Properties

Label 1872.4.a.h.1.1
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1872,4,Mod(1,1872)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1872, 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("1872.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.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: \(110.451575531\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 234)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1872.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} +26.0000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} +26.0000 q^{7} -52.0000 q^{11} -13.0000 q^{13} +48.0000 q^{17} -18.0000 q^{19} +52.0000 q^{23} -121.000 q^{25} +224.000 q^{29} -310.000 q^{31} +52.0000 q^{35} -18.0000 q^{37} +330.000 q^{41} -328.000 q^{43} -616.000 q^{47} +333.000 q^{49} -324.000 q^{53} -104.000 q^{55} -188.000 q^{59} -110.000 q^{61} -26.0000 q^{65} -118.000 q^{67} +656.000 q^{71} -178.000 q^{73} -1352.00 q^{77} -836.000 q^{79} -60.0000 q^{83} +96.0000 q^{85} +870.000 q^{89} -338.000 q^{91} -36.0000 q^{95} +1238.00 q^{97} +O(q^{100})\)

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
\(5\) 2.00000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) 26.0000 1.40387 0.701934 0.712242i \(-0.252320\pi\)
0.701934 + 0.712242i \(0.252320\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −52.0000 −1.42533 −0.712663 0.701506i \(-0.752511\pi\)
−0.712663 + 0.701506i \(0.752511\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 48.0000 0.684806 0.342403 0.939553i \(-0.388759\pi\)
0.342403 + 0.939553i \(0.388759\pi\)
\(18\) 0 0
\(19\) −18.0000 −0.217341 −0.108671 0.994078i \(-0.534659\pi\)
−0.108671 + 0.994078i \(0.534659\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 52.0000 0.471424 0.235712 0.971823i \(-0.424258\pi\)
0.235712 + 0.971823i \(0.424258\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 224.000 1.43434 0.717168 0.696900i \(-0.245438\pi\)
0.717168 + 0.696900i \(0.245438\pi\)
\(30\) 0 0
\(31\) −310.000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 52.0000 0.251132
\(36\) 0 0
\(37\) −18.0000 −0.0799779 −0.0399889 0.999200i \(-0.512732\pi\)
−0.0399889 + 0.999200i \(0.512732\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 330.000 1.25701 0.628504 0.777806i \(-0.283668\pi\)
0.628504 + 0.777806i \(0.283668\pi\)
\(42\) 0 0
\(43\) −328.000 −1.16324 −0.581622 0.813459i \(-0.697582\pi\)
−0.581622 + 0.813459i \(0.697582\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −616.000 −1.91176 −0.955881 0.293753i \(-0.905096\pi\)
−0.955881 + 0.293753i \(0.905096\pi\)
\(48\) 0 0
\(49\) 333.000 0.970845
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −324.000 −0.839714 −0.419857 0.907590i \(-0.637920\pi\)
−0.419857 + 0.907590i \(0.637920\pi\)
\(54\) 0 0
\(55\) −104.000 −0.254970
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −188.000 −0.414839 −0.207420 0.978252i \(-0.566507\pi\)
−0.207420 + 0.978252i \(0.566507\pi\)
\(60\) 0 0
\(61\) −110.000 −0.230886 −0.115443 0.993314i \(-0.536829\pi\)
−0.115443 + 0.993314i \(0.536829\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −26.0000 −0.0496139
\(66\) 0 0
\(67\) −118.000 −0.215164 −0.107582 0.994196i \(-0.534311\pi\)
−0.107582 + 0.994196i \(0.534311\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 656.000 1.09652 0.548260 0.836308i \(-0.315291\pi\)
0.548260 + 0.836308i \(0.315291\pi\)
\(72\) 0 0
\(73\) −178.000 −0.285388 −0.142694 0.989767i \(-0.545576\pi\)
−0.142694 + 0.989767i \(0.545576\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1352.00 −2.00097
\(78\) 0 0
\(79\) −836.000 −1.19060 −0.595300 0.803504i \(-0.702967\pi\)
−0.595300 + 0.803504i \(0.702967\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −60.0000 −0.0793477 −0.0396738 0.999213i \(-0.512632\pi\)
−0.0396738 + 0.999213i \(0.512632\pi\)
\(84\) 0 0
\(85\) 96.0000 0.122502
