Properties

Label 1296.4.a.m.1.1
Level $1296$
Weight $4$
Character 1296.1
Self dual yes
Analytic conductor $76.466$
Analytic rank $0$
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] = [1296,4,Mod(1,1296)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1296, 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("1296.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1296.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: \(76.4664753674\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{201}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 50 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 648)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(7.58872\) of defining polynomial
Character \(\chi\) \(=\) 1296.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-18.1774 q^{5} +0.822553 q^{7} +O(q^{10})\) \(q-18.1774 q^{5} +0.822553 q^{7} -65.5323 q^{11} +31.8226 q^{13} -124.420 q^{17} -27.8872 q^{19} -43.1774 q^{23} +205.420 q^{25} -39.8226 q^{29} -294.839 q^{31} -14.9519 q^{35} -104.177 q^{37} -307.645 q^{41} +361.081 q^{43} +397.645 q^{47} -342.323 q^{49} -107.161 q^{53} +1191.21 q^{55} +188.935 q^{59} -99.0166 q^{61} -578.453 q^{65} -425.048 q^{67} -445.532 q^{71} -499.806 q^{73} -53.9038 q^{77} -570.275 q^{79} +1308.74 q^{83} +2261.63 q^{85} -1323.00 q^{89} +26.1757 q^{91} +506.919 q^{95} +944.872 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{5} + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{5} + 30 q^{7} - 46 q^{11} + 92 q^{13} - 22 q^{17} + 86 q^{19} - 58 q^{23} + 184 q^{25} - 108 q^{29} - 136 q^{31} + 282 q^{35} - 180 q^{37} - 672 q^{41} + 70 q^{43} + 852 q^{47} + 166 q^{49} - 668 q^{53} + 1390 q^{55} + 548 q^{59} + 284 q^{61} + 34 q^{65} - 1162 q^{67} - 806 q^{71} - 1510 q^{73} + 516 q^{77} + 22 q^{79} + 1540 q^{83} + 3304 q^{85} - 2646 q^{89} + 1782 q^{91} + 1666 q^{95} + 472 q^{97}+O(q^{100}) \) 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
\(5\) −18.1774 −1.62584 −0.812920 0.582375i \(-0.802123\pi\)
−0.812920 + 0.582375i \(0.802123\pi\)
\(6\) 0 0
\(7\) 0.822553 0.0444137 0.0222068 0.999753i \(-0.492931\pi\)
0.0222068 + 0.999753i \(0.492931\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −65.5323 −1.79625 −0.898125 0.439741i \(-0.855070\pi\)
−0.898125 + 0.439741i \(0.855070\pi\)
\(12\) 0 0
\(13\) 31.8226 0.678922 0.339461 0.940620i \(-0.389755\pi\)
0.339461 + 0.940620i \(0.389755\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −124.420 −1.77507 −0.887535 0.460741i \(-0.847584\pi\)
−0.887535 + 0.460741i \(0.847584\pi\)
\(18\) 0 0
\(19\) −27.8872 −0.336725 −0.168362 0.985725i \(-0.553848\pi\)
−0.168362 + 0.985725i \(0.553848\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −43.1774 −0.391440 −0.195720 0.980660i \(-0.562704\pi\)
−0.195720 + 0.980660i \(0.562704\pi\)
\(24\) 0 0
\(25\) 205.420 1.64336
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −39.8226 −0.254995 −0.127498 0.991839i \(-0.540695\pi\)
−0.127498 + 0.991839i \(0.540695\pi\)
\(30\) 0 0
\(31\) −294.839 −1.70822 −0.854108 0.520096i \(-0.825896\pi\)
−0.854108 + 0.520096i \(0.825896\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14.9519 −0.0722096
\(36\) 0 0
\(37\) −104.177 −0.462883 −0.231441 0.972849i \(-0.574344\pi\)
−0.231441 + 0.972849i \(0.574344\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −307.645 −1.17186 −0.585928 0.810363i \(-0.699270\pi\)
−0.585928 + 0.810363i \(0.699270\pi\)
\(42\) 0 0
\(43\) 361.081 1.28057 0.640283 0.768139i \(-0.278817\pi\)
0.640283 + 0.768139i \(0.278817\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 397.645 1.23410 0.617048 0.786926i \(-0.288328\pi\)
0.617048 + 0.786926i \(0.288328\pi\)
\(48\) 0 0
\(49\) −342.323 −0.998027
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −107.161 −0.277730 −0.138865 0.990311i \(-0.544345\pi\)
−0.138865 + 0.990311i \(0.544345\pi\)
\(54\) 0 0
\(55\) 1191.21 2.92041
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 188.935 0.416903 0.208452 0.978033i \(-0.433158\pi\)
0.208452 + 0.978033i \(0.433158\pi\)
\(60\) 0 0
