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Properties

Label 720.4.a.b.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
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] = [720,4,Mod(1,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, 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("720.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.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: \(42.4813752041\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -32.0000 q^{7} -60.0000 q^{11} -34.0000 q^{13} -42.0000 q^{17} +76.0000 q^{19} +25.0000 q^{25} -6.00000 q^{29} +232.000 q^{31} +160.000 q^{35} +134.000 q^{37} -234.000 q^{41} +412.000 q^{43} -360.000 q^{47} +681.000 q^{49} -222.000 q^{53} +300.000 q^{55} +660.000 q^{59} -490.000 q^{61} +170.000 q^{65} -812.000 q^{67} +120.000 q^{71} +746.000 q^{73} +1920.00 q^{77} -152.000 q^{79} -804.000 q^{83} +210.000 q^{85} +678.000 q^{89} +1088.00 q^{91} -380.000 q^{95} +194.000 q^{97} +O(q^{100})\)

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
\(7\) −32.0000 −1.72784 −0.863919 − 0.503631i \(-0.831997\pi\)
−0.863919 + 0.503631i \(0.831997\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −60.0000 −1.64461 −0.822304 − 0.569049i \(-0.807311\pi\)
−0.822304 + 0.569049i \(0.807311\pi\)
\(12\) 0 0
\(13\) −34.0000 −0.725377 −0.362689 − 0.931910i \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −42.0000 −0.599206 −0.299603 − 0.954064i \(-0.596854\pi\)
−0.299603 + 0.954064i \(0.596854\pi\)
\(18\) 0 0
\(19\) 76.0000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −0.0384197 −0.0192099 − 0.999815i \(-0.506115\pi\)
−0.0192099 + 0.999815i \(0.506115\pi\)
\(30\) 0 0
\(31\) 232.000 1.34414 0.672071 − 0.740486i \(-0.265405\pi\)
0.672071 + 0.740486i \(0.265405\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 160.000 0.772712
\(36\) 0 0
\(37\) 134.000 0.595391 0.297695 − 0.954661i \(-0.403782\pi\)
0.297695 + 0.954661i \(0.403782\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −234.000 −0.891333 −0.445667 − 0.895199i \(-0.647033\pi\)
−0.445667 + 0.895199i \(0.647033\pi\)
\(42\) 0 0
\(43\) 412.000 1.46115 0.730575 − 0.682833i \(-0.239252\pi\)
0.730575 + 0.682833i \(0.239252\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −360.000 −1.11726 −0.558632 − 0.829416i \(-0.688674\pi\)
−0.558632 + 0.829416i \(0.688674\pi\)
\(48\) 0 0
\(49\) 681.000 1.98542
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −222.000 −0.575359 −0.287680 − 0.957727i \(-0.592884\pi\)
−0.287680 + 0.957727i \(0.592884\pi\)
\(54\) 0 0
\(55\) 300.000 0.735491
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 660.000 1.45635 0.728175 − 0.685391i \(-0.240369\pi\)
0.728175 + 0.685391i \(0.240369\pi\)
\(60\) 0 0
\(61\) −490.000 −1.02849 −0.514246 − 0.857642i \(-0.671928\pi\)
−0.514246 + 0.857642i \(0.671928\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 170.000 0.324399
\(66\) 0 0
\(67\) −812.000 −1.48062 −0.740310 − 0.672265i \(-0.765321\pi\)
−0.740310 + 0.672265i \(0.765321\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 120.000 0.200583 0.100291 − 0.994958i \(-0.468022\pi\)
0.100291 + 0.994958i \(0.468022\pi\)
\(72\) 0 0
\(73\) 746.000 1.19606 0.598032 − 0.801472i \(-0.295949\pi\)
0.598032 + 0.801472i \(0.295949\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1920.00 2.84161
\(78\) 0 0
\(79\) −152.000 −0.216473 −0.108236 − 0.994125i \(-0.534520\pi\)
−0.108236 + 0.994125i \(0.534520\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −804.000 −1.06326 −0.531629 − 0.846977i \(-0.678420\pi\)
−0.531629 + 0.846977i \(0.678420\pi\)
\(84\) 0 0
\(85\) 210.000 0.267973
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 678.000 0.807504 0.403752 − 0.914868i \(-0.367706\pi\)
0.403752 + 0.914868i \(0.367706\pi\)
\(90\) 0 0
\(91\) 1088.00 1.25333
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −380.000 −0.410391
\(96\) 0 0
