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Properties

Label 720.4.a.q.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 120)
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)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -20.0000 q^{7} -56.0000 q^{11} -86.0000 q^{13} +106.000 q^{17} -4.00000 q^{19} +136.000 q^{23} +25.0000 q^{25} +206.000 q^{29} +152.000 q^{31} -100.000 q^{35} +282.000 q^{37} +246.000 q^{41} -412.000 q^{43} +40.0000 q^{47} +57.0000 q^{49} +126.000 q^{53} -280.000 q^{55} +56.0000 q^{59} -2.00000 q^{61} -430.000 q^{65} +388.000 q^{67} -672.000 q^{71} +1170.00 q^{73} +1120.00 q^{77} -408.000 q^{79} +668.000 q^{83} +530.000 q^{85} -66.0000 q^{89} +1720.00 q^{91} -20.0000 q^{95} -926.000 q^{97} +O(q^{100})\)

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
\(7\) −20.0000 −1.07990 −0.539949 − 0.841698i \(-0.681557\pi\)
−0.539949 + 0.841698i \(0.681557\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −56.0000 −1.53497 −0.767483 − 0.641069i \(-0.778491\pi\)
−0.767483 + 0.641069i \(0.778491\pi\)
\(12\) 0 0
\(13\) −86.0000 −1.83478 −0.917389 − 0.397992i \(-0.869707\pi\)
−0.917389 + 0.397992i \(0.869707\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 106.000 1.51228 0.756140 − 0.654409i \(-0.227083\pi\)
0.756140 + 0.654409i \(0.227083\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 − 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 136.000 1.23295 0.616477 − 0.787373i \(-0.288559\pi\)
0.616477 + 0.787373i \(0.288559\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 206.000 1.31908 0.659539 − 0.751671i \(-0.270752\pi\)
0.659539 + 0.751671i \(0.270752\pi\)
\(30\) 0 0
\(31\) 152.000 0.880645 0.440323 − 0.897840i \(-0.354864\pi\)
0.440323 + 0.897840i \(0.354864\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −100.000 −0.482945
\(36\) 0 0
\(37\) 282.000 1.25299 0.626493 − 0.779427i \(-0.284490\pi\)
0.626493 + 0.779427i \(0.284490\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 246.000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −412.000 −1.46115 −0.730575 − 0.682833i \(-0.760748\pi\)
−0.730575 + 0.682833i \(0.760748\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 40.0000 0.124140 0.0620702 − 0.998072i \(-0.480230\pi\)
0.0620702 + 0.998072i \(0.480230\pi\)
\(48\) 0 0
\(49\) 57.0000 0.166181
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 126.000 0.326555 0.163278 − 0.986580i \(-0.447793\pi\)
0.163278 + 0.986580i \(0.447793\pi\)
\(54\) 0 0
\(55\) −280.000 −0.686458
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 56.0000 0.123569 0.0617846 − 0.998090i \(-0.480321\pi\)
0.0617846 + 0.998090i \(0.480321\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.00419793 −0.00209897 − 0.999998i \(-0.500668\pi\)
−0.00209897 + 0.999998i \(0.500668\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −430.000 −0.820537
\(66\) 0 0
\(67\) 388.000 0.707489 0.353744 − 0.935342i \(-0.384908\pi\)
0.353744 + 0.935342i \(0.384908\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −672.000 −1.12326 −0.561632 − 0.827387i \(-0.689826\pi\)
−0.561632 + 0.827387i \(0.689826\pi\)
\(72\) 0 0
\(73\) 1170.00 1.87586 0.937932 − 0.346818i \(-0.112738\pi\)
0.937932 + 0.346818i \(0.112738\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1120.00 1.65761
\(78\) 0 0
\(79\) −408.000 −0.581058 −0.290529 − 0.956866i \(-0.593831\pi\)
−0.290529 + 0.956866i \(0.593831\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 668.000 0.883404 0.441702 − 0.897162i \(-0.354375\pi\)
0.441702 + 0.897162i \(0.354375\pi\)
\(84\) 0 0
\(85\) 530.000 0.676313
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −66.0000 −0.0786066 −0.0393033 − 0.999227i \(-0.512514\pi\)
−0.0393033 + 0.999227i \(0.512514\pi\)
\(90\) 0 0
\(91\) 1720.00 1.98137
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −20.0000 −0.0215995
\(96\) 0 0
\(97\) −926.000 −0.969289 −0.484645 − 0.874711i \(-0.661051\pi\)
