↑

Properties

Label 1152.4.a.a.1.1
Level $1152$
Weight $4$
Character 1152.1
Self dual yes
Analytic conductor $67.970$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,4,Mod(1,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1152.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1152.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: \(67.9702003266\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 384)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1152.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-8.00000 q^{5} -10.0000 q^{7} +O(q^{10})\) \(q-8.00000 q^{5} -10.0000 q^{7} +68.0000 q^{11} -46.0000 q^{13} +74.0000 q^{17} -16.0000 q^{19} +20.0000 q^{23} -61.0000 q^{25} -228.000 q^{29} -162.000 q^{31} +80.0000 q^{35} +262.000 q^{37} -30.0000 q^{41} -264.000 q^{43} -124.000 q^{47} -243.000 q^{49} +204.000 q^{53} -544.000 q^{55} +340.000 q^{59} +950.000 q^{61} +368.000 q^{65} +436.000 q^{67} +780.000 q^{71} +518.000 q^{73} -680.000 q^{77} -1010.00 q^{79} +852.000 q^{83} -592.000 q^{85} +686.000 q^{89} +460.000 q^{91} +128.000 q^{95} -806.000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −8.00000 −0.715542 −0.357771 − 0.933809i \(-0.616463\pi\)
−0.357771 + 0.933809i \(0.616463\pi\)
\(6\) 0 0
\(7\) −10.0000 −0.539949 −0.269975 − 0.962867i \(-0.587015\pi\)
−0.269975 + 0.962867i \(0.587015\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 68.0000 1.86389 0.931944 − 0.362602i \(-0.118111\pi\)
0.931944 + 0.362602i \(0.118111\pi\)
\(12\) 0 0
\(13\) −46.0000 −0.981393 −0.490696 − 0.871331i \(-0.663258\pi\)
−0.490696 + 0.871331i \(0.663258\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 74.0000 1.05574 0.527872 − 0.849324i \(-0.322990\pi\)
0.527872 + 0.849324i \(0.322990\pi\)
\(18\) 0 0
\(19\) −16.0000 −0.193192 −0.0965961 − 0.995324i \(-0.530796\pi\)
−0.0965961 + 0.995324i \(0.530796\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 20.0000 0.181317 0.0906584 − 0.995882i \(-0.471103\pi\)
0.0906584 + 0.995882i \(0.471103\pi\)
\(24\) 0 0
\(25\) −61.0000 −0.488000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −228.000 −1.45995 −0.729975 − 0.683474i \(-0.760468\pi\)
−0.729975 + 0.683474i \(0.760468\pi\)
\(30\) 0 0
\(31\) −162.000 −0.938583 −0.469291 − 0.883043i \(-0.655491\pi\)
−0.469291 + 0.883043i \(0.655491\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 80.0000 0.386356
\(36\) 0 0
\(37\) 262.000 1.16412 0.582061 − 0.813145i \(-0.302246\pi\)
0.582061 + 0.813145i \(0.302246\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −30.0000 −0.114273 −0.0571367 − 0.998366i \(-0.518197\pi\)
−0.0571367 + 0.998366i \(0.518197\pi\)
\(42\) 0 0
\(43\) −264.000 −0.936270 −0.468135 − 0.883657i \(-0.655074\pi\)
−0.468135 + 0.883657i \(0.655074\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −124.000 −0.384835 −0.192418 − 0.981313i \(-0.561633\pi\)
−0.192418 + 0.981313i \(0.561633\pi\)
\(48\) 0 0
\(49\) −243.000 −0.708455
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 204.000 0.528709 0.264354 − 0.964426i \(-0.414841\pi\)
0.264354 + 0.964426i \(0.414841\pi\)
\(54\) 0 0
\(55\) −544.000 −1.33369
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 340.000 0.750241 0.375121 − 0.926976i \(-0.377601\pi\)
0.375121 + 0.926976i \(0.377601\pi\)
\(60\) 0 0
\(61\) 950.000 1.99402 0.997008 − 0.0772921i \(-0.0246274\pi\)
0.997008 + 0.0772921i \(0.0246274\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 368.000 0.702227
\(66\) 0 0
\(67\) 436.000 0.795013 0.397507 − 0.917599i \(-0.369876\pi\)
0.397507 + 0.917599i \(0.369876\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 780.000 1.30379 0.651894 − 0.758310i \(-0.273975\pi\)
0.651894 + 0.758310i \(0.273975\pi\)
\(72\) 0 0
\(73\) 518.000 0.830511 0.415256 − 0.909705i \(-0.363692\pi\)
0.415256 + 0.909705i \(0.363692\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −680.000 −1.00641
\(78\) 0 0
\(79\) −1010.00 −1.43840 −0.719202 − 0.694801i \(-0.755492\pi\)
−0.719202 + 0.694801i \(0.755492\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 852.000 1.12674 0.563368 − 0.826206i \(-0.309505\pi\)
