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Properties

Label 3024.2.a.bd.1.1
Level $3024$
Weight $2$
Character 3024.1
Self dual yes
Analytic conductor $24.147$
Analytic rank $0$
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] = [3024,2,Mod(1,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3024.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+4.00000 q^{5} +1.00000 q^{7} +4.00000 q^{11} +3.00000 q^{13} -7.00000 q^{17} -2.00000 q^{19} +1.00000 q^{23} +11.0000 q^{25} +1.00000 q^{29} +9.00000 q^{31} +4.00000 q^{35} +2.00000 q^{37} +6.00000 q^{41} -11.0000 q^{43} +6.00000 q^{47} +1.00000 q^{49} -9.00000 q^{53} +16.0000 q^{55} +5.00000 q^{59} -6.00000 q^{61} +12.0000 q^{65} -7.00000 q^{67} +7.00000 q^{71} -14.0000 q^{73} +4.00000 q^{77} +6.00000 q^{79} +4.00000 q^{83} -28.0000 q^{85} -3.00000 q^{89} +3.00000 q^{91} -8.00000 q^{95} -8.00000 q^{97} +O(q^{100})\)

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
\(5\) 4.00000 1.78885 0.894427 − 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 − 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.00000 −1.69775 −0.848875 − 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 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
\(23\) 1.00000 0.208514 0.104257 − 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 − 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 9.00000 1.61645 0.808224 − 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 − 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 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
\(55\) 16.0000 2.15744
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.00000 0.650945 0.325472 − 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 − 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 − 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 − 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 6.00000 0.675053 0.337526 − 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 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
\(85\) −28.0000 −3.03703
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 − 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 − 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 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
\(103\) −17.0000 −1.67506 −0.837530 − 0.546392i \(-0.816001\pi\)
−0.837530 + 0.546392i \(0.816001\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 − 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 − 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 − 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 − 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 22.0000 1.87959 0.939793 − 0.341743i \(-0.111017\pi\)
0.939793 + 0.341743i \(0.111017\pi\)
\(138\) 0 0
\(139\) −10.0000 −0.848189 −0.424094 − 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 −0.245770 −0.122885 − 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 36.0000 2.89159
\(156\) 0 0
\(157\) 17.0000 1.35675 0.678374 − 0.734717i \(-0.262685\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 1.00000 0.0783260 0.0391630 − 0.999233i \(-0.487531\pi\)
0.0391630 + 0.999233i \(0.487531\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 − 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.00000 −0.608229 −0.304114 − 0.952636i \(-0.598361\pi\)
−0.304114 + 0.952636i \(0.598361\pi\)
\(174\) 0 0
\(175\) 11.0000 0.831522
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −9.00000 −0.668965 −0.334482 − 0.942402i \(-0.608561\pi\)
−0.334482 + 0.942402i \(0.608561\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) 0 0
\(187\) −28.0000 −2.04756
\(188\) 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
\(193\) 5.00000 0.359908 0.179954 − 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 26.0000 1.85242 0.926212 − 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) 0 0
\(199\) 7.00000 0.496217 0.248108 − 0.968732i \(-0.420191\pi\)
0.248108 + 0.968732i \(0.420191\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.00000 0.0701862
\(204\) 0 0
\(205\) 24.0000 1.67623
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) 1.00000 0.0688428 0.0344214 − 0.999407i \(-0.489041\pi\)
0.0344214 + 0.999407i \(0.489041\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −44.0000 −3.00078
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −21.0000 −1.41261
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 − 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.00000 0.597351 0.298675 − 0.954355i \(-0.403455\pi\)
0.298675 + 0.954355i \(0.403455\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 − 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 −0.262049 −0.131024 − 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) 0 0
\(235\) 24.0000 1.56559
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 − 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 − 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.00000 0.255551
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 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
\(257\) 30.0000 1.87135 0.935674 − 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) 0 0
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.00000 −0.554964 −0.277482 − 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 0 0
\(265\) −36.0000 −2.21146
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.00000 0.243884 0.121942 − 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(270\) 0 0
\(271\) −3.00000 −0.182237 −0.0911185 − 0.995840i \(-0.529044\pi\)