−0.484645 + 0.874711i \(0.661051\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 198.000 0.195067 0.0975333 − 0.995232i \(-0.468905\pi\)
0.0975333 + 0.995232i \(0.468905\pi\)
\(102\) 0 0
\(103\) 1532.00 1.46556 0.732779 − 0.680467i \(-0.238223\pi\)
0.732779 + 0.680467i \(0.238223\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −444.000 −0.401150 −0.200575 − 0.979678i \(-0.564281\pi\)
−0.200575 + 0.979678i \(0.564281\pi\)
\(108\) 0 0
\(109\) 62.0000 0.0544819 0.0272409 − 0.999629i \(-0.491328\pi\)
0.0272409 + 0.999629i \(0.491328\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −414.000 −0.344653 −0.172327 − 0.985040i \(-0.555128\pi\)
−0.172327 + 0.985040i \(0.555128\pi\)
\(114\) 0 0
\(115\) 680.000 0.551394
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2120.00 −1.63311
\(120\) 0 0
\(121\) 1805.00 1.35612
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 996.000 0.695911 0.347956 − 0.937511i \(-0.386876\pi\)
0.347956 + 0.937511i \(0.386876\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −264.000 −0.176075 −0.0880374 − 0.996117i \(-0.528059\pi\)
−0.0880374 + 0.996117i \(0.528059\pi\)
\(132\) 0 0
\(133\) 80.0000 0.0521570
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2278.00 −1.42060 −0.710302 − 0.703897i \(-0.751442\pi\)
−0.710302 + 0.703897i \(0.751442\pi\)
\(138\) 0 0
\(139\) −1812.00 −1.10570 −0.552848 − 0.833282i \(-0.686459\pi\)
−0.552848 + 0.833282i \(0.686459\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4816.00 2.81632
\(144\) 0 0
\(145\) 1030.00 0.589909
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1534.00 0.843424 0.421712 − 0.906730i \(-0.361429\pi\)
0.421712 + 0.906730i \(0.361429\pi\)
\(150\) 0 0
\(151\) 3016.00 1.62542 0.812711 − 0.582668i \(-0.197991\pi\)
0.812711 + 0.582668i \(0.197991\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 760.000 0.393837
\(156\) 0 0
\(157\) −1814.00 −0.922121 −0.461060 − 0.887369i \(-0.652531\pi\)
−0.461060 + 0.887369i \(0.652531\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2720.00 −1.33147
\(162\) 0 0
\(163\) 1844.00 0.886093 0.443047 − 0.896499i \(-0.353898\pi\)
0.443047 + 0.896499i \(0.353898\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3768.00 1.74597 0.872984 − 0.487749i \(-0.162182\pi\)
0.872984 + 0.487749i \(0.162182\pi\)
\(168\) 0 0
\(169\) 5199.00 2.36641
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −938.000 −0.412224 −0.206112 − 0.978528i \(-0.566081\pi\)
−0.206112 + 0.978528i \(0.566081\pi\)
\(174\) 0 0
\(175\) −500.000 −0.215980
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3968.00 1.65688 0.828442 − 0.560075i \(-0.189228\pi\)
0.828442 + 0.560075i \(0.189228\pi\)
\(180\) 0 0
\(181\) −3514.00 −1.44306 −0.721529 − 0.692384i \(-0.756560\pi\)
−0.721529 + 0.692384i \(0.756560\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1410.00 0.560353
\(186\) 0 0
\(187\) −5936.00 −2.32130
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1480.00 −0.560676 −0.280338 − 0.959901i \(-0.590446\pi\)
−0.280338 + 0.959901i \(0.590446\pi\)
\(192\) 0 0
\(193\) −2774.00 −1.03460 −0.517298 − 0.855806i \(-0.673062\pi\)
−0.517298 + 0.855806i \(0.673062\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3806.00 1.37648 0.688239 − 0.725484i \(-0.258384\pi\)
0.688239 + 0.725484i \(0.258384\pi\)
\(198\) 0 0
\(199\) 856.000 0.304926 0.152463 − 0.988309i \(-0.451280\pi\)
0.152463 + 0.988309i \(0.451280\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4120.00 −1.42447
\(204\) 0 0
\(205\) 1230.00 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 224.000 0.0741359
\(210\) 0 0
\(211\) −3020.00 −0.985334 −0.492667 − 0.870218i \(-0.663978\pi\)
−0.492667 + 0.870218i \(0.663978\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2060.00 −0.653446
\(216\) 0 0
\(217\) −3040.00 −0.951008
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −9116.00 −2.77470
\(222\) 0 0
\(223\) 1684.00 0.505690 0.252845 − 0.967507i \(-0.418634\pi\)
