Properties

Label 1872.4.a.bh.1.1
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
Analytic rank $1$
Dimension $2$
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] = [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: \(2\)
Coefficient field: \(\Q(\sqrt{321}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 80 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 104)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(9.45824\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-3.45824 q^{5} +26.3747 q^{7} +O(q^{10})\) \(q-3.45824 q^{5} +26.3747 q^{7} +58.0000 q^{11} -13.0000 q^{13} -88.2077 q^{17} -99.8329 q^{19} +9.49884 q^{23} -113.041 q^{25} +6.00000 q^{29} -23.4176 q^{31} -91.2100 q^{35} +44.9571 q^{37} -58.0812 q^{41} -457.955 q^{43} -496.208 q^{47} +352.625 q^{49} -601.747 q^{53} -200.578 q^{55} +211.336 q^{59} +414.912 q^{61} +44.9571 q^{65} -744.167 q^{67} +882.537 q^{71} -319.499 q^{73} +1529.73 q^{77} +490.664 q^{79} -224.420 q^{83} +305.043 q^{85} +580.501 q^{89} -342.871 q^{91} +345.246 q^{95} +403.499 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 11 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 11 q^{5} - q^{7} + 116 q^{11} - 26 q^{13} - 51 q^{17} - 128 q^{19} - 196 q^{23} - 29 q^{25} + 12 q^{29} - 226 q^{31} - 487 q^{35} - 143 q^{37} + 278 q^{41} - 253 q^{43} - 867 q^{47} + 759 q^{49} - 666 q^{53} + 638 q^{55} + 996 q^{59} - 66 q^{61} - 143 q^{65} - 1560 q^{67} + 923 q^{71} - 424 q^{73} - 58 q^{77} + 408 q^{79} - 1058 q^{83} + 843 q^{85} + 1376 q^{89} + 13 q^{91} - 62 q^{95} + 592 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −3.45824 −0.309314 −0.154657 0.987968i \(-0.549427\pi\)
−0.154657 + 0.987968i \(0.549427\pi\)
\(6\) 0 0
\(7\) 26.3747 1.42410 0.712050 0.702129i \(-0.247767\pi\)
0.712050 + 0.702129i \(0.247767\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 58.0000 1.58979 0.794894 0.606749i \(-0.207527\pi\)
0.794894 + 0.606749i \(0.207527\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −88.2077 −1.25844 −0.629221 0.777227i \(-0.716626\pi\)
−0.629221 + 0.777227i \(0.716626\pi\)
\(18\) 0 0
\(19\) −99.8329 −1.20543 −0.602717 0.797955i \(-0.705915\pi\)
−0.602717 + 0.797955i \(0.705915\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 9.49884 0.0861150 0.0430575 0.999073i \(-0.486290\pi\)
0.0430575 + 0.999073i \(0.486290\pi\)
\(24\) 0 0
\(25\) −113.041 −0.904325
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 0.0384197 0.0192099 0.999815i \(-0.493885\pi\)
0.0192099 + 0.999815i \(0.493885\pi\)
\(30\) 0 0
\(31\) −23.4176 −0.135675 −0.0678376 0.997696i \(-0.521610\pi\)
−0.0678376 + 0.997696i \(0.521610\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −91.2100 −0.440494
\(36\) 0 0
\(37\) 44.9571 0.199754 0.0998770 0.995000i \(-0.468155\pi\)
0.0998770 + 0.995000i \(0.468155\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −58.0812 −0.221238 −0.110619 0.993863i \(-0.535283\pi\)
−0.110619 + 0.993863i \(0.535283\pi\)
\(42\) 0 0
\(43\) −457.955 −1.62413 −0.812063 0.583569i \(-0.801656\pi\)
−0.812063 + 0.583569i \(0.801656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −496.208 −1.53999 −0.769993 0.638053i \(-0.779740\pi\)
−0.769993 + 0.638053i \(0.779740\pi\)
\(48\) 0 0
\(49\) 352.625 1.02806
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −601.747 −1.55955 −0.779777 0.626058i \(-0.784667\pi\)
−0.779777 + 0.626058i \(0.784667\pi\)
\(54\) 0 0
\(55\) −200.578 −0.491744
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 211.336 0.466333 0.233167 0.972437i \(-0.425091\pi\)
0.233167 + 0.972437i \(0.425091\pi\)
\(60\) 0 0
\(61\) 414.912 0.870885 0.435443 0.900216i \(-0.356592\pi\)
0.435443 + 0.900216i \(0.356592\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 44.9571 0.0857883
\(66\) 0 0
\(67\) −744.167 −1.35693 −0.678466 0.734632i \(-0.737355\pi\)
−0.678466 + 0.734632i \(0.737355\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 882.537 1.47518 0.737591 0.675248i \(-0.235963\pi\)
0.737591 + 0.675248i \(0.235963\pi\)
