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Properties

Label 4026.2.a.d.1.1
Level $4026$
Weight $2$
Character 4026.1
Self dual yes
Analytic conductor $32.148$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4026,2,Mod(1,4026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.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: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +4.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +4.00000 q^{20} -1.00000 q^{22} +8.00000 q^{23} -1.00000 q^{24} +11.0000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +2.00000 q^{29} -4.00000 q^{30} -2.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -4.00000 q^{38} +2.00000 q^{39} -4.00000 q^{40} -8.00000 q^{41} -10.0000 q^{43} +1.00000 q^{44} +4.00000 q^{45} -8.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} -11.0000 q^{50} +2.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +4.00000 q^{55} +4.00000 q^{57} -2.00000 q^{58} +4.00000 q^{59} +4.00000 q^{60} +1.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +8.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} +2.00000 q^{68} +8.00000 q^{69} +4.00000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +11.0000 q^{75} +4.00000 q^{76} -2.00000 q^{78} +8.00000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} +6.00000 q^{83} +8.00000 q^{85} +10.0000 q^{86} +2.00000 q^{87} -1.00000 q^{88} +6.00000 q^{89} -4.00000 q^{90} +8.00000 q^{92} -2.00000 q^{93} +6.00000 q^{94} +16.0000 q^{95} -1.00000 q^{96} +2.00000 q^{97} +7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
\(4\) 1.00000 0.500000
\(5\) 4.00000 1.78885 0.894427 − 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −4.00000 −1.26491
\(11\) 1.00000 0.301511
\(12\) 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
\(15\) 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
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 8.00000 1.66812 0.834058 − 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) −1.00000 −0.204124
\(25\) 11.0000 2.20000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 − 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −4.00000 −0.730297
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −4.00000 −0.648886
\(39\) 2.00000 0.320256
\(40\) −4.00000 −0.632456
\(41\) −8.00000 −1.24939 −0.624695 − 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 − 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 1.00000 0.150756
\(45\) 4.00000 0.596285
\(46\) −8.00000 −1.17954
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) −11.0000 −1.55563
\(51\) 2.00000 0.280056
\(52\) 2.00000 0.277350
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −2.00000 −0.262613
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 4.00000 0.516398
\(61\) 1.00000 0.128037
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.00000 0.992278
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 − 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 2.00000 0.242536
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 − 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 11.0000 1.27017
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) 8.00000 0.883452
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 10.0000 1.07833
\(87\) 2.00000 0.214423
\(88\) −1.00000 −0.106600
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −4.00000 −0.421637
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) −2.00000 −0.207390
\(94\) 6.00000 0.618853
\(95\) 16.0000 1.64157
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 7.00000 0.707107
\(99\) 1.00000 0.100504
\(100\) 11.0000 1.10000
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) −2.00000 −0.198030
\(103\) −12.0000 −1.18240 −0.591198 − 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −10.0000 −0.966736 −0.483368 − 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 1.00000 0.0962250
\(109\) −18.0000 −1.72409 −0.862044 − 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) −4.00000 −0.381385
\(111\) 0 0