0.252845 + 0.967507i \(0.418634\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2004.00 0.585948 0.292974 − 0.956120i \(-0.405355\pi\)
0.292974 + 0.956120i \(0.405355\pi\)
\(228\) 0 0
\(229\) −5042.00 −1.45496 −0.727478 − 0.686131i \(-0.759307\pi\)
−0.727478 + 0.686131i \(0.759307\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3090.00 0.868810 0.434405 − 0.900718i \(-0.356959\pi\)
0.434405 + 0.900718i \(0.356959\pi\)
\(234\) 0 0
\(235\) 200.000 0.0555173
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2136.00 0.578102 0.289051 − 0.957314i \(-0.406660\pi\)
0.289051 + 0.957314i \(0.406660\pi\)
\(240\) 0 0
\(241\) 98.0000 0.0261939 0.0130970 − 0.999914i \(-0.495831\pi\)
0.0130970 + 0.999914i \(0.495831\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 285.000 0.0743183
\(246\) 0 0
\(247\) 344.000 0.0886162
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5040.00 −1.26742 −0.633709 − 0.773571i \(-0.718468\pi\)
−0.633709 + 0.773571i \(0.718468\pi\)
\(252\) 0 0
\(253\) −7616.00 −1.89254
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1986.00 0.482036 0.241018 − 0.970521i \(-0.422519\pi\)
0.241018 + 0.970521i \(0.422519\pi\)
\(258\) 0 0
\(259\) −5640.00 −1.35310
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1416.00 0.331994 0.165997 − 0.986126i \(-0.446916\pi\)
0.165997 + 0.986126i \(0.446916\pi\)
\(264\) 0 0
\(265\) 630.000 0.146040
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6670.00 1.51181 0.755905 − 0.654681i \(-0.227197\pi\)
0.755905 + 0.654681i \(0.227197\pi\)
\(270\) 0 0
\(271\) −48.0000 −0.0107594 −0.00537969 − 0.999986i \(-0.501712\pi\)
−0.00537969 + 0.999986i \(0.501712\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1400.00 −0.306993
\(276\) 0 0
\(277\) 6938.00 1.50492 0.752462 − 0.658636i \(-0.228866\pi\)
0.752462 + 0.658636i \(0.228866\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1694.00 0.359628 0.179814 − 0.983701i \(-0.442450\pi\)
0.179814 + 0.983701i \(0.442450\pi\)
\(282\) 0 0
\(283\) 6364.00 1.33675 0.668376 − 0.743824i \(-0.266990\pi\)
0.668376 + 0.743824i \(0.266990\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4920.00 −1.01191
\(288\) 0 0
\(289\) 6323.00 1.28699
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3134.00 0.624881 0.312441 − 0.949937i \(-0.398853\pi\)
0.312441 + 0.949937i \(0.398853\pi\)
\(294\) 0 0
\(295\) 280.000 0.0552618
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −11696.0 −2.26220
\(300\) 0 0
\(301\) 8240.00 1.57789
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.0000 −0.00187737
\(306\) 0 0
\(307\) 236.000 0.0438737 0.0219369 − 0.999759i \(-0.493017\pi\)
0.0219369 + 0.999759i \(0.493017\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3776.00 0.688480 0.344240 − 0.938882i \(-0.388137\pi\)
0.344240 + 0.938882i \(0.388137\pi\)
\(312\) 0 0
\(313\) −7918.00 −1.42988 −0.714939 − 0.699187i \(-0.753546\pi\)
−0.714939 + 0.699187i \(0.753546\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4362.00 −0.772853 −0.386426 − 0.922320i \(-0.626291\pi\)
−0.386426 + 0.922320i \(0.626291\pi\)
\(318\) 0 0
\(319\) −11536.0 −2.02474
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −424.000 −0.0730402
\(324\) 0 0
\(325\) −2150.00 −0.366956
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −800.000 −0.134059
\(330\) 0 0
\(331\) −7980.00 −1.32514 −0.662569 − 0.749001i \(-0.730534\pi\)
−0.662569 + 0.749001i \(0.730534\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1940.00 0.316399
\(336\) 0 0
\(337\) −8294.00 −1.34066 −0.670331 − 0.742062i \(-0.733848\pi\)
−0.670331 + 0.742062i \(0.733848\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8512.00 −1.35176
\(342\) 0 0
\(343\) 5720.00 0.900440
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −964.000 −0.149136 −0.0745681 − 0.997216i \(-0.523758\pi\)
−0.0745681 + 0.997216i \(0.523758\pi\)
\(348\) 0 0
\(349\) 8670.00 1.32978 0.664892 − 0.746940i \(-0.268478\pi\)
0.664892 + 0.746940i \(0.268478\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2314.00 0.348900 0.174450 − 0.984666i \(-0.444185\pi\)
