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Properties

Label 1944.2.a.g.1.1
Level $1944$
Weight $2$
Character 1944.1
Self dual yes
Analytic conductor $15.523$
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] = [1944,2,Mod(1,1944)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1944, 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("1944.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1944 = 2^{3} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1944.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: \(15.5229181529\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1944.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} -3.00000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} -3.00000 q^{7} +2.00000 q^{11} +1.00000 q^{13} -8.00000 q^{17} -7.00000 q^{19} -4.00000 q^{23} -1.00000 q^{25} +6.00000 q^{29} -1.00000 q^{31} -6.00000 q^{35} +3.00000 q^{37} -6.00000 q^{41} +1.00000 q^{43} -6.00000 q^{47} +2.00000 q^{49} +2.00000 q^{53} +4.00000 q^{55} -10.0000 q^{59} +10.0000 q^{61} +2.00000 q^{65} +8.00000 q^{67} -14.0000 q^{71} +10.0000 q^{73} -6.00000 q^{77} -11.0000 q^{79} +4.00000 q^{83} -16.0000 q^{85} -18.0000 q^{89} -3.00000 q^{91} -14.0000 q^{95} +17.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 − 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 − 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 − 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −8.00000 −1.94029 −0.970143 − 0.242536i \(-0.922021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) −7.00000 −1.60591 −0.802955 − 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 − 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.00000 −1.01419
\(36\) 0 0
\(37\) 3.00000 0.493197 0.246598 − 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 − 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.0000 −1.30189 −0.650945 − 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 − 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 − 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.0000 −1.66149 −0.830747 − 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 − 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 − 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −18.0000 −1.90800 −0.953998 − 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −14.0000 −1.43637
\(96\) 0 0
\(97\) 17.0000 1.72609 0.863044 − 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 −0.580042 −0.290021 − 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −11.0000 −1.05361 −0.526804 − 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 − 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 24.0000 2.20008
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 − 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 22.0000 1.92215 0.961074 − 0.276289i \(-0.0891049\pi\)
0.961074 + 0.276289i \(0.0891049\pi\)
\(132\) 0 0
\(133\) 21.0000 1.82093
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) 21.0000 1.78120 0.890598 − 0.454791i \(-0.150286\pi\)
0.890598 + 0.454791i \(0.150286\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −20.0000 −1.63846 −0.819232 − 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 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 \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 9.00000 0.704934 0.352467 − 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.0000 1.39288 0.696441 − 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 24.0000 1.82469 0.912343 − 0.409426i \(-0.134271\pi\)
0.912343 + 0.409426i \(0.134271\pi\)
\(174\) 0 0
\(175\) 3.00000 0.226779
\(176\) 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
\(181\) −3.00000 −0.222988 −0.111494 − 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −17.0000 −1.20510 −0.602549 − 0.798082i \(-0.705848\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −18.0000 −1.26335
\(204\) 0 0
\(205\) −12.0000 −0.838116
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −14.0000 −0.968400
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 − 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 7.00000 0.468755 0.234377 − 0.972146i \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −23.0000 −1.51988 −0.759941 − 0.649992i \(-0.774772\pi\)
−0.759941 + 0.649992i \(0.774772\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.00000 0.524097 0.262049 − 0.965055i \(-0.415602\pi\)
0.262049 + 0.965055i \(0.415602\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 − 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 21.0000 1.35273 0.676364 − 0.736567i \(-0.263554\pi\)
0.676364 + 0.736567i \(0.263554\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.00000 0.255551
\(246\) 0 0
\(247\) −7.00000 −0.445399
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.00000 0.252478 0.126239 − 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.0000 −0.873296 −0.436648 − 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) −9.00000 −0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.0000 0.975537 0.487769 − 0.872973i \(-0.337811\pi\)
0.487769 + 0.872973i \(0.337811\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) 13.0000 0.781094 0.390547 − 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.00000 −0.477240 −0.238620 − 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 0 0
