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Properties

Label 7440.2.a.k.1.1
Level $7440$
Weight $2$
Character 7440.1
Self dual yes
Analytic conductor $59.409$
Analytic rank $1$
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] = [7440,2,Mod(1,7440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("7440.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7440.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: \(59.4086991038\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7440.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +3.00000 q^{11} +2.00000 q^{13} -1.00000 q^{15} -5.00000 q^{19} -1.00000 q^{21} -9.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} -1.00000 q^{31} -3.00000 q^{33} +1.00000 q^{35} +8.00000 q^{37} -2.00000 q^{39} -11.0000 q^{43} +1.00000 q^{45} +6.00000 q^{47} -6.00000 q^{49} -9.00000 q^{53} +3.00000 q^{55} +5.00000 q^{57} -6.00000 q^{59} -10.0000 q^{61} +1.00000 q^{63} +2.00000 q^{65} -14.0000 q^{67} +9.00000 q^{69} -9.00000 q^{71} -1.00000 q^{73} -1.00000 q^{75} +3.00000 q^{77} +1.00000 q^{79} +1.00000 q^{81} +12.0000 q^{83} -9.00000 q^{89} +2.00000 q^{91} +1.00000 q^{93} -5.00000 q^{95} +14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 − 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −9.00000 −1.87663 −0.938315 − 0.345782i \(-0.887614\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 − 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) −6.00000 −0.781133 −0.390567 − 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) 1.00000 0.125988
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −14.0000 −1.71037 −0.855186 − 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 − 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) −1.00000 −0.117041 −0.0585206 − 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 1.00000 0.112509 0.0562544 − 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 − 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 1.00000 0.103695
\(94\) 0 0
\(95\) −5.00000 −0.512989
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 − 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −15.0000 −1.49256 −0.746278 − 0.665635i \(-0.768161\pi\)
−0.746278 + 0.665635i \(0.768161\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) 0 0
\(107\) 3.00000 0.290021 0.145010 − 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 − 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 0 0
\(115\) −9.00000 −0.839254
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 11.0000 0.968496
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −5.00000 −0.433555
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 − 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 − 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) 3.00000 0.245770 0.122885 − 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 − 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 0 0
\(159\) 9.00000 0.713746
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 0 0
\(163\) 22.0000 1.72317 0.861586 − 0.507611i \(-0.169471\pi\)
0.861586 + 0.507611i \(0.169471\pi\)
\(164\) 0 0
\(165\) −3.00000 −0.233550
\(166\) 0 0
\(167\) −9.00000 −0.696441 −0.348220 − 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −5.00000 −0.382360
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −10.0000 −0.719816 −0.359908 − 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 0 0
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 25.0000 1.77220 0.886102 − 0.463491i \(-0.153403\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(200\) 0 0
\(201\) 14.0000 0.987484
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −9.00000 −0.625543
\(208\) 0 0
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 − 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) 0 0
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) −11.0000 −0.750194
\(216\) 0 0
\(217\) −1.00000 −0.0678844
\(218\) 0 0
\(219\) 1.00000 0.0675737
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 10.0000 0.669650 0.334825 − 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 15.0000 0.995585 0.497792 − 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) 0 0
\(229\) 5.00000 0.330409 0.165205 − 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) −3.00000 −0.197386
\(232\) 0 0