0.563368 + 0.826206i \(0.309505\pi\)
\(84\) 0 0
\(85\) −592.000 −0.755428
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 686.000 0.817032 0.408516 − 0.912751i \(-0.366046\pi\)
0.408516 + 0.912751i \(0.366046\pi\)
\(90\) 0 0
\(91\) 460.000 0.529902
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 128.000 0.138237
\(96\) 0 0
\(97\) −806.000 −0.843679 −0.421840 − 0.906670i \(-0.638615\pi\)
−0.421840 + 0.906670i \(0.638615\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 636.000 0.626578 0.313289 − 0.949658i \(-0.398569\pi\)
0.313289 + 0.949658i \(0.398569\pi\)
\(102\) 0 0
\(103\) 1586.00 1.51722 0.758608 − 0.651547i \(-0.225880\pi\)
0.758608 + 0.651547i \(0.225880\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 92.0000 0.0831213 0.0415606 − 0.999136i \(-0.486767\pi\)
0.0415606 + 0.999136i \(0.486767\pi\)
\(108\) 0 0
\(109\) 2010.00 1.76627 0.883133 − 0.469122i \(-0.155430\pi\)
0.883133 + 0.469122i \(0.155430\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2062.00 1.71661 0.858304 − 0.513142i \(-0.171519\pi\)
0.858304 + 0.513142i \(0.171519\pi\)
\(114\) 0 0
\(115\) −160.000 −0.129740
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −740.000 −0.570048
\(120\) 0 0
\(121\) 3293.00 2.47408
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1488.00 1.06473
\(126\) 0 0
\(127\) −1046.00 −0.730846 −0.365423 − 0.930841i \(-0.619076\pi\)
−0.365423 + 0.930841i \(0.619076\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1884.00 −1.25653 −0.628267 − 0.777998i \(-0.716235\pi\)
−0.628267 + 0.777998i \(0.716235\pi\)
\(132\) 0 0
\(133\) 160.000 0.104314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2374.00 −1.48047 −0.740235 − 0.672348i \(-0.765286\pi\)
−0.740235 + 0.672348i \(0.765286\pi\)
\(138\) 0 0
\(139\) 2156.00 1.31561 0.657804 − 0.753189i \(-0.271485\pi\)
0.657804 + 0.753189i \(0.271485\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3128.00 −1.82921
\(144\) 0 0
\(145\) 1824.00 1.04465
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2952.00 1.62307 0.811534 − 0.584305i \(-0.198633\pi\)
0.811534 + 0.584305i \(0.198633\pi\)
\(150\) 0 0
\(151\) −3410.00 −1.83776 −0.918880 − 0.394536i \(-0.870905\pi\)
−0.918880 + 0.394536i \(0.870905\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1296.00 0.671595
\(156\) 0 0
\(157\) −666.000 −0.338552 −0.169276 − 0.985569i \(-0.554143\pi\)
−0.169276 + 0.985569i \(0.554143\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −200.000 −0.0979019
\(162\) 0 0
\(163\) 704.000 0.338292 0.169146 − 0.985591i \(-0.445899\pi\)
0.169146 + 0.985591i \(0.445899\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1648.00 −0.763629 −0.381815 − 0.924239i \(-0.624701\pi\)
−0.381815 + 0.924239i \(0.624701\pi\)
\(168\) 0 0
\(169\) −81.0000 −0.0368685
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 360.000 0.158210 0.0791049 − 0.996866i \(-0.474794\pi\)
0.0791049 + 0.996866i \(0.474794\pi\)
\(174\) 0 0
\(175\) 610.000 0.263495
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1956.00 −0.816750 −0.408375 − 0.912814i \(-0.633904\pi\)
−0.408375 + 0.912814i \(0.633904\pi\)
\(180\) 0 0
\(181\) 218.000 0.0895238 0.0447619 − 0.998998i \(-0.485747\pi\)
0.0447619 + 0.998998i \(0.485747\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2096.00 −0.832978
\(186\) 0 0
\(187\) 5032.00 1.96779
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −680.000 −0.257608 −0.128804 − 0.991670i \(-0.541114\pi\)
−0.128804 + 0.991670i \(0.541114\pi\)
\(192\) 0 0
\(193\) 4510.00 1.68206 0.841028 − 0.540991i \(-0.181951\pi\)
0.841028 + 0.540991i \(0.181951\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −796.000 −0.287881 −0.143941 − 0.989586i \(-0.545977\pi\)
−0.143941 + 0.989586i \(0.545977\pi\)
\(198\) 0 0
\(199\) 986.000 0.351235 0.175617 − 0.984459i \(-0.443808\pi\)
0.175617 + 0.984459i \(0.443808\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2280.00 0.788299
\(204\) 0 0
\(205\) 240.000 0.0817674
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1088.00 −0.360089
