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Properties

Label 366.2.a.f.1.1
Level $366$
Weight $2$
Character 366.1
Self dual yes
Analytic conductor $2.923$
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] = [366,2,Mod(1,366)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(366, 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("366.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 366 = 2 \cdot 3 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 366.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: \(2.92252471398\)
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 \(\chi\) \(=\) 366.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.00000 q^{17} +1.00000 q^{18} +1.00000 q^{20} -2.00000 q^{21} +2.00000 q^{22} +9.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} -10.0000 q^{29} +1.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{33} -7.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} +4.00000 q^{39} +1.00000 q^{40} +12.0000 q^{41} -2.00000 q^{42} -1.00000 q^{43} +2.00000 q^{44} +1.00000 q^{45} +9.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -4.00000 q^{50} -7.00000 q^{51} +4.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{55} -2.00000 q^{56} -10.0000 q^{58} +1.00000 q^{60} +1.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +2.00000 q^{66} -12.0000 q^{67} -7.00000 q^{68} +9.00000 q^{69} -2.00000 q^{70} -3.00000 q^{71} +1.00000 q^{72} -1.00000 q^{73} -7.00000 q^{74} -4.00000 q^{75} -4.00000 q^{77} +4.00000 q^{78} +10.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{82} -1.00000 q^{83} -2.00000 q^{84} -7.00000 q^{85} -1.00000 q^{86} -10.0000 q^{87} +2.00000 q^{88} +5.00000 q^{89} +1.00000 q^{90} -8.00000 q^{91} +9.00000 q^{92} -8.00000 q^{93} +8.00000 q^{94} +1.00000 q^{96} -17.0000 q^{97} -3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.00000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 2.00000 0.603023 0.301511 − 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000 0.288675
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −7.00000 −1.69775 −0.848875 − 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 1.00000 0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) 2.00000 0.426401
\(23\) 9.00000 1.87663 0.938315 − 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) −2.00000 −0.377964
\(29\) −10.0000 −1.85695 −0.928477 − 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 1.00000 0.182574
\(31\) −8.00000 −1.43684 −0.718421 − 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.00000 0.348155
\(34\) −7.00000 −1.20049
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) −7.00000 −1.15079 −0.575396 − 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 1.00000 0.158114
\(41\) 12.0000 1.87409 0.937043 − 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −2.00000 −0.308607
\(43\) −1.00000 −0.152499 −0.0762493 − 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 2.00000 0.301511
\(45\) 1.00000 0.149071
\(46\) 9.00000 1.32698
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −4.00000 −0.565685
\(51\) −7.00000 −0.980196
\(52\) 4.00000 0.554700
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.00000 0.269680
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.00000 0.129099
\(61\) 1.00000 0.128037
\(62\) −8.00000 −1.01600
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 2.00000 0.246183
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −7.00000 −0.848875
\(69\) 9.00000 1.08347
\(70\) −2.00000 −0.239046
\(71\) −3.00000 −0.356034 −0.178017 − 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 1.00000 0.117851
\(73\) −1.00000 −0.117041 −0.0585206 − 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −7.00000 −0.813733
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 4.00000 0.452911
\(79\) 10.0000 1.12509 0.562544 − 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 12.0000 1.32518
\(83\) −1.00000 −0.109764 −0.0548821 − 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) −2.00000 −0.218218
\(85\) −7.00000 −0.759257
\(86\) −1.00000 −0.107833
\(87\) −10.0000 −1.07211
\(88\) 2.00000 0.213201
\(89\) 5.00000 0.529999 0.264999 − 0.964249i \(-0.414628\pi\)
0.264999 + 0.964249i \(0.414628\pi\)
\(90\) 1.00000 0.105409
\(91\) −8.00000 −0.838628
\(92\) 9.00000 0.938315
\(93\) −8.00000 −0.829561
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −17.0000 −1.72609 −0.863044 − 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) −3.00000 −0.303046