0.174450 + 0.984666i \(0.444185\pi\)
\(354\) 0 0
\(355\) −3360.00 −0.502339
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1896.00 −0.278738 −0.139369 − 0.990240i \(-0.544507\pi\)
−0.139369 + 0.990240i \(0.544507\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5850.00 0.838912
\(366\) 0 0
\(367\) −1484.00 −0.211074 −0.105537 − 0.994415i \(-0.533656\pi\)
−0.105537 + 0.994415i \(0.533656\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2520.00 −0.352647
\(372\) 0 0
\(373\) 12370.0 1.71714 0.858571 − 0.512694i \(-0.171352\pi\)
0.858571 + 0.512694i \(0.171352\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17716.0 −2.42021
\(378\) 0 0
\(379\) −5620.00 −0.761689 −0.380844 − 0.924639i \(-0.624367\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5880.00 0.784475 0.392238 − 0.919864i \(-0.371701\pi\)
0.392238 + 0.919864i \(0.371701\pi\)
\(384\) 0 0
\(385\) 5600.00 0.741305
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2082.00 −0.271367 −0.135683 − 0.990752i \(-0.543323\pi\)
−0.135683 + 0.990752i \(0.543323\pi\)
\(390\) 0 0
\(391\) 14416.0 1.86457
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2040.00 −0.259857
\(396\) 0 0
\(397\) −1742.00 −0.220223 −0.110111 − 0.993919i \(-0.535121\pi\)
−0.110111 + 0.993919i \(0.535121\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3270.00 0.407222 0.203611 − 0.979052i \(-0.434732\pi\)
0.203611 + 0.979052i \(0.434732\pi\)
\(402\) 0 0
\(403\) −13072.0 −1.61579
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15792.0 −1.92329
\(408\) 0 0
\(409\) −6134.00 −0.741581 −0.370791 − 0.928716i \(-0.620913\pi\)
−0.370791 + 0.928716i \(0.620913\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1120.00 −0.133442
\(414\) 0 0
\(415\) 3340.00 0.395070
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10392.0 −1.21165 −0.605826 − 0.795597i \(-0.707157\pi\)
−0.605826 + 0.795597i \(0.707157\pi\)
\(420\) 0 0
\(421\) −12690.0 −1.46906 −0.734528 − 0.678578i \(-0.762596\pi\)
−0.734528 + 0.678578i \(0.762596\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2650.00 0.302456
\(426\) 0 0
\(427\) 40.0000 0.00453334
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7408.00 −0.827914 −0.413957 − 0.910297i \(-0.635854\pi\)
−0.413957 + 0.910297i \(0.635854\pi\)
\(432\) 0 0
\(433\) −5062.00 −0.561811 −0.280906 − 0.959735i \(-0.590635\pi\)
−0.280906 + 0.959735i \(0.590635\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −544.000 −0.0595493
\(438\) 0 0
\(439\) 7160.00 0.778424 0.389212 − 0.921148i \(-0.372747\pi\)
0.389212 + 0.921148i \(0.372747\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17100.0 1.83396 0.916981 − 0.398930i \(-0.130618\pi\)
0.916981 + 0.398930i \(0.130618\pi\)
\(444\) 0 0
\(445\) −330.000 −0.0351539
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8634.00 −0.907491 −0.453746 − 0.891131i \(-0.649913\pi\)
−0.453746 + 0.891131i \(0.649913\pi\)
\(450\) 0 0
\(451\) −13776.0 −1.43833
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8600.00 0.886097
\(456\) 0 0
\(457\) 2986.00 0.305644 0.152822 − 0.988254i \(-0.451164\pi\)
0.152822 + 0.988254i \(0.451164\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2406.00 0.243077 0.121539 − 0.992587i \(-0.461217\pi\)
0.121539 + 0.992587i \(0.461217\pi\)
\(462\) 0 0
\(463\) 14316.0 1.43698 0.718489 − 0.695538i \(-0.244834\pi\)
0.718489 + 0.695538i \(0.244834\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −292.000 −0.0289339 −0.0144670 − 0.999895i \(-0.504605\pi\)
−0.0144670 + 0.999895i \(0.504605\pi\)
\(468\) 0 0
\(469\) −7760.00 −0.764016
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 23072.0 2.24282
\(474\) 0 0
\(475\) −100.000 −0.00965961
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14056.0 1.34078 0.670391 − 0.742008i \(-0.266126\pi\)
0.670391 + 0.742008i \(0.266126\pi\)
\(480\) 0 0
\(481\) −24252.0 −2.29895
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4630.00 −0.433479
