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Properties

Label 4018.2.a.m.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: yes
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} +4.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +3.00000 q^{15} +1.00000 q^{16} -7.00000 q^{17} -2.00000 q^{18} +4.00000 q^{19} -3.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} +2.00000 q^{26} +5.00000 q^{27} +9.00000 q^{29} +3.00000 q^{30} +1.00000 q^{31} +1.00000 q^{32} -4.00000 q^{33} -7.00000 q^{34} -2.00000 q^{36} +8.00000 q^{37} +4.00000 q^{38} -2.00000 q^{39} -3.00000 q^{40} -1.00000 q^{41} -3.00000 q^{43} +4.00000 q^{44} +6.00000 q^{45} -4.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} +4.00000 q^{50} +7.00000 q^{51} +2.00000 q^{52} -11.0000 q^{53} +5.00000 q^{54} -12.0000 q^{55} -4.00000 q^{57} +9.00000 q^{58} -6.00000 q^{59} +3.00000 q^{60} -9.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} -4.00000 q^{66} -2.00000 q^{67} -7.00000 q^{68} +4.00000 q^{69} -7.00000 q^{71} -2.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} -4.00000 q^{75} +4.00000 q^{76} -2.00000 q^{78} -15.0000 q^{79} -3.00000 q^{80} +1.00000 q^{81} -1.00000 q^{82} +4.00000 q^{83} +21.0000 q^{85} -3.00000 q^{86} -9.00000 q^{87} +4.00000 q^{88} -1.00000 q^{89} +6.00000 q^{90} -4.00000 q^{92} -1.00000 q^{93} -8.00000 q^{94} -12.0000 q^{95} -1.00000 q^{96} -5.00000 q^{97} -8.00000 q^{99} +O(q^{100})\)

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
\(5\) −3.00000 −1.34164 −0.670820 − 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) −3.00000 −0.948683
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) −7.00000 −1.69775 −0.848875 − 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) −2.00000 −0.471405
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) −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
\(29\) 9.00000 1.67126 0.835629 − 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 3.00000 0.547723
\(31\) 1.00000 0.179605 0.0898027 − 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.00000 −0.696311
\(34\) −7.00000 −1.20049
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 4.00000 0.648886
\(39\) −2.00000 −0.320256
\(40\) −3.00000 −0.474342
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.00000 −0.457496 −0.228748 − 0.973486i \(-0.573463\pi\)
−0.228748 + 0.973486i \(0.573463\pi\)
\(44\) 4.00000 0.603023
\(45\) 6.00000 0.894427
\(46\) −4.00000 −0.589768
\(47\) −8.00000 −1.16692 −0.583460 − 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 4.00000 0.565685
\(51\) 7.00000 0.980196
\(52\) 2.00000 0.277350
\(53\) −11.0000 −1.51097 −0.755483 − 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) 5.00000 0.680414
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 9.00000 1.18176
\(59\) −6.00000 −0.781133 −0.390567 − 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 3.00000 0.387298
\(61\) −9.00000 −1.15233 −0.576166 − 0.817333i \(-0.695452\pi\)
−0.576166 + 0.817333i \(0.695452\pi\)
\(62\) 1.00000 0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 −0.744208
\(66\) −4.00000 −0.492366
\(67\) −2.00000 −0.244339 −0.122169 − 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −7.00000 −0.848875
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −7.00000 −0.830747 −0.415374 − 0.909651i \(-0.636349\pi\)
−0.415374 + 0.909651i \(0.636349\pi\)
\(72\) −2.00000 −0.235702
\(73\) −4.00000 −0.468165 −0.234082 − 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 8.00000 0.929981
\(75\) −4.00000 −0.461880
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −15.0000 −1.68763 −0.843816 − 0.536633i \(-0.819696\pi\)
−0.843816 + 0.536633i \(0.819696\pi\)
\(80\) −3.00000 −0.335410
\(81\) 1.00000 0.111111
\(82\) −1.00000 −0.110432
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 21.0000 2.27777
\(86\) −3.00000 −0.323498
\(87\) −9.00000 −0.964901
\(88\) 4.00000 0.426401
\(89\) −1.00000 −0.106000 −0.0529999 − 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −1.00000 −0.103695
\(94\) −8.00000 −0.825137
\(95\) −12.0000 −1.23117
\(96\) −1.00000 −0.102062
\(97\) −5.00000 −0.507673 −0.253837 − 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) −8.00000 −0.804030
\(100\) 4.00000 0.400000
