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Properties

Label 9660.2.a.e.1.1
Level $9660$
Weight $2$
Character 9660.1
Self dual yes
Analytic conductor $77.135$
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] = [9660,2,Mod(1,9660)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9660, 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("9660.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9660 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9660.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: \(77.1354883526\)
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 \(\chi\) \(=\) 9660.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} +2.00000 q^{13} -1.00000 q^{15} +2.00000 q^{17} -6.00000 q^{19} +1.00000 q^{21} +1.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} -2.00000 q^{29} +4.00000 q^{31} -1.00000 q^{35} -12.0000 q^{37} +2.00000 q^{39} -10.0000 q^{41} -12.0000 q^{43} -1.00000 q^{45} +4.00000 q^{47} +1.00000 q^{49} +2.00000 q^{51} -2.00000 q^{53} -6.00000 q^{57} -6.00000 q^{59} -2.00000 q^{61} +1.00000 q^{63} -2.00000 q^{65} -4.00000 q^{67} +1.00000 q^{69} -6.00000 q^{71} +2.00000 q^{73} +1.00000 q^{75} +14.0000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -2.00000 q^{85} -2.00000 q^{87} +2.00000 q^{89} +2.00000 q^{91} +4.00000 q^{93} +6.00000 q^{95} +4.00000 q^{97} +O(q^{100})\)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 − 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 − 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −12.0000 −1.97279 −0.986394 − 0.164399i \(-0.947432\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 − 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 4.00000 0.583460 0.291730 − 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) 0 0
\(59\) −6.00000 −0.781133 −0.390567 − 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 1.00000 0.125988
\(64\) 0 0
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 − 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 − 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) −2.00000 −0.214423
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 − 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 4.00000 0.414781
\(94\) 0 0
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) 4.00000 0.406138 0.203069 − 0.979164i \(-0.434908\pi\)
0.203069 + 0.979164i \(0.434908\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 − 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 − 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −12.0000 −1.13899
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 − 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −10.0000 −0.901670
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 − 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 22.0000 1.87959 0.939793 − 0.341743i \(-0.111017\pi\)
0.939793 + 0.341743i \(0.111017\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) 1.00000 0.0824786
\(148\) 0 0
\(149\) 14.0000 1.14692 0.573462 − 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −24.0000 −1.91541 −0.957704 − 0.287754i \(-0.907091\pi\)
−0.957704 + 0.287754i \(0.907091\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) 0 0
\(173\) 8.00000 0.608229 0.304114 − 0.952636i \(-0.401639\pi\)
0.304114 + 0.952636i \(0.401639\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 0 0
\(179\) −14.0000 −1.04641 −0.523205 − 0.852207i \(-0.675264\pi\)
−0.523205 + 0.852207i \(0.675264\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 − 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0 0
\(185\) 12.0000 0.882258
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 − 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 − 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 0 0
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) −24.0000 −1.70993 −0.854965 − 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 − 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) 10.0000 0.698430
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −24.0000 −1.65223 −0.826114 − 0.563503i \(-0.809453\pi\)
−0.826114 + 0.563503i \(0.809453\pi\)
\(212\) 0 0
\(213\) −6.00000 −0.411113
\(214\) 0 0
\(215\) 12.0000 0.818393
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 20.0000 1.32745 0.663723 − 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 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
\(235\) −4.00000 −0.260931
\(236\) 0 0
\(237\) 14.0000 0.909398
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 − 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −26.0000 −1.67481 −0.837404 − 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −12.0000 −0.763542
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 − 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −2.00000 −0.125245
\(256\) 0 0
\(257\) 20.0000 1.24757 0.623783 − 0.781598i \(-0.285595\pi\)
0.623783 + 0.781598i \(0.285595\pi\)
\(258\) 0 0
\(259\) −12.0000 −0.745644
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 0 0
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 − 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 − 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 0 0
\(273\) 2.00000 0.121046
