Properties

Label 2535.2.a.b.1.1
Level $2535$
Weight $2$
Character 2535.1
Self dual yes
Analytic conductor $20.242$
Analytic rank $0$
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] = [2535,2,Mod(1,2535)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2535, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2535.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2535.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: \(20.2420769124\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2535.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +3.00000 q^{7} +1.00000 q^{9} +2.00000 q^{10} +5.00000 q^{11} +2.00000 q^{12} -6.00000 q^{14} -1.00000 q^{15} -4.00000 q^{16} +5.00000 q^{17} -2.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} +3.00000 q^{21} -10.0000 q^{22} -1.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} +6.00000 q^{28} +10.0000 q^{29} +2.00000 q^{30} +2.00000 q^{31} +8.00000 q^{32} +5.00000 q^{33} -10.0000 q^{34} -3.00000 q^{35} +2.00000 q^{36} +3.00000 q^{37} +4.00000 q^{38} +9.00000 q^{41} -6.00000 q^{42} -4.00000 q^{43} +10.0000 q^{44} -1.00000 q^{45} +2.00000 q^{46} -10.0000 q^{47} -4.00000 q^{48} +2.00000 q^{49} -2.00000 q^{50} +5.00000 q^{51} +9.00000 q^{53} -2.00000 q^{54} -5.00000 q^{55} -2.00000 q^{57} -20.0000 q^{58} -2.00000 q^{60} -11.0000 q^{61} -4.00000 q^{62} +3.00000 q^{63} -8.00000 q^{64} -10.0000 q^{66} +4.00000 q^{67} +10.0000 q^{68} -1.00000 q^{69} +6.00000 q^{70} -15.0000 q^{71} -6.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +15.0000 q^{77} -11.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -18.0000 q^{82} -8.00000 q^{83} +6.00000 q^{84} -5.00000 q^{85} +8.00000 q^{86} +10.0000 q^{87} +11.0000 q^{89} +2.00000 q^{90} -2.00000 q^{92} +2.00000 q^{93} +20.0000 q^{94} +2.00000 q^{95} +8.00000 q^{96} +9.00000 q^{97} -4.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.00000 1.00000
\(5\) −1.00000 −0.447214
\(6\) −2.00000 −0.816497
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 2.00000 0.577350
\(13\) 0 0
\(14\) −6.00000 −1.60357
\(15\) −1.00000 −0.258199
\(16\) −4.00000 −1.00000
\(17\) 5.00000 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(18\) −2.00000 −0.471405
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) 3.00000 0.654654
\(22\) −10.0000 −2.13201
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 6.00000 1.13389
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 2.00000 0.365148
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 8.00000 1.41421
\(33\) 5.00000 0.870388
\(34\) −10.0000 −1.71499
\(35\) −3.00000 −0.507093
\(36\) 2.00000 0.333333
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) −6.00000 −0.925820
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 10.0000 1.50756
\(45\) −1.00000 −0.149071
\(46\) 2.00000 0.294884
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) −4.00000 −0.577350
\(49\) 2.00000 0.285714
\(50\) −2.00000 −0.282843
\(51\) 5.00000 0.700140
\(52\) 0 0
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) −2.00000 −0.272166
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) −20.0000 −2.62613
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −2.00000 −0.258199
\(61\) −11.0000 −1.40841 −0.704203 0.709999i \(-0.748695\pi\)
−0.704203 + 0.709999i \(0.748695\pi\)
\(62\) −4.00000 −0.508001
\(63\) 3.00000 0.377964
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) −10.0000 −1.23091
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 10.0000 1.21268
\(69\) −1.00000 −0.120386
\(70\) 6.00000 0.717137
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −6.00000 −0.697486
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) 15.0000 1.70941
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) −18.0000 −1.98777
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 6.00000 0.654654
\(85\) −5.00000 −0.542326
\(86\) 8.00000 0.862662
\(87\) 10.0000 1.07211