\(61\) −99.0166 −0.207832 −0.103916 0.994586i \(-0.533137\pi\)
−0.103916 + 0.994586i \(0.533137\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −578.453 −1.10382
\(66\) 0 0
\(67\) −425.048 −0.775043 −0.387522 0.921861i \(-0.626669\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −445.532 −0.744718 −0.372359 0.928089i \(-0.621451\pi\)
−0.372359 + 0.928089i \(0.621451\pi\)
\(72\) 0 0
\(73\) −499.806 −0.801341 −0.400670 0.916222i \(-0.631223\pi\)
−0.400670 + 0.916222i \(0.631223\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −53.9038 −0.0797781
\(78\) 0 0
\(79\) −570.275 −0.812164 −0.406082 0.913837i \(-0.633105\pi\)
−0.406082 + 0.913837i \(0.633105\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1308.74 1.73076 0.865381 0.501115i \(-0.167077\pi\)
0.865381 + 0.501115i \(0.167077\pi\)
\(84\) 0 0
\(85\) 2261.63 2.88598
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1323.00 −1.57570 −0.787852 0.615864i \(-0.788807\pi\)
−0.787852 + 0.615864i \(0.788807\pi\)
\(90\) 0 0
\(91\) 26.1757 0.0301534
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 506.919 0.547461
\(96\) 0 0
\(97\) 944.872 0.989044 0.494522 0.869165i \(-0.335343\pi\)
0.494522 + 0.869165i \(0.335343\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1398.10 1.37739 0.688694 0.725052i \(-0.258185\pi\)
0.688694 + 0.725052i \(0.258185\pi\)
\(102\) 0 0
\(103\) 960.551 0.918892 0.459446 0.888206i \(-0.348048\pi\)
0.459446 + 0.888206i \(0.348048\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1935.87 1.74905 0.874523 0.484983i \(-0.161174\pi\)
0.874523 + 0.484983i \(0.161174\pi\)
\(108\) 0 0
\(109\) −1305.40 −1.14711 −0.573555 0.819167i \(-0.694436\pi\)
−0.573555 + 0.819167i \(0.694436\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1094.03 −0.910777 −0.455389 0.890293i \(-0.650500\pi\)
−0.455389 + 0.890293i \(0.650500\pi\)
\(114\) 0 0
\(115\) 784.856 0.636419
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −102.342 −0.0788374
\(120\) 0 0
\(121\) 2963.49 2.22651
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1461.82 −1.04600
\(126\) 0 0
\(127\) 1301.05 0.909050 0.454525 0.890734i \(-0.349809\pi\)
0.454525 + 0.890734i \(0.349809\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1957.67 1.30566 0.652832 0.757503i \(-0.273581\pi\)
0.652832 + 0.757503i \(0.273581\pi\)
\(132\) 0 0
\(133\) −22.9387 −0.0149552
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2553.97 1.59270 0.796351 0.604834i \(-0.206761\pi\)
0.796351 + 0.604834i \(0.206761\pi\)
\(138\) 0 0
\(139\) −205.260 −0.125252 −0.0626258 0.998037i \(-0.519947\pi\)
−0.0626258 + 0.998037i \(0.519947\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2085.41 −1.21951
\(144\) 0 0
\(145\) 723.872 0.414582
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −164.240 −0.0903027 −0.0451513 0.998980i \(-0.514377\pi\)
−0.0451513 + 0.998980i \(0.514377\pi\)
\(150\) 0 0
\(151\) −3427.71 −1.84731 −0.923654 0.383228i \(-0.874812\pi\)
−0.923654 + 0.383228i \(0.874812\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5359.42 2.77729
\(156\) 0 0
\(157\) −988.085 −0.502279 −0.251139 0.967951i \(-0.580805\pi\)
−0.251139 + 0.967951i \(0.580805\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −35.5157 −0.0173853
\(162\) 0 0
\(163\) 2845.45 1.36732 0.683660 0.729801i \(-0.260387\pi\)
0.683660 + 0.729801i \(0.260387\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3205.89 −1.48550 −0.742752 0.669566i \(-0.766480\pi\)
−0.742752 + 0.669566i \(0.766480\pi\)
\(168\) 0 0
\(169\) −1184.33 −0.539065
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1785.63 −0.784735 −0.392368 0.919808i \(-0.628344\pi\)
−0.392368 + 0.919808i \(0.628344\pi\)
\(174\) 0 0
\(175\) 168.969 0.0729875
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1318.84 −0.550696 −0.275348 0.961345i \(-0.588793\pi\)
−0.275348 + 0.961345i \(0.588793\pi\)
\(180\) 0 0
\(181\) 3462.97 1.42210 0.711051 0.703141i \(-0.248220\pi\)
0.711051 + 0.703141i \(0.248220\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1893.68 0.752574
\(186\) 0 0
\(187\) 8153.51 3.18847
