Properties

Label 1014.2.a.a.1.1
Level $1014$
Weight $2$
Character 1014.1
Self dual yes
Analytic conductor $8.097$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,2,Mod(1,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, 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("1014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.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: \(8.09683076496\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{12} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} -2.00000 q^{22} +6.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{27} -2.00000 q^{28} -9.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} -5.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} -11.0000 q^{37} +2.00000 q^{38} +1.00000 q^{40} +5.00000 q^{41} -2.00000 q^{42} +10.0000 q^{43} +2.00000 q^{44} -1.00000 q^{45} -6.00000 q^{46} +2.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +4.00000 q^{50} -5.00000 q^{51} -1.00000 q^{53} +1.00000 q^{54} -2.00000 q^{55} +2.00000 q^{56} +2.00000 q^{57} +9.00000 q^{58} -8.00000 q^{59} +1.00000 q^{60} -11.0000 q^{61} +4.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} +2.00000 q^{67} +5.00000 q^{68} -6.00000 q^{69} -2.00000 q^{70} -14.0000 q^{71} -1.00000 q^{72} -13.0000 q^{73} +11.0000 q^{74} +4.00000 q^{75} -2.00000 q^{76} -4.00000 q^{77} -4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -5.00000 q^{82} +6.00000 q^{83} +2.00000 q^{84} -5.00000 q^{85} -10.0000 q^{86} +9.00000 q^{87} -2.00000 q^{88} +2.00000 q^{89} +1.00000 q^{90} +6.00000 q^{92} +4.00000 q^{93} -2.00000 q^{94} +2.00000 q^{95} +1.00000 q^{96} -2.00000 q^{97} +3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) −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
\(13\) 0 0
\(14\) 2.00000 0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 5.00000 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.00000 0.436436
\(22\) −2.00000 −0.426401
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.00000 −0.348155
\(34\) −5.00000 −0.857493
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) −11.0000 −1.80839 −0.904194 0.427121i \(-0.859528\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) −2.00000 −0.308607
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 2.00000 0.301511
\(45\) −1.00000 −0.149071
\(46\) −6.00000 −0.884652
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) 4.00000 0.565685
\(51\) −5.00000 −0.700140
\(52\) 0 0
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.00000 −0.269680
\(56\) 2.00000 0.267261
\(57\) 2.00000 0.264906
\(58\) 9.00000 1.18176
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 1.00000 0.129099
\(61\) −11.0000 −1.40841 −0.704203 0.709999i \(-0.748695\pi\)
−0.704203 + 0.709999i \(0.748695\pi\)
\(62\) 4.00000 0.508001
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.00000 0.246183
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 5.00000 0.606339
\(69\) −6.00000 −0.722315
\(70\) −2.00000 −0.239046
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) −1.00000 −0.117851
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) 11.0000 1.27872
\(75\) 4.00000 0.461880
\(76\) −2.00000 −0.229416
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −5.00000 −0.552158
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 2.00000 0.218218
\(85\) −5.00000 −0.542326
\(86\) −10.0000 −1.07833
\(87\) 9.00000 0.964901
\(88\) −2.00000 −0.213201
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 4.00000 0.414781
\(94\) −2.00000 −0.206284
\(95\) 2.00000 0.205196
\(96\) 1.00000 0.102062
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 3.00000 0.303046
\(99\) 2.00000 0.201008
\(100\) −4.00000 −0.400000
\(101\) −5.00000 −0.497519 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(102\) 5.00000 0.495074
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 1.00000 0.0971286
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 2.00000 0.190693
\(111\) 11.0000 1.04407
\(112\) −2.00000 −0.188982
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) −2.00000 −0.187317
\(115\) −6.00000 −0.559503
\(116\) −9.00000 −0.835629
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) −10.0000 −0.916698