\(101\) 14.0000 1.39305 0.696526 − 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 7.00000 0.693103
\(103\) −11.0000 −1.08386 −0.541931 − 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −11.0000 −1.06841
\(107\) −3.00000 −0.290021 −0.145010 − 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 5.00000 0.481125
\(109\) 18.0000 1.72409 0.862044 − 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) −12.0000 −1.14416
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 − 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) −4.00000 −0.374634
\(115\) 12.0000 1.11901
\(116\) 9.00000 0.835629
\(117\) −4.00000 −0.369800
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 3.00000 0.273861
\(121\) 5.00000 0.454545
\(122\) −9.00000 −0.814822
\(123\) 1.00000 0.0901670
\(124\) 1.00000 0.0898027
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.00000 0.264135
\(130\) −6.00000 −0.526235
\(131\) −14.0000 −1.22319 −0.611593 − 0.791173i \(-0.709471\pi\)
−0.611593 + 0.791173i \(0.709471\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) −15.0000 −1.29099
\(136\) −7.00000 −0.600245
\(137\) −16.0000 −1.36697 −0.683486 − 0.729964i \(-0.739537\pi\)
−0.683486 + 0.729964i \(0.739537\pi\)
\(138\) 4.00000 0.340503
\(139\) 22.0000 1.86602 0.933008 − 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) −7.00000 −0.587427
\(143\) 8.00000 0.668994
\(144\) −2.00000 −0.166667
\(145\) −27.0000 −2.24223
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) −15.0000 −1.22885 −0.614424 − 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) −4.00000 −0.326599
\(151\) 19.0000 1.54620 0.773099 − 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 4.00000 0.324443
\(153\) 14.0000 1.13183
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) −2.00000 −0.160128
\(157\) −4.00000 −0.319235 −0.159617 − 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −15.0000 −1.19334
\(159\) 11.0000 0.872357
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 12.0000 0.934199
\(166\) 4.00000 0.310460
\(167\) −24.0000 −1.85718 −0.928588 − 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 21.0000 1.61063
\(171\) −8.00000 −0.611775
\(172\) −3.00000 −0.228748
\(173\) 5.00000 0.380143 0.190071 − 0.981770i \(-0.439128\pi\)
0.190071 + 0.981770i \(0.439128\pi\)
\(174\) −9.00000 −0.682288
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 6.00000 0.450988
\(178\) −1.00000 −0.0749532
\(179\) −6.00000 −0.448461 −0.224231 − 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 6.00000 0.447214
\(181\) −8.00000 −0.594635 −0.297318 − 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 9.00000 0.665299
\(184\) −4.00000 −0.294884
\(185\) −24.0000 −1.76452
\(186\) −1.00000 −0.0733236
\(187\) −28.0000 −2.04756
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) −15.0000 −1.08536 −0.542681 − 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −5.00000 −0.358979
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 − 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) −8.00000 −0.568535
\(199\) 8.00000 0.567105 0.283552 − 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 4.00000 0.282843
\(201\) 2.00000 0.141069
\(202\) 14.0000 0.985037
\(203\) 0 0
\(204\) 7.00000 0.490098
\(205\) 3.00000 0.209529
\(206\) −11.0000 −0.766406
\(207\) 8.00000 0.556038
\(208\) 2.00000 0.138675
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 − 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −11.0000 −0.755483
\(213\) 7.00000 0.479632
\(214\) −3.00000 −0.205076
\(215\) 9.00000 0.613795
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) 4.00000 0.270295
\(220\) −12.0000 −0.809040
\(221\) −14.0000 −0.941742
\(222\) −8.00000 −0.536925
\(223\) 9.00000 0.602685 0.301342 − 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) −3.00000 −0.199557
\(227\) −13.0000 −0.862840 −0.431420 − 0.902151i \(-0.641987\pi\)
−0.431420 + 0.902151i \(0.641987\pi\)
\(228\) −4.00000 −0.264906
\(229\) −22.0000 −1.45380 −0.726900 − 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 12.0000 0.791257
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) −4.00000 −0.261488
\(235\) 24.0000 1.56559
\(236\) −6.00000 −0.390567
\(237\) 15.0000 0.974355
