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Properties

Label 4018.2.a.e.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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{18} +3.00000 q^{19} -1.00000 q^{20} -1.00000 q^{22} -4.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +2.00000 q^{26} +5.00000 q^{27} +8.00000 q^{29} -1.00000 q^{30} +10.0000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -2.00000 q^{36} -2.00000 q^{37} -3.00000 q^{38} +2.00000 q^{39} +1.00000 q^{40} -1.00000 q^{41} -4.00000 q^{43} +1.00000 q^{44} +2.00000 q^{45} +4.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +4.00000 q^{50} -2.00000 q^{52} -2.00000 q^{53} -5.00000 q^{54} -1.00000 q^{55} -3.00000 q^{57} -8.00000 q^{58} -10.0000 q^{59} +1.00000 q^{60} +5.00000 q^{61} -10.0000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +1.00000 q^{66} -8.00000 q^{67} +4.00000 q^{69} -9.00000 q^{71} +2.00000 q^{72} -2.00000 q^{73} +2.00000 q^{74} +4.00000 q^{75} +3.00000 q^{76} -2.00000 q^{78} +15.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +6.00000 q^{83} +4.00000 q^{86} -8.00000 q^{87} -1.00000 q^{88} +6.00000 q^{89} -2.00000 q^{90} -4.00000 q^{92} -10.0000 q^{93} -8.00000 q^{94} -3.00000 q^{95} +1.00000 q^{96} -16.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350 −0.288675 − 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511 0.150756 − 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 2.00000 0.471405
\(19\) 3.00000 0.688247 0.344124 − 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 2.00000 0.392232
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 − 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) −1.00000 −0.182574
\(31\) 10.0000 1.79605 0.898027 − 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −3.00000 −0.486664
\(39\) 2.00000 0.320256
\(40\) 1.00000 0.158114
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 1.00000 0.150756
\(45\) 2.00000 0.298142
\(46\) 4.00000 0.589768
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −5.00000 −0.680414
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) −8.00000 −1.05045
\(59\) −10.0000 −1.30189 −0.650945 − 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 1.00000 0.129099
\(61\) 5.00000 0.640184 0.320092 − 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) −10.0000 −1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 1.00000 0.123091
\(67\) −8.00000 −0.977356 −0.488678 − 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 − 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 2.00000 0.235702
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 2.00000 0.232495
\(75\) 4.00000 0.461880
\(76\) 3.00000 0.344124
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 15.0000 1.68763 0.843816 − 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 1.00000 0.110432
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000 0.431331
\(87\) −8.00000 −0.857690
\(88\) −1.00000 −0.106600
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −10.0000 −1.03695
\(94\) −8.00000 −0.825137
\(95\) −3.00000 −0.307794
\(96\) 1.00000 0.102062
\(97\) −16.0000 −1.62455 −0.812277 − 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) −4.00000 −0.400000
\(101\) −8.00000 −0.796030 −0.398015 − 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 − 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −10.0000 −0.966736 −0.483368 − 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 5.00000 0.481125
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 1.00000 0.0953463
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 − 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 3.00000 0.280976
\(115\) 4.00000 0.373002
\(116\) 8.00000 0.742781
\(117\) 4.00000 0.369800
\(118\) 10.0000 0.920575
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −10.0000 −0.909091
\(122\) −5.00000 −0.452679
\(123\) 1.00000 0.0901670