\(120\) −1.00000 −0.0912871
\(121\) −7.00000 −0.636364
\(122\) 11.0000 0.995893
\(123\) −5.00000 −0.450835
\(124\) −4.00000 −0.359211
\(125\) 9.00000 0.804984
\(126\) 2.00000 0.178174
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −2.00000 −0.174078
\(133\) 4.00000 0.346844
\(134\) −2.00000 −0.172774
\(135\) 1.00000 0.0860663
\(136\) −5.00000 −0.428746
\(137\) 17.0000 1.45241 0.726204 0.687479i \(-0.241283\pi\)
0.726204 + 0.687479i \(0.241283\pi\)
\(138\) 6.00000 0.510754
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 2.00000 0.169031
\(141\) −2.00000 −0.168430
\(142\) 14.0000 1.17485
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 9.00000 0.747409
\(146\) 13.0000 1.07589
\(147\) 3.00000 0.247436
\(148\) −11.0000 −0.904194
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −4.00000 −0.326599
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) 2.00000 0.162221
\(153\) 5.00000 0.404226
\(154\) 4.00000 0.322329
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 4.00000 0.318223
\(159\) 1.00000 0.0793052
\(160\) 1.00000 0.0790569
\(161\) −12.0000 −0.945732
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 5.00000 0.390434
\(165\) 2.00000 0.155700
\(166\) −6.00000 −0.465690
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) −2.00000 −0.154303
\(169\) 0 0
\(170\) 5.00000 0.383482
\(171\) −2.00000 −0.152944
\(172\) 10.0000 0.762493
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) −9.00000 −0.682288
\(175\) 8.00000 0.604743
\(176\) 2.00000 0.150756
\(177\) 8.00000 0.601317
\(178\) −2.00000 −0.149906
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 11.0000 0.813143
\(184\) −6.00000 −0.442326
\(185\) 11.0000 0.808736
\(186\) −4.00000 −0.293294
\(187\) 10.0000 0.731272
\(188\) 2.00000 0.145865
\(189\) 2.00000 0.145479
\(190\) −2.00000 −0.145095
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −2.00000 −0.142134
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 4.00000 0.282843
\(201\) −2.00000 −0.141069
\(202\) 5.00000 0.351799
\(203\) 18.0000 1.26335
\(204\) −5.00000 −0.350070
\(205\) −5.00000 −0.349215
\(206\) −10.0000 −0.696733
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 2.00000 0.138013
\(211\) 24.0000 1.65223 0.826114 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(212\) −1.00000 −0.0686803
\(213\) 14.0000 0.959264
\(214\) 18.0000 1.23045
\(215\) −10.0000 −0.681994
\(216\) 1.00000 0.0680414
\(217\) 8.00000 0.543075
\(218\) 2.00000 0.135457
\(219\) 13.0000 0.878459
\(220\) −2.00000 −0.134840
\(221\) 0 0
\(222\) −11.0000 −0.738272
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 2.00000 0.133631
\(225\) −4.00000 −0.266667
\(226\) 3.00000 0.199557
\(227\) 14.0000 0.929213 0.464606 0.885517i \(-0.346196\pi\)
0.464606 + 0.885517i \(0.346196\pi\)
\(228\) 2.00000 0.132453
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 6.00000 0.395628
\(231\) 4.00000 0.263181
\(232\) 9.00000 0.590879
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −2.00000 −0.130466
\(236\) −8.00000 −0.520756
\(237\) 4.00000 0.259828
\(238\) 10.0000 0.648204
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 1.00000 0.0645497
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 7.00000 0.449977
\(243\) −1.00000 −0.0641500
\(244\) −11.0000 −0.704203
\(245\) 3.00000 0.191663
\(246\) 5.00000 0.318788
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −6.00000 −0.380235
\(250\) −9.00000 −0.569210
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) −2.00000 −0.125988
\(253\) 12.0000 0.754434
\(254\) 12.0000 0.752947
\(255\) 5.00000 0.313112
\(256\) 1.00000 0.0625000
\(257\) −3.00000 −0.187135 −0.0935674 0.995613i \(-0.529827\pi\)
−0.0935674 + 0.995613i \(0.529827\pi\)
\(258\) 10.0000 0.622573
\(259\) 22.0000 1.36701
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) 8.00000 0.494242
\(263\) 14.0000 0.863277 0.431638 0.902047i \(-0.357936\pi\)
0.431638 + 0.902047i \(0.357936\pi\)
\(264\) 2.00000 0.123091
\(265\) 1.00000 0.0614295
\(266\) −4.00000 −0.245256
\(267\) −2.00000 −0.122398
\(268\) 2.00000 0.122169
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) −17.0000 −1.02701
\(275\) −8.00000 −0.482418
\(276\) −6.00000 −0.361158