\(233\) 3.00000 0.196537 0.0982683 − 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 − 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) −10.0000 −0.636285
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −27.0000 −1.69748
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −27.0000 −1.68421 −0.842107 − 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 9.00000 0.550791
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −5.00000 −0.303728 −0.151864 − 0.988401i \(-0.548528\pi\)
−0.151864 + 0.988401i \(0.548528\pi\)
\(272\) 0 0
\(273\) −2.00000 −0.121046
\(274\) 0 0
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 − 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 − 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 5.00000 0.296174
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −14.0000 −0.820695
\(292\) 0 0
\(293\) 18.0000 1.05157 0.525786 − 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) 0 0
\(297\) −3.00000 −0.174078
\(298\) 0 0
\(299\) −18.0000 −1.04097
\(300\) 0 0
\(301\) −11.0000 −0.634029
\(302\) 0 0
\(303\) 15.0000 0.861727
\(304\) 0 0
\(305\) −10.0000 −0.572598
\(306\) 0 0
\(307\) −32.0000 −1.82634 −0.913168 − 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 1.00000 0.0563436
\(316\) 0 0
\(317\) 24.0000 1.34797 0.673987 − 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) −8.00000 −0.442401
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 − 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 8.00000 0.438397
\(334\) 0 0
\(335\) −14.0000 −0.764902
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 3.00000 0.162938
\(340\) 0 0
\(341\) −3.00000 −0.162459
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 9.00000 0.484544
\(346\) 0 0
\(347\) 36.0000 1.93258 0.966291 − 0.257454i \(-0.0828835\pi\)
0.966291 + 0.257454i \(0.0828835\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 − 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.00000 −0.475002 −0.237501 − 0.971387i \(-0.576328\pi\)
−0.237501 + 0.971387i \(0.576328\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −1.00000 −0.0523424
\(366\) 0 0
\(367\) −26.0000 −1.35719 −0.678594 − 0.734513i \(-0.737411\pi\)
−0.678594 + 0.734513i \(0.737411\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.00000 −0.467257
\(372\) 0 0
\(373\) −19.0000 −0.983783 −0.491891 − 0.870657i \(-0.663694\pi\)
−0.491891 + 0.870657i \(0.663694\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 − 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) −36.0000 −1.83951 −0.919757 − 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 0 0
\(387\) −11.0000 −0.559161
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) −7.00000 −0.351320 −0.175660 − 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) 0 0
\(399\) 5.00000 0.250313
\(400\) 0 0
\(401\) 15.0000 0.749064 0.374532 − 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −28.0000 −1.38451 −0.692255 − 0.721653i \(-0.743383\pi\)
−0.692255 + 0.721653i \(0.743383\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 0 0
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) 14.0000 0.685583
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 − 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) 0 0
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 − 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 45.0000 2.15264
\(438\) 0 0
\(439\) −14.0000 −0.668184 −0.334092 − 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) −27.0000 −1.28281 −0.641404 − 0.767203i \(-0.721648\pi\)
−0.641404 + 0.767203i \(0.721648\pi\)
\(444\) 0 0
\(445\) −9.00000 −0.426641
\(446\) 0 0
\(447\) −3.00000 −0.141895
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 − 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −16.0000 −0.751746
\(454\) 0 0
\(455\) 2.00000 0.0937614
\(456\) 0 0
\(457\) 38.0000 1.77757 0.888783 − 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 − 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 0 0
\(465\) 1.00000 0.0463739
\(466\) 0 0
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −14.0000 −0.646460
\(470\) 0 0
\(471\) 7.00000 0.322543
\(472\) 0 0
\(473\) −33.0000 −1.51734
\(474\) 0 0
\(475\) −5.00000 −0.229416
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) 0 0
\(479\) −21.0000 −0.959514 −0.479757 − 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 0 0
