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Properties

Label 2960.2.a.d.1.1
Level $2960$
Weight $2$
Character 2960.1
Self dual yes
Analytic conductor $23.636$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2960,2,Mod(1,2960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2960.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2960, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-1,0,1,0,-2,0,3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(23.6357189983\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 740)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2960.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} -2.00000 q^{9} +3.00000 q^{11} -4.00000 q^{13} +1.00000 q^{15} +4.00000 q^{19} -1.00000 q^{21} +1.00000 q^{25} +5.00000 q^{27} -2.00000 q^{31} -3.00000 q^{33} -1.00000 q^{35} +1.00000 q^{37} +4.00000 q^{39} +3.00000 q^{41} -2.00000 q^{43} +2.00000 q^{45} -3.00000 q^{47} -6.00000 q^{49} -9.00000 q^{53} -3.00000 q^{55} -4.00000 q^{57} +2.00000 q^{61} -2.00000 q^{63} +4.00000 q^{65} +4.00000 q^{67} -15.0000 q^{71} -7.00000 q^{73} -1.00000 q^{75} +3.00000 q^{77} +10.0000 q^{79} +1.00000 q^{81} +3.00000 q^{83} +6.00000 q^{89} -4.00000 q^{91} +2.00000 q^{93} -4.00000 q^{95} -10.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)

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 −0.288675 − 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 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
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 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
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 − 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 − 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) −3.00000 −0.437595 −0.218797 − 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 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
\(57\) −4.00000 −0.529813
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 − 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 − 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 − 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.00000 0.329293 0.164646 − 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) 3.00000 0.298511 0.149256 − 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 − 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 1.00000 0.0975900
\(106\) 0 0
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 8.00000 0.739600
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −3.00000 −0.270501
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 7.00000 0.621150 0.310575 − 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 0 0
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 − 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) 15.0000 1.22885 0.614424 − 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 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
\(161\) 0 0
\(162\) 0 0
\(163\) −8.00000 −0.626608 −0.313304 − 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 − 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −8.00000 −0.611775
\(172\) 0 0
\(173\) −9.00000 −0.684257 −0.342129 − 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0 0
\(185\) −1.00000 −0.0735215
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) −16.0000 −1.15171 −0.575853 − 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 0 0
\(195\) −4.00000 −0.286446
\(196\) 0 0
\(197\) 9.00000 0.641223 0.320612 − 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 − 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.00000 −0.209529
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 − 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 0 0
\(213\) 15.0000 1.02778
\(214\) 0 0
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 0 0
\(219\) 7.00000 0.473016
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −11.0000 −0.736614 −0.368307 − 0.929704i \(-0.620063\pi\)
−0.368307 + 0.929704i \(0.620063\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) −25.0000 −1.65205 −0.826023 − 0.563636i \(-0.809402\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(230\) 0 0
\(231\) −3.00000 −0.197386
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 8.00000 0.515325 0.257663 − 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 6.00000 0.383326
\(246\) 0 0
\(247\) −16.0000 −1.01806
\(248\) 0 0
\(249\) −3.00000 −0.190117
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.00000 −0.374270 −0.187135 − 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.00000 0.554964 0.277482 − 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −11.0000 −0.668202 −0.334101 − 0.942537i \(-0.608433\pi\)
−0.334101 + 0.942537i \(0.608433\pi\)
\(272\) 0 0
\(273\) 4.00000 0.242091
\(274\) 0 0
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 − 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 − 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 28.0000 1.66443 0.832214 − 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 15.0000 0.870388
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 0 0
\(303\) −3.00000 −0.172345
\(304\) 0 0