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1591.31 0.602844 0.301422 0.953491i \(-0.402539\pi\)
0.301422 + 0.953491i \(0.402539\pi\)
\(192\) 0 0
\(193\) −764.456 −0.285113 −0.142556 0.989787i \(-0.545532\pi\)
−0.142556 + 0.989787i \(0.545532\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1191.63 −0.430965 −0.215483 0.976508i \(-0.569132\pi\)
−0.215483 + 0.976508i \(0.569132\pi\)
\(198\) 0 0
\(199\) 2708.20 0.964719 0.482360 0.875973i \(-0.339780\pi\)
0.482360 + 0.875973i \(0.339780\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −32.7562 −0.0113253
\(204\) 0 0
\(205\) 5592.20 1.90525
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1827.52 0.604842
\(210\) 0 0
\(211\) 3298.95 1.07635 0.538173 0.842834i \(-0.319115\pi\)
0.538173 + 0.842834i \(0.319115\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6563.54 −2.08200
\(216\) 0 0
\(217\) −242.521 −0.0758682
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3959.35 −1.20513
\(222\) 0 0
\(223\) 2521.67 0.757234 0.378617 0.925553i \(-0.376400\pi\)
0.378617 + 0.925553i \(0.376400\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3314.67 −0.969173 −0.484586 0.874743i \(-0.661030\pi\)
−0.484586 + 0.874743i \(0.661030\pi\)
\(228\) 0 0
\(229\) −4129.66 −1.19168 −0.595842 0.803101i \(-0.703182\pi\)
−0.595842 + 0.803101i \(0.703182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −986.257 −0.277304 −0.138652 0.990341i \(-0.544277\pi\)
−0.138652 + 0.990341i \(0.544277\pi\)
\(234\) 0 0
\(235\) −7228.17 −2.00644
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 358.998 0.0971618 0.0485809 0.998819i \(-0.484530\pi\)
0.0485809 + 0.998819i \(0.484530\pi\)
\(240\) 0 0
\(241\) 2042.03 0.545804 0.272902 0.962042i \(-0.412016\pi\)
0.272902 + 0.962042i \(0.412016\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6222.57 1.62263
\(246\) 0 0
\(247\) −887.443 −0.228610
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2609.69 −0.656264 −0.328132 0.944632i \(-0.606419\pi\)
−0.328132 + 0.944632i \(0.606419\pi\)
\(252\) 0 0
\(253\) 2829.52 0.703124
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 878.837 0.213309 0.106654 0.994296i \(-0.465986\pi\)
0.106654 + 0.994296i \(0.465986\pi\)
\(258\) 0 0
\(259\) −85.6915 −0.0205583
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3217.33 −0.754332 −0.377166 0.926146i \(-0.623101\pi\)
−0.377166 + 0.926146i \(0.623101\pi\)
\(264\) 0 0
\(265\) 1947.91 0.451544
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7978.38 −1.80837 −0.904183 0.427146i \(-0.859519\pi\)
−0.904183 + 0.427146i \(0.859519\pi\)
\(270\) 0 0
\(271\) −4248.21 −0.952251 −0.476126 0.879377i \(-0.657959\pi\)
−0.476126 + 0.879377i \(0.657959\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13461.6 −2.95188
\(276\) 0 0
\(277\) 831.035 0.180260 0.0901301 0.995930i \(-0.471272\pi\)
0.0901301 + 0.995930i \(0.471272\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2962.00 0.628819 0.314410 0.949287i \(-0.398193\pi\)
0.314410 + 0.949287i \(0.398193\pi\)
\(282\) 0 0
\(283\) 4430.84 0.930693 0.465346 0.885129i \(-0.345930\pi\)
0.465346 + 0.885129i \(0.345930\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −253.054 −0.0520465
\(288\) 0 0
\(289\) 10567.2 2.15087
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3422.86 0.682477 0.341239 0.939977i \(-0.389154\pi\)
0.341239 + 0.939977i \(0.389154\pi\)
\(294\) 0 0
\(295\) −3434.36 −0.677818
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1374.02 −0.265757
\(300\) 0 0
\(301\) 297.009 0.0568747
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1799.87 0.337902
\(306\) 0 0
\(307\) −139.734 −0.0259774 −0.0129887 0.999916i \(-0.504135\pi\)
−0.0129887 + 0.999916i \(0.504135\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7599.88 1.38569 0.692845 0.721086i \(-0.256357\pi\)
0.692845 + 0.721086i \(0.256357\pi\)
\(312\) 0 0
\(313\) −3017.52 −0.544921 −0.272460 0.962167i \(-0.587837\pi\)
−0.272460 + 0.962167i \(0.587837\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1921.21 0.340396 0.170198 0.985410i \(-0.445559\pi\)