\(210\) 0 0
\(211\) 4196.00 1.36903 0.684513 − 0.729001i \(-0.260015\pi\)
0.684513 + 0.729001i \(0.260015\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2112.00 0.669940
\(216\) 0 0
\(217\) 1620.00 0.506787
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3404.00 −1.03610
\(222\) 0 0
\(223\) −2502.00 −0.751329 −0.375664 − 0.926756i \(-0.622585\pi\)
−0.375664 + 0.926756i \(0.622585\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 324.000 0.0947341 0.0473670 − 0.998878i \(-0.484917\pi\)
0.0473670 + 0.998878i \(0.484917\pi\)
\(228\) 0 0
\(229\) 2194.00 0.633116 0.316558 − 0.948573i \(-0.397473\pi\)
0.316558 + 0.948573i \(0.397473\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4230.00 1.18934 0.594671 − 0.803969i \(-0.297282\pi\)
0.594671 + 0.803969i \(0.297282\pi\)
\(234\) 0 0
\(235\) 992.000 0.275366
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6672.00 −1.80576 −0.902878 − 0.429896i \(-0.858550\pi\)
−0.902878 + 0.429896i \(0.858550\pi\)
\(240\) 0 0
\(241\) −1490.00 −0.398255 −0.199127 − 0.979974i \(-0.563811\pi\)
−0.199127 + 0.979974i \(0.563811\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1944.00 0.506929
\(246\) 0 0
\(247\) 736.000 0.189597
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7380.00 1.85586 0.927931 − 0.372751i \(-0.121586\pi\)
0.927931 + 0.372751i \(0.121586\pi\)
\(252\) 0 0
\(253\) 1360.00 0.337954
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1998.00 0.484949 0.242474 − 0.970158i \(-0.422041\pi\)
0.242474 + 0.970158i \(0.422041\pi\)
\(258\) 0 0
\(259\) −2620.00 −0.628567
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3768.00 0.883440 0.441720 − 0.897153i \(-0.354368\pi\)
0.441720 + 0.897153i \(0.354368\pi\)
\(264\) 0 0
\(265\) −1632.00 −0.378313
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7964.00 1.80511 0.902553 − 0.430578i \(-0.141690\pi\)
0.902553 + 0.430578i \(0.141690\pi\)
\(270\) 0 0
\(271\) 2330.00 0.522278 0.261139 − 0.965301i \(-0.415902\pi\)
0.261139 + 0.965301i \(0.415902\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4148.00 −0.909577
\(276\) 0 0
\(277\) 2154.00 0.467225 0.233612 − 0.972330i \(-0.424945\pi\)
0.233612 + 0.972330i \(0.424945\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5598.00 1.18843 0.594215 − 0.804306i \(-0.297463\pi\)
0.594215 + 0.804306i \(0.297463\pi\)
\(282\) 0 0
\(283\) −1884.00 −0.395732 −0.197866 − 0.980229i \(-0.563401\pi\)
−0.197866 + 0.980229i \(0.563401\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 300.000 0.0617019
\(288\) 0 0
\(289\) 563.000 0.114594
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2788.00 −0.555893 −0.277947 − 0.960597i \(-0.589654\pi\)
−0.277947 + 0.960597i \(0.589654\pi\)
\(294\) 0 0
\(295\) −2720.00 −0.536829
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −920.000 −0.177943
\(300\) 0 0
\(301\) 2640.00 0.505538
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7600.00 −1.42680
\(306\) 0 0
\(307\) −9180.00 −1.70661 −0.853307 − 0.521409i \(-0.825406\pi\)
−0.853307 + 0.521409i \(0.825406\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8032.00 1.46448 0.732239 − 0.681047i \(-0.238475\pi\)
0.732239 + 0.681047i \(0.238475\pi\)
\(312\) 0 0
\(313\) 214.000 0.0386454 0.0193227 − 0.999813i \(-0.493849\pi\)
0.0193227 + 0.999813i \(0.493849\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1428.00 0.253011 0.126505 − 0.991966i \(-0.459624\pi\)
0.126505 + 0.991966i \(0.459624\pi\)
\(318\) 0 0
\(319\) −15504.0 −2.72118
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1184.00 −0.203961
\(324\) 0 0
\(325\) 2806.00 0.478920
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1240.00 0.207792
\(330\) 0 0
\(331\) 2708.00 0.449683 0.224842 − 0.974395i \(-0.427814\pi\)
0.224842 + 0.974395i \(0.427814\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3488.00 −0.568865
\(336\) 0 0
\(337\) −6338.00 −1.02449 −0.512245 − 0.858840i \(-0.671186\pi\)
−0.512245 + 0.858840i \(0.671186\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11016.0 −1.74941