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 − 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 3.00000 0.193649
\(241\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 5.00000 0.321412
\(243\) −16.0000 −1.02640
\(244\) −9.00000 −0.576166
\(245\) 0 0
\(246\) 1.00000 0.0637577
\(247\) 8.00000 0.509028
\(248\) 1.00000 0.0635001
\(249\) −4.00000 −0.253490
\(250\) 3.00000 0.189737
\(251\) −10.0000 −0.631194 −0.315597 − 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) −8.00000 −0.501965
\(255\) −21.0000 −1.31507
\(256\) 1.00000 0.0625000
\(257\) 21.0000 1.30994 0.654972 − 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 3.00000 0.186772
\(259\) 0 0
\(260\) −6.00000 −0.372104
\(261\) −18.0000 −1.11417
\(262\) −14.0000 −0.864923
\(263\) −8.00000 −0.493301 −0.246651 − 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) −4.00000 −0.246183
\(265\) 33.0000 2.02717
\(266\) 0 0
\(267\) 1.00000 0.0611990
\(268\) −2.00000 −0.122169
\(269\) 10.0000 0.609711 0.304855 − 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) −15.0000 −0.912871
\(271\) 20.0000 1.21491 0.607457 − 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) −16.0000 −0.966595
\(275\) 16.0000 0.964836
\(276\) 4.00000 0.240772
\(277\) −18.0000 −1.08152 −0.540758 − 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 22.0000 1.31947
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 − 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 8.00000 0.476393
\(283\) 10.0000 0.594438 0.297219 − 0.954809i \(-0.403941\pi\)
0.297219 + 0.954809i \(0.403941\pi\)
\(284\) −7.00000 −0.415374
\(285\) 12.0000 0.710819
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) 32.0000 1.88235
\(290\) −27.0000 −1.58549
\(291\) 5.00000 0.293105
\(292\) −4.00000 −0.234082
\(293\) 18.0000 1.05157 0.525786 − 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 18.0000 1.04800
\(296\) 8.00000 0.464991
\(297\) 20.0000 1.16052
\(298\) −15.0000 −0.868927
\(299\) −8.00000 −0.462652
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 19.0000 1.09333
\(303\) −14.0000 −0.804279
\(304\) 4.00000 0.229416
\(305\) 27.0000 1.54602
\(306\) 14.0000 0.800327
\(307\) 8.00000 0.456584 0.228292 − 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) −3.00000 −0.170389
\(311\) 30.0000 1.70114 0.850572 − 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) −2.00000 −0.113228
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −15.0000 −0.843816
\(317\) 22.0000 1.23564 0.617822 − 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 11.0000 0.616849
\(319\) 36.0000 2.01561
\(320\) −3.00000 −0.167705
\(321\) 3.00000 0.167444
\(322\) 0 0
\(323\) −28.0000 −1.55796
\(324\) 1.00000 0.0555556
\(325\) 8.00000 0.443760
\(326\) 4.00000 0.221540
\(327\) −18.0000 −0.995402
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) 12.0000 0.660578
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) 4.00000 0.219529
\(333\) −16.0000 −0.876795
\(334\) −24.0000 −1.31322
\(335\) 6.00000 0.327815
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 − 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −9.00000 −0.489535
\(339\) 3.00000 0.162938
\(340\) 21.0000 1.13888
\(341\) 4.00000 0.216612
\(342\) −8.00000 −0.432590
\(343\) 0 0
\(344\) −3.00000 −0.161749
\(345\) −12.0000 −0.646058
\(346\) 5.00000 0.268802
\(347\) 16.0000 0.858925 0.429463 − 0.903085i \(-0.358703\pi\)
0.429463 + 0.903085i \(0.358703\pi\)
\(348\) −9.00000 −0.482451
\(349\) 18.0000 0.963518 0.481759 − 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) 10.0000 0.533761
\(352\) 4.00000 0.213201
\(353\) −8.00000 −0.425797 −0.212899 − 0.977074i \(-0.568290\pi\)
−0.212899 + 0.977074i \(0.568290\pi\)
\(354\) 6.00000 0.318896
\(355\) 21.0000 1.11456
\(356\) −1.00000 −0.0529999
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 22.0000 1.16112 0.580558 − 0.814219i \(-0.302835\pi\)
0.580558 + 0.814219i \(0.302835\pi\)
\(360\) 6.00000 0.316228
\(361\) −3.00000 −0.157895
\(362\) −8.00000 −0.420471
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 9.00000 0.470438
\(367\) −37.0000 −1.93138 −0.965692 − 0.259690i \(-0.916380\pi\)
−0.965692 + 0.259690i \(0.916380\pi\)
\(368\) −4.00000 −0.208514
\(369\) 2.00000 0.104116
\(370\) −24.0000 −1.24770