\(124\) 10.0000 0.898027
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 − 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.00000 0.352180
\(130\) −2.00000 −0.175412
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −4.00000 −0.340503
\(139\) −2.00000 −0.169638 −0.0848189 − 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 9.00000 0.755263
\(143\) −2.00000 −0.167248
\(144\) −2.00000 −0.166667
\(145\) −8.00000 −0.664364
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −22.0000 −1.80231 −0.901155 − 0.433497i \(-0.857280\pi\)
−0.901155 + 0.433497i \(0.857280\pi\)
\(150\) −4.00000 −0.326599
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) −3.00000 −0.243332
\(153\) 0 0
\(154\) 0 0
\(155\) −10.0000 −0.803219
\(156\) 2.00000 0.160128
\(157\) −12.0000 −0.957704 −0.478852 − 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) −15.0000 −1.19334
\(159\) 2.00000 0.158610
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 10.0000 0.783260 0.391630 − 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 1.00000 0.0778499
\(166\) −6.00000 −0.465690
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) −4.00000 −0.304997
\(173\) −3.00000 −0.228086 −0.114043 − 0.993476i \(-0.536380\pi\)
−0.114043 + 0.993476i \(0.536380\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 10.0000 0.751646
\(178\) −6.00000 −0.449719
\(179\) −11.0000 −0.822179 −0.411089 − 0.911595i \(-0.634852\pi\)
−0.411089 + 0.911595i \(0.634852\pi\)
\(180\) 2.00000 0.149071
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −5.00000 −0.369611
\(184\) 4.00000 0.294884
\(185\) 2.00000 0.147043
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 3.00000 0.217643
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 16.0000 1.14873
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 5.00000 0.356235 0.178118 − 0.984009i \(-0.442999\pi\)
0.178118 + 0.984009i \(0.442999\pi\)
\(198\) 2.00000 0.142134
\(199\) −24.0000 −1.70131 −0.850657 − 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 4.00000 0.282843
\(201\) 8.00000 0.564276
\(202\) 8.00000 0.562878
\(203\) 0 0
\(204\) 0 0
\(205\) 1.00000 0.0698430
\(206\) −14.0000 −0.975426
\(207\) 8.00000 0.556038
\(208\) −2.00000 −0.138675
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 − 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) −2.00000 −0.137361
\(213\) 9.00000 0.616670
\(214\) 10.0000 0.683586
\(215\) 4.00000 0.272798
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) −8.00000 −0.541828
\(219\) 2.00000 0.135147
\(220\) −1.00000 −0.0674200
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) 8.00000 0.535720 0.267860 − 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 3.00000 0.199557
\(227\) −9.00000 −0.597351 −0.298675 − 0.954355i \(-0.596545\pi\)
−0.298675 + 0.954355i \(0.596545\pi\)
\(228\) −3.00000 −0.198680
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) 10.0000 0.655122 0.327561 − 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) −4.00000 −0.261488
\(235\) −8.00000 −0.521862
\(236\) −10.0000 −0.650945
\(237\) −15.0000 −0.974355
\(238\) 0 0
\(239\) −7.00000 −0.452792 −0.226396 − 0.974035i \(-0.572694\pi\)
−0.226396 + 0.974035i \(0.572694\pi\)
\(240\) 1.00000 0.0645497
\(241\) 10.0000 0.644157 0.322078 − 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 10.0000 0.642824
\(243\) −16.0000 −1.02640
\(244\) 5.00000 0.320092
\(245\) 0 0
\(246\) −1.00000 −0.0637577
\(247\) −6.00000 −0.381771
\(248\) −10.0000 −0.635001
\(249\) −6.00000 −0.380235
\(250\) −9.00000 −0.569210
\(251\) −18.0000 −1.13615 −0.568075 − 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −16.0000 −0.998053 −0.499026 − 0.866587i \(-0.666309\pi\)
−0.499026 + 0.866587i \(0.666309\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) −16.0000 −0.990375
\(262\) −12.0000 −0.741362
\(263\) −8.00000 −0.493301 −0.246651 − 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 1.00000 0.0615457