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) −4.00000 −0.374634
\(115\) 32.0000 2.98402
\(116\) 2.00000 0.185695
\(117\) 2.00000 0.184900
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) −4.00000 −0.365148
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −8.00000 −0.721336
\(124\) −2.00000 −0.179605
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 − 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.0000 −0.880451
\(130\) −8.00000 −0.701646
\(131\) −22.0000 −1.92215 −0.961074 − 0.276289i \(-0.910895\pi\)
−0.961074 + 0.276289i \(0.910895\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 4.00000 0.344265
\(136\) −2.00000 −0.171499
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −8.00000 −0.681005
\(139\) −2.00000 −0.169638 −0.0848189 − 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −4.00000 −0.335673
\(143\) 2.00000 0.167248
\(144\) 1.00000 0.0833333
\(145\) 8.00000 0.664364
\(146\) 14.0000 1.15865
\(147\) −7.00000 −0.577350
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −11.0000 −0.898146
\(151\) 12.0000 0.976546 0.488273 − 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) −4.00000 −0.324443
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 2.00000 0.160128
\(157\) 20.0000 1.59617 0.798087 − 0.602542i \(-0.205846\pi\)
0.798087 + 0.602542i \(0.205846\pi\)
\(158\) −8.00000 −0.636446
\(159\) −6.00000 −0.475831
\(160\) −4.00000 −0.316228
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −8.00000 −0.624695
\(165\) 4.00000 0.311400
\(166\) −6.00000 −0.465690
\(167\) −16.0000 −1.23812 −0.619059 − 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −8.00000 −0.613572
\(171\) 4.00000 0.305888
\(172\) −10.0000 −0.762493
\(173\) 14.0000 1.06440 0.532200 − 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 4.00000 0.300658
\(178\) −6.00000 −0.449719
\(179\) 16.0000 1.19590 0.597948 − 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 4.00000 0.298142
\(181\) 4.00000 0.297318 0.148659 − 0.988889i \(-0.452504\pi\)
0.148659 + 0.988889i \(0.452504\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) −8.00000 −0.589768
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 2.00000 0.146254
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) −16.0000 −1.16076
\(191\) −4.00000 −0.289430 −0.144715 − 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 − 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −2.00000 −0.143592
\(195\) 8.00000 0.572892
\(196\) −7.00000 −0.500000
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 12.0000 0.850657 0.425329 − 0.905039i \(-0.360158\pi\)
0.425329 + 0.905039i \(0.360158\pi\)
\(200\) −11.0000 −0.777817
\(201\) 8.00000 0.564276
\(202\) 10.0000 0.703598
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −32.0000 −2.23498
\(206\) 12.0000 0.836080
\(207\) 8.00000 0.556038
\(208\) 2.00000 0.138675
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 10.0000 0.688428 0.344214 − 0.938891i \(-0.388145\pi\)
0.344214 + 0.938891i \(0.388145\pi\)
\(212\) −6.00000 −0.412082
\(213\) 4.00000 0.274075
\(214\) 10.0000 0.683586
\(215\) −40.0000 −2.72798
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) −14.0000 −0.946032
\(220\) 4.00000 0.269680
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 − 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 0 0
\(225\) 11.0000 0.733333
\(226\) 2.00000 0.133038
\(227\) 8.00000 0.530979 0.265489 − 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 4.00000 0.264906
\(229\) 2.00000 0.132164 0.0660819 − 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) −32.0000 −2.11002
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 6.00000 0.393073 0.196537 − 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) −2.00000 −0.130744
\(235\) −24.0000 −1.56559
\(236\) 4.00000 0.260378
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 4.00000 0.258199
\(241\) 18.0000 1.15948 0.579741 − 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) 1.00000 0.0640184
\(245\) −28.0000 −1.78885