\(99\) 2.00000 0.201008
\(100\) −4.00000 −0.400000
\(101\) 12.0000 1.19404 0.597022 − 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −7.00000 −0.693103
\(103\) −1.00000 −0.0985329 −0.0492665 − 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 4.00000 0.392232
\(105\) −2.00000 −0.195180
\(106\) −6.00000 −0.582772
\(107\) 13.0000 1.25676 0.628379 − 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) 1.00000 0.0962250
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 2.00000 0.190693
\(111\) −7.00000 −0.664411
\(112\) −2.00000 −0.188982
\(113\) 4.00000 0.376288 0.188144 − 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) −10.0000 −0.928477
\(117\) 4.00000 0.369800
\(118\) 0 0
\(119\) 14.0000 1.28338
\(120\) 1.00000 0.0912871
\(121\) −7.00000 −0.636364
\(122\) 1.00000 0.0905357
\(123\) 12.0000 1.08200
\(124\) −8.00000 −0.718421
\(125\) −9.00000 −0.804984
\(126\) −2.00000 −0.178174
\(127\) 13.0000 1.15356 0.576782 − 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 4.00000 0.350823
\(131\) −3.00000 −0.262111 −0.131056 − 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 2.00000 0.174078
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 1.00000 0.0860663
\(136\) −7.00000 −0.600245
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 9.00000 0.766131
\(139\) 5.00000 0.424094 0.212047 − 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) −2.00000 −0.169031
\(141\) 8.00000 0.673722
\(142\) −3.00000 −0.251754
\(143\) 8.00000 0.668994
\(144\) 1.00000 0.0833333
\(145\) −10.0000 −0.830455
\(146\) −1.00000 −0.0827606
\(147\) −3.00000 −0.247436
\(148\) −7.00000 −0.575396
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) −4.00000 −0.326599
\(151\) 22.0000 1.79033 0.895167 − 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) 0 0
\(153\) −7.00000 −0.565916
\(154\) −4.00000 −0.322329
\(155\) −8.00000 −0.642575
\(156\) 4.00000 0.320256
\(157\) 18.0000 1.43656 0.718278 − 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 10.0000 0.795557
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) −18.0000 −1.41860
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 12.0000 0.937043
\(165\) 2.00000 0.155700
\(166\) −1.00000 −0.0776151
\(167\) −2.00000 −0.154765 −0.0773823 − 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) −2.00000 −0.154303
\(169\) 3.00000 0.230769
\(170\) −7.00000 −0.536875
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 14.0000 1.06440 0.532200 − 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) −10.0000 −0.758098
\(175\) 8.00000 0.604743
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) 5.00000 0.374766
\(179\) 15.0000 1.12115 0.560576 − 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 1.00000 0.0745356
\(181\) 7.00000 0.520306 0.260153 − 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) −8.00000 −0.592999
\(183\) 1.00000 0.0739221
\(184\) 9.00000 0.663489
\(185\) −7.00000 −0.514650
\(186\) −8.00000 −0.586588
\(187\) −14.0000 −1.02378
\(188\) 8.00000 0.583460
\(189\) −2.00000 −0.145479
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 − 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000 0.0721688
\(193\) 4.00000 0.287926 0.143963 − 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) −17.0000 −1.22053
\(195\) 4.00000 0.286446
\(196\) −3.00000 −0.214286
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 2.00000 0.142134
\(199\) 5.00000 0.354441 0.177220 − 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) −4.00000 −0.282843
\(201\) −12.0000 −0.846415
\(202\) 12.0000 0.844317
\(203\) 20.0000 1.40372
\(204\) −7.00000 −0.490098
\(205\) 12.0000 0.838116
\(206\) −1.00000 −0.0696733
\(207\) 9.00000 0.625543
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) −2.00000 −0.138013
\(211\) 12.0000 0.826114 0.413057 − 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −6.00000 −0.412082
\(213\) −3.00000 −0.205557
\(214\) 13.0000 0.888662
\(215\) −1.00000 −0.0681994
\(216\) 1.00000 0.0680414
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) −1.00000 −0.0675737
\(220\) 2.00000 0.134840
\(221\) −28.0000 −1.88348
\(222\) −7.00000 −0.469809
\(223\) −6.00000 −0.401790 −0.200895 − 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) −2.00000 −0.133631
\(225\) −4.00000 −0.266667
\(226\) 4.00000 0.266076
\(227\) 18.0000 1.19470 0.597351 − 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 9.00000 0.593442