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 2.00000 0.207390
\(94\) 20.0000 2.06284
\(95\) 2.00000 0.205196
\(96\) 8.00000 0.816497
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) −4.00000 −0.404061
\(99\) 5.00000 0.502519
\(100\) 2.00000 0.200000
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) −10.0000 −0.990148
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) −18.0000 −1.74831
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 2.00000 0.192450
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 10.0000 0.953463
\(111\) 3.00000 0.284747
\(112\) −12.0000 −1.13389
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 4.00000 0.374634
\(115\) 1.00000 0.0932505
\(116\) 20.0000 1.85695
\(117\) 0 0
\(118\) 0 0
\(119\) 15.0000 1.37505
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 22.0000 1.99179
\(123\) 9.00000 0.811503
\(124\) 4.00000 0.359211
\(125\) −1.00000 −0.0894427
\(126\) −6.00000 −0.534522
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) 0 0
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 10.0000 0.870388
\(133\) −6.00000 −0.520266
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 2.00000 0.170251
\(139\) −17.0000 −1.44192 −0.720961 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) −6.00000 −0.507093
\(141\) −10.0000 −0.842152
\(142\) 30.0000 2.51754
\(143\) 0 0
\(144\) −4.00000 −0.333333
\(145\) −10.0000 −0.830455
\(146\) 12.0000 0.993127
\(147\) 2.00000 0.164957
\(148\) 6.00000 0.493197
\(149\) 7.00000 0.573462 0.286731 0.958011i \(-0.407431\pi\)
0.286731 + 0.958011i \(0.407431\pi\)
\(150\) −2.00000 −0.163299
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) 5.00000 0.404226
\(154\) −30.0000 −2.41747
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 22.0000 1.75023
\(159\) 9.00000 0.713746
\(160\) −8.00000 −0.632456
\(161\) −3.00000 −0.236433
\(162\) −2.00000 −0.157135
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 18.0000 1.40556
\(165\) −5.00000 −0.389249
\(166\) 16.0000 1.24184
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 10.0000 0.766965
\(171\) −2.00000 −0.152944
\(172\) −8.00000 −0.609994
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) −20.0000 −1.51620
\(175\) 3.00000 0.226779
\(176\) −20.0000 −1.50756
\(177\) 0 0
\(178\) −22.0000 −1.64897
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) −2.00000 −0.149071
\(181\) −23.0000 −1.70958 −0.854788 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) 0 0
\(183\) −11.0000 −0.813143
\(184\) 0 0
\(185\) −3.00000 −0.220564
\(186\) −4.00000 −0.293294
\(187\) 25.0000 1.82818
\(188\) −20.0000 −1.45865
\(189\) 3.00000 0.218218
\(190\) −4.00000 −0.290191
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) −8.00000 −0.577350
\(193\) −13.0000 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) −18.0000 −1.29232
\(195\) 0 0
\(196\) 4.00000 0.285714
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) −10.0000 −0.710669
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 24.0000 1.68863
\(203\) 30.0000 2.10559
\(204\) 10.0000 0.700140
\(205\) −9.00000 −0.628587
\(206\) −8.00000 −0.557386
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) −10.0000 −0.691714
\(210\) 6.00000 0.414039
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 18.0000 1.23625
\(213\) −15.0000 −1.02778
\(214\) −6.00000 −0.410152
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 32.0000 2.16731
\(219\) −6.00000 −0.405442
\(220\) −10.0000 −0.674200
\(221\) 0 0
\(222\) −6.00000 −0.402694
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 24.0000 1.60357
\(225\) 1.00000 0.0666667
\(226\) −4.00000 −0.266076
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) −4.00000 −0.264906
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −2.00000 −0.131876
\(231\) 15.0000 0.986928
\(232\) 0 0
\(233\) −25.0000 −1.63780 −0.818902 0.573933i \(-0.805417\pi\)
−0.818902 + 0.573933i \(0.805417\pi\)
\(234\) 0 0
