Properties

Label 106.2.a.d.1.1
Level $106$
Weight $2$
Character 106.1
Self dual yes
Analytic conductor $0.846$
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] = [106,2,Mod(1,106)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(106, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("106.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 106 = 2 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 106.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: \(0.846414261426\)
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 \(\chi\) \(=\) 106.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{12} +5.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} -4.00000 q^{21} +3.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} +5.00000 q^{26} -5.00000 q^{27} -4.00000 q^{28} +9.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} -2.00000 q^{36} +5.00000 q^{37} -1.00000 q^{38} +5.00000 q^{39} +6.00000 q^{41} -4.00000 q^{42} -10.0000 q^{43} +3.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -5.00000 q^{50} -3.00000 q^{51} +5.00000 q^{52} -1.00000 q^{53} -5.00000 q^{54} -4.00000 q^{56} -1.00000 q^{57} +9.00000 q^{58} +6.00000 q^{59} +8.00000 q^{61} -4.00000 q^{62} +8.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} -3.00000 q^{68} +3.00000 q^{69} -3.00000 q^{71} -2.00000 q^{72} -4.00000 q^{73} +5.00000 q^{74} -5.00000 q^{75} -1.00000 q^{76} +5.00000 q^{78} -13.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +3.00000 q^{83} -4.00000 q^{84} -10.0000 q^{86} +9.00000 q^{87} +18.0000 q^{89} -20.0000 q^{91} +3.00000 q^{92} -4.00000 q^{93} +6.00000 q^{94} +1.00000 q^{96} -7.00000 q^{97} +9.00000 q^{98} +O(q^{100})\)

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 \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) 5.00000 0.980581
\(27\) −5.00000 −0.962250
\(28\) −4.00000 −0.755929
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) −1.00000 −0.162221
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −4.00000 −0.617213
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) −5.00000 −0.707107
\(51\) −3.00000 −0.420084
\(52\) 5.00000 0.693375
\(53\) −1.00000 −0.137361
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) −1.00000 −0.132453
\(58\) 9.00000 1.18176
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −4.00000 −0.508001
\(63\) 8.00000 1.00791
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −3.00000 −0.363803
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) −2.00000 −0.235702
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 5.00000 0.581238
\(75\) −5.00000 −0.577350
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) −13.0000 −1.46261 −0.731307 0.682048i \(-0.761089\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −10.0000 −1.07833
\(87\) 9.00000 0.964901
\(88\) 0 0
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 0 0
\(91\) −20.0000 −2.09657
\(92\) 3.00000 0.312772
\(93\) −4.00000 −0.414781
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) −3.00000 −0.297044
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −5.00000 −0.481125
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) −4.00000 −0.377964
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 0 0
\(116\) 9.00000 0.835629
\(117\) −10.0000 −0.924500
\(118\) 6.00000 0.552345
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 8.00000 0.724286
\(123\) 6.00000 0.541002
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 8.00000 0.712697
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 3.00000 0.255377
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −3.00000 −0.251754
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 9.00000 0.742307
\(148\) 5.00000 0.410997
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −5.00000 −0.408248
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −13.0000 −1.03422
\(159\) −1.00000 −0.0793052
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 1.00000 0.0785674
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 3.00000 0.232845
\(167\) −15.0000 −1.16073 −0.580367 0.814355i \(-0.697091\pi\)
−0.580367 + 0.814355i \(0.697091\pi\)
\(168\) −4.00000 −0.308607
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) −10.0000 −0.762493
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 9.00000 0.682288
\(175\) 20.0000 1.51186
