\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −12.0000 −0.712069
\(285\) 8.00000 0.473879
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −20.0000 −1.17242
\(292\) 6.00000 0.351123
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 16.0000 0.931556
\(296\) −10.0000 −0.581238
\(297\) −24.0000 −1.39262
\(298\) 20.0000 1.15857
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) −4.00000 −0.230174
\(303\) 24.0000 1.37876
\(304\) −2.00000 −0.114708
\(305\) −20.0000 −1.14520
\(306\) −2.00000 −0.114332
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 − 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 8.00000 0.452911
\(313\) −30.0000 −1.69570 −0.847850 − 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(314\) 12.0000 0.677199
\(315\) 0 0
\(316\) 0 0
\(317\) −28.0000 −1.57264 −0.786318 − 0.617822i \(-0.788015\pi\)
−0.786318 + 0.617822i \(0.788015\pi\)
\(318\) −8.00000 −0.448618
\(319\) 0 0
\(320\) 2.00000 0.111803
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) −11.0000 −0.611111
\(325\) −4.00000 −0.221880
\(326\) −12.0000 −0.664619
\(327\) −8.00000 −0.442401
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) −24.0000 −1.32116
\(331\) −34.0000 −1.86881 −0.934405 − 0.356214i \(-0.884068\pi\)
−0.934405 + 0.356214i \(0.884068\pi\)
\(332\) −4.00000 −0.219529
\(333\) 10.0000 0.547997
\(334\) −12.0000 −0.656611
\(335\) −28.0000 −1.52980
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 − 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) −3.00000 −0.163178
\(339\) 28.0000 1.52075
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) −6.00000 −0.322097 −0.161048 − 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 16.0000 0.854017
\(352\) 6.00000 0.319801
\(353\) 2.00000 0.106449 0.0532246 − 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 16.0000 0.850390
\(355\) −24.0000 −1.27379
\(356\) 14.0000 0.741999
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −2.00000 −0.105409
\(361\) −15.0000 −0.789474
\(362\) −24.0000 −1.26141
\(363\) −50.0000 −2.62432
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) −20.0000 −1.04542
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 1.00000 0.0520579
\(370\) −20.0000 −1.03975
\(371\) 0 0
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 12.0000 0.620505
\(375\) 24.0000 1.23935
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −4.00000 −0.205196
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) −28.0000 −1.43073 −0.715367 − 0.698749i \(-0.753740\pi\)
−0.715367 + 0.698749i \(0.753740\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) 4.00000 0.203331
\(388\) 10.0000 0.507673
\(389\) 2.00000 0.101404 0.0507020 − 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 16.0000 0.810191
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) 0 0
\(396\) −6.00000 −0.301511
\(397\) −16.0000 −0.803017 −0.401508 − 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 34.0000 1.69788 0.848939 − 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) −28.0000 −1.39651
\(403\) 0 0
\(404\) −12.0000 −0.597022
\(405\) −22.0000 −1.09319
\(406\) 0 0
\(407\) −60.0000 −2.97409
\(408\) 4.00000 0.198030
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −2.00000 −0.0987730
\(411\) −12.0000 −0.591916
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) −8.00000 −0.392705
\(416\) −4.00000 −0.196116
\(417\) 16.0000 0.783523
\(418\) −12.0000 −0.586939
\(419\) 20.0000 0.977064 0.488532 − 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 − 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) −2.00000 −0.0973585
\(423\) −8.00000 −0.388973
\(424\) 4.00000 0.194257
\(425\) −2.00000 −0.0970143
\(426\) −24.0000 −1.16280
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 48.0000 2.31746
\(430\) −8.00000 −0.385794
\(431\) −40.0000 −1.92673 −0.963366 − 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) 4.00000 0.192450
\(433\) 18.0000 0.865025 0.432512 − 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) 0 0
\(438\) 12.0000 0.573382
\(439\) −20.0000 −0.954548 −0.477274 − 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 12.0000 0.572078