\(246\) 8.00000 0.510061
\(247\) 8.00000 0.509028
\(248\) 2.00000 0.127000
\(249\) 6.00000 0.380235
\(250\) −24.0000 −1.51789
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −16.0000 −1.00393
\(255\) 8.00000 0.500979
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 − 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) 10.0000 0.622573
\(259\) 0 0
\(260\) 8.00000 0.496139
\(261\) 2.00000 0.123797
\(262\) 22.0000 1.35916
\(263\) −20.0000 −1.23325 −0.616626 − 0.787256i \(-0.711501\pi\)
−0.616626 + 0.787256i \(0.711501\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 8.00000 0.488678
\(269\) −20.0000 −1.21942 −0.609711 − 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) −4.00000 −0.243432
\(271\) 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
\(275\) 11.0000 0.663325
\(276\) 8.00000 0.481543
\(277\) −14.0000 −0.841178 −0.420589 − 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 2.00000 0.119952
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 − 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 6.00000 0.357295
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 4.00000 0.237356
\(285\) 16.0000 0.947758
\(286\) −2.00000 −0.118262
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) −8.00000 −0.469776
\(291\) 2.00000 0.117242
\(292\) −14.0000 −0.819288
\(293\) −2.00000 −0.116841 −0.0584206 − 0.998292i \(-0.518606\pi\)
−0.0584206 + 0.998292i \(0.518606\pi\)
\(294\) 7.00000 0.408248
\(295\) 16.0000 0.931556
\(296\) 0 0
\(297\) 1.00000 0.0580259
\(298\) 6.00000 0.347571
\(299\) 16.0000 0.925304
\(300\) 11.0000 0.635085
\(301\) 0 0
\(302\) −12.0000 −0.690522
\(303\) −10.0000 −0.574485
\(304\) 4.00000 0.229416
\(305\) 4.00000 0.229039
\(306\) −2.00000 −0.114332
\(307\) −2.00000 −0.114146 −0.0570730 − 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 8.00000 0.454369
\(311\) 4.00000 0.226819 0.113410 − 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) −2.00000 −0.113228
\(313\) 30.0000 1.69570 0.847850 − 0.530236i \(-0.177897\pi\)
0.847850 + 0.530236i \(0.177897\pi\)
\(314\) −20.0000 −1.12867
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 4.00000 0.224662 0.112331 − 0.993671i \(-0.464168\pi\)
0.112331 + 0.993671i \(0.464168\pi\)
\(318\) 6.00000 0.336463
\(319\) 2.00000 0.111979
\(320\) 4.00000 0.223607
\(321\) −10.0000 −0.558146
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 1.00000 0.0555556
\(325\) 22.0000 1.22034
\(326\) −4.00000 −0.221540
\(327\) −18.0000 −0.995402
\(328\) 8.00000 0.441726
\(329\) 0 0
\(330\) −4.00000 −0.220193
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 6.00000 0.329293
\(333\) 0 0
\(334\) 16.0000 0.875481
\(335\) 32.0000 1.74835
\(336\) 0 0
\(337\) 12.0000 0.653682 0.326841 − 0.945079i \(-0.394016\pi\)
0.326841 + 0.945079i \(0.394016\pi\)
\(338\) 9.00000 0.489535
\(339\) −2.00000 −0.108625
\(340\) 8.00000 0.433861
\(341\) −2.00000 −0.108306
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 10.0000 0.539164
\(345\) 32.0000 1.72282
\(346\) −14.0000 −0.752645
\(347\) 10.0000 0.536828 0.268414 − 0.963304i \(-0.413500\pi\)
0.268414 + 0.963304i \(0.413500\pi\)
\(348\) 2.00000 0.107211
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) −1.00000 −0.0533002
\(353\) −6.00000 −0.319348 −0.159674 − 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −4.00000 −0.212598
\(355\) 16.0000 0.849192
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −16.0000 −0.845626
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −4.00000 −0.210819
\(361\) −3.00000 −0.157895
\(362\) −4.00000 −0.210235
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) −56.0000 −2.93117
\(366\) −1.00000 −0.0522708
\(367\) 12.0000 0.626395 0.313197 − 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(368\) 8.00000 0.417029
\(369\) −8.00000 −0.416463
\(370\) 0 0
\(371\) 0 0
\(372\) −2.00000 −0.103695
\(373\) 26.0000 1.34623 0.673114 − 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) −2.00000 −0.103418
\(375\) 24.0000 1.23935
\(376\) 6.00000 0.309426