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 870.000 1.03618 0.518089 0.855327i \(-0.326644\pi\)
0.518089 + 0.855327i \(0.326644\pi\)
\(90\) 0 0
\(91\) −338.000 −0.389363
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −36.0000 −0.0388792
\(96\) 0 0
\(97\) 1238.00 1.29587 0.647937 0.761694i \(-0.275632\pi\)
0.647937 + 0.761694i \(0.275632\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −920.000 −0.906371 −0.453185 0.891416i \(-0.649712\pi\)
−0.453185 + 0.891416i \(0.649712\pi\)
\(102\) 0 0
\(103\) 836.000 0.799743 0.399871 0.916571i \(-0.369055\pi\)
0.399871 + 0.916571i \(0.369055\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −260.000 −0.234908 −0.117454 0.993078i \(-0.537473\pi\)
−0.117454 + 0.993078i \(0.537473\pi\)
\(108\) 0 0
\(109\) −2078.00 −1.82602 −0.913011 0.407936i \(-0.866249\pi\)
−0.913011 + 0.407936i \(0.866249\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1156.00 −0.962366 −0.481183 0.876620i \(-0.659793\pi\)
−0.481183 + 0.876620i \(0.659793\pi\)
\(114\) 0 0
\(115\) 104.000 0.0843309
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1248.00 0.961378
\(120\) 0 0
\(121\) 1373.00 1.03156
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) 752.000 0.525427 0.262713 0.964874i \(-0.415383\pi\)
0.262713 + 0.964874i \(0.415383\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1972.00 1.31522 0.657612 0.753356i \(-0.271566\pi\)
0.657612 + 0.753356i \(0.271566\pi\)
\(132\) 0 0
\(133\) −468.000 −0.305118
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 258.000 0.160894 0.0804468 0.996759i \(-0.474365\pi\)
0.0804468 + 0.996759i \(0.474365\pi\)
\(138\) 0 0
\(139\) −1468.00 −0.895785 −0.447893 0.894087i \(-0.647825\pi\)
−0.447893 + 0.894087i \(0.647825\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 676.000 0.395314
\(144\) 0 0
\(145\) 448.000 0.256582
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3414.00 1.87709 0.938543 0.345163i \(-0.112176\pi\)
0.938543 + 0.345163i \(0.112176\pi\)
\(150\) 0 0
\(151\) 2214.00 1.19320 0.596599 0.802540i \(-0.296518\pi\)
0.596599 + 0.802540i \(0.296518\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −620.000 −0.321288
\(156\) 0 0
\(157\) −2230.00 −1.13359 −0.566794 0.823859i \(-0.691817\pi\)
−0.566794 + 0.823859i \(0.691817\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1352.00 0.661817
\(162\) 0 0
\(163\) −1118.00 −0.537230 −0.268615 0.963248i \(-0.586566\pi\)
−0.268615 + 0.963248i \(0.586566\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 288.000 0.133450 0.0667249 0.997771i \(-0.478745\pi\)
0.0667249 + 0.997771i \(0.478745\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −328.000 −0.144147 −0.0720733 0.997399i \(-0.522962\pi\)
−0.0720733 + 0.997399i \(0.522962\pi\)
\(174\) 0 0
\(175\) −3146.00 −1.35894
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2820.00 −1.17752 −0.588762 0.808307i \(-0.700384\pi\)
−0.588762 + 0.808307i \(0.700384\pi\)
\(180\) 0 0
\(181\) −2250.00 −0.923984 −0.461992 0.886884i \(-0.652865\pi\)
−0.461992 + 0.886884i \(0.652865\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −36.0000 −0.0143069
\(186\) 0 0
\(187\) −2496.00 −0.976073
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3604.00 −1.36532 −0.682660 0.730736i \(-0.739177\pi\)
−0.682660 + 0.730736i \(0.739177\pi\)
\(192\) 0 0
\(193\) −1198.00 −0.446808 −0.223404 0.974726i \(-0.571717\pi\)
−0.223404 + 0.974726i \(0.571717\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1026.00 0.371063 0.185532 0.982638i \(-0.440599\pi\)
0.185532 + 0.982638i \(0.440599\pi\)
\(198\) 0 0
\(199\) −2528.00 −0.900528 −0.450264 0.892895i \(-0.648670\pi\)
−0.450264 + 0.892895i \(0.648670\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5824.00 2.01362
\(204\) 0 0
\(205\) 660.000 0.224860
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 936.000 0.309782
\(210\) 0 0
\(211\) 3160.00 1.03101 0.515506 0.856886i \(-0.327604\pi\)