\(283\) 5.00000 0.297219 0.148610 − 0.988896i \(-0.452520\pi\)
0.148610 + 0.988896i \(0.452520\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 18.0000 1.06251
\(288\) 0 0
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.0000 1.40209 0.701047 − 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) −20.0000 −1.16445
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 20.0000 1.14520
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −9.00000 −0.508710 −0.254355 − 0.967111i \(-0.581863\pi\)
−0.254355 + 0.967111i \(0.581863\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.0000 −1.34797 −0.673987 − 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 56.0000 3.11592
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 18.0000 0.992372
\(330\) 0 0
\(331\) 11.0000 0.604615 0.302307 − 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 16.0000 0.874173
\(336\) 0 0
\(337\) −3.00000 −0.163420 −0.0817102 − 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.00000 −0.108306
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 −0.322097 −0.161048 − 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 0 0
\(349\) 27.0000 1.44528 0.722638 − 0.691226i \(-0.242929\pi\)
0.722638 + 0.691226i \(0.242929\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.0000 0.532246 0.266123 − 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 0 0
\(355\) −28.0000 −1.48609
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.0000 −0.950004 −0.475002 − 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 20.0000 1.04685
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 − 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) 11.0000 0.569558 0.284779 − 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) 11.0000 0.565032 0.282516 − 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.0000 0.919757 0.459879 − 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) −12.0000 −0.611577
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.00000 −0.202808 −0.101404 − 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −22.0000 −1.10694
\(396\) 0 0
\(397\) −37.0000 −1.85698 −0.928488 − 0.371361i \(-0.878891\pi\)
−0.928488 + 0.371361i \(0.878891\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 − 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) −1.00000 −0.0498135
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 21.0000 1.03838 0.519192 − 0.854658i \(-0.326233\pi\)
0.519192 + 0.854658i \(0.326233\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 30.0000 1.47620
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 − 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 − 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) −30.0000 −1.45180
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 28.0000 1.34871 0.674356 − 0.738406i \(-0.264421\pi\)
0.674356 + 0.738406i \(0.264421\pi\)
\(432\) 0 0
\(433\) −17.0000 −0.816968 −0.408484 − 0.912766i \(-0.633942\pi\)
−0.408484 + 0.912766i \(0.633942\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 28.0000 1.33942
\(438\) 0 0
\(439\) 36.0000 1.71819 0.859093 − 0.511819i \(-0.171028\pi\)
0.859093 + 0.511819i \(0.171028\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.00000 −0.380091 −0.190046 − 0.981775i \(-0.560864\pi\)
−0.190046 + 0.981775i \(0.560864\pi\)
\(444\) 0 0
\(445\) −36.0000 −1.70656
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 − 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) −12.0000 −0.565058
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) −7.00000 −0.327446 −0.163723 − 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.0000 −0.745194 −0.372597 − 0.927993i \(-0.621533\pi\)
−0.372597 + 0.927993i \(0.621533\pi\)
\(462\) 0 0
\(463\) 11.0000 0.511213 0.255607 − 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 30.0000 1.38823 0.694117 − 0.719862i \(-0.255795\pi\)
0.694117 + 0.719862i \(0.255795\pi\)
\(468\) 0 0
\(469\) −24.0000 −1.10822
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.00000 0.0919601
\(474\) 0 0
\(475\) 7.00000 0.321182
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −32.0000 −1.46212 −0.731059 − 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) 0 0
\(481\) 3.00000 0.136788
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 34.0000 1.54386
\(486\) 0 0
\(487\) 31.0000 1.40474 0.702372 − 0.711810i \(-0.252124\pi\)
0.702372 + 0.711810i \(0.252124\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 − 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) −48.0000 −2.16181
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 42.0000 1.88396
\(498\) 0 0
\(499\) −12.0000 −0.537194 −0.268597 − 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 − 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −30.0000 −1.32712
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.00000 0.175243 0.0876216 − 0.996154i \(-0.472073\pi\)
0.0876216 + 0.996154i \(0.472073\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 − 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −27.0000 −1.16082 −0.580410 − 0.814324i \(-0.697108\pi\)