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) −24.0000 −1.14027 −0.570137 − 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −20.0000 −0.949158
\(445\) 28.0000 1.32733
\(446\) 24.0000 1.13643
\(447\) 40.0000 1.89194
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 − 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 1.00000 0.0471405
\(451\) −6.00000 −0.282529
\(452\) −14.0000 −0.658505
\(453\) −8.00000 −0.375873
\(454\) 10.0000 0.469323
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −18.0000 −0.842004 −0.421002 − 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −16.0000 −0.747631
\(459\) 8.00000 0.373408
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 − 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) −8.00000 −0.370196 −0.185098 − 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 16.0000 0.738025
\(471\) 24.0000 1.10586
\(472\) −8.00000 −0.368230
\(473\) −24.0000 −1.10352
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) −4.00000 −0.183147
\(478\) 12.0000 0.548867
\(479\) 32.0000 1.46212 0.731059 − 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 4.00000 0.182574
\(481\) 40.0000 1.82384
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) 20.0000 0.908153
\(486\) −10.0000 −0.453609
\(487\) 32.0000 1.45006 0.725029 − 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 10.0000 0.452679
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 32.0000 1.44414 0.722070 − 0.691820i \(-0.243191\pi\)
0.722070 + 0.691820i \(0.243191\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 0 0
\(494\) 8.00000 0.359937
\(495\) −12.0000 −0.539360
\(496\) 0 0
\(497\) 0 0
\(498\) −8.00000 −0.358489
\(499\) −26.0000 −1.16392 −0.581960 − 0.813217i \(-0.697714\pi\)
−0.581960 + 0.813217i \(0.697714\pi\)
\(500\) −12.0000 −0.536656
\(501\) −24.0000 −1.07224
\(502\) 16.0000 0.714115
\(503\) −32.0000 −1.42681 −0.713405 − 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −24.0000 −1.06799
\(506\) 0 0
\(507\) −6.00000 −0.266469
\(508\) 0 0
\(509\) −24.0000 −1.06378 −0.531891 − 0.846813i \(-0.678518\pi\)
−0.531891 + 0.846813i \(0.678518\pi\)
\(510\) 8.00000 0.354246
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 −0.353209
\(514\) −6.00000 −0.264649
\(515\) 16.0000 0.705044
\(516\) −8.00000 −0.352180
\(517\) 48.0000 2.11104
\(518\) 0 0
\(519\) 36.0000 1.58022
\(520\) −8.00000 −0.350823
\(521\) −38.0000 −1.66481 −0.832405 − 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) 12.0000 0.524723 0.262362 − 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 12.0000 0.522233
\(529\) −23.0000 −1.00000
\(530\) 8.00000 0.347498
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 28.0000 1.21168
\(535\) 24.0000 1.03761
\(536\) 14.0000 0.604708
\(537\) −12.0000 −0.517838
\(538\) −26.0000 −1.12094
\(539\) 0 0
\(540\) 8.00000 0.344265
\(541\) −18.0000 −0.773880 −0.386940 − 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) −8.00000 −0.343629
\(543\) −48.0000 −2.05988
\(544\) −2.00000 −0.0857493
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 30.0000 1.28271 0.641354 − 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(548\) 6.00000 0.256307
\(549\) −10.0000 −0.426790
\(550\) −6.00000 −0.255841
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) −40.0000 −1.69791
\(556\) −8.00000 −0.339276
\(557\) 40.0000 1.69485 0.847427 − 0.530912i \(-0.178150\pi\)
0.847427 + 0.530912i \(0.178150\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) −2.00000 −0.0843649
\(563\) 10.0000 0.421450 0.210725 − 0.977545i \(-0.432418\pi\)
0.210725 + 0.977545i \(0.432418\pi\)
\(564\) 16.0000 0.673722
\(565\) −28.0000 −1.17797
\(566\) 0 0
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −8.00000 −0.335083
\(571\) 22.0000 0.920671 0.460336 − 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) −24.0000 −1.00349
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 30.0000 1.24892 0.624458 − 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) 13.0000 0.540729
\(579\) 52.0000 2.16105
\(580\) 0 0
\(581\) 0 0
\(582\) 20.0000 0.829027
\(583\) 24.0000 0.993978
\(584\) −6.00000 −0.248282
\(585\) 8.00000 0.330759
\(586\) 0 0