\(483\) 9.00000 0.409514
\(484\) 0 0
\(485\) 14.0000 0.635707
\(486\) 0 0
\(487\) 40.0000 1.81257 0.906287 − 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) 0 0
\(489\) −22.0000 −0.994874
\(490\) 0 0
\(491\) −21.0000 −0.947717 −0.473858 − 0.880601i \(-0.657139\pi\)
−0.473858 + 0.880601i \(0.657139\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) 0 0
\(497\) −9.00000 −0.403705
\(498\) 0 0
\(499\) −32.0000 −1.43252 −0.716258 − 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 − 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 0 0
\(509\) 36.0000 1.59567 0.797836 − 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) −1.00000 −0.0442374
\(512\) 0 0
\(513\) 5.00000 0.220755
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 18.0000 0.791639
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 25.0000 1.09317 0.546587 − 0.837402i \(-0.315927\pi\)
0.546587 + 0.837402i \(0.315927\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 58.0000 2.52174
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 3.00000 0.129701
\(536\) 0 0
\(537\) −12.0000 −0.517838
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 − 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 0 0
\(543\) −5.00000 −0.214571
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 34.0000 1.45374 0.726868 − 0.686778i \(-0.240975\pi\)
0.726868 + 0.686778i \(0.240975\pi\)
\(548\) 0 0
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.00000 0.0425243
\(554\) 0 0
\(555\) −8.00000 −0.339581
\(556\) 0 0
\(557\) 3.00000 0.127114 0.0635570 − 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) 0 0
\(559\) −22.0000 −0.930501
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 − 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −3.00000 −0.126211
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) 15.0000 0.628833 0.314416 − 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 0 0
\(571\) −14.0000 −0.585882 −0.292941 − 0.956131i \(-0.594634\pi\)
−0.292941 + 0.956131i \(0.594634\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9.00000 −0.375326
\(576\) 0 0
\(577\) −16.0000 −0.666089 −0.333044 − 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 0 0
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) −27.0000 −1.11823
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 − 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 − 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −25.0000 −1.02318
\(598\) 0 0
\(599\) −27.0000 −1.10319 −0.551595 − 0.834112i \(-0.685981\pi\)
−0.551595 + 0.834112i \(0.685981\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) −2.00000 −0.0813116
\(606\) 0 0
\(607\) 1.00000 0.0405887 0.0202944 − 0.999794i \(-0.493540\pi\)
0.0202944 + 0.999794i \(0.493540\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −22.0000 −0.888572 −0.444286 − 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.0000 −0.603877 −0.301939 − 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) 0 0
\(619\) −14.0000 −0.562708 −0.281354 − 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) 0 0
\(621\) 9.00000 0.361158
\(622\) 0 0
\(623\) −9.00000 −0.360577
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 15.0000 0.599042
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 − 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) −19.0000 −0.755182
\(634\) 0 0
\(635\) −8.00000 −0.317470
\(636\) 0 0
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) −9.00000 −0.356034
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 31.0000 1.22252 0.611260 − 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 0 0
\(645\) 11.0000 0.433125
\(646\) 0 0
\(647\) 33.0000 1.29736 0.648682 − 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) 0 0
\(651\) 1.00000 0.0391931
\(652\) 0 0
\(653\) 30.0000 1.17399 0.586995 − 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 0 0
\(655\) 6.00000 0.234439
\(656\) 0 0
\(657\) −1.00000 −0.0390137
\(658\) 0 0
\(659\) 48.0000 1.86981 0.934907 − 0.354892i \(-0.115482\pi\)
0.934907 + 0.354892i \(0.115482\pi\)
\(660\) 0 0
\(661\) −46.0000 −1.78919 −0.894596 − 0.446875i \(-0.852537\pi\)
−0.894596 + 0.446875i \(0.852537\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.00000 −0.193892
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −10.0000 −0.386622