\(235\) 10.0000 0.652328
\(236\) 0 0
\(237\) −11.0000 −0.714527
\(238\) −30.0000 −1.94461
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 4.00000 0.258199
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −28.0000 −1.79991
\(243\) 1.00000 0.0641500
\(244\) −22.0000 −1.40841
\(245\) −2.00000 −0.127775
\(246\) −18.0000 −1.14764
\(247\) 0 0
\(248\) 0 0
\(249\) −8.00000 −0.506979
\(250\) 2.00000 0.126491
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 6.00000 0.377964
\(253\) −5.00000 −0.314347
\(254\) −28.0000 −1.75688
\(255\) −5.00000 −0.313112
\(256\) 16.0000 1.00000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 8.00000 0.498058
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) −12.0000 −0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 12.0000 0.735767
\(267\) 11.0000 0.673189
\(268\) 8.00000 0.488678
\(269\) 32.0000 1.95107 0.975537 0.219834i \(-0.0705517\pi\)
0.975537 + 0.219834i \(0.0705517\pi\)
\(270\) 2.00000 0.121716
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −20.0000 −1.21268
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 5.00000 0.301511
\(276\) −2.00000 −0.120386
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 34.0000 2.03918
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 20.0000 1.19098
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) −30.0000 −1.78017
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) 27.0000 1.59376
\(288\) 8.00000 0.471405
\(289\) 8.00000 0.470588
\(290\) 20.0000 1.17444
\(291\) 9.00000 0.527589
\(292\) −12.0000 −0.702247
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) −4.00000 −0.233285
\(295\) 0 0
\(296\) 0 0
\(297\) 5.00000 0.290129
\(298\) −14.0000 −0.810998
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) −12.0000 −0.691669
\(302\) −24.0000 −1.38104
\(303\) −12.0000 −0.689382
\(304\) 8.00000 0.458831
\(305\) 11.0000 0.629858
\(306\) −10.0000 −0.571662
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 30.0000 1.70941
\(309\) 4.00000 0.227552
\(310\) 4.00000 0.227185
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −44.0000 −2.48306
\(315\) −3.00000 −0.169031
\(316\) −22.0000 −1.23760
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −18.0000 −1.00939
\(319\) 50.0000 2.79946
\(320\) 8.00000 0.447214
\(321\) 3.00000 0.167444
\(322\) 6.00000 0.334367
\(323\) −10.0000 −0.556415
\(324\) 2.00000 0.111111
\(325\) 0 0
\(326\) −22.0000 −1.21847
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) −30.0000 −1.65395
\(330\) 10.0000 0.550482
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) −16.0000 −0.878114
\(333\) 3.00000 0.164399
\(334\) −16.0000 −0.875481
\(335\) −4.00000 −0.218543
\(336\) −12.0000 −0.654654
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 0 0
\(339\) 2.00000 0.108625
\(340\) −10.0000 −0.542326
\(341\) 10.0000 0.541530
\(342\) 4.00000 0.216295
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 1.00000 0.0538382
\(346\) 4.00000 0.215041
\(347\) −1.00000 −0.0536828 −0.0268414 0.999640i \(-0.508545\pi\)
−0.0268414 + 0.999640i \(0.508545\pi\)
\(348\) 20.0000 1.07211
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) −6.00000 −0.320713
\(351\) 0 0
\(352\) 40.0000 2.13201
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 15.0000 0.796117
\(356\) 22.0000 1.16600
\(357\) 15.0000 0.793884
\(358\) 12.0000 0.634220
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 46.0000 2.41771
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 22.0000 1.14996
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 4.00000 0.208514
\(369\) 9.00000 0.468521
\(370\) 6.00000 0.311925
\(371\) 27.0000 1.40177
\(372\) 4.00000 0.207390
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) −50.0000 −2.58544
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 0 0
\(378\) −6.00000 −0.308607
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 4.00000 0.205196
\(381\) 14.0000 0.717242