\(72\) 0 0
\(73\) −319.499 −0.512254 −0.256127 0.966643i \(-0.582446\pi\)
−0.256127 + 0.966643i \(0.582446\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1529.73 2.26402
\(78\) 0 0
\(79\) 490.664 0.698784 0.349392 0.936977i \(-0.386388\pi\)
0.349392 + 0.936977i \(0.386388\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −224.420 −0.296787 −0.148393 0.988928i \(-0.547410\pi\)
−0.148393 + 0.988928i \(0.547410\pi\)
\(84\) 0 0
\(85\) 305.043 0.389254
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 580.501 0.691382 0.345691 0.938348i \(-0.387645\pi\)
0.345691 + 0.938348i \(0.387645\pi\)
\(90\) 0 0
\(91\) −342.871 −0.394974
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 345.246 0.372858
\(96\) 0 0
\(97\) 403.499 0.422362 0.211181 0.977447i \(-0.432269\pi\)
0.211181 + 0.977447i \(0.432269\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 698.244 0.687899 0.343950 0.938988i \(-0.388235\pi\)
0.343950 + 0.938988i \(0.388235\pi\)
\(102\) 0 0
\(103\) −1285.33 −1.22958 −0.614791 0.788690i \(-0.710760\pi\)
−0.614791 + 0.788690i \(0.710760\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1329.82 1.20149 0.600743 0.799443i \(-0.294872\pi\)
0.600743 + 0.799443i \(0.294872\pi\)
\(108\) 0 0
\(109\) −951.034 −0.835711 −0.417856 0.908513i \(-0.637218\pi\)
−0.417856 + 0.908513i \(0.637218\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −89.8283 −0.0747817 −0.0373909 0.999301i \(-0.511905\pi\)
−0.0373909 + 0.999301i \(0.511905\pi\)
\(114\) 0 0
\(115\) −32.8492 −0.0266366
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2326.45 −1.79215
\(120\) 0 0
\(121\) 2033.00 1.52742
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 823.201 0.589034
\(126\) 0 0
\(127\) −345.012 −0.241062 −0.120531 0.992710i \(-0.538460\pi\)
−0.120531 + 0.992710i \(0.538460\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2052.03 −1.36860 −0.684301 0.729200i \(-0.739892\pi\)
−0.684301 + 0.729200i \(0.739892\pi\)
\(132\) 0 0
\(133\) −2633.06 −1.71666
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1952.58 −1.21767 −0.608833 0.793298i \(-0.708362\pi\)
−0.608833 + 0.793298i \(0.708362\pi\)
\(138\) 0 0
\(139\) 2238.69 1.36606 0.683032 0.730389i \(-0.260661\pi\)
0.683032 + 0.730389i \(0.260661\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −754.000 −0.440928
\(144\) 0 0
\(145\) −20.7494 −0.0118838
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1097.81 0.603598 0.301799 0.953372i \(-0.402413\pi\)
0.301799 + 0.953372i \(0.402413\pi\)
\(150\) 0 0
\(151\) −3593.17 −1.93648 −0.968239 0.250026i \(-0.919561\pi\)
−0.968239 + 0.250026i \(0.919561\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 80.9837 0.0419663
\(156\) 0 0
\(157\) −2517.48 −1.27972 −0.639861 0.768490i \(-0.721008\pi\)
−0.639861 + 0.768490i \(0.721008\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 250.529 0.122636
\(162\) 0 0
\(163\) 251.084 0.120653 0.0603263 0.998179i \(-0.480786\pi\)
0.0603263 + 0.998179i \(0.480786\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −450.596 −0.208792 −0.104396 0.994536i \(-0.533291\pi\)
−0.104396 + 0.994536i \(0.533291\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 247.914 0.108951 0.0544756 0.998515i \(-0.482651\pi\)
0.0544756 + 0.998515i \(0.482651\pi\)
\(174\) 0 0
\(175\) −2981.41 −1.28785
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1266.87 −0.528995 −0.264497 0.964386i \(-0.585206\pi\)
−0.264497 + 0.964386i \(0.585206\pi\)
\(180\) 0 0
\(181\) 4048.38 1.66251 0.831254 0.555893i \(-0.187624\pi\)
0.831254 + 0.555893i \(0.187624\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −155.472 −0.0617867
\(186\) 0 0
\(187\) −5116.04 −2.00065
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4021.38 −1.52344 −0.761720 0.647907i \(-0.775645\pi\)
−0.761720 + 0.647907i \(0.775645\pi\)
\(192\) 0 0
\(193\) −1529.58 −0.570476 −0.285238 0.958457i \(-0.592073\pi\)
−0.285238 + 0.958457i \(0.592073\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1146.04 −0.414477 −0.207239 0.978290i \(-0.566448\pi\)