0.515506 + 0.856886i \(0.327604\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −656.000 −0.208088
\(216\) 0 0
\(217\) −8060.00 −2.52142
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −624.000 −0.189931
\(222\) 0 0
\(223\) −2670.00 −0.801778 −0.400889 0.916127i \(-0.631299\pi\)
−0.400889 + 0.916127i \(0.631299\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5220.00 −1.52627 −0.763136 0.646238i \(-0.776341\pi\)
−0.763136 + 0.646238i \(0.776341\pi\)
\(228\) 0 0
\(229\) −6246.00 −1.80239 −0.901195 0.433414i \(-0.857309\pi\)
−0.901195 + 0.433414i \(0.857309\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2860.00 0.804141 0.402070 0.915609i \(-0.368291\pi\)
0.402070 + 0.915609i \(0.368291\pi\)
\(234\) 0 0
\(235\) −1232.00 −0.341986
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7176.00 −1.94216 −0.971081 0.238749i \(-0.923263\pi\)
−0.971081 + 0.238749i \(0.923263\pi\)
\(240\) 0 0
\(241\) −2922.00 −0.781006 −0.390503 0.920602i \(-0.627699\pi\)
−0.390503 + 0.920602i \(0.627699\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 666.000 0.173670
\(246\) 0 0
\(247\) 234.000 0.0602796
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1440.00 0.362119 0.181060 0.983472i \(-0.442047\pi\)
0.181060 + 0.983472i \(0.442047\pi\)
\(252\) 0 0
\(253\) −2704.00 −0.671933
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3852.00 −0.934946 −0.467473 0.884007i \(-0.654836\pi\)
−0.467473 + 0.884007i \(0.654836\pi\)
\(258\) 0 0
\(259\) −468.000 −0.112278
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7008.00 −1.64309 −0.821543 0.570146i \(-0.806887\pi\)
−0.821543 + 0.570146i \(0.806887\pi\)
\(264\) 0 0
\(265\) −648.000 −0.150213
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1992.00 −0.451503 −0.225752 0.974185i \(-0.572484\pi\)
−0.225752 + 0.974185i \(0.572484\pi\)
\(270\) 0 0
\(271\) 3362.00 0.753605 0.376803 0.926294i \(-0.377024\pi\)
0.376803 + 0.926294i \(0.377024\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6292.00 1.37972
\(276\) 0 0
\(277\) 1506.00 0.326667 0.163334 0.986571i \(-0.447775\pi\)
0.163334 + 0.986571i \(0.447775\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3638.00 −0.772331 −0.386165 0.922430i \(-0.626201\pi\)
−0.386165 + 0.922430i \(0.626201\pi\)
\(282\) 0 0
\(283\) −5404.00 −1.13510 −0.567552 0.823338i \(-0.692109\pi\)
−0.567552 + 0.823338i \(0.692109\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8580.00 1.76467
\(288\) 0 0
\(289\) −2609.00 −0.531040
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4994.00 −0.995743 −0.497871 0.867251i \(-0.665885\pi\)
−0.497871 + 0.867251i \(0.665885\pi\)
\(294\) 0 0
\(295\) −376.000 −0.0742087
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −676.000 −0.130749
\(300\) 0 0
\(301\) −8528.00 −1.63304
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −220.000 −0.0413022
\(306\) 0 0
\(307\) −2474.00 −0.459930 −0.229965 0.973199i \(-0.573861\pi\)
−0.229965 + 0.973199i \(0.573861\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9156.00 1.66942 0.834709 0.550691i \(-0.185636\pi\)
0.834709 + 0.550691i \(0.185636\pi\)
\(312\) 0 0
\(313\) 3818.00 0.689476 0.344738 0.938699i \(-0.387968\pi\)
0.344738 + 0.938699i \(0.387968\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6234.00 1.10453 0.552265 0.833668i \(-0.313763\pi\)
0.552265 + 0.833668i \(0.313763\pi\)
\(318\) 0 0
\(319\) −11648.0 −2.04440
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −864.000 −0.148837
\(324\) 0 0
\(325\) 1573.00 0.268475
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −16016.0 −2.68386
\(330\) 0 0
\(331\) −5054.00 −0.839254 −0.419627 0.907697i \(-0.637839\pi\)
−0.419627 + 0.907697i \(0.637839\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −236.000 −0.0384897
\(336\) 0 0
\(337\) 10238.0 1.65489 0.827447 0.561544i \(-0.189792\pi\)
0.827447 + 0.561544i \(0.189792\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16120.0 2.55996