\(342\) 0 0
\(343\) 5860.00 0.922479
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1980.00 0.306317 0.153158 − 0.988202i \(-0.451056\pi\)
0.153158 + 0.988202i \(0.451056\pi\)
\(348\) 0 0
\(349\) −7418.00 −1.13775 −0.568877 − 0.822422i \(-0.692622\pi\)
−0.568877 + 0.822422i \(0.692622\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3438.00 0.518375 0.259187 − 0.965827i \(-0.416545\pi\)
0.259187 + 0.965827i \(0.416545\pi\)
\(354\) 0 0
\(355\) −6240.00 −0.932915
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2372.00 −0.348717 −0.174358 − 0.984682i \(-0.555785\pi\)
−0.174358 + 0.984682i \(0.555785\pi\)
\(360\) 0 0
\(361\) −6603.00 −0.962677
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4144.00 −0.594265
\(366\) 0 0
\(367\) 6046.00 0.859942 0.429971 − 0.902843i \(-0.358524\pi\)
0.429971 + 0.902843i \(0.358524\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2040.00 −0.285476
\(372\) 0 0
\(373\) 9238.00 1.28237 0.641187 − 0.767385i \(-0.278442\pi\)
0.641187 + 0.767385i \(0.278442\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10488.0 1.43278
\(378\) 0 0
\(379\) −2936.00 −0.397921 −0.198961 − 0.980007i \(-0.563757\pi\)
−0.198961 + 0.980007i \(0.563757\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12600.0 1.68102 0.840509 − 0.541798i \(-0.182256\pi\)
0.840509 + 0.541798i \(0.182256\pi\)
\(384\) 0 0
\(385\) 5440.00 0.720125
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3112.00 −0.405616 −0.202808 − 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) 1480.00 0.191424
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8080.00 1.02924
\(396\) 0 0
\(397\) −2130.00 −0.269274 −0.134637 − 0.990895i \(-0.542987\pi\)
−0.134637 + 0.990895i \(0.542987\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1554.00 0.193524 0.0967619 − 0.995308i \(-0.469151\pi\)
0.0967619 + 0.995308i \(0.469151\pi\)
\(402\) 0 0
\(403\) 7452.00 0.921118
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 17816.0 2.16979
\(408\) 0 0
\(409\) −8942.00 −1.08106 −0.540530 − 0.841325i \(-0.681776\pi\)
−0.540530 + 0.841325i \(0.681776\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3400.00 −0.405092
\(414\) 0 0
\(415\) −6816.00 −0.806227
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6908.00 −0.805436 −0.402718 − 0.915324i \(-0.631935\pi\)
−0.402718 + 0.915324i \(0.631935\pi\)
\(420\) 0 0
\(421\) −7862.00 −0.910144 −0.455072 − 0.890455i \(-0.650386\pi\)
−0.455072 + 0.890455i \(0.650386\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4514.00 −0.515203
\(426\) 0 0
\(427\) −9500.00 −1.07667
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12100.0 −1.35229 −0.676144 − 0.736769i \(-0.736350\pi\)
−0.676144 + 0.736769i \(0.736350\pi\)
\(432\) 0 0
\(433\) 12882.0 1.42972 0.714861 − 0.699267i \(-0.246490\pi\)
0.714861 + 0.699267i \(0.246490\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −320.000 −0.0350290
\(438\) 0 0
\(439\) 10818.0 1.17612 0.588058 − 0.808819i \(-0.299893\pi\)
0.588058 + 0.808819i \(0.299893\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −852.000 −0.0913764 −0.0456882 − 0.998956i \(-0.514548\pi\)
−0.0456882 + 0.998956i \(0.514548\pi\)
\(444\) 0 0
\(445\) −5488.00 −0.584621
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5222.00 −0.548867 −0.274434 − 0.961606i \(-0.588490\pi\)
−0.274434 + 0.961606i \(0.588490\pi\)
\(450\) 0 0
\(451\) −2040.00 −0.212993
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3680.00 −0.379167
\(456\) 0 0
\(457\) −11598.0 −1.18716 −0.593579 − 0.804775i \(-0.702286\pi\)
−0.593579 + 0.804775i \(0.702286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4088.00 0.413009 0.206504 − 0.978446i \(-0.433791\pi\)
0.206504 + 0.978446i \(0.433791\pi\)
\(462\) 0 0
\(463\) 15394.0 1.54518 0.772592 − 0.634903i \(-0.218960\pi\)
0.772592 + 0.634903i \(0.218960\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3092.00 0.306383 0.153191 − 0.988197i \(-0.451045\pi\)
0.153191 + 0.988197i \(0.451045\pi\)
\(468\) 0 0
\(469\) −4360.00 −0.429267
