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Properties

Label 2160.4.a.j.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
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] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.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: \(127.444125612\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +34.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +34.0000 q^{7} -48.0000 q^{11} -70.0000 q^{13} +27.0000 q^{17} -119.000 q^{19} -51.0000 q^{23} +25.0000 q^{25} +30.0000 q^{29} +133.000 q^{31} -170.000 q^{35} +218.000 q^{37} -156.000 q^{41} +88.0000 q^{43} -516.000 q^{47} +813.000 q^{49} +639.000 q^{53} +240.000 q^{55} -654.000 q^{59} +461.000 q^{61} +350.000 q^{65} -182.000 q^{67} +900.000 q^{71} +704.000 q^{73} -1632.00 q^{77} +1375.00 q^{79} +915.000 q^{83} -135.000 q^{85} +1116.00 q^{89} -2380.00 q^{91} +595.000 q^{95} -16.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 34.0000 1.83583 0.917914 − 0.396780i \(-0.129872\pi\)
0.917914 + 0.396780i \(0.129872\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −48.0000 −1.31569 −0.657843 − 0.753155i \(-0.728531\pi\)
−0.657843 + 0.753155i \(0.728531\pi\)
\(12\) 0 0
\(13\) −70.0000 −1.49342 −0.746712 − 0.665148i \(-0.768369\pi\)
−0.746712 + 0.665148i \(0.768369\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 27.0000 0.385204 0.192602 − 0.981277i \(-0.438307\pi\)
0.192602 + 0.981277i \(0.438307\pi\)
\(18\) 0 0
\(19\) −119.000 −1.43687 −0.718433 − 0.695596i \(-0.755141\pi\)
−0.718433 + 0.695596i \(0.755141\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −51.0000 −0.462358 −0.231179 − 0.972911i \(-0.574258\pi\)
−0.231179 + 0.972911i \(0.574258\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 30.0000 0.192099 0.0960493 − 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) 0 0
\(31\) 133.000 0.770565 0.385282 − 0.922799i \(-0.374104\pi\)
0.385282 + 0.922799i \(0.374104\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −170.000 −0.821007
\(36\) 0 0
\(37\) 218.000 0.968621 0.484311 − 0.874896i \(-0.339070\pi\)
0.484311 + 0.874896i \(0.339070\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −156.000 −0.594222 −0.297111 − 0.954843i \(-0.596023\pi\)
−0.297111 + 0.954843i \(0.596023\pi\)
\(42\) 0 0
\(43\) 88.0000 0.312090 0.156045 − 0.987750i \(-0.450125\pi\)
0.156045 + 0.987750i \(0.450125\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −516.000 −1.60141 −0.800706 − 0.599058i \(-0.795542\pi\)
−0.800706 + 0.599058i \(0.795542\pi\)
\(48\) 0 0
\(49\) 813.000 2.37026
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 639.000 1.65610 0.828051 − 0.560653i \(-0.189450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(54\) 0 0
\(55\) 240.000 0.588393
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −654.000 −1.44311 −0.721555 − 0.692357i \(-0.756573\pi\)
−0.721555 + 0.692357i \(0.756573\pi\)
\(60\) 0 0
\(61\) 461.000 0.967623 0.483811 − 0.875172i \(-0.339252\pi\)
0.483811 + 0.875172i \(0.339252\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 350.000 0.667879
\(66\) 0 0
\(67\) −182.000 −0.331863 −0.165932 − 0.986137i \(-0.553063\pi\)
−0.165932 + 0.986137i \(0.553063\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 900.000 1.50437 0.752186 − 0.658951i \(-0.229000\pi\)
0.752186 + 0.658951i \(0.229000\pi\)
\(72\) 0 0
\(73\) 704.000 1.12873 0.564363 − 0.825527i \(-0.309122\pi\)
0.564363 + 0.825527i \(0.309122\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1632.00 −2.41537
\(78\) 0 0
\(79\) 1375.00 1.95822 0.979111 − 0.203325i \(-0.0651748\pi\)
0.979111 + 0.203325i \(0.0651748\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 915.000 1.21005 0.605026 − 0.796206i \(-0.293163\pi\)
0.605026 + 0.796206i \(0.293163\pi\)
\(84\) 0 0
\(85\) −135.000 −0.172268
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1116.00 1.32917 0.664583 − 0.747215i \(-0.268609\pi\)
0.664583 + 0.747215i \(0.268609\pi\)
\(90\) 0 0
\(91\) −2380.00 −2.74167