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 − 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −33.0000 −1.26829 −0.634147 − 0.773213i \(-0.718648\pi\)
−0.634147 + 0.773213i \(0.718648\pi\)
\(678\) 0 0
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 15.0000 0.573959 0.286980 − 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) −5.00000 −0.190762
\(688\) 0 0
\(689\) −18.0000 −0.685745
\(690\) 0 0
\(691\) −17.0000 −0.646710 −0.323355 − 0.946278i \(-0.604811\pi\)
−0.323355 + 0.946278i \(0.604811\pi\)
\(692\) 0 0
\(693\) 3.00000 0.113961
\(694\) 0 0
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −3.00000 −0.113470
\(700\) 0 0
\(701\) −3.00000 −0.113308 −0.0566542 − 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 0 0
\(703\) −40.0000 −1.50863
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) 0 0
\(707\) −15.0000 −0.564133
\(708\) 0 0
\(709\) 23.0000 0.863783 0.431892 − 0.901926i \(-0.357846\pi\)
0.431892 + 0.901926i \(0.357846\pi\)
\(710\) 0 0
\(711\) 1.00000 0.0375029
\(712\) 0 0
\(713\) 9.00000 0.337053
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) 0 0
\(717\) 12.0000 0.448148
\(718\) 0 0
\(719\) −18.0000 −0.671287 −0.335643 − 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) 22.0000 0.818189
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −23.0000 −0.853023 −0.426511 − 0.904482i \(-0.640258\pi\)
−0.426511 + 0.904482i \(0.640258\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 26.0000 0.960332 0.480166 − 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) 0 0
\(735\) 6.00000 0.221313
\(736\) 0 0
\(737\) −42.0000 −1.54709
\(738\) 0 0
\(739\) −32.0000 −1.17714 −0.588570 − 0.808447i \(-0.700309\pi\)
−0.588570 + 0.808447i \(0.700309\pi\)
\(740\) 0 0
\(741\) 10.0000 0.367359
\(742\) 0 0
\(743\) 9.00000 0.330178 0.165089 − 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 0 0
\(745\) 3.00000 0.109911
\(746\) 0 0
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 3.00000 0.109618
\(750\) 0 0
\(751\) −26.0000 −0.948753 −0.474377 − 0.880322i \(-0.657327\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(752\) 0 0
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 27.0000 0.980038
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 − 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 0 0
\(763\) 8.00000 0.289619
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) −31.0000 −1.11789 −0.558944 − 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 0 0
\(771\) 27.0000 0.972381
\(772\) 0 0
\(773\) −27.0000 −0.971123 −0.485561 − 0.874203i \(-0.661385\pi\)
−0.485561 + 0.874203i \(0.661385\pi\)
\(774\) 0 0
\(775\) −1.00000 −0.0359211
\(776\) 0 0
\(777\) −8.00000 −0.286998
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −27.0000 −0.966136
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.00000 −0.249841
\(786\) 0 0
\(787\) 25.0000 0.891154 0.445577 − 0.895244i \(-0.352999\pi\)
0.445577 + 0.895244i \(0.352999\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.00000 −0.106668
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) 0 0
\(795\) 9.00000 0.319197
\(796\) 0 0
\(797\) 18.0000 0.637593 0.318796 − 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −9.00000 −0.317999
\(802\) 0 0
\(803\) −3.00000 −0.105868
\(804\) 0 0
\(805\) −9.00000 −0.317208
\(806\) 0 0
\(807\) −6.00000 −0.211210
\(808\) 0 0
\(809\) 39.0000 1.37117 0.685583 − 0.727994i \(-0.259547\pi\)
0.685583 + 0.727994i \(0.259547\pi\)
\(810\) 0 0
\(811\) 43.0000 1.50993 0.754967 − 0.655763i \(-0.227653\pi\)
0.754967 + 0.655763i \(0.227653\pi\)
\(812\) 0 0
\(813\) 5.00000 0.175358
\(814\) 0 0
\(815\) 22.0000 0.770626
\(816\) 0 0
\(817\) 55.0000 1.92421
\(818\) 0 0
\(819\) 2.00000 0.0698857
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 − 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) 0 0
\(823\) 22.0000 0.766872 0.383436 − 0.923567i \(-0.374741\pi\)
0.383436 + 0.923567i \(0.374741\pi\)
\(824\) 0 0
\(825\) −3.00000 −0.104447
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 − 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 29.0000 1.00721 0.503606 − 0.863934i \(-0.332006\pi\)
0.503606 + 0.863934i \(0.332006\pi\)
\(830\) 0 0
\(831\) −8.00000 −0.277517
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −9.00000 −0.311458
\(836\) 0 0
\(837\) 1.00000 0.0345651