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −17952.0 −1.74510
\(474\) 0 0
\(475\) 976.000 0.0942778
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9612.00 −0.916876 −0.458438 − 0.888726i \(-0.651591\pi\)
−0.458438 + 0.888726i \(0.651591\pi\)
\(480\) 0 0
\(481\) −12052.0 −1.14246
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6448.00 0.603688
\(486\) 0 0
\(487\) 13606.0 1.26601 0.633005 − 0.774148i \(-0.281821\pi\)
0.633005 + 0.774148i \(0.281821\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2020.00 0.185665 0.0928323 − 0.995682i \(-0.470408\pi\)
0.0928323 + 0.995682i \(0.470408\pi\)
\(492\) 0 0
\(493\) −16872.0 −1.54133
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7800.00 −0.703980
\(498\) 0 0
\(499\) −19348.0 −1.73574 −0.867871 − 0.496789i \(-0.834512\pi\)
−0.867871 + 0.496789i \(0.834512\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −596.000 −0.0528317 −0.0264158 − 0.999651i \(-0.508409\pi\)
−0.0264158 + 0.999651i \(0.508409\pi\)
\(504\) 0 0
\(505\) −5088.00 −0.448343
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4300.00 −0.374448 −0.187224 − 0.982317i \(-0.559949\pi\)
−0.187224 + 0.982317i \(0.559949\pi\)
\(510\) 0 0
\(511\) −5180.00 −0.448434
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12688.0 −1.08563
\(516\) 0 0
\(517\) −8432.00 −0.717290
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9158.00 −0.770095 −0.385047 − 0.922897i \(-0.625815\pi\)
−0.385047 + 0.922897i \(0.625815\pi\)
\(522\) 0 0
\(523\) 10040.0 0.839424 0.419712 − 0.907657i \(-0.362131\pi\)
0.419712 + 0.907657i \(0.362131\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11988.0 −0.990902
\(528\) 0 0
\(529\) −11767.0 −0.967124
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1380.00 0.112147
\(534\) 0 0
\(535\) −736.000 −0.0594767
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16524.0 −1.32048
\(540\) 0 0
\(541\) 1906.00 0.151470 0.0757351 − 0.997128i \(-0.475870\pi\)
0.0757351 + 0.997128i \(0.475870\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −16080.0 −1.26384
\(546\) 0 0
\(547\) 10264.0 0.802298 0.401149 − 0.916013i \(-0.368611\pi\)
0.401149 + 0.916013i \(0.368611\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3648.00 0.282051
\(552\) 0 0
\(553\) 10100.0 0.776665
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15856.0 1.20618 0.603088 − 0.797674i \(-0.293937\pi\)
0.603088 + 0.797674i \(0.293937\pi\)
\(558\) 0 0
\(559\) 12144.0 0.918849
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19764.0 −1.47949 −0.739745 − 0.672887i \(-0.765054\pi\)
−0.739745 + 0.672887i \(0.765054\pi\)
\(564\) 0 0
\(565\) −16496.0 −1.22830
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6302.00 −0.464312 −0.232156 − 0.972679i \(-0.574578\pi\)
−0.232156 + 0.972679i \(0.574578\pi\)
\(570\) 0 0
\(571\) 764.000 0.0559937 0.0279969 − 0.999608i \(-0.491087\pi\)
0.0279969 + 0.999608i \(0.491087\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1220.00 −0.0884826
\(576\) 0 0
\(577\) −10618.0 −0.766089 −0.383044 − 0.923730i \(-0.625124\pi\)
−0.383044 + 0.923730i \(0.625124\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8520.00 −0.608381
\(582\) 0 0
\(583\) 13872.0 0.985454
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4036.00 0.283788 0.141894 − 0.989882i \(-0.454681\pi\)
0.141894 + 0.989882i \(0.454681\pi\)
\(588\) 0 0
\(589\) 2592.00 0.181327
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 24750.0 1.71393 0.856965 − 0.515374i \(-0.172347\pi\)
0.856965 + 0.515374i \(0.172347\pi\)
\(594\) 0 0
\(595\) 5920.00 0.407893
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4908.00 0.334784 0.167392 − 0.985890i \(-0.446465\pi\)
0.167392 + 0.985890i \(0.446465\pi\)
\(600\) 0 0
\(601\) 22062.0 1.49738 0.748692 − 0.662918i \(-0.230682\pi\)
0.748692 + 0.662918i \(0.230682\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −26344.0 −1.77031
\(606\) 0 0
\(607\) 12986.0 0.868345 0.434173 − 0.900830i \(-0.357041\pi\)
0.434173 + 0.900830i \(0.357041\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5704.00 0.377675