\(97\) 194.000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −798.000 −0.786178 −0.393089 − 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(102\) 0 0
\(103\) −1088.00 −1.04081 −0.520407 − 0.853918i \(-0.674220\pi\)
−0.520407 + 0.853918i \(0.674220\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1716.00 1.55039 0.775196 − 0.631721i \(-0.217651\pi\)
0.775196 + 0.631721i \(0.217651\pi\)
\(108\) 0 0
\(109\) −970.000 −0.852378 −0.426189 − 0.904634i \(-0.640144\pi\)
−0.426189 + 0.904634i \(0.640144\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −426.000 −0.354643 −0.177322 − 0.984153i \(-0.556743\pi\)
−0.177322 + 0.984153i \(0.556743\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1344.00 1.03533
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −200.000 −0.139741 −0.0698706 − 0.997556i \(-0.522259\pi\)
−0.0698706 + 0.997556i \(0.522259\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 60.0000 0.0400170 0.0200085 − 0.999800i \(-0.493631\pi\)
0.0200085 + 0.999800i \(0.493631\pi\)
\(132\) 0 0
\(133\) −2432.00 −1.58557
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −642.000 −0.400363 −0.200182 − 0.979759i \(-0.564153\pi\)
−0.200182 + 0.979759i \(0.564153\pi\)
\(138\) 0 0
\(139\) 2836.00 1.73055 0.865275 − 0.501298i \(-0.167144\pi\)
0.865275 + 0.501298i \(0.167144\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2040.00 1.19296
\(144\) 0 0
\(145\) 30.0000 0.0171818
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1554.00 0.854420 0.427210 − 0.904152i \(-0.359496\pi\)
0.427210 + 0.904152i \(0.359496\pi\)
\(150\) 0 0
\(151\) 2272.00 1.22446 0.612228 − 0.790682i \(-0.290274\pi\)
0.612228 + 0.790682i \(0.290274\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1160.00 −0.601119
\(156\) 0 0
\(157\) 1694.00 0.861120 0.430560 − 0.902562i \(-0.358316\pi\)
0.430560 + 0.902562i \(0.358316\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 52.0000 0.0249874 0.0124937 − 0.999922i \(-0.496023\pi\)
0.0124937 + 0.999922i \(0.496023\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1200.00 −0.556041 −0.278020 − 0.960575i \(-0.589678\pi\)
−0.278020 + 0.960575i \(0.589678\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −54.0000 −0.0237315 −0.0118657 − 0.999930i \(-0.503777\pi\)
−0.0118657 + 0.999930i \(0.503777\pi\)
\(174\) 0 0
\(175\) −800.000 −0.345568
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 876.000 0.365784 0.182892 − 0.983133i \(-0.441454\pi\)
0.182892 + 0.983133i \(0.441454\pi\)
\(180\) 0 0
\(181\) 3854.00 1.58268 0.791341 − 0.611375i \(-0.209383\pi\)
0.791341 + 0.611375i \(0.209383\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −670.000 −0.266267
\(186\) 0 0
\(187\) 2520.00 0.985458
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2784.00 −1.05468 −0.527338 − 0.849656i \(-0.676810\pi\)
−0.527338 + 0.849656i \(0.676810\pi\)
\(192\) 0 0
\(193\) 914.000 0.340887 0.170443 − 0.985367i \(-0.445480\pi\)
0.170443 + 0.985367i \(0.445480\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5202.00 1.88136 0.940678 − 0.339300i \(-0.110190\pi\)
0.940678 + 0.339300i \(0.110190\pi\)
\(198\) 0 0
\(199\) −3152.00 −1.12281 −0.561405 − 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 192.000 0.0663830
\(204\) 0 0
\(205\) 1170.00 0.398616
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4560.00 −1.50920
\(210\) 0 0
\(211\) −740.000 −0.241439 −0.120720 − 0.992687i \(-0.538520\pi\)
−0.120720 + 0.992687i \(0.538520\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2060.00 −0.653446
\(216\) 0 0
\(217\) −7424.00 −2.32246
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1428.00 0.434650
\(222\) 0 0
\(223\) 520.000 0.156151 0.0780757 − 0.996947i \(-0.475122\pi\)
0.0780757 + 0.996947i \(0.475122\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 396.000 0.115786 0.0578930 − 0.998323i \(-0.481562\pi\)
0.0578930 + 0.998323i \(0.481562\pi\)
\(228\) 0 0