−0.207239 + 0.978290i \(0.566448\pi\)
\(198\) 0 0
\(199\) 5190.08 1.84882 0.924409 0.381403i \(-0.124559\pi\)
0.924409 + 0.381403i \(0.124559\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 158.248 0.0547135
\(204\) 0 0
\(205\) 200.859 0.0684320
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5790.31 −1.91638
\(210\) 0 0
\(211\) −1272.63 −0.415219 −0.207610 0.978212i \(-0.566568\pi\)
−0.207610 + 0.978212i \(0.566568\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1583.72 0.502365
\(216\) 0 0
\(217\) −617.633 −0.193215
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1146.70 0.349029
\(222\) 0 0
\(223\) −3340.87 −1.00323 −0.501617 0.865090i \(-0.667261\pi\)
−0.501617 + 0.865090i \(0.667261\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3577.07 −1.04590 −0.522948 0.852365i \(-0.675168\pi\)
−0.522948 + 0.852365i \(0.675168\pi\)
\(228\) 0 0
\(229\) 6215.35 1.79355 0.896773 0.442492i \(-0.145905\pi\)
0.896773 + 0.442492i \(0.145905\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2163.02 −0.608171 −0.304085 0.952645i \(-0.598351\pi\)
−0.304085 + 0.952645i \(0.598351\pi\)
\(234\) 0 0
\(235\) 1716.00 0.476339
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2908.51 −0.787180 −0.393590 0.919286i \(-0.628767\pi\)
−0.393590 + 0.919286i \(0.628767\pi\)
\(240\) 0 0
\(241\) 1391.63 0.371963 0.185981 0.982553i \(-0.440454\pi\)
0.185981 + 0.982553i \(0.440454\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1219.46 −0.317994
\(246\) 0 0
\(247\) 1297.83 0.334327
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2634.12 0.662407 0.331204 0.943559i \(-0.392545\pi\)
0.331204 + 0.943559i \(0.392545\pi\)
\(252\) 0 0
\(253\) 550.933 0.136904
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −441.841 −0.107242 −0.0536212 0.998561i \(-0.517076\pi\)
−0.0536212 + 0.998561i \(0.517076\pi\)
\(258\) 0 0
\(259\) 1185.73 0.284470
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2100.32 −0.492439 −0.246220 0.969214i \(-0.579188\pi\)
−0.246220 + 0.969214i \(0.579188\pi\)
\(264\) 0 0
\(265\) 2080.98 0.482392
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6432.40 −1.45796 −0.728978 0.684537i \(-0.760005\pi\)
−0.728978 + 0.684537i \(0.760005\pi\)
\(270\) 0 0
\(271\) −3093.14 −0.693339 −0.346669 0.937987i \(-0.612687\pi\)
−0.346669 + 0.937987i \(0.612687\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6556.35 −1.43768
\(276\) 0 0
\(277\) −1082.57 −0.234820 −0.117410 0.993084i \(-0.537459\pi\)
−0.117410 + 0.993084i \(0.537459\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4885.85 −1.03724 −0.518621 0.855004i \(-0.673555\pi\)
−0.518621 + 0.855004i \(0.673555\pi\)
\(282\) 0 0
\(283\) 8190.58 1.72042 0.860211 0.509938i \(-0.170332\pi\)
0.860211 + 0.509938i \(0.170332\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1531.87 −0.315065
\(288\) 0 0
\(289\) 2867.59 0.583674
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1167.54 0.232793 0.116397 0.993203i \(-0.462866\pi\)
0.116397 + 0.993203i \(0.462866\pi\)
\(294\) 0 0
\(295\) −730.851 −0.144243
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −123.485 −0.0238840
\(300\) 0 0
\(301\) −12078.4 −2.31292
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1434.86 −0.269377
\(306\) 0 0
\(307\) −3928.01 −0.730240 −0.365120 0.930961i \(-0.618972\pi\)
−0.365120 + 0.930961i \(0.618972\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2848.86 −0.519433 −0.259717 0.965685i \(-0.583629\pi\)
−0.259717 + 0.965685i \(0.583629\pi\)
\(312\) 0 0
\(313\) −5990.54 −1.08181 −0.540903 0.841085i \(-0.681917\pi\)
−0.540903 + 0.841085i \(0.681917\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3521.83 0.623992 0.311996 0.950083i \(-0.399002\pi\)
0.311996 + 0.950083i \(0.399002\pi\)
\(318\) 0 0
\(319\) 348.000 0.0610792
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8806.03 1.51697
\(324\) 0 0
\(325\) 1469.53 0.250815
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −13087.3 −2.19309
\(330\) 0 0