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 595.000 0.642586
\(96\) 0 0
\(97\) −16.0000 −0.0167480 −0.00837399 − 0.999965i \(-0.502666\pi\)
−0.00837399 + 0.999965i \(0.502666\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −348.000 −0.342844 −0.171422 − 0.985198i \(-0.554836\pi\)
−0.171422 + 0.985198i \(0.554836\pi\)
\(102\) 0 0
\(103\) 412.000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −900.000 −0.813143 −0.406571 − 0.913619i \(-0.633276\pi\)
−0.406571 + 0.913619i \(0.633276\pi\)
\(108\) 0 0
\(109\) −115.000 −0.101055 −0.0505275 − 0.998723i \(-0.516090\pi\)
−0.0505275 + 0.998723i \(0.516090\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −966.000 −0.804191 −0.402096 − 0.915598i \(-0.631718\pi\)
−0.402096 + 0.915598i \(0.631718\pi\)
\(114\) 0 0
\(115\) 255.000 0.206773
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 918.000 0.707167
\(120\) 0 0
\(121\) 973.000 0.731029
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1406.00 −0.982381 −0.491190 − 0.871052i \(-0.663438\pi\)
−0.491190 + 0.871052i \(0.663438\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 246.000 0.164070 0.0820348 − 0.996629i \(-0.473858\pi\)
0.0820348 + 0.996629i \(0.473858\pi\)
\(132\) 0 0
\(133\) −4046.00 −2.63784
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −519.000 −0.323658 −0.161829 − 0.986819i \(-0.551739\pi\)
−0.161829 + 0.986819i \(0.551739\pi\)
\(138\) 0 0
\(139\) −1316.00 −0.803034 −0.401517 − 0.915852i \(-0.631517\pi\)
−0.401517 + 0.915852i \(0.631517\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3360.00 1.96488
\(144\) 0 0
\(145\) −150.000 −0.0859091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −372.000 −0.204533 −0.102267 − 0.994757i \(-0.532609\pi\)
−0.102267 + 0.994757i \(0.532609\pi\)
\(150\) 0 0
\(151\) 1456.00 0.784686 0.392343 − 0.919819i \(-0.371665\pi\)
0.392343 + 0.919819i \(0.371665\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −665.000 −0.344607
\(156\) 0 0
\(157\) 956.000 0.485969 0.242984 − 0.970030i \(-0.421874\pi\)
0.242984 + 0.970030i \(0.421874\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1734.00 −0.848810
\(162\) 0 0
\(163\) 2446.00 1.17537 0.587686 − 0.809089i \(-0.300039\pi\)
0.587686 + 0.809089i \(0.300039\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3111.00 −1.44154 −0.720768 − 0.693177i \(-0.756211\pi\)
−0.720768 + 0.693177i \(0.756211\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2397.00 1.05341 0.526707 − 0.850047i \(-0.323427\pi\)
0.526707 + 0.850047i \(0.323427\pi\)
\(174\) 0 0
\(175\) 850.000 0.367165
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −540.000 −0.225483 −0.112742 − 0.993624i \(-0.535963\pi\)
−0.112742 + 0.993624i \(0.535963\pi\)
\(180\) 0 0
\(181\) 2333.00 0.958069 0.479035 − 0.877796i \(-0.340987\pi\)
0.479035 + 0.877796i \(0.340987\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1090.00 −0.433181
\(186\) 0 0
\(187\) −1296.00 −0.506807
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2730.00 −1.03422 −0.517110 − 0.855919i \(-0.672992\pi\)
−0.517110 + 0.855919i \(0.672992\pi\)
\(192\) 0 0
\(193\) −4570.00 −1.70443 −0.852217 − 0.523188i \(-0.824742\pi\)
−0.852217 + 0.523188i \(0.824742\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −675.000 −0.244121 −0.122060 − 0.992523i \(-0.538950\pi\)
−0.122060 + 0.992523i \(0.538950\pi\)
\(198\) 0 0
\(199\) 3112.00 1.10856 0.554281 − 0.832330i \(-0.312993\pi\)
0.554281 + 0.832330i \(0.312993\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1020.00 0.352660
\(204\) 0 0
\(205\) 780.000 0.265744
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5712.00 1.89047
\(210\) 0 0
\(211\) −2441.00 −0.796424 −0.398212 − 0.917294i \(-0.630369\pi\)
−0.398212 + 0.917294i \(0.630369\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −440.000 −0.139571
\(216\) 0 0
\(217\) 4522.00 1.41462
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1890.00 −0.575272
\(222\) 0 0
\(223\) 3418.00 1.02640 0.513198 − 0.858270i \(-0.328461\pi\)