\(229\) −1330.00 −0.383794 −0.191897 − 0.981415i \(-0.561464\pi\)
−0.191897 + 0.981415i \(0.561464\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4866.00 −1.36816 −0.684082 − 0.729405i \(-0.739797\pi\)
−0.684082 + 0.729405i \(0.739797\pi\)
\(234\) 0 0
\(235\) 1800.00 0.499656
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1824.00 −0.493660 −0.246830 − 0.969059i \(-0.579389\pi\)
−0.246830 + 0.969059i \(0.579389\pi\)
\(240\) 0 0
\(241\) 6482.00 1.73254 0.866270 − 0.499575i \(-0.166511\pi\)
0.866270 + 0.499575i \(0.166511\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3405.00 −0.887908
\(246\) 0 0
\(247\) −2584.00 −0.665652
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1476.00 0.371172 0.185586 − 0.982628i \(-0.440582\pi\)
0.185586 + 0.982628i \(0.440582\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4314.00 −1.04708 −0.523541 − 0.852001i \(-0.675389\pi\)
−0.523541 + 0.852001i \(0.675389\pi\)
\(258\) 0 0
\(259\) −4288.00 −1.02874
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5280.00 −1.23794 −0.618971 − 0.785414i \(-0.712450\pi\)
−0.618971 + 0.785414i \(0.712450\pi\)
\(264\) 0 0
\(265\) 1110.00 0.257309
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5526.00 −1.25251 −0.626257 − 0.779617i \(-0.715414\pi\)
−0.626257 + 0.779617i \(0.715414\pi\)
\(270\) 0 0
\(271\) −2024.00 −0.453687 −0.226844 − 0.973931i \(-0.572841\pi\)
−0.226844 + 0.973931i \(0.572841\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1500.00 −0.328921
\(276\) 0 0
\(277\) 2054.00 0.445534 0.222767 − 0.974872i \(-0.428491\pi\)
0.222767 + 0.974872i \(0.428491\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7302.00 1.55018 0.775090 − 0.631850i \(-0.217704\pi\)
0.775090 + 0.631850i \(0.217704\pi\)
\(282\) 0 0
\(283\) 3724.00 0.782222 0.391111 − 0.920344i \(-0.372091\pi\)
0.391111 + 0.920344i \(0.372091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7488.00 1.54008
\(288\) 0 0
\(289\) −3149.00 −0.640953
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7218.00 1.43918 0.719591 − 0.694399i \(-0.244330\pi\)
0.719591 + 0.694399i \(0.244330\pi\)
\(294\) 0 0
\(295\) −3300.00 −0.651300
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −13184.0 −2.52463
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2450.00 0.459956
\(306\) 0 0
\(307\) −2540.00 −0.472200 −0.236100 − 0.971729i \(-0.575869\pi\)
−0.236100 + 0.971729i \(0.575869\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1560.00 0.284436 0.142218 − 0.989835i \(-0.454577\pi\)
0.142218 + 0.989835i \(0.454577\pi\)
\(312\) 0 0
\(313\) −934.000 −0.168667 −0.0843335 − 0.996438i \(-0.526876\pi\)
−0.0843335 + 0.996438i \(0.526876\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1674.00 0.296597 0.148298 − 0.988943i \(-0.452620\pi\)
0.148298 + 0.988943i \(0.452620\pi\)
\(318\) 0 0
\(319\) 360.000 0.0631854
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3192.00 −0.549869
\(324\) 0 0
\(325\) −850.000 −0.145075
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11520.0 1.93045
\(330\) 0 0
\(331\) 3988.00 0.662237 0.331118 − 0.943589i \(-0.392574\pi\)
0.331118 + 0.943589i \(0.392574\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4060.00 0.662154
\(336\) 0 0
\(337\) 2.00000 0.000323285 0 0.000161642 − 1.00000i \(-0.499949\pi\)
0.000161642 1.00000i \(0.499949\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13920.0 −2.21059
\(342\) 0 0
\(343\) −10816.0 −1.70265
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1764.00 0.272901 0.136450 − 0.990647i \(-0.456431\pi\)
0.136450 + 0.990647i \(0.456431\pi\)
\(348\) 0 0
\(349\) 4310.00 0.661057 0.330529 − 0.943796i \(-0.392773\pi\)
0.330529 + 0.943796i \(0.392773\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −138.000 −0.0208074 −0.0104037 − 0.999946i \(-0.503312\pi\)
−0.0104037 + 0.999946i \(0.503312\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11976.0 −1.76064 −0.880319 − 0.474382i \(-0.842672\pi\)