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 − 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 16.0000 0.820783
\(381\) 16.0000 0.819705
\(382\) 4.00000 0.204658
\(383\) −12.0000 −0.613171 −0.306586 − 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) −10.0000 −0.508329
\(388\) 2.00000 0.101535
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) −8.00000 −0.405096
\(391\) 16.0000 0.809155
\(392\) 7.00000 0.353553
\(393\) −22.0000 −1.10975
\(394\) 6.00000 0.302276
\(395\) 32.0000 1.61009
\(396\) 1.00000 0.0502519
\(397\) −16.0000 −0.803017 −0.401508 − 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(398\) −12.0000 −0.601506
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) −30.0000 −1.49813 −0.749064 − 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) −8.00000 −0.399004
\(403\) −4.00000 −0.199254
\(404\) −10.0000 −0.497519
\(405\) 4.00000 0.198762
\(406\) 0 0
\(407\) 0 0
\(408\) −2.00000 −0.0990148
\(409\) −28.0000 −1.38451 −0.692255 − 0.721653i \(-0.743383\pi\)
−0.692255 + 0.721653i \(0.743383\pi\)
\(410\) 32.0000 1.58037
\(411\) −6.00000 −0.295958
\(412\) −12.0000 −0.591198
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 24.0000 1.17811
\(416\) −2.00000 −0.0980581
\(417\) −2.00000 −0.0979404
\(418\) −4.00000 −0.195646
\(419\) −12.0000 −0.586238 −0.293119 − 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 12.0000 0.584844 0.292422 − 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) −10.0000 −0.486792
\(423\) −6.00000 −0.291730
\(424\) 6.00000 0.291386
\(425\) 22.0000 1.06716
\(426\) −4.00000 −0.193801
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) 2.00000 0.0965609
\(430\) 40.0000 1.92897
\(431\) −12.0000 −0.578020 −0.289010 − 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 1.00000 0.0481125
\(433\) 10.0000 0.480569 0.240285 − 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) −18.0000 −0.862044
\(437\) 32.0000 1.53077
\(438\) 14.0000 0.668946
\(439\) −8.00000 −0.381819 −0.190910 − 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −4.00000 −0.190693
\(441\) −7.00000 −0.333333
\(442\) −4.00000 −0.190261
\(443\) −20.0000 −0.950229 −0.475114 − 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) 24.0000 1.13771
\(446\) −6.00000 −0.284108
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 − 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −11.0000 −0.518545
\(451\) −8.00000 −0.376705
\(452\) −2.00000 −0.0940721
\(453\) 12.0000 0.563809
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −8.00000 −0.374224 −0.187112 − 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 2.00000 0.0933520
\(460\) 32.0000 1.49201
\(461\) 26.0000 1.21094 0.605470 − 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(462\) 0 0
\(463\) 36.0000 1.67306 0.836531 − 0.547920i \(-0.184580\pi\)
0.836531 + 0.547920i \(0.184580\pi\)
\(464\) 2.00000 0.0928477
\(465\) −8.00000 −0.370991
\(466\) −6.00000 −0.277945
\(467\) 28.0000 1.29569 0.647843 − 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 24.0000 1.10704
\(471\) 20.0000 0.921551
\(472\) −4.00000 −0.184115
\(473\) −10.0000 −0.459800
\(474\) −8.00000 −0.367452
\(475\) 44.0000 2.01886
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 20.0000 0.913823 0.456912 − 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) −4.00000 −0.182574
\(481\) 0 0
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 8.00000 0.363261
\(486\) −1.00000 −0.0453609
\(487\) 20.0000 0.906287 0.453143 − 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 4.00000 0.180886
\(490\) 28.0000 1.26491
\(491\) 42.0000 1.89543 0.947717 − 0.319113i \(-0.103385\pi\)
0.947717 + 0.319113i \(0.103385\pi\)
\(492\) −8.00000 −0.360668
\(493\) 4.00000 0.180151
\(494\) −8.00000 −0.359937
\(495\) 4.00000 0.179787
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) −12.0000 −0.537194 −0.268597 − 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 24.0000 1.07331
\(501\) −16.0000 −0.714827
\(502\) −12.0000 −0.535586