\(277\) −11.0000 −0.660926 −0.330463 0.943819i \(-0.607205\pi\)
−0.330463 + 0.943819i \(0.607205\pi\)
\(278\) 12.0000 0.719712
\(279\) −4.00000 −0.239474
\(280\) −2.00000 −0.119523
\(281\) 25.0000 1.49137 0.745687 0.666296i \(-0.232121\pi\)
0.745687 + 0.666296i \(0.232121\pi\)
\(282\) 2.00000 0.119098
\(283\) 26.0000 1.54554 0.772770 0.634686i \(-0.218871\pi\)
0.772770 + 0.634686i \(0.218871\pi\)
\(284\) −14.0000 −0.830747
\(285\) −2.00000 −0.118470
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) −1.00000 −0.0589256
\(289\) 8.00000 0.470588
\(290\) −9.00000 −0.528498
\(291\) 2.00000 0.117242
\(292\) −13.0000 −0.760767
\(293\) −1.00000 −0.0584206 −0.0292103 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) −3.00000 −0.174964
\(295\) 8.00000 0.465778
\(296\) 11.0000 0.639362
\(297\) −2.00000 −0.116052
\(298\) −3.00000 −0.173785
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) −20.0000 −1.15278
\(302\) 6.00000 0.345261
\(303\) 5.00000 0.287242
\(304\) −2.00000 −0.114708
\(305\) 11.0000 0.629858
\(306\) −5.00000 −0.285831
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) −4.00000 −0.227921
\(309\) −10.0000 −0.568880
\(310\) −4.00000 −0.227185
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 7.00000 0.395033
\(315\) 2.00000 0.112687
\(316\) −4.00000 −0.225018
\(317\) −33.0000 −1.85346 −0.926732 0.375722i \(-0.877395\pi\)
−0.926732 + 0.375722i \(0.877395\pi\)
\(318\) −1.00000 −0.0560772
\(319\) −18.0000 −1.00781
\(320\) −1.00000 −0.0559017
\(321\) 18.0000 1.00466
\(322\) 12.0000 0.668734
\(323\) −10.0000 −0.556415
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) 2.00000 0.110600
\(328\) −5.00000 −0.276079
\(329\) −4.00000 −0.220527
\(330\) −2.00000 −0.110096
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 6.00000 0.329293
\(333\) −11.0000 −0.602796
\(334\) −24.0000 −1.31322
\(335\) −2.00000 −0.109272
\(336\) 2.00000 0.109109
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 0 0
\(339\) 3.00000 0.162938
\(340\) −5.00000 −0.271163
\(341\) −8.00000 −0.433224
\(342\) 2.00000 0.108148
\(343\) 20.0000 1.07990
\(344\) −10.0000 −0.539164
\(345\) 6.00000 0.323029
\(346\) 22.0000 1.18273
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 9.00000 0.482451
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) −8.00000 −0.427618
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) 17.0000 0.904819 0.452409 0.891810i \(-0.350565\pi\)
0.452409 + 0.891810i \(0.350565\pi\)
\(354\) −8.00000 −0.425195
\(355\) 14.0000 0.743043
\(356\) 2.00000 0.106000
\(357\) 10.0000 0.529256
\(358\) 6.00000 0.317110
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 1.00000 0.0527046
\(361\) −15.0000 −0.789474
\(362\) −5.00000 −0.262794
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 13.0000 0.680451
\(366\) −11.0000 −0.574979
\(367\) −2.00000 −0.104399 −0.0521996 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) 6.00000 0.312772
\(369\) 5.00000 0.260290
\(370\) −11.0000 −0.571863
\(371\) 2.00000 0.103835
\(372\) 4.00000 0.207390
\(373\) 9.00000 0.466002 0.233001 0.972476i \(-0.425145\pi\)
0.233001 + 0.972476i \(0.425145\pi\)
\(374\) −10.0000 −0.517088
\(375\) −9.00000 −0.464758
\(376\) −2.00000 −0.103142
\(377\) 0 0
\(378\) −2.00000 −0.102869
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 2.00000 0.102598
\(381\) 12.0000 0.614779
\(382\) −4.00000 −0.204658
\(383\) 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
\(386\) 17.0000 0.865277
\(387\) 10.0000 0.508329
\(388\) −2.00000 −0.101535
\(389\) 19.0000 0.963338 0.481669 0.876353i \(-0.340031\pi\)
0.481669 + 0.876353i \(0.340031\pi\)
\(390\) 0 0
\(391\) 30.0000 1.51717
\(392\) 3.00000 0.151523
\(393\) 8.00000 0.403547
\(394\) −6.00000 −0.302276
\(395\) 4.00000 0.201262
\(396\) 2.00000 0.100504
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) −10.0000 −0.501255
\(399\) −4.00000 −0.200250
\(400\) −4.00000 −0.200000
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 2.00000 0.0997509
\(403\) 0 0
\(404\) −5.00000 −0.248759
\(405\) −1.00000 −0.0496904
\(406\) −18.0000 −0.893325
\(407\) −22.0000 −1.09050
\(408\) 5.00000 0.247537
\(409\) 23.0000 1.13728 0.568638 0.822588i \(-0.307470\pi\)
0.568638 + 0.822588i \(0.307470\pi\)