−0.880319 + 0.474382i \(0.842672\pi\)
\(360\) 0 0
\(361\) −1083.00 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3730.00 −0.534896
\(366\) 0 0
\(367\) −9704.00 −1.38023 −0.690115 − 0.723699i \(-0.742440\pi\)
−0.690115 + 0.723699i \(0.742440\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7104.00 0.994128
\(372\) 0 0
\(373\) −8122.00 −1.12746 −0.563728 − 0.825960i \(-0.690633\pi\)
−0.563728 + 0.825960i \(0.690633\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 204.000 0.0278688
\(378\) 0 0
\(379\) −3404.00 −0.461350 −0.230675 − 0.973031i \(-0.574093\pi\)
−0.230675 + 0.973031i \(0.574093\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2520.00 −0.336204 −0.168102 − 0.985770i \(-0.553764\pi\)
−0.168102 + 0.985770i \(0.553764\pi\)
\(384\) 0 0
\(385\) −9600.00 −1.27081
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1566.00 −0.204111 −0.102056 − 0.994779i \(-0.532542\pi\)
−0.102056 + 0.994779i \(0.532542\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 760.000 0.0968095
\(396\) 0 0
\(397\) −4354.00 −0.550431 −0.275215 − 0.961383i \(-0.588749\pi\)
−0.275215 + 0.961383i \(0.588749\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8046.00 1.00199 0.500995 − 0.865450i \(-0.332967\pi\)
0.500995 + 0.865450i \(0.332967\pi\)
\(402\) 0 0
\(403\) −7888.00 −0.975011
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8040.00 −0.979184
\(408\) 0 0
\(409\) −2806.00 −0.339237 −0.169618 − 0.985510i \(-0.554253\pi\)
−0.169618 + 0.985510i \(0.554253\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −21120.0 −2.51634
\(414\) 0 0
\(415\) 4020.00 0.475504
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11580.0 1.35017 0.675084 − 0.737741i \(-0.264108\pi\)
0.675084 + 0.737741i \(0.264108\pi\)
\(420\) 0 0
\(421\) −370.000 −0.0428330 −0.0214165 − 0.999771i \(-0.506818\pi\)
−0.0214165 + 0.999771i \(0.506818\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1050.00 −0.119841
\(426\) 0 0
\(427\) 15680.0 1.77707
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5040.00 0.563267 0.281634 − 0.959522i \(-0.409124\pi\)
0.281634 + 0.959522i \(0.409124\pi\)
\(432\) 0 0
\(433\) −3742.00 −0.415310 −0.207655 − 0.978202i \(-0.566583\pi\)
−0.207655 + 0.978202i \(0.566583\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 6208.00 0.674924 0.337462 − 0.941339i \(-0.390432\pi\)
0.337462 + 0.941339i \(0.390432\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15564.0 −1.66923 −0.834614 − 0.550835i \(-0.814309\pi\)
−0.834614 + 0.550835i \(0.814309\pi\)
\(444\) 0 0
\(445\) −3390.00 −0.361127
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 15774.0 1.65795 0.828977 − 0.559283i \(-0.188924\pi\)
0.828977 + 0.559283i \(0.188924\pi\)
\(450\) 0 0
\(451\) 14040.0 1.46589
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5440.00 −0.560508
\(456\) 0 0
\(457\) 9722.00 0.995133 0.497567 − 0.867426i \(-0.334227\pi\)
0.497567 + 0.867426i \(0.334227\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10890.0 1.10021 0.550106 − 0.835095i \(-0.314587\pi\)
0.550106 + 0.835095i \(0.314587\pi\)
\(462\) 0 0
\(463\) −15128.0 −1.51848 −0.759242 − 0.650809i \(-0.774430\pi\)
−0.759242 + 0.650809i \(0.774430\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10668.0 1.05708 0.528540 − 0.848909i \(-0.322740\pi\)
0.528540 + 0.848909i \(0.322740\pi\)
\(468\) 0 0
\(469\) 25984.0 2.55827
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24720.0 −2.40302
\(474\) 0 0
\(475\) 1900.00 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15264.0 1.45601 0.728006 − 0.685571i \(-0.240447\pi\)
0.728006 + 0.685571i \(0.240447\pi\)
\(480\) 0 0
\(481\) −4556.00 −0.431883
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −970.000 −0.0908153
\(486\) 0 0
\(487\) 5776.00 0.537445 0.268722 − 0.963218i \(-0.413399\pi\)
0.268722 + 0.963218i \(0.413399\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14244.0 1.30921 0.654606 − 0.755971i \(-0.272835\pi\)