\(342\) 0 0
\(343\) −260.000 −0.0409291
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2184.00 0.337877 0.168938 0.985627i \(-0.445966\pi\)
0.168938 + 0.985627i \(0.445966\pi\)
\(348\) 0 0
\(349\) 6766.00 1.03775 0.518876 0.854849i \(-0.326351\pi\)
0.518876 + 0.854849i \(0.326351\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8290.00 1.24995 0.624975 0.780645i \(-0.285109\pi\)
0.624975 + 0.780645i \(0.285109\pi\)
\(354\) 0 0
\(355\) 1312.00 0.196151
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9456.00 1.39016 0.695082 0.718931i \(-0.255368\pi\)
0.695082 + 0.718931i \(0.255368\pi\)
\(360\) 0 0
\(361\) −6535.00 −0.952763
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −356.000 −0.0510518
\(366\) 0 0
\(367\) 10096.0 1.43599 0.717993 0.696050i \(-0.245061\pi\)
0.717993 + 0.696050i \(0.245061\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8424.00 −1.17885
\(372\) 0 0
\(373\) −1234.00 −0.171298 −0.0856489 0.996325i \(-0.527296\pi\)
−0.0856489 + 0.996325i \(0.527296\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2912.00 −0.397813
\(378\) 0 0
\(379\) −11218.0 −1.52040 −0.760198 0.649692i \(-0.774898\pi\)
−0.760198 + 0.649692i \(0.774898\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7488.00 0.999005 0.499503 0.866312i \(-0.333516\pi\)
0.499503 + 0.866312i \(0.333516\pi\)
\(384\) 0 0
\(385\) −2704.00 −0.357944
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −14364.0 −1.87219 −0.936097 0.351741i \(-0.885590\pi\)
−0.936097 + 0.351741i \(0.885590\pi\)
\(390\) 0 0
\(391\) 2496.00 0.322834
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1672.00 −0.212981
\(396\) 0 0
\(397\) 7454.00 0.942331 0.471166 0.882045i \(-0.343833\pi\)
0.471166 + 0.882045i \(0.343833\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5766.00 0.718056 0.359028 0.933327i \(-0.383108\pi\)
0.359028 + 0.933327i \(0.383108\pi\)
\(402\) 0 0
\(403\) 4030.00 0.498135
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 936.000 0.113995
\(408\) 0 0
\(409\) 11926.0 1.44182 0.720908 0.693031i \(-0.243725\pi\)
0.720908 + 0.693031i \(0.243725\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4888.00 −0.582380
\(414\) 0 0
\(415\) −120.000 −0.0141941
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9996.00 −1.16548 −0.582741 0.812658i \(-0.698020\pi\)
−0.582741 + 0.812658i \(0.698020\pi\)
\(420\) 0 0
\(421\) −2030.00 −0.235003 −0.117501 0.993073i \(-0.537488\pi\)
−0.117501 + 0.993073i \(0.537488\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5808.00 −0.662893
\(426\) 0 0
\(427\) −2860.00 −0.324134
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15888.0 −1.77563 −0.887817 0.460197i \(-0.847779\pi\)
−0.887817 + 0.460197i \(0.847779\pi\)
\(432\) 0 0
\(433\) −14402.0 −1.59842 −0.799210 0.601052i \(-0.794749\pi\)
−0.799210 + 0.601052i \(0.794749\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −936.000 −0.102460
\(438\) 0 0
\(439\) −404.000 −0.0439223 −0.0219611 0.999759i \(-0.506991\pi\)
−0.0219611 + 0.999759i \(0.506991\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16692.0 1.79021 0.895103 0.445860i \(-0.147102\pi\)
0.895103 + 0.445860i \(0.147102\pi\)
\(444\) 0 0
\(445\) 1740.00 0.185357
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4058.00 −0.426523 −0.213262 0.976995i \(-0.568409\pi\)
−0.213262 + 0.976995i \(0.568409\pi\)
\(450\) 0 0
\(451\) −17160.0 −1.79165
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −676.000 −0.0696514
\(456\) 0 0
\(457\) −14642.0 −1.49874 −0.749370 0.662152i \(-0.769643\pi\)
−0.749370 + 0.662152i \(0.769643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 17970.0 1.81550 0.907751 0.419510i \(-0.137798\pi\)
0.907751 + 0.419510i \(0.137798\pi\)
\(462\) 0 0
\(463\) 6242.00 0.626545 0.313273 0.949663i \(-0.398575\pi\)
0.313273 + 0.949663i \(0.398575\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5000.00 −0.495444 −0.247722 0.968831i \(-0.579682\pi\)