\(371\) 0 0
\(372\) −1.00000 −0.0518476
\(373\) 24.0000 1.24267 0.621336 − 0.783544i \(-0.286590\pi\)
0.621336 + 0.783544i \(0.286590\pi\)
\(374\) −28.0000 −1.44785
\(375\) −3.00000 −0.154919
\(376\) −8.00000 −0.412568
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) 15.0000 0.770498 0.385249 − 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) −12.0000 −0.615587
\(381\) 8.00000 0.409852
\(382\) −15.0000 −0.767467
\(383\) −20.0000 −1.02195 −0.510976 − 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 6.00000 0.304997
\(388\) −5.00000 −0.253837
\(389\) −34.0000 −1.72387 −0.861934 − 0.507020i \(-0.830747\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(390\) 6.00000 0.303822
\(391\) 28.0000 1.41602
\(392\) 0 0
\(393\) 14.0000 0.706207
\(394\) −8.00000 −0.403034
\(395\) 45.0000 2.26420
\(396\) −8.00000 −0.402015
\(397\) −10.0000 −0.501886 −0.250943 − 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 27.0000 1.34832 0.674158 − 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) 2.00000 0.0997509
\(403\) 2.00000 0.0996271
\(404\) 14.0000 0.696526
\(405\) −3.00000 −0.149071
\(406\) 0 0
\(407\) 32.0000 1.58618
\(408\) 7.00000 0.346552
\(409\) −20.0000 −0.988936 −0.494468 − 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 3.00000 0.148159
\(411\) 16.0000 0.789222
\(412\) −11.0000 −0.541931
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −12.0000 −0.589057
\(416\) 2.00000 0.0980581
\(417\) −22.0000 −1.07734
\(418\) 16.0000 0.782586
\(419\) −26.0000 −1.27018 −0.635092 − 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) −29.0000 −1.41337 −0.706687 − 0.707527i \(-0.749811\pi\)
−0.706687 + 0.707527i \(0.749811\pi\)
\(422\) −16.0000 −0.778868
\(423\) 16.0000 0.777947
\(424\) −11.0000 −0.534207
\(425\) −28.0000 −1.35820
\(426\) 7.00000 0.339151
\(427\) 0 0
\(428\) −3.00000 −0.145010
\(429\) −8.00000 −0.386244
\(430\) 9.00000 0.434019
\(431\) −12.0000 −0.578020 −0.289010 − 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 5.00000 0.240563
\(433\) 16.0000 0.768911 0.384455 − 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 27.0000 1.29455
\(436\) 18.0000 0.862044
\(437\) −16.0000 −0.765384
\(438\) 4.00000 0.191127
\(439\) 14.0000 0.668184 0.334092 − 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) −12.0000 −0.572078
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) −31.0000 −1.47285 −0.736427 − 0.676517i \(-0.763489\pi\)
−0.736427 + 0.676517i \(0.763489\pi\)
\(444\) −8.00000 −0.379663
\(445\) 3.00000 0.142214
\(446\) 9.00000 0.426162
\(447\) 15.0000 0.709476
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 − 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) −8.00000 −0.377124
\(451\) −4.00000 −0.188353
\(452\) −3.00000 −0.141108
\(453\) −19.0000 −0.892698
\(454\) −13.0000 −0.610120
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) 8.00000 0.374224 0.187112 − 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −22.0000 −1.02799
\(459\) −35.0000 −1.63366
\(460\) 12.0000 0.559503
\(461\) −27.0000 −1.25752 −0.628758 − 0.777601i \(-0.716436\pi\)
−0.628758 + 0.777601i \(0.716436\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 − 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 9.00000 0.417815
\(465\) 3.00000 0.139122
\(466\) 0 0
\(467\) 22.0000 1.01804 0.509019 − 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(468\) −4.00000 −0.184900
\(469\) 0 0
\(470\) 24.0000 1.10704
\(471\) 4.00000 0.184310
\(472\) −6.00000 −0.276172
\(473\) −12.0000 −0.551761
\(474\) 15.0000 0.688973
\(475\) 16.0000 0.734130
\(476\) 0 0
\(477\) 22.0000 1.00731
\(478\) −24.0000 −1.09773
\(479\) 8.00000 0.365529 0.182765 − 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 3.00000 0.136931
\(481\) 16.0000 0.729537
\(482\) 0 0
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 15.0000 0.681115
\(486\) −16.0000 −0.725775
\(487\) −30.0000 −1.35943 −0.679715 − 0.733476i \(-0.737896\pi\)
−0.679715 + 0.733476i \(0.737896\pi\)
\(488\) −9.00000 −0.407411
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 23.0000 1.03798 0.518988 − 0.854782i \(-0.326309\pi\)
0.518988 + 0.854782i \(0.326309\pi\)
\(492\) 1.00000 0.0450835
\(493\) −63.0000 −2.83738
\(494\) 8.00000 0.359937