0.654606 + 0.755971i \(0.272835\pi\)
\(492\) 0 0
\(493\) 252.000 0.0230213
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3840.00 −0.346575
\(498\) 0 0
\(499\) 17116.0 1.53551 0.767753 − 0.640746i \(-0.221375\pi\)
0.767753 + 0.640746i \(0.221375\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16848.0 −1.49347 −0.746735 − 0.665122i \(-0.768380\pi\)
−0.746735 + 0.665122i \(0.768380\pi\)
\(504\) 0 0
\(505\) 3990.00 0.351589
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3834.00 0.333868 0.166934 − 0.985968i \(-0.446613\pi\)
0.166934 + 0.985968i \(0.446613\pi\)
\(510\) 0 0
\(511\) −23872.0 −2.06660
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5440.00 0.465466
\(516\) 0 0
\(517\) 21600.0 1.83746
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18822.0 1.58274 0.791369 − 0.611338i \(-0.209369\pi\)
0.791369 + 0.611338i \(0.209369\pi\)
\(522\) 0 0
\(523\) 15340.0 1.28255 0.641273 − 0.767313i \(-0.278407\pi\)
0.641273 + 0.767313i \(0.278407\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9744.00 −0.805418
\(528\) 0 0
\(529\) −12167.0 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7956.00 0.646553
\(534\) 0 0
\(535\) −8580.00 −0.693357
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −40860.0 −3.26524
\(540\) 0 0
\(541\) 18950.0 1.50596 0.752980 − 0.658044i \(-0.228616\pi\)
0.752980 + 0.658044i \(0.228616\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4850.00 0.381195
\(546\) 0 0
\(547\) 10036.0 0.784476 0.392238 − 0.919864i \(-0.371701\pi\)
0.392238 + 0.919864i \(0.371701\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −456.000 −0.0352564
\(552\) 0 0
\(553\) 4864.00 0.374030
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10326.0 −0.785506 −0.392753 − 0.919644i \(-0.628477\pi\)
−0.392753 + 0.919644i \(0.628477\pi\)
\(558\) 0 0
\(559\) −14008.0 −1.05988
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4524.00 0.338657 0.169328 − 0.985560i \(-0.445840\pi\)
0.169328 + 0.985560i \(0.445840\pi\)
\(564\) 0 0
\(565\) 2130.00 0.158601
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16362.0 −1.20550 −0.602751 − 0.797929i \(-0.705929\pi\)
−0.602751 + 0.797929i \(0.705929\pi\)
\(570\) 0 0
\(571\) −6620.00 −0.485181 −0.242591 − 0.970129i \(-0.577997\pi\)
−0.242591 + 0.970129i \(0.577997\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8834.00 0.637373 0.318687 − 0.947860i \(-0.396758\pi\)
0.318687 + 0.947860i \(0.396758\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 25728.0 1.83714
\(582\) 0 0
\(583\) 13320.0 0.946240
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3636.00 0.255662 0.127831 − 0.991796i \(-0.459198\pi\)
0.127831 + 0.991796i \(0.459198\pi\)
\(588\) 0 0
\(589\) 17632.0 1.23347
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6570.00 −0.454971 −0.227485 − 0.973782i \(-0.573050\pi\)
−0.227485 + 0.973782i \(0.573050\pi\)
\(594\) 0 0
\(595\) −6720.00 −0.463014
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16584.0 1.13123 0.565613 − 0.824671i \(-0.308640\pi\)
0.565613 + 0.824671i \(0.308640\pi\)
\(600\) 0 0
\(601\) −502.000 −0.0340716 −0.0170358 − 0.999855i \(-0.505423\pi\)
−0.0170358 + 0.999855i \(0.505423\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11345.0 −0.762380
\(606\) 0 0
\(607\) 18568.0 1.24160 0.620801 − 0.783969i \(-0.286808\pi\)
0.620801 + 0.783969i \(0.286808\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12240.0 0.810438
\(612\) 0 0
\(613\) −13114.0 −0.864061 −0.432031 − 0.901859i \(-0.642203\pi\)
−0.432031 + 0.901859i \(0.642203\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5250.00 −0.342556 −0.171278 − 0.985223i \(-0.554790\pi\)
−0.171278 + 0.985223i \(0.554790\pi\)
\(618\) 0 0
\(619\) 10804.0 0.701534 0.350767 − 0.936463i \(-0.385921\pi\)
0.350767 + 0.936463i \(0.385921\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21696.0 −1.39524