\(382\) 40.0000 2.04658
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) −15.0000 −0.764471
\(386\) 26.0000 1.32337
\(387\) −4.00000 −0.203331
\(388\) 18.0000 0.913812
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) −24.0000 −1.20910
\(395\) 11.0000 0.553470
\(396\) 10.0000 0.502519
\(397\) 19.0000 0.953583 0.476791 0.879017i \(-0.341800\pi\)
0.476791 + 0.879017i \(0.341800\pi\)
\(398\) −8.00000 −0.401004
\(399\) −6.00000 −0.300376
\(400\) −4.00000 −0.200000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −8.00000 −0.399004
\(403\) 0 0
\(404\) −24.0000 −1.19404
\(405\) −1.00000 −0.0496904
\(406\) −60.0000 −2.97775
\(407\) 15.0000 0.743522
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 18.0000 0.888957
\(411\) −6.00000 −0.295958
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 2.00000 0.0982946
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) −17.0000 −0.832494
\(418\) 20.0000 0.978232
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) −6.00000 −0.292770
\(421\) −32.0000 −1.55958 −0.779792 0.626038i \(-0.784675\pi\)
−0.779792 + 0.626038i \(0.784675\pi\)
\(422\) 8.00000 0.389434
\(423\) −10.0000 −0.486217
\(424\) 0 0
\(425\) 5.00000 0.242536
\(426\) 30.0000 1.45350
\(427\) −33.0000 −1.59698
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) −4.00000 −0.192450
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) −12.0000 −0.576018
\(435\) −10.0000 −0.479463
\(436\) −32.0000 −1.53252
\(437\) 2.00000 0.0956730
\(438\) 12.0000 0.573382
\(439\) −33.0000 −1.57500 −0.787502 0.616312i \(-0.788626\pi\)
−0.787502 + 0.616312i \(0.788626\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 35.0000 1.66290 0.831450 0.555599i \(-0.187511\pi\)
0.831450 + 0.555599i \(0.187511\pi\)
\(444\) 6.00000 0.284747
\(445\) −11.0000 −0.521450
\(446\) 0 0
\(447\) 7.00000 0.331089
\(448\) −24.0000 −1.13389
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) −2.00000 −0.0942809
\(451\) 45.0000 2.11897
\(452\) 4.00000 0.188144
\(453\) 12.0000 0.563809
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 13.0000 0.608114 0.304057 0.952654i \(-0.401659\pi\)
0.304057 + 0.952654i \(0.401659\pi\)
\(458\) −28.0000 −1.30835
\(459\) 5.00000 0.233380
\(460\) 2.00000 0.0932505
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) −30.0000 −1.39573
\(463\) −5.00000 −0.232370 −0.116185 0.993228i \(-0.537067\pi\)
−0.116185 + 0.993228i \(0.537067\pi\)
\(464\) −40.0000 −1.85695
\(465\) −2.00000 −0.0927478
\(466\) 50.0000 2.31621
\(467\) −29.0000 −1.34196 −0.670980 0.741475i \(-0.734126\pi\)
−0.670980 + 0.741475i \(0.734126\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) −20.0000 −0.922531
\(471\) 22.0000 1.01371
\(472\) 0 0
\(473\) −20.0000 −0.919601
\(474\) 22.0000 1.01049
\(475\) −2.00000 −0.0917663
\(476\) 30.0000 1.37505
\(477\) 9.00000 0.412082
\(478\) 30.0000 1.37217
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) −8.00000 −0.365148
\(481\) 0 0
\(482\) −28.0000 −1.27537
\(483\) −3.00000 −0.136505
\(484\) 28.0000 1.27273
\(485\) −9.00000 −0.408669
\(486\) −2.00000 −0.0907218
\(487\) −7.00000 −0.317200 −0.158600 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(488\) 0 0
\(489\) 11.0000 0.497437
\(490\) 4.00000 0.180702
\(491\) 16.0000 0.722070 0.361035 0.932552i \(-0.382424\pi\)
0.361035 + 0.932552i \(0.382424\pi\)
\(492\) 18.0000 0.811503
\(493\) 50.0000 2.25189
\(494\) 0 0
\(495\) −5.00000 −0.224733
\(496\) −8.00000 −0.359211
\(497\) −45.0000 −2.01853
\(498\) 16.0000 0.716977
\(499\) −34.0000 −1.52205 −0.761025 0.648723i \(-0.775303\pi\)
−0.761025 + 0.648723i \(0.775303\pi\)
\(500\) −2.00000 −0.0894427
\(501\) 8.00000 0.357414
\(502\) −40.0000 −1.78529
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 10.0000 0.444554
\(507\) 0 0
\(508\) 28.0000 1.24230
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 10.0000 0.442807
\(511\) −18.0000 −0.796273
\(512\) −32.0000 −1.41421
\(513\) −2.00000 −0.0883022
