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Properties

Label 9360.2.a.n.1.1
Level $9360$
Weight $2$
Character 9360.1
Self dual yes
Analytic conductor $74.740$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9360,2,Mod(1,9360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9360, 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("9360.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.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: \(74.7399762919\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 520)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9360.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +O(q^{10})\) \(q-1.00000 q^{5} +2.00000 q^{11} +1.00000 q^{13} -2.00000 q^{17} -2.00000 q^{19} +2.00000 q^{23} +1.00000 q^{25} +6.00000 q^{29} -2.00000 q^{31} -6.00000 q^{37} -2.00000 q^{41} -6.00000 q^{43} -8.00000 q^{47} -7.00000 q^{49} +2.00000 q^{53} -2.00000 q^{55} +6.00000 q^{59} -14.0000 q^{61} -1.00000 q^{65} +10.0000 q^{71} -2.00000 q^{73} +4.00000 q^{79} +12.0000 q^{83} +2.00000 q^{85} +6.00000 q^{89} +2.00000 q^{95} +2.00000 q^{97} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 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
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 − 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 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
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 − 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 − 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 − 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 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
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 − 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 − 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 − 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 − 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 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
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 0.205196
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −2.00000 −0.197066 −0.0985329 − 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.00000 −0.193347 −0.0966736 − 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −2.00000 −0.186501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 10.0000 0.887357 0.443678 − 0.896186i \(-0.353673\pi\)
0.443678 + 0.896186i \(0.353673\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 − 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0000 −0.854358 −0.427179 − 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 − 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 − 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 6.00000 0.478852 0.239426 − 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −22.0000 −1.67263 −0.836315 − 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.00000 −0.298974 −0.149487 − 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 − 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.00000 0.409197
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.0000 1.59294 0.796468 − 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 − 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 − 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.00000 0.447214
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 30.0000 1.84988 0.924940 − 0.380114i \(-0.124115\pi\)
0.924940 + 0.380114i \(0.124115\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 − 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 − 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 0.120605
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 − 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 − 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) −22.0000 −1.30776 −0.653882 − 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 14.0000 0.801638
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 − 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.0000 1.58773 0.793867 − 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) 0 0
\(313\) −30.0000 −1.69570 −0.847850 − 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 0.336994 0.168497 − 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −22.0000 −1.20923 −0.604615 − 0.796518i \(-0.706673\pi\)
−0.604615 + 0.796518i \(0.706673\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 − 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.0000 −0.966291 −0.483145 − 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 − 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) −10.0000 −0.530745
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.0000 0.527780 0.263890 − 0.964553i \(-0.414994\pi\)
0.263890 + 0.964553i \(0.414994\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 30.0000 1.55334 0.776671 − 0.629907i \(-0.216907\pi\)
0.776671 + 0.629907i \(0.216907\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) 30.0000 1.54100 0.770498 − 0.637442i \(-0.220007\pi\)
0.770498 + 0.637442i \(0.220007\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 − 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.00000 −0.0998752 −0.0499376 − 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 − 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8.00000 −0.390826 −0.195413 − 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 − 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.0000 0.867029 0.433515 − 0.901146i \(-0.357273\pi\)
0.433515 + 0.901146i \(0.357273\pi\)
\(432\) 0 0
\(433\) −38.0000 −1.82616 −0.913082 − 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −38.0000 −1.80543 −0.902717 − 0.430234i \(-0.858431\pi\)
−0.902717 + 0.430234i \(0.858431\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 − 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.0000 1.21623 0.608114 − 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) 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
\(463\) 4.00000 0.185896 0.0929479 − 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.00000 −0.277647 −0.138823 − 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.0000 −0.639676 −0.319838 − 0.947472i \(-0.603629\pi\)
−0.319838 + 0.947472i \(0.603629\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 − 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 38.0000 1.70111 0.850557 − 0.525883i \(-0.176265\pi\)
0.850557 + 0.525883i \(0.176265\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10.0000 −0.445878 −0.222939 − 0.974832i \(-0.571565\pi\)
−0.222939 + 0.974832i \(0.571565\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.00000 −0.265945 −0.132973 − 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.00000 0.0881305
\(516\) 0 0
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −38.0000 −1.66481 −0.832405 − 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) −34.0000 −1.48672 −0.743358 − 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.00000 0.174243
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) 2.00000 0.0864675
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −14.0000 −0.603023
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 − 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) 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
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.00000 0.252870 0.126435 − 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 − 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.00000 0.0834058
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 − 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 0.165663
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40.0000 −1.65098 −0.825488 − 0.564419i \(-0.809100\pi\)