−0.247722 + 0.968831i \(0.579682\pi\)
\(468\) 0 0
\(469\) −3068.00 −0.302062
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 17056.0 1.65800
\(474\) 0 0
\(475\) 2178.00 0.210386
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9408.00 −0.897416 −0.448708 0.893678i \(-0.648116\pi\)
−0.448708 + 0.893678i \(0.648116\pi\)
\(480\) 0 0
\(481\) 234.000 0.0221819
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2476.00 0.231813
\(486\) 0 0
\(487\) 7090.00 0.659710 0.329855 0.944032i \(-0.393000\pi\)
0.329855 + 0.944032i \(0.393000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8176.00 −0.751482 −0.375741 0.926725i \(-0.622612\pi\)
−0.375741 + 0.926725i \(0.622612\pi\)
\(492\) 0 0
\(493\) 10752.0 0.982243
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17056.0 1.53937
\(498\) 0 0
\(499\) −9646.00 −0.865359 −0.432680 0.901548i \(-0.642432\pi\)
−0.432680 + 0.901548i \(0.642432\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4352.00 0.385778 0.192889 0.981221i \(-0.438214\pi\)
0.192889 + 0.981221i \(0.438214\pi\)
\(504\) 0 0
\(505\) −1840.00 −0.162136
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14582.0 −1.26981 −0.634907 0.772588i \(-0.718962\pi\)
−0.634907 + 0.772588i \(0.718962\pi\)
\(510\) 0 0
\(511\) −4628.00 −0.400647
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1672.00 0.143062
\(516\) 0 0
\(517\) 32032.0 2.72489
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11820.0 −0.993942 −0.496971 0.867767i \(-0.665554\pi\)
−0.496971 + 0.867767i \(0.665554\pi\)
\(522\) 0 0
\(523\) −2676.00 −0.223735 −0.111867 0.993723i \(-0.535683\pi\)
−0.111867 + 0.993723i \(0.535683\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14880.0 −1.22995
\(528\) 0 0
\(529\) −9463.00 −0.777760
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4290.00 −0.348631
\(534\) 0 0
\(535\) −520.000 −0.0420216
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −17316.0 −1.38377
\(540\) 0 0
\(541\) 842.000 0.0669139 0.0334569 0.999440i \(-0.489348\pi\)
0.0334569 + 0.999440i \(0.489348\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4156.00 −0.326649
\(546\) 0 0
\(547\) −1036.00 −0.0809802 −0.0404901 0.999180i \(-0.512892\pi\)
−0.0404901 + 0.999180i \(0.512892\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4032.00 −0.311740
\(552\) 0 0
\(553\) −21736.0 −1.67144
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3342.00 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 0 0
\(559\) 4264.00 0.322626
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12412.0 0.929136 0.464568 0.885538i \(-0.346210\pi\)
0.464568 + 0.885538i \(0.346210\pi\)
\(564\) 0 0
\(565\) −2312.00 −0.172153
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21556.0 1.58818 0.794090 0.607800i \(-0.207948\pi\)
0.794090 + 0.607800i \(0.207948\pi\)
\(570\) 0 0
\(571\) −9012.00 −0.660491 −0.330246 0.943895i \(-0.607132\pi\)
−0.330246 + 0.943895i \(0.607132\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6292.00 −0.456338
\(576\) 0 0
\(577\) −10446.0 −0.753679 −0.376839 0.926279i \(-0.622989\pi\)
−0.376839 + 0.926279i \(0.622989\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1560.00 −0.111394
\(582\) 0 0
\(583\) 16848.0 1.19687
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23452.0 1.64901 0.824504 0.565856i \(-0.191454\pi\)
0.824504 + 0.565856i \(0.191454\pi\)
\(588\) 0 0
\(589\) 5580.00 0.390356
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −23914.0 −1.65604 −0.828019 0.560700i \(-0.810532\pi\)
−0.828019 + 0.560700i \(0.810532\pi\)
\(594\) 0 0
\(595\) 2496.00 0.171977
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2552.00 0.174077 0.0870383 0.996205i \(-0.472260\pi\)
0.0870383 + 0.996205i \(0.472260\pi\)
\(600\) 0 0
\(601\) 3418.00 0.231985 0.115993 0.993250i \(-0.462995\pi\)