\(612\) 0 0
\(613\) −24986.0 −1.64629 −0.823144 − 0.567832i \(-0.807782\pi\)
−0.823144 + 0.567832i \(0.807782\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3230.00 0.210753 0.105377 − 0.994432i \(-0.466395\pi\)
0.105377 + 0.994432i \(0.466395\pi\)
\(618\) 0 0
\(619\) −15500.0 −1.00646 −0.503229 − 0.864153i \(-0.667855\pi\)
−0.503229 + 0.864153i \(0.667855\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6860.00 −0.441156
\(624\) 0 0
\(625\) −4279.00 −0.273856
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 19388.0 1.22901
\(630\) 0 0
\(631\) −16874.0 −1.06457 −0.532285 − 0.846565i \(-0.678666\pi\)
−0.532285 + 0.846565i \(0.678666\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8368.00 0.522951
\(636\) 0 0
\(637\) 11178.0 0.695272
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 978.000 0.0602631 0.0301316 − 0.999546i \(-0.490407\pi\)
0.0301316 + 0.999546i \(0.490407\pi\)
\(642\) 0 0
\(643\) −1992.00 −0.122172 −0.0610862 − 0.998132i \(-0.519456\pi\)
−0.0610862 + 0.998132i \(0.519456\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3588.00 0.218020 0.109010 − 0.994041i \(-0.465232\pi\)
0.109010 + 0.994041i \(0.465232\pi\)
\(648\) 0 0
\(649\) 23120.0 1.39837
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7536.00 0.451618 0.225809 − 0.974172i \(-0.427497\pi\)
0.225809 + 0.974172i \(0.427497\pi\)
\(654\) 0 0
\(655\) 15072.0 0.899102
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3684.00 −0.217767 −0.108883 − 0.994055i \(-0.534728\pi\)
−0.108883 + 0.994055i \(0.534728\pi\)
\(660\) 0 0
\(661\) −4418.00 −0.259970 −0.129985 − 0.991516i \(-0.541493\pi\)
−0.129985 + 0.991516i \(0.541493\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1280.00 −0.0746410
\(666\) 0 0
\(667\) −4560.00 −0.264714
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 64600.0 3.71662
\(672\) 0 0
\(673\) −158.000 −0.00904971 −0.00452485 − 0.999990i \(-0.501440\pi\)
−0.00452485 + 0.999990i \(0.501440\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10736.0 −0.609480 −0.304740 − 0.952436i \(-0.598570\pi\)
−0.304740 + 0.952436i \(0.598570\pi\)
\(678\) 0 0
\(679\) 8060.00 0.455544
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6132.00 −0.343535 −0.171768 − 0.985138i \(-0.554948\pi\)
−0.171768 + 0.985138i \(0.554948\pi\)
\(684\) 0 0
\(685\) 18992.0 1.05934
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9384.00 −0.518871
\(690\) 0 0
\(691\) −28320.0 −1.55911 −0.779554 − 0.626335i \(-0.784554\pi\)
−0.779554 + 0.626335i \(0.784554\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −17248.0 −0.941373
\(696\) 0 0
\(697\) −2220.00 −0.120643
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23420.0 −1.26186 −0.630928 − 0.775841i \(-0.717326\pi\)
−0.630928 + 0.775841i \(0.717326\pi\)
\(702\) 0 0
\(703\) −4192.00 −0.224899
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6360.00 −0.338320
\(708\) 0 0
\(709\) 13634.0 0.722194 0.361097 − 0.932528i \(-0.382402\pi\)
0.361097 + 0.932528i \(0.382402\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3240.00 −0.170181
\(714\) 0 0
\(715\) 25024.0 1.30887
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4044.00 0.209758 0.104879 − 0.994485i \(-0.466555\pi\)
0.104879 + 0.994485i \(0.466555\pi\)
\(720\) 0 0
\(721\) −15860.0 −0.819220
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 13908.0 0.712455
\(726\) 0 0
\(727\) −25842.0 −1.31833 −0.659166 − 0.751998i \(-0.729090\pi\)
−0.659166 + 0.751998i \(0.729090\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −19536.0 −0.988461
\(732\) 0 0
\(733\) −33414.0 −1.68373 −0.841865 − 0.539688i \(-0.818542\pi\)
−0.841865 + 0.539688i \(0.818542\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29648.0 1.48182
\(738\) 0 0
\(739\) −21708.0 −1.08057 −0.540285 − 0.841482i \(-0.681684\pi\)
−0.540285 + 0.841482i \(0.681684\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −12488.0 −0.616609 −0.308304 − 0.951288i \(-0.599762\pi\)
−0.308304 + 0.951288i \(0.599762\pi\)
\(744\) 0 0
\(745\) −23616.0 −1.16137