\(231\) −4.00000 −0.263181
\(232\) −10.0000 −0.656532
\(233\) −26.0000 −1.70332 −0.851658 − 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.00000 0.261488
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 10.0000 0.649570
\(238\) 14.0000 0.907485
\(239\) −10.0000 −0.646846 −0.323423 − 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) 1.00000 0.0645497
\(241\) 17.0000 1.09507 0.547533 − 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −7.00000 −0.449977
\(243\) 1.00000 0.0641500
\(244\) 1.00000 0.0640184
\(245\) −3.00000 −0.191663
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) −8.00000 −0.508001
\(249\) −1.00000 −0.0633724
\(250\) −9.00000 −0.569210
\(251\) −18.0000 −1.13615 −0.568075 − 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) −2.00000 −0.125988
\(253\) 18.0000 1.13165
\(254\) 13.0000 0.815693
\(255\) −7.00000 −0.438357
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 14.0000 0.869918
\(260\) 4.00000 0.248069
\(261\) −10.0000 −0.618984
\(262\) −3.00000 −0.185341
\(263\) 4.00000 0.246651 0.123325 − 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) 2.00000 0.123091
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 5.00000 0.305995
\(268\) −12.0000 −0.733017
\(269\) 10.0000 0.609711 0.304855 − 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 1.00000 0.0608581
\(271\) 27.0000 1.64013 0.820067 − 0.572268i \(-0.193936\pi\)
0.820067 + 0.572268i \(0.193936\pi\)
\(272\) −7.00000 −0.424437
\(273\) −8.00000 −0.484182
\(274\) −12.0000 −0.724947
\(275\) −8.00000 −0.482418
\(276\) 9.00000 0.541736
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 5.00000 0.299880
\(279\) −8.00000 −0.478947
\(280\) −2.00000 −0.119523
\(281\) −18.0000 −1.07379 −0.536895 − 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 8.00000 0.476393
\(283\) −16.0000 −0.951101 −0.475551 − 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) −3.00000 −0.178017
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) −24.0000 −1.41668
\(288\) 1.00000 0.0589256
\(289\) 32.0000 1.88235
\(290\) −10.0000 −0.587220
\(291\) −17.0000 −0.996558
\(292\) −1.00000 −0.0585206
\(293\) 9.00000 0.525786 0.262893 − 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −7.00000 −0.406867
\(297\) 2.00000 0.116052
\(298\) 10.0000 0.579284
\(299\) 36.0000 2.08193
\(300\) −4.00000 −0.230940
\(301\) 2.00000 0.115278
\(302\) 22.0000 1.26596
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) 1.00000 0.0572598
\(306\) −7.00000 −0.400163
\(307\) 13.0000 0.741949 0.370975 − 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) −4.00000 −0.227921
\(309\) −1.00000 −0.0568880
\(310\) −8.00000 −0.454369
\(311\) −8.00000 −0.453638 −0.226819 − 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 4.00000 0.226455
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 18.0000 1.01580
\(315\) −2.00000 −0.112687
\(316\) 10.0000 0.562544
\(317\) −27.0000 −1.51647 −0.758236 − 0.651981i \(-0.773938\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(318\) −6.00000 −0.336463
\(319\) −20.0000 −1.11979
\(320\) 1.00000 0.0559017
\(321\) 13.0000 0.725589
\(322\) −18.0000 −1.00310
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −16.0000 −0.887520
\(326\) −16.0000 −0.886158
\(327\) 0 0
\(328\) 12.0000 0.662589
\(329\) −16.0000 −0.882109
\(330\) 2.00000 0.110096
\(331\) 7.00000 0.384755 0.192377 − 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) −1.00000 −0.0548821
\(333\) −7.00000 −0.383598
\(334\) −2.00000 −0.109435
\(335\) −12.0000 −0.655630
\(336\) −2.00000 −0.109109
\(337\) −2.00000 −0.108947 −0.0544735 − 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 3.00000 0.163178
\(339\) 4.00000 0.217250
\(340\) −7.00000 −0.379628
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −1.00000 −0.0539164
\(345\) 9.00000 0.484544
\(346\) 14.0000 0.752645
\(347\) −27.0000 −1.44944 −0.724718 − 0.689046i \(-0.758030\pi\)
−0.724718 + 0.689046i \(0.758030\pi\)
\(348\) −10.0000 −0.536056
\(349\) 15.0000 0.802932 0.401466 − 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(350\) 8.00000 0.427618
\(351\) 4.00000 0.213504
\(352\) 2.00000 0.106600
\(353\) 34.0000 1.80964 0.904819 − 0.425797i \(-0.140006\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) 0 0
\(355\) −3.00000 −0.159223
\(356\) 5.00000 0.264999
\(357\) 14.0000 0.740959
\(358\) 15.0000 0.792775
\(359\) −25.0000 −1.31945 −0.659725 − 0.751507i \(-0.729327\pi\)