\(495\) 24.0000 1.07872
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) −4.00000 −0.179244
\(499\) 14.0000 0.626726 0.313363 − 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 3.00000 0.134164
\(501\) 24.0000 1.07224
\(502\) −10.0000 −0.446322
\(503\) 36.0000 1.60516 0.802580 − 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) −16.0000 −0.711287
\(507\) 9.00000 0.399704
\(508\) −8.00000 −0.354943
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) −21.0000 −0.929896
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 20.0000 0.883022
\(514\) 21.0000 0.926270
\(515\) 33.0000 1.45415
\(516\) 3.00000 0.132068
\(517\) −32.0000 −1.40736
\(518\) 0 0
\(519\) −5.00000 −0.219476
\(520\) −6.00000 −0.263117
\(521\) −38.0000 −1.66481 −0.832405 − 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) −18.0000 −0.787839
\(523\) 36.0000 1.57417 0.787085 − 0.616844i \(-0.211589\pi\)
0.787085 + 0.616844i \(0.211589\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −7.00000 −0.304925
\(528\) −4.00000 −0.174078
\(529\) −7.00000 −0.304348
\(530\) 33.0000 1.43343
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 1.00000 0.0432742
\(535\) 9.00000 0.389104
\(536\) −2.00000 −0.0863868
\(537\) 6.00000 0.258919
\(538\) 10.0000 0.431131
\(539\) 0 0
\(540\) −15.0000 −0.645497
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 20.0000 0.859074
\(543\) 8.00000 0.343313
\(544\) −7.00000 −0.300123
\(545\) −54.0000 −2.31311
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 − 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −16.0000 −0.683486
\(549\) 18.0000 0.768221
\(550\) 16.0000 0.682242
\(551\) 36.0000 1.53365
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) −18.0000 −0.764747
\(555\) 24.0000 1.01874
\(556\) 22.0000 0.933008
\(557\) 3.00000 0.127114 0.0635570 − 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) −2.00000 −0.0846668
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 28.0000 1.18216
\(562\) 6.00000 0.253095
\(563\) 44.0000 1.85438 0.927189 − 0.374593i \(-0.122217\pi\)
0.927189 + 0.374593i \(0.122217\pi\)
\(564\) 8.00000 0.336861
\(565\) 9.00000 0.378633
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) −7.00000 −0.293713
\(569\) 7.00000 0.293455 0.146728 − 0.989177i \(-0.453126\pi\)
0.146728 + 0.989177i \(0.453126\pi\)
\(570\) 12.0000 0.502625
\(571\) 4.00000 0.167395 0.0836974 − 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 8.00000 0.334497
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) −2.00000 −0.0833333
\(577\) −30.0000 −1.24892 −0.624458 − 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 32.0000 1.33102
\(579\) 14.0000 0.581820
\(580\) −27.0000 −1.12111
\(581\) 0 0
\(582\) 5.00000 0.207257
\(583\) −44.0000 −1.82229
\(584\) −4.00000 −0.165521
\(585\) 12.0000 0.496139
\(586\) 18.0000 0.743573
\(587\) −7.00000 −0.288921 −0.144460 − 0.989511i \(-0.546145\pi\)
−0.144460 + 0.989511i \(0.546145\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 18.0000 0.741048
\(591\) 8.00000 0.329076
\(592\) 8.00000 0.328798
\(593\) −15.0000 −0.615976 −0.307988 − 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 20.0000 0.820610
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) −8.00000 −0.327418
\(598\) −8.00000 −0.327144
\(599\) 22.0000 0.898896 0.449448 − 0.893307i \(-0.351621\pi\)
0.449448 + 0.893307i \(0.351621\pi\)
\(600\) −4.00000 −0.163299
\(601\) 41.0000 1.67242 0.836212 − 0.548406i \(-0.184765\pi\)
0.836212 + 0.548406i \(0.184765\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 19.0000 0.773099
\(605\) −15.0000 −0.609837
\(606\) −14.0000 −0.568711
\(607\) −7.00000 −0.284121 −0.142061 − 0.989858i \(-0.545373\pi\)
−0.142061 + 0.989858i \(0.545373\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 27.0000 1.09320
\(611\) −16.0000 −0.647291
\(612\) 14.0000 0.565916
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 8.00000 0.322854
\(615\) −3.00000 −0.120972
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 − 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 11.0000 0.442485
\(619\) −2.00000 −0.0803868 −0.0401934 − 0.999192i \(-0.512797\pi\)
−0.0401934 + 0.999192i \(0.512797\pi\)
\(620\) −3.00000 −0.120483
\(621\) −20.0000 −0.802572