\(838\) 0 0
\(839\) −21.0000 −0.725001 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 24.0000 0.826604
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 0 0
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) −72.0000 −2.46813
\(852\) 0 0
\(853\) −19.0000 −0.650548 −0.325274 − 0.945620i \(-0.605456\pi\)
−0.325274 + 0.945620i \(0.605456\pi\)
\(854\) 0 0
\(855\) −5.00000 −0.170996
\(856\) 0 0
\(857\) −6.00000 −0.204956 −0.102478 − 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) −8.00000 −0.272956 −0.136478 − 0.990643i \(-0.543578\pi\)
−0.136478 + 0.990643i \(0.543578\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −15.0000 −0.510606 −0.255303 − 0.966861i \(-0.582175\pi\)
−0.255303 + 0.966861i \(0.582175\pi\)
\(864\) 0 0
\(865\) 6.00000 0.204006
\(866\) 0 0
\(867\) 17.0000 0.577350
\(868\) 0 0
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) −28.0000 −0.948744
\(872\) 0 0
\(873\) 14.0000 0.473828
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 0 0
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 31.0000 1.04323 0.521617 − 0.853180i \(-0.325329\pi\)
0.521617 + 0.853180i \(0.325329\pi\)
\(884\) 0 0
\(885\) 6.00000 0.201688
\(886\) 0 0
\(887\) 18.0000 0.604381 0.302190 − 0.953248i \(-0.402282\pi\)
0.302190 + 0.953248i \(0.402282\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 3.00000 0.100504
\(892\) 0 0
\(893\) −30.0000 −1.00391
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) 18.0000 0.601003
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 11.0000 0.366057
\(904\) 0 0
\(905\) 5.00000 0.166206
\(906\) 0 0
\(907\) −8.00000 −0.265636 −0.132818 − 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) 0 0
\(909\) −15.0000 −0.497519
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 − 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 36.0000 1.19143
\(914\) 0 0
\(915\) 10.0000 0.330590
\(916\) 0 0
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) −26.0000 −0.857661 −0.428830 − 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) 0 0
\(921\) 32.0000 1.05444
\(922\) 0 0
\(923\) −18.0000 −0.592477
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) −15.0000 −0.492134 −0.246067 − 0.969253i \(-0.579138\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(930\) 0 0
\(931\) 30.0000 0.983210
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 20.0000 0.653372 0.326686 − 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(938\) 0 0
\(939\) 22.0000 0.717943
\(940\) 0 0
\(941\) −12.0000 −0.391189 −0.195594 − 0.980685i \(-0.562664\pi\)
−0.195594 + 0.980685i \(0.562664\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) −54.0000 −1.75476 −0.877382 − 0.479792i \(-0.840712\pi\)
−0.877382 + 0.479792i \(0.840712\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 − 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.0000 0.581250
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 0 0
\(963\) 3.00000 0.0966736
\(964\) 0 0
\(965\) −10.0000 −0.321911
\(966\) 0 0
\(967\) 4.00000 0.128631 0.0643157 − 0.997930i \(-0.479514\pi\)
0.0643157 + 0.997930i \(0.479514\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 − 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 0 0
\(973\) −14.0000 −0.448819
\(974\) 0 0
\(975\) −2.00000 −0.0640513
\(976\) 0 0
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) −27.0000 −0.862924
\(980\) 0 0
\(981\) 8.00000 0.255420
\(982\) 0 0
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) 0 0
\(987\) −6.00000 −0.190982
\(988\) 0 0
\(989\) 99.0000 3.14802
\(990\) 0 0
\(991\) −23.0000 −0.730619 −0.365310 − 0.930886i \(-0.619037\pi\)
−0.365310 + 0.930886i \(0.619037\pi\)
\(992\) 0 0
\(993\) 8.00000 0.253872
\(994\) 0 0
\(995\) 25.0000 0.792553
\(996\) 0 0
\(997\) 26.0000 0.823428 0.411714 − 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) 0 0
\(999\) −8.00000 −0.253109
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 7440.2.a.k.1.1 1
4.3 odd 2 930.2.a.i.1.1 ✓ 1
12.11 even 2 2790.2.a.r.1.1 1
20.3 even 4 4650.2.d.d.3349.2 2
20.7 even 4 4650.2.d.d.3349.1 2
20.19 odd 2 4650.2.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.i.1.1 ✓ 1 4.3 odd 2
2790.2.a.r.1.1 1 12.11 even 2
4650.2.a.bd.1.1 1 20.19 odd 2
4650.2.d.d.3349.1 2 20.7 even 4
4650.2.d.d.3349.2 2 20.3 even 4
7440.2.a.k.1.1 1 1.1 even 1 trivial