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5628.00 −0.356762
\(630\) 0 0
\(631\) 27088.0 1.70896 0.854482 − 0.519481i \(-0.173875\pi\)
0.854482 + 0.519481i \(0.173875\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1000.00 0.0624942
\(636\) 0 0
\(637\) −23154.0 −1.44018
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18930.0 −1.16644 −0.583222 − 0.812313i \(-0.698208\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(642\) 0 0
\(643\) −20108.0 −1.23325 −0.616627 − 0.787256i \(-0.711501\pi\)
−0.616627 + 0.787256i \(0.711501\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7152.00 −0.434581 −0.217291 − 0.976107i \(-0.569722\pi\)
−0.217291 + 0.976107i \(0.569722\pi\)
\(648\) 0 0
\(649\) −39600.0 −2.39512
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31626.0 1.89528 0.947642 − 0.319333i \(-0.103459\pi\)
0.947642 + 0.319333i \(0.103459\pi\)
\(654\) 0 0
\(655\) −300.000 −0.0178961
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28092.0 1.66056 0.830280 − 0.557347i \(-0.188181\pi\)
0.830280 + 0.557347i \(0.188181\pi\)
\(660\) 0 0
\(661\) −13186.0 −0.775909 −0.387955 − 0.921678i \(-0.626818\pi\)
−0.387955 + 0.921678i \(0.626818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 12160.0 0.709090
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 29400.0 1.69147
\(672\) 0 0
\(673\) 5138.00 0.294287 0.147144 − 0.989115i \(-0.452992\pi\)
0.147144 + 0.989115i \(0.452992\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6078.00 −0.345047 −0.172523 − 0.985005i \(-0.555192\pi\)
−0.172523 + 0.985005i \(0.555192\pi\)
\(678\) 0 0
\(679\) −6208.00 −0.350871
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 32244.0 1.80642 0.903208 − 0.429203i \(-0.141205\pi\)
0.903208 + 0.429203i \(0.141205\pi\)
\(684\) 0 0
\(685\) 3210.00 0.179048
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7548.00 0.417353
\(690\) 0 0
\(691\) −4484.00 −0.246859 −0.123429 − 0.992353i \(-0.539389\pi\)
−0.123429 + 0.992353i \(0.539389\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14180.0 −0.773925
\(696\) 0 0
\(697\) 9828.00 0.534092
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30426.0 1.63934 0.819668 − 0.572839i \(-0.194158\pi\)
0.819668 + 0.572839i \(0.194158\pi\)
\(702\) 0 0
\(703\) 10184.0 0.546368
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25536.0 1.35839
\(708\) 0 0
\(709\) 13262.0 0.702489 0.351245 − 0.936284i \(-0.385759\pi\)
0.351245 + 0.936284i \(0.385759\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −10200.0 −0.533508
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13920.0 0.722014 0.361007 − 0.932563i \(-0.382433\pi\)
0.361007 + 0.932563i \(0.382433\pi\)
\(720\) 0 0
\(721\) 34816.0 1.79836
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −150.000 −0.00768395
\(726\) 0 0
\(727\) 9376.00 0.478317 0.239159 − 0.970981i \(-0.423128\pi\)
0.239159 + 0.970981i \(0.423128\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −17304.0 −0.875529
\(732\) 0 0
\(733\) 6014.00 0.303045 0.151523 − 0.988454i \(-0.451582\pi\)
0.151523 + 0.988454i \(0.451582\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 48720.0 2.43504
\(738\) 0 0
\(739\) 7468.00 0.371739 0.185869 − 0.982574i \(-0.440490\pi\)
0.185869 + 0.982574i \(0.440490\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 31248.0 1.54290 0.771452 − 0.636287i \(-0.219531\pi\)
0.771452 + 0.636287i \(0.219531\pi\)
\(744\) 0 0
\(745\) −7770.00 −0.382108
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −54912.0 −2.67883
\(750\) 0 0
\(751\) −32840.0 −1.59567 −0.797835 − 0.602875i \(-0.794022\pi\)
−0.797835 + 0.602875i \(0.794022\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −11360.0 −0.547593
\(756\) 0 0
\(757\) −19066.0 −0.915410 −0.457705 − 0.889104i \(-0.651328\pi\)
−0.457705 + 0.889104i \(0.651328\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6858.00 −0.326678 −0.163339 − 0.986570i \(-0.552227\pi\)