\(410\) 5.00000 0.246932
\(411\) −17.0000 −0.838548
\(412\) 10.0000 0.492665
\(413\) 16.0000 0.787309
\(414\) −6.00000 −0.294884
\(415\) −6.00000 −0.294528
\(416\) 0 0
\(417\) 12.0000 0.587643
\(418\) 4.00000 0.195646
\(419\) −32.0000 −1.56330 −0.781651 0.623716i \(-0.785622\pi\)
−0.781651 + 0.623716i \(0.785622\pi\)
\(420\) −2.00000 −0.0975900
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) −24.0000 −1.16830
\(423\) 2.00000 0.0972433
\(424\) 1.00000 0.0485643
\(425\) −20.0000 −0.970143
\(426\) −14.0000 −0.678302
\(427\) 22.0000 1.06465
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 10.0000 0.482243
\(431\) −2.00000 −0.0963366 −0.0481683 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −21.0000 −1.00920 −0.504598 0.863355i \(-0.668359\pi\)
−0.504598 + 0.863355i \(0.668359\pi\)
\(434\) −8.00000 −0.384012
\(435\) −9.00000 −0.431517
\(436\) −2.00000 −0.0957826
\(437\) −12.0000 −0.574038
\(438\) −13.0000 −0.621164
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 2.00000 0.0953463
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 20.0000 0.950229 0.475114 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) 11.0000 0.522037
\(445\) −2.00000 −0.0948091
\(446\) 16.0000 0.757622
\(447\) −3.00000 −0.141895
\(448\) −2.00000 −0.0944911
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 4.00000 0.188562
\(451\) 10.0000 0.470882
\(452\) −3.00000 −0.141108
\(453\) 6.00000 0.281905
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 3.00000 0.140334 0.0701670 0.997535i \(-0.477647\pi\)
0.0701670 + 0.997535i \(0.477647\pi\)
\(458\) −10.0000 −0.467269
\(459\) −5.00000 −0.233380
\(460\) −6.00000 −0.279751
\(461\) 3.00000 0.139724 0.0698620 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) −4.00000 −0.186097
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) −9.00000 −0.417815
\(465\) −4.00000 −0.185496
\(466\) 6.00000 0.277945
\(467\) −22.0000 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 2.00000 0.0922531
\(471\) 7.00000 0.322543
\(472\) 8.00000 0.368230
\(473\) 20.0000 0.919601
\(474\) −4.00000 −0.183726
\(475\) 8.00000 0.367065
\(476\) −10.0000 −0.458349
\(477\) −1.00000 −0.0457869
\(478\) 6.00000 0.274434
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0 0
\(482\) −7.00000 −0.318841
\(483\) 12.0000 0.546019
\(484\) −7.00000 −0.318182
\(485\) 2.00000 0.0908153
\(486\) 1.00000 0.0453609
\(487\) −26.0000 −1.17817 −0.589086 0.808070i \(-0.700512\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(488\) 11.0000 0.497947
\(489\) −20.0000 −0.904431
\(490\) −3.00000 −0.135526
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) −5.00000 −0.225417
\(493\) −45.0000 −2.02670
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) −4.00000 −0.179605
\(497\) 28.0000 1.25597
\(498\) 6.00000 0.268866
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 9.00000 0.402492
\(501\) −24.0000 −1.07224
\(502\) −4.00000 −0.178529
\(503\) −14.0000 −0.624229 −0.312115 0.950044i \(-0.601037\pi\)
−0.312115 + 0.950044i \(0.601037\pi\)
\(504\) 2.00000 0.0890871
\(505\) 5.00000 0.222497
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) −12.0000 −0.532414
\(509\) 15.0000 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) −5.00000 −0.221404
\(511\) 26.0000 1.15017
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) 3.00000 0.132324
\(515\) −10.0000 −0.440653
\(516\) −10.0000 −0.440225
\(517\) 4.00000 0.175920
\(518\) −22.0000 −0.966625
\(519\) 22.0000 0.965693
\(520\) 0 0
\(521\) 25.0000 1.09527 0.547635 0.836717i \(-0.315528\pi\)
0.547635 + 0.836717i \(0.315528\pi\)
\(522\) 9.00000 0.393919
\(523\) −38.0000 −1.66162 −0.830812 0.556553i \(-0.812124\pi\)
−0.830812 + 0.556553i \(0.812124\pi\)
\(524\) −8.00000 −0.349482
\(525\) −8.00000 −0.349149
\(526\) −14.0000 −0.610429
\(527\) −20.0000 −0.871214
\(528\) −2.00000 −0.0870388
\(529\) 13.0000 0.565217
\(530\) −1.00000 −0.0434372
\(531\) −8.00000 −0.347170
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) 2.00000 0.0865485
\(535\) 18.0000 0.778208
\(536\) −2.00000 −0.0863868
\(537\) 6.00000 0.258919
\(538\) 14.0000 0.603583
\(539\) −6.00000 −0.258438
\(540\) 1.00000 0.0430331
\(541\) −7.00000 −0.300954 −0.150477 0.988614i \(-0.548081\pi\)