\(265\) 2.00000 0.122859
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) −8.00000 −0.488678
\(269\) 23.0000 1.40233 0.701167 − 0.712997i \(-0.252663\pi\)
0.701167 + 0.712997i \(0.252663\pi\)
\(270\) 5.00000 0.304290
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) −4.00000 −0.241209
\(276\) 4.00000 0.240772
\(277\) 17.0000 1.02143 0.510716 − 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) 2.00000 0.119952
\(279\) −20.0000 −1.19737
\(280\) 0 0
\(281\) 4.00000 0.238620 0.119310 − 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 8.00000 0.476393
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −9.00000 −0.534052
\(285\) 3.00000 0.177705
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) −17.0000 −1.00000
\(290\) 8.00000 0.469776
\(291\) 16.0000 0.937937
\(292\) −2.00000 −0.117041
\(293\) 12.0000 0.701047 0.350524 − 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) 2.00000 0.116248
\(297\) 5.00000 0.290129
\(298\) 22.0000 1.27443
\(299\) 8.00000 0.462652
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 8.00000 0.459588
\(304\) 3.00000 0.172062
\(305\) −5.00000 −0.286299
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 10.0000 0.567962
\(311\) −16.0000 −0.907277 −0.453638 − 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) −2.00000 −0.113228
\(313\) −8.00000 −0.452187 −0.226093 − 0.974106i \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) 12.0000 0.677199
\(315\) 0 0
\(316\) 15.0000 0.843816
\(317\) −28.0000 −1.57264 −0.786318 − 0.617822i \(-0.788015\pi\)
−0.786318 + 0.617822i \(0.788015\pi\)
\(318\) −2.00000 −0.112154
\(319\) 8.00000 0.447914
\(320\) −1.00000 −0.0559017
\(321\) 10.0000 0.558146
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 8.00000 0.443760
\(326\) −10.0000 −0.553849
\(327\) −8.00000 −0.442401
\(328\) 1.00000 0.0552158
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 12.0000 0.659580 0.329790 − 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 6.00000 0.329293
\(333\) 4.00000 0.219199
\(334\) 8.00000 0.437741
\(335\) 8.00000 0.437087
\(336\) 0 0
\(337\) −5.00000 −0.272367 −0.136184 − 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 9.00000 0.489535
\(339\) 3.00000 0.162938
\(340\) 0 0
\(341\) 10.0000 0.541530
\(342\) 6.00000 0.324443
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) −4.00000 −0.215353
\(346\) 3.00000 0.161281
\(347\) −33.0000 −1.77153 −0.885766 − 0.464131i \(-0.846367\pi\)
−0.885766 + 0.464131i \(0.846367\pi\)
\(348\) −8.00000 −0.428845
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) −1.00000 −0.0533002
\(353\) −3.00000 −0.159674 −0.0798369 − 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) −10.0000 −0.531494
\(355\) 9.00000 0.477670
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 11.0000 0.581368
\(359\) −26.0000 −1.37223 −0.686114 − 0.727494i \(-0.740685\pi\)
−0.686114 + 0.727494i \(0.740685\pi\)
\(360\) −2.00000 −0.105409
\(361\) −10.0000 −0.526316
\(362\) −14.0000 −0.735824
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 5.00000 0.261354
\(367\) 18.0000 0.939592 0.469796 − 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) −4.00000 −0.208514
\(369\) 2.00000 0.104116
\(370\) −2.00000 −0.103975
\(371\) 0 0
\(372\) −10.0000 −0.518476
\(373\) −17.0000 −0.880227 −0.440113 − 0.897942i \(-0.645062\pi\)
−0.440113 + 0.897942i \(0.645062\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) −8.00000 −0.412568
\(377\) −16.0000 −0.824042
\(378\) 0 0
\(379\) −38.0000 −1.95193 −0.975964 − 0.217930i \(-0.930070\pi\)
−0.975964 + 0.217930i \(0.930070\pi\)
\(380\) −3.00000 −0.153897
\(381\) 2.00000 0.102463
\(382\) 8.00000 0.409316
\(383\) −39.0000 −1.99281 −0.996403 − 0.0847358i \(-0.972995\pi\)
−0.996403 + 0.0847358i \(0.972995\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 8.00000 0.406663
\(388\) −16.0000 −0.812277