−0.163339 + 0.986570i \(0.552227\pi\)
\(762\) 0 0
\(763\) 31040.0 1.47277
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22440.0 −1.05640
\(768\) 0 0
\(769\) 22178.0 1.04000 0.519999 − 0.854167i \(-0.325932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −14286.0 −0.664724 −0.332362 − 0.943152i \(-0.607846\pi\)
−0.332362 + 0.943152i \(0.607846\pi\)
\(774\) 0 0
\(775\) 5800.00 0.268829
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −17784.0 −0.817943
\(780\) 0 0
\(781\) −7200.00 −0.329880
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8470.00 −0.385105
\(786\) 0 0
\(787\) 18868.0 0.854602 0.427301 − 0.904109i \(-0.359465\pi\)
0.427301 + 0.904109i \(0.359465\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 13632.0 0.612766
\(792\) 0 0
\(793\) 16660.0 0.746045
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21690.0 0.963989 0.481994 − 0.876174i \(-0.339913\pi\)
0.481994 + 0.876174i \(0.339913\pi\)
\(798\) 0 0
\(799\) 15120.0 0.669471
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −44760.0 −1.96706
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 24726.0 1.07456 0.537281 − 0.843404i \(-0.319452\pi\)
0.537281 + 0.843404i \(0.319452\pi\)
\(810\) 0 0
\(811\) 2644.00 0.114480 0.0572401 − 0.998360i \(-0.481770\pi\)
0.0572401 + 0.998360i \(0.481770\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −260.000 −0.0111747
\(816\) 0 0
\(817\) 31312.0 1.34084
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 37842.0 1.60864 0.804321 − 0.594195i \(-0.202529\pi\)
0.804321 + 0.594195i \(0.202529\pi\)
\(822\) 0 0
\(823\) 880.000 0.0372720 0.0186360 − 0.999826i \(-0.494068\pi\)
0.0186360 + 0.999826i \(0.494068\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12876.0 −0.541406 −0.270703 − 0.962663i \(-0.587256\pi\)
−0.270703 + 0.962663i \(0.587256\pi\)
\(828\) 0 0
\(829\) −25498.0 −1.06825 −0.534127 − 0.845404i \(-0.679359\pi\)
−0.534127 + 0.845404i \(0.679359\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −28602.0 −1.18968
\(834\) 0 0
\(835\) 6000.00 0.248669
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −40584.0 −1.66998 −0.834991 − 0.550263i \(-0.814527\pi\)
−0.834991 + 0.550263i \(0.814527\pi\)
\(840\) 0 0
\(841\) −24353.0 −0.998524
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 5205.00 0.211902
\(846\) 0 0
\(847\) −72608.0 −2.94550
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −25738.0 −1.03312 −0.516561 − 0.856251i \(-0.672788\pi\)
−0.516561 + 0.856251i \(0.672788\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −13314.0 −0.530686 −0.265343 − 0.964154i \(-0.585485\pi\)
−0.265343 + 0.964154i \(0.585485\pi\)
\(858\) 0 0
\(859\) −24524.0 −0.974096 −0.487048 − 0.873375i \(-0.661926\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 5592.00 0.220572 0.110286 − 0.993900i \(-0.464823\pi\)
0.110286 + 0.993900i \(0.464823\pi\)
\(864\) 0 0
\(865\) 270.000 0.0106130
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 9120.00 0.356012
\(870\) 0 0
\(871\) 27608.0 1.07401
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4000.00 0.154542
\(876\) 0 0
\(877\) −14386.0 −0.553912 −0.276956 − 0.960883i \(-0.589326\pi\)
−0.276956 + 0.960883i \(0.589326\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −47106.0 −1.80141 −0.900705 − 0.434432i \(-0.856949\pi\)
−0.900705 + 0.434432i \(0.856949\pi\)
\(882\) 0 0
\(883\) −51548.0 −1.96458 −0.982292 − 0.187354i \(-0.940009\pi\)
−0.982292 + 0.187354i \(0.940009\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 34080.0 1.29007 0.645036 − 0.764152i \(-0.276842\pi\)
0.645036 + 0.764152i \(0.276842\pi\)
\(888\) 0 0
\(889\) 6400.00 0.241450
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −27360.0 −1.02527
\(894\) 0 0
\(895\) −4380.00 −0.163584
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1392.00 −0.0516416
\(900\) 0 0
\(901\) 9324.00 0.344759
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −19270.0 −0.707797