\(503\) 4.00000 0.178351 0.0891756 − 0.996016i \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) 0 0
\(505\) −40.0000 −1.77998
\(506\) −8.00000 −0.355643
\(507\) −9.00000 −0.399704
\(508\) 16.0000 0.709885
\(509\) 18.0000 0.797836 0.398918 − 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) −8.00000 −0.354246
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 0.176604
\(514\) 30.0000 1.32324
\(515\) −48.0000 −2.11513
\(516\) −10.0000 −0.440225
\(517\) −6.00000 −0.263880
\(518\) 0 0
\(519\) 14.0000 0.614532
\(520\) −8.00000 −0.350823
\(521\) 22.0000 0.963837 0.481919 − 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 2.00000 0.0874539 0.0437269 − 0.999044i \(-0.486077\pi\)
0.0437269 + 0.999044i \(0.486077\pi\)
\(524\) −22.0000 −0.961074
\(525\) 0 0
\(526\) 20.0000 0.872041
\(527\) −4.00000 −0.174243
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) 24.0000 1.04249
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) −16.0000 −0.693037
\(534\) −6.00000 −0.259645
\(535\) −40.0000 −1.72935
\(536\) −8.00000 −0.345547
\(537\) 16.0000 0.690451
\(538\) 20.0000 0.862261
\(539\) −7.00000 −0.301511
\(540\) 4.00000 0.172133
\(541\) −10.0000 −0.429934 −0.214967 − 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −8.00000 −0.343629
\(543\) 4.00000 0.171656
\(544\) −2.00000 −0.0857493
\(545\) −72.0000 −3.08414
\(546\) 0 0
\(547\) 38.0000 1.62476 0.812381 − 0.583127i \(-0.198171\pi\)
0.812381 + 0.583127i \(0.198171\pi\)
\(548\) −6.00000 −0.256307
\(549\) 1.00000 0.0426790
\(550\) −11.0000 −0.469042
\(551\) 8.00000 0.340811
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) 14.0000 0.594803
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 2.00000 0.0846668
\(559\) −20.0000 −0.845910
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 22.0000 0.928014
\(563\) −22.0000 −0.927189 −0.463595 − 0.886047i \(-0.653441\pi\)
−0.463595 + 0.886047i \(0.653441\pi\)
\(564\) −6.00000 −0.252646
\(565\) −8.00000 −0.336563
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −4.00000 −0.167689 −0.0838444 − 0.996479i \(-0.526720\pi\)
−0.0838444 + 0.996479i \(0.526720\pi\)
\(570\) −16.0000 −0.670166
\(571\) −16.0000 −0.669579 −0.334790 − 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 2.00000 0.0836242
\(573\) −4.00000 −0.167102
\(574\) 0 0
\(575\) 88.0000 3.66985
\(576\) 1.00000 0.0416667
\(577\) −2.00000 −0.0832611 −0.0416305 − 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 13.0000 0.540729
\(579\) −4.00000 −0.166234
\(580\) 8.00000 0.332182
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) −6.00000 −0.248495
\(584\) 14.0000 0.579324
\(585\) 8.00000 0.330759
\(586\) 2.00000 0.0826192
\(587\) −28.0000 −1.15568 −0.577842 − 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) −7.00000 −0.288675
\(589\) −8.00000 −0.329634
\(590\) −16.0000 −0.658710
\(591\) −6.00000 −0.246807
\(592\) 0 0
\(593\) 2.00000 0.0821302 0.0410651 − 0.999156i \(-0.486925\pi\)
0.0410651 + 0.999156i \(0.486925\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 12.0000 0.491127
\(598\) −16.0000 −0.654289
\(599\) −24.0000 −0.980613 −0.490307 − 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −11.0000 −0.449073
\(601\) 46.0000 1.87638 0.938190 − 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 12.0000 0.488273
\(605\) 4.00000 0.162623
\(606\) 10.0000 0.406222
\(607\) −32.0000 −1.29884 −0.649420 − 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) −12.0000 −0.485468
\(612\) 2.00000 0.0808452
\(613\) 6.00000 0.242338 0.121169 − 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) 2.00000 0.0807134
\(615\) −32.0000 −1.29036
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 − 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 12.0000 0.482711
\(619\) 4.00000 0.160774 0.0803868 − 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) −8.00000 −0.321288
\(621\) 8.00000 0.321029
\(622\) −4.00000 −0.160385
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 41.0000 1.64000
\(626\) −30.0000 −1.19904
\(627\) 4.00000 0.159745
\(628\) 20.0000 0.798087