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 18.0000 1.34916
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −20.0000 −1.48250
\(183\) 8.00000 0.591377
\(184\) 3.00000 0.221163
\(185\) 0 0
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 6.00000 0.437595
\(189\) 20.0000 1.45479
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 1.00000 0.0721688
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −28.0000 −1.98487 −0.992434 0.122782i \(-0.960818\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) −5.00000 −0.353553
\(201\) −4.00000 −0.282138
\(202\) −18.0000 −1.26648
\(203\) −36.0000 −2.52670
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 11.0000 0.766406
\(207\) −6.00000 −0.417029
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) −1.00000 −0.0686803
\(213\) −3.00000 −0.205557
\(214\) −18.0000 −1.23045
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 16.0000 1.08615
\(218\) −16.0000 −1.08366
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −15.0000 −1.00901
\(222\) 5.00000 0.335578
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) −4.00000 −0.267261
\(225\) 10.0000 0.666667
\(226\) −9.00000 −0.598671
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −10.0000 −0.653720
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) −13.0000 −0.844441
\(238\) 12.0000 0.777844
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) −11.0000 −0.707107
\(243\) 16.0000 1.02640
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −5.00000 −0.318142
\(248\) −4.00000 −0.254000
\(249\) 3.00000 0.190117
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 8.00000 0.503953
\(253\) 0 0
\(254\) −7.00000 −0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) −10.0000 −0.622573
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) −18.0000 −1.11417
\(262\) 6.00000 0.370681
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 0.245256
\(267\) 18.0000 1.10158
\(268\) −4.00000 −0.244339
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 0 0
\(271\) 26.0000 1.57939 0.789694 0.613501i \(-0.210239\pi\)
0.789694 + 0.613501i \(0.210239\pi\)
\(272\) −3.00000 −0.181902
\(273\) −20.0000 −1.21046
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 3.00000 0.180579
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 20.0000 1.19952
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 6.00000 0.357295
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) −3.00000 −0.178017
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) −2.00000 −0.117851
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) −4.00000 −0.234082
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 9.00000 0.524891
\(295\) 0 0
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) 3.00000 0.173785
\(299\) 15.0000 0.867472
\(300\) −5.00000 −0.288675
\(301\) 40.0000 2.30556
\(302\) 17.0000 0.978240
\(303\) −18.0000 −1.03407
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 5.00000 0.283069
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −13.0000 −0.731307
\(317\) 27.0000 1.51647 0.758236 0.651981i \(-0.226062\pi\)
0.758236 + 0.651981i \(0.226062\pi\)
\(318\) −1.00000 −0.0560772
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −12.0000 −0.668734
\(323\) 3.00000 0.166924
\(324\) 1.00000 0.0555556
\(325\) −25.0000 −1.38675
\(326\) 2.00000 0.110770
\(327\) −16.0000 −0.884802
\(328\) 6.00000 0.331295
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 3.00000 0.164646
\(333\) −10.0000 −0.547997
\(334\) −15.0000 −0.820763
\(335\) 0 0
\(336\) −4.00000 −0.218218
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 12.0000 0.652714
\(339\) −9.00000 −0.488813
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) −8.00000 −0.431959
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 9.00000 0.482451
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 20.0000 1.06904
\(351\) −25.0000 −1.33440
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) 12.0000 0.635107
\(358\) 15.0000 0.792775
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 14.0000 0.735824
\(363\) −11.0000 −0.577350
\(364\) −20.0000 −1.04828
\(365\) 0 0
\(366\) 8.00000 0.418167
\(367\) 14.0000 0.730794 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(368\) 3.00000 0.156386
\(369\) −12.0000 −0.624695
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) −4.00000 −0.207390