−0.0911185 + 0.995840i \(0.529044\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 44.0000 2.65330
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 − 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −28.0000 −1.66443 −0.832214 − 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 20.0000 1.16445
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.00000 0.173494
\(300\) 0 0
\(301\) −11.0000 −0.634029
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −24.0000 −1.37424
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 − 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 − 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 − 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 14.0000 0.778981
\(324\) 0 0
\(325\) 33.0000 1.83051
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) 31.0000 1.70391 0.851957 − 0.523612i \(-0.175416\pi\)
0.851957 + 0.523612i \(0.175416\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −28.0000 −1.52980
\(336\) 0 0
\(337\) 27.0000 1.47078 0.735392 − 0.677642i \(-0.236998\pi\)
0.735392 + 0.677642i \(0.236998\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.0000 1.94951
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 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
\(349\) 25.0000 1.33822 0.669110 − 0.743164i \(-0.266676\pi\)
0.669110 + 0.743164i \(0.266676\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 0.798369 0.399185 − 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 0 0
\(355\) 28.0000 1.48609
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.0000 0.580558 0.290279 − 0.956942i \(-0.406252\pi\)
0.290279 + 0.956942i \(0.406252\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −56.0000 −2.93117
\(366\) 0 0
\(367\) 25.0000 1.30499 0.652495 − 0.757793i \(-0.273722\pi\)
0.652495 + 0.757793i \(0.273722\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.00000 −0.467257
\(372\) 0 0
\(373\) −38.0000 −1.96757 −0.983783 − 0.179364i \(-0.942596\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 − 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.00000 0.204390 0.102195 − 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) 0 0
\(385\) 16.0000 0.815436
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −14.0000 −0.709828 −0.354914 − 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) −7.00000 −0.354005
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 24.0000 1.20757
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 − 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 − 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 27.0000 1.34497
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 − 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.00000 0.246034
\(414\) 0 0
\(415\) 16.0000 0.785409
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 33.0000 1.61216 0.806078 − 0.591810i \(-0.201586\pi\)
0.806078 + 0.591810i \(0.201586\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 − 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −77.0000 −3.73505
\(426\) 0 0
\(427\) −6.00000 −0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 8.00000 0.384455 0.192228 − 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) −9.00000 −0.429547 −0.214773 − 0.976664i \(-0.568901\pi\)
−0.214773 + 0.976664i \(0.568901\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −26.0000 −1.23530 −0.617649 − 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) 0 0
\(445\) −12.0000 −0.568855
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.00000 0.188772 0.0943858 − 0.995536i \(-0.469911\pi\)
0.0943858 + 0.995536i \(0.469911\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −29.0000 −1.35656 −0.678281 − 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 − 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 − 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.00000 0.370196 0.185098 − 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −44.0000 −2.02312
\(474\) 0 0
\(475\) −22.0000 −1.00943
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.00000 −0.365529 −0.182765 − 0.983157i \(-0.558505\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −32.0000 −1.45305
\(486\) 0 0
\(487\) −26.0000 −1.17817 −0.589086 − 0.808070i \(-0.700512\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 − 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) −7.00000 −0.315264
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.00000 0.313993
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 − 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) 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
\(505\) 40.0000 1.77998
\(506\) 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
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −68.0000 −2.99644
\(516\) 0 0
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0000 −0.657162 −0.328581 − 0.944476i \(-0.606570\pi\)
−0.328581 + 0.944476i \(0.606570\pi\)
\(522\) 0 0
\(523\) 16.0000 0.699631 0.349816 − 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −63.0000 −2.74432
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) −48.0000 −2.07522
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −36.0000 −1.54776 −0.773880 − 0.633332i \(-0.781687\pi\)
−0.773880 + 0.633332i \(0.781687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 64.0000 2.74146
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 − 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.00000 −0.0852029
\(552\) 0 0
\(553\) 6.00000 0.255146