0.170198 + 0.985410i \(0.445559\pi\)
\(318\) 0 0
\(319\) 2609.67 0.458035
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3469.72 0.597710
\(324\) 0 0
\(325\) 6536.98 1.11571
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 327.084 0.0548108
\(330\) 0 0
\(331\) −912.412 −0.151513 −0.0757563 0.997126i \(-0.524137\pi\)
−0.0757563 + 0.997126i \(0.524137\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7726.29 1.26010
\(336\) 0 0
\(337\) −6014.62 −0.972218 −0.486109 0.873898i \(-0.661584\pi\)
−0.486109 + 0.873898i \(0.661584\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 19321.5 3.06838
\(342\) 0 0
\(343\) −563.715 −0.0887398
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2739.83 0.423867 0.211934 0.977284i \(-0.432024\pi\)
0.211934 + 0.977284i \(0.432024\pi\)
\(348\) 0 0
\(349\) −7608.69 −1.16700 −0.583501 0.812112i \(-0.698318\pi\)
−0.583501 + 0.812112i \(0.698318\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8725.11 1.31555 0.657777 0.753212i \(-0.271497\pi\)
0.657777 + 0.753212i \(0.271497\pi\)
\(354\) 0 0
\(355\) 8098.64 1.21079
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10470.0 −1.53923 −0.769614 0.638509i \(-0.779551\pi\)
−0.769614 + 0.638509i \(0.779551\pi\)
\(360\) 0 0
\(361\) −6081.30 −0.886616
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9085.20 1.30285
\(366\) 0 0
\(367\) 7894.14 1.12281 0.561405 0.827542i \(-0.310261\pi\)
0.561405 + 0.827542i \(0.310261\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −88.1455 −0.0123350
\(372\) 0 0
\(373\) −269.940 −0.0374718 −0.0187359 0.999824i \(-0.505964\pi\)
−0.0187359 + 0.999824i \(0.505964\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1267.26 −0.173122
\(378\) 0 0
\(379\) 8580.72 1.16296 0.581480 0.813561i \(-0.302474\pi\)
0.581480 + 0.813561i \(0.302474\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3414.93 0.455599 0.227800 0.973708i \(-0.426847\pi\)
0.227800 + 0.973708i \(0.426847\pi\)
\(384\) 0 0
\(385\) 979.834 0.129706
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3304.00 −0.430642 −0.215321 0.976543i \(-0.569080\pi\)
−0.215321 + 0.976543i \(0.569080\pi\)
\(390\) 0 0
\(391\) 5372.12 0.694833
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10366.1 1.32045
\(396\) 0 0
\(397\) −12756.1 −1.61262 −0.806311 0.591492i \(-0.798539\pi\)
−0.806311 + 0.591492i \(0.798539\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4628.52 0.576402 0.288201 0.957570i \(-0.406943\pi\)
0.288201 + 0.957570i \(0.406943\pi\)
\(402\) 0 0
\(403\) −9382.53 −1.15975
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6826.99 0.831453
\(408\) 0 0
\(409\) −2965.55 −0.358526 −0.179263 0.983801i \(-0.557371\pi\)
−0.179263 + 0.983801i \(0.557371\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 155.409 0.0185162
\(414\) 0 0
\(415\) −23789.6 −2.81394
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1870.26 −0.218063 −0.109031 0.994038i \(-0.534775\pi\)
−0.109031 + 0.994038i \(0.534775\pi\)
\(420\) 0 0
\(421\) −12650.6 −1.46450 −0.732248 0.681038i \(-0.761529\pi\)
−0.732248 + 0.681038i \(0.761529\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −25558.2 −2.91707
\(426\) 0 0
\(427\) −81.4464 −0.00923060
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3266.47 0.365059 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(432\) 0 0
\(433\) 6788.95 0.753478 0.376739 0.926319i \(-0.377045\pi\)
0.376739 + 0.926319i \(0.377045\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1204.10 0.131808
\(438\) 0 0
\(439\) −4918.55 −0.534737 −0.267368 0.963594i \(-0.586154\pi\)
−0.267368 + 0.963594i \(0.586154\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14033.5 −1.50508 −0.752540 0.658546i \(-0.771172\pi\)
−0.752540 + 0.658546i \(0.771172\pi\)
\(444\) 0 0
\(445\) 24048.8 2.56184
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5374.04 0.564848 0.282424 0.959290i \(-0.408862\pi\)
0.282424 + 0.959290i \(0.408862\pi\)
\(450\) 0 0
\(451\) 20160.7 2.10495
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −475.808 −0.0490247
\(456\) 0 0