0.513198 + 0.858270i \(0.328461\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4377.00 −1.27979 −0.639894 − 0.768464i \(-0.721022\pi\)
−0.639894 + 0.768464i \(0.721022\pi\)
\(228\) 0 0
\(229\) 4187.00 1.20823 0.604115 − 0.796897i \(-0.293527\pi\)
0.604115 + 0.796897i \(0.293527\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1098.00 0.308723 0.154361 − 0.988014i \(-0.450668\pi\)
0.154361 + 0.988014i \(0.450668\pi\)
\(234\) 0 0
\(235\) 2580.00 0.716173
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6474.00 1.75217 0.876084 − 0.482158i \(-0.160147\pi\)
0.876084 + 0.482158i \(0.160147\pi\)
\(240\) 0 0
\(241\) 3251.00 0.868943 0.434472 − 0.900686i \(-0.356935\pi\)
0.434472 + 0.900686i \(0.356935\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4065.00 −1.06001
\(246\) 0 0
\(247\) 8330.00 2.14585
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1728.00 0.434543 0.217272 − 0.976111i \(-0.430284\pi\)
0.217272 + 0.976111i \(0.430284\pi\)
\(252\) 0 0
\(253\) 2448.00 0.608318
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5469.00 1.32742 0.663710 − 0.747990i \(-0.268981\pi\)
0.663710 + 0.747990i \(0.268981\pi\)
\(258\) 0 0
\(259\) 7412.00 1.77822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3216.00 −0.754019 −0.377010 − 0.926209i \(-0.623048\pi\)
−0.377010 + 0.926209i \(0.623048\pi\)
\(264\) 0 0
\(265\) −3195.00 −0.740631
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8010.00 1.81553 0.907766 − 0.419476i \(-0.137786\pi\)
0.907766 + 0.419476i \(0.137786\pi\)
\(270\) 0 0
\(271\) 3805.00 0.852905 0.426453 − 0.904510i \(-0.359763\pi\)
0.426453 + 0.904510i \(0.359763\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1200.00 −0.263137
\(276\) 0 0
\(277\) 3224.00 0.699319 0.349660 − 0.936877i \(-0.386297\pi\)
0.349660 + 0.936877i \(0.386297\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4530.00 0.961698 0.480849 − 0.876803i \(-0.340329\pi\)
0.480849 + 0.876803i \(0.340329\pi\)
\(282\) 0 0
\(283\) 3292.00 0.691481 0.345740 − 0.938330i \(-0.387628\pi\)
0.345740 + 0.938330i \(0.387628\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5304.00 −1.09089
\(288\) 0 0
\(289\) −4184.00 −0.851618
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7953.00 1.58573 0.792866 − 0.609397i \(-0.208588\pi\)
0.792866 + 0.609397i \(0.208588\pi\)
\(294\) 0 0
\(295\) 3270.00 0.645379
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3570.00 0.690496
\(300\) 0 0
\(301\) 2992.00 0.572944
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2305.00 −0.432734
\(306\) 0 0
\(307\) 5290.00 0.983441 0.491720 − 0.870753i \(-0.336368\pi\)
0.491720 + 0.870753i \(0.336368\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5358.00 0.976927 0.488464 − 0.872584i \(-0.337558\pi\)
0.488464 + 0.872584i \(0.337558\pi\)
\(312\) 0 0
\(313\) 5600.00 1.01128 0.505640 − 0.862744i \(-0.331256\pi\)
0.505640 + 0.862744i \(0.331256\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7341.00 −1.30067 −0.650334 − 0.759649i \(-0.725371\pi\)
−0.650334 + 0.759649i \(0.725371\pi\)
\(318\) 0 0
\(319\) −1440.00 −0.252741
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3213.00 −0.553486
\(324\) 0 0
\(325\) −1750.00 −0.298685
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −17544.0 −2.93991
\(330\) 0 0
\(331\) −380.000 −0.0631018 −0.0315509 − 0.999502i \(-0.510045\pi\)
−0.0315509 + 0.999502i \(0.510045\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 910.000 0.148414
\(336\) 0 0
\(337\) 434.000 0.0701528 0.0350764 − 0.999385i \(-0.488833\pi\)
0.0350764 + 0.999385i \(0.488833\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6384.00 −1.01382
\(342\) 0 0
\(343\) 15980.0 2.51557
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8004.00 1.23826 0.619131 − 0.785287i \(-0.287485\pi\)
0.619131 + 0.785287i \(0.287485\pi\)
\(348\) 0 0
\(349\) 1109.00 0.170096 0.0850479 − 0.996377i \(-0.472896\pi\)