−0.580410 + 0.814324i \(0.697108\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −22.0000 −0.942376
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −42.0000 −1.78926
\(552\) 0 0
\(553\) 33.0000 1.40330
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.0000 0.593199 0.296600 − 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 0 0
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 12.0000 0.504844
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.00000 0.0838444 0.0419222 − 0.999121i \(-0.486652\pi\)
0.0419222 + 0.999121i \(0.486652\pi\)
\(570\) 0 0
\(571\) 39.0000 1.63210 0.816050 − 0.577982i \(-0.196160\pi\)
0.816050 + 0.577982i \(0.196160\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 − 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 4.00000 0.165663
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.0000 0.825488 0.412744 − 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 0 0
\(589\) 7.00000 0.288430
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.00000 −0.164260 −0.0821302 − 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) 0 0
\(595\) 48.0000 1.96781
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 − 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −29.0000 −1.18293 −0.591467 − 0.806329i \(-0.701451\pi\)
−0.591467 + 0.806329i \(0.701451\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) 41.0000 1.66414 0.832069 − 0.554672i \(-0.187156\pi\)
0.832069 + 0.554672i \(0.187156\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 −0.242734
\(612\) 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
\(617\) −12.0000 −0.483102 −0.241551 − 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 − 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 54.0000 2.16346
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) −29.0000 −1.15447 −0.577236 − 0.816577i \(-0.695869\pi\)
−0.577236 + 0.816577i \(0.695869\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10.0000 −0.396838
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −34.0000 −1.34292 −0.671460 − 0.741041i \(-0.734332\pi\)
−0.671460 + 0.741041i \(0.734332\pi\)
\(642\) 0 0
\(643\) −36.0000 −1.41970 −0.709851 − 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.0000 −0.786281 −0.393141 − 0.919478i \(-0.628611\pi\)
−0.393141 + 0.919478i \(0.628611\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18.0000 −0.704394 −0.352197 − 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 0 0
\(655\) 44.0000 1.71922
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 − 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 42.0000 1.62869
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) −29.0000 −1.11787 −0.558934 − 0.829212i \(-0.688789\pi\)
−0.558934 + 0.829212i \(0.688789\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −46.0000 −1.76792 −0.883962 − 0.467559i \(-0.845134\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(678\) 0 0
\(679\) −51.0000 −1.95720
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 − 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) 0 0
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.00000 0.0761939
\(690\) 0 0
\(691\) 23.0000 0.874961 0.437481 − 0.899228i \(-0.355871\pi\)
0.437481 + 0.899228i \(0.355871\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 42.0000 1.59315
\(696\) 0 0
\(697\) 48.0000 1.81813
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −48.0000 −1.81293 −0.906467 − 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 0 0
\(703\) −21.0000 −0.792030
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 17.0000 0.638448 0.319224 − 0.947679i \(-0.396578\pi\)
0.319224 + 0.947679i \(0.396578\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 26.0000 0.969636 0.484818 − 0.874615i \(-0.338886\pi\)
0.484818 + 0.874615i \(0.338886\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) −19.0000 −0.701781 −0.350891 − 0.936416i \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.0000 0.589368
\(738\) 0 0
\(739\) 35.0000 1.28750 0.643748 − 0.765238i \(-0.277379\pi\)
0.643748 + 0.765238i \(0.277379\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.00000 −0.146746 −0.0733729 − 0.997305i \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 18.0000 0.657706
\(750\) 0 0
\(751\) 15.0000 0.547358 0.273679 − 0.961821i \(-0.411759\pi\)
0.273679 + 0.961821i \(0.411759\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 − 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.00000 −0.290000 −0.145000 − 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) 0 0
\(763\) 33.0000 1.19468
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.0000 −0.361079
\(768\) 0 0
\(769\) 11.0000 0.396670 0.198335 − 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.0000 −0.431610 −0.215805 − 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 0 0
\(775\) 1.00000 0.0359211
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 42.0000 1.50481
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14.0000 0.499681
\(786\) 0 0
\(787\) 4.00000 0.142585 0.0712923 − 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 32.0000 1.13350 0.566749 − 0.823890i \(-0.308201\pi\)