−0.150477 + 0.988614i \(0.548081\pi\)
\(542\) −8.00000 −0.343629
\(543\) −5.00000 −0.214571
\(544\) −5.00000 −0.214373
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 17.0000 0.726204
\(549\) −11.0000 −0.469469
\(550\) 8.00000 0.341121
\(551\) 18.0000 0.766826
\(552\) 6.00000 0.255377
\(553\) 8.00000 0.340195
\(554\) 11.0000 0.467345
\(555\) −11.0000 −0.466924
\(556\) −12.0000 −0.508913
\(557\) −9.00000 −0.381342 −0.190671 0.981654i \(-0.561066\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 2.00000 0.0845154
\(561\) −10.0000 −0.422200
\(562\) −25.0000 −1.05456
\(563\) 40.0000 1.68580 0.842900 0.538071i \(-0.180847\pi\)
0.842900 + 0.538071i \(0.180847\pi\)
\(564\) −2.00000 −0.0842152
\(565\) 3.00000 0.126211
\(566\) −26.0000 −1.09286
\(567\) −2.00000 −0.0839921
\(568\) 14.0000 0.587427
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 2.00000 0.0837708
\(571\) −2.00000 −0.0836974 −0.0418487 0.999124i \(-0.513325\pi\)
−0.0418487 + 0.999124i \(0.513325\pi\)
\(572\) 0 0
\(573\) −4.00000 −0.167102
\(574\) 10.0000 0.417392
\(575\) −24.0000 −1.00087
\(576\) 1.00000 0.0416667
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) −8.00000 −0.332756
\(579\) 17.0000 0.706496
\(580\) 9.00000 0.373705
\(581\) −12.0000 −0.497844
\(582\) −2.00000 −0.0829027
\(583\) −2.00000 −0.0828315
\(584\) 13.0000 0.537944
\(585\) 0 0
\(586\) 1.00000 0.0413096
\(587\) −32.0000 −1.32078 −0.660391 0.750922i \(-0.729609\pi\)
−0.660391 + 0.750922i \(0.729609\pi\)
\(588\) 3.00000 0.123718
\(589\) 8.00000 0.329634
\(590\) −8.00000 −0.329355
\(591\) −6.00000 −0.246807
\(592\) −11.0000 −0.452097
\(593\) −39.0000 −1.60154 −0.800769 0.598973i \(-0.795576\pi\)
−0.800769 + 0.598973i \(0.795576\pi\)
\(594\) 2.00000 0.0820610
\(595\) 10.0000 0.409960
\(596\) 3.00000 0.122885
\(597\) −10.0000 −0.409273
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −4.00000 −0.163299
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) 20.0000 0.815139
\(603\) 2.00000 0.0814463
\(604\) −6.00000 −0.244137
\(605\) 7.00000 0.284590
\(606\) −5.00000 −0.203111
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 2.00000 0.0811107
\(609\) −18.0000 −0.729397
\(610\) −11.0000 −0.445377
\(611\) 0 0
\(612\) 5.00000 0.202113
\(613\) 13.0000 0.525065 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(614\) 14.0000 0.564994
\(615\) 5.00000 0.201619
\(616\) 4.00000 0.161165
\(617\) −15.0000 −0.603877 −0.301939 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) 10.0000 0.402259
\(619\) 32.0000 1.28619 0.643094 0.765787i \(-0.277650\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 4.00000 0.160644
\(621\) −6.00000 −0.240772
\(622\) −6.00000 −0.240578
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) −6.00000 −0.239808
\(627\) 4.00000 0.159745
\(628\) −7.00000 −0.279330
\(629\) −55.0000 −2.19299
\(630\) −2.00000 −0.0796819
\(631\) 12.0000 0.477712 0.238856 0.971055i \(-0.423228\pi\)
0.238856 + 0.971055i \(0.423228\pi\)
\(632\) 4.00000 0.159111
\(633\) −24.0000 −0.953914
\(634\) 33.0000 1.31060
\(635\) 12.0000 0.476205
\(636\) 1.00000 0.0396526
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) −14.0000 −0.553831
\(640\) 1.00000 0.0395285
\(641\) 5.00000 0.197488 0.0987441 0.995113i \(-0.468517\pi\)
0.0987441 + 0.995113i \(0.468517\pi\)
\(642\) −18.0000 −0.710403
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) −12.0000 −0.472866
\(645\) 10.0000 0.393750
\(646\) 10.0000 0.393445
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −16.0000 −0.628055
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 20.0000 0.783260
\(653\) −22.0000 −0.860927 −0.430463 0.902608i \(-0.641650\pi\)
−0.430463 + 0.902608i \(0.641650\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 8.00000 0.312586
\(656\) 5.00000 0.195217
\(657\) −13.0000 −0.507178
\(658\) 4.00000 0.155936
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 2.00000 0.0778499
\(661\) 25.0000 0.972387 0.486194 0.873851i \(-0.338385\pi\)
0.486194 + 0.873851i \(0.338385\pi\)
\(662\) 28.0000 1.08825
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −4.00000 −0.155113
\(666\) 11.0000 0.426241
\(667\) −54.0000 −2.09089
\(668\) 24.0000 0.928588
\(669\) 16.0000 0.618596