\(622\) 30.0000 1.20289
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −29.0000 −1.16000
\(626\) −26.0000 −1.03917
\(627\) −16.0000 −0.638978
\(628\) −4.00000 −0.159617
\(629\) −56.0000 −2.23287
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 − 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) −15.0000 −0.596668
\(633\) 16.0000 0.635943
\(634\) 22.0000 0.873732
\(635\) 24.0000 0.952411
\(636\) 11.0000 0.436178
\(637\) 0 0
\(638\) 36.0000 1.42525
\(639\) 14.0000 0.553831
\(640\) −3.00000 −0.118585
\(641\) −8.00000 −0.315981 −0.157991 − 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) 3.00000 0.118401
\(643\) −13.0000 −0.512670 −0.256335 − 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 0 0
\(645\) −9.00000 −0.354375
\(646\) −28.0000 −1.10165
\(647\) 13.0000 0.511083 0.255541 − 0.966798i \(-0.417746\pi\)
0.255541 + 0.966798i \(0.417746\pi\)
\(648\) 1.00000 0.0392837
\(649\) −24.0000 −0.942082
\(650\) 8.00000 0.313786
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 29.0000 1.13486 0.567429 − 0.823422i \(-0.307938\pi\)
0.567429 + 0.823422i \(0.307938\pi\)
\(654\) −18.0000 −0.703856
\(655\) 42.0000 1.64108
\(656\) −1.00000 −0.0390434
\(657\) 8.00000 0.312110
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 − 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 12.0000 0.467099
\(661\) 22.0000 0.855701 0.427850 − 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 10.0000 0.388661
\(663\) 14.0000 0.543715
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −16.0000 −0.619987
\(667\) −36.0000 −1.39393
\(668\) −24.0000 −0.928588
\(669\) −9.00000 −0.347960
\(670\) 6.00000 0.231800
\(671\) −36.0000 −1.38976
\(672\) 0 0
\(673\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) −19.0000 −0.731853
\(675\) 20.0000 0.769800
\(676\) −9.00000 −0.346154
\(677\) 26.0000 0.999261 0.499631 − 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) 3.00000 0.115214
\(679\) 0 0
\(680\) 21.0000 0.805313
\(681\) 13.0000 0.498161
\(682\) 4.00000 0.153168
\(683\) −24.0000 −0.918334 −0.459167 − 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −8.00000 −0.305888
\(685\) 48.0000 1.83399
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) −3.00000 −0.114374
\(689\) −22.0000 −0.838133
\(690\) −12.0000 −0.456832
\(691\) 7.00000 0.266293 0.133146 − 0.991096i \(-0.457492\pi\)
0.133146 + 0.991096i \(0.457492\pi\)
\(692\) 5.00000 0.190071
\(693\) 0 0
\(694\) 16.0000 0.607352
\(695\) −66.0000 −2.50352
\(696\) −9.00000 −0.341144
\(697\) 7.00000 0.265144
\(698\) 18.0000 0.681310
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 10.0000 0.377426
\(703\) 32.0000 1.20690
\(704\) 4.00000 0.150756
\(705\) −24.0000 −0.903892
\(706\) −8.00000 −0.301084
\(707\) 0 0
\(708\) 6.00000 0.225494
\(709\) −35.0000 −1.31445 −0.657226 − 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(710\) 21.0000 0.788116
\(711\) 30.0000 1.12509
\(712\) −1.00000 −0.0374766
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) −6.00000 −0.224231
\(717\) 24.0000 0.896296
\(718\) 22.0000 0.821033
\(719\) 26.0000 0.969636 0.484818 − 0.874615i \(-0.338886\pi\)
0.484818 + 0.874615i \(0.338886\pi\)
\(720\) 6.00000 0.223607
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 0 0
\(724\) −8.00000 −0.297318
\(725\) 36.0000 1.33701
\(726\) −5.00000 −0.185567
\(727\) 30.0000 1.11264 0.556319 − 0.830969i \(-0.312213\pi\)
0.556319 + 0.830969i \(0.312213\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 12.0000 0.444140
\(731\) 21.0000 0.776713
\(732\) 9.00000 0.332650
\(733\) 7.00000 0.258551 0.129275 − 0.991609i \(-0.458735\pi\)
0.129275 + 0.991609i \(0.458735\pi\)
\(734\) −37.0000 −1.36569
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −8.00000 −0.294684
\(738\) 2.00000 0.0736210
\(739\) −19.0000 −0.698926 −0.349463 − 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) −24.0000 −0.882258
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 − 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 45.0000 1.64867
\(746\) 24.0000 0.878702
\(747\) −8.00000 −0.292705
\(748\) −28.0000 −1.02378
\(749\) 0 0
\(750\) −3.00000 −0.109545
\(751\) −24.0000 −0.875772 −0.437886 − 0.899030i \(-0.644273\pi\)
−0.437886 + 0.899030i \(0.644273\pi\)