−0.659725 + 0.751507i \(0.729327\pi\)
\(360\) 1.00000 0.0527046
\(361\) −19.0000 −1.00000
\(362\) 7.00000 0.367912
\(363\) −7.00000 −0.367405
\(364\) −8.00000 −0.419314
\(365\) −1.00000 −0.0523424
\(366\) 1.00000 0.0522708
\(367\) −32.0000 −1.67039 −0.835193 − 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) 9.00000 0.469157
\(369\) 12.0000 0.624695
\(370\) −7.00000 −0.363913
\(371\) 12.0000 0.623009
\(372\) −8.00000 −0.414781
\(373\) −31.0000 −1.60512 −0.802560 − 0.596572i \(-0.796529\pi\)
−0.802560 + 0.596572i \(0.796529\pi\)
\(374\) −14.0000 −0.723923
\(375\) −9.00000 −0.464758
\(376\) 8.00000 0.412568
\(377\) −40.0000 −2.06010
\(378\) −2.00000 −0.102869
\(379\) −20.0000 −1.02733 −0.513665 − 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 13.0000 0.666010
\(382\) 12.0000 0.613973
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) −4.00000 −0.203859
\(386\) 4.00000 0.203595
\(387\) −1.00000 −0.0508329
\(388\) −17.0000 −0.863044
\(389\) −10.0000 −0.507020 −0.253510 − 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 4.00000 0.202548
\(391\) −63.0000 −3.18605
\(392\) −3.00000 −0.151523
\(393\) −3.00000 −0.151330
\(394\) 18.0000 0.906827
\(395\) 10.0000 0.503155
\(396\) 2.00000 0.100504
\(397\) 23.0000 1.15434 0.577168 − 0.816625i \(-0.304158\pi\)
0.577168 + 0.816625i \(0.304158\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −23.0000 −1.14857 −0.574283 − 0.818657i \(-0.694719\pi\)
−0.574283 + 0.818657i \(0.694719\pi\)
\(402\) −12.0000 −0.598506
\(403\) −32.0000 −1.59403
\(404\) 12.0000 0.597022
\(405\) 1.00000 0.0496904
\(406\) 20.0000 0.992583
\(407\) −14.0000 −0.693954
\(408\) −7.00000 −0.346552
\(409\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 12.0000 0.592638
\(411\) −12.0000 −0.591916
\(412\) −1.00000 −0.0492665
\(413\) 0 0
\(414\) 9.00000 0.442326
\(415\) −1.00000 −0.0490881
\(416\) 4.00000 0.196116
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.00000 −0.0975900
\(421\) 17.0000 0.828529 0.414265 − 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 12.0000 0.584151
\(423\) 8.00000 0.388973
\(424\) −6.00000 −0.291386
\(425\) 28.0000 1.35820
\(426\) −3.00000 −0.145350
\(427\) −2.00000 −0.0967868
\(428\) 13.0000 0.628379
\(429\) 8.00000 0.386244
\(430\) −1.00000 −0.0482243
\(431\) −18.0000 −0.867029 −0.433515 − 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 1.00000 0.0481125
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 16.0000 0.768025
\(435\) −10.0000 −0.479463
\(436\) 0 0
\(437\) 0 0
\(438\) −1.00000 −0.0477818
\(439\) 15.0000 0.715911 0.357955 − 0.933739i \(-0.383474\pi\)
0.357955 + 0.933739i \(0.383474\pi\)
\(440\) 2.00000 0.0953463
\(441\) −3.00000 −0.142857
\(442\) −28.0000 −1.33182
\(443\) 19.0000 0.902717 0.451359 − 0.892343i \(-0.350940\pi\)
0.451359 + 0.892343i \(0.350940\pi\)
\(444\) −7.00000 −0.332205
\(445\) 5.00000 0.237023
\(446\) −6.00000 −0.284108
\(447\) 10.0000 0.472984
\(448\) −2.00000 −0.0944911
\(449\) 10.0000 0.471929 0.235965 − 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) −4.00000 −0.188562
\(451\) 24.0000 1.13012
\(452\) 4.00000 0.188144
\(453\) 22.0000 1.03365
\(454\) 18.0000 0.844782
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) −2.00000 −0.0935561 −0.0467780 − 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) −10.0000 −0.467269
\(459\) −7.00000 −0.326732
\(460\) 9.00000 0.419627
\(461\) −13.0000 −0.605470 −0.302735 − 0.953075i \(-0.597900\pi\)
−0.302735 + 0.953075i \(0.597900\pi\)
\(462\) −4.00000 −0.186097
\(463\) −1.00000 −0.0464739 −0.0232370 − 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) −10.0000 −0.464238
\(465\) −8.00000 −0.370991
\(466\) −26.0000 −1.20443
\(467\) 8.00000 0.370196 0.185098 − 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 4.00000 0.184900
\(469\) 24.0000 1.10822
\(470\) 8.00000 0.369012
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) −2.00000 −0.0919601
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) 14.0000 0.641689
\(477\) −6.00000 −0.274721
\(478\) −10.0000 −0.457389
\(479\) 10.0000 0.456912 0.228456 − 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) 1.00000 0.0456435
\(481\) −28.0000 −1.27669
\(482\) 17.0000 0.774329
\(483\) −18.0000 −0.819028
\(484\) −7.00000 −0.318182
\(485\) −17.0000 −0.771930
\(486\) 1.00000 0.0453609
\(487\) −32.0000 −1.45006 −0.725029 − 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 1.00000 0.0452679
\(489\) −16.0000 −0.723545