\(331\) −1487.38 −0.246990 −0.123495 0.992345i \(-0.539410\pi\)
−0.123495 + 0.992345i \(0.539410\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2573.51 0.419718
\(336\) 0 0
\(337\) −2559.21 −0.413676 −0.206838 0.978375i \(-0.566317\pi\)
−0.206838 + 0.978375i \(0.566317\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1358.22 −0.215695
\(342\) 0 0
\(343\) 253.864 0.0399632
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11229.6 1.73728 0.868639 0.495446i \(-0.164996\pi\)
0.868639 + 0.495446i \(0.164996\pi\)
\(348\) 0 0
\(349\) 2570.45 0.394249 0.197124 0.980378i \(-0.436840\pi\)
0.197124 + 0.980378i \(0.436840\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5401.58 −0.814439 −0.407219 0.913330i \(-0.633502\pi\)
−0.407219 + 0.913330i \(0.633502\pi\)
\(354\) 0 0
\(355\) −3052.02 −0.456294
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2650.71 0.389691 0.194846 0.980834i \(-0.437579\pi\)
0.194846 + 0.980834i \(0.437579\pi\)
\(360\) 0 0
\(361\) 3107.62 0.453071
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1104.90 0.158447
\(366\) 0 0
\(367\) 7298.53 1.03809 0.519046 0.854746i \(-0.326287\pi\)
0.519046 + 0.854746i \(0.326287\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −15870.9 −2.22096
\(372\) 0 0
\(373\) −8960.03 −1.24379 −0.621894 0.783102i \(-0.713636\pi\)
−0.621894 + 0.783102i \(0.713636\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −78.0000 −0.0106557
\(378\) 0 0
\(379\) 3470.36 0.470344 0.235172 0.971954i \(-0.424435\pi\)
0.235172 + 0.971954i \(0.424435\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7611.42 −1.01547 −0.507736 0.861513i \(-0.669517\pi\)
−0.507736 + 0.861513i \(0.669517\pi\)
\(384\) 0 0
\(385\) −5290.18 −0.700292
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9394.26 1.22444 0.612221 0.790687i \(-0.290276\pi\)
0.612221 + 0.790687i \(0.290276\pi\)
\(390\) 0 0
\(391\) −837.870 −0.108371
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1696.83 −0.216144
\(396\) 0 0
\(397\) 8377.68 1.05910 0.529551 0.848278i \(-0.322360\pi\)
0.529551 + 0.848278i \(0.322360\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1171.50 0.145890 0.0729448 0.997336i \(-0.476760\pi\)
0.0729448 + 0.997336i \(0.476760\pi\)
\(402\) 0 0
\(403\) 304.429 0.0376295
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2607.51 0.317566
\(408\) 0 0
\(409\) 1320.85 0.159687 0.0798434 0.996807i \(-0.474558\pi\)
0.0798434 + 0.996807i \(0.474558\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5573.94 0.664105
\(414\) 0 0
\(415\) 776.097 0.0918003
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1553.50 −0.181129 −0.0905647 0.995891i \(-0.528867\pi\)
−0.0905647 + 0.995891i \(0.528867\pi\)
\(420\) 0 0
\(421\) −6746.63 −0.781022 −0.390511 0.920598i \(-0.627702\pi\)
−0.390511 + 0.920598i \(0.627702\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9971.05 1.13804
\(426\) 0 0
\(427\) 10943.2 1.24023
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2646.81 −0.295805 −0.147903 0.989002i \(-0.547252\pi\)
−0.147903 + 0.989002i \(0.547252\pi\)
\(432\) 0 0
\(433\) 9197.82 1.02083 0.510415 0.859928i \(-0.329492\pi\)
0.510415 + 0.859928i \(0.329492\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −948.297 −0.103806
\(438\) 0 0
\(439\) 9360.53 1.01766 0.508831 0.860866i \(-0.330078\pi\)
0.508831 + 0.860866i \(0.330078\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3196.32 0.342803 0.171401 0.985201i \(-0.445170\pi\)
0.171401 + 0.985201i \(0.445170\pi\)
\(444\) 0 0
\(445\) −2007.51 −0.213854
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2844.45 0.298970 0.149485 0.988764i \(-0.452238\pi\)
0.149485 + 0.988764i \(0.452238\pi\)
\(450\) 0 0
\(451\) −3368.71 −0.351721
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1185.73 0.122171
\(456\) 0 0
\(457\) −4468.90 −0.457431 −0.228716 0.973493i \(-0.573453\pi\)
−0.228716 + 0.973493i \(0.573453\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15006.8 −1.51613 −0.758067 0.652177i \(-0.773856\pi\)