\(752\) −8.00000 −0.291730
\(753\) 10.0000 0.364420
\(754\) 18.0000 0.655521
\(755\) −57.0000 −2.07444
\(756\) 0 0
\(757\) 5.00000 0.181728 0.0908640 − 0.995863i \(-0.471037\pi\)
0.0908640 + 0.995863i \(0.471037\pi\)
\(758\) 15.0000 0.544825
\(759\) 16.0000 0.580763
\(760\) −12.0000 −0.435286
\(761\) −28.0000 −1.01500 −0.507500 − 0.861652i \(-0.669430\pi\)
−0.507500 + 0.861652i \(0.669430\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) −15.0000 −0.542681
\(765\) −42.0000 −1.51851
\(766\) −20.0000 −0.722629
\(767\) −12.0000 −0.433295
\(768\) −1.00000 −0.0360844
\(769\) −34.0000 −1.22607 −0.613036 − 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −21.0000 −0.756297
\(772\) −14.0000 −0.503871
\(773\) 20.0000 0.719350 0.359675 − 0.933078i \(-0.382888\pi\)
0.359675 + 0.933078i \(0.382888\pi\)
\(774\) 6.00000 0.215666
\(775\) 4.00000 0.143684
\(776\) −5.00000 −0.179490
\(777\) 0 0
\(778\) −34.0000 −1.21896
\(779\) −4.00000 −0.143315
\(780\) 6.00000 0.214834
\(781\) −28.0000 −1.00192
\(782\) 28.0000 1.00128
\(783\) 45.0000 1.60817
\(784\) 0 0
\(785\) 12.0000 0.428298
\(786\) 14.0000 0.499363
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) −8.00000 −0.284988
\(789\) 8.00000 0.284808
\(790\) 45.0000 1.60103
\(791\) 0 0
\(792\) −8.00000 −0.284268
\(793\) −18.0000 −0.639199
\(794\) −10.0000 −0.354887
\(795\) −33.0000 −1.17039
\(796\) 8.00000 0.283552
\(797\) 3.00000 0.106265 0.0531327 − 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 56.0000 1.98114
\(800\) 4.00000 0.141421
\(801\) 2.00000 0.0706665
\(802\) 27.0000 0.953403
\(803\) −16.0000 −0.564628
\(804\) 2.00000 0.0705346
\(805\) 0 0
\(806\) 2.00000 0.0704470
\(807\) −10.0000 −0.352017
\(808\) 14.0000 0.492518
\(809\) 24.0000 0.843795 0.421898 − 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) −3.00000 −0.105409
\(811\) 42.0000 1.47482 0.737410 − 0.675446i \(-0.236049\pi\)
0.737410 + 0.675446i \(0.236049\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 32.0000 1.12160
\(815\) −12.0000 −0.420342
\(816\) 7.00000 0.245049
\(817\) −12.0000 −0.419827
\(818\) −20.0000 −0.699284
\(819\) 0 0
\(820\) 3.00000 0.104765
\(821\) −38.0000 −1.32621 −0.663105 − 0.748527i \(-0.730762\pi\)
−0.663105 + 0.748527i \(0.730762\pi\)
\(822\) 16.0000 0.558064
\(823\) 25.0000 0.871445 0.435723 − 0.900081i \(-0.356493\pi\)
0.435723 + 0.900081i \(0.356493\pi\)
\(824\) −11.0000 −0.383203
\(825\) −16.0000 −0.557048
\(826\) 0 0
\(827\) −22.0000 −0.765015 −0.382507 − 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 8.00000 0.278019
\(829\) 49.0000 1.70184 0.850920 − 0.525295i \(-0.176045\pi\)
0.850920 + 0.525295i \(0.176045\pi\)
\(830\) −12.0000 −0.416526
\(831\) 18.0000 0.624413
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) −22.0000 −0.761798
\(835\) 72.0000 2.49166
\(836\) 16.0000 0.553372
\(837\) 5.00000 0.172825
\(838\) −26.0000 −0.898155
\(839\) −14.0000 −0.483334 −0.241667 − 0.970359i \(-0.577694\pi\)
−0.241667 + 0.970359i \(0.577694\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) −29.0000 −0.999406
\(843\) −6.00000 −0.206651
\(844\) −16.0000 −0.550743
\(845\) 27.0000 0.928828
\(846\) 16.0000 0.550091
\(847\) 0 0
\(848\) −11.0000 −0.377742
\(849\) −10.0000 −0.343199
\(850\) −28.0000 −0.960392
\(851\) −32.0000 −1.09695
\(852\) 7.00000 0.239816
\(853\) −39.0000 −1.33533 −0.667667 − 0.744460i \(-0.732707\pi\)
−0.667667 + 0.744460i \(0.732707\pi\)
\(854\) 0 0
\(855\) 24.0000 0.820783
\(856\) −3.00000 −0.102538
\(857\) −22.0000 −0.751506 −0.375753 − 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) −8.00000 −0.273115
\(859\) −14.0000 −0.477674 −0.238837 − 0.971060i \(-0.576766\pi\)
−0.238837 + 0.971060i \(0.576766\pi\)
\(860\) 9.00000 0.306897
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) 14.0000 0.476566 0.238283 − 0.971196i \(-0.423415\pi\)
0.238283 + 0.971196i \(0.423415\pi\)
\(864\) 5.00000 0.170103
\(865\) −15.0000 −0.510015
\(866\) 16.0000 0.543702
\(867\) −32.0000 −1.08678
\(868\) 0 0
\(869\) −60.0000 −2.03536
\(870\) 27.0000 0.915386
\(871\) −4.00000 −0.135535
\(872\) 18.0000 0.609557
\(873\) 10.0000 0.338449
\(874\) −16.0000 −0.541208
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) 8.00000 0.270141 0.135070 − 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(878\) 14.0000 0.472477