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −26.0000 −1.56219 −0.781094 − 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 − 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 − 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 0 0
\(285\) 6.00000 0.355409
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 4.00000 0.234484
\(292\) 0 0
\(293\) −2.00000 −0.116841 −0.0584206 − 0.998292i \(-0.518606\pi\)
−0.0584206 + 0.998292i \(0.518606\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) −12.0000 −0.691669
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 0 0
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 − 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0 0
\(315\) −1.00000 −0.0563436
\(316\) 0 0
\(317\) −12.0000 −0.673987 −0.336994 − 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 10.0000 0.553001
\(328\) 0 0
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 − 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 0 0
\(333\) −12.0000 −0.657596
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 4.00000 0.217894 0.108947 − 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 0 0
\(339\) 14.0000 0.760376
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −1.00000 −0.0538382
\(346\) 0 0
\(347\) −12.0000 −0.644194 −0.322097 − 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) 18.0000 0.963518 0.481759 − 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 4.00000 0.212899 0.106449 − 0.994318i \(-0.466052\pi\)
0.106449 + 0.994318i \(0.466052\pi\)
\(354\) 0 0
\(355\) 6.00000 0.318447
\(356\) 0 0
\(357\) 2.00000 0.105851
\(358\) 0 0
\(359\) 12.0000 0.633336 0.316668 − 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −28.0000 −1.46159 −0.730794 − 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 0 0
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) 8.00000 0.414224 0.207112 − 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 34.0000 1.74646 0.873231 − 0.487306i \(-0.162020\pi\)
0.873231 + 0.487306i \(0.162020\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.0000 −0.609994
\(388\) 0 0
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) −14.0000 −0.704416
\(396\) 0 0
\(397\) −10.0000 −0.501886 −0.250943 − 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) 0 0
\(399\) −6.00000 −0.300376
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 − 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 − 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) 22.0000 1.08518
\(412\) 0 0
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 − 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) 4.00000 0.194487
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) −2.00000 −0.0967868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 32.0000 1.54139 0.770693 − 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 0 0
\(433\) 4.00000 0.192228 0.0961139 − 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 0 0
\(435\) 2.00000 0.0958927
\(436\) 0 0
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) −32.0000 −1.52728 −0.763638 − 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 − 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) −2.00000 −0.0948091
\(446\) 0 0
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 − 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −8.00000 −0.375873
\(454\) 0 0
\(455\) −2.00000 −0.0937614
\(456\) 0 0
\(457\) −28.0000 −1.30978 −0.654892 − 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) 0 0
\(459\) 2.00000 0.0933520
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 − 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 − 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 0 0
\(465\) −4.00000 −0.185496
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) −24.0000 −1.10586
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −6.00000 −0.275299
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) 28.0000 1.27935 0.639676 − 0.768644i \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) 0 0
\(481\) −24.0000 −1.09431
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) −4.00000 −0.181631
\(486\) 0 0
\(487\) −24.0000 −1.08754 −0.543772 − 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 10.0000 0.451294 0.225647 − 0.974209i \(-0.427550\pi\)
0.225647 + 0.974209i \(0.427550\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.00000 −0.269137
\(498\) 0 0
\(499\) 20.0000 0.895323 0.447661 − 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 0 0
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) −6.00000 −0.264906
\(514\) 0 0
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 − 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −32.0000 −1.39926 −0.699631 − 0.714504i \(-0.746652\pi\)
−0.699631 + 0.714504i \(0.746652\pi\)
\(524\) 0 0
\(525\) 1.00000 0.0436436
\(526\) 0 0
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) −20.0000 −0.866296
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) −14.0000 −0.604145
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −14.0000 −0.601907 −0.300954 − 0.953639i \(-0.597305\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(542\) 0 0
\(543\) 10.0000 0.429141