0.115993 + 0.993250i \(0.462995\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2746.00 0.184530
\(606\) 0 0
\(607\) −12336.0 −0.824881 −0.412441 0.910985i \(-0.635324\pi\)
−0.412441 + 0.910985i \(0.635324\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8008.00 0.530228
\(612\) 0 0
\(613\) −21946.0 −1.44599 −0.722994 0.690854i \(-0.757235\pi\)
−0.722994 + 0.690854i \(0.757235\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 23890.0 1.55879 0.779396 0.626531i \(-0.215526\pi\)
0.779396 + 0.626531i \(0.215526\pi\)
\(618\) 0 0
\(619\) −10042.0 −0.652055 −0.326028 0.945360i \(-0.605710\pi\)
−0.326028 + 0.945360i \(0.605710\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22620.0 1.45466
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −864.000 −0.0547694
\(630\) 0 0
\(631\) 21830.0 1.37724 0.688620 0.725122i \(-0.258217\pi\)
0.688620 + 0.725122i \(0.258217\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1504.00 0.0939912
\(636\) 0 0
\(637\) −4329.00 −0.269264
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −776.000 −0.0478162 −0.0239081 0.999714i \(-0.507611\pi\)
−0.0239081 + 0.999714i \(0.507611\pi\)
\(642\) 0 0
\(643\) −4094.00 −0.251091 −0.125546 0.992088i \(-0.540068\pi\)
−0.125546 + 0.992088i \(0.540068\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13064.0 0.793816 0.396908 0.917858i \(-0.370083\pi\)
0.396908 + 0.917858i \(0.370083\pi\)
\(648\) 0 0
\(649\) 9776.00 0.591281
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24504.0 −1.46848 −0.734239 0.678891i \(-0.762461\pi\)
−0.734239 + 0.678891i \(0.762461\pi\)
\(654\) 0 0
\(655\) 3944.00 0.235275
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4752.00 −0.280898 −0.140449 0.990088i \(-0.544855\pi\)
−0.140449 + 0.990088i \(0.544855\pi\)
\(660\) 0 0
\(661\) −9514.00 −0.559836 −0.279918 0.960024i \(-0.590307\pi\)
−0.279918 + 0.960024i \(0.590307\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −936.000 −0.0545812
\(666\) 0 0
\(667\) 11648.0 0.676180
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5720.00 0.329088
\(672\) 0 0
\(673\) 8374.00 0.479634 0.239817 0.970818i \(-0.422912\pi\)
0.239817 + 0.970818i \(0.422912\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14556.0 −0.826341 −0.413170 0.910654i \(-0.635579\pi\)
−0.413170 + 0.910654i \(0.635579\pi\)
\(678\) 0 0
\(679\) 32188.0 1.81924
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23276.0 1.30400 0.652000 0.758219i \(-0.273930\pi\)
0.652000 + 0.758219i \(0.273930\pi\)
\(684\) 0 0
\(685\) 516.000 0.0287815
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4212.00 0.232895
\(690\) 0 0
\(691\) 29522.0 1.62528 0.812641 0.582765i \(-0.198029\pi\)
0.812641 + 0.582765i \(0.198029\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2936.00 −0.160243
\(696\) 0 0
\(697\) 15840.0 0.860807
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27252.0 1.46832 0.734161 0.678975i \(-0.237576\pi\)
0.734161 + 0.678975i \(0.237576\pi\)
\(702\) 0 0
\(703\) 324.000 0.0173825
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −23920.0 −1.27242
\(708\) 0 0
\(709\) 2162.00 0.114521 0.0572607 0.998359i \(-0.481763\pi\)
0.0572607 + 0.998359i \(0.481763\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −16120.0 −0.846702
\(714\) 0 0
\(715\) 1352.00 0.0707160
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 8044.00 0.417233 0.208617 0.977998i \(-0.433104\pi\)
0.208617 + 0.977998i \(0.433104\pi\)
\(720\) 0 0
\(721\) 21736.0 1.12273
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −27104.0 −1.38844
\(726\) 0 0
\(727\) 22496.0 1.14763 0.573817 0.818983i \(-0.305462\pi\)
0.573817 + 0.818983i \(0.305462\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15744.0 −0.796598
\(732\) 0 0
\(733\) −15934.0 −0.802914 −0.401457 0.915878i \(-0.631496\pi\)
−0.401457 + 0.915878i \(0.631496\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6136.00 0.306679
\(738\) 0 0