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −920.000 −0.0448813
\(750\) 0 0
\(751\) −13522.0 −0.657024 −0.328512 − 0.944500i \(-0.606547\pi\)
−0.328512 + 0.944500i \(0.606547\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 27280.0 1.31499
\(756\) 0 0
\(757\) 10178.0 0.488673 0.244337 − 0.969690i \(-0.421430\pi\)
0.244337 + 0.969690i \(0.421430\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 482.000 0.0229599 0.0114800 − 0.999934i \(-0.496346\pi\)
0.0114800 + 0.999934i \(0.496346\pi\)
\(762\) 0 0
\(763\) −20100.0 −0.953694
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15640.0 −0.736281
\(768\) 0 0
\(769\) −6706.00 −0.314466 −0.157233 − 0.987562i \(-0.550257\pi\)
−0.157233 + 0.987562i \(0.550257\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 40788.0 1.89786 0.948928 − 0.315493i \(-0.102170\pi\)
0.948928 + 0.315493i \(0.102170\pi\)
\(774\) 0 0
\(775\) 9882.00 0.458028
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 480.000 0.0220767
\(780\) 0 0
\(781\) 53040.0 2.43012
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5328.00 0.242248
\(786\) 0 0
\(787\) 29720.0 1.34613 0.673065 − 0.739584i \(-0.264978\pi\)
0.673065 + 0.739584i \(0.264978\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20620.0 −0.926881
\(792\) 0 0
\(793\) −43700.0 −1.95691
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20736.0 −0.921589 −0.460795 − 0.887507i \(-0.652436\pi\)
−0.460795 + 0.887507i \(0.652436\pi\)
\(798\) 0 0
\(799\) −9176.00 −0.406287
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 35224.0 1.54798
\(804\) 0 0
\(805\) 1600.00 0.0700529
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 9834.00 0.427373 0.213687 − 0.976902i \(-0.431453\pi\)
0.213687 + 0.976902i \(0.431453\pi\)
\(810\) 0 0
\(811\) −4176.00 −0.180813 −0.0904064 − 0.995905i \(-0.528817\pi\)
−0.0904064 + 0.995905i \(0.528817\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5632.00 −0.242062
\(816\) 0 0
\(817\) 4224.00 0.180880
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1996.00 −0.0848488 −0.0424244 − 0.999100i \(-0.513508\pi\)
−0.0424244 + 0.999100i \(0.513508\pi\)
\(822\) 0 0
\(823\) −14386.0 −0.609313 −0.304656 − 0.952462i \(-0.598542\pi\)
−0.304656 + 0.952462i \(0.598542\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33836.0 1.42272 0.711362 − 0.702826i \(-0.248079\pi\)
0.711362 + 0.702826i \(0.248079\pi\)
\(828\) 0 0
\(829\) −16358.0 −0.685328 −0.342664 − 0.939458i \(-0.611329\pi\)
−0.342664 + 0.939458i \(0.611329\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −17982.0 −0.747946
\(834\) 0 0
\(835\) 13184.0 0.546409
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26244.0 1.07991 0.539954 − 0.841694i \(-0.318441\pi\)
0.539954 + 0.841694i \(0.318441\pi\)
\(840\) 0 0
\(841\) 27595.0 1.13145
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 648.000 0.0263809
\(846\) 0 0
\(847\) −32930.0 −1.33588
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5240.00 0.211075
\(852\) 0 0
\(853\) 39854.0 1.59974 0.799868 − 0.600176i \(-0.204903\pi\)
0.799868 + 0.600176i \(0.204903\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2706.00 0.107859 0.0539295 − 0.998545i \(-0.482825\pi\)
0.0539295 + 0.998545i \(0.482825\pi\)
\(858\) 0 0
\(859\) 17728.0 0.704158 0.352079 − 0.935970i \(-0.385475\pi\)
0.352079 + 0.935970i \(0.385475\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −20056.0 −0.791094 −0.395547 − 0.918446i \(-0.629445\pi\)
−0.395547 + 0.918446i \(0.629445\pi\)
\(864\) 0 0
\(865\) −2880.00 −0.113206
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −68680.0 −2.68102
\(870\) 0 0
\(871\) −20056.0 −0.780220
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −14880.0 −0.574898
\(876\) 0 0
\(877\) 26534.0 1.02165 0.510826 − 0.859684i \(-0.329339\pi\)
0.510826 + 0.859684i \(0.329339\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 45838.0 1.75292 0.876459 − 0.481476i \(-0.159899\pi\)
0.876459 + 0.481476i \(0.159899\pi\)
\(882\) 0 0
\(883\) 23200.0 0.884193 0.442096 − 0.896968i \(-0.354235\pi\)