\(514\) −36.0000 −1.58789
\(515\) −4.00000 −0.176261
\(516\) −8.00000 −0.352180
\(517\) −50.0000 −2.19900
\(518\) −18.0000 −0.790875
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) −20.0000 −0.875376
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 12.0000 0.524222
\(525\) 3.00000 0.130931
\(526\) 0 0
\(527\) 10.0000 0.435607
\(528\) −20.0000 −0.870388
\(529\) −22.0000 −0.956522
\(530\) 18.0000 0.781870
\(531\) 0 0
\(532\) −12.0000 −0.520266
\(533\) 0 0
\(534\) −22.0000 −0.952033
\(535\) −3.00000 −0.129701
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) −64.0000 −2.75924
\(539\) 10.0000 0.430730
\(540\) −2.00000 −0.0860663
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) −4.00000 −0.171815
\(543\) −23.0000 −0.987024
\(544\) 40.0000 1.71499
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −12.0000 −0.512615
\(549\) −11.0000 −0.469469
\(550\) −10.0000 −0.426401
\(551\) −20.0000 −0.852029
\(552\) 0 0
\(553\) −33.0000 −1.40330
\(554\) −52.0000 −2.20927
\(555\) −3.00000 −0.127343
\(556\) −34.0000 −1.44192
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) 12.0000 0.507093
\(561\) 25.0000 1.05550
\(562\) −20.0000 −0.843649
\(563\) −41.0000 −1.72794 −0.863972 0.503540i \(-0.832031\pi\)
−0.863972 + 0.503540i \(0.832031\pi\)
\(564\) −20.0000 −0.842152
\(565\) −2.00000 −0.0841406
\(566\) 16.0000 0.672530
\(567\) 3.00000 0.125988
\(568\) 0 0
\(569\) 16.0000 0.670755 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(570\) −4.00000 −0.167542
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) 0 0
\(573\) −20.0000 −0.835512
\(574\) −54.0000 −2.25392
\(575\) −1.00000 −0.0417029
\(576\) −8.00000 −0.333333
\(577\) 21.0000 0.874241 0.437121 0.899403i \(-0.355998\pi\)
0.437121 + 0.899403i \(0.355998\pi\)
\(578\) −16.0000 −0.665512
\(579\) −13.0000 −0.540262
\(580\) −20.0000 −0.830455
\(581\) −24.0000 −0.995688
\(582\) −18.0000 −0.746124
\(583\) 45.0000 1.86371
\(584\) 0 0
\(585\) 0 0
\(586\) 48.0000 1.98286
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 4.00000 0.164957
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) −12.0000 −0.493197
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) −10.0000 −0.410305
\(595\) −15.0000 −0.614940
\(596\) 14.0000 0.573462
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) 4.00000 0.163436 0.0817178 0.996656i \(-0.473959\pi\)
0.0817178 + 0.996656i \(0.473959\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) 24.0000 0.978167
\(603\) 4.00000 0.162893
\(604\) 24.0000 0.976546
\(605\) −14.0000 −0.569181
\(606\) 24.0000 0.974933
\(607\) −40.0000 −1.62355 −0.811775 0.583970i \(-0.801498\pi\)
−0.811775 + 0.583970i \(0.801498\pi\)
\(608\) −16.0000 −0.648886
\(609\) 30.0000 1.21566
\(610\) −22.0000 −0.890754
\(611\) 0 0
\(612\) 10.0000 0.404226
\(613\) −3.00000 −0.121169 −0.0605844 0.998163i \(-0.519296\pi\)
−0.0605844 + 0.998163i \(0.519296\pi\)
\(614\) −38.0000 −1.53356
\(615\) −9.00000 −0.362915
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) −8.00000 −0.321807
\(619\) 2.00000 0.0803868 0.0401934 0.999192i \(-0.487203\pi\)
0.0401934 + 0.999192i \(0.487203\pi\)
\(620\) −4.00000 −0.160644
\(621\) −1.00000 −0.0401286
\(622\) −48.0000 −1.92462
\(623\) 33.0000 1.32212
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 20.0000 0.799361
\(627\) −10.0000 −0.399362
\(628\) 44.0000 1.75579
\(629\) 15.0000 0.598089
\(630\) 6.00000 0.239046
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 24.0000 0.953162
\(635\) −14.0000 −0.555573
\(636\) 18.0000 0.713746
\(637\) 0 0
\(638\) −100.000 −3.95904
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) −6.00000 −0.236801
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) −6.00000 −0.236433
\(645\) 4.00000 0.157500
\(646\) 20.0000 0.786889
\(647\) 21.0000 0.825595 0.412798 0.910823i \(-0.364552\pi\)
0.412798 + 0.910823i \(0.364552\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 6.00000 0.235159