\(906\) 0 0
\(907\) −25748.0 −0.942611 −0.471306 − 0.881970i \(-0.656217\pi\)
−0.471306 + 0.881970i \(0.656217\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24768.0 −0.900769 −0.450384 − 0.892835i \(-0.648713\pi\)
−0.450384 + 0.892835i \(0.648713\pi\)
\(912\) 0 0
\(913\) 48240.0 1.74864
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1920.00 −0.0691428
\(918\) 0 0
\(919\) 31264.0 1.12220 0.561101 − 0.827747i \(-0.310378\pi\)
0.561101 + 0.827747i \(0.310378\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4080.00 −0.145498
\(924\) 0 0
\(925\) 3350.00 0.119078
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6174.00 0.218043 0.109022 − 0.994039i \(-0.465228\pi\)
0.109022 + 0.994039i \(0.465228\pi\)
\(930\) 0 0
\(931\) 51756.0 1.82195
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −12600.0 −0.440710
\(936\) 0 0
\(937\) 28922.0 1.00837 0.504184 − 0.863596i \(-0.331793\pi\)
0.504184 + 0.863596i \(0.331793\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −29238.0 −1.01289 −0.506446 − 0.862272i \(-0.669041\pi\)
−0.506446 + 0.862272i \(0.669041\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2868.00 −0.0984134 −0.0492067 − 0.998789i \(-0.515669\pi\)
−0.0492067 + 0.998789i \(0.515669\pi\)
\(948\) 0 0
\(949\) −25364.0 −0.867598
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −24018.0 −0.816390 −0.408195 − 0.912895i \(-0.633842\pi\)
−0.408195 + 0.912895i \(0.633842\pi\)
\(954\) 0 0
\(955\) 13920.0 0.471666
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 20544.0 0.691763
\(960\) 0 0
\(961\) 24033.0 0.806720
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4570.00 −0.152449
\(966\) 0 0
\(967\) −25712.0 −0.855059 −0.427530 − 0.904001i \(-0.640616\pi\)
−0.427530 + 0.904001i \(0.640616\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12396.0 −0.409688 −0.204844 − 0.978795i \(-0.565669\pi\)
−0.204844 + 0.978795i \(0.565669\pi\)
\(972\) 0 0
\(973\) −90752.0 −2.99011
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46614.0 1.52642 0.763211 − 0.646150i \(-0.223622\pi\)
0.763211 + 0.646150i \(0.223622\pi\)
\(978\) 0 0
\(979\) −40680.0 −1.32803
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −672.000 −0.0218041 −0.0109021 − 0.999941i \(-0.503470\pi\)
−0.0109021 + 0.999941i \(0.503470\pi\)
\(984\) 0 0
\(985\) −26010.0 −0.841368
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 38776.0 1.24295 0.621473 − 0.783435i \(-0.286534\pi\)
0.621473 + 0.783435i \(0.286534\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 15760.0 0.502136
\(996\) 0 0
\(997\) 30422.0 0.966374 0.483187 − 0.875517i \(-0.339479\pi\)
0.483187 + 0.875517i \(0.339479\pi\)
\(998\) 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 720.4.a.b.1.1 1
3.2 odd 2 240.4.a.c.1.1 1
4.3 odd 2 90.4.a.d.1.1 1
12.11 even 2 30.4.a.a.1.1 ✓ 1
15.2 even 4 1200.4.f.u.49.2 2
15.8 even 4 1200.4.f.u.49.1 2
15.14 odd 2 1200.4.a.bk.1.1 1
20.3 even 4 450.4.c.k.199.1 2
20.7 even 4 450.4.c.k.199.2 2
20.19 odd 2 450.4.a.b.1.1 1
24.5 odd 2 960.4.a.s.1.1 1
24.11 even 2 960.4.a.j.1.1 1
36.7 odd 6 810.4.e.e.271.1 2
36.11 even 6 810.4.e.m.271.1 2
36.23 even 6 810.4.e.m.541.1 2
36.31 odd 6 810.4.e.e.541.1 2
60.23 odd 4 150.4.c.a.49.2 2
60.47 odd 4 150.4.c.a.49.1 2
60.59 even 2 150.4.a.e.1.1 1
84.83 odd 2 1470.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.4.a.a.1.1 ✓ 1 12.11 even 2
90.4.a.d.1.1 1 4.3 odd 2
150.4.a.e.1.1 1 60.59 even 2
150.4.c.a.49.1 2 60.47 odd 4
150.4.c.a.49.2 2 60.23 odd 4
240.4.a.c.1.1 1 3.2 odd 2
450.4.a.b.1.1 1 20.19 odd 2
450.4.c.k.199.1 2 20.3 even 4
450.4.c.k.199.2 2 20.7 even 4
720.4.a.b.1.1 1 1.1 even 1 trivial
810.4.e.e.271.1 2 36.7 odd 6
810.4.e.e.541.1 2 36.31 odd 6
810.4.e.m.271.1 2 36.11 even 6
810.4.e.m.541.1 2 36.23 even 6
960.4.a.j.1.1 1 24.11 even 2
960.4.a.s.1.1 1 24.5 odd 2
1200.4.a.bk.1.1 1 15.14 odd 2
1200.4.f.u.49.1 2 15.8 even 4
1200.4.f.u.49.2 2 15.2 even 4
1470.4.a.a.1.1 1 84.83 odd 2