\(389\) −27.0000 −1.36895 −0.684477 − 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) 2.00000 0.101274
\(391\) 0 0
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) −5.00000 −0.251896
\(395\) −15.0000 −0.754732
\(396\) −2.00000 −0.100504
\(397\) −22.0000 −1.10415 −0.552074 − 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 24.0000 1.20301
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 23.0000 1.14857 0.574283 − 0.818657i \(-0.305281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(402\) −8.00000 −0.399004
\(403\) −20.0000 −0.996271
\(404\) −8.00000 −0.398015
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 − 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) −1.00000 −0.0493865
\(411\) 18.0000 0.887875
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) −6.00000 −0.294528
\(416\) 2.00000 0.0980581
\(417\) 2.00000 0.0979404
\(418\) −3.00000 −0.146735
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 − 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 15.0000 0.730189
\(423\) −16.0000 −0.777947
\(424\) 2.00000 0.0971286
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) 2.00000 0.0965609
\(430\) −4.00000 −0.192897
\(431\) −8.00000 −0.385346 −0.192673 − 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 5.00000 0.240563
\(433\) 11.0000 0.528626 0.264313 − 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 8.00000 0.383131
\(437\) −12.0000 −0.574038
\(438\) −2.00000 −0.0955637
\(439\) −1.00000 −0.0477274 −0.0238637 − 0.999715i \(-0.507597\pi\)
−0.0238637 + 0.999715i \(0.507597\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 − 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 2.00000 0.0949158
\(445\) −6.00000 −0.284427
\(446\) −8.00000 −0.378811
\(447\) 22.0000 1.04056
\(448\) 0 0
\(449\) 25.0000 1.17982 0.589911 − 0.807468i \(-0.299163\pi\)
0.589911 + 0.807468i \(0.299163\pi\)
\(450\) −8.00000 −0.377124
\(451\) −1.00000 −0.0470882
\(452\) −3.00000 −0.141108
\(453\) −16.0000 −0.751746
\(454\) 9.00000 0.422391
\(455\) 0 0
\(456\) 3.00000 0.140488
\(457\) −4.00000 −0.187112 −0.0935561 − 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) −19.0000 −0.884918 −0.442459 − 0.896789i \(-0.645894\pi\)
−0.442459 + 0.896789i \(0.645894\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 − 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 8.00000 0.371391
\(465\) 10.0000 0.463739
\(466\) −10.0000 −0.463241
\(467\) 36.0000 1.66588 0.832941 − 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) 12.0000 0.552931
\(472\) 10.0000 0.460287
\(473\) −4.00000 −0.183920
\(474\) 15.0000 0.688973
\(475\) −12.0000 −0.550598
\(476\) 0 0
\(477\) 4.00000 0.183147
\(478\) 7.00000 0.320173
\(479\) 1.00000 0.0456912 0.0228456 − 0.999739i \(-0.492727\pi\)
0.0228456 + 0.999739i \(0.492727\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 4.00000 0.182384
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 16.0000 0.726523
\(486\) 16.0000 0.725775
\(487\) −14.0000 −0.634401 −0.317200 − 0.948359i \(-0.602743\pi\)
−0.317200 + 0.948359i \(0.602743\pi\)
\(488\) −5.00000 −0.226339
\(489\) −10.0000 −0.452216
\(490\) 0 0
\(491\) −14.0000 −0.631811 −0.315906 − 0.948791i \(-0.602308\pi\)
−0.315906 + 0.948791i \(0.602308\pi\)
\(492\) 1.00000 0.0450835
\(493\) 0 0
\(494\) 6.00000 0.269953
\(495\) 2.00000 0.0898933
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 9.00000 0.402492
\(501\) 8.00000 0.357414
\(502\) 18.0000 0.803379
\(503\) −23.0000 −1.02552 −0.512760 − 0.858532i \(-0.671377\pi\)
−0.512760 + 0.858532i \(0.671377\pi\)
\(504\) 0 0
\(505\) 8.00000 0.355995
\(506\) 4.00000 0.177822
\(507\) 9.00000 0.399704
\(508\) −2.00000 −0.0887357
\(509\) −4.00000 −0.177297 −0.0886484 − 0.996063i \(-0.528255\pi\)
−0.0886484 + 0.996063i \(0.528255\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 15.0000 0.662266
\(514\) 16.0000 0.705730
\(515\) −14.0000 −0.616914