\(879\) −18.0000 −0.607125
\(880\) −12.0000 −0.404520
\(881\) 54.0000 1.81931 0.909653 − 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 0 0
\(883\) −14.0000 −0.471138 −0.235569 − 0.971858i \(-0.575695\pi\)
−0.235569 + 0.971858i \(0.575695\pi\)
\(884\) −14.0000 −0.470871
\(885\) −18.0000 −0.605063
\(886\) −31.0000 −1.04147
\(887\) −32.0000 −1.07445 −0.537227 − 0.843437i \(-0.680528\pi\)
−0.537227 + 0.843437i \(0.680528\pi\)
\(888\) −8.00000 −0.268462
\(889\) 0 0
\(890\) 3.00000 0.100560
\(891\) 4.00000 0.134005
\(892\) 9.00000 0.301342
\(893\) −32.0000 −1.07084
\(894\) 15.0000 0.501675
\(895\) 18.0000 0.601674
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) 15.0000 0.500556
\(899\) 9.00000 0.300167
\(900\) −8.00000 −0.266667
\(901\) 77.0000 2.56524
\(902\) −4.00000 −0.133185
\(903\) 0 0
\(904\) −3.00000 −0.0997785
\(905\) 24.0000 0.797787
\(906\) −19.0000 −0.631233
\(907\) −35.0000 −1.16216 −0.581078 − 0.813848i \(-0.697369\pi\)
−0.581078 + 0.813848i \(0.697369\pi\)
\(908\) −13.0000 −0.431420
\(909\) −28.0000 −0.928701
\(910\) 0 0
\(911\) 34.0000 1.12647 0.563235 − 0.826297i \(-0.309557\pi\)
0.563235 + 0.826297i \(0.309557\pi\)
\(912\) −4.00000 −0.132453
\(913\) 16.0000 0.529523
\(914\) 8.00000 0.264616
\(915\) −27.0000 −0.892592
\(916\) −22.0000 −0.726900
\(917\) 0 0
\(918\) −35.0000 −1.15517
\(919\) 59.0000 1.94623 0.973115 − 0.230319i \(-0.0739769\pi\)
0.973115 + 0.230319i \(0.0739769\pi\)
\(920\) 12.0000 0.395628
\(921\) −8.00000 −0.263609
\(922\) −27.0000 −0.889198
\(923\) −14.0000 −0.460816
\(924\) 0 0
\(925\) 32.0000 1.05215
\(926\) 16.0000 0.525793
\(927\) 22.0000 0.722575
\(928\) 9.00000 0.295439
\(929\) 38.0000 1.24674 0.623370 − 0.781927i \(-0.285763\pi\)
0.623370 + 0.781927i \(0.285763\pi\)
\(930\) 3.00000 0.0983739
\(931\) 0 0
\(932\) 0 0
\(933\) −30.0000 −0.982156
\(934\) 22.0000 0.719862
\(935\) 84.0000 2.74709
\(936\) −4.00000 −0.130744
\(937\) −9.00000 −0.294017 −0.147009 − 0.989135i \(-0.546964\pi\)
−0.147009 + 0.989135i \(0.546964\pi\)
\(938\) 0 0
\(939\) 26.0000 0.848478
\(940\) 24.0000 0.782794
\(941\) −22.0000 −0.717180 −0.358590 − 0.933495i \(-0.616742\pi\)
−0.358590 + 0.933495i \(0.616742\pi\)
\(942\) 4.00000 0.130327
\(943\) 4.00000 0.130258
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 15.0000 0.487177
\(949\) −8.00000 −0.259691
\(950\) 16.0000 0.519109
\(951\) −22.0000 −0.713399
\(952\) 0 0
\(953\) −50.0000 −1.61966 −0.809829 − 0.586665i \(-0.800440\pi\)
−0.809829 + 0.586665i \(0.800440\pi\)
\(954\) 22.0000 0.712276
\(955\) 45.0000 1.45617
\(956\) −24.0000 −0.776215
\(957\) −36.0000 −1.16371
\(958\) 8.00000 0.258468
\(959\) 0 0
\(960\) 3.00000 0.0968246
\(961\) −30.0000 −0.967742
\(962\) 16.0000 0.515861
\(963\) 6.00000 0.193347
\(964\) 0 0
\(965\) 42.0000 1.35203
\(966\) 0 0
\(967\) 9.00000 0.289420 0.144710 − 0.989474i \(-0.453775\pi\)
0.144710 + 0.989474i \(0.453775\pi\)
\(968\) 5.00000 0.160706
\(969\) 28.0000 0.899490
\(970\) 15.0000 0.481621
\(971\) 15.0000 0.481373 0.240686 − 0.970603i \(-0.422627\pi\)
0.240686 + 0.970603i \(0.422627\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) −30.0000 −0.961262
\(975\) −8.00000 −0.256205
\(976\) −9.00000 −0.288083
\(977\) −42.0000 −1.34370 −0.671850 − 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) −4.00000 −0.127906
\(979\) −4.00000 −0.127841
\(980\) 0 0
\(981\) −36.0000 −1.14939
\(982\) 23.0000 0.733959
\(983\) 9.00000 0.287055 0.143528 − 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(984\) 1.00000 0.0318788
\(985\) 24.0000 0.764704
\(986\) −63.0000 −2.00633
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) 12.0000 0.381578
\(990\) 24.0000 0.762770
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 1.00000 0.0317500
\(993\) −10.0000 −0.317340
\(994\) 0 0
\(995\) −24.0000 −0.760851
\(996\) −4.00000 −0.126745
\(997\) −20.0000 −0.633406 −0.316703 − 0.948525i \(-0.602576\pi\)
−0.316703 + 0.948525i \(0.602576\pi\)
\(998\) 14.0000 0.443162
\(999\) 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.m.1.1 ✓ 1
7.6 odd 2 4018.2.a.q.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4018.2.a.m.1.1 ✓ 1 1.1 even 1 trivial
4018.2.a.q.1.1 yes 1 7.6 odd 2