\(457\) 12169.2 1.24563 0.622815 0.782369i \(-0.285989\pi\)
0.622815 + 0.782369i \(0.285989\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6186.08 0.624977 0.312489 0.949922i \(-0.398837\pi\)
0.312489 + 0.949922i \(0.398837\pi\)
\(462\) 0 0
\(463\) −15197.8 −1.52549 −0.762743 0.646701i \(-0.776148\pi\)
−0.762743 + 0.646701i \(0.776148\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1981.82 0.196377 0.0981883 0.995168i \(-0.468695\pi\)
0.0981883 + 0.995168i \(0.468695\pi\)
\(468\) 0 0
\(469\) −349.625 −0.0344225
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23662.5 −2.30022
\(474\) 0 0
\(475\) −5728.58 −0.553359
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9779.52 −0.932855 −0.466427 0.884559i \(-0.654459\pi\)
−0.466427 + 0.884559i \(0.654459\pi\)
\(480\) 0 0
\(481\) −3315.19 −0.314261
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17175.4 −1.60803
\(486\) 0 0
\(487\) −18668.9 −1.73710 −0.868549 0.495603i \(-0.834947\pi\)
−0.868549 + 0.495603i \(0.834947\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16006.2 −1.47118 −0.735591 0.677426i \(-0.763095\pi\)
−0.735591 + 0.677426i \(0.763095\pi\)
\(492\) 0 0
\(493\) 4954.71 0.452634
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −366.474 −0.0330757
\(498\) 0 0
\(499\) −9860.57 −0.884609 −0.442304 0.896865i \(-0.645839\pi\)
−0.442304 + 0.896865i \(0.645839\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10512.0 0.931825 0.465913 0.884831i \(-0.345726\pi\)
0.465913 + 0.884831i \(0.345726\pi\)
\(504\) 0 0
\(505\) −25413.9 −2.23941
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16667.3 −1.45140 −0.725700 0.688011i \(-0.758484\pi\)
−0.725700 + 0.688011i \(0.758484\pi\)
\(510\) 0 0
\(511\) −411.117 −0.0355905
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17460.4 −1.49397
\(516\) 0 0
\(517\) −26058.6 −2.21674
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10923.9 −0.918586 −0.459293 0.888285i \(-0.651897\pi\)
−0.459293 + 0.888285i \(0.651897\pi\)
\(522\) 0 0
\(523\) 17488.0 1.46213 0.731067 0.682305i \(-0.239022\pi\)
0.731067 + 0.682305i \(0.239022\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 36683.8 3.03220
\(528\) 0 0
\(529\) −10302.7 −0.846775
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9790.05 −0.795599
\(534\) 0 0
\(535\) −35189.2 −2.84367
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22433.3 1.79271
\(540\) 0 0
\(541\) −8724.14 −0.693309 −0.346655 0.937993i \(-0.612682\pi\)
−0.346655 + 0.937993i \(0.612682\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 23728.9 1.86502
\(546\) 0 0
\(547\) 959.834 0.0750266 0.0375133 0.999296i \(-0.488056\pi\)
0.0375133 + 0.999296i \(0.488056\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1110.54 0.0858632
\(552\) 0 0
\(553\) −469.082 −0.0360712
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14212.0 1.08112 0.540558 0.841307i \(-0.318213\pi\)
0.540558 + 0.841307i \(0.318213\pi\)
\(558\) 0 0
\(559\) 11490.5 0.869405
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7110.56 −0.532281 −0.266141 0.963934i \(-0.585749\pi\)
−0.266141 + 0.963934i \(0.585749\pi\)
\(564\) 0 0
\(565\) 19886.7 1.48078
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4859.18 −0.358010 −0.179005 0.983848i \(-0.557288\pi\)
−0.179005 + 0.983848i \(0.557288\pi\)
\(570\) 0 0
\(571\) −8580.29 −0.628851 −0.314425 0.949282i \(-0.601812\pi\)
−0.314425 + 0.949282i \(0.601812\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8869.49 −0.643276
\(576\) 0 0
\(577\) −1029.99 −0.0743136 −0.0371568 0.999309i \(-0.511830\pi\)
−0.0371568 + 0.999309i \(0.511830\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1076.51 0.0768695
\(582\) 0 0
\(583\) 7022.50 0.498872
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15541.4 1.09278 0.546391 0.837530i \(-0.316001\pi\)
0.546391 + 0.837530i \(0.316001\pi\)
\(588\) 0 0
\(589\) 8222.25 0.575198
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12643.5 0.875562 0.437781 0.899082i \(-0.355765\pi\)
0.437781 + 0.899082i \(0.355765\pi\)
\(594\) 0 0
\(595\) 1860.31 0.128177
