Properties

Label 1008.6.a.i.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-26.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-26.0000 q^{5} +49.0000 q^{7} -470.000 q^{11} +642.000 q^{13} +1010.00 q^{17} -1532.00 q^{19} +430.000 q^{23} -2449.00 q^{25} +6736.00 q^{29} -2268.00 q^{31} -1274.00 q^{35} -9574.00 q^{37} +14406.0 q^{41} +9748.00 q^{43} -17004.0 q^{47} +2401.00 q^{49} +7596.00 q^{53} +12220.0 q^{55} +18908.0 q^{59} -36762.0 q^{61} -16692.0 q^{65} +36788.0 q^{67} -18326.0 q^{71} +36382.0 q^{73} -23030.0 q^{77} -29784.0 q^{79} +28240.0 q^{83} -26260.0 q^{85} -75954.0 q^{89} +31458.0 q^{91} +39832.0 q^{95} -80690.0 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −26.0000 −0.465102 −0.232551 0.972584i \(-0.574707\pi\)
−0.232551 + 0.972584i \(0.574707\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −470.000 −1.17116 −0.585580 0.810615i \(-0.699133\pi\)
−0.585580 + 0.810615i \(0.699133\pi\)
\(12\) 0 0
\(13\) 642.000 1.05360 0.526801 0.849989i \(-0.323391\pi\)
0.526801 + 0.849989i \(0.323391\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1010.00 0.847616 0.423808 0.905752i \(-0.360693\pi\)
0.423808 + 0.905752i \(0.360693\pi\)
\(18\) 0 0
\(19\) −1532.00 −0.973587 −0.486793 0.873517i \(-0.661834\pi\)
−0.486793 + 0.873517i \(0.661834\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 430.000 0.169492 0.0847459 0.996403i \(-0.472992\pi\)
0.0847459 + 0.996403i \(0.472992\pi\)
\(24\) 0 0
\(25\) −2449.00 −0.783680
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6736.00 1.48733 0.743665 0.668553i \(-0.233086\pi\)
0.743665 + 0.668553i \(0.233086\pi\)
\(30\) 0 0
\(31\) −2268.00 −0.423876 −0.211938 0.977283i \(-0.567977\pi\)
−0.211938 + 0.977283i \(0.567977\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1274.00 −0.175792
\(36\) 0 0
\(37\) −9574.00 −1.14971 −0.574856 0.818255i \(-0.694942\pi\)
−0.574856 + 0.818255i \(0.694942\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 14406.0 1.33839 0.669197 0.743085i \(-0.266638\pi\)
0.669197 + 0.743085i \(0.266638\pi\)
\(42\) 0 0
\(43\) 9748.00 0.803978 0.401989 0.915644i \(-0.368319\pi\)
0.401989 + 0.915644i \(0.368319\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −17004.0 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7596.00 0.371446 0.185723 0.982602i \(-0.440537\pi\)
0.185723 + 0.982602i \(0.440537\pi\)
\(54\) 0 0
\(55\) 12220.0 0.544709
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 18908.0 0.707157 0.353578 0.935405i \(-0.384965\pi\)
0.353578 + 0.935405i \(0.384965\pi\)
\(60\) 0 0
\(61\) −36762.0 −1.26495 −0.632477 0.774579i \(-0.717962\pi\)
−0.632477 + 0.774579i \(0.717962\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −16692.0 −0.490033
\(66\) 0 0
\(67\) 36788.0 1.00120 0.500598 0.865680i \(-0.333113\pi\)
0.500598 + 0.865680i \(0.333113\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −18326.0 −0.431441 −0.215721 0.976455i \(-0.569210\pi\)
−0.215721 + 0.976455i \(0.569210\pi\)
\(72\) 0 0
\(73\) 36382.0 0.799060 0.399530 0.916720i \(-0.369173\pi\)
0.399530 + 0.916720i \(0.369173\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −23030.0 −0.442657
\(78\) 0 0
\(79\) −29784.0 −0.536927 −0.268464 0.963290i \(-0.586516\pi\)
−0.268464 + 0.963290i \(0.586516\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 28240.0 0.449955 0.224978 0.974364i \(-0.427769\pi\)
0.224978 + 0.974364i \(0.427769\pi\)
\(84\) 0 0
\(85\) −26260.0 −0.394228
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −75954.0 −1.01643 −0.508213 0.861232i \(-0.669694\pi\)
−0.508213 + 0.861232i \(0.669694\pi\)
\(90\) 0 0
\(91\) 31458.0 0.398224
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 39832.0 0.452817
\(96\) 0 0
\(97\) −80690.0 −0.870744 −0.435372 0.900251i \(-0.643383\pi\)