\(670\) 2.00000 0.0772667
\(671\) −22.0000 −0.849301
\(672\) −2.00000 −0.0771517
\(673\) 43.0000 1.65753 0.828764 0.559598i \(-0.189045\pi\)
0.828764 + 0.559598i \(0.189045\pi\)
\(674\) 9.00000 0.346667
\(675\) 4.00000 0.153960
\(676\) 0 0
\(677\) −46.0000 −1.76792 −0.883962 0.467559i \(-0.845134\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(678\) −3.00000 −0.115214
\(679\) 4.00000 0.153506
\(680\) 5.00000 0.191741
\(681\) −14.0000 −0.536481
\(682\) 8.00000 0.306336
\(683\) −40.0000 −1.53056 −0.765279 0.643699i \(-0.777399\pi\)
−0.765279 + 0.643699i \(0.777399\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −17.0000 −0.649537
\(686\) −20.0000 −0.763604
\(687\) −10.0000 −0.381524
\(688\) 10.0000 0.381246
\(689\) 0 0
\(690\) −6.00000 −0.228416
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) −22.0000 −0.836315
\(693\) −4.00000 −0.151947
\(694\) −6.00000 −0.227757
\(695\) 12.0000 0.455186
\(696\) −9.00000 −0.341144
\(697\) 25.0000 0.946943
\(698\) −6.00000 −0.227103
\(699\) 6.00000 0.226941
\(700\) 8.00000 0.302372
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) 22.0000 0.829746
\(704\) 2.00000 0.0753778
\(705\) 2.00000 0.0753244
\(706\) −17.0000 −0.639803
\(707\) 10.0000 0.376089
\(708\) 8.00000 0.300658
\(709\) −15.0000 −0.563337 −0.281668 0.959512i \(-0.590888\pi\)
−0.281668 + 0.959512i \(0.590888\pi\)
\(710\) −14.0000 −0.525411
\(711\) −4.00000 −0.150012
\(712\) −2.00000 −0.0749532
\(713\) −24.0000 −0.898807
\(714\) −10.0000 −0.374241
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 6.00000 0.224074
\(718\) 30.0000 1.11959
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −20.0000 −0.744839
\(722\) 15.0000 0.558242
\(723\) −7.00000 −0.260333
\(724\) 5.00000 0.185824
\(725\) 36.0000 1.33701
\(726\) −7.00000 −0.259794
\(727\) 2.00000 0.0741759 0.0370879 0.999312i \(-0.488192\pi\)
0.0370879 + 0.999312i \(0.488192\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −13.0000 −0.481152
\(731\) 50.0000 1.84932
\(732\) 11.0000 0.406572
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) 2.00000 0.0738213
\(735\) −3.00000 −0.110657
\(736\) −6.00000 −0.221163
\(737\) 4.00000 0.147342
\(738\) −5.00000 −0.184053
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 11.0000 0.404368
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) −4.00000 −0.146647
\(745\) −3.00000 −0.109911
\(746\) −9.00000 −0.329513
\(747\) 6.00000 0.219529
\(748\) 10.0000 0.365636
\(749\) 36.0000 1.31541
\(750\) 9.00000 0.328634
\(751\) 26.0000 0.948753 0.474377 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(752\) 2.00000 0.0729325
\(753\) −4.00000 −0.145768
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 2.00000 0.0727393
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) −12.0000 −0.435860
\(759\) −12.0000 −0.435572
\(760\) −2.00000 −0.0725476
\(761\) 34.0000 1.23250 0.616250 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) −12.0000 −0.434714
\(763\) 4.00000 0.144810
\(764\) 4.00000 0.144715
\(765\) −5.00000 −0.180775
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) −4.00000 −0.144150
\(771\) 3.00000 0.108042
\(772\) −17.0000 −0.611843
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −10.0000 −0.359443
\(775\) 16.0000 0.574737
\(776\) 2.00000 0.0717958
\(777\) −22.0000 −0.789246
\(778\) −19.0000 −0.681183
\(779\) −10.0000 −0.358287
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) −30.0000 −1.07280
\(783\) 9.00000 0.321634
\(784\) −3.00000 −0.107143
\(785\) 7.00000 0.249841
\(786\) −8.00000 −0.285351
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 6.00000 0.213741
\(789\) −14.0000 −0.498413
\(790\) −4.00000 −0.142314
\(791\) 6.00000 0.213335
\(792\) −2.00000 −0.0710669
\(793\) 0 0
\(794\) 18.0000 0.638796
\(795\) −1.00000 −0.0354663
\(796\) 10.0000 0.354441
\(797\) −2.00000 −0.0708436 −0.0354218 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) 4.00000 0.141598
\(799\) 10.0000 0.353775
\(800\) 4.00000 0.141421
\(801\) 2.00000 0.0706665
\(802\) 27.0000 0.953403
\(803\) −26.0000 −0.917520
\(804\) −2.00000 −0.0705346
\(805\) 12.0000 0.422944
\(806\) 0 0
\(807\) 14.0000 0.492823
\(808\) 5.00000 0.175899
\(809\) 5.00000 0.175791 0.0878953 0.996130i \(-0.471986\pi\)