\(587\) −42.0000 −1.73353 −0.866763 − 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −16.0000 −0.658710
\(591\) 12.0000 0.493614
\(592\) 10.0000 0.410997
\(593\) −42.0000 −1.72473 −0.862367 − 0.506284i \(-0.831019\pi\)
−0.862367 + 0.506284i \(0.831019\pi\)
\(594\) 24.0000 0.984732
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 32.0000 1.30967
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 − 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −2.00000 −0.0816497
\(601\) 46.0000 1.87638 0.938190 − 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 4.00000 0.162758
\(605\) 50.0000 2.03279
\(606\) −24.0000 −0.974933
\(607\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 20.0000 0.809776
\(611\) −32.0000 −1.29458
\(612\) 2.00000 0.0808452
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 8.00000 0.322854
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −38.0000 −1.52982 −0.764911 − 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 16.0000 0.643614
\(619\) 16.0000 0.643094 0.321547 − 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) −8.00000 −0.320256
\(625\) −19.0000 −0.760000
\(626\) 30.0000 1.19904
\(627\) −24.0000 −0.958468
\(628\) −12.0000 −0.478852
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 − 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 28.0000 1.11202
\(635\) 0 0
\(636\) 8.00000 0.317221
\(637\) 0 0
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) −2.00000 −0.0790569
\(641\) −34.0000 −1.34292 −0.671460 − 0.741041i \(-0.734332\pi\)
−0.671460 + 0.741041i \(0.734332\pi\)
\(642\) 24.0000 0.947204
\(643\) 2.00000 0.0788723 0.0394362 − 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 4.00000 0.157378
\(647\) 24.0000 0.943537 0.471769 − 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 11.0000 0.432121
\(649\) −48.0000 −1.88416
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 24.0000 0.939193 0.469596 − 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 8.00000 0.312825
\(655\) 0 0
\(656\) 1.00000 0.0390434
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 − 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 24.0000 0.934199
\(661\) 2.00000 0.0777910 0.0388955 − 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 34.0000 1.32145
\(663\) −16.0000 −0.621389
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) 48.0000 1.85579
\(670\) 28.0000 1.08173
\(671\) 60.0000 2.31627
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 − 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 26.0000 1.00148
\(675\) −4.00000 −0.153960
\(676\) 3.00000 0.115385
\(677\) −30.0000 −1.15299 −0.576497 − 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) −28.0000 −1.07533
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −18.0000 −0.688751 −0.344375 − 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) −32.0000 −1.22088
\(688\) 4.00000 0.152499
\(689\) −16.0000 −0.609551
\(690\) 0 0
\(691\) 34.0000 1.29342 0.646710 − 0.762736i \(-0.276144\pi\)
0.646710 + 0.762736i \(0.276144\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 2.00000 0.0757554
\(698\) −10.0000 −0.378506
\(699\) 12.0000 0.453882
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 − 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) −16.0000 −0.603881
\(703\) −20.0000 −0.754314
\(704\) −6.00000 −0.226134
\(705\) 32.0000 1.20519
\(706\) −2.00000 −0.0752710
\(707\) 0 0
\(708\) −16.0000 −0.601317
\(709\) −16.0000 −0.600893 −0.300446 − 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 24.0000 0.900704
\(711\) 0 0
\(712\) −14.0000 −0.524672
\(713\) 0 0
\(714\) 0 0
\(715\) −48.0000 −1.79510
\(716\) 6.00000 0.224231
\(717\) 24.0000 0.896296
\(718\) 24.0000 0.895672
\(719\) 12.0000 0.447524 0.223762 − 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) −4.00000 −0.148762
\(724\) 24.0000 0.891953
\(725\) 0 0
\(726\) 50.0000 1.85567
\(727\) −4.00000 −0.148352 −0.0741759 − 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −12.0000 −0.444140
\(731\) 8.00000 0.295891
\(732\) 20.0000 0.739221
\(733\) −34.0000 −1.25582 −0.627909 − 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 0 0
\(737\) 84.0000 3.09418