\(739\) 29838.0 1.48526 0.742631 0.669701i \(-0.233578\pi\)
0.742631 + 0.669701i \(0.233578\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10760.0 0.531287 0.265643 0.964071i \(-0.414416\pi\)
0.265643 + 0.964071i \(0.414416\pi\)
\(744\) 0 0
\(745\) 6828.00 0.335783
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6760.00 −0.329780
\(750\) 0 0
\(751\) 14916.0 0.724757 0.362379 0.932031i \(-0.381965\pi\)
0.362379 + 0.932031i \(0.381965\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4428.00 0.213446
\(756\) 0 0
\(757\) 29046.0 1.39458 0.697289 0.716791i \(-0.254390\pi\)
0.697289 + 0.716791i \(0.254390\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2766.00 −0.131757 −0.0658787 0.997828i \(-0.520985\pi\)
−0.0658787 + 0.997828i \(0.520985\pi\)
\(762\) 0 0
\(763\) −54028.0 −2.56349
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2444.00 0.115056
\(768\) 0 0
\(769\) 5394.00 0.252942 0.126471 0.991970i \(-0.459635\pi\)
0.126471 + 0.991970i \(0.459635\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −19378.0 −0.901654 −0.450827 0.892611i \(-0.648871\pi\)
−0.450827 + 0.892611i \(0.648871\pi\)
\(774\) 0 0
\(775\) 37510.0 1.73858
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5940.00 −0.273200
\(780\) 0 0
\(781\) −34112.0 −1.56290
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4460.00 −0.202782
\(786\) 0 0
\(787\) 8350.00 0.378202 0.189101 0.981958i \(-0.439443\pi\)
0.189101 + 0.981958i \(0.439443\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −30056.0 −1.35103
\(792\) 0 0
\(793\) 1430.00 0.0640363
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 22116.0 0.982922 0.491461 0.870900i \(-0.336463\pi\)
0.491461 + 0.870900i \(0.336463\pi\)
\(798\) 0 0
\(799\) −29568.0 −1.30919
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9256.00 0.406771
\(804\) 0 0
\(805\) 2704.00 0.118389
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6444.00 0.280048 0.140024 0.990148i \(-0.455282\pi\)
0.140024 + 0.990148i \(0.455282\pi\)
\(810\) 0 0
\(811\) 8998.00 0.389596 0.194798 0.980843i \(-0.437595\pi\)
0.194798 + 0.980843i \(0.437595\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2236.00 −0.0961027
\(816\) 0 0
\(817\) 5904.00 0.252821
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −11938.0 −0.507478 −0.253739 0.967273i \(-0.581660\pi\)
−0.253739 + 0.967273i \(0.581660\pi\)
\(822\) 0 0
\(823\) 41028.0 1.73772 0.868862 0.495055i \(-0.164852\pi\)
0.868862 + 0.495055i \(0.164852\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20460.0 −0.860295 −0.430147 0.902759i \(-0.641538\pi\)
−0.430147 + 0.902759i \(0.641538\pi\)
\(828\) 0 0
\(829\) 27814.0 1.16528 0.582642 0.812729i \(-0.302019\pi\)
0.582642 + 0.812729i \(0.302019\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 15984.0 0.664841
\(834\) 0 0
\(835\) 576.000 0.0238722
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 24880.0 1.02378 0.511891 0.859050i \(-0.328945\pi\)
0.511891 + 0.859050i \(0.328945\pi\)
\(840\) 0 0
\(841\) 25787.0 1.05732
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 338.000 0.0137604
\(846\) 0 0
\(847\) 35698.0 1.44817
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −936.000 −0.0377035
\(852\) 0 0
\(853\) 37678.0 1.51239 0.756196 0.654345i \(-0.227056\pi\)
0.756196 + 0.654345i \(0.227056\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −14708.0 −0.586249 −0.293125 0.956074i \(-0.594695\pi\)
−0.293125 + 0.956074i \(0.594695\pi\)
\(858\) 0 0
\(859\) −16472.0 −0.654269 −0.327135 0.944978i \(-0.606083\pi\)
−0.327135 + 0.944978i \(0.606083\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 13640.0 0.538020 0.269010 0.963137i \(-0.413304\pi\)
0.269010 + 0.963137i \(0.413304\pi\)
\(864\) 0 0
\(865\) −656.000 −0.0257857
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 43472.0 1.69699
\(870\) 0 0
\(871\) 1534.00 0.0596758
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −12792.0 −0.494227