\(652\) 22.0000 0.861586
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 32.0000 1.25130
\(655\) −6.00000 −0.234439
\(656\) −36.0000 −1.40556
\(657\) −6.00000 −0.234082
\(658\) 60.0000 2.33904
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) −10.0000 −0.389249
\(661\) 16.0000 0.622328 0.311164 0.950356i \(-0.399281\pi\)
0.311164 + 0.950356i \(0.399281\pi\)
\(662\) 64.0000 2.48743
\(663\) 0 0
\(664\) 0 0
\(665\) 6.00000 0.232670
\(666\) −6.00000 −0.232495
\(667\) −10.0000 −0.387202
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) 8.00000 0.309067
\(671\) −55.0000 −2.12325
\(672\) 24.0000 0.925820
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) −8.00000 −0.308148
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −7.00000 −0.269032 −0.134516 0.990911i \(-0.542948\pi\)
−0.134516 + 0.990911i \(0.542948\pi\)
\(678\) −4.00000 −0.153619
\(679\) 27.0000 1.03616
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) −20.0000 −0.765840
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) −4.00000 −0.152944
\(685\) 6.00000 0.229248
\(686\) 30.0000 1.14541
\(687\) 14.0000 0.534133
\(688\) 16.0000 0.609994
\(689\) 0 0
\(690\) −2.00000 −0.0761387
\(691\) −6.00000 −0.228251 −0.114125 0.993466i \(-0.536407\pi\)
−0.114125 + 0.993466i \(0.536407\pi\)
\(692\) −4.00000 −0.152057
\(693\) 15.0000 0.569803
\(694\) 2.00000 0.0759190
\(695\) 17.0000 0.644847
\(696\) 0 0
\(697\) 45.0000 1.70450
\(698\) 40.0000 1.51402
\(699\) −25.0000 −0.945587
\(700\) 6.00000 0.226779
\(701\) −4.00000 −0.151078 −0.0755390 0.997143i \(-0.524068\pi\)
−0.0755390 + 0.997143i \(0.524068\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −40.0000 −1.50756
\(705\) 10.0000 0.376622
\(706\) −28.0000 −1.05379
\(707\) −36.0000 −1.35392
\(708\) 0 0
\(709\) −20.0000 −0.751116 −0.375558 0.926799i \(-0.622549\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(710\) −30.0000 −1.12588
\(711\) −11.0000 −0.412532
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) −30.0000 −1.12272
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −15.0000 −0.560185
\(718\) 32.0000 1.19423
\(719\) 12.0000 0.447524 0.223762 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) 4.00000 0.149071
\(721\) 12.0000 0.446903
\(722\) 30.0000 1.11648
\(723\) 14.0000 0.520666
\(724\) −46.0000 −1.70958
\(725\) 10.0000 0.371391
\(726\) −28.0000 −1.03918
\(727\) 6.00000 0.222528 0.111264 0.993791i \(-0.464510\pi\)
0.111264 + 0.993791i \(0.464510\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −12.0000 −0.444140
\(731\) −20.0000 −0.739727
\(732\) −22.0000 −0.813143
\(733\) 15.0000 0.554038 0.277019 0.960864i \(-0.410654\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(734\) −16.0000 −0.590571
\(735\) −2.00000 −0.0737711
\(736\) −8.00000 −0.294884
\(737\) 20.0000 0.736709
\(738\) −18.0000 −0.662589
\(739\) −38.0000 −1.39785 −0.698926 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) −6.00000 −0.220564
\(741\) 0 0
\(742\) −54.0000 −1.98240
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) −7.00000 −0.256460
\(746\) −32.0000 −1.17160
\(747\) −8.00000 −0.292705
\(748\) 50.0000 1.82818
\(749\) 9.00000 0.328853
\(750\) 2.00000 0.0730297
\(751\) −45.0000 −1.64207 −0.821037 0.570875i \(-0.806604\pi\)
−0.821037 + 0.570875i \(0.806604\pi\)
\(752\) 40.0000 1.45865
\(753\) 20.0000 0.728841
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 6.00000 0.218218
\(757\) 36.0000 1.30844 0.654221 0.756303i \(-0.272997\pi\)
0.654221 + 0.756303i \(0.272997\pi\)
\(758\) 12.0000 0.435860
\(759\) −5.00000 −0.181489
\(760\) 0 0
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) −28.0000 −1.01433
\(763\) −48.0000 −1.73772
\(764\) −40.0000 −1.44715
\(765\) −5.00000 −0.180775
\(766\) −36.0000 −1.30073
\(767\) 0 0
\(768\) 16.0000 0.577350
\(769\) 12.0000 0.432731 0.216366 0.976312i \(-0.430580\pi\)
0.216366 + 0.976312i \(0.430580\pi\)
\(770\) 30.0000 1.08112