−0.758067 + 0.652177i \(0.773856\pi\)
\(462\) 0 0
\(463\) −6247.37 −0.627084 −0.313542 0.949574i \(-0.601516\pi\)
−0.313542 + 0.949574i \(0.601516\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −977.327 −0.0968422 −0.0484211 0.998827i \(-0.515419\pi\)
−0.0484211 + 0.998827i \(0.515419\pi\)
\(468\) 0 0
\(469\) −19627.2 −1.93241
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −26561.4 −2.58202
\(474\) 0 0
\(475\) 11285.2 1.09010
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8832.44 0.842515 0.421257 0.906941i \(-0.361589\pi\)
0.421257 + 0.906941i \(0.361589\pi\)
\(480\) 0 0
\(481\) −584.442 −0.0554018
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1395.39 −0.130642
\(486\) 0 0
\(487\) 9906.44 0.921774 0.460887 0.887459i \(-0.347531\pi\)
0.460887 + 0.887459i \(0.347531\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11073.6 1.01781 0.508906 0.860822i \(-0.330050\pi\)
0.508906 + 0.860822i \(0.330050\pi\)
\(492\) 0 0
\(493\) −529.246 −0.0483490
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 23276.7 2.10081
\(498\) 0 0
\(499\) 3268.09 0.293186 0.146593 0.989197i \(-0.453169\pi\)
0.146593 + 0.989197i \(0.453169\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −18758.6 −1.66283 −0.831416 0.555651i \(-0.812469\pi\)
−0.831416 + 0.555651i \(0.812469\pi\)
\(504\) 0 0
\(505\) −2414.69 −0.212777
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6121.28 −0.533047 −0.266523 0.963828i \(-0.585875\pi\)
−0.266523 + 0.963828i \(0.585875\pi\)
\(510\) 0 0
\(511\) −8426.69 −0.729501
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4444.97 0.380327
\(516\) 0 0
\(517\) −28780.0 −2.44825
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12976.1 1.09116 0.545578 0.838060i \(-0.316310\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(522\) 0 0
\(523\) 11563.9 0.966832 0.483416 0.875391i \(-0.339396\pi\)
0.483416 + 0.875391i \(0.339396\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2065.61 0.170739
\(528\) 0 0
\(529\) −12076.8 −0.992584
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 755.056 0.0613604
\(534\) 0 0
\(535\) −4598.84 −0.371636
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 20452.3 1.63440
\(540\) 0 0
\(541\) −11231.9 −0.892603 −0.446302 0.894883i \(-0.647259\pi\)
−0.446302 + 0.894883i \(0.647259\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3288.90 0.258497
\(546\) 0 0
\(547\) −5604.16 −0.438056 −0.219028 0.975719i \(-0.570289\pi\)
−0.219028 + 0.975719i \(0.570289\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −598.998 −0.0463124
\(552\) 0 0
\(553\) 12941.1 0.995139
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13863.4 −1.05460 −0.527299 0.849680i \(-0.676795\pi\)
−0.527299 + 0.849680i \(0.676795\pi\)
\(558\) 0 0
\(559\) 5953.41 0.450452
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9602.64 0.718833 0.359417 0.933177i \(-0.382976\pi\)
0.359417 + 0.933177i \(0.382976\pi\)
\(564\) 0 0
\(565\) 310.647 0.0231310
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21102.9 1.55480 0.777399 0.629008i \(-0.216539\pi\)
0.777399 + 0.629008i \(0.216539\pi\)
\(570\) 0 0
\(571\) −20570.0 −1.50758 −0.753790 0.657115i \(-0.771776\pi\)
−0.753790 + 0.657115i \(0.771776\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1073.75 −0.0778759
\(576\) 0 0
\(577\) 7896.95 0.569765 0.284882 0.958562i \(-0.408045\pi\)
0.284882 + 0.958562i \(0.408045\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5919.01 −0.422654
\(582\) 0 0
\(583\) −34901.3 −2.47936
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15872.7 −1.11608 −0.558039 0.829815i \(-0.688446\pi\)
−0.558039 + 0.829815i \(0.688446\pi\)
\(588\) 0 0
\(589\) 2337.85 0.163548
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4037.35 0.279585 0.139793 0.990181i \(-0.455356\pi\)
0.139793 + 0.990181i \(0.455356\pi\)
\(594\) 0 0
\(595\) 8045.42 0.554336
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18225.7 −1.24321 −0.621606 0.783330i \(-0.713519\pi\)
−0.621606 + 0.783330i \(0.713519\pi\)