\(486\) 0 0
\(487\) 11204.0 1.04251 0.521254 − 0.853401i \(-0.325464\pi\)
0.521254 + 0.853401i \(0.325464\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4608.00 0.423536 0.211768 − 0.977320i \(-0.432078\pi\)
0.211768 + 0.977320i \(0.432078\pi\)
\(492\) 0 0
\(493\) 21836.0 1.99482
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13440.0 1.21301
\(498\) 0 0
\(499\) −2468.00 −0.221409 −0.110704 − 0.993853i \(-0.535311\pi\)
−0.110704 + 0.993853i \(0.535311\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12192.0 1.08074 0.540372 − 0.841426i \(-0.318283\pi\)
0.540372 + 0.841426i \(0.318283\pi\)
\(504\) 0 0
\(505\) 990.000 0.0872365
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1714.00 −0.149257 −0.0746284 − 0.997211i \(-0.523777\pi\)
−0.0746284 + 0.997211i \(0.523777\pi\)
\(510\) 0 0
\(511\) −23400.0 −2.02574
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7660.00 0.655417
\(516\) 0 0
\(517\) −2240.00 −0.190551
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18014.0 1.51479 0.757397 − 0.652955i \(-0.226471\pi\)
0.757397 + 0.652955i \(0.226471\pi\)
\(522\) 0 0
\(523\) 16748.0 1.40027 0.700133 − 0.714013i \(-0.253124\pi\)
0.700133 + 0.714013i \(0.253124\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16112.0 1.33178
\(528\) 0 0
\(529\) 6329.00 0.520178
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −21156.0 −1.71926
\(534\) 0 0
\(535\) −2220.00 −0.179400
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3192.00 −0.255082
\(540\) 0 0
\(541\) −14018.0 −1.11401 −0.557006 − 0.830508i \(-0.688050\pi\)
−0.557006 + 0.830508i \(0.688050\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 310.000 0.0243650
\(546\) 0 0
\(547\) 412.000 0.0322045 0.0161022 − 0.999870i \(-0.494874\pi\)
0.0161022 + 0.999870i \(0.494874\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −824.000 −0.0637089
\(552\) 0 0
\(553\) 8160.00 0.627484
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18218.0 −1.38586 −0.692928 − 0.721007i \(-0.743679\pi\)
−0.692928 + 0.721007i \(0.743679\pi\)
\(558\) 0 0
\(559\) 35432.0 2.68088
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23524.0 1.76096 0.880478 − 0.474087i \(-0.157222\pi\)
0.880478 + 0.474087i \(0.157222\pi\)
\(564\) 0 0
\(565\) −2070.00 −0.154134
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23330.0 −1.71888 −0.859442 − 0.511234i \(-0.829189\pi\)
−0.859442 + 0.511234i \(0.829189\pi\)
\(570\) 0 0
\(571\) 13124.0 0.961860 0.480930 − 0.876759i \(-0.340299\pi\)
0.480930 + 0.876759i \(0.340299\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3400.00 0.246591
\(576\) 0 0
\(577\) 11714.0 0.845165 0.422582 − 0.906324i \(-0.361124\pi\)
0.422582 + 0.906324i \(0.361124\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −13360.0 −0.953987
\(582\) 0 0
\(583\) −7056.00 −0.501252
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17628.0 −1.23950 −0.619749 − 0.784800i \(-0.712766\pi\)
−0.619749 + 0.784800i \(0.712766\pi\)
\(588\) 0 0
\(589\) −608.000 −0.0425335
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2802.00 0.194038 0.0970188 − 0.995283i \(-0.469069\pi\)
0.0970188 + 0.995283i \(0.469069\pi\)
\(594\) 0 0
\(595\) −10600.0 −0.730349
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2664.00 −0.181716 −0.0908582 − 0.995864i \(-0.528961\pi\)
−0.0908582 + 0.995864i \(0.528961\pi\)
\(600\) 0 0
\(601\) 23962.0 1.62634 0.813170 − 0.582026i \(-0.197740\pi\)
0.813170 + 0.582026i \(0.197740\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9025.00 0.606477
\(606\) 0 0
\(607\) −11940.0 −0.798401 −0.399201 − 0.916864i \(-0.630712\pi\)
−0.399201 + 0.916864i \(0.630712\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3440.00 −0.227770
\(612\) 0 0
\(613\) 16794.0 1.10653 0.553265 − 0.833005i \(-0.313382\pi\)
0.553265 + 0.833005i \(0.313382\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20706.0 1.35104 0.675520 − 0.737341i \(-0.263919\pi\)
0.675520 + 0.737341i \(0.263919\pi\)