\(771\) 18.0000 0.648254
\(772\) −26.0000 −0.935760
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 8.00000 0.287554
\(775\) 2.00000 0.0718421
\(776\) 0 0
\(777\) 9.00000 0.322873
\(778\) 48.0000 1.72088
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) −75.0000 −2.68371
\(782\) 10.0000 0.357599
\(783\) 10.0000 0.357371
\(784\) −8.00000 −0.285714
\(785\) −22.0000 −0.785214
\(786\) −12.0000 −0.428026
\(787\) −44.0000 −1.56843 −0.784215 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) 24.0000 0.854965
\(789\) 0 0
\(790\) −22.0000 −0.782725
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) 0 0
\(794\) −38.0000 −1.34857
\(795\) −9.00000 −0.319197
\(796\) 8.00000 0.283552
\(797\) −5.00000 −0.177109 −0.0885545 0.996071i \(-0.528225\pi\)
−0.0885545 + 0.996071i \(0.528225\pi\)
\(798\) 12.0000 0.424795
\(799\) −50.0000 −1.76887
\(800\) 8.00000 0.282843
\(801\) 11.0000 0.388666
\(802\) −36.0000 −1.27120
\(803\) −30.0000 −1.05868
\(804\) 8.00000 0.282138
\(805\) 3.00000 0.105736
\(806\) 0 0
\(807\) 32.0000 1.12645
\(808\) 0 0
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 2.00000 0.0702728
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 60.0000 2.10559
\(813\) 2.00000 0.0701431
\(814\) −30.0000 −1.05150
\(815\) −11.0000 −0.385313
\(816\) −20.0000 −0.700140
\(817\) 8.00000 0.279885
\(818\) −52.0000 −1.81814
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) 41.0000 1.43091 0.715455 0.698659i \(-0.246219\pi\)
0.715455 + 0.698659i \(0.246219\pi\)
\(822\) 12.0000 0.418548
\(823\) −48.0000 −1.67317 −0.836587 0.547833i \(-0.815453\pi\)
−0.836587 + 0.547833i \(0.815453\pi\)
\(824\) 0 0
\(825\) 5.00000 0.174078
\(826\) 0 0
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) −2.00000 −0.0695048
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −16.0000 −0.555368
\(831\) 26.0000 0.901930
\(832\) 0 0
\(833\) 10.0000 0.346479
\(834\) 34.0000 1.17732
\(835\) −8.00000 −0.276851
\(836\) −20.0000 −0.691714
\(837\) 2.00000 0.0691301
\(838\) −52.0000 −1.79631
\(839\) −7.00000 −0.241667 −0.120833 0.992673i \(-0.538557\pi\)
−0.120833 + 0.992673i \(0.538557\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 64.0000 2.20559
\(843\) 10.0000 0.344418
\(844\) −8.00000 −0.275371
\(845\) 0 0
\(846\) 20.0000 0.687614
\(847\) 42.0000 1.44314
\(848\) −36.0000 −1.23625
\(849\) −8.00000 −0.274559
\(850\) −10.0000 −0.342997
\(851\) −3.00000 −0.102839
\(852\) −30.0000 −1.02778
\(853\) −51.0000 −1.74621 −0.873103 0.487535i \(-0.837896\pi\)
−0.873103 + 0.487535i \(0.837896\pi\)
\(854\) 66.0000 2.25847
\(855\) 2.00000 0.0683986
\(856\) 0 0
\(857\) −17.0000 −0.580709 −0.290354 0.956919i \(-0.593773\pi\)
−0.290354 + 0.956919i \(0.593773\pi\)
\(858\) 0 0
\(859\) 35.0000 1.19418 0.597092 0.802173i \(-0.296323\pi\)
0.597092 + 0.802173i \(0.296323\pi\)
\(860\) 8.00000 0.272798
\(861\) 27.0000 0.920158
\(862\) −32.0000 −1.08992
\(863\) 22.0000 0.748889 0.374444 0.927249i \(-0.377833\pi\)
0.374444 + 0.927249i \(0.377833\pi\)
\(864\) 8.00000 0.272166
\(865\) 2.00000 0.0680020
\(866\) −48.0000 −1.63111
\(867\) 8.00000 0.271694
\(868\) 12.0000 0.407307
\(869\) −55.0000 −1.86575
\(870\) 20.0000 0.678064
\(871\) 0 0
\(872\) 0 0
\(873\) 9.00000 0.304604
\(874\) −4.00000 −0.135302
\(875\) −3.00000 −0.101419
\(876\) −12.0000 −0.405442
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 66.0000 2.22739
\(879\) −24.0000 −0.809500
\(880\) 20.0000 0.674200
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) −4.00000 −0.134687
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −70.0000 −2.35170
\(887\) −15.0000 −0.503651 −0.251825 0.967773i \(-0.581031\pi\)
−0.251825 + 0.967773i \(0.581031\pi\)
\(888\) 0 0
\(889\) 42.0000 1.40863
\(890\) 22.0000 0.737442
\(891\) 5.00000 0.167506
\(892\) 0 0
\(893\) 20.0000 0.669274
\(894\) −14.0000 −0.468230
\(895\) 6.00000 0.200558
\(896\) 0 0
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) 20.0000 0.667037