\(600\) 0 0
\(601\) 5555.22 0.377042 0.188521 0.982069i \(-0.439631\pi\)
0.188521 + 0.982069i \(0.439631\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7030.59 −0.472453
\(606\) 0 0
\(607\) −4083.66 −0.273066 −0.136533 0.990636i \(-0.543596\pi\)
−0.136533 + 0.990636i \(0.543596\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6450.70 0.427115
\(612\) 0 0
\(613\) 1065.87 0.0702285 0.0351143 0.999383i \(-0.488820\pi\)
0.0351143 + 0.999383i \(0.488820\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3183.51 0.207720 0.103860 0.994592i \(-0.466881\pi\)
0.103860 + 0.994592i \(0.466881\pi\)
\(618\) 0 0
\(619\) 3361.17 0.218250 0.109125 0.994028i \(-0.465195\pi\)
0.109125 + 0.994028i \(0.465195\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15310.5 0.984597
\(624\) 0 0
\(625\) 11283.3 0.722128
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3965.56 −0.251379
\(630\) 0 0
\(631\) −17306.6 −1.09186 −0.545932 0.837829i \(-0.683824\pi\)
−0.545932 + 0.837829i \(0.683824\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1193.13 0.0745638
\(636\) 0 0
\(637\) −4584.13 −0.285133
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20526.1 −1.26479 −0.632397 0.774644i \(-0.717929\pi\)
−0.632397 + 0.774644i \(0.717929\pi\)
\(642\) 0 0
\(643\) −17395.8 −1.06691 −0.533456 0.845828i \(-0.679107\pi\)
−0.533456 + 0.845828i \(0.679107\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1475.37 0.0896486 0.0448243 0.998995i \(-0.485727\pi\)
0.0448243 + 0.998995i \(0.485727\pi\)
\(648\) 0 0
\(649\) 12257.5 0.741371
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4918.78 0.294773 0.147387 0.989079i \(-0.452914\pi\)
0.147387 + 0.989079i \(0.452914\pi\)
\(654\) 0 0
\(655\) 7096.41 0.423328
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3938.97 −0.232839 −0.116419 0.993200i \(-0.537142\pi\)
−0.116419 + 0.993200i \(0.537142\pi\)
\(660\) 0 0
\(661\) 31950.2 1.88006 0.940028 0.341097i \(-0.110798\pi\)
0.940028 + 0.341097i \(0.110798\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9105.76 0.530987
\(666\) 0 0
\(667\) 56.9930 0.00330851
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 24064.9 1.38452
\(672\) 0 0
\(673\) 14912.6 0.854141 0.427070 0.904218i \(-0.359546\pi\)
0.427070 + 0.904218i \(0.359546\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 24876.2 1.41221 0.706107 0.708105i \(-0.250450\pi\)
0.706107 + 0.708105i \(0.250450\pi\)
\(678\) 0 0
\(679\) 10642.2 0.601486
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5819.10 −0.326005 −0.163003 0.986626i \(-0.552118\pi\)
−0.163003 + 0.986626i \(0.552118\pi\)
\(684\) 0 0
\(685\) 6752.49 0.376642
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7822.71 0.432542
\(690\) 0 0
\(691\) 23926.4 1.31722 0.658612 0.752483i \(-0.271144\pi\)
0.658612 + 0.752483i \(0.271144\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7741.90 −0.422543
\(696\) 0 0
\(697\) 5123.21 0.278415
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11493.3 0.619251 0.309626 0.950859i \(-0.399796\pi\)
0.309626 + 0.950859i \(0.399796\pi\)
\(702\) 0 0
\(703\) −4488.20 −0.240790
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18416.0 0.979638
\(708\) 0 0
\(709\) 11011.4 0.583276 0.291638 0.956529i \(-0.405800\pi\)
0.291638 + 0.956529i \(0.405800\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −222.440 −0.0116837
\(714\) 0 0
\(715\) 2607.51 0.136385
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14546.9 −0.754529 −0.377265 0.926106i \(-0.623135\pi\)
−0.377265 + 0.926106i \(0.623135\pi\)
\(720\) 0 0
\(721\) −33900.1 −1.75105
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −678.244 −0.0347439
\(726\) 0 0
\(727\) −7971.12 −0.406647 −0.203323 0.979112i \(-0.565174\pi\)
−0.203323 + 0.979112i \(0.565174\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 40395.1 2.04387
\(732\) 0 0
\(733\) −4191.29 −0.211199 −0.105599 0.994409i \(-0.533676\pi\)
−0.105599 + 0.994409i \(0.533676\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −43161.7 −2.15723