0.442096 + 0.896968i \(0.354235\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 25272.0 0.956652 0.478326 − 0.878182i \(-0.341244\pi\)
0.478326 + 0.878182i \(0.341244\pi\)
\(888\) 0 0
\(889\) 10460.0 0.394620
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1984.00 0.0743472
\(894\) 0 0
\(895\) 15648.0 0.584419
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 36936.0 1.37028
\(900\) 0 0
\(901\) 15096.0 0.558181
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1744.00 −0.0640580
\(906\) 0 0
\(907\) −42448.0 −1.55398 −0.776992 − 0.629511i \(-0.783255\pi\)
−0.776992 + 0.629511i \(0.783255\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 49776.0 1.81027 0.905133 − 0.425128i \(-0.139771\pi\)
0.905133 + 0.425128i \(0.139771\pi\)
\(912\) 0 0
\(913\) 57936.0 2.10011
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18840.0 0.678464
\(918\) 0 0
\(919\) −3042.00 −0.109191 −0.0545954 − 0.998509i \(-0.517387\pi\)
−0.0545954 + 0.998509i \(0.517387\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −35880.0 −1.27953
\(924\) 0 0
\(925\) −15982.0 −0.568092
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 11490.0 0.405785 0.202893 − 0.979201i \(-0.434966\pi\)
0.202893 + 0.979201i \(0.434966\pi\)
\(930\) 0 0
\(931\) 3888.00 0.136868
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −40256.0 −1.40803
\(936\) 0 0
\(937\) 19882.0 0.693187 0.346594 − 0.938015i \(-0.387338\pi\)
0.346594 + 0.938015i \(0.387338\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 41336.0 1.43200 0.716002 − 0.698099i \(-0.245970\pi\)
0.716002 + 0.698099i \(0.245970\pi\)
\(942\) 0 0
\(943\) −600.000 −0.0207197
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35036.0 1.20224 0.601118 − 0.799160i \(-0.294722\pi\)
0.601118 + 0.799160i \(0.294722\pi\)
\(948\) 0 0
\(949\) −23828.0 −0.815058
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −9814.00 −0.333585 −0.166793 − 0.985992i \(-0.553341\pi\)
−0.166793 + 0.985992i \(0.553341\pi\)
\(954\) 0 0
\(955\) 5440.00 0.184329
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 23740.0 0.799379
\(960\) 0 0
\(961\) −3547.00 −0.119063
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −36080.0 −1.20358
\(966\) 0 0
\(967\) −26006.0 −0.864836 −0.432418 − 0.901673i \(-0.642340\pi\)
−0.432418 + 0.901673i \(0.642340\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 17404.0 0.575202 0.287601 − 0.957750i \(-0.407142\pi\)
0.287601 + 0.957750i \(0.407142\pi\)
\(972\) 0 0
\(973\) −21560.0 −0.710362
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −44526.0 −1.45805 −0.729024 − 0.684488i \(-0.760026\pi\)
−0.729024 + 0.684488i \(0.760026\pi\)
\(978\) 0 0
\(979\) 46648.0 1.52286
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −47480.0 −1.54057 −0.770283 − 0.637702i \(-0.779885\pi\)
−0.770283 + 0.637702i \(0.779885\pi\)
\(984\) 0 0
\(985\) 6368.00 0.205991
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5280.00 −0.169762
\(990\) 0 0
\(991\) −18866.0 −0.604741 −0.302370 − 0.953190i \(-0.597778\pi\)
−0.302370 + 0.953190i \(0.597778\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −7888.00 −0.251323
\(996\) 0 0
\(997\) 17550.0 0.557487 0.278743 − 0.960366i \(-0.410082\pi\)
0.278743 + 0.960366i \(0.410082\pi\)
\(998\) 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 1152.4.a.a.1.1 1
3.2 odd 2 384.4.a.h.1.1 yes 1
4.3 odd 2 1152.4.a.b.1.1 1
8.3 odd 2 1152.4.a.l.1.1 1
8.5 even 2 1152.4.a.k.1.1 1
12.11 even 2 384.4.a.d.1.1 yes 1
24.5 odd 2 384.4.a.a.1.1 ✓ 1
24.11 even 2 384.4.a.e.1.1 yes 1
48.5 odd 4 768.4.d.l.385.1 2
48.11 even 4 768.4.d.e.385.2 2
48.29 odd 4 768.4.d.l.385.2 2
48.35 even 4 768.4.d.e.385.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.4.a.a.1.1 ✓ 1 24.5 odd 2
384.4.a.d.1.1 yes 1 12.11 even 2
384.4.a.e.1.1 yes 1 24.11 even 2
384.4.a.h.1.1 yes 1 3.2 odd 2
768.4.d.e.385.1 2 48.35 even 4
768.4.d.e.385.2 2 48.11 even 4
768.4.d.l.385.1 2 48.5 odd 4
768.4.d.l.385.2 2 48.29 odd 4
1152.4.a.a.1.1 1 1.1 even 1 trivial
1152.4.a.b.1.1 1 4.3 odd 2
1152.4.a.k.1.1 1 8.5 even 2
1152.4.a.l.1.1 1 8.3 odd 2