−0.825488 + 0.564419i \(0.809100\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 30.0000 1.23195 0.615976 − 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 36.0000 1.47092 0.735460 − 0.677568i \(-0.236966\pi\)
0.735460 + 0.677568i \(0.236966\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) −18.0000 −0.730597 −0.365299 − 0.930890i \(-0.619033\pi\)
−0.365299 + 0.930890i \(0.619033\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 − 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 − 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −30.0000 −1.20580 −0.602901 − 0.797816i \(-0.705989\pi\)
−0.602901 + 0.797816i \(0.705989\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 34.0000 1.35352 0.676759 − 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10.0000 −0.396838
\(636\) 0 0
\(637\) −7.00000 −0.277350
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 − 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.00000 0.235884 0.117942 − 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.00000 −0.234798 −0.117399 − 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) 4.00000 0.156293
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.0000 −0.623272 −0.311636 − 0.950202i \(-0.600877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(660\) 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
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −28.0000 −1.08093
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 − 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 − 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 − 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) 10.0000 0.382080
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.00000 0.0761939
\(690\) 0 0
\(691\) −14.0000 −0.532585 −0.266293 − 0.963892i \(-0.585799\pi\)
−0.266293 + 0.963892i \(0.585799\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 4.00000 0.151511
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 50.0000 1.88847 0.944237 − 0.329267i \(-0.106802\pi\)
0.944237 + 0.329267i \(0.106802\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 48.0000 1.79010 0.895049 − 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −6.00000 −0.222528 −0.111264 − 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 12.0000 0.443836
\(732\) 0 0
\(733\) −2.00000 −0.0738717 −0.0369358 − 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 18.0000 0.662141 0.331070 − 0.943606i \(-0.392590\pi\)
0.331070 + 0.943606i \(0.392590\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 − 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.0000 0.437886 0.218943 − 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) 46.0000 1.67190 0.835949 − 0.548807i \(-0.184918\pi\)
0.835949 + 0.548807i \(0.184918\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.0000 −0.942499 −0.471250 − 0.882000i \(-0.656197\pi\)
−0.471250 + 0.882000i \(0.656197\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.00000 0.216647
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 − 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −42.0000 −1.51064 −0.755318 − 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) 20.0000 0.715656
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.00000 −0.214149
\(786\) 0 0
\(787\) −44.0000 −1.56843 −0.784215 − 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −14.0000 −0.497155
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.00000 −0.141157
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 50.0000 1.75791 0.878953 − 0.476908i \(-0.158243\pi\)
0.878953 + 0.476908i \(0.158243\pi\)
\(810\) 0 0
\(811\) 42.0000 1.47482 0.737410 − 0.675446i \(-0.236049\pi\)
0.737410 + 0.675446i \(0.236049\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) 0 0
\(817\) 12.0000 0.419827
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 − 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) −26.0000 −0.906303 −0.453152 − 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −14.0000 −0.486240 −0.243120 − 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 14.0000 0.485071
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 34.0000 1.17381 0.586905 − 0.809656i \(-0.300346\pi\)
0.586905 + 0.809656i \(0.300346\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 0 0
\(853\) −46.0000 −1.57501 −0.787505 − 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −18.0000 −0.614868 −0.307434 − 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 − 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.00000 0.272323 0.136162 − 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) 0 0
\(865\) 22.0000 0.748022
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 46.0000 1.55331 0.776655 − 0.629926i \(-0.216915\pi\)
0.776655 + 0.629926i \(0.216915\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 26.0000 0.875962 0.437981 − 0.898984i \(-0.355694\pi\)
0.437981 + 0.898984i \(0.355694\pi\)
\(882\) 0 0
\(883\) 26.0000 0.874970 0.437485 − 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22.0000 −0.738688 −0.369344 − 0.929293i \(-0.620418\pi\)
−0.369344 + 0.929293i \(0.620418\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 16.0000 0.535420
\(894\) 0 0
\(895\) 4.00000 0.133705
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −12.0000 −0.400222
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.0000 0.465376
\(906\) 0 0
\(907\) −18.0000 −0.597680 −0.298840 − 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) 24.0000 0.794284
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −4.00000 −0.131948 −0.0659739 − 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.00000 0.196854 0.0984268 − 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) 14.0000 0.458831
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.00000 0.130814
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 − 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 − 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 0 0
\(943\) −4.00000 −0.130258
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.0000 0.453504 0.226752 − 0.973952i \(-0.427189\pi\)
0.226752 + 0.973952i \(0.427189\pi\)
\(954\) 0 0
\(955\) 24.0000 0.776622
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 14.0000 0.450676
\(966\) 0 0
\(967\) 12.0000 0.385894 0.192947 − 0.981209i \(-0.438195\pi\)
0.192947 + 0.981209i \(0.438195\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −52.0000 −1.66876 −0.834380 − 0.551190i \(-0.814174\pi\)
−0.834380 + 0.551190i \(0.814174\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −38.0000 −1.21573 −0.607864 − 0.794041i \(-0.707973\pi\)
−0.607864 + 0.794041i \(0.707973\pi\)
\(978\) 0 0
\(979\) 12.0000 0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −52.0000 −1.65854 −0.829271 − 0.558846i \(-0.811244\pi\)
−0.829271 + 0.558846i \(0.811244\pi\)
\(984\) 0 0
\(985\) 22.0000 0.700978
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) 40.0000 1.27064 0.635321 − 0.772248i \(-0.280868\pi\)
0.635321 + 0.772248i \(0.280868\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 14.0000 0.443384 0.221692 − 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) 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 9360.2.a.n.1.1 1
3.2 odd 2 1040.2.a.c.1.1 1
4.3 odd 2 4680.2.a.e.1.1 1
12.11 even 2 520.2.a.b.1.1 ✓ 1
15.14 odd 2 5200.2.a.bf.1.1 1
24.5 odd 2 4160.2.a.p.1.1 1
24.11 even 2 4160.2.a.a.1.1 1
60.23 odd 4 2600.2.d.c.1249.2 2
60.47 odd 4 2600.2.d.c.1249.1 2
60.59 even 2 2600.2.a.c.1.1 1
156.155 even 2 6760.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
520.2.a.b.1.1 ✓ 1 12.11 even 2
1040.2.a.c.1.1 1 3.2 odd 2
2600.2.a.c.1.1 1 60.59 even 2
2600.2.d.c.1249.1 2 60.47 odd 4
2600.2.d.c.1249.2 2 60.23 odd 4
4160.2.a.a.1.1 1 24.11 even 2
4160.2.a.p.1.1 1 24.5 odd 2
4680.2.a.e.1.1 1 4.3 odd 2
5200.2.a.bf.1.1 1 15.14 odd 2
6760.2.a.k.1.1 1 156.155 even 2
9360.2.a.n.1.1 1 1.1 even 1 trivial