\(738\) 0 0
\(739\) −15062.1 −0.749756 −0.374878 0.927074i \(-0.622315\pi\)
−0.374878 + 0.927074i \(0.622315\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8785.14 −0.433776 −0.216888 0.976197i \(-0.569591\pi\)
−0.216888 + 0.976197i \(0.569591\pi\)
\(744\) 0 0
\(745\) −3796.49 −0.186701
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 35073.7 1.71104
\(750\) 0 0
\(751\) −18437.0 −0.895841 −0.447920 0.894073i \(-0.647835\pi\)
−0.447920 + 0.894073i \(0.647835\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12426.0 0.598980
\(756\) 0 0
\(757\) −26856.4 −1.28945 −0.644725 0.764415i \(-0.723028\pi\)
−0.644725 + 0.764415i \(0.723028\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21550.1 1.02653 0.513265 0.858230i \(-0.328436\pi\)
0.513265 + 0.858230i \(0.328436\pi\)
\(762\) 0 0
\(763\) −25083.2 −1.19014
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2747.37 −0.129338
\(768\) 0 0
\(769\) 35567.3 1.66787 0.833934 0.551864i \(-0.186083\pi\)
0.833934 + 0.551864i \(0.186083\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −20762.0 −0.966053 −0.483026 0.875606i \(-0.660462\pi\)
−0.483026 + 0.875606i \(0.660462\pi\)
\(774\) 0 0
\(775\) 2647.14 0.122694
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5798.42 0.266688
\(780\) 0 0
\(781\) 51187.2 2.34522
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8706.03 0.395836
\(786\) 0 0
\(787\) 19483.4 0.882475 0.441237 0.897390i \(-0.354540\pi\)
0.441237 + 0.897390i \(0.354540\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2369.20 −0.106497
\(792\) 0 0
\(793\) −5393.85 −0.241540
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11672.8 0.518783 0.259392 0.965772i \(-0.416478\pi\)
0.259392 + 0.965772i \(0.416478\pi\)
\(798\) 0 0
\(799\) 43769.3 1.93798
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −18530.9 −0.814374
\(804\) 0 0
\(805\) −866.389 −0.0379332
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 18423.5 0.800663 0.400331 0.916370i \(-0.368895\pi\)
0.400331 + 0.916370i \(0.368895\pi\)
\(810\) 0 0
\(811\) −16287.6 −0.705222 −0.352611 0.935770i \(-0.614706\pi\)
−0.352611 + 0.935770i \(0.614706\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −868.306 −0.0373196
\(816\) 0 0
\(817\) 45719.0 1.95778
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26118.8 1.11030 0.555148 0.831751i \(-0.312661\pi\)
0.555148 + 0.831751i \(0.312661\pi\)
\(822\) 0 0
\(823\) 13571.1 0.574798 0.287399 0.957811i \(-0.407209\pi\)
0.287399 + 0.957811i \(0.407209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 45842.8 1.92758 0.963790 0.266662i \(-0.0859209\pi\)
0.963790 + 0.266662i \(0.0859209\pi\)
\(828\) 0 0
\(829\) 2847.06 0.119279 0.0596397 0.998220i \(-0.481005\pi\)
0.0596397 + 0.998220i \(0.481005\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −31104.2 −1.29376
\(834\) 0 0
\(835\) 1558.27 0.0645822
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −28995.5 −1.19313 −0.596564 0.802565i \(-0.703468\pi\)
−0.596564 + 0.802565i \(0.703468\pi\)
\(840\) 0 0
\(841\) −24353.0 −0.998524
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −584.442 −0.0237934
\(846\) 0 0
\(847\) 53619.8 2.17520
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 427.040 0.0172018
\(852\) 0 0
\(853\) 14179.1 0.569148 0.284574 0.958654i \(-0.408148\pi\)
0.284574 + 0.958654i \(0.408148\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 28026.0 1.11709 0.558547 0.829473i \(-0.311359\pi\)
0.558547 + 0.829473i \(0.311359\pi\)
\(858\) 0 0
\(859\) 20995.6 0.833946 0.416973 0.908919i \(-0.363091\pi\)
0.416973 + 0.908919i \(0.363091\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −25139.2 −0.991596 −0.495798 0.868438i \(-0.665124\pi\)
−0.495798 + 0.868438i \(0.665124\pi\)
\(864\) 0 0
\(865\) −857.346 −0.0337001
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 28458.5 1.11092
\(870\) 0 0
\(871\) 9674.17 0.376345
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 21711.7 0.838844
\(876\) 0 0