0.0850479 + 0.996377i \(0.472896\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7662.00 1.15526 0.577630 − 0.816298i \(-0.303977\pi\)
0.577630 + 0.816298i \(0.303977\pi\)
\(354\) 0 0
\(355\) −4500.00 −0.672775
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8478.00 −1.24638 −0.623192 − 0.782069i \(-0.714164\pi\)
−0.623192 + 0.782069i \(0.714164\pi\)
\(360\) 0 0
\(361\) 7302.00 1.06459
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3520.00 −0.504781
\(366\) 0 0
\(367\) −13286.0 −1.88971 −0.944855 − 0.327489i \(-0.893798\pi\)
−0.944855 + 0.327489i \(0.893798\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 21726.0 3.04032
\(372\) 0 0
\(373\) 3080.00 0.427551 0.213775 − 0.976883i \(-0.431424\pi\)
0.213775 + 0.976883i \(0.431424\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2100.00 −0.286885
\(378\) 0 0
\(379\) −10109.0 −1.37009 −0.685045 − 0.728500i \(-0.740218\pi\)
−0.685045 + 0.728500i \(0.740218\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8727.00 −1.16431 −0.582153 − 0.813080i \(-0.697789\pi\)
−0.582153 + 0.813080i \(0.697789\pi\)
\(384\) 0 0
\(385\) 8160.00 1.08019
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2712.00 0.353480 0.176740 − 0.984258i \(-0.443445\pi\)
0.176740 + 0.984258i \(0.443445\pi\)
\(390\) 0 0
\(391\) −1377.00 −0.178102
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6875.00 −0.875744
\(396\) 0 0
\(397\) −8818.00 −1.11477 −0.557384 − 0.830255i \(-0.688195\pi\)
−0.557384 + 0.830255i \(0.688195\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3306.00 −0.411705 −0.205853 − 0.978583i \(-0.565997\pi\)
−0.205853 + 0.978583i \(0.565997\pi\)
\(402\) 0 0
\(403\) −9310.00 −1.15078
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10464.0 −1.27440
\(408\) 0 0
\(409\) 6401.00 0.773861 0.386930 − 0.922109i \(-0.373535\pi\)
0.386930 + 0.922109i \(0.373535\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −22236.0 −2.64930
\(414\) 0 0
\(415\) −4575.00 −0.541152
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2256.00 −0.263038 −0.131519 − 0.991314i \(-0.541985\pi\)
−0.131519 + 0.991314i \(0.541985\pi\)
\(420\) 0 0
\(421\) 1811.00 0.209650 0.104825 − 0.994491i \(-0.466572\pi\)
0.104825 + 0.994491i \(0.466572\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 675.000 0.0770407
\(426\) 0 0
\(427\) 15674.0 1.77639
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5454.00 −0.609536 −0.304768 − 0.952427i \(-0.598579\pi\)
−0.304768 + 0.952427i \(0.598579\pi\)
\(432\) 0 0
\(433\) 2990.00 0.331848 0.165924 − 0.986139i \(-0.446939\pi\)
0.165924 + 0.986139i \(0.446939\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6069.00 0.664347
\(438\) 0 0
\(439\) −9371.00 −1.01880 −0.509400 − 0.860530i \(-0.670133\pi\)
−0.509400 + 0.860530i \(0.670133\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6171.00 0.661835 0.330918 − 0.943660i \(-0.392642\pi\)
0.330918 + 0.943660i \(0.392642\pi\)
\(444\) 0 0
\(445\) −5580.00 −0.594421
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4122.00 −0.433250 −0.216625 − 0.976255i \(-0.569505\pi\)
−0.216625 + 0.976255i \(0.569505\pi\)
\(450\) 0 0
\(451\) 7488.00 0.781810
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11900.0 1.22611
\(456\) 0 0
\(457\) 7076.00 0.724292 0.362146 − 0.932121i \(-0.382044\pi\)
0.362146 + 0.932121i \(0.382044\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −762.000 −0.0769846 −0.0384923 − 0.999259i \(-0.512255\pi\)
−0.0384923 + 0.999259i \(0.512255\pi\)
\(462\) 0 0
\(463\) −8822.00 −0.885514 −0.442757 − 0.896642i \(-0.646000\pi\)
−0.442757 + 0.896642i \(0.646000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4977.00 −0.493165 −0.246583 − 0.969122i \(-0.579308\pi\)
−0.246583 + 0.969122i \(0.579308\pi\)
\(468\) 0 0
\(469\) −6188.00 −0.609244
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4224.00 −0.410613
\(474\) 0 0
\(475\) −2975.00 −0.287373
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10104.0 0.963807 0.481903 − 0.876224i \(-0.339946\pi\)
0.481903 + 0.876224i \(0.339946\pi\)
\(480\) 0 0