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 45.0000 2.31762
\(378\) 20.0000 1.02869
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) −7.00000 −0.358621
\(382\) 15.0000 0.767467
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 20.0000 1.01666
\(388\) −7.00000 −0.355371
\(389\) −36.0000 −1.82527 −0.912636 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 9.00000 0.454569
\(393\) 6.00000 0.302660
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −28.0000 −1.40351
\(399\) 4.00000 0.200250
\(400\) −5.00000 −0.250000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) −4.00000 −0.199502
\(403\) −20.0000 −0.996271
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) −36.0000 −1.78665
\(407\) 0 0
\(408\) −3.00000 −0.148522
\(409\) 11.0000 0.543915 0.271957 0.962309i \(-0.412329\pi\)
0.271957 + 0.962309i \(0.412329\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 11.0000 0.541931
\(413\) −24.0000 −1.18096
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) 5.00000 0.245145
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) −10.0000 −0.486792
\(423\) −12.0000 −0.583460
\(424\) −1.00000 −0.0485643
\(425\) 15.0000 0.727607
\(426\) −3.00000 −0.145350
\(427\) −32.0000 −1.54859
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −5.00000 −0.240563
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 16.0000 0.768025
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −3.00000 −0.143509
\(438\) −4.00000 −0.191127
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −18.0000 −0.857143
\(442\) −15.0000 −0.713477
\(443\) 3.00000 0.142534 0.0712672 0.997457i \(-0.477296\pi\)
0.0712672 + 0.997457i \(0.477296\pi\)
\(444\) 5.00000 0.237289
\(445\) 0 0
\(446\) 26.0000 1.23114
\(447\) 3.00000 0.141895
\(448\) −4.00000 −0.188982
\(449\) −27.0000 −1.27421 −0.637104 0.770778i \(-0.719868\pi\)
−0.637104 + 0.770778i \(0.719868\pi\)
\(450\) 10.0000 0.471405
\(451\) 0 0
\(452\) −9.00000 −0.423324
\(453\) 17.0000 0.798730
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −1.00000 −0.0468293
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 5.00000 0.233635
\(459\) 15.0000 0.700140
\(460\) 0 0
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) 0 0
\(463\) 29.0000 1.34774 0.673872 0.738848i \(-0.264630\pi\)
0.673872 + 0.738848i \(0.264630\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) −24.0000 −1.11178
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −10.0000 −0.462250
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) −4.00000 −0.184310
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) −13.0000 −0.597110
\(475\) 5.00000 0.229416
\(476\) 12.0000 0.550019
\(477\) 2.00000 0.0915737
\(478\) 24.0000 1.09773
\(479\) −9.00000 −0.411220 −0.205610 0.978634i \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 0 0
\(481\) 25.0000 1.13990
\(482\) 5.00000 0.227744
\(483\) −12.0000 −0.546019
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 8.00000 0.362143
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) 39.0000 1.76005 0.880023 0.474932i \(-0.157527\pi\)
0.880023 + 0.474932i \(0.157527\pi\)
\(492\) 6.00000 0.270501
\(493\) −27.0000 −1.21602
\(494\) −5.00000 −0.224961
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 12.0000 0.538274
\(498\) 3.00000 0.134433
\(499\) 5.00000 0.223831 0.111915 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) 0 0
\(501\) −15.0000 −0.670151
\(502\) 12.0000 0.535586
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 8.00000 0.356348
\(505\) 0 0
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −7.00000 −0.310575
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) 16.0000 0.707798
\(512\) 1.00000 0.0441942
\(513\) 5.00000 0.220755
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) −10.0000 −0.440225
\(517\) 0 0
\(518\) −20.0000 −0.878750
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) −18.0000 −0.787839
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 6.00000 0.262111
\(525\) 20.0000 0.872872
\(526\) 12.0000 0.523225
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 4.00000 0.173422
\(533\) 30.0000 1.29944
\(534\) 18.0000 0.778936
\(535\) 0 0
\(536\) −4.00000 −0.172774
\(537\) 15.0000 0.647298
\(538\) 9.00000 0.388018
\(539\) 0 0
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 26.0000 1.11680
\(543\) 14.0000 0.600798
\(544\) −3.00000 −0.128624