\(516\) 4.00000 0.176090
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) −2.00000 −0.0877058
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 16.0000 0.700301
\(523\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) −1.00000 −0.0435194
\(529\) −7.00000 −0.304348
\(530\) −2.00000 −0.0868744
\(531\) 20.0000 0.867926
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 6.00000 0.259645
\(535\) 10.0000 0.432338
\(536\) 8.00000 0.345547
\(537\) 11.0000 0.474685
\(538\) −23.0000 −0.991600
\(539\) 0 0
\(540\) −5.00000 −0.215166
\(541\) 26.0000 1.11783 0.558914 − 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 16.0000 0.687259
\(543\) −14.0000 −0.600798
\(544\) 0 0
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 − 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −18.0000 −0.768922
\(549\) −10.0000 −0.426790
\(550\) 4.00000 0.170561
\(551\) 24.0000 1.02243
\(552\) −4.00000 −0.170251
\(553\) 0 0
\(554\) −17.0000 −0.722261
\(555\) −2.00000 −0.0848953
\(556\) −2.00000 −0.0848189
\(557\) −6.00000 −0.254228 −0.127114 − 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 20.0000 0.846668
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −4.00000 −0.168730
\(563\) −1.00000 −0.0421450 −0.0210725 − 0.999778i \(-0.506708\pi\)
−0.0210725 + 0.999778i \(0.506708\pi\)
\(564\) −8.00000 −0.336861
\(565\) 3.00000 0.126211
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 9.00000 0.377632
\(569\) 6.00000 0.251533 0.125767 − 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −3.00000 −0.125656
\(571\) 39.0000 1.63210 0.816050 − 0.577982i \(-0.196160\pi\)
0.816050 + 0.577982i \(0.196160\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 16.0000 0.667246
\(576\) −2.00000 −0.0833333
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 17.0000 0.707107
\(579\) −14.0000 −0.581820
\(580\) −8.00000 −0.332182
\(581\) 0 0
\(582\) −16.0000 −0.663221
\(583\) −2.00000 −0.0828315
\(584\) 2.00000 0.0827606
\(585\) −4.00000 −0.165380
\(586\) −12.0000 −0.495715
\(587\) −3.00000 −0.123823 −0.0619116 − 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(588\) 0 0
\(589\) 30.0000 1.23613
\(590\) −10.0000 −0.411693
\(591\) −5.00000 −0.205673
\(592\) −2.00000 −0.0821995
\(593\) 20.0000 0.821302 0.410651 − 0.911793i \(-0.365302\pi\)
0.410651 + 0.911793i \(0.365302\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) −22.0000 −0.901155
\(597\) 24.0000 0.982255
\(598\) −8.00000 −0.327144
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −4.00000 −0.163299
\(601\) −46.0000 −1.87638 −0.938190 − 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) 16.0000 0.651570
\(604\) 16.0000 0.651031
\(605\) 10.0000 0.406558
\(606\) −8.00000 −0.324978
\(607\) 2.00000 0.0811775 0.0405887 − 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 5.00000 0.202444
\(611\) −16.0000 −0.647291
\(612\) 0 0
\(613\) −9.00000 −0.363507 −0.181753 − 0.983344i \(-0.558177\pi\)
−0.181753 + 0.983344i \(0.558177\pi\)
\(614\) 12.0000 0.484281
\(615\) −1.00000 −0.0403239
\(616\) 0 0
\(617\) −3.00000 −0.120775 −0.0603877 − 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 14.0000 0.563163
\(619\) −2.00000 −0.0803868 −0.0401934 − 0.999192i \(-0.512797\pi\)
−0.0401934 + 0.999192i \(0.512797\pi\)
\(620\) −10.0000 −0.401610
\(621\) −20.0000 −0.802572
\(622\) 16.0000 0.641542
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 11.0000 0.440000
\(626\) 8.00000 0.319744
\(627\) −3.00000 −0.119808
\(628\) −12.0000 −0.478852
\(629\) 0 0
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 − 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) −15.0000 −0.596668
\(633\) 15.0000 0.596196
\(634\) 28.0000 1.11202
\(635\) 2.00000 0.0793676
\(636\) 2.00000 0.0793052
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 18.0000 0.712069
\(640\) 1.00000 0.0395285
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) −10.0000 −0.394669