\(618\) 0 0
\(619\) −10724.0 −0.696339 −0.348170 − 0.937432i \(-0.613197\pi\)
−0.348170 + 0.937432i \(0.613197\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1320.00 0.0848871
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 29892.0 1.89487
\(630\) 0 0
\(631\) 5744.00 0.362385 0.181193 − 0.983448i \(-0.442004\pi\)
0.181193 + 0.983448i \(0.442004\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4980.00 0.311221
\(636\) 0 0
\(637\) −4902.00 −0.304905
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −27906.0 −1.71953 −0.859767 − 0.510687i \(-0.829391\pi\)
−0.859767 + 0.510687i \(0.829391\pi\)
\(642\) 0 0
\(643\) −20556.0 −1.26073 −0.630365 − 0.776299i \(-0.717095\pi\)
−0.630365 + 0.776299i \(0.717095\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10224.0 −0.621247 −0.310624 − 0.950533i \(-0.600538\pi\)
−0.310624 + 0.950533i \(0.600538\pi\)
\(648\) 0 0
\(649\) −3136.00 −0.189675
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12982.0 0.777986 0.388993 − 0.921241i \(-0.372823\pi\)
0.388993 + 0.921241i \(0.372823\pi\)
\(654\) 0 0
\(655\) −1320.00 −0.0787430
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1512.00 −0.0893766 −0.0446883 − 0.999001i \(-0.514229\pi\)
−0.0446883 + 0.999001i \(0.514229\pi\)
\(660\) 0 0
\(661\) 16710.0 0.983273 0.491637 − 0.870800i \(-0.336399\pi\)
0.491637 + 0.870800i \(0.336399\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 400.000 0.0233253
\(666\) 0 0
\(667\) 28016.0 1.62636
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 112.000 0.00644368
\(672\) 0 0
\(673\) 7962.00 0.456036 0.228018 − 0.973657i \(-0.426775\pi\)
0.228018 + 0.973657i \(0.426775\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12226.0 −0.694067 −0.347033 − 0.937853i \(-0.612811\pi\)
−0.347033 + 0.937853i \(0.612811\pi\)
\(678\) 0 0
\(679\) 18520.0 1.04673
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8748.00 −0.490092 −0.245046 − 0.969511i \(-0.578803\pi\)
−0.245046 + 0.969511i \(0.578803\pi\)
\(684\) 0 0
\(685\) −11390.0 −0.635313
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10836.0 −0.599156
\(690\) 0 0
\(691\) 7324.00 0.403210 0.201605 − 0.979467i \(-0.435384\pi\)
0.201605 + 0.979467i \(0.435384\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9060.00 −0.494483
\(696\) 0 0
\(697\) 26076.0 1.41707
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21934.0 1.18179 0.590896 − 0.806748i \(-0.298774\pi\)
0.590896 + 0.806748i \(0.298774\pi\)
\(702\) 0 0
\(703\) −1128.00 −0.0605168
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3960.00 −0.210652
\(708\) 0 0
\(709\) −10690.0 −0.566250 −0.283125 − 0.959083i \(-0.591371\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20672.0 1.08580
\(714\) 0 0
\(715\) 24080.0 1.25950
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13792.0 0.715375 0.357688 − 0.933841i \(-0.383565\pi\)
0.357688 + 0.933841i \(0.383565\pi\)
\(720\) 0 0
\(721\) −30640.0 −1.58265
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5150.00 0.263815
\(726\) 0 0
\(727\) 24004.0 1.22457 0.612283 − 0.790639i \(-0.290251\pi\)
0.612283 + 0.790639i \(0.290251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −43672.0 −2.20967
\(732\) 0 0
\(733\) 8562.00 0.431439 0.215719 − 0.976455i \(-0.430790\pi\)
0.215719 + 0.976455i \(0.430790\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21728.0 −1.08597
\(738\) 0 0
\(739\) 13836.0 0.688722 0.344361 − 0.938837i \(-0.388096\pi\)
0.344361 + 0.938837i \(0.388096\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −22224.0 −1.09733 −0.548667 − 0.836041i \(-0.684865\pi\)
−0.548667 + 0.836041i \(0.684865\pi\)
\(744\) 0 0
\(745\) 7670.00 0.377191
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8880.00 0.433202
\(750\) 0 0
\(751\) −11544.0 −0.560914 −0.280457 − 0.959867i \(-0.590486\pi\)
−0.280457 + 0.959867i \(0.590486\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15080.0 0.726910
\(756\) 0 0