\(545\) 0 0
\(546\) −20.0000 −0.855921
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 12.0000 0.512615
\(549\) −16.0000 −0.682863
\(550\) 0 0
\(551\) −9.00000 −0.383413
\(552\) 3.00000 0.127688
\(553\) 52.0000 2.21126
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 20.0000 0.848189
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 8.00000 0.338667
\(559\) −50.0000 −2.11477
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000 0.379642
\(563\) 27.0000 1.13791 0.568957 0.822367i \(-0.307347\pi\)
0.568957 + 0.822367i \(0.307347\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) −13.0000 −0.546431
\(567\) −4.00000 −0.167984
\(568\) −3.00000 −0.125877
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 15.0000 0.626634
\(574\) −24.0000 −1.00174
\(575\) −15.0000 −0.625543
\(576\) −2.00000 −0.0833333
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) −8.00000 −0.332756
\(579\) −16.0000 −0.664937
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) −7.00000 −0.290159
\(583\) 0 0
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 9.00000 0.371154
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) 5.00000 0.205499
\(593\) −15.0000 −0.615976 −0.307988 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) −28.0000 −1.14596
\(598\) 15.0000 0.613396
\(599\) −6.00000 −0.245153 −0.122577 0.992459i \(-0.539116\pi\)
−0.122577 + 0.992459i \(0.539116\pi\)
\(600\) −5.00000 −0.204124
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 40.0000 1.63028
\(603\) 8.00000 0.325785
\(604\) 17.0000 0.691720
\(605\) 0 0
\(606\) −18.0000 −0.731200
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −36.0000 −1.45879
\(610\) 0 0
\(611\) 30.0000 1.21367
\(612\) 6.00000 0.242536
\(613\) 32.0000 1.29247 0.646234 0.763139i \(-0.276343\pi\)
0.646234 + 0.763139i \(0.276343\pi\)
\(614\) −16.0000 −0.645707
\(615\) 0 0
\(616\) 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
\(619\) −16.0000 −0.643094 −0.321547 0.946894i \(-0.604203\pi\)
−0.321547 + 0.946894i \(0.604203\pi\)
\(620\) 0 0
\(621\) −15.0000 −0.601929
\(622\) 0 0
\(623\) −72.0000 −2.88462
\(624\) 5.00000 0.200160
\(625\) 25.0000 1.00000
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) −13.0000 −0.517112
\(633\) −10.0000 −0.397464
\(634\) 27.0000 1.07231
\(635\) 0 0
\(636\) −1.00000 −0.0396526
\(637\) 45.0000 1.78296
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −18.0000 −0.710403
\(643\) −40.0000 −1.57745 −0.788723 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) −12.0000 −0.472866
\(645\) 0 0
\(646\) 3.00000 0.118033
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −25.0000 −0.980581
\(651\) 16.0000 0.627089
\(652\) 2.00000 0.0783260
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −16.0000 −0.625650
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 8.00000 0.312110
\(658\) −24.0000 −0.935617
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −25.0000 −0.972387 −0.486194 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) −4.00000 −0.155464
\(663\) −15.0000 −0.582552
\(664\) 3.00000 0.116423
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 27.0000 1.04544
\(668\) −15.0000 −0.580367
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) 0 0
\(672\) −4.00000 −0.154303
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 26.0000 1.00148
\(675\) 25.0000 0.962250
\(676\) 12.0000 0.461538
\(677\) −24.0000 −0.922395 −0.461197 0.887298i \(-0.652580\pi\)
−0.461197 + 0.887298i \(0.652580\pi\)
\(678\) −9.00000 −0.345643
\(679\) 28.0000 1.07454
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) −8.00000 −0.305441
\(687\) 5.00000 0.190762
\(688\) −10.0000 −0.381246
\(689\) −5.00000 −0.190485
\(690\) 0 0
\(691\) −19.0000 −0.722794 −0.361397 0.932412i \(-0.617700\pi\)
−0.361397 + 0.932412i \(0.617700\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −6.00000 −0.227757
\(695\) 0 0
\(696\) 9.00000 0.341144
\(697\) −18.0000 −0.681799
\(698\) 8.00000 0.302804
\(699\) −24.0000 −0.907763
\(700\) 20.0000 0.755929
\(701\) −36.0000 −1.35970 −0.679851 0.733351i \(-0.737955\pi\)
−0.679851 + 0.733351i \(0.737955\pi\)
\(702\) −25.0000 −0.943564
\(703\) −5.00000 −0.188579
\(704\) 0 0
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) 72.0000 2.70784
\(708\) 6.00000 0.225494
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) 26.0000 0.975076