\(481\) −15260.0 −1.44656
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 80.0000 0.00748992
\(486\) 0 0
\(487\) −14924.0 −1.38865 −0.694323 − 0.719663i \(-0.744296\pi\)
−0.694323 + 0.719663i \(0.744296\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1146.00 0.105332 0.0526662 − 0.998612i \(-0.483228\pi\)
0.0526662 + 0.998612i \(0.483228\pi\)
\(492\) 0 0
\(493\) 810.000 0.0739971
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 30600.0 2.76177
\(498\) 0 0
\(499\) 14965.0 1.34254 0.671268 − 0.741215i \(-0.265750\pi\)
0.671268 + 0.741215i \(0.265750\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15525.0 1.37619 0.688097 − 0.725619i \(-0.258446\pi\)
0.688097 + 0.725619i \(0.258446\pi\)
\(504\) 0 0
\(505\) 1740.00 0.153325
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8196.00 0.713716 0.356858 − 0.934159i \(-0.383848\pi\)
0.356858 + 0.934159i \(0.383848\pi\)
\(510\) 0 0
\(511\) 23936.0 2.07215
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2060.00 −0.176261
\(516\) 0 0
\(517\) 24768.0 2.10695
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4932.00 −0.414731 −0.207365 − 0.978264i \(-0.566489\pi\)
−0.207365 + 0.978264i \(0.566489\pi\)
\(522\) 0 0
\(523\) 5938.00 0.496464 0.248232 − 0.968701i \(-0.420150\pi\)
0.248232 + 0.968701i \(0.420150\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3591.00 0.296824
\(528\) 0 0
\(529\) −9566.00 −0.786225
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10920.0 0.887425
\(534\) 0 0
\(535\) 4500.00 0.363649
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −39024.0 −3.11852
\(540\) 0 0
\(541\) −6730.00 −0.534834 −0.267417 − 0.963581i \(-0.586170\pi\)
−0.267417 + 0.963581i \(0.586170\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 575.000 0.0451932
\(546\) 0 0
\(547\) 17656.0 1.38010 0.690051 − 0.723761i \(-0.257588\pi\)
0.690051 + 0.723761i \(0.257588\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3570.00 −0.276020
\(552\) 0 0
\(553\) 46750.0 3.59496
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7974.00 −0.606587 −0.303294 − 0.952897i \(-0.598086\pi\)
−0.303294 + 0.952897i \(0.598086\pi\)
\(558\) 0 0
\(559\) −6160.00 −0.466083
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −25332.0 −1.89630 −0.948150 − 0.317824i \(-0.897048\pi\)
−0.948150 + 0.317824i \(0.897048\pi\)
\(564\) 0 0
\(565\) 4830.00 0.359645
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1038.00 0.0764767 0.0382383 − 0.999269i \(-0.487825\pi\)
0.0382383 + 0.999269i \(0.487825\pi\)
\(570\) 0 0
\(571\) −15671.0 −1.14853 −0.574265 − 0.818669i \(-0.694712\pi\)
−0.574265 + 0.818669i \(0.694712\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1275.00 −0.0924716
\(576\) 0 0
\(577\) −916.000 −0.0660894 −0.0330447 − 0.999454i \(-0.510520\pi\)
−0.0330447 + 0.999454i \(0.510520\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 31110.0 2.22145
\(582\) 0 0
\(583\) −30672.0 −2.17891
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9141.00 0.642742 0.321371 − 0.946953i \(-0.395856\pi\)
0.321371 + 0.946953i \(0.395856\pi\)
\(588\) 0 0
\(589\) −15827.0 −1.10720
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5247.00 −0.363353 −0.181677 − 0.983358i \(-0.558152\pi\)
−0.181677 + 0.983358i \(0.558152\pi\)
\(594\) 0 0
\(595\) −4590.00 −0.316255
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24162.0 −1.64813 −0.824067 − 0.566492i \(-0.808300\pi\)
−0.824067 + 0.566492i \(0.808300\pi\)
\(600\) 0 0
\(601\) 14357.0 0.974433 0.487217 − 0.873281i \(-0.338012\pi\)
0.487217 + 0.873281i \(0.338012\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4865.00 −0.326926
\(606\) 0 0
\(607\) −3152.00 −0.210767 −0.105384 − 0.994432i \(-0.533607\pi\)
−0.105384 + 0.994432i \(0.533607\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 36120.0 2.39159
\(612\) 0 0
\(613\) 4592.00 0.302560 0.151280 − 0.988491i \(-0.451661\pi\)
0.151280 + 0.988491i \(0.451661\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7359.00 0.480166 0.240083 − 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(618\) 0 0