\(757\) −3814.00 −0.183120 −0.0915602 − 0.995800i \(-0.529185\pi\)
−0.0915602 + 0.995800i \(0.529185\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 25662.0 1.22240 0.611200 − 0.791476i \(-0.290687\pi\)
0.611200 + 0.791476i \(0.290687\pi\)
\(762\) 0 0
\(763\) −1240.00 −0.0588349
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4816.00 −0.226722
\(768\) 0 0
\(769\) 30658.0 1.43765 0.718827 − 0.695189i \(-0.244679\pi\)
0.718827 + 0.695189i \(0.244679\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30894.0 1.43749 0.718745 − 0.695274i \(-0.244717\pi\)
0.718745 + 0.695274i \(0.244717\pi\)
\(774\) 0 0
\(775\) 3800.00 0.176129
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −984.000 −0.0452573
\(780\) 0 0
\(781\) 37632.0 1.72417
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9070.00 −0.412385
\(786\) 0 0
\(787\) −21596.0 −0.978163 −0.489081 − 0.872238i \(-0.662668\pi\)
−0.489081 + 0.872238i \(0.662668\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8280.00 0.372191
\(792\) 0 0
\(793\) 172.000 0.00770227
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8646.00 0.384262 0.192131 − 0.981369i \(-0.438460\pi\)
0.192131 + 0.981369i \(0.438460\pi\)
\(798\) 0 0
\(799\) 4240.00 0.187735
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −65520.0 −2.87939
\(804\) 0 0
\(805\) −13600.0 −0.595450
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −24954.0 −1.08447 −0.542235 − 0.840227i \(-0.682422\pi\)
−0.542235 + 0.840227i \(0.682422\pi\)
\(810\) 0 0
\(811\) −40004.0 −1.73210 −0.866048 − 0.499960i \(-0.833348\pi\)
−0.866048 + 0.499960i \(0.833348\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9220.00 0.396273
\(816\) 0 0
\(817\) 1648.00 0.0705707
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −16570.0 −0.704381 −0.352191 − 0.935928i \(-0.614563\pi\)
−0.352191 + 0.935928i \(0.614563\pi\)
\(822\) 0 0
\(823\) 4388.00 0.185852 0.0929259 − 0.995673i \(-0.470378\pi\)
0.0929259 + 0.995673i \(0.470378\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14364.0 0.603972 0.301986 − 0.953312i \(-0.402350\pi\)
0.301986 + 0.953312i \(0.402350\pi\)
\(828\) 0 0
\(829\) −21170.0 −0.886929 −0.443465 − 0.896292i \(-0.646251\pi\)
−0.443465 + 0.896292i \(0.646251\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6042.00 0.251312
\(834\) 0 0
\(835\) 18840.0 0.780820
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10664.0 0.438811 0.219405 − 0.975634i \(-0.429588\pi\)
0.219405 + 0.975634i \(0.429588\pi\)
\(840\) 0 0
\(841\) 18047.0 0.739965
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 25995.0 1.05829
\(846\) 0 0
\(847\) −36100.0 −1.46448
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 38352.0 1.54488
\(852\) 0 0
\(853\) −3190.00 −0.128046 −0.0640232 − 0.997948i \(-0.520393\pi\)
−0.0640232 + 0.997948i \(0.520393\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −20814.0 −0.829630 −0.414815 − 0.909906i \(-0.636154\pi\)
−0.414815 + 0.909906i \(0.636154\pi\)
\(858\) 0 0
\(859\) 18988.0 0.754205 0.377103 − 0.926172i \(-0.376920\pi\)
0.377103 + 0.926172i \(0.376920\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11664.0 0.460078 0.230039 − 0.973181i \(-0.426115\pi\)
0.230039 + 0.973181i \(0.426115\pi\)
\(864\) 0 0
\(865\) −4690.00 −0.184352
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 22848.0 0.891905
\(870\) 0 0
\(871\) −33368.0 −1.29808
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2500.00 −0.0965891
\(876\) 0 0
\(877\) −8246.00 −0.317500 −0.158750 − 0.987319i \(-0.550746\pi\)
−0.158750 + 0.987319i \(0.550746\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −22890.0 −0.875350 −0.437675 − 0.899133i \(-0.644198\pi\)
−0.437675 + 0.899133i \(0.644198\pi\)
\(882\) 0 0
\(883\) −33548.0 −1.27857 −0.639287 − 0.768969i \(-0.720770\pi\)
−0.639287 + 0.768969i \(0.720770\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −32264.0 −1.22133 −0.610665 − 0.791889i \(-0.709098\pi\)
−0.610665 + 0.791889i \(0.709098\pi\)
\(888\) 0 0