\(712\) 18.0000 0.674579
\(713\) −12.0000 −0.449404
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) 15.0000 0.560576
\(717\) 24.0000 0.896296
\(718\) −3.00000 −0.111959
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −44.0000 −1.63865
\(722\) −18.0000 −0.669891
\(723\) 5.00000 0.185952
\(724\) 14.0000 0.520306
\(725\) −45.0000 −1.67126
\(726\) −11.0000 −0.408248
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) −20.0000 −0.741249
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 30.0000 1.10959
\(732\) 8.00000 0.295689
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 14.0000 0.516749
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) 0 0
\(738\) −12.0000 −0.441726
\(739\) 11.0000 0.404642 0.202321 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 0 0
\(741\) −5.00000 −0.183680
\(742\) 4.00000 0.146845
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) −4.00000 −0.146647
\(745\) 0 0
\(746\) −10.0000 −0.366126
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) 72.0000 2.63082
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 6.00000 0.218797
\(753\) 12.0000 0.437304
\(754\) 45.0000 1.63880
\(755\) 0 0
\(756\) 20.0000 0.727393
\(757\) −19.0000 −0.690567 −0.345283 0.938498i \(-0.612217\pi\)
−0.345283 + 0.938498i \(0.612217\pi\)
\(758\) 23.0000 0.835398
\(759\) 0 0
\(760\) 0 0
\(761\) −12.0000 −0.435000 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(762\) −7.00000 −0.253583
\(763\) 64.0000 2.31696
\(764\) 15.0000 0.542681
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 30.0000 1.08324
\(768\) 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
\(771\) −12.0000 −0.432169
\(772\) −16.0000 −0.575853
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 20.0000 0.718885
\(775\) 20.0000 0.718421
\(776\) −7.00000 −0.251285
\(777\) −20.0000 −0.717496
\(778\) −36.0000 −1.29066
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) 0 0
\(782\) −9.00000 −0.321839
\(783\) −45.0000 −1.60817
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) 6.00000 0.214013
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) −18.0000 −0.641223
\(789\) 12.0000 0.427211
\(790\) 0 0
\(791\) 36.0000 1.28001
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) −28.0000 −0.992434
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 4.00000 0.141598
\(799\) −18.0000 −0.636794
\(800\) −5.00000 −0.176777
\(801\) −36.0000 −1.27200
\(802\) 0 0
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −20.0000 −0.704470
\(807\) 9.00000 0.316815
\(808\) −18.0000 −0.633238
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) −36.0000 −1.26335
\(813\) 26.0000 0.911860
\(814\) 0 0
\(815\) 0 0
\(816\) −3.00000 −0.105021
\(817\) 10.0000 0.349856
\(818\) 11.0000 0.384606
\(819\) 40.0000 1.39771
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) 12.0000 0.418548
\(823\) 2.00000 0.0697156 0.0348578 0.999392i \(-0.488902\pi\)
0.0348578 + 0.999392i \(0.488902\pi\)
\(824\) 11.0000 0.383203
\(825\) 0 0
\(826\) −24.0000 −0.835067
\(827\) 3.00000 0.104320 0.0521601 0.998639i \(-0.483389\pi\)
0.0521601 + 0.998639i \(0.483389\pi\)
\(828\) −6.00000 −0.208514
\(829\) 2.00000 0.0694629 0.0347314 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 0 0
\(831\) 8.00000 0.277517
\(832\) 5.00000 0.173344
\(833\) −27.0000 −0.935495
\(834\) 20.0000 0.692543
\(835\) 0 0
\(836\) 0 0
\(837\) 20.0000 0.691301
\(838\) 12.0000 0.414533
\(839\) −6.00000 −0.207143 −0.103572 0.994622i \(-0.533027\pi\)
−0.103572 + 0.994622i \(0.533027\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 14.0000 0.482472
\(843\) 9.00000 0.309976
\(844\) −10.0000 −0.344214
\(845\) 0 0
\(846\) −12.0000 −0.412568
\(847\) 44.0000 1.51186
\(848\) −1.00000 −0.0343401
\(849\) −13.0000 −0.446159
\(850\) 15.0000 0.514496
\(851\) 15.0000 0.514193
\(852\) −3.00000 −0.102778
\(853\) −40.0000 −1.36957 −0.684787 0.728743i \(-0.740105\pi\)
−0.684787 + 0.728743i \(0.740105\pi\)
\(854\) −32.0000 −1.09502
\(855\) 0 0
\(856\) −18.0000 −0.615227
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −34.0000 −1.16007 −0.580033 0.814593i \(-0.696960\pi\)
−0.580033 + 0.814593i \(0.696960\pi\)
\(860\) 0 0
\(861\) −24.0000 −0.817918
\(862\) 12.0000 0.408722
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) −5.00000 −0.170103
\(865\) 0 0
\(866\) −7.00000 −0.237870
\(867\) −8.00000 −0.271694