\(629\) 0 0
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 − 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −8.00000 −0.318223
\(633\) 10.0000 0.397464
\(634\) −4.00000 −0.158860
\(635\) 64.0000 2.53976
\(636\) −6.00000 −0.237915
\(637\) −14.0000 −0.554700
\(638\) −2.00000 −0.0791808
\(639\) 4.00000 0.158238
\(640\) −4.00000 −0.158114
\(641\) −6.00000 −0.236986 −0.118493 − 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) 10.0000 0.394669
\(643\) −40.0000 −1.57745 −0.788723 − 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) −40.0000 −1.57500
\(646\) −8.00000 −0.314756
\(647\) 4.00000 0.157256 0.0786281 − 0.996904i \(-0.474946\pi\)
0.0786281 + 0.996904i \(0.474946\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 4.00000 0.157014
\(650\) −22.0000 −0.862911
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −38.0000 −1.48705 −0.743527 − 0.668705i \(-0.766849\pi\)
−0.743527 + 0.668705i \(0.766849\pi\)
\(654\) 18.0000 0.703856
\(655\) −88.0000 −3.43844
\(656\) −8.00000 −0.312348
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) −22.0000 −0.856998 −0.428499 − 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 4.00000 0.155700
\(661\) 8.00000 0.311164 0.155582 − 0.987823i \(-0.450275\pi\)
0.155582 + 0.987823i \(0.450275\pi\)
\(662\) −8.00000 −0.310929
\(663\) 4.00000 0.155347
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 16.0000 0.619522
\(668\) −16.0000 −0.619059
\(669\) 6.00000 0.231973
\(670\) −32.0000 −1.23627
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 − 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) −12.0000 −0.462223
\(675\) 11.0000 0.423390
\(676\) −9.00000 −0.346154
\(677\) 6.00000 0.230599 0.115299 − 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 2.00000 0.0768095
\(679\) 0 0
\(680\) −8.00000 −0.306786
\(681\) 8.00000 0.306561
\(682\) 2.00000 0.0765840
\(683\) 8.00000 0.306111 0.153056 − 0.988218i \(-0.451089\pi\)
0.153056 + 0.988218i \(0.451089\pi\)
\(684\) 4.00000 0.152944
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) 2.00000 0.0763048
\(688\) −10.0000 −0.381246
\(689\) −12.0000 −0.457164
\(690\) −32.0000 −1.21822
\(691\) −36.0000 −1.36950 −0.684752 − 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) 14.0000 0.532200
\(693\) 0 0
\(694\) −10.0000 −0.379595
\(695\) −8.00000 −0.303457
\(696\) −2.00000 −0.0758098
\(697\) −16.0000 −0.606043
\(698\) −10.0000 −0.378506
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 − 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 0 0
\(704\) 1.00000 0.0376889
\(705\) −24.0000 −0.903892
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 44.0000 1.65245 0.826227 − 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) −16.0000 −0.600469
\(711\) 8.00000 0.300023
\(712\) −6.00000 −0.224860
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 16.0000 0.597948
\(717\) 0 0
\(718\) 0 0
\(719\) 30.0000 1.11881 0.559406 − 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 4.00000 0.149071
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 18.0000 0.669427
\(724\) 4.00000 0.148659
\(725\) 22.0000 0.817059
\(726\) −1.00000 −0.0371135
\(727\) 28.0000 1.03846 0.519231 − 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 56.0000 2.07265
\(731\) −20.0000 −0.739727
\(732\) 1.00000 0.0369611
\(733\) −30.0000 −1.10808 −0.554038 − 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) −12.0000 −0.442928
\(735\) −28.0000 −1.03280
\(736\) −8.00000 −0.294884
\(737\) 8.00000 0.294684
\(738\) 8.00000 0.294484
\(739\) 42.0000 1.54499 0.772497 − 0.635018i \(-0.219007\pi\)
0.772497 + 0.635018i \(0.219007\pi\)
\(740\) 0 0
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 2.00000 0.0733236
\(745\) −24.0000 −0.879292
\(746\) −26.0000 −0.951928
\(747\) 6.00000 0.219529
\(748\) 2.00000 0.0731272
\(749\) 0 0
\(750\) −24.0000 −0.876356
\(751\) 12.0000 0.437886 0.218943 − 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) −6.00000 −0.218797
\(753\) 12.0000 0.437304
\(754\) −4.00000 −0.145671