0.566749 + 0.823890i \(0.308201\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 20.0000 0.705785
\(804\) 0 0
\(805\) 24.0000 0.845889
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.00000 −0.0703163 −0.0351581 − 0.999382i \(-0.511193\pi\)
−0.0351581 + 0.999382i \(0.511193\pi\)
\(810\) 0 0
\(811\) 37.0000 1.29925 0.649623 − 0.760257i \(-0.274927\pi\)
0.649623 + 0.760257i \(0.274927\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 18.0000 0.630512
\(816\) 0 0
\(817\) −7.00000 −0.244899
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6.00000 0.209401 0.104701 − 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 0 0
\(823\) −43.0000 −1.49889 −0.749443 − 0.662069i \(-0.769679\pi\)
−0.749443 + 0.662069i \(0.769679\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −26.0000 −0.904109 −0.452054 − 0.891990i \(-0.649309\pi\)
−0.452054 + 0.891990i \(0.649309\pi\)
\(828\) 0 0
\(829\) 25.0000 0.868286 0.434143 − 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −16.0000 −0.554367
\(834\) 0 0
\(835\) 36.0000 1.24583
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −30.0000 −1.03572 −0.517858 − 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −24.0000 −0.825625
\(846\) 0 0
\(847\) 21.0000 0.721569
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 0 0
\(853\) −22.0000 −0.753266 −0.376633 − 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 54.0000 1.84460 0.922302 − 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) 0 0
\(859\) −15.0000 −0.511793 −0.255897 − 0.966704i \(-0.582371\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −46.0000 −1.56586 −0.782929 − 0.622111i \(-0.786275\pi\)
−0.782929 + 0.622111i \(0.786275\pi\)
\(864\) 0 0
\(865\) 48.0000 1.63205
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −22.0000 −0.746299
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 36.0000 1.21702
\(876\) 0 0
\(877\) 3.00000 0.101303 0.0506514 − 0.998716i \(-0.483870\pi\)
0.0506514 + 0.998716i \(0.483870\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −8.00000 −0.269527 −0.134763 − 0.990878i \(-0.543027\pi\)
−0.134763 + 0.990878i \(0.543027\pi\)
\(882\) 0 0
\(883\) −13.0000 −0.437485 −0.218742 − 0.975783i \(-0.570195\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −56.0000 −1.88030 −0.940148 − 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 0 0
\(889\) 15.0000 0.503084
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 42.0000 1.40548
\(894\) 0 0
\(895\) −24.0000 −0.802232
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) −16.0000 −0.533037
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6.00000 −0.199447
\(906\) 0 0
\(907\) 13.0000 0.431658 0.215829 − 0.976431i \(-0.430755\pi\)
0.215829 + 0.976431i \(0.430755\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −16.0000 −0.530104 −0.265052 − 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) 0 0
\(913\) 8.00000 0.264761
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −66.0000 −2.17951
\(918\) 0 0
\(919\) 16.0000 0.527791 0.263896 − 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14.0000 −0.460816
\(924\) 0 0
\(925\) −3.00000 −0.0986394
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −20.0000 −0.656179 −0.328089 − 0.944647i \(-0.606405\pi\)
−0.328089 + 0.944647i \(0.606405\pi\)
\(930\) 0 0
\(931\) −14.0000 −0.458831
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −32.0000 −1.04651
\(936\) 0 0
\(937\) 27.0000 0.882052 0.441026 − 0.897494i \(-0.354615\pi\)
0.441026 + 0.897494i \(0.354615\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.00000 −0.195594 −0.0977972 − 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) 0 0
\(943\) 24.0000 0.781548
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −24.0000 −0.779895 −0.389948 − 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) 0 0
\(949\) 10.0000 0.324614
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) −24.0000 −0.776622
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 28.0000 0.901352
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 − 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −30.0000 −0.962746 −0.481373 − 0.876516i \(-0.659862\pi\)
−0.481373 + 0.876516i \(0.659862\pi\)
\(972\) 0 0
\(973\) −63.0000 −2.01969
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.00000 −0.191957 −0.0959785 − 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 0 0
\(979\) −36.0000 −1.15056
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 36.0000 1.14822 0.574111 − 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 − 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −34.0000 −1.07787
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 0 0
\(999\) 0 0
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 1944.2.a.g.1.1 yes 1
3.2 odd 2 1944.2.a.b.1.1 ✓ 1
4.3 odd 2 3888.2.a.s.1.1 1
9.2 odd 6 1944.2.i.i.1297.1 2
9.4 even 3 1944.2.i.d.649.1 2
9.5 odd 6 1944.2.i.i.649.1 2
9.7 even 3 1944.2.i.d.1297.1 2
12.11 even 2 3888.2.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1944.2.a.b.1.1 ✓ 1 3.2 odd 2
1944.2.a.g.1.1 yes 1 1.1 even 1 trivial
1944.2.i.d.649.1 2 9.4 even 3
1944.2.i.d.1297.1 2 9.7 even 3
1944.2.i.i.649.1 2 9.5 odd 6
1944.2.i.i.1297.1 2 9.2 odd 6
3888.2.a.f.1.1 1 12.11 even 2
3888.2.a.s.1.1 1 4.3 odd 2