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 − 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 − 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 − 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) 2.00000 0.112687
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 − 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) 0 0
\(327\) 10.0000 0.553001
\(328\) 0 0
\(329\) −3.00000 −0.165395
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −31.0000 −1.68868 −0.844339 − 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 − 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) −20.0000 −1.06752
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 − 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 15.0000 0.796117
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −15.0000 −0.791670 −0.395835 − 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 7.00000 0.366397
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 − 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −9.00000 −0.467257
\(372\) 0 0
\(373\) −25.0000 −1.29445 −0.647225 − 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 19.0000 0.975964 0.487982 − 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) −7.00000 −0.358621
\(382\) 0 0
\(383\) 18.0000 0.919757 0.459879 − 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) −3.00000 −0.152894
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 0 0
\(389\) 24.0000 1.21685 0.608424 − 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 0 0
\(395\) −10.0000 −0.503155
\(396\) 0 0
\(397\) 17.0000 0.853206 0.426603 − 0.904439i \(-0.359710\pi\)
0.426603 + 0.904439i \(0.359710\pi\)
\(398\) 0 0
\(399\) −4.00000 −0.200250
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 − 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) 32.0000 1.58230 0.791149 − 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3.00000 −0.147264
\(416\) 0 0
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) 27.0000 1.31904 0.659518 − 0.751689i \(-0.270760\pi\)
0.659518 + 0.751689i \(0.270760\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 − 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) 0 0
\(429\) 12.0000 0.579365
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 − 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 − 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −9.00000 −0.427603 −0.213801 − 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) −15.0000 −0.709476
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 − 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) 0 0
\(453\) 8.00000 0.375873
\(454\) 0 0
\(455\) 4.00000 0.187523
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 − 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 − 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 0 0
\(465\) −2.00000 −0.0927478
\(466\) 0 0
\(467\) −6.00000 −0.277647 −0.138823 − 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 7.00000 0.322543
\(472\) 0 0
\(473\) −6.00000 −0.275880
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 18.0000 0.824163
\(478\) 0 0
\(479\) 36.0000 1.64488 0.822441 − 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 0 0
\(487\) −44.0000 −1.99383 −0.996915 − 0.0784867i \(-0.974991\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) −15.0000 −0.672842
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 − 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 0 0
\(501\) 6.00000 0.268060
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 − 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) −3.00000 −0.133235
\(508\) 0 0
\(509\) 21.0000 0.930809 0.465404 − 0.885098i \(-0.345909\pi\)
0.465404 + 0.885098i \(0.345909\pi\)
\(510\) 0 0
\(511\) −7.00000 −0.309662
\(512\) 0 0
\(513\) 20.0000 0.883022
\(514\) 0 0
\(515\) 14.0000 0.616914
\(516\) 0 0
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 − 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 0 0
\(523\) −2.00000 −0.0874539 −0.0437269 − 0.999044i \(-0.513923\pi\)
−0.0437269 + 0.999044i \(0.513923\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 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
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 − 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 10.0000 0.425243
\(554\) 0 0
\(555\) 1.00000 0.0424476
\(556\) 0 0
\(557\) 12.0000 0.508456 0.254228 − 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24.0000 1.01148 0.505740 − 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 6.00000 0.252422
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 − 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 31.0000 1.29731 0.648655 − 0.761083i \(-0.275332\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 − 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) 0 0
\(579\) 16.0000 0.664937
\(580\) 0 0
\(581\) 3.00000 0.124461
\(582\) 0 0
\(583\) −27.0000 −1.11823
\(584\) 0 0
\(585\) −8.00000 −0.330759
\(586\) 0 0
\(587\) −18.0000 −0.742940 −0.371470 − 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −9.00000 −0.370211
\(592\) 0 0
\(593\) 21.0000 0.862367 0.431183 − 0.902264i \(-0.358096\pi\)