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000 0.0423714 0.0211857 − 0.999776i \(-0.493256\pi\)
0.0211857 + 0.999776i \(0.493256\pi\)
\(558\) 0 0
\(559\) −33.0000 −1.39575
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.0000 −0.463595 −0.231797 − 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 0 0
\(565\) −32.0000 −1.34625
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.0000 0.503066 0.251533 − 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 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
\(575\) 11.0000 0.458732
\(576\) 0 0
\(577\) 10.0000 0.416305 0.208153 − 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.00000 0.165948
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 25.0000 1.03186 0.515930 − 0.856631i \(-0.327446\pi\)
0.515930 + 0.856631i \(0.327446\pi\)
\(588\) 0 0
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18.0000 −0.739171 −0.369586 − 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) −28.0000 −1.14789
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −21.0000 −0.858037 −0.429018 − 0.903296i \(-0.641140\pi\)
−0.429018 + 0.903296i \(0.641140\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 − 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.0000 0.813116
\(606\) 0 0
\(607\) −39.0000 −1.58296 −0.791481 − 0.611194i \(-0.790689\pi\)
−0.791481 + 0.611194i \(0.790689\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0000 0.728202
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 − 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.0000 0.563619 0.281809 − 0.959470i \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) 0 0
\(619\) 14.0000 0.562708 0.281354 − 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.00000 −0.120192
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14.0000 −0.558217
\(630\) 0 0
\(631\) 4.00000 0.159237 0.0796187 − 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −28.0000 −1.10593 −0.552967 − 0.833203i \(-0.686504\pi\)
−0.552967 + 0.833203i \(0.686504\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −42.0000 −1.65119 −0.825595 − 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.00000 0.117399 0.0586995 − 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) 0 0
\(655\) −4.00000 −0.156293
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 − 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 − 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 23.0000 0.886585 0.443292 − 0.896377i \(-0.353810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 48.0000 1.83667 0.918334 − 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 0 0
\(685\) 88.0000 3.36231
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −27.0000 −1.02862
\(690\) 0 0
\(691\) 40.0000 1.52167 0.760836 − 0.648944i \(-0.224789\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −40.0000 −1.51729
\(696\) 0 0
\(697\) −42.0000 −1.59086
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 − 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.0000 0.376089
\(708\) 0 0
\(709\) −40.0000 −1.50223 −0.751116 − 0.660171i \(-0.770484\pi\)
−0.751116 + 0.660171i \(0.770484\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.00000 0.337053
\(714\) 0 0
\(715\) 48.0000 1.79510
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) −17.0000 −0.633113
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 11.0000 0.408530
\(726\) 0 0
\(727\) 29.0000 1.07555 0.537775 − 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 77.0000 2.84795
\(732\) 0 0
\(733\) −15.0000 −0.554038 −0.277019 − 0.960864i \(-0.589346\pi\)
−0.277019 + 0.960864i \(0.589346\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −28.0000 −1.03139
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 − 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −51.0000 −1.87101 −0.935504 − 0.353315i \(-0.885054\pi\)
−0.935504 + 0.353315i \(0.885054\pi\)
\(744\) 0 0
\(745\) −12.0000 −0.439646
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −6.00000 −0.218943 −0.109472 − 0.993990i \(-0.534916\pi\)
−0.109472 + 0.993990i \(0.534916\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −40.0000 −1.45575
\(756\) 0 0
\(757\) −12.0000 −0.436147 −0.218074 − 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13.0000 −0.471250 −0.235625 − 0.971844i \(-0.575714\pi\)
−0.235625 + 0.971844i \(0.575714\pi\)
\(762\) 0 0
\(763\) 16.0000 0.579239
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.0000 0.541619
\(768\) 0 0
\(769\) 4.00000 0.144244 0.0721218 − 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.00000 0.143870 0.0719350 − 0.997409i \(-0.477083\pi\)
0.0719350 + 0.997409i \(0.477083\pi\)
\(774\) 0 0
\(775\) 99.0000 3.55618
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 28.0000 1.00192
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 68.0000 2.42702
\(786\) 0 0
\(787\) −18.0000 −0.641631 −0.320815 − 0.947142i \(-0.603957\pi\)
−0.320815 + 0.947142i \(0.603957\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −8.00000 −0.284447
\(792\) 0 0
\(793\) −18.0000 −0.639199
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) −42.0000 −1.48585
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −56.0000 −1.97620
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −32.0000 −1.12506 −0.562530 − 0.826777i \(-0.690172\pi\)
−0.562530 + 0.826777i \(0.690172\pi\)
\(810\) 0 0
\(811\) 26.0000 0.912983 0.456492 − 0.889728i \(-0.349106\pi\)
0.456492 + 0.889728i \(0.349106\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 0 0