\(738\) −1.00000 −0.0368105
\(739\) 52.0000 1.91285 0.956425 − 0.291977i \(-0.0943129\pi\)
0.956425 + 0.291977i \(0.0943129\pi\)
\(740\) 20.0000 0.735215
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 8.00000 0.293492 0.146746 − 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) −14.0000 −0.512576
\(747\) −4.00000 −0.146352
\(748\) −12.0000 −0.438763
\(749\) 0 0
\(750\) −24.0000 −0.876356
\(751\) 52.0000 1.89751 0.948753 − 0.316017i \(-0.102346\pi\)
0.948753 + 0.316017i \(0.102346\pi\)
\(752\) −8.00000 −0.291730
\(753\) 32.0000 1.16614
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 24.0000 0.872295 0.436147 − 0.899875i \(-0.356343\pi\)
0.436147 + 0.899875i \(0.356343\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) −34.0000 −1.23250 −0.616250 − 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 4.00000 0.144620
\(766\) 28.0000 1.01168
\(767\) 32.0000 1.15545
\(768\) −2.00000 −0.0721688
\(769\) 30.0000 1.08183 0.540914 − 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −26.0000 −0.935760
\(773\) 32.0000 1.15096 0.575480 − 0.817816i \(-0.304815\pi\)
0.575480 + 0.817816i \(0.304815\pi\)
\(774\) −4.00000 −0.143777
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) −2.00000 −0.0717035
\(779\) −2.00000 −0.0716574
\(780\) −16.0000 −0.572892
\(781\) 72.0000 2.57636
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.0000 −0.856597
\(786\) 0 0
\(787\) −32.0000 −1.14068 −0.570338 − 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) −6.00000 −0.213741
\(789\) −48.0000 −1.70885
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000 0.213201
\(793\) −40.0000 −1.42044
\(794\) 16.0000 0.567819
\(795\) 16.0000 0.567462
\(796\) −16.0000 −0.567105
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) 1.00000 0.0353553
\(801\) 14.0000 0.494666
\(802\) −34.0000 −1.20058
\(803\) −36.0000 −1.27041
\(804\) 28.0000 0.987484
\(805\) 0 0
\(806\) 0 0
\(807\) −52.0000 −1.83049
\(808\) 12.0000 0.422159
\(809\) −10.0000 −0.351581 −0.175791 − 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 22.0000 0.773001
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 60.0000 2.10300
\(815\) 24.0000 0.840683
\(816\) −4.00000 −0.140028
\(817\) −8.00000 −0.279885
\(818\) −10.0000 −0.349642
\(819\) 0 0
\(820\) 2.00000 0.0698430
\(821\) 10.0000 0.349002 0.174501 − 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) 12.0000 0.418548
\(823\) −4.00000 −0.139431 −0.0697156 − 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) −8.00000 −0.278693
\(825\) −12.0000 −0.417786
\(826\) 0 0
\(827\) 30.0000 1.04320 0.521601 − 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) 0 0
\(829\) 50.0000 1.73657 0.868286 − 0.496064i \(-0.165222\pi\)
0.868286 + 0.496064i \(0.165222\pi\)
\(830\) 8.00000 0.277684
\(831\) 44.0000 1.52634
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) −16.0000 −0.554035
\(835\) 24.0000 0.830554
\(836\) 12.0000 0.415029
\(837\) 0 0
\(838\) −20.0000 −0.690889
\(839\) 16.0000 0.552381 0.276191 − 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 16.0000 0.551396
\(843\) −4.00000 −0.137767
\(844\) 2.00000 0.0688428
\(845\) 6.00000 0.206406
\(846\) 8.00000 0.275046
\(847\) 0 0
\(848\) −4.00000 −0.137361
\(849\) 0 0
\(850\) 2.00000 0.0685994
\(851\) 0 0
\(852\) 24.0000 0.822226
\(853\) 22.0000 0.753266 0.376633 − 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) −4.00000 −0.136797
\(856\) −12.0000 −0.410152
\(857\) −6.00000 −0.204956 −0.102478 − 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) −48.0000 −1.63869
\(859\) 32.0000 1.09183 0.545913 − 0.837842i \(-0.316183\pi\)
0.545913 + 0.837842i \(0.316183\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) 40.0000 1.36241
\(863\) 8.00000 0.272323 0.136162 − 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) −4.00000 −0.136083
\(865\) −36.0000 −1.22404
\(866\) −18.0000 −0.611665
\(867\) 26.0000 0.883006
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −56.0000 −1.89749
\(872\) −4.00000 −0.135457
\(873\) 10.0000 0.338449
\(874\) 0 0
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) −42.0000 −1.41824 −0.709120 − 0.705088i \(-0.750907\pi\)