\(643\) −21.0000 −0.828159 −0.414080 − 0.910241i \(-0.635896\pi\)
−0.414080 + 0.910241i \(0.635896\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −10.0000 −0.393141 −0.196570 − 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −10.0000 −0.392534
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −48.0000 −1.87839 −0.939193 − 0.343391i \(-0.888424\pi\)
−0.939193 + 0.343391i \(0.888424\pi\)
\(654\) 8.00000 0.312825
\(655\) −12.0000 −0.468879
\(656\) −1.00000 −0.0390434
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 − 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 1.00000 0.0389249
\(661\) −21.0000 −0.816805 −0.408403 − 0.912802i \(-0.633914\pi\)
−0.408403 + 0.912802i \(0.633914\pi\)
\(662\) −12.0000 −0.466393
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −32.0000 −1.23904
\(668\) −8.00000 −0.309529
\(669\) −8.00000 −0.309298
\(670\) −8.00000 −0.309067
\(671\) 5.00000 0.193023
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 − 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 5.00000 0.192593
\(675\) −20.0000 −0.769800
\(676\) −9.00000 −0.346154
\(677\) −21.0000 −0.807096 −0.403548 − 0.914959i \(-0.632223\pi\)
−0.403548 + 0.914959i \(0.632223\pi\)
\(678\) −3.00000 −0.115214
\(679\) 0 0
\(680\) 0 0
\(681\) 9.00000 0.344881
\(682\) −10.0000 −0.382920
\(683\) 16.0000 0.612223 0.306111 − 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) −6.00000 −0.229416
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) 4.00000 0.152388
\(690\) 4.00000 0.152277
\(691\) 45.0000 1.71188 0.855940 − 0.517075i \(-0.172979\pi\)
0.855940 + 0.517075i \(0.172979\pi\)
\(692\) −3.00000 −0.114043
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 2.00000 0.0758643
\(696\) 8.00000 0.303239
\(697\) 0 0
\(698\) 14.0000 0.529908
\(699\) −10.0000 −0.378235
\(700\) 0 0
\(701\) 29.0000 1.09531 0.547657 − 0.836703i \(-0.315520\pi\)
0.547657 + 0.836703i \(0.315520\pi\)
\(702\) 10.0000 0.377426
\(703\) −6.00000 −0.226294
\(704\) 1.00000 0.0376889
\(705\) 8.00000 0.301297
\(706\) 3.00000 0.112906
\(707\) 0 0
\(708\) 10.0000 0.375823
\(709\) 8.00000 0.300446 0.150223 − 0.988652i \(-0.452001\pi\)
0.150223 + 0.988652i \(0.452001\pi\)
\(710\) −9.00000 −0.337764
\(711\) −30.0000 −1.12509
\(712\) −6.00000 −0.224860
\(713\) −40.0000 −1.49801
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) −11.0000 −0.411089
\(717\) 7.00000 0.261420
\(718\) 26.0000 0.970311
\(719\) −29.0000 −1.08152 −0.540759 − 0.841178i \(-0.681863\pi\)
−0.540759 + 0.841178i \(0.681863\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) 10.0000 0.372161
\(723\) −10.0000 −0.371904
\(724\) 14.0000 0.520306
\(725\) −32.0000 −1.18845
\(726\) −10.0000 −0.371135
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −2.00000 −0.0740233
\(731\) 0 0
\(732\) −5.00000 −0.184805
\(733\) 30.0000 1.10808 0.554038 − 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −8.00000 −0.294684
\(738\) −2.00000 −0.0736210
\(739\) −6.00000 −0.220714 −0.110357 − 0.993892i \(-0.535199\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(740\) 2.00000 0.0735215
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 10.0000 0.366618
\(745\) 22.0000 0.806018
\(746\) 17.0000 0.622414
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 9.00000 0.328634
\(751\) 29.0000 1.05823 0.529113 − 0.848552i \(-0.322525\pi\)
0.529113 + 0.848552i \(0.322525\pi\)
\(752\) 8.00000 0.291730
\(753\) 18.0000 0.655956
\(754\) 16.0000 0.582686
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 52.0000 1.88997 0.944986 − 0.327111i \(-0.106075\pi\)
0.944986 + 0.327111i \(0.106075\pi\)
\(758\) 38.0000 1.38022
\(759\) 4.00000 0.145191
\(760\) 3.00000 0.108821
\(761\) 50.0000 1.81250 0.906249 − 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 39.0000 1.40913
\(767\) 20.0000 0.722158
\(768\) −1.00000 −0.0360844
\(769\) 11.0000 0.396670 0.198335 − 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) 14.0000 0.503871