\(876\) 0 0
\(877\) 44430.0 1.71071 0.855356 0.518041i \(-0.173338\pi\)
0.855356 + 0.518041i \(0.173338\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6684.00 0.255607 0.127803 0.991800i \(-0.459207\pi\)
0.127803 + 0.991800i \(0.459207\pi\)
\(882\) 0 0
\(883\) −9196.00 −0.350476 −0.175238 0.984526i \(-0.556069\pi\)
−0.175238 + 0.984526i \(0.556069\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −34852.0 −1.31930 −0.659648 0.751575i \(-0.729295\pi\)
−0.659648 + 0.751575i \(0.729295\pi\)
\(888\) 0 0
\(889\) 19552.0 0.737630
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11088.0 0.415505
\(894\) 0 0
\(895\) −5640.00 −0.210642
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −69440.0 −2.57614
\(900\) 0 0
\(901\) −15552.0 −0.575041
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4500.00 −0.165287
\(906\) 0 0
\(907\) −36780.0 −1.34648 −0.673241 0.739423i \(-0.735099\pi\)
−0.673241 + 0.739423i \(0.735099\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −22980.0 −0.835742 −0.417871 0.908506i \(-0.637224\pi\)
−0.417871 + 0.908506i \(0.637224\pi\)
\(912\) 0 0
\(913\) 3120.00 0.113096
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 51272.0 1.84640
\(918\) 0 0
\(919\) 19980.0 0.717170 0.358585 0.933497i \(-0.383259\pi\)
0.358585 + 0.933497i \(0.383259\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8528.00 −0.304120
\(924\) 0 0
\(925\) 2178.00 0.0774186
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −51486.0 −1.81830 −0.909150 0.416469i \(-0.863268\pi\)
−0.909150 + 0.416469i \(0.863268\pi\)
\(930\) 0 0
\(931\) −5994.00 −0.211005
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4992.00 −0.174605
\(936\) 0 0
\(937\) 21774.0 0.759152 0.379576 0.925161i \(-0.376070\pi\)
0.379576 + 0.925161i \(0.376070\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 29158.0 1.01012 0.505060 0.863084i \(-0.331470\pi\)
0.505060 + 0.863084i \(0.331470\pi\)
\(942\) 0 0
\(943\) 17160.0 0.592584
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 47844.0 1.64173 0.820866 0.571120i \(-0.193491\pi\)
0.820866 + 0.571120i \(0.193491\pi\)
\(948\) 0 0
\(949\) 2314.00 0.0791524
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20716.0 −0.704152 −0.352076 0.935971i \(-0.614524\pi\)
−0.352076 + 0.935971i \(0.614524\pi\)
\(954\) 0 0
\(955\) −7208.00 −0.244236
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6708.00 0.225873
\(960\) 0 0
\(961\) 66309.0 2.22581
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2396.00 −0.0799274
\(966\) 0 0
\(967\) −1406.00 −0.0467569 −0.0233784 0.999727i \(-0.507442\pi\)
−0.0233784 + 0.999727i \(0.507442\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40176.0 1.32782 0.663908 0.747814i \(-0.268897\pi\)
0.663908 + 0.747814i \(0.268897\pi\)
\(972\) 0 0
\(973\) −38168.0 −1.25756
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 20910.0 0.684719 0.342359 0.939569i \(-0.388774\pi\)
0.342359 + 0.939569i \(0.388774\pi\)
\(978\) 0 0
\(979\) −45240.0 −1.47689
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −26288.0 −0.852957 −0.426479 0.904498i \(-0.640246\pi\)
−0.426479 + 0.904498i \(0.640246\pi\)
\(984\) 0 0
\(985\) 2052.00 0.0663778
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −17056.0 −0.548381
\(990\) 0 0
\(991\) 25608.0 0.820853 0.410426 0.911894i \(-0.365380\pi\)
0.410426 + 0.911894i \(0.365380\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5056.00 −0.161091
\(996\) 0 0
\(997\) −20098.0 −0.638425 −0.319213 0.947683i \(-0.603418\pi\)
−0.319213 + 0.947683i \(0.603418\pi\)
\(998\) 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 1872.4.a.h.1.1 1
3.2 odd 2 1872.4.a.g.1.1 1
4.3 odd 2 234.4.a.d.1.1 1
12.11 even 2 234.4.a.i.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
234.4.a.d.1.1 1 4.3 odd 2
234.4.a.i.1.1 yes 1 12.11 even 2
1872.4.a.g.1.1 1 3.2 odd 2
1872.4.a.h.1.1 1 1.1 even 1 trivial