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17162.9 1.17071 0.585357 0.810776i \(-0.300954\pi\)
0.585357 + 0.810776i \(0.300954\pi\)
\(600\) 0 0
\(601\) −4010.19 −0.272178 −0.136089 0.990697i \(-0.543453\pi\)
−0.136089 + 0.990697i \(0.543453\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −53868.6 −3.61995
\(606\) 0 0
\(607\) −17321.2 −1.15823 −0.579114 0.815247i \(-0.696601\pi\)
−0.579114 + 0.815247i \(0.696601\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12654.1 0.837855
\(612\) 0 0
\(613\) 2474.79 0.163060 0.0815300 0.996671i \(-0.474019\pi\)
0.0815300 + 0.996671i \(0.474019\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11844.4 −0.772831 −0.386416 0.922325i \(-0.626287\pi\)
−0.386416 + 0.922325i \(0.626287\pi\)
\(618\) 0 0
\(619\) 7848.64 0.509634 0.254817 0.966989i \(-0.417985\pi\)
0.254817 + 0.966989i \(0.417985\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1088.24 −0.0699829
\(624\) 0 0
\(625\) 894.755 0.0572643
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12961.7 0.821649
\(630\) 0 0
\(631\) 11346.0 0.715811 0.357906 0.933758i \(-0.383491\pi\)
0.357906 + 0.933758i \(0.383491\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −23649.7 −1.47797
\(636\) 0 0
\(637\) −10893.6 −0.677583
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17585.2 −1.08358 −0.541791 0.840513i \(-0.682253\pi\)
−0.541791 + 0.840513i \(0.682253\pi\)
\(642\) 0 0
\(643\) 10644.9 0.652866 0.326433 0.945220i \(-0.394153\pi\)
0.326433 + 0.945220i \(0.394153\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7872.89 0.478385 0.239193 0.970972i \(-0.423117\pi\)
0.239193 + 0.970972i \(0.423117\pi\)
\(648\) 0 0
\(649\) −12381.4 −0.748862
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2721.08 0.163069 0.0815347 0.996671i \(-0.474018\pi\)
0.0815347 + 0.996671i \(0.474018\pi\)
\(654\) 0 0
\(655\) −35585.4 −2.12280
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2000.76 −0.118268 −0.0591338 0.998250i \(-0.518834\pi\)
−0.0591338 + 0.998250i \(0.518834\pi\)
\(660\) 0 0
\(661\) −27738.0 −1.63220 −0.816100 0.577911i \(-0.803868\pi\)
−0.816100 + 0.577911i \(0.803868\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 416.968 0.0243148
\(666\) 0 0
\(667\) 1719.44 0.0998153
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6488.79 0.373319
\(672\) 0 0
\(673\) −24693.0 −1.41433 −0.707166 0.707047i \(-0.750027\pi\)
−0.707166 + 0.707047i \(0.750027\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14764.7 0.838189 0.419095 0.907943i \(-0.362348\pi\)
0.419095 + 0.907943i \(0.362348\pi\)
\(678\) 0 0
\(679\) 777.208 0.0439271
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 571.548 0.0320200 0.0160100 0.999872i \(-0.494904\pi\)
0.0160100 + 0.999872i \(0.494904\pi\)
\(684\) 0 0
\(685\) −46424.6 −2.58948
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3410.13 −0.188557
\(690\) 0 0
\(691\) 3507.58 0.193104 0.0965519 0.995328i \(-0.469219\pi\)
0.0965519 + 0.995328i \(0.469219\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3731.11 0.203639
\(696\) 0 0
\(697\) 38277.1 2.08013
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −21145.2 −1.13929 −0.569644 0.821891i \(-0.692919\pi\)
−0.569644 + 0.821891i \(0.692919\pi\)
\(702\) 0 0
\(703\) 2905.22 0.155864
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1150.01 0.0611749
\(708\) 0 0
\(709\) −15815.2 −0.837734 −0.418867 0.908048i \(-0.637573\pi\)
−0.418867 + 0.908048i \(0.637573\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12730.4 0.668664
\(714\) 0 0
\(715\) 37907.4 1.98273
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −33309.8 −1.72774 −0.863871 0.503713i \(-0.831967\pi\)
−0.863871 + 0.503713i \(0.831967\pi\)
\(720\) 0 0
\(721\) 790.104 0.0408114
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8180.33 −0.419048
\(726\) 0 0
\(727\) −7037.29 −0.359008 −0.179504 0.983757i \(-0.557449\pi\)
−0.179504 + 0.983757i \(0.557449\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −44925.6 −2.27310
\(732\) 0 0
\(733\) 12661.3 0.638000 0.319000 0.947755i \(-0.396653\pi\)