−0.709120 + 0.705088i \(0.750907\pi\)
\(878\) 20.0000 0.674967
\(879\) 0 0
\(880\) −12.0000 −0.404520
\(881\) −46.0000 −1.54978 −0.774890 − 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 0 0
\(883\) −18.0000 −0.605748 −0.302874 − 0.953031i \(-0.597946\pi\)
−0.302874 + 0.953031i \(0.597946\pi\)
\(884\) 8.00000 0.269069
\(885\) −32.0000 −1.07567
\(886\) 24.0000 0.806296
\(887\) −8.00000 −0.268614 −0.134307 − 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) 20.0000 0.671156
\(889\) 0 0
\(890\) −28.0000 −0.938562
\(891\) 66.0000 2.21108
\(892\) −24.0000 −0.803579
\(893\) 16.0000 0.535420
\(894\) −40.0000 −1.33780
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 6.00000 0.200223
\(899\) 0 0
\(900\) −1.00000 −0.0333333
\(901\) −8.00000 −0.266519
\(902\) 6.00000 0.199778
\(903\) 0 0
\(904\) 14.0000 0.465633
\(905\) 48.0000 1.59557
\(906\) 8.00000 0.265782
\(907\) −40.0000 −1.32818 −0.664089 − 0.747653i \(-0.731180\pi\)
−0.664089 + 0.747653i \(0.731180\pi\)
\(908\) −10.0000 −0.331862
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 4.00000 0.132453
\(913\) 24.0000 0.794284
\(914\) 18.0000 0.595387
\(915\) 40.0000 1.32236
\(916\) 16.0000 0.528655
\(917\) 0 0
\(918\) −8.00000 −0.264039
\(919\) −36.0000 −1.18753 −0.593765 − 0.804638i \(-0.702359\pi\)
−0.593765 + 0.804638i \(0.702359\pi\)
\(920\) 0 0
\(921\) 16.0000 0.527218
\(922\) 18.0000 0.592798
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 0 0
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 2.00000 0.0656179 0.0328089 − 0.999462i \(-0.489555\pi\)
0.0328089 + 0.999462i \(0.489555\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −6.00000 −0.196537
\(933\) 24.0000 0.785725
\(934\) 8.00000 0.261768
\(935\) −24.0000 −0.784884
\(936\) −4.00000 −0.130744
\(937\) −18.0000 −0.588034 −0.294017 − 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) 0 0
\(939\) 60.0000 1.95803
\(940\) −16.0000 −0.521862
\(941\) 38.0000 1.23876 0.619382 − 0.785090i \(-0.287383\pi\)
0.619382 + 0.785090i \(0.287383\pi\)
\(942\) −24.0000 −0.781962
\(943\) 0 0
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) 24.0000 0.780307
\(947\) 48.0000 1.55979 0.779895 − 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) 0 0
\(949\) 24.0000 0.779073
\(950\) −2.00000 −0.0648886
\(951\) 56.0000 1.81592
\(952\) 0 0
\(953\) 22.0000 0.712650 0.356325 − 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) 4.00000 0.129505
\(955\) −24.0000 −0.776622
\(956\) −12.0000 −0.388108
\(957\) 0 0
\(958\) −32.0000 −1.03387
\(959\) 0 0
\(960\) −4.00000 −0.129099
\(961\) −31.0000 −1.00000
\(962\) −40.0000 −1.28965
\(963\) 12.0000 0.386695
\(964\) 2.00000 0.0644157
\(965\) −52.0000 −1.67394
\(966\) 0 0
\(967\) −48.0000 −1.54358 −0.771788 − 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(968\) −25.0000 −0.803530
\(969\) 8.00000 0.256997
\(970\) −20.0000 −0.642161
\(971\) 30.0000 0.962746 0.481373 − 0.876516i \(-0.340138\pi\)
0.481373 + 0.876516i \(0.340138\pi\)
\(972\) 10.0000 0.320750
\(973\) 0 0
\(974\) −32.0000 −1.02535
\(975\) 8.00000 0.256205
\(976\) −10.0000 −0.320092
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 24.0000 0.767435
\(979\) −84.0000 −2.68465
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) −32.0000 −1.02116
\(983\) −24.0000 −0.765481 −0.382741 − 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 2.00000 0.0637577
\(985\) −12.0000 −0.382352
\(986\) 0 0
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 0 0
\(990\) 12.0000 0.381385
\(991\) −52.0000 −1.65183 −0.825917 − 0.563791i \(-0.809342\pi\)
−0.825917 + 0.563791i \(0.809342\pi\)
\(992\) 0 0
\(993\) 68.0000 2.15791
\(994\) 0 0
\(995\) −32.0000 −1.01447
\(996\) 8.00000 0.253490
\(997\) −4.00000 −0.126681 −0.0633406 − 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) 26.0000 0.823016
\(999\) 40.0000 1.26554
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 4018.2.a.d.1.1 1
7.6 odd 2 574.2.a.d.1.1 ✓ 1
21.20 even 2 5166.2.a.bj.1.1 1
28.27 even 2 4592.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.a.d.1.1 ✓ 1 7.6 odd 2
4018.2.a.d.1.1 1 1.1 even 1 trivial
4592.2.a.b.1.1 1 28.27 even 2
5166.2.a.bj.1.1 1 21.20 even 2