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 − 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 14.0000 0.595341
\(554\) 0 0
\(555\) 12.0000 0.509372
\(556\) 0 0
\(557\) −2.00000 −0.0847427 −0.0423714 − 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −14.0000 −0.588984
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 2.00000 0.0836974 0.0418487 − 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 − 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 0 0
\(579\) −2.00000 −0.0831172
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −2.00000 −0.0826898
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 − 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) −24.0000 −0.988903
\(590\) 0 0
\(591\) −24.0000 −0.987228
\(592\) 0 0
\(593\) 28.0000 1.14982 0.574911 − 0.818216i \(-0.305037\pi\)
0.574911 + 0.818216i \(0.305037\pi\)
\(594\) 0 0
\(595\) −2.00000 −0.0819920
\(596\) 0 0
\(597\) −10.0000 −0.409273
\(598\) 0 0
\(599\) −14.0000 −0.572024 −0.286012 − 0.958226i \(-0.592330\pi\)
−0.286012 + 0.958226i \(0.592330\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 − 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 0 0
\(609\) −2.00000 −0.0810441
\(610\) 0 0
\(611\) 8.00000 0.323645
\(612\) 0 0
\(613\) 16.0000 0.646234 0.323117 − 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 0 0
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) −10.0000 −0.402585 −0.201292 − 0.979531i \(-0.564514\pi\)
−0.201292 + 0.979531i \(0.564514\pi\)
\(618\) 0 0
\(619\) −6.00000 −0.241160 −0.120580 − 0.992704i \(-0.538475\pi\)
−0.120580 + 0.992704i \(0.538475\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 2.00000 0.0801283
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) 22.0000 0.875806 0.437903 − 0.899022i \(-0.355721\pi\)
0.437903 + 0.899022i \(0.355721\pi\)
\(632\) 0 0
\(633\) −24.0000 −0.953914
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) −14.0000 −0.552967 −0.276483 − 0.961019i \(-0.589169\pi\)
−0.276483 + 0.961019i \(0.589169\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) −28.0000 −1.10079 −0.550397 − 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 0 0
\(653\) −24.0000 −0.939193 −0.469596 − 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) 18.0000 0.703318
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 − 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 − 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 0 0
\(663\) 4.00000 0.155347
\(664\) 0 0
\(665\) 6.00000 0.232670
\(666\) 0 0
\(667\) −2.00000 −0.0774403
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −6.00000 −0.231283 −0.115642 − 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 42.0000 1.61419 0.807096 − 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 − 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) −22.0000 −0.840577
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 0 0
\(689\) −4.00000 −0.152388
\(690\) 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
\(695\) 4.00000 0.151729
\(696\) 0 0
\(697\) −20.0000 −0.757554
\(698\) 0 0
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 72.0000 2.71553
\(704\) 0 0
\(705\) −4.00000 −0.150649
\(706\) 0 0
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) 30.0000 1.12667 0.563337 − 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) 0 0
\(711\) 14.0000 0.525041
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.00000 −0.224074
\(718\) 0 0
\(719\) 6.00000 0.223762 0.111881 − 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) −26.0000 −0.966950
\(724\) 0 0
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) −48.0000 −1.78022 −0.890111 − 0.455744i \(-0.849373\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) −24.0000 −0.886460 −0.443230 − 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(734\) 0 0
\(735\) −1.00000 −0.0368856
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 − 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −14.0000 −0.512920
\(746\) 0 0
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −18.0000 −0.656829 −0.328415 − 0.944534i \(-0.606514\pi\)
−0.328415 + 0.944534i \(0.606514\pi\)
\(752\) 0 0
\(753\) −4.00000 −0.145768
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 36.0000 1.30844 0.654221 − 0.756303i \(-0.272997\pi\)
0.654221 + 0.756303i \(0.272997\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 50.0000 1.81250 0.906249 − 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) −2.00000 −0.0723102
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 30.0000 1.08183 0.540914 − 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) 0 0
\(773\) 18.0000 0.647415 0.323708 − 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −12.0000 −0.430498
\(778\) 0 0
\(779\) 60.0000 2.14972
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 24.0000 0.856597
\(786\) 0 0
\(787\) 12.0000 0.427754 0.213877 − 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 0 0
\(789\) −16.0000 −0.569615
\(790\) 0 0
\(791\) 14.0000 0.497783
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) 0 0
\(795\) 2.00000 0.0709327
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 2.00000 0.0706665
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −1.00000 −0.0352454
\(806\) 0 0