0.0878953 + 0.996130i \(0.471986\pi\)
\(810\) 1.00000 0.0351364
\(811\) −36.0000 −1.26413 −0.632065 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 18.0000 0.631676
\(813\) −8.00000 −0.280572
\(814\) 22.0000 0.771100
\(815\) −20.0000 −0.700569
\(816\) −5.00000 −0.175035
\(817\) −20.0000 −0.699711
\(818\) −23.0000 −0.804176
\(819\) 0 0
\(820\) −5.00000 −0.174608
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 17.0000 0.592943
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −10.0000 −0.348367
\(825\) 8.00000 0.278524
\(826\) −16.0000 −0.556711
\(827\) −8.00000 −0.278187 −0.139094 0.990279i \(-0.544419\pi\)
−0.139094 + 0.990279i \(0.544419\pi\)
\(828\) 6.00000 0.208514
\(829\) −35.0000 −1.21560 −0.607800 0.794090i \(-0.707948\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(830\) 6.00000 0.208263
\(831\) 11.0000 0.381586
\(832\) 0 0
\(833\) −15.0000 −0.519719
\(834\) −12.0000 −0.415526
\(835\) −24.0000 −0.830554
\(836\) −4.00000 −0.138343
\(837\) 4.00000 0.138260
\(838\) 32.0000 1.10542
\(839\) 44.0000 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(840\) 2.00000 0.0690066
\(841\) 52.0000 1.79310
\(842\) 23.0000 0.792632
\(843\) −25.0000 −0.861046
\(844\) 24.0000 0.826114
\(845\) 0 0
\(846\) −2.00000 −0.0687614
\(847\) 14.0000 0.481046
\(848\) −1.00000 −0.0343401
\(849\) −26.0000 −0.892318
\(850\) 20.0000 0.685994
\(851\) −66.0000 −2.26245
\(852\) 14.0000 0.479632
\(853\) 49.0000 1.67773 0.838864 0.544341i \(-0.183220\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(854\) −22.0000 −0.752825
\(855\) 2.00000 0.0683986
\(856\) 18.0000 0.615227
\(857\) 45.0000 1.53717 0.768585 0.639747i \(-0.220961\pi\)
0.768585 + 0.639747i \(0.220961\pi\)
\(858\) 0 0
\(859\) −50.0000 −1.70598 −0.852989 0.521929i \(-0.825213\pi\)
−0.852989 + 0.521929i \(0.825213\pi\)
\(860\) −10.0000 −0.340997
\(861\) 10.0000 0.340799
\(862\) 2.00000 0.0681203
\(863\) 46.0000 1.56586 0.782929 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) 1.00000 0.0340207
\(865\) 22.0000 0.748022
\(866\) 21.0000 0.713609
\(867\) −8.00000 −0.271694
\(868\) 8.00000 0.271538
\(869\) −8.00000 −0.271381
\(870\) 9.00000 0.305129
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) −2.00000 −0.0676897
\(874\) 12.0000 0.405906
\(875\) −18.0000 −0.608511
\(876\) 13.0000 0.439229
\(877\) 37.0000 1.24940 0.624701 0.780864i \(-0.285221\pi\)
0.624701 + 0.780864i \(0.285221\pi\)
\(878\) −10.0000 −0.337484
\(879\) 1.00000 0.0337292
\(880\) −2.00000 −0.0674200
\(881\) 17.0000 0.572745 0.286372 0.958118i \(-0.407551\pi\)
0.286372 + 0.958118i \(0.407551\pi\)
\(882\) 3.00000 0.101015
\(883\) −8.00000 −0.269221 −0.134611 0.990899i \(-0.542978\pi\)
−0.134611 + 0.990899i \(0.542978\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) −20.0000 −0.671913
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) −11.0000 −0.369136
\(889\) 24.0000 0.804934
\(890\) 2.00000 0.0670402
\(891\) 2.00000 0.0670025
\(892\) −16.0000 −0.535720
\(893\) −4.00000 −0.133855
\(894\) 3.00000 0.100335
\(895\) 6.00000 0.200558
\(896\) 2.00000 0.0668153
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) 36.0000 1.20067
\(900\) −4.00000 −0.133333
\(901\) −5.00000 −0.166574
\(902\) −10.0000 −0.332964
\(903\) 20.0000 0.665558
\(904\) 3.00000 0.0997785
\(905\) −5.00000 −0.166206
\(906\) −6.00000 −0.199337
\(907\) −44.0000 −1.46100 −0.730498 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(908\) 14.0000 0.464606
\(909\) −5.00000 −0.165840
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) 2.00000 0.0662266
\(913\) 12.0000 0.397142
\(914\) −3.00000 −0.0992312
\(915\) −11.0000 −0.363649
\(916\) 10.0000 0.330409
\(917\) 16.0000 0.528367
\(918\) 5.00000 0.165025
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 6.00000 0.197814
\(921\) 14.0000 0.461316
\(922\) −3.00000 −0.0987997
\(923\) 0 0
\(924\) 4.00000 0.131590
\(925\) 44.0000 1.44671
\(926\) 14.0000 0.460069
\(927\) 10.0000 0.328443
\(928\) 9.00000 0.295439
\(929\) −23.0000 −0.754606 −0.377303 0.926090i \(-0.623148\pi\)
−0.377303 + 0.926090i \(0.623148\pi\)
\(930\) 4.00000 0.131165
\(931\) 6.00000 0.196642
\(932\) −6.00000 −0.196537
\(933\) −6.00000 −0.196431
\(934\) 22.0000 0.719862