0.319000 + 0.947755i \(0.396653\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27854.4 1.39217
\(738\) 0 0
\(739\) −32709.4 −1.62819 −0.814096 0.580730i \(-0.802767\pi\)
−0.814096 + 0.580730i \(0.802767\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29381.2 1.45073 0.725364 0.688365i \(-0.241671\pi\)
0.725364 + 0.688365i \(0.241671\pi\)
\(744\) 0 0
\(745\) 2985.47 0.146818
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1592.36 0.0776816
\(750\) 0 0
\(751\) −2225.64 −0.108142 −0.0540712 0.998537i \(-0.517220\pi\)
−0.0540712 + 0.998537i \(0.517220\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 62307.1 3.00343
\(756\) 0 0
\(757\) 32628.1 1.56656 0.783281 0.621668i \(-0.213545\pi\)
0.783281 + 0.621668i \(0.213545\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18690.6 0.890322 0.445161 0.895451i \(-0.353146\pi\)
0.445161 + 0.895451i \(0.353146\pi\)
\(762\) 0 0
\(763\) −1073.76 −0.0509474
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6012.40 0.283045
\(768\) 0 0
\(769\) 6845.67 0.321016 0.160508 0.987035i \(-0.448687\pi\)
0.160508 + 0.987035i \(0.448687\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −161.873 −0.00753190 −0.00376595 0.999993i \(-0.501199\pi\)
−0.00376595 + 0.999993i \(0.501199\pi\)
\(774\) 0 0
\(775\) −60565.7 −2.80721
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8579.37 0.394593
\(780\) 0 0
\(781\) 29196.8 1.33770
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17960.9 0.816625
\(786\) 0 0
\(787\) −9959.12 −0.451085 −0.225543 0.974233i \(-0.572416\pi\)
−0.225543 + 0.974233i \(0.572416\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −899.899 −0.0404510
\(792\) 0 0
\(793\) −3150.96 −0.141102
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4656.36 −0.206947 −0.103473 0.994632i \(-0.532996\pi\)
−0.103473 + 0.994632i \(0.532996\pi\)
\(798\) 0 0
\(799\) −49474.8 −2.19061
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 32753.5 1.43941
\(804\) 0 0
\(805\) 645.586 0.0282657
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 173.564 0.00754289 0.00377144 0.999993i \(-0.498800\pi\)
0.00377144 + 0.999993i \(0.498800\pi\)
\(810\) 0 0
\(811\) 22674.1 0.981744 0.490872 0.871232i \(-0.336678\pi\)
0.490872 + 0.871232i \(0.336678\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −51723.1 −2.22304
\(816\) 0 0
\(817\) −10069.6 −0.431199
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 40832.2 1.73575 0.867877 0.496779i \(-0.165484\pi\)
0.867877 + 0.496779i \(0.165484\pi\)
\(822\) 0 0
\(823\) 4881.01 0.206733 0.103367 0.994643i \(-0.467039\pi\)
0.103367 + 0.994643i \(0.467039\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22213.4 0.934022 0.467011 0.884251i \(-0.345331\pi\)
0.467011 + 0.884251i \(0.345331\pi\)
\(828\) 0 0
\(829\) 35477.2 1.48634 0.743168 0.669104i \(-0.233322\pi\)
0.743168 + 0.669104i \(0.233322\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 42591.7 1.77157
\(834\) 0 0
\(835\) 58274.9 2.41519
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −23505.3 −0.967213 −0.483607 0.875285i \(-0.660673\pi\)
−0.483607 + 0.875285i \(0.660673\pi\)
\(840\) 0 0
\(841\) −22803.2 −0.934977
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 21528.0 0.876433
\(846\) 0 0
\(847\) 2437.63 0.0988876
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4498.12 0.181191
\(852\) 0 0
\(853\) −12434.1 −0.499103 −0.249551 0.968362i \(-0.580283\pi\)
−0.249551 + 0.968362i \(0.580283\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 795.866 0.0317226 0.0158613 0.999874i \(-0.494951\pi\)
0.0158613 + 0.999874i \(0.494951\pi\)
\(858\) 0 0
\(859\) 8583.95 0.340955 0.170478 0.985362i \(-0.445469\pi\)
0.170478 + 0.985362i \(0.445469\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −37865.4 −1.49357 −0.746787 0.665063i \(-0.768405\pi\)
−0.746787 + 0.665063i \(0.768405\pi\)
\(864\) 0 0
\(865\) 32458.3 1.27585
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 37371.5 1.45885
\(870\) 0 0
\(871\) −13526.1 −0.526194
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1202.43 −0.0464565