\(490\) −3.00000 −0.135526
\(491\) −8.00000 −0.361035 −0.180517 − 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 12.0000 0.541002
\(493\) 70.0000 3.15264
\(494\) 0 0
\(495\) 2.00000 0.0898933
\(496\) −8.00000 −0.359211
\(497\) 6.00000 0.269137
\(498\) −1.00000 −0.0448111
\(499\) −5.00000 −0.223831 −0.111915 − 0.993718i \(-0.535699\pi\)
−0.111915 + 0.993718i \(0.535699\pi\)
\(500\) −9.00000 −0.402492
\(501\) −2.00000 −0.0893534
\(502\) −18.0000 −0.803379
\(503\) 4.00000 0.178351 0.0891756 − 0.996016i \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 12.0000 0.533993
\(506\) 18.0000 0.800198
\(507\) 3.00000 0.133235
\(508\) 13.0000 0.576782
\(509\) 20.0000 0.886484 0.443242 − 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) −7.00000 −0.309965
\(511\) 2.00000 0.0884748
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) −1.00000 −0.0440653
\(516\) −1.00000 −0.0440225
\(517\) 16.0000 0.703679
\(518\) 14.0000 0.615125
\(519\) 14.0000 0.614532
\(520\) 4.00000 0.175412
\(521\) 22.0000 0.963837 0.481919 − 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) −10.0000 −0.437688
\(523\) −41.0000 −1.79280 −0.896402 − 0.443241i \(-0.853829\pi\)
−0.896402 + 0.443241i \(0.853829\pi\)
\(524\) −3.00000 −0.131056
\(525\) 8.00000 0.349149
\(526\) 4.00000 0.174408
\(527\) 56.0000 2.43940
\(528\) 2.00000 0.0870388
\(529\) 58.0000 2.52174
\(530\) −6.00000 −0.260623
\(531\) 0 0
\(532\) 0 0
\(533\) 48.0000 2.07911
\(534\) 5.00000 0.216371
\(535\) 13.0000 0.562039
\(536\) −12.0000 −0.518321
\(537\) 15.0000 0.647298
\(538\) 10.0000 0.431131
\(539\) −6.00000 −0.258438
\(540\) 1.00000 0.0430331
\(541\) −23.0000 −0.988847 −0.494424 − 0.869221i \(-0.664621\pi\)
−0.494424 + 0.869221i \(0.664621\pi\)
\(542\) 27.0000 1.15975
\(543\) 7.00000 0.300399
\(544\) −7.00000 −0.300123
\(545\) 0 0
\(546\) −8.00000 −0.342368
\(547\) −12.0000 −0.513083 −0.256541 − 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −12.0000 −0.512615
\(549\) 1.00000 0.0426790
\(550\) −8.00000 −0.341121
\(551\) 0 0
\(552\) 9.00000 0.383065
\(553\) −20.0000 −0.850487
\(554\) −22.0000 −0.934690
\(555\) −7.00000 −0.297133
\(556\) 5.00000 0.212047
\(557\) 18.0000 0.762684 0.381342 − 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −8.00000 −0.338667
\(559\) −4.00000 −0.169182
\(560\) −2.00000 −0.0845154
\(561\) −14.0000 −0.591080
\(562\) −18.0000 −0.759284
\(563\) −16.0000 −0.674320 −0.337160 − 0.941447i \(-0.609466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(564\) 8.00000 0.336861
\(565\) 4.00000 0.168281
\(566\) −16.0000 −0.672530
\(567\) −2.00000 −0.0839921
\(568\) −3.00000 −0.125877
\(569\) 20.0000 0.838444 0.419222 − 0.907884i \(-0.362303\pi\)
0.419222 + 0.907884i \(0.362303\pi\)
\(570\) 0 0
\(571\) −8.00000 −0.334790 −0.167395 − 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 8.00000 0.334497
\(573\) 12.0000 0.501307
\(574\) −24.0000 −1.00174
\(575\) −36.0000 −1.50130
\(576\) 1.00000 0.0416667
\(577\) −12.0000 −0.499567 −0.249783 − 0.968302i \(-0.580359\pi\)
−0.249783 + 0.968302i \(0.580359\pi\)
\(578\) 32.0000 1.33102
\(579\) 4.00000 0.166234
\(580\) −10.0000 −0.415227
\(581\) 2.00000 0.0829740
\(582\) −17.0000 −0.704673
\(583\) −12.0000 −0.496989
\(584\) −1.00000 −0.0413803
\(585\) 4.00000 0.165380
\(586\) 9.00000 0.371787
\(587\) 18.0000 0.742940 0.371470 − 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) −3.00000 −0.123718
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) −7.00000 −0.287698
\(593\) −21.0000 −0.862367 −0.431183 − 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 2.00000 0.0820610
\(595\) 14.0000 0.573944
\(596\) 10.0000 0.409616
\(597\) 5.00000 0.204636
\(598\) 36.0000 1.47215
\(599\) 15.0000 0.612883 0.306442 − 0.951889i \(-0.400862\pi\)
0.306442 + 0.951889i \(0.400862\pi\)
\(600\) −4.00000 −0.163299
\(601\) −3.00000 −0.122373 −0.0611863 − 0.998126i \(-0.519488\pi\)
−0.0611863 + 0.998126i \(0.519488\pi\)
\(602\) 2.00000 0.0815139
\(603\) −12.0000 −0.488678
\(604\) 22.0000 0.895167
\(605\) −7.00000 −0.284590
\(606\) 12.0000 0.487467
\(607\) 23.0000 0.933541 0.466771 − 0.884378i \(-0.345417\pi\)
0.466771 + 0.884378i \(0.345417\pi\)
\(608\) 0 0
\(609\) 20.0000 0.810441
\(610\) 1.00000 0.0404888
\(611\) 32.0000 1.29458
\(612\) −7.00000 −0.282958
\(613\) 4.00000 0.161558 0.0807792 − 0.996732i \(-0.474259\pi\)
0.0807792 + 0.996732i \(0.474259\pi\)
\(614\) 13.0000 0.524637
\(615\) 12.0000 0.483887
\(616\) −4.00000 −0.161165