−0.435372 + 0.900251i \(0.643383\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 31306.0 0.305368 0.152684 0.988275i \(-0.451208\pi\)
0.152684 + 0.988275i \(0.451208\pi\)
\(102\) 0 0
\(103\) −102908. −0.955776 −0.477888 0.878421i \(-0.658598\pi\)
−0.477888 + 0.878421i \(0.658598\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 172482. 1.45641 0.728206 0.685358i \(-0.240354\pi\)
0.728206 + 0.685358i \(0.240354\pi\)
\(108\) 0 0
\(109\) −135470. −1.09214 −0.546068 0.837741i \(-0.683876\pi\)
−0.546068 + 0.837741i \(0.683876\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −135632. −0.999231 −0.499616 0.866247i \(-0.666525\pi\)
−0.499616 + 0.866247i \(0.666525\pi\)
\(114\) 0 0
\(115\) −11180.0 −0.0788310
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 49490.0 0.320369
\(120\) 0 0
\(121\) 59849.0 0.371615
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 144924. 0.829593
\(126\) 0 0
\(127\) 275976. 1.51832 0.759158 0.650907i \(-0.225611\pi\)
0.759158 + 0.650907i \(0.225611\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −50488.0 −0.257045 −0.128523 0.991707i \(-0.541024\pi\)
−0.128523 + 0.991707i \(0.541024\pi\)
\(132\) 0 0
\(133\) −75068.0 −0.367981
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 137212. 0.624584 0.312292 0.949986i \(-0.398903\pi\)
0.312292 + 0.949986i \(0.398903\pi\)
\(138\) 0 0
\(139\) −21040.0 −0.0923653 −0.0461826 0.998933i \(-0.514706\pi\)
−0.0461826 + 0.998933i \(0.514706\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −301740. −1.23394
\(144\) 0 0
\(145\) −175136. −0.691760
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 240468. 0.887343 0.443672 0.896189i \(-0.353676\pi\)
0.443672 + 0.896189i \(0.353676\pi\)
\(150\) 0 0
\(151\) −325048. −1.16013 −0.580063 0.814572i \(-0.696972\pi\)
−0.580063 + 0.814572i \(0.696972\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 58968.0 0.197146
\(156\) 0 0
\(157\) 537734. 1.74108 0.870539 0.492099i \(-0.163770\pi\)
0.870539 + 0.492099i \(0.163770\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 21070.0 0.0640619
\(162\) 0 0
\(163\) −403748. −1.19026 −0.595129 0.803630i \(-0.702899\pi\)
−0.595129 + 0.803630i \(0.702899\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −702412. −1.94895 −0.974475 0.224496i \(-0.927927\pi\)
−0.974475 + 0.224496i \(0.927927\pi\)
\(168\) 0 0
\(169\) 40871.0 0.110077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −726926. −1.84661 −0.923304 0.384069i \(-0.874523\pi\)
−0.923304 + 0.384069i \(0.874523\pi\)
\(174\) 0 0
\(175\) −120001. −0.296203
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −722418. −1.68522 −0.842609 0.538526i \(-0.818981\pi\)
−0.842609 + 0.538526i \(0.818981\pi\)
\(180\) 0 0
\(181\) −333486. −0.756626 −0.378313 0.925678i \(-0.623496\pi\)
−0.378313 + 0.925678i \(0.623496\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 248924. 0.534734
\(186\) 0 0
\(187\) −474700. −0.992694
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 669138. 1.32719 0.663594 0.748093i \(-0.269030\pi\)
0.663594 + 0.748093i \(0.269030\pi\)
\(192\) 0 0
\(193\) −115066. −0.222359 −0.111179 0.993800i \(-0.535463\pi\)
−0.111179 + 0.993800i \(0.535463\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −213364. −0.391702 −0.195851 0.980634i \(-0.562747\pi\)
−0.195851 + 0.980634i \(0.562747\pi\)
\(198\) 0 0
\(199\) −795296. −1.42363 −0.711813 0.702369i \(-0.752126\pi\)
−0.711813 + 0.702369i \(0.752126\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 330064. 0.562158
\(204\) 0 0
\(205\) −374556. −0.622490
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 720040. 1.14023
\(210\) 0 0
\(211\) −218468. −0.337817 −0.168909 0.985632i \(-0.554024\pi\)
−0.168909 + 0.985632i \(0.554024\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −253448. −0.373932