\(807\) −14.0000 −0.492823
\(808\) 0 0
\(809\) 54.0000 1.89854 0.949269 − 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 0 0
\(811\) 4.00000 0.140459 0.0702295 − 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 0 0
\(813\) 24.0000 0.841717
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 0 0
\(817\) 72.0000 2.51896
\(818\) 0 0
\(819\) 2.00000 0.0698857
\(820\) 0 0
\(821\) −34.0000 −1.18661 −0.593304 − 0.804978i \(-0.702177\pi\)
−0.593304 + 0.804978i \(0.702177\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 − 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 − 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) 0 0
\(829\) 50.0000 1.73657 0.868286 − 0.496064i \(-0.165222\pi\)
0.868286 + 0.496064i \(0.165222\pi\)
\(830\) 0 0
\(831\) −26.0000 −0.901930
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 4.00000 0.138260
\(838\) 0 0
\(839\) −8.00000 −0.276191 −0.138095 − 0.990419i \(-0.544098\pi\)
−0.138095 + 0.990419i \(0.544098\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 6.00000 0.206651
\(844\) 0 0
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) 0 0
\(849\) 16.0000 0.549119
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 0 0
\(853\) −10.0000 −0.342393 −0.171197 − 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 0 0
\(855\) 6.00000 0.205196
\(856\) 0 0
\(857\) 24.0000 0.819824 0.409912 − 0.912125i \(-0.365559\pi\)
0.409912 + 0.912125i \(0.365559\pi\)
\(858\) 0 0
\(859\) 48.0000 1.63774 0.818869 − 0.573980i \(-0.194601\pi\)
0.818869 + 0.573980i \(0.194601\pi\)
\(860\) 0 0
\(861\) −10.0000 −0.340799
\(862\) 0 0
\(863\) −16.0000 −0.544646 −0.272323 − 0.962206i \(-0.587792\pi\)
−0.272323 + 0.962206i \(0.587792\pi\)
\(864\) 0 0
\(865\) −8.00000 −0.272008
\(866\) 0 0
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 0 0
\(873\) 4.00000 0.135379
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 34.0000 1.14810 0.574049 − 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 0 0
\(879\) −2.00000 −0.0674583
\(880\) 0 0
\(881\) −2.00000 −0.0673817 −0.0336909 − 0.999432i \(-0.510726\pi\)
−0.0336909 + 0.999432i \(0.510726\pi\)
\(882\) 0 0
\(883\) 12.0000 0.403832 0.201916 − 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 0 0
\(885\) 6.00000 0.201688
\(886\) 0 0
\(887\) −48.0000 −1.61168 −0.805841 − 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −24.0000 −0.803129
\(894\) 0 0
\(895\) 14.0000 0.467968
\(896\) 0 0
\(897\) 2.00000 0.0667781
\(898\) 0 0
\(899\) −8.00000 −0.266815
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) −12.0000 −0.399335
\(904\) 0 0
\(905\) −10.0000 −0.332411
\(906\) 0 0
\(907\) −16.0000 −0.531271 −0.265636 − 0.964073i \(-0.585582\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) −60.0000 −1.98789 −0.993944 − 0.109885i \(-0.964952\pi\)
−0.993944 + 0.109885i \(0.964952\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 2.00000 0.0661180
\(916\) 0 0
\(917\) −18.0000 −0.594412
\(918\) 0 0
\(919\) −38.0000 −1.25350 −0.626752 − 0.779219i \(-0.715616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) −12.0000 −0.394558
\(926\) 0 0
\(927\) 4.00000 0.131377
\(928\) 0 0
\(929\) 58.0000 1.90292 0.951459 − 0.307775i \(-0.0995844\pi\)
0.951459 + 0.307775i \(0.0995844\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 0 0
\(933\) −18.0000 −0.589294
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −56.0000 −1.82944 −0.914720 − 0.404088i \(-0.867589\pi\)
−0.914720 + 0.404088i \(0.867589\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −10.0000 −0.325991 −0.162995 − 0.986627i \(-0.552116\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(942\) 0 0
\(943\) −10.0000 −0.325645
\(944\) 0 0
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) −48.0000 −1.55979 −0.779895 − 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) 0 0
\(949\) 4.00000 0.129845
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −14.0000 −0.453504 −0.226752 − 0.973952i \(-0.572811\pi\)
−0.226752 + 0.973952i \(0.572811\pi\)
\(954\) 0 0
\(955\) −8.00000 −0.258874
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.0000 0.710417
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) 0 0
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 − 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 0 0
\(969\) −12.0000 −0.385496
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 0 0
\(975\) 2.00000 0.0640513
\(976\) 0 0
\(977\) −10.0000 −0.319928 −0.159964 − 0.987123i \(-0.551138\pi\)
−0.159964 + 0.987123i \(0.551138\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 10.0000 0.319275
\(982\) 0 0
\(983\) −40.0000 −1.27580 −0.637901 − 0.770118i \(-0.720197\pi\)
−0.637901 + 0.770118i \(0.720197\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) 0 0
\(987\) 4.00000 0.127321
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) −4.00000 −0.127064 −0.0635321 − 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) 0 0
\(993\) −28.0000 −0.888553
\(994\) 0 0
\(995\) 10.0000 0.317021
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 0 0
\(999\) −12.0000 −0.379663
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 9660.2.a.e.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9660.2.a.e.1.1 ✓ 1 1.1 even 1 trivial