\(617\) −27.0000 −1.08698 −0.543490 − 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 10.0000 0.401934 0.200967 − 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) −8.00000 −0.321288
\(621\) 9.00000 0.361158
\(622\) −8.00000 −0.320771
\(623\) −10.0000 −0.400642
\(624\) 4.00000 0.160128
\(625\) 11.0000 0.440000
\(626\) −6.00000 −0.239808
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) 49.0000 1.95376
\(630\) −2.00000 −0.0796819
\(631\) 22.0000 0.875806 0.437903 − 0.899022i \(-0.355721\pi\)
0.437903 + 0.899022i \(0.355721\pi\)
\(632\) 10.0000 0.397779
\(633\) 12.0000 0.476957
\(634\) −27.0000 −1.07231
\(635\) 13.0000 0.515889
\(636\) −6.00000 −0.237915
\(637\) −12.0000 −0.475457
\(638\) −20.0000 −0.791808
\(639\) −3.00000 −0.118678
\(640\) 1.00000 0.0395285
\(641\) 27.0000 1.06644 0.533218 − 0.845978i \(-0.320983\pi\)
0.533218 + 0.845978i \(0.320983\pi\)
\(642\) 13.0000 0.513069
\(643\) 19.0000 0.749287 0.374643 − 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) −18.0000 −0.709299
\(645\) −1.00000 −0.0393750
\(646\) 0 0
\(647\) −37.0000 −1.45462 −0.727310 − 0.686309i \(-0.759230\pi\)
−0.727310 + 0.686309i \(0.759230\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −16.0000 −0.627572
\(651\) 16.0000 0.627089
\(652\) −16.0000 −0.626608
\(653\) 24.0000 0.939193 0.469596 − 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 0 0
\(655\) −3.00000 −0.117220
\(656\) 12.0000 0.468521
\(657\) −1.00000 −0.0390137
\(658\) −16.0000 −0.623745
\(659\) 15.0000 0.584317 0.292159 − 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 2.00000 0.0778499
\(661\) 42.0000 1.63361 0.816805 − 0.576913i \(-0.195743\pi\)
0.816805 + 0.576913i \(0.195743\pi\)
\(662\) 7.00000 0.272063
\(663\) −28.0000 −1.08743
\(664\) −1.00000 −0.0388075
\(665\) 0 0
\(666\) −7.00000 −0.271244
\(667\) −90.0000 −3.48481
\(668\) −2.00000 −0.0773823
\(669\) −6.00000 −0.231973
\(670\) −12.0000 −0.463600
\(671\) 2.00000 0.0772091
\(672\) −2.00000 −0.0771517
\(673\) −46.0000 −1.77317 −0.886585 − 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −2.00000 −0.0770371
\(675\) −4.00000 −0.153960
\(676\) 3.00000 0.115385
\(677\) −12.0000 −0.461197 −0.230599 − 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 4.00000 0.153619
\(679\) 34.0000 1.30480
\(680\) −7.00000 −0.268438
\(681\) 18.0000 0.689761
\(682\) −16.0000 −0.612672
\(683\) −11.0000 −0.420903 −0.210452 − 0.977604i \(-0.567493\pi\)
−0.210452 + 0.977604i \(0.567493\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 20.0000 0.763604
\(687\) −10.0000 −0.381524
\(688\) −1.00000 −0.0381246
\(689\) −24.0000 −0.914327
\(690\) 9.00000 0.342624
\(691\) 42.0000 1.59776 0.798878 − 0.601494i \(-0.205427\pi\)
0.798878 + 0.601494i \(0.205427\pi\)
\(692\) 14.0000 0.532200
\(693\) −4.00000 −0.151947
\(694\) −27.0000 −1.02491
\(695\) 5.00000 0.189661
\(696\) −10.0000 −0.379049
\(697\) −84.0000 −3.18173
\(698\) 15.0000 0.567758
\(699\) −26.0000 −0.983410
\(700\) 8.00000 0.302372
\(701\) −38.0000 −1.43524 −0.717620 − 0.696435i \(-0.754769\pi\)
−0.717620 + 0.696435i \(0.754769\pi\)
\(702\) 4.00000 0.150970
\(703\) 0 0
\(704\) 2.00000 0.0753778
\(705\) 8.00000 0.301297
\(706\) 34.0000 1.27961
\(707\) −24.0000 −0.902613
\(708\) 0 0
\(709\) −5.00000 −0.187779 −0.0938895 − 0.995583i \(-0.529930\pi\)
−0.0938895 + 0.995583i \(0.529930\pi\)
\(710\) −3.00000 −0.112588
\(711\) 10.0000 0.375029
\(712\) 5.00000 0.187383
\(713\) −72.0000 −2.69642
\(714\) 14.0000 0.523937
\(715\) 8.00000 0.299183
\(716\) 15.0000 0.560576
\(717\) −10.0000 −0.373457
\(718\) −25.0000 −0.932992
\(719\) −20.0000 −0.745874 −0.372937 − 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 1.00000 0.0372678
\(721\) 2.00000 0.0744839
\(722\) −19.0000 −0.707107
\(723\) 17.0000 0.632237
\(724\) 7.00000 0.260153
\(725\) 40.0000 1.48556
\(726\) −7.00000 −0.259794
\(727\) −32.0000 −1.18681 −0.593407 − 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) −1.00000 −0.0370117
\(731\) 7.00000 0.258904
\(732\) 1.00000 0.0369611
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −32.0000 −1.18114
\(735\) −3.00000 −0.110657
\(736\) 9.00000 0.331744
\(737\) −24.0000 −0.884051
\(738\) 12.0000 0.441726
\(739\) 35.0000 1.28750 0.643748 − 0.765238i \(-0.277379\pi\)
0.643748 + 0.765238i \(0.277379\pi\)
\(740\) −7.00000 −0.257325
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) −41.0000 −1.50414 −0.752072 − 0.659081i \(-0.770945\pi\)
−0.752072 + 0.659081i \(0.770945\pi\)