\(817\) 22.0000 0.769683
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −13.0000 −0.453703 −0.226852 − 0.973929i \(-0.572843\pi\)
−0.226852 + 0.973929i \(0.572843\pi\)
\(822\) 0 0
\(823\) 38.0000 1.32460 0.662298 − 0.749240i \(-0.269581\pi\)
0.662298 + 0.749240i \(0.269581\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −42.0000 −1.46048 −0.730242 − 0.683189i \(-0.760592\pi\)
−0.730242 + 0.683189i \(0.760592\pi\)
\(828\) 0 0
\(829\) −26.0000 −0.903017 −0.451509 − 0.892267i \(-0.649114\pi\)
−0.451509 + 0.892267i \(0.649114\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −7.00000 −0.242536
\(834\) 0 0
\(835\) 32.0000 1.10741
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.0000 0.345238 0.172619 − 0.984989i \(-0.444777\pi\)
0.172619 + 0.984989i \(0.444777\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −16.0000 −0.550417
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.00000 0.0685591
\(852\) 0 0
\(853\) 53.0000 1.81469 0.907343 − 0.420392i \(-0.138107\pi\)
0.907343 + 0.420392i \(0.138107\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 27.0000 0.922302 0.461151 − 0.887322i \(-0.347437\pi\)
0.461151 + 0.887322i \(0.347437\pi\)
\(858\) 0 0
\(859\) −2.00000 −0.0682391 −0.0341196 − 0.999418i \(-0.510863\pi\)
−0.0341196 + 0.999418i \(0.510863\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.00000 −0.0340404 −0.0170202 − 0.999855i \(-0.505418\pi\)
−0.0170202 + 0.999855i \(0.505418\pi\)
\(864\) 0 0
\(865\) −32.0000 −1.08803
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 24.0000 0.814144
\(870\) 0 0
\(871\) −21.0000 −0.711558
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) 0 0
\(877\) −8.00000 −0.270141 −0.135070 − 0.990836i \(-0.543126\pi\)
−0.135070 + 0.990836i \(0.543126\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 15.0000 0.505363 0.252681 − 0.967550i \(-0.418688\pi\)
0.252681 + 0.967550i \(0.418688\pi\)
\(882\) 0 0
\(883\) 19.0000 0.639401 0.319700 − 0.947519i \(-0.396418\pi\)
0.319700 + 0.947519i \(0.396418\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.0000 0.402921 0.201460 − 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 48.0000 1.60446
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 9.00000 0.300167
\(900\) 0 0
\(901\) 63.0000 2.09883
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −36.0000 −1.19668
\(906\) 0 0
\(907\) −12.0000 −0.398453 −0.199227 − 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 − 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 0 0
\(913\) 16.0000 0.529523
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.00000 −0.0330229
\(918\) 0 0
\(919\) −22.0000 −0.725713 −0.362857 − 0.931845i \(-0.618198\pi\)
−0.362857 + 0.931845i \(0.618198\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 21.0000 0.691223
\(924\) 0 0
\(925\) 22.0000 0.723356
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 − 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −112.000 −3.66279
\(936\) 0 0
\(937\) −52.0000 −1.69877 −0.849383 − 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.00000 −0.0651981 −0.0325991 − 0.999469i \(-0.510378\pi\)
−0.0325991 + 0.999469i \(0.510378\pi\)
\(942\) 0 0
\(943\) 6.00000 0.195387
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.00000 0.0649913 0.0324956 − 0.999472i \(-0.489654\pi\)
0.0324956 + 0.999472i \(0.489654\pi\)
\(948\) 0 0
\(949\) −42.0000 −1.36338
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 8.00000 0.259145 0.129573 − 0.991570i \(-0.458639\pi\)
0.129573 + 0.991570i \(0.458639\pi\)
\(954\) 0 0
\(955\) −48.0000 −1.55324
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.0000 0.710417
\(960\) 0 0
\(961\) 50.0000 1.61290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.0000 0.643823
\(966\) 0 0
\(967\) 40.0000 1.28631 0.643157 − 0.765735i \(-0.277624\pi\)
0.643157 + 0.765735i \(0.277624\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 15.0000 0.481373 0.240686 − 0.970603i \(-0.422627\pi\)
0.240686 + 0.970603i \(0.422627\pi\)
\(972\) 0 0
\(973\) −10.0000 −0.320585
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −42.0000 −1.34370 −0.671850 − 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 0 0
\(979\) −12.0000 −0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −36.0000 −1.14822 −0.574111 − 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 104.000 3.31372
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −11.0000 −0.349780
\(990\) 0 0
\(991\) −26.0000 −0.825917 −0.412959 − 0.910750i \(-0.635505\pi\)
−0.412959 + 0.910750i \(0.635505\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 28.0000 0.887660
\(996\) 0 0
\(997\) 35.0000 1.10846 0.554231 − 0.832363i \(-0.313013\pi\)
0.554231 + 0.832363i \(0.313013\pi\)
\(998\) 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 3024.2.a.bd.1.1 1
3.2 odd 2 3024.2.a.a.1.1 1
4.3 odd 2 378.2.a.h.1.1 yes 1
12.11 even 2 378.2.a.a.1.1 ✓ 1
20.19 odd 2 9450.2.a.bc.1.1 1
28.27 even 2 2646.2.a.p.1.1 1
36.7 odd 6 1134.2.f.a.757.1 2
36.11 even 6 1134.2.f.p.757.1 2
36.23 even 6 1134.2.f.p.379.1 2
36.31 odd 6 1134.2.f.a.379.1 2
60.59 even 2 9450.2.a.dv.1.1 1
84.83 odd 2 2646.2.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.a.a.1.1 ✓ 1 12.11 even 2
378.2.a.h.1.1 yes 1 4.3 odd 2
1134.2.f.a.379.1 2 36.31 odd 6
1134.2.f.a.757.1 2 36.7 odd 6
1134.2.f.p.379.1 2 36.23 even 6
1134.2.f.p.757.1 2 36.11 even 6
2646.2.a.o.1.1 1 84.83 odd 2
2646.2.a.p.1.1 1 28.27 even 2
3024.2.a.a.1.1 1 3.2 odd 2
3024.2.a.bd.1.1 1 1.1 even 1 trivial
9450.2.a.bc.1.1 1 20.19 odd 2
9450.2.a.dv.1.1 1 60.59 even 2