\(900\) 2.00000 0.0666667
\(901\) 45.0000 1.49917
\(902\) −90.0000 −2.99667
\(903\) −12.0000 −0.399335
\(904\) 0 0
\(905\) 23.0000 0.764546
\(906\) −24.0000 −0.797347
\(907\) 2.00000 0.0664089 0.0332045 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) 36.0000 1.19470
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 8.00000 0.264906
\(913\) −40.0000 −1.32381
\(914\) −26.0000 −0.860004
\(915\) 11.0000 0.363649
\(916\) 28.0000 0.925146
\(917\) 18.0000 0.594412
\(918\) −10.0000 −0.330049
\(919\) 29.0000 0.956622 0.478311 0.878191i \(-0.341249\pi\)
0.478311 + 0.878191i \(0.341249\pi\)
\(920\) 0 0
\(921\) 19.0000 0.626071
\(922\) 6.00000 0.197599
\(923\) 0 0
\(924\) 30.0000 0.986928
\(925\) 3.00000 0.0986394
\(926\) 10.0000 0.328620
\(927\) 4.00000 0.131377
\(928\) 80.0000 2.62613
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) 4.00000 0.131165
\(931\) −4.00000 −0.131095
\(932\) −50.0000 −1.63780
\(933\) 24.0000 0.785725
\(934\) 58.0000 1.89782
\(935\) −25.0000 −0.817587
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −24.0000 −0.783628
\(939\) −10.0000 −0.326338
\(940\) 20.0000 0.652328
\(941\) 23.0000 0.749779 0.374889 0.927070i \(-0.377681\pi\)
0.374889 + 0.927070i \(0.377681\pi\)
\(942\) −44.0000 −1.43360
\(943\) −9.00000 −0.293080
\(944\) 0 0
\(945\) −3.00000 −0.0975900
\(946\) 40.0000 1.30051
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) −22.0000 −0.714527
\(949\) 0 0
\(950\) 4.00000 0.129777
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −11.0000 −0.356325 −0.178162 0.984001i \(-0.557015\pi\)
−0.178162 + 0.984001i \(0.557015\pi\)
\(954\) −18.0000 −0.582772
\(955\) 20.0000 0.647185
\(956\) −30.0000 −0.970269
\(957\) 50.0000 1.61627
\(958\) 10.0000 0.323085
\(959\) −18.0000 −0.581250
\(960\) 8.00000 0.258199
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 3.00000 0.0966736
\(964\) 28.0000 0.901819
\(965\) 13.0000 0.418485
\(966\) 6.00000 0.193047
\(967\) 40.0000 1.28631 0.643157 0.765735i \(-0.277624\pi\)
0.643157 + 0.765735i \(0.277624\pi\)
\(968\) 0 0
\(969\) −10.0000 −0.321246
\(970\) 18.0000 0.577945
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 2.00000 0.0641500
\(973\) −51.0000 −1.63498
\(974\) 14.0000 0.448589
\(975\) 0 0
\(976\) 44.0000 1.40841
\(977\) −12.0000 −0.383914 −0.191957 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) −22.0000 −0.703482
\(979\) 55.0000 1.75781
\(980\) −4.00000 −0.127775
\(981\) −16.0000 −0.510841
\(982\) −32.0000 −1.02116
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) −100.000 −3.18465
\(987\) −30.0000 −0.954911
\(988\) 0 0
\(989\) 4.00000 0.127193
\(990\) 10.0000 0.317821
\(991\) 39.0000 1.23888 0.619438 0.785046i \(-0.287361\pi\)
0.619438 + 0.785046i \(0.287361\pi\)
\(992\) 16.0000 0.508001
\(993\) −32.0000 −1.01549
\(994\) 90.0000 2.85463
\(995\) −4.00000 −0.126809
\(996\) −16.0000 −0.506979
\(997\) −16.0000 −0.506725 −0.253363 0.967371i \(-0.581537\pi\)
−0.253363 + 0.967371i \(0.581537\pi\)
\(998\) 68.0000 2.15250
\(999\) 3.00000 0.0949158
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 2535.2.a.b.1.1 1
3.2 odd 2 7605.2.a.v.1.1 1
13.12 even 2 195.2.a.d.1.1 1
39.38 odd 2 585.2.a.a.1.1 1
52.51 odd 2 3120.2.a.n.1.1 1
65.12 odd 4 975.2.c.b.274.2 2
65.38 odd 4 975.2.c.b.274.1 2
65.64 even 2 975.2.a.b.1.1 1
91.90 odd 2 9555.2.a.t.1.1 1
156.155 even 2 9360.2.a.w.1.1 1
195.38 even 4 2925.2.c.d.2224.2 2
195.77 even 4 2925.2.c.d.2224.1 2
195.194 odd 2 2925.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.d.1.1 1 13.12 even 2
585.2.a.a.1.1 1 39.38 odd 2
975.2.a.b.1.1 1 65.64 even 2
975.2.c.b.274.1 2 65.38 odd 4
975.2.c.b.274.2 2 65.12 odd 4
2535.2.a.b.1.1 1 1.1 even 1 trivial
2925.2.a.t.1.1 1 195.194 odd 2
2925.2.c.d.2224.1 2 195.77 even 4
2925.2.c.d.2224.2 2 195.38 even 4
3120.2.a.n.1.1 1 52.51 odd 2
7605.2.a.v.1.1 1 3.2 odd 2
9360.2.a.w.1.1 1 156.155 even 2
9555.2.a.t.1.1 1 91.90 odd 2