\(619\) 15712.0 1.02022 0.510112 − 0.860108i \(-0.329604\pi\)
0.510112 + 0.860108i \(0.329604\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 37944.0 2.44012
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5886.00 0.373116
\(630\) 0 0
\(631\) 3175.00 0.200309 0.100154 − 0.994972i \(-0.468066\pi\)
0.100154 + 0.994972i \(0.468066\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7030.00 0.439334
\(636\) 0 0
\(637\) −56910.0 −3.53981
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −96.0000 −0.00591540 −0.00295770 − 0.999996i \(-0.500941\pi\)
−0.00295770 + 0.999996i \(0.500941\pi\)
\(642\) 0 0
\(643\) 18070.0 1.10826 0.554130 − 0.832430i \(-0.313051\pi\)
0.554130 + 0.832430i \(0.313051\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1341.00 0.0814840 0.0407420 − 0.999170i \(-0.487028\pi\)
0.0407420 + 0.999170i \(0.487028\pi\)
\(648\) 0 0
\(649\) 31392.0 1.89868
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24495.0 1.46794 0.733969 − 0.679183i \(-0.237666\pi\)
0.733969 + 0.679183i \(0.237666\pi\)
\(654\) 0 0
\(655\) −1230.00 −0.0733742
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12378.0 −0.731682 −0.365841 − 0.930677i \(-0.619219\pi\)
−0.365841 + 0.930677i \(0.619219\pi\)
\(660\) 0 0
\(661\) −24442.0 −1.43825 −0.719125 − 0.694880i \(-0.755457\pi\)
−0.719125 + 0.694880i \(0.755457\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 20230.0 1.17968
\(666\) 0 0
\(667\) −1530.00 −0.0888183
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −22128.0 −1.27309
\(672\) 0 0
\(673\) 2378.00 0.136204 0.0681019 − 0.997678i \(-0.478306\pi\)
0.0681019 + 0.997678i \(0.478306\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5478.00 −0.310985 −0.155492 − 0.987837i \(-0.549696\pi\)
−0.155492 + 0.987837i \(0.549696\pi\)
\(678\) 0 0
\(679\) −544.000 −0.0307464
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8595.00 0.481521 0.240760 − 0.970585i \(-0.422603\pi\)
0.240760 + 0.970585i \(0.422603\pi\)
\(684\) 0 0
\(685\) 2595.00 0.144744
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −44730.0 −2.47326
\(690\) 0 0
\(691\) 31615.0 1.74051 0.870254 − 0.492603i \(-0.163954\pi\)
0.870254 + 0.492603i \(0.163954\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6580.00 0.359128
\(696\) 0 0
\(697\) −4212.00 −0.228897
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −29790.0 −1.60507 −0.802534 − 0.596606i \(-0.796515\pi\)
−0.802534 + 0.596606i \(0.796515\pi\)
\(702\) 0 0
\(703\) −25942.0 −1.39178
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11832.0 −0.629403
\(708\) 0 0
\(709\) 3818.00 0.202240 0.101120 − 0.994874i \(-0.467757\pi\)
0.101120 + 0.994874i \(0.467757\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6783.00 −0.356277
\(714\) 0 0
\(715\) −16800.0 −0.878719
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −28314.0 −1.46861 −0.734307 − 0.678817i \(-0.762493\pi\)
−0.734307 + 0.678817i \(0.762493\pi\)
\(720\) 0 0
\(721\) 14008.0 0.723558
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 750.000 0.0384197
\(726\) 0 0
\(727\) −56.0000 −0.00285684 −0.00142842 − 0.999999i \(-0.500455\pi\)
−0.00142842 + 0.999999i \(0.500455\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2376.00 0.120218
\(732\) 0 0
\(733\) −34432.0 −1.73503 −0.867514 − 0.497413i \(-0.834283\pi\)
−0.867514 + 0.497413i \(0.834283\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8736.00 0.436628
\(738\) 0 0
\(739\) 1051.00 0.0523162 0.0261581 − 0.999658i \(-0.491673\pi\)
0.0261581 + 0.999658i \(0.491673\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 39144.0 1.93278 0.966389 − 0.257084i \(-0.0827618\pi\)
0.966389 + 0.257084i \(0.0827618\pi\)
\(744\) 0 0
\(745\) 1860.00 0.0914700
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −30600.0 −1.49279
\(750\) 0 0
\(751\) 1735.00 0.0843023 0.0421512 − 0.999111i \(-0.486579\pi\)
0.0421512 + 0.999111i \(0.486579\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7280.00 −0.350922