\(889\) −19920.0 −0.751513
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −160.000 −0.00599574
\(894\) 0 0
\(895\) 19840.0 0.740981
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 31312.0 1.16164
\(900\) 0 0
\(901\) 13356.0 0.493843
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17570.0 −0.645355
\(906\) 0 0
\(907\) −51228.0 −1.87541 −0.937706 − 0.347431i \(-0.887054\pi\)
−0.937706 + 0.347431i \(0.887054\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2144.00 −0.0779735 −0.0389868 − 0.999240i \(-0.512413\pi\)
−0.0389868 + 0.999240i \(0.512413\pi\)
\(912\) 0 0
\(913\) −37408.0 −1.35600
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5280.00 0.190143
\(918\) 0 0
\(919\) −33584.0 −1.20548 −0.602739 − 0.797939i \(-0.705924\pi\)
−0.602739 + 0.797939i \(0.705924\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 57792.0 2.06094
\(924\) 0 0
\(925\) 7050.00 0.250597
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3590.00 0.126786 0.0633929 − 0.997989i \(-0.479808\pi\)
0.0633929 + 0.997989i \(0.479808\pi\)
\(930\) 0 0
\(931\) −228.000 −0.00802621
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −29680.0 −1.03812
\(936\) 0 0
\(937\) −21686.0 −0.756084 −0.378042 − 0.925788i \(-0.623403\pi\)
−0.378042 + 0.925788i \(0.623403\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5174.00 0.179243 0.0896215 − 0.995976i \(-0.471434\pi\)
0.0896215 + 0.995976i \(0.471434\pi\)
\(942\) 0 0
\(943\) 33456.0 1.15533
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35524.0 1.21898 0.609490 − 0.792793i \(-0.291374\pi\)
0.609490 + 0.792793i \(0.291374\pi\)
\(948\) 0 0
\(949\) −100620. −3.44179
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 16122.0 0.547999 0.273999 − 0.961730i \(-0.411653\pi\)
0.273999 + 0.961730i \(0.411653\pi\)
\(954\) 0 0
\(955\) −7400.00 −0.250742
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 45560.0 1.53411
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −13870.0 −0.462685
\(966\) 0 0
\(967\) −19188.0 −0.638102 −0.319051 − 0.947738i \(-0.603364\pi\)
−0.319051 + 0.947738i \(0.603364\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −38464.0 −1.27123 −0.635617 − 0.772004i \(-0.719254\pi\)
−0.635617 + 0.772004i \(0.719254\pi\)
\(972\) 0 0
\(973\) 36240.0 1.19404
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43930.0 1.43853 0.719266 − 0.694735i \(-0.244478\pi\)
0.719266 + 0.694735i \(0.244478\pi\)
\(978\) 0 0
\(979\) 3696.00 0.120659
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 17328.0 0.562235 0.281118 − 0.959673i \(-0.409295\pi\)
0.281118 + 0.959673i \(0.409295\pi\)
\(984\) 0 0
\(985\) 19030.0 0.615580
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −56032.0 −1.80153
\(990\) 0 0
\(991\) 18160.0 0.582110 0.291055 − 0.956706i \(-0.405994\pi\)
0.291055 + 0.956706i \(0.405994\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4280.00 0.136367
\(996\) 0 0
\(997\) −9102.00 −0.289131 −0.144565 − 0.989495i \(-0.546178\pi\)
−0.144565 + 0.989495i \(0.546178\pi\)
\(998\) 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.q.1.1 1
3.2 odd 2 240.4.a.g.1.1 1
4.3 odd 2 360.4.a.n.1.1 1
12.11 even 2 120.4.a.b.1.1 ✓ 1
15.2 even 4 1200.4.f.t.49.1 2
15.8 even 4 1200.4.f.t.49.2 2
15.14 odd 2 1200.4.a.p.1.1 1
20.3 even 4 1800.4.f.v.649.1 2
20.7 even 4 1800.4.f.v.649.2 2
20.19 odd 2 1800.4.a.f.1.1 1
24.5 odd 2 960.4.a.k.1.1 1
24.11 even 2 960.4.a.bj.1.1 1
60.23 odd 4 600.4.f.a.49.1 2
60.47 odd 4 600.4.f.a.49.2 2
60.59 even 2 600.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.b.1.1 ✓ 1 12.11 even 2
240.4.a.g.1.1 1 3.2 odd 2
360.4.a.n.1.1 1 4.3 odd 2
600.4.a.i.1.1 1 60.59 even 2
600.4.f.a.49.1 2 60.23 odd 4
600.4.f.a.49.2 2 60.47 odd 4
720.4.a.q.1.1 1 1.1 even 1 trivial
960.4.a.k.1.1 1 24.5 odd 2
960.4.a.bj.1.1 1 24.11 even 2
1200.4.a.p.1.1 1 15.14 odd 2
1200.4.f.t.49.1 2 15.2 even 4
1200.4.f.t.49.2 2 15.8 even 4
1800.4.a.f.1.1 1 20.19 odd 2
1800.4.f.v.649.1 2 20.3 even 4
1800.4.f.v.649.2 2 20.7 even 4