\(755\) 48.0000 1.74690
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 − 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) −4.00000 −0.145287
\(759\) 8.00000 0.290382
\(760\) −16.0000 −0.580381
\(761\) −26.0000 −0.942499 −0.471250 − 0.882000i \(-0.656197\pi\)
−0.471250 + 0.882000i \(0.656197\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) −4.00000 −0.144715
\(765\) 8.00000 0.289241
\(766\) 12.0000 0.433578
\(767\) 8.00000 0.288863
\(768\) 1.00000 0.0360844
\(769\) −24.0000 −0.865462 −0.432731 − 0.901523i \(-0.642450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) −4.00000 −0.143963
\(773\) −32.0000 −1.15096 −0.575480 − 0.817816i \(-0.695185\pi\)
−0.575480 + 0.817816i \(0.695185\pi\)
\(774\) 10.0000 0.359443
\(775\) −22.0000 −0.790263
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) −32.0000 −1.14652
\(780\) 8.00000 0.286446
\(781\) 4.00000 0.143131
\(782\) −16.0000 −0.572159
\(783\) 2.00000 0.0714742
\(784\) −7.00000 −0.250000
\(785\) 80.0000 2.85532
\(786\) 22.0000 0.784714
\(787\) 2.00000 0.0712923 0.0356462 − 0.999364i \(-0.488651\pi\)
0.0356462 + 0.999364i \(0.488651\pi\)
\(788\) −6.00000 −0.213741
\(789\) −20.0000 −0.712019
\(790\) −32.0000 −1.13851
\(791\) 0 0
\(792\) −1.00000 −0.0355335
\(793\) 2.00000 0.0710221
\(794\) 16.0000 0.567819
\(795\) −24.0000 −0.851192
\(796\) 12.0000 0.425329
\(797\) −28.0000 −0.991811 −0.495905 − 0.868377i \(-0.665164\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) −11.0000 −0.388909
\(801\) 6.00000 0.212000
\(802\) 30.0000 1.05934
\(803\) −14.0000 −0.494049
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) −20.0000 −0.704033
\(808\) 10.0000 0.351799
\(809\) 36.0000 1.26569 0.632846 − 0.774277i \(-0.281886\pi\)
0.632846 + 0.774277i \(0.281886\pi\)
\(810\) −4.00000 −0.140546
\(811\) 38.0000 1.33436 0.667180 − 0.744896i \(-0.267501\pi\)
0.667180 + 0.744896i \(0.267501\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) 2.00000 0.0700140
\(817\) −40.0000 −1.39942
\(818\) 28.0000 0.978997
\(819\) 0 0
\(820\) −32.0000 −1.11749
\(821\) −18.0000 −0.628204 −0.314102 − 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 6.00000 0.209274
\(823\) −54.0000 −1.88232 −0.941161 − 0.337959i \(-0.890263\pi\)
−0.941161 + 0.337959i \(0.890263\pi\)
\(824\) 12.0000 0.418040
\(825\) 11.0000 0.382971
\(826\) 0 0
\(827\) −54.0000 −1.87776 −0.938882 − 0.344239i \(-0.888137\pi\)
−0.938882 + 0.344239i \(0.888137\pi\)
\(828\) 8.00000 0.278019
\(829\) 54.0000 1.87550 0.937749 − 0.347314i \(-0.112906\pi\)
0.937749 + 0.347314i \(0.112906\pi\)
\(830\) −24.0000 −0.833052
\(831\) −14.0000 −0.485655
\(832\) 2.00000 0.0693375
\(833\) −14.0000 −0.485071
\(834\) 2.00000 0.0692543
\(835\) −64.0000 −2.21481
\(836\) 4.00000 0.138343
\(837\) −2.00000 −0.0691301
\(838\) 12.0000 0.414533
\(839\) −2.00000 −0.0690477 −0.0345238 − 0.999404i \(-0.510991\pi\)
−0.0345238 + 0.999404i \(0.510991\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −12.0000 −0.413547
\(843\) −22.0000 −0.757720
\(844\) 10.0000 0.344214
\(845\) −36.0000 −1.23844
\(846\) 6.00000 0.206284
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −4.00000 −0.137280
\(850\) −22.0000 −0.754594
\(851\) 0 0
\(852\) 4.00000 0.137038
\(853\) 22.0000 0.753266 0.376633 − 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) 16.0000 0.547188
\(856\) 10.0000 0.341793
\(857\) 28.0000 0.956462 0.478231 − 0.878234i \(-0.341278\pi\)
0.478231 + 0.878234i \(0.341278\pi\)
\(858\) −2.00000 −0.0682789
\(859\) −44.0000 −1.50126 −0.750630 − 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) −40.0000 −1.36399
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) −2.00000 −0.0680808 −0.0340404 − 0.999420i \(-0.510837\pi\)
−0.0340404 + 0.999420i \(0.510837\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 56.0000 1.90406
\(866\) −10.0000 −0.339814
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) −8.00000 −0.271225
\(871\) 16.0000 0.542139
\(872\) 18.0000 0.609557
\(873\) 2.00000 0.0676897