\(744\) −8.00000 −0.293294
\(745\) 10.0000 0.366372
\(746\) −31.0000 −1.13499
\(747\) −1.00000 −0.0365881
\(748\) −14.0000 −0.511891
\(749\) −26.0000 −0.950019
\(750\) −9.00000 −0.328634
\(751\) −23.0000 −0.839282 −0.419641 − 0.907690i \(-0.637844\pi\)
−0.419641 + 0.907690i \(0.637844\pi\)
\(752\) 8.00000 0.291730
\(753\) −18.0000 −0.655956
\(754\) −40.0000 −1.45671
\(755\) 22.0000 0.800662
\(756\) −2.00000 −0.0727393
\(757\) 38.0000 1.38113 0.690567 − 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −20.0000 −0.726433
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 − 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 13.0000 0.470940
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) −7.00000 −0.253086
\(766\) 24.0000 0.867155
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −4.00000 −0.144150
\(771\) −12.0000 −0.432169
\(772\) 4.00000 0.143963
\(773\) −31.0000 −1.11499 −0.557496 − 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 32.0000 1.14947
\(776\) −17.0000 −0.610264
\(777\) 14.0000 0.502247
\(778\) −10.0000 −0.358517
\(779\) 0 0
\(780\) 4.00000 0.143223
\(781\) −6.00000 −0.214697
\(782\) −63.0000 −2.25288
\(783\) −10.0000 −0.357371
\(784\) −3.00000 −0.107143
\(785\) 18.0000 0.642448
\(786\) −3.00000 −0.107006
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 18.0000 0.641223
\(789\) 4.00000 0.142404
\(790\) 10.0000 0.355784
\(791\) −8.00000 −0.284447
\(792\) 2.00000 0.0710669
\(793\) 4.00000 0.142044
\(794\) 23.0000 0.816239
\(795\) −6.00000 −0.212798
\(796\) 5.00000 0.177220
\(797\) −2.00000 −0.0708436 −0.0354218 − 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) 0 0
\(799\) −56.0000 −1.98114
\(800\) −4.00000 −0.141421
\(801\) 5.00000 0.176666
\(802\) −23.0000 −0.812158
\(803\) −2.00000 −0.0705785
\(804\) −12.0000 −0.423207
\(805\) −18.0000 −0.634417
\(806\) −32.0000 −1.12715
\(807\) 10.0000 0.352017
\(808\) 12.0000 0.422159
\(809\) 30.0000 1.05474 0.527372 − 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 1.00000 0.0351364
\(811\) −33.0000 −1.15879 −0.579393 − 0.815048i \(-0.696710\pi\)
−0.579393 + 0.815048i \(0.696710\pi\)
\(812\) 20.0000 0.701862
\(813\) 27.0000 0.946931
\(814\) −14.0000 −0.490700
\(815\) −16.0000 −0.560456
\(816\) −7.00000 −0.245049
\(817\) 0 0
\(818\) 0 0
\(819\) −8.00000 −0.279543
\(820\) 12.0000 0.419058
\(821\) 22.0000 0.767805 0.383903 − 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −12.0000 −0.418548
\(823\) −26.0000 −0.906303 −0.453152 − 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −8.00000 −0.278524
\(826\) 0 0
\(827\) 43.0000 1.49526 0.747628 − 0.664117i \(-0.231193\pi\)
0.747628 + 0.664117i \(0.231193\pi\)
\(828\) 9.00000 0.312772
\(829\) −10.0000 −0.347314 −0.173657 − 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) −1.00000 −0.0347105
\(831\) −22.0000 −0.763172
\(832\) 4.00000 0.138675
\(833\) 21.0000 0.727607
\(834\) 5.00000 0.173136
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) −8.00000 −0.276520
\(838\) 0 0
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) −2.00000 −0.0690066
\(841\) 71.0000 2.44828
\(842\) 17.0000 0.585859
\(843\) −18.0000 −0.619953
\(844\) 12.0000 0.413057
\(845\) 3.00000 0.103203
\(846\) 8.00000 0.275046
\(847\) 14.0000 0.481046
\(848\) −6.00000 −0.206041
\(849\) −16.0000 −0.549119
\(850\) 28.0000 0.960392
\(851\) −63.0000 −2.15961
\(852\) −3.00000 −0.102778
\(853\) 14.0000 0.479351 0.239675 − 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 0 0
\(856\) 13.0000 0.444331
\(857\) −22.0000 −0.751506 −0.375753 − 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) 8.00000 0.273115
\(859\) −40.0000 −1.36478 −0.682391 − 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) −1.00000 −0.0340997
\(861\) −24.0000 −0.817918
\(862\) −18.0000 −0.613082
\(863\) 24.0000 0.816970 0.408485 − 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 1.00000 0.0340207
\(865\) 14.0000 0.476014
\(866\) −16.0000 −0.543702
\(867\) 32.0000 1.08678
\(868\) 16.0000 0.543075
\(869\) 20.0000 0.678454
\(870\) −10.0000 −0.339032
\(871\) −48.0000 −1.62642
\(872\) 0 0
\(873\) −17.0000 −0.575363
\(874\) 0 0
\(875\) 18.0000 0.608511
\(876\) −1.00000 −0.0337869
\(877\) −27.0000 −0.911725 −0.455863 − 0.890050i \(-0.650669\pi\)
−0.455863 + 0.890050i \(0.650669\pi\)
\(878\) 15.0000 0.506225
\(879\) 9.00000 0.303562
\(880\) 2.00000 0.0674200
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) −3.00000 −0.101015