\(773\) −10.0000 −0.359675 −0.179838 − 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) −8.00000 −0.287554
\(775\) −40.0000 −1.43684
\(776\) 16.0000 0.574367
\(777\) 0 0
\(778\) 27.0000 0.967997
\(779\) −3.00000 −0.107486
\(780\) −2.00000 −0.0716115
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) 40.0000 1.42948
\(784\) 0 0
\(785\) 12.0000 0.428298
\(786\) 12.0000 0.428026
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 5.00000 0.178118
\(789\) 8.00000 0.284808
\(790\) 15.0000 0.533676
\(791\) 0 0
\(792\) 2.00000 0.0710669
\(793\) −10.0000 −0.355110
\(794\) 22.0000 0.780751
\(795\) −2.00000 −0.0709327
\(796\) −24.0000 −0.850657
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 4.00000 0.141421
\(801\) −12.0000 −0.423999
\(802\) −23.0000 −0.812158
\(803\) −2.00000 −0.0705785
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) 20.0000 0.704470
\(807\) −23.0000 −0.809638
\(808\) 8.00000 0.281439
\(809\) 32.0000 1.12506 0.562530 − 0.826777i \(-0.309828\pi\)
0.562530 + 0.826777i \(0.309828\pi\)
\(810\) 1.00000 0.0351364
\(811\) −30.0000 −1.05344 −0.526721 − 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 2.00000 0.0701000
\(815\) −10.0000 −0.350285
\(816\) 0 0
\(817\) −12.0000 −0.419827
\(818\) −5.00000 −0.174821
\(819\) 0 0
\(820\) 1.00000 0.0349215
\(821\) 37.0000 1.29131 0.645654 − 0.763630i \(-0.276585\pi\)
0.645654 + 0.763630i \(0.276585\pi\)
\(822\) −18.0000 −0.627822
\(823\) 13.0000 0.453152 0.226576 − 0.973994i \(-0.427247\pi\)
0.226576 + 0.973994i \(0.427247\pi\)
\(824\) −14.0000 −0.487713
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 8.00000 0.278019
\(829\) −6.00000 −0.208389 −0.104194 − 0.994557i \(-0.533226\pi\)
−0.104194 + 0.994557i \(0.533226\pi\)
\(830\) 6.00000 0.208263
\(831\) −17.0000 −0.589723
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −2.00000 −0.0692543
\(835\) 8.00000 0.276851
\(836\) 3.00000 0.103757
\(837\) 50.0000 1.72825
\(838\) −12.0000 −0.414533
\(839\) −19.0000 −0.655953 −0.327976 − 0.944686i \(-0.606367\pi\)
−0.327976 + 0.944686i \(0.606367\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) −18.0000 −0.620321
\(843\) −4.00000 −0.137767
\(844\) −15.0000 −0.516321
\(845\) 9.00000 0.309609
\(846\) 16.0000 0.550091
\(847\) 0 0
\(848\) −2.00000 −0.0686803
\(849\) −14.0000 −0.480479
\(850\) 0 0
\(851\) 8.00000 0.274236
\(852\) 9.00000 0.308335
\(853\) 49.0000 1.67773 0.838864 − 0.544341i \(-0.183220\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(854\) 0 0
\(855\) 6.00000 0.205196
\(856\) 10.0000 0.341793
\(857\) 5.00000 0.170797 0.0853984 − 0.996347i \(-0.472784\pi\)
0.0853984 + 0.996347i \(0.472784\pi\)
\(858\) −2.00000 −0.0682789
\(859\) −46.0000 −1.56950 −0.784750 − 0.619813i \(-0.787209\pi\)
−0.784750 + 0.619813i \(0.787209\pi\)
\(860\) 4.00000 0.136399
\(861\) 0 0
\(862\) 8.00000 0.272481
\(863\) −54.0000 −1.83818 −0.919091 − 0.394046i \(-0.871075\pi\)
−0.919091 + 0.394046i \(0.871075\pi\)
\(864\) −5.00000 −0.170103
\(865\) 3.00000 0.102003
\(866\) −11.0000 −0.373795
\(867\) 17.0000 0.577350
\(868\) 0 0
\(869\) 15.0000 0.508840
\(870\) −8.00000 −0.271225
\(871\) 16.0000 0.542139
\(872\) −8.00000 −0.270914
\(873\) 32.0000 1.08304
\(874\) 12.0000 0.405906
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 35.0000 1.18187 0.590933 − 0.806721i \(-0.298760\pi\)
0.590933 + 0.806721i \(0.298760\pi\)
\(878\) 1.00000 0.0337484
\(879\) −12.0000 −0.404750
\(880\) −1.00000 −0.0337100
\(881\) −47.0000 −1.58347 −0.791735 − 0.610865i \(-0.790822\pi\)
−0.791735 + 0.610865i \(0.790822\pi\)
\(882\) 0 0
\(883\) 52.0000 1.74994 0.874970 − 0.484178i \(-0.160881\pi\)
0.874970 + 0.484178i \(0.160881\pi\)
\(884\) 0 0
\(885\) −10.0000 −0.336146
\(886\) 36.0000 1.20944
\(887\) −49.0000 −1.64526 −0.822629 − 0.568578i \(-0.807494\pi\)
−0.822629 + 0.568578i \(0.807494\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 0 0