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) −14.0000 −0.473016
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 8.00000 0.269987
\(879\) −2.00000 −0.0674583
\(880\) 4.00000 0.134840
\(881\) 54.0000 1.81931 0.909653 − 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 7.00000 0.235702
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 4.00000 0.134535
\(885\) 16.0000 0.537834
\(886\) 20.0000 0.671913
\(887\) 48.0000 1.61168 0.805841 − 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −24.0000 −0.804482
\(891\) 1.00000 0.0335013
\(892\) 6.00000 0.200895
\(893\) −24.0000 −0.803129
\(894\) 6.00000 0.200670
\(895\) 64.0000 2.13928
\(896\) 0 0
\(897\) 16.0000 0.534224
\(898\) −30.0000 −1.00111
\(899\) −4.00000 −0.133407
\(900\) 11.0000 0.366667
\(901\) −12.0000 −0.399778
\(902\) 8.00000 0.266371
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 16.0000 0.531858
\(906\) −12.0000 −0.398673
\(907\) −48.0000 −1.59381 −0.796907 − 0.604102i \(-0.793532\pi\)
−0.796907 + 0.604102i \(0.793532\pi\)
\(908\) 8.00000 0.265489
\(909\) −10.0000 −0.331679
\(910\) 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
\(913\) 6.00000 0.198571
\(914\) 8.00000 0.264616
\(915\) 4.00000 0.132236
\(916\) 2.00000 0.0660819
\(917\) 0 0
\(918\) −2.00000 −0.0660098
\(919\) −56.0000 −1.84727 −0.923635 − 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) −32.0000 −1.05501
\(921\) −2.00000 −0.0659022
\(922\) −26.0000 −0.856264
\(923\) 8.00000 0.263323
\(924\) 0 0
\(925\) 0 0
\(926\) −36.0000 −1.18303
\(927\) −12.0000 −0.394132
\(928\) −2.00000 −0.0656532
\(929\) 34.0000 1.11550 0.557752 − 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 8.00000 0.262330
\(931\) −28.0000 −0.917663
\(932\) 6.00000 0.196537
\(933\) 4.00000 0.130954
\(934\) −28.0000 −0.916188
\(935\) 8.00000 0.261628
\(936\) −2.00000 −0.0653720
\(937\) −14.0000 −0.457360 −0.228680 − 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) 0 0
\(939\) 30.0000 0.979013
\(940\) −24.0000 −0.782794
\(941\) 30.0000 0.977972 0.488986 − 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −20.0000 −0.651635
\(943\) −64.0000 −2.08413
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) 10.0000 0.325128
\(947\) −20.0000 −0.649913 −0.324956 − 0.945729i \(-0.605350\pi\)
−0.324956 + 0.945729i \(0.605350\pi\)
\(948\) 8.00000 0.259828
\(949\) −28.0000 −0.908918
\(950\) −44.0000 −1.42755
\(951\) 4.00000 0.129709
\(952\) 0 0
\(953\) 58.0000 1.87880 0.939402 − 0.342817i \(-0.111381\pi\)
0.939402 + 0.342817i \(0.111381\pi\)
\(954\) 6.00000 0.194257
\(955\) −16.0000 −0.517748
\(956\) 0 0
\(957\) 2.00000 0.0646508
\(958\) −20.0000 −0.646171
\(959\) 0 0
\(960\) 4.00000 0.129099
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) −10.0000 −0.322245
\(964\) 18.0000 0.579741
\(965\) −16.0000 −0.515058
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 − 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 8.00000 0.256997
\(970\) −8.00000 −0.256865
\(971\) 48.0000 1.54039 0.770197 − 0.637806i \(-0.220158\pi\)
0.770197 + 0.637806i \(0.220158\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −20.0000 −0.640841
\(975\) 22.0000 0.704564
\(976\) 1.00000 0.0320092
\(977\) −6.00000 −0.191957 −0.0959785 − 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) −4.00000 −0.127906
\(979\) 6.00000 0.191761
\(980\) −28.0000 −0.894427
\(981\) −18.0000 −0.574696
\(982\) −42.0000 −1.34027
\(983\) −36.0000 −1.14822 −0.574111 − 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 8.00000 0.255031
\(985\) −24.0000 −0.764704
\(986\) −4.00000 −0.127386
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) −80.0000 −2.54385
\(990\) −4.00000 −0.127128
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 2.00000 0.0635001
\(993\) 8.00000 0.253872
\(994\) 0 0
\(995\) 48.0000 1.52170
\(996\) 6.00000 0.190117
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 12.0000 0.379853
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4026.2.a.d.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.d.1.1 ✓ 1 1.1 even 1 trivial