\(868\) 16.0000 0.543075
\(869\) 0 0
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) −16.0000 −0.541828
\(873\) 14.0000 0.473828
\(874\) −3.00000 −0.101477
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) −10.0000 −0.337484
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −48.0000 −1.61716 −0.808581 0.588386i \(-0.799764\pi\)
−0.808581 + 0.588386i \(0.799764\pi\)
\(882\) −18.0000 −0.606092
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −15.0000 −0.504505
\(885\) 0 0
\(886\) 3.00000 0.100787
\(887\) −51.0000 −1.71241 −0.856206 0.516634i \(-0.827185\pi\)
−0.856206 + 0.516634i \(0.827185\pi\)
\(888\) 5.00000 0.167789
\(889\) 28.0000 0.939090
\(890\) 0 0
\(891\) 0 0
\(892\) 26.0000 0.870544
\(893\) −6.00000 −0.200782
\(894\) 3.00000 0.100335
\(895\) 0 0
\(896\) −4.00000 −0.133631
\(897\) 15.0000 0.500835
\(898\) −27.0000 −0.901002
\(899\) −36.0000 −1.20067
\(900\) 10.0000 0.333333
\(901\) 3.00000 0.0999445
\(902\) 0 0
\(903\) 40.0000 1.33112
\(904\) −9.00000 −0.299336
\(905\) 0 0
\(906\) 17.0000 0.564787
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) −18.0000 −0.597351
\(909\) 36.0000 1.19404
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) −10.0000 −0.330771
\(915\) 0 0
\(916\) 5.00000 0.165205
\(917\) −24.0000 −0.792550
\(918\) 15.0000 0.495074
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) 0 0
\(921\) −16.0000 −0.527218
\(922\) 15.0000 0.493999
\(923\) −15.0000 −0.493731
\(924\) 0 0
\(925\) −25.0000 −0.821995
\(926\) 29.0000 0.952999
\(927\) −22.0000 −0.722575
\(928\) 9.00000 0.295439
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) −9.00000 −0.294963
\(932\) −24.0000 −0.786146
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −10.0000 −0.326860
\(937\) 17.0000 0.555366 0.277683 0.960673i \(-0.410434\pi\)
0.277683 + 0.960673i \(0.410434\pi\)
\(938\) 16.0000 0.522419
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −4.00000 −0.130327
\(943\) 18.0000 0.586161
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) −13.0000 −0.422220
\(949\) −20.0000 −0.649227
\(950\) 5.00000 0.162221
\(951\) 27.0000 0.875535
\(952\) 12.0000 0.388922
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 2.00000 0.0647524
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −9.00000 −0.290777
\(959\) −48.0000 −1.55000
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 25.0000 0.806032
\(963\) 36.0000 1.16008
\(964\) 5.00000 0.161039
\(965\) 0 0
\(966\) −12.0000 −0.386094
\(967\) −28.0000 −0.900419 −0.450210 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) −11.0000 −0.353553
\(969\) 3.00000 0.0963739
\(970\) 0 0
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 16.0000 0.513200
\(973\) −80.0000 −2.56468
\(974\) −28.0000 −0.897178
\(975\) −25.0000 −0.800641
\(976\) 8.00000 0.256074
\(977\) 60.0000 1.91957 0.959785 0.280736i \(-0.0905785\pi\)
0.959785 + 0.280736i \(0.0905785\pi\)
\(978\) 2.00000 0.0639529
\(979\) 0 0
\(980\) 0 0
\(981\) 32.0000 1.02168
\(982\) 39.0000 1.24454
\(983\) 6.00000 0.191370 0.0956851 0.995412i \(-0.469496\pi\)
0.0956851 + 0.995412i \(0.469496\pi\)
\(984\) 6.00000 0.191273
\(985\) 0 0
\(986\) −27.0000 −0.859855
\(987\) −24.0000 −0.763928
\(988\) −5.00000 −0.159071
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) 26.0000 0.825917 0.412959 0.910750i \(-0.364495\pi\)
0.412959 + 0.910750i \(0.364495\pi\)
\(992\) −4.00000 −0.127000
\(993\) −4.00000 −0.126936
\(994\) 12.0000 0.380617
\(995\) 0 0
\(996\) 3.00000 0.0950586
\(997\) −37.0000 −1.17180 −0.585901 0.810383i \(-0.699259\pi\)
−0.585901 + 0.810383i \(0.699259\pi\)
\(998\) 5.00000 0.158272
\(999\) −25.0000 −0.790965
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 106.2.a.d.1.1 1
3.2 odd 2 954.2.a.c.1.1 1
4.3 odd 2 848.2.a.c.1.1 1
5.2 odd 4 2650.2.b.g.849.2 2
5.3 odd 4 2650.2.b.g.849.1 2
5.4 even 2 2650.2.a.b.1.1 1
7.6 odd 2 5194.2.a.n.1.1 1
8.3 odd 2 3392.2.a.k.1.1 1
8.5 even 2 3392.2.a.g.1.1 1
12.11 even 2 7632.2.a.k.1.1 1
53.52 even 2 5618.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
106.2.a.d.1.1 1 1.1 even 1 trivial
848.2.a.c.1.1 1 4.3 odd 2
954.2.a.c.1.1 1 3.2 odd 2
2650.2.a.b.1.1 1 5.4 even 2
2650.2.b.g.849.1 2 5.3 odd 4
2650.2.b.g.849.2 2 5.2 odd 4
3392.2.a.g.1.1 1 8.5 even 2
3392.2.a.k.1.1 1 8.3 odd 2
5194.2.a.n.1.1 1 7.6 odd 2
5618.2.a.a.1.1 1 53.52 even 2
7632.2.a.k.1.1 1 12.11 even 2