\(877\) 34676.4 1.33516 0.667582 0.744537i \(-0.267330\pi\)
0.667582 + 0.744537i \(0.267330\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25864.8 0.989110 0.494555 0.869146i \(-0.335331\pi\)
0.494555 + 0.869146i \(0.335331\pi\)
\(882\) 0 0
\(883\) 29347.0 1.11847 0.559233 0.829011i \(-0.311096\pi\)
0.559233 + 0.829011i \(0.311096\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14292.1 0.541015 0.270508 0.962718i \(-0.412808\pi\)
0.270508 + 0.962718i \(0.412808\pi\)
\(888\) 0 0
\(889\) −9099.58 −0.343296
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 49537.9 1.85635
\(894\) 0 0
\(895\) 4381.12 0.163626
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −140.506 −0.00521260
\(900\) 0 0
\(901\) 53078.7 1.96261
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14000.3 −0.514237
\(906\) 0 0
\(907\) 19319.4 0.707264 0.353632 0.935385i \(-0.384946\pi\)
0.353632 + 0.935385i \(0.384946\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −47558.1 −1.72961 −0.864803 0.502112i \(-0.832557\pi\)
−0.864803 + 0.502112i \(0.832557\pi\)
\(912\) 0 0
\(913\) −13016.4 −0.471828
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −54121.7 −1.94903
\(918\) 0 0
\(919\) −49795.2 −1.78737 −0.893684 0.448696i \(-0.851889\pi\)
−0.893684 + 0.448696i \(0.851889\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −11473.0 −0.409142
\(924\) 0 0
\(925\) −5081.97 −0.180642
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18163.8 0.641479 0.320739 0.947167i \(-0.396069\pi\)
0.320739 + 0.947167i \(0.396069\pi\)
\(930\) 0 0
\(931\) −35203.6 −1.23926
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 17692.5 0.618830
\(936\) 0 0
\(937\) 3915.72 0.136522 0.0682610 0.997667i \(-0.478255\pi\)
0.0682610 + 0.997667i \(0.478255\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 38184.8 1.32284 0.661418 0.750017i \(-0.269955\pi\)
0.661418 + 0.750017i \(0.269955\pi\)
\(942\) 0 0
\(943\) −551.704 −0.0190519
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −35496.7 −1.21804 −0.609022 0.793154i \(-0.708438\pi\)
−0.609022 + 0.793154i \(0.708438\pi\)
\(948\) 0 0
\(949\) 4153.48 0.142074
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −51103.0 −1.73703 −0.868515 0.495663i \(-0.834925\pi\)
−0.868515 + 0.495663i \(0.834925\pi\)
\(954\) 0 0
\(955\) 13906.9 0.471221
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −51498.8 −1.73408
\(960\) 0 0
\(961\) −29242.6 −0.981592
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5289.67 0.176456
\(966\) 0 0
\(967\) −52681.0 −1.75192 −0.875961 0.482383i \(-0.839771\pi\)
−0.875961 + 0.482383i \(0.839771\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 28878.6 0.954437 0.477219 0.878785i \(-0.341645\pi\)
0.477219 + 0.878785i \(0.341645\pi\)
\(972\) 0 0
\(973\) 59044.7 1.94541
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 20043.8 0.656355 0.328178 0.944616i \(-0.393566\pi\)
0.328178 + 0.944616i \(0.393566\pi\)
\(978\) 0 0
\(979\) 33669.1 1.09915
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −14937.1 −0.484659 −0.242330 0.970194i \(-0.577912\pi\)
−0.242330 + 0.970194i \(0.577912\pi\)
\(984\) 0 0
\(985\) 3963.28 0.128204
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4350.04 −0.139862
\(990\) 0 0
\(991\) −24226.9 −0.776582 −0.388291 0.921537i \(-0.626934\pi\)
−0.388291 + 0.921537i \(0.626934\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −17948.5 −0.571865
\(996\) 0 0
\(997\) −38.6217 −0.00122684 −0.000613421 1.00000i \(-0.500195\pi\)
−0.000613421 1.00000i \(0.500195\pi\)
\(998\) 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.bh.1.1 2
3.2 odd 2 208.4.a.i.1.2 2
4.3 odd 2 936.4.a.i.1.1 2
12.11 even 2 104.4.a.d.1.1 2
24.5 odd 2 832.4.a.v.1.1 2
24.11 even 2 832.4.a.w.1.2 2
156.155 even 2 1352.4.a.g.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
104.4.a.d.1.1 2 12.11 even 2
208.4.a.i.1.2 2 3.2 odd 2
832.4.a.v.1.1 2 24.5 odd 2
832.4.a.w.1.2 2 24.11 even 2
936.4.a.i.1.1 2 4.3 odd 2
1352.4.a.g.1.1 2 156.155 even 2
1872.4.a.bh.1.1 2 1.1 even 1 trivial