\(890\) 6.00000 0.201120
\(891\) 1.00000 0.0335013
\(892\) 8.00000 0.267860
\(893\) 24.0000 0.803129
\(894\) −22.0000 −0.735790
\(895\) 11.0000 0.367689
\(896\) 0 0
\(897\) −8.00000 −0.267112
\(898\) −25.0000 −0.834261
\(899\) 80.0000 2.66815
\(900\) 8.00000 0.266667
\(901\) 0 0
\(902\) 1.00000 0.0332964
\(903\) 0 0
\(904\) 3.00000 0.0997785
\(905\) −14.0000 −0.465376
\(906\) 16.0000 0.531564
\(907\) 38.0000 1.26177 0.630885 − 0.775877i \(-0.282692\pi\)
0.630885 + 0.775877i \(0.282692\pi\)
\(908\) −9.00000 −0.298675
\(909\) 16.0000 0.530687
\(910\) 0 0
\(911\) −28.0000 −0.927681 −0.463841 − 0.885919i \(-0.653529\pi\)
−0.463841 + 0.885919i \(0.653529\pi\)
\(912\) −3.00000 −0.0993399
\(913\) 6.00000 0.198571
\(914\) 4.00000 0.132308
\(915\) 5.00000 0.165295
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −49.0000 −1.61636 −0.808180 − 0.588935i \(-0.799547\pi\)
−0.808180 + 0.588935i \(0.799547\pi\)
\(920\) −4.00000 −0.131876
\(921\) 12.0000 0.395413
\(922\) 19.0000 0.625732
\(923\) 18.0000 0.592477
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 13.0000 0.427207
\(927\) −28.0000 −0.919641
\(928\) −8.00000 −0.262613
\(929\) 2.00000 0.0656179 0.0328089 − 0.999462i \(-0.489555\pi\)
0.0328089 + 0.999462i \(0.489555\pi\)
\(930\) −10.0000 −0.327913
\(931\) 0 0
\(932\) 10.0000 0.327561
\(933\) 16.0000 0.523816
\(934\) −36.0000 −1.17796
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −12.0000 −0.392023 −0.196011 − 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 0 0
\(939\) 8.00000 0.261070
\(940\) −8.00000 −0.260931
\(941\) 33.0000 1.07577 0.537885 − 0.843018i \(-0.319224\pi\)
0.537885 + 0.843018i \(0.319224\pi\)
\(942\) −12.0000 −0.390981
\(943\) 4.00000 0.130258
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 24.0000 0.779895 0.389948 − 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) −15.0000 −0.487177
\(949\) 4.00000 0.129845
\(950\) 12.0000 0.389331
\(951\) 28.0000 0.907962
\(952\) 0 0
\(953\) −6.00000 −0.194359 −0.0971795 − 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) −4.00000 −0.129505
\(955\) 8.00000 0.258874
\(956\) −7.00000 −0.226396
\(957\) −8.00000 −0.258603
\(958\) −1.00000 −0.0323085
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) 69.0000 2.22581
\(962\) −4.00000 −0.128965
\(963\) 20.0000 0.644491
\(964\) 10.0000 0.322078
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) −41.0000 −1.31847 −0.659236 − 0.751936i \(-0.729120\pi\)
−0.659236 + 0.751936i \(0.729120\pi\)
\(968\) 10.0000 0.321412
\(969\) 0 0
\(970\) −16.0000 −0.513729
\(971\) 4.00000 0.128366 0.0641831 − 0.997938i \(-0.479556\pi\)
0.0641831 + 0.997938i \(0.479556\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) 14.0000 0.448589
\(975\) −8.00000 −0.256205
\(976\) 5.00000 0.160046
\(977\) 2.00000 0.0639857 0.0319928 − 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 10.0000 0.319765
\(979\) 6.00000 0.191761
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 14.0000 0.446758
\(983\) 28.0000 0.893061 0.446531 − 0.894768i \(-0.352659\pi\)
0.446531 + 0.894768i \(0.352659\pi\)
\(984\) −1.00000 −0.0318788
\(985\) −5.00000 −0.159313
\(986\) 0 0
\(987\) 0 0
\(988\) −6.00000 −0.190885
\(989\) 16.0000 0.508770
\(990\) −2.00000 −0.0635642
\(991\) 53.0000 1.68360 0.841800 − 0.539789i \(-0.181496\pi\)
0.841800 + 0.539789i \(0.181496\pi\)
\(992\) −10.0000 −0.317500
\(993\) −12.0000 −0.380808
\(994\) 0 0
\(995\) 24.0000 0.760851
\(996\) −6.00000 −0.190117
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 0 0
\(999\) −10.0000 −0.316386
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.e.1.1 1
7.2 even 3 574.2.e.b.165.1 ✓ 2
7.4 even 3 574.2.e.b.247.1 yes 2
7.6 odd 2 4018.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.e.b.165.1 ✓ 2 7.2 even 3
574.2.e.b.247.1 yes 2 7.4 even 3
4018.2.a.e.1.1 1 1.1 even 1 trivial
4018.2.a.h.1.1 1 7.6 odd 2