\(756\) 0 0
\(757\) 6698.00 0.321589 0.160795 − 0.986988i \(-0.448594\pi\)
0.160795 + 0.986988i \(0.448594\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38766.0 −1.84660 −0.923302 − 0.384074i \(-0.874521\pi\)
−0.923302 + 0.384074i \(0.874521\pi\)
\(762\) 0 0
\(763\) −3910.00 −0.185520
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 45780.0 2.15518
\(768\) 0 0
\(769\) 23501.0 1.10204 0.551019 − 0.834492i \(-0.314239\pi\)
0.551019 + 0.834492i \(0.314239\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3591.00 0.167088 0.0835442 − 0.996504i \(-0.473376\pi\)
0.0835442 + 0.996504i \(0.473376\pi\)
\(774\) 0 0
\(775\) 3325.00 0.154113
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18564.0 0.853818
\(780\) 0 0
\(781\) −43200.0 −1.97928
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4780.00 −0.217332
\(786\) 0 0
\(787\) 20716.0 0.938305 0.469152 − 0.883117i \(-0.344560\pi\)
0.469152 + 0.883117i \(0.344560\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −32844.0 −1.47636
\(792\) 0 0
\(793\) −32270.0 −1.44507
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42981.0 1.91024 0.955122 − 0.296211i \(-0.0957233\pi\)
0.955122 + 0.296211i \(0.0957233\pi\)
\(798\) 0 0
\(799\) −13932.0 −0.616869
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −33792.0 −1.48505
\(804\) 0 0
\(805\) 8670.00 0.379599
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2268.00 0.0985644 0.0492822 − 0.998785i \(-0.484307\pi\)
0.0492822 + 0.998785i \(0.484307\pi\)
\(810\) 0 0
\(811\) −11756.0 −0.509012 −0.254506 − 0.967071i \(-0.581913\pi\)
−0.254506 + 0.967071i \(0.581913\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −12230.0 −0.525642
\(816\) 0 0
\(817\) −10472.0 −0.448432
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −8646.00 −0.367537 −0.183768 − 0.982970i \(-0.558830\pi\)
−0.183768 + 0.982970i \(0.558830\pi\)
\(822\) 0 0
\(823\) −10784.0 −0.456752 −0.228376 − 0.973573i \(-0.573341\pi\)
−0.228376 + 0.973573i \(0.573341\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 42597.0 1.79110 0.895552 − 0.444957i \(-0.146781\pi\)
0.895552 + 0.444957i \(0.146781\pi\)
\(828\) 0 0
\(829\) −26458.0 −1.10847 −0.554237 − 0.832359i \(-0.686990\pi\)
−0.554237 + 0.832359i \(0.686990\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21951.0 0.913034
\(834\) 0 0
\(835\) 15555.0 0.644674
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −11496.0 −0.473046 −0.236523 − 0.971626i \(-0.576008\pi\)
−0.236523 + 0.971626i \(0.576008\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −13515.0 −0.550213
\(846\) 0 0
\(847\) 33082.0 1.34204
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −11118.0 −0.447850
\(852\) 0 0
\(853\) 21548.0 0.864935 0.432467 − 0.901650i \(-0.357643\pi\)
0.432467 + 0.901650i \(0.357643\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6261.00 −0.249559 −0.124779 − 0.992185i \(-0.539822\pi\)
−0.124779 + 0.992185i \(0.539822\pi\)
\(858\) 0 0
\(859\) 3355.00 0.133261 0.0666305 − 0.997778i \(-0.478775\pi\)
0.0666305 + 0.997778i \(0.478775\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 19701.0 0.777091 0.388546 − 0.921429i \(-0.372978\pi\)
0.388546 + 0.921429i \(0.372978\pi\)
\(864\) 0 0
\(865\) −11985.0 −0.471101
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −66000.0 −2.57641
\(870\) 0 0
\(871\) 12740.0 0.495612
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4250.00 −0.164201
\(876\) 0 0
\(877\) 16292.0 0.627300 0.313650 − 0.949539i \(-0.398448\pi\)
0.313650 + 0.949539i \(0.398448\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −9270.00 −0.354500 −0.177250 − 0.984166i \(-0.556720\pi\)
−0.177250 + 0.984166i \(0.556720\pi\)
\(882\) 0 0
\(883\) −38486.0 −1.46677 −0.733384 − 0.679814i \(-0.762060\pi\)
−0.733384 + 0.679814i \(0.762060\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1893.00 0.0716581 0.0358290 − 0.999358i \(-0.488593\pi\)
0.0358290 + 0.999358i \(0.488593\pi\)
\(888\) 0 0