\(883\) −31.0000 −1.04323 −0.521617 − 0.853180i \(-0.674671\pi\)
−0.521617 + 0.853180i \(0.674671\pi\)
\(884\) −28.0000 −0.941742
\(885\) 0 0
\(886\) 19.0000 0.638317
\(887\) −37.0000 −1.24234 −0.621169 − 0.783676i \(-0.713342\pi\)
−0.621169 + 0.783676i \(0.713342\pi\)
\(888\) −7.00000 −0.234905
\(889\) −26.0000 −0.872012
\(890\) 5.00000 0.167600
\(891\) 2.00000 0.0670025
\(892\) −6.00000 −0.200895
\(893\) 0 0
\(894\) 10.0000 0.334450
\(895\) 15.0000 0.501395
\(896\) −2.00000 −0.0668153
\(897\) 36.0000 1.20201
\(898\) 10.0000 0.333704
\(899\) 80.0000 2.66815
\(900\) −4.00000 −0.133333
\(901\) 42.0000 1.39922
\(902\) 24.0000 0.799113
\(903\) 2.00000 0.0665558
\(904\) 4.00000 0.133038
\(905\) 7.00000 0.232688
\(906\) 22.0000 0.730901
\(907\) −7.00000 −0.232431 −0.116216 − 0.993224i \(-0.537076\pi\)
−0.116216 + 0.993224i \(0.537076\pi\)
\(908\) 18.0000 0.597351
\(909\) 12.0000 0.398015
\(910\) −8.00000 −0.265197
\(911\) 12.0000 0.397578 0.198789 − 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −2.00000 −0.0661903
\(914\) −2.00000 −0.0661541
\(915\) 1.00000 0.0330590
\(916\) −10.0000 −0.330409
\(917\) 6.00000 0.198137
\(918\) −7.00000 −0.231034
\(919\) 5.00000 0.164935 0.0824674 − 0.996594i \(-0.473720\pi\)
0.0824674 + 0.996594i \(0.473720\pi\)
\(920\) 9.00000 0.296721
\(921\) 13.0000 0.428365
\(922\) −13.0000 −0.428132
\(923\) −12.0000 −0.394985
\(924\) −4.00000 −0.131590
\(925\) 28.0000 0.920634
\(926\) −1.00000 −0.0328620
\(927\) −1.00000 −0.0328443
\(928\) −10.0000 −0.328266
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) −8.00000 −0.262330
\(931\) 0 0
\(932\) −26.0000 −0.851658
\(933\) −8.00000 −0.261908
\(934\) 8.00000 0.261768
\(935\) −14.0000 −0.457849
\(936\) 4.00000 0.130744
\(937\) −57.0000 −1.86211 −0.931054 − 0.364880i \(-0.881110\pi\)
−0.931054 + 0.364880i \(0.881110\pi\)
\(938\) 24.0000 0.783628
\(939\) −6.00000 −0.195803
\(940\) 8.00000 0.260931
\(941\) 12.0000 0.391189 0.195594 − 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(942\) 18.0000 0.586472
\(943\) 108.000 3.51696
\(944\) 0 0
\(945\) −2.00000 −0.0650600
\(946\) −2.00000 −0.0650256
\(947\) 48.0000 1.55979 0.779895 − 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) 10.0000 0.324785
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) −27.0000 −0.875535
\(952\) 14.0000 0.453743
\(953\) −11.0000 −0.356325 −0.178162 − 0.984001i \(-0.557015\pi\)
−0.178162 + 0.984001i \(0.557015\pi\)
\(954\) −6.00000 −0.194257
\(955\) 12.0000 0.388311
\(956\) −10.0000 −0.323423
\(957\) −20.0000 −0.646508
\(958\) 10.0000 0.323085
\(959\) 24.0000 0.775000
\(960\) 1.00000 0.0322749
\(961\) 33.0000 1.06452
\(962\) −28.0000 −0.902756
\(963\) 13.0000 0.418919
\(964\) 17.0000 0.547533
\(965\) 4.00000 0.128765
\(966\) −18.0000 −0.579141
\(967\) 53.0000 1.70437 0.852183 − 0.523245i \(-0.175279\pi\)
0.852183 + 0.523245i \(0.175279\pi\)
\(968\) −7.00000 −0.224989
\(969\) 0 0
\(970\) −17.0000 −0.545837
\(971\) −23.0000 −0.738105 −0.369053 − 0.929409i \(-0.620318\pi\)
−0.369053 + 0.929409i \(0.620318\pi\)
\(972\) 1.00000 0.0320750
\(973\) −10.0000 −0.320585
\(974\) −32.0000 −1.02535
\(975\) −16.0000 −0.512410
\(976\) 1.00000 0.0320092
\(977\) −52.0000 −1.66363 −0.831814 − 0.555055i \(-0.812697\pi\)
−0.831814 + 0.555055i \(0.812697\pi\)
\(978\) −16.0000 −0.511624
\(979\) 10.0000 0.319601
\(980\) −3.00000 −0.0958315
\(981\) 0 0
\(982\) −8.00000 −0.255290
\(983\) −16.0000 −0.510321 −0.255160 − 0.966899i \(-0.582128\pi\)
−0.255160 + 0.966899i \(0.582128\pi\)
\(984\) 12.0000 0.382546
\(985\) 18.0000 0.573528
\(986\) 70.0000 2.22925
\(987\) −16.0000 −0.509286
\(988\) 0 0
\(989\) −9.00000 −0.286183
\(990\) 2.00000 0.0635642
\(991\) −28.0000 −0.889449 −0.444725 − 0.895667i \(-0.646698\pi\)
−0.444725 + 0.895667i \(0.646698\pi\)
\(992\) −8.00000 −0.254000
\(993\) 7.00000 0.222138
\(994\) 6.00000 0.190308
\(995\) 5.00000 0.158511
\(996\) −1.00000 −0.0316862
\(997\) 53.0000 1.67853 0.839263 − 0.543725i \(-0.182987\pi\)
0.839263 + 0.543725i \(0.182987\pi\)
\(998\) −5.00000 −0.158272
\(999\) −7.00000 −0.221470
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 366.2.a.f.1.1 ✓ 1
3.2 odd 2 1098.2.a.a.1.1 1
4.3 odd 2 2928.2.a.f.1.1 1
5.4 even 2 9150.2.a.e.1.1 1
12.11 even 2 8784.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
366.2.a.f.1.1 ✓ 1 1.1 even 1 trivial
1098.2.a.a.1.1 1 3.2 odd 2
2928.2.a.f.1.1 1 4.3 odd 2
8784.2.a.g.1.1 1 12.11 even 2
9150.2.a.e.1.1 1 5.4 even 2