0.431183 + 0.902264i \(0.358096\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.0000 0.572982
\(598\) 0 0
\(599\) 33.0000 1.34834 0.674172 − 0.738575i \(-0.264501\pi\)
0.674172 + 0.738575i \(0.264501\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 − 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) 0 0
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) 4.00000 0.162355 0.0811775 − 0.996700i \(-0.474132\pi\)
0.0811775 + 0.996700i \(0.474132\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −43.0000 −1.73675 −0.868377 − 0.495905i \(-0.834836\pi\)
−0.868377 + 0.495905i \(0.834836\pi\)
\(614\) 0 0
\(615\) 3.00000 0.120972
\(616\) 0 0
\(617\) 39.0000 1.57008 0.785040 − 0.619445i \(-0.212642\pi\)
0.785040 + 0.619445i \(0.212642\pi\)
\(618\) 0 0
\(619\) −5.00000 −0.200967 −0.100483 − 0.994939i \(-0.532039\pi\)
−0.100483 + 0.994939i \(0.532039\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.00000 0.240385
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −12.0000 −0.479234
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −14.0000 −0.557331 −0.278666 − 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) 0 0
\(633\) 5.00000 0.198732
\(634\) 0 0
\(635\) −7.00000 −0.277787
\(636\) 0 0
\(637\) 24.0000 0.950915
\(638\) 0 0
\(639\) 30.0000 1.18678
\(640\) 0 0
\(641\) −9.00000 −0.355479 −0.177739 − 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 − 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) −2.00000 −0.0787499
\(646\) 0 0
\(647\) −18.0000 −0.707653 −0.353827 − 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 2.00000 0.0783862
\(652\) 0 0
\(653\) −18.0000 −0.704394 −0.352197 − 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 0 0
\(655\) 6.00000 0.234439
\(656\) 0 0
\(657\) 14.0000 0.546192
\(658\) 0 0
\(659\) 21.0000 0.818044 0.409022 − 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 −0.155113
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 11.0000 0.425285
\(670\) 0 0
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 − 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) 27.0000 1.03769 0.518847 − 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(678\) 0 0
\(679\) −10.0000 −0.383765
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 − 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) 25.0000 0.953809
\(688\) 0 0
\(689\) 36.0000 1.37149
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 − 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 0 0
\(693\) −6.00000 −0.227921
\(694\) 0 0
\(695\) −4.00000 −0.151729
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) −3.00000 −0.112987
\(706\) 0 0
\(707\) 3.00000 0.112827
\(708\) 0 0
\(709\) 8.00000 0.300446 0.150223 − 0.988652i \(-0.452001\pi\)
0.150223 + 0.988652i \(0.452001\pi\)
\(710\) 0 0
\(711\) −20.0000 −0.750059
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) −6.00000 −0.224074
\(718\) 0 0
\(719\) −21.0000 −0.783168 −0.391584 − 0.920142i \(-0.628073\pi\)
−0.391584 + 0.920142i \(0.628073\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) −8.00000 −0.297523
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 − 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 41.0000 1.51437 0.757185 − 0.653201i \(-0.226574\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(734\) 0 0
\(735\) −6.00000 −0.221313
\(736\) 0 0
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) 7.00000 0.257499 0.128750 − 0.991677i \(-0.458904\pi\)
0.128750 + 0.991677i \(0.458904\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) −9.00000 −0.330178 −0.165089 − 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) 0 0
\(745\) −15.0000 −0.549557
\(746\) 0 0
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −23.0000 −0.839282 −0.419641 − 0.907690i \(-0.637844\pi\)
−0.419641 + 0.907690i \(0.637844\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 − 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15.0000 −0.543750 −0.271875 − 0.962333i \(-0.587644\pi\)
−0.271875 + 0.962333i \(0.587644\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 44.0000 1.58668 0.793340 − 0.608778i \(-0.208340\pi\)
0.793340 + 0.608778i \(0.208340\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 0 0
\(773\) −39.0000 −1.40273 −0.701366 − 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) −1.00000 −0.0358748
\(778\) 0 0
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) −45.0000 −1.61023
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.00000 0.249841
\(786\) 0 0
\(787\) −23.0000 −0.819861 −0.409931 − 0.912117i \(-0.634447\pi\)
−0.409931 + 0.912117i \(0.634447\pi\)
\(788\) 0 0
\(789\) −9.00000 −0.320408
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) 0 0
\(795\) −9.00000 −0.319197
\(796\) 0 0
\(797\) −12.0000 −0.425062 −0.212531 − 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −12.0000 −0.423999
\(802\) 0 0
\(803\) −21.0000 −0.741074
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.00000 0.211210
\(808\) 0 0
\(809\) 24.0000 0.843795 0.421898 − 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 0 0
\(811\) 7.00000 0.245803 0.122902 − 0.992419i \(-0.460780\pi\)