\(889\) −47804.0 −1.80348
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 61404.0 2.30102
\(894\) 0 0
\(895\) 2700.00 0.100839
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3990.00 0.148024
\(900\) 0 0
\(901\) 17253.0 0.637936
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11665.0 −0.428462
\(906\) 0 0
\(907\) −44876.0 −1.64287 −0.821435 − 0.570302i \(-0.806826\pi\)
−0.821435 + 0.570302i \(0.806826\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 23802.0 0.865637 0.432819 − 0.901481i \(-0.357519\pi\)
0.432819 + 0.901481i \(0.357519\pi\)
\(912\) 0 0
\(913\) −43920.0 −1.59205
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8364.00 0.301204
\(918\) 0 0
\(919\) 24784.0 0.889607 0.444803 − 0.895628i \(-0.353274\pi\)
0.444803 + 0.895628i \(0.353274\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −63000.0 −2.24666
\(924\) 0 0
\(925\) 5450.00 0.193724
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −9060.00 −0.319967 −0.159983 − 0.987120i \(-0.551144\pi\)
−0.159983 + 0.987120i \(0.551144\pi\)
\(930\) 0 0
\(931\) −96747.0 −3.40575
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6480.00 0.226651
\(936\) 0 0
\(937\) 6176.00 0.215327 0.107663 − 0.994187i \(-0.465663\pi\)
0.107663 + 0.994187i \(0.465663\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4182.00 0.144877 0.0724385 − 0.997373i \(-0.476922\pi\)
0.0724385 + 0.997373i \(0.476922\pi\)
\(942\) 0 0
\(943\) 7956.00 0.274743
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 44079.0 1.51254 0.756270 − 0.654260i \(-0.227020\pi\)
0.756270 + 0.654260i \(0.227020\pi\)
\(948\) 0 0
\(949\) −49280.0 −1.68567
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −12726.0 −0.432566 −0.216283 − 0.976331i \(-0.569393\pi\)
−0.216283 + 0.976331i \(0.569393\pi\)
\(954\) 0 0
\(955\) 13650.0 0.462517
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −17646.0 −0.594180
\(960\) 0 0
\(961\) −12102.0 −0.406230
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 22850.0 0.762246
\(966\) 0 0
\(967\) −45218.0 −1.50374 −0.751868 − 0.659314i \(-0.770847\pi\)
−0.751868 + 0.659314i \(0.770847\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3978.00 −0.131473 −0.0657364 − 0.997837i \(-0.520940\pi\)
−0.0657364 + 0.997837i \(0.520940\pi\)
\(972\) 0 0
\(973\) −44744.0 −1.47423
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −23466.0 −0.768417 −0.384209 − 0.923246i \(-0.625526\pi\)
−0.384209 + 0.923246i \(0.625526\pi\)
\(978\) 0 0
\(979\) −53568.0 −1.74876
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 47913.0 1.55462 0.777308 − 0.629120i \(-0.216585\pi\)
0.777308 + 0.629120i \(0.216585\pi\)
\(984\) 0 0
\(985\) 3375.00 0.109174
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4488.00 −0.144297
\(990\) 0 0
\(991\) −31997.0 −1.02565 −0.512825 − 0.858493i \(-0.671401\pi\)
−0.512825 + 0.858493i \(0.671401\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −15560.0 −0.495764
\(996\) 0 0
\(997\) −45628.0 −1.44940 −0.724701 − 0.689064i \(-0.758022\pi\)
−0.724701 + 0.689064i \(0.758022\pi\)
\(998\) 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 2160.4.a.j.1.1 1
3.2 odd 2 2160.4.a.t.1.1 1
4.3 odd 2 270.4.a.a.1.1 ✓ 1
12.11 even 2 270.4.a.k.1.1 yes 1
20.3 even 4 1350.4.c.r.649.2 2
20.7 even 4 1350.4.c.r.649.1 2
20.19 odd 2 1350.4.a.bb.1.1 1
36.7 odd 6 810.4.e.x.271.1 2
36.11 even 6 810.4.e.d.271.1 2
36.23 even 6 810.4.e.d.541.1 2
36.31 odd 6 810.4.e.x.541.1 2
60.23 odd 4 1350.4.c.c.649.1 2
60.47 odd 4 1350.4.c.c.649.2 2
60.59 even 2 1350.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.a.1.1 ✓ 1 4.3 odd 2
270.4.a.k.1.1 yes 1 12.11 even 2
810.4.e.d.271.1 2 36.11 even 6
810.4.e.d.541.1 2 36.23 even 6
810.4.e.x.271.1 2 36.7 odd 6
810.4.e.x.541.1 2 36.31 odd 6
1350.4.a.n.1.1 1 60.59 even 2
1350.4.a.bb.1.1 1 20.19 odd 2
1350.4.c.c.649.1 2 60.23 odd 4
1350.4.c.c.649.2 2 60.47 odd 4
1350.4.c.r.649.1 2 20.7 even 4
1350.4.c.r.649.2 2 20.3 even 4
2160.4.a.j.1.1 1 1.1 even 1 trivial
2160.4.a.t.1.1 1 3.2 odd 2