\(876\) 0 0
\(877\) 4604.56 0.177292 0.0886459 0.996063i \(-0.471746\pi\)
0.0886459 + 0.996063i \(0.471746\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −13021.9 −0.497979 −0.248990 0.968506i \(-0.580099\pi\)
−0.248990 + 0.968506i \(0.580099\pi\)
\(882\) 0 0
\(883\) 4301.10 0.163923 0.0819613 0.996636i \(-0.473882\pi\)
0.0819613 + 0.996636i \(0.473882\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 15195.8 0.575225 0.287613 0.957747i \(-0.407138\pi\)
0.287613 + 0.957747i \(0.407138\pi\)
\(888\) 0 0
\(889\) 1070.18 0.0403743
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −11089.2 −0.415551
\(894\) 0 0
\(895\) 23973.1 0.895344
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 11741.2 0.435587
\(900\) 0 0
\(901\) 13332.9 0.492990
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −62947.9 −2.31211
\(906\) 0 0
\(907\) 4657.99 0.170525 0.0852624 0.996359i \(-0.472827\pi\)
0.0852624 + 0.996359i \(0.472827\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12892.8 −0.468889 −0.234444 0.972130i \(-0.575327\pi\)
−0.234444 + 0.972130i \(0.575327\pi\)
\(912\) 0 0
\(913\) −85765.0 −3.10888
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1610.28 0.0579894
\(918\) 0 0
\(919\) 36405.3 1.30675 0.653373 0.757036i \(-0.273353\pi\)
0.653373 + 0.757036i \(0.273353\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14178.0 −0.505605
\(924\) 0 0
\(925\) −21400.1 −0.760682
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4279.70 −0.151143 −0.0755717 0.997140i \(-0.524078\pi\)
−0.0755717 + 0.997140i \(0.524078\pi\)
\(930\) 0 0
\(931\) 9546.45 0.336061
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −148210. −5.18394
\(936\) 0 0
\(937\) 21006.6 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 13529.1 0.468688 0.234344 0.972154i \(-0.424706\pi\)
0.234344 + 0.972154i \(0.424706\pi\)
\(942\) 0 0
\(943\) 13283.3 0.458711
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4153.14 −0.142512 −0.0712561 0.997458i \(-0.522701\pi\)
−0.0712561 + 0.997458i \(0.522701\pi\)
\(948\) 0 0
\(949\) −15905.1 −0.544048
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 18387.5 0.625005 0.312503 0.949917i \(-0.398833\pi\)
0.312503 + 0.949917i \(0.398833\pi\)
\(954\) 0 0
\(955\) −28926.0 −0.980128
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2100.77 0.0707378
\(960\) 0 0
\(961\) 57139.1 1.91800
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13895.9 0.463548
\(966\) 0 0
\(967\) 34454.1 1.14578 0.572889 0.819633i \(-0.305822\pi\)
0.572889 + 0.819633i \(0.305822\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2689.17 −0.0888770 −0.0444385 0.999012i \(-0.514150\pi\)
−0.0444385 + 0.999012i \(0.514150\pi\)
\(972\) 0 0
\(973\) −168.838 −0.00556288
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −148.959 −0.00487782 −0.00243891 0.999997i \(-0.500776\pi\)
−0.00243891 + 0.999997i \(0.500776\pi\)
\(978\) 0 0
\(979\) 86699.3 2.83036
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 32221.8 1.04549 0.522744 0.852490i \(-0.324908\pi\)
0.522744 + 0.852490i \(0.324908\pi\)
\(984\) 0 0
\(985\) 21660.8 0.700681
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −15590.6 −0.501265
\(990\) 0 0
\(991\) −2979.37 −0.0955023 −0.0477512 0.998859i \(-0.515205\pi\)
−0.0477512 + 0.998859i \(0.515205\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −49228.1 −1.56848
\(996\) 0 0
\(997\) −32093.8 −1.01948 −0.509740 0.860328i \(-0.670258\pi\)
−0.509740 + 0.860328i \(0.670258\pi\)
\(998\) 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 1296.4.a.m.1.1 2
3.2 odd 2 1296.4.a.q.1.2 2
4.3 odd 2 648.4.a.c.1.1 2
12.11 even 2 648.4.a.f.1.2 yes 2
36.7 odd 6 648.4.i.t.433.2 4
36.11 even 6 648.4.i.n.433.1 4
36.23 even 6 648.4.i.n.217.1 4
36.31 odd 6 648.4.i.t.217.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.4.a.c.1.1 2 4.3 odd 2
648.4.a.f.1.2 yes 2 12.11 even 2
648.4.i.n.217.1 4 36.23 even 6
648.4.i.n.433.1 4 36.11 even 6
648.4.i.t.217.2 4 36.31 odd 6
648.4.i.t.433.2 4 36.7 odd 6
1296.4.a.m.1.1 2 1.1 even 1 trivial
1296.4.a.q.1.2 2 3.2 odd 2