0.122902 + 0.992419i \(0.460780\pi\)
\(812\) 0 0
\(813\) 11.0000 0.385787
\(814\) 0 0
\(815\) 8.00000 0.280228
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) 8.00000 0.279543
\(820\) 0 0
\(821\) −27.0000 −0.942306 −0.471153 − 0.882051i \(-0.656162\pi\)
−0.471153 + 0.882051i \(0.656162\pi\)
\(822\) 0 0
\(823\) 40.0000 1.39431 0.697156 − 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) 0 0
\(825\) −3.00000 −0.104447
\(826\) 0 0
\(827\) −48.0000 −1.66912 −0.834562 − 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 0 0
\(829\) 20.0000 0.694629 0.347314 − 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) 0 0
\(831\) 10.0000 0.346896
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 6.00000 0.207639
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) 0 0
\(839\) −48.0000 −1.65714 −0.828572 − 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −30.0000 −1.03325
\(844\) 0 0
\(845\) −3.00000 −0.103203
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 0 0
\(849\) −28.0000 −0.960958
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −4.00000 −0.136957 −0.0684787 − 0.997653i \(-0.521815\pi\)
−0.0684787 + 0.997653i \(0.521815\pi\)
\(854\) 0 0
\(855\) 8.00000 0.273594
\(856\) 0 0
\(857\) 30.0000 1.02478 0.512390 − 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 − 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) −3.00000 −0.102240
\(862\) 0 0
\(863\) −24.0000 −0.816970 −0.408485 − 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 0 0
\(865\) 9.00000 0.306009
\(866\) 0 0
\(867\) 17.0000 0.577350
\(868\) 0 0
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) 0 0
\(873\) 20.0000 0.676897
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 14.0000 0.472746 0.236373 − 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 0 0
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 − 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) 0 0
\(883\) 4.00000 0.134611 0.0673054 − 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 39.0000 1.30949 0.654746 − 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(888\) 0 0
\(889\) 7.00000 0.234772
\(890\) 0 0
\(891\) 3.00000 0.100504
\(892\) 0 0
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 2.00000 0.0665558
\(904\) 0 0
\(905\) −5.00000 −0.166206
\(906\) 0 0
\(907\) 10.0000 0.332045 0.166022 − 0.986122i \(-0.446908\pi\)
0.166022 + 0.986122i \(0.446908\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 − 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 2.00000 0.0661180
\(916\) 0 0
\(917\) −6.00000 −0.198137
\(918\) 0 0
\(919\) 4.00000 0.131948 0.0659739 − 0.997821i \(-0.478985\pi\)
0.0659739 + 0.997821i \(0.478985\pi\)
\(920\) 0 0
\(921\) −13.0000 −0.428365
\(922\) 0 0
\(923\) 60.0000 1.97492
\(924\) 0 0
\(925\) 1.00000 0.0328798
\(926\) 0 0
\(927\) 28.0000 0.919641
\(928\) 0 0
\(929\) 6.00000 0.196854 0.0984268 − 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) −24.0000 −0.786568
\(932\) 0 0
\(933\) −12.0000 −0.392862
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 35.0000 1.14340 0.571700 − 0.820463i \(-0.306284\pi\)
0.571700 + 0.820463i \(0.306284\pi\)
\(938\) 0 0
\(939\) 10.0000 0.326338
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −5.00000 −0.162650
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) 28.0000 0.908918
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 27.0000 0.874616 0.437308 − 0.899312i \(-0.355932\pi\)
0.437308 + 0.899312i \(0.355932\pi\)
\(954\) 0 0
\(955\) 24.0000 0.776622
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18.0000 −0.581250
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 16.0000 0.515058
\(966\) 0 0
\(967\) 22.0000 0.707472 0.353736 − 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 60.0000 1.92549 0.962746 − 0.270408i \(-0.0871586\pi\)
0.962746 + 0.270408i \(0.0871586\pi\)
\(972\) 0 0
\(973\) 4.00000 0.128234
\(974\) 0 0
\(975\) 4.00000 0.128103
\(976\) 0 0
\(977\) −60.0000 −1.91957 −0.959785 − 0.280736i \(-0.909421\pi\)
−0.959785 + 0.280736i \(0.909421\pi\)
\(978\) 0 0
\(979\) 18.0000 0.575282
\(980\) 0 0
\(981\) 20.0000 0.638551
\(982\) 0 0
\(983\) 3.00000 0.0956851 0.0478426 − 0.998855i \(-0.484765\pi\)
0.0478426 + 0.998855i \(0.484765\pi\)
\(984\) 0 0
\(985\) −9.00000 −0.286764
\(986\) 0 0
\(987\) 3.00000 0.0954911
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −50.0000 −1.58830 −0.794151 − 0.607720i \(-0.792084\pi\)
−0.794151 + 0.607720i \(0.792084\pi\)
\(992\) 0 0
\(993\) −28.0000 −0.888553
\(994\) 0 0
\(995\) 14.0000 0.443830
\(996\) 0 0
\(997\) 44.0000 1.39349 0.696747 − 0.717317i \(-0.254630\pi\)
0.696747 + 0.717317i \(0.254630\pi\)
\(998\) 0 0
\(999\) 5.00000 0.158193
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 2960.2.a.d.1.1 1
4.3 odd 2 740.2.a.b.1.1 ✓ 1
12.11 even 2 6660.2.a.c.1.1 1
20.3 even 4 3700.2.d.d.149.2 2
20.7 even 4 3700.2.d.d.149.1 2
20.19 odd 2 3700.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
740.2.a.b.1.1 ✓ 1 4.3 odd 2
2960.2.a.d.1.1 1 1.1 even 1 trivial
3700.2.a.c.1.1 1 20.19 odd 2
3700.2.d.d.149.1 2 20.7 even 4
3700.2.d.d.149.2 2 20.3 even 4
6660.2.a.c.1.1 1 12.11 even 2