\(935\) −10.0000 −0.327035
\(936\) 0 0
\(937\) −1.00000 −0.0326686 −0.0163343 0.999867i \(-0.505200\pi\)
−0.0163343 + 0.999867i \(0.505200\pi\)
\(938\) 4.00000 0.130605
\(939\) −6.00000 −0.195803
\(940\) −2.00000 −0.0652328
\(941\) −22.0000 −0.717180 −0.358590 0.933495i \(-0.616742\pi\)
−0.358590 + 0.933495i \(0.616742\pi\)
\(942\) −7.00000 −0.228072
\(943\) 30.0000 0.976934
\(944\) −8.00000 −0.260378
\(945\) −2.00000 −0.0650600
\(946\) −20.0000 −0.650256
\(947\) 8.00000 0.259965 0.129983 0.991516i \(-0.458508\pi\)
0.129983 + 0.991516i \(0.458508\pi\)
\(948\) 4.00000 0.129914
\(949\) 0 0
\(950\) −8.00000 −0.259554
\(951\) 33.0000 1.07010
\(952\) 10.0000 0.324102
\(953\) 54.0000 1.74923 0.874616 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 1.00000 0.0323762
\(955\) −4.00000 −0.129437
\(956\) −6.00000 −0.194054
\(957\) 18.0000 0.581857
\(958\) −32.0000 −1.03387
\(959\) −34.0000 −1.09792
\(960\) 1.00000 0.0322749
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 7.00000 0.225455
\(965\) 17.0000 0.547249
\(966\) −12.0000 −0.386094
\(967\) −50.0000 −1.60789 −0.803946 0.594703i \(-0.797270\pi\)
−0.803946 + 0.594703i \(0.797270\pi\)
\(968\) 7.00000 0.224989
\(969\) 10.0000 0.321246
\(970\) −2.00000 −0.0642161
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 24.0000 0.769405
\(974\) 26.0000 0.833094
\(975\) 0 0
\(976\) −11.0000 −0.352101
\(977\) 21.0000 0.671850 0.335925 0.941889i \(-0.390951\pi\)
0.335925 + 0.941889i \(0.390951\pi\)
\(978\) 20.0000 0.639529
\(979\) 4.00000 0.127841
\(980\) 3.00000 0.0958315
\(981\) −2.00000 −0.0638551
\(982\) 30.0000 0.957338
\(983\) 60.0000 1.91370 0.956851 0.290578i \(-0.0938475\pi\)
0.956851 + 0.290578i \(0.0938475\pi\)
\(984\) 5.00000 0.159394
\(985\) −6.00000 −0.191176
\(986\) 45.0000 1.43309
\(987\) 4.00000 0.127321
\(988\) 0 0
\(989\) 60.0000 1.90789
\(990\) 2.00000 0.0635642
\(991\) 18.0000 0.571789 0.285894 0.958261i \(-0.407709\pi\)
0.285894 + 0.958261i \(0.407709\pi\)
\(992\) 4.00000 0.127000
\(993\) 28.0000 0.888553
\(994\) −28.0000 −0.888106
\(995\) −10.0000 −0.317021
\(996\) −6.00000 −0.190117
\(997\) −23.0000 −0.728417 −0.364209 0.931317i \(-0.618661\pi\)
−0.364209 + 0.931317i \(0.618661\pi\)
\(998\) 0 0
\(999\) 11.0000 0.348025
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 1014.2.a.a.1.1 1
3.2 odd 2 3042.2.a.m.1.1 1
4.3 odd 2 8112.2.a.x.1.1 1
13.2 odd 12 1014.2.i.e.823.1 4
13.3 even 3 78.2.e.b.61.1 yes 2
13.4 even 6 1014.2.e.d.991.1 2
13.5 odd 4 1014.2.b.a.337.2 2
13.6 odd 12 1014.2.i.e.361.2 4
13.7 odd 12 1014.2.i.e.361.1 4
13.8 odd 4 1014.2.b.a.337.1 2
13.9 even 3 78.2.e.b.55.1 2
13.10 even 6 1014.2.e.d.529.1 2
13.11 odd 12 1014.2.i.e.823.2 4
13.12 even 2 1014.2.a.e.1.1 1
39.5 even 4 3042.2.b.d.1351.1 2
39.8 even 4 3042.2.b.d.1351.2 2
39.29 odd 6 234.2.h.b.217.1 2
39.35 odd 6 234.2.h.b.55.1 2
39.38 odd 2 3042.2.a.d.1.1 1
52.3 odd 6 624.2.q.b.529.1 2
52.35 odd 6 624.2.q.b.289.1 2
52.51 odd 2 8112.2.a.bb.1.1 1
65.3 odd 12 1950.2.z.b.1699.1 4
65.9 even 6 1950.2.i.b.601.1 2
65.22 odd 12 1950.2.z.b.1849.1 4
65.29 even 6 1950.2.i.b.451.1 2
65.42 odd 12 1950.2.z.b.1699.2 4
65.48 odd 12 1950.2.z.b.1849.2 4
156.35 even 6 1872.2.t.i.289.1 2
156.107 even 6 1872.2.t.i.1153.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.e.b.55.1 2 13.9 even 3
78.2.e.b.61.1 yes 2 13.3 even 3
234.2.h.b.55.1 2 39.35 odd 6
234.2.h.b.217.1 2 39.29 odd 6
624.2.q.b.289.1 2 52.35 odd 6
624.2.q.b.529.1 2 52.3 odd 6
1014.2.a.a.1.1 1 1.1 even 1 trivial
1014.2.a.e.1.1 1 13.12 even 2
1014.2.b.a.337.1 2 13.8 odd 4
1014.2.b.a.337.2 2 13.5 odd 4
1014.2.e.d.529.1 2 13.10 even 6
1014.2.e.d.991.1 2 13.4 even 6
1014.2.i.e.361.1 4 13.7 odd 12
1014.2.i.e.361.2 4 13.6 odd 12
1014.2.i.e.823.1 4 13.2 odd 12
1014.2.i.e.823.2 4 13.11 odd 12
1872.2.t.i.289.1 2 156.35 even 6
1872.2.t.i.1153.1 2 156.107 even 6
1950.2.i.b.451.1 2 65.29 even 6
1950.2.i.b.601.1 2 65.9 even 6
1950.2.z.b.1699.1 4 65.3 odd 12
1950.2.z.b.1699.2 4 65.42 odd 12
1950.2.z.b.1849.1 4 65.22 odd 12
1950.2.z.b.1849.2 4 65.48 odd 12
3042.2.a.d.1.1 1 39.38 odd 2
3042.2.a.m.1.1 1 3.2 odd 2
3042.2.b.d.1351.1 2 39.5 even 4
3042.2.b.d.1351.2 2 39.8 even 4
8112.2.a.x.1.1 1 4.3 odd 2
8112.2.a.bb.1.1 1 52.51 odd 2