\(216\) 0 0
\(217\) −111132. −0.160210
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 648420. 0.893050
\(222\) 0 0
\(223\) −656888. −0.884564 −0.442282 0.896876i \(-0.645831\pi\)
−0.442282 + 0.896876i \(0.645831\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 971532. 1.25139 0.625695 0.780068i \(-0.284816\pi\)
0.625695 + 0.780068i \(0.284816\pi\)
\(228\) 0 0
\(229\) −459350. −0.578835 −0.289418 0.957203i \(-0.593462\pi\)
−0.289418 + 0.957203i \(0.593462\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.23704e6 −1.49277 −0.746384 0.665515i \(-0.768212\pi\)
−0.746384 + 0.665515i \(0.768212\pi\)
\(234\) 0 0
\(235\) 442104. 0.522222
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.53433e6 1.73749 0.868746 0.495258i \(-0.164926\pi\)
0.868746 + 0.495258i \(0.164926\pi\)
\(240\) 0 0
\(241\) −1.41990e6 −1.57476 −0.787380 0.616468i \(-0.788563\pi\)
−0.787380 + 0.616468i \(0.788563\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −62426.0 −0.0664432
\(246\) 0 0
\(247\) −983544. −1.02577
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.61197e6 −1.61500 −0.807501 0.589866i \(-0.799181\pi\)
−0.807501 + 0.589866i \(0.799181\pi\)
\(252\) 0 0
\(253\) −202100. −0.198502
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −851442. −0.804123 −0.402061 0.915613i \(-0.631706\pi\)
−0.402061 + 0.915613i \(0.631706\pi\)
\(258\) 0 0
\(259\) −469126. −0.434550
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.06738e6 0.951548 0.475774 0.879568i \(-0.342168\pi\)
0.475774 + 0.879568i \(0.342168\pi\)
\(264\) 0 0
\(265\) −197496. −0.172760
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 871870. 0.734634 0.367317 0.930096i \(-0.380276\pi\)
0.367317 + 0.930096i \(0.380276\pi\)
\(270\) 0 0
\(271\) 1.40737e6 1.16409 0.582044 0.813157i \(-0.302253\pi\)
0.582044 + 0.813157i \(0.302253\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.15103e6 0.917814
\(276\) 0 0
\(277\) 888782. 0.695979 0.347989 0.937499i \(-0.386865\pi\)
0.347989 + 0.937499i \(0.386865\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00038e6 −1.51129 −0.755643 0.654984i \(-0.772676\pi\)
−0.755643 + 0.654984i \(0.772676\pi\)
\(282\) 0 0
\(283\) −150460. −0.111675 −0.0558374 0.998440i \(-0.517783\pi\)
−0.0558374 + 0.998440i \(0.517783\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 705894. 0.505865
\(288\) 0 0
\(289\) −399757. −0.281547
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.73669e6 1.86233 0.931165 0.364599i \(-0.118794\pi\)
0.931165 + 0.364599i \(0.118794\pi\)
\(294\) 0 0
\(295\) −491608. −0.328900
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 276060. 0.178577
\(300\) 0 0
\(301\) 477652. 0.303875
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 955812. 0.588333
\(306\) 0 0
\(307\) −714436. −0.432631 −0.216315 0.976324i \(-0.569404\pi\)
−0.216315 + 0.976324i \(0.569404\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.34019e6 −0.785714 −0.392857 0.919599i \(-0.628513\pi\)
−0.392857 + 0.919599i \(0.628513\pi\)
\(312\) 0 0
\(313\) −2.59201e6 −1.49547 −0.747733 0.664000i \(-0.768858\pi\)
−0.747733 + 0.664000i \(0.768858\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.54753e6 −0.864951 −0.432475 0.901646i \(-0.642360\pi\)
−0.432475 + 0.901646i \(0.642360\pi\)
\(318\) 0 0
\(319\) −3.16592e6 −1.74190
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.54732e6 −0.825228
\(324\) 0 0
\(325\) −1.57226e6 −0.825687
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −833196. −0.424382
\(330\) 0 0
\(331\) 672892. 0.337579 0.168789 0.985652i \(-0.446014\pi\)
0.168789 + 0.985652i \(0.446014\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −956488. −0.465658
\(336\) 0 0
\(337\) −3.00127e6 −1.43956 −0.719780 0.694202i \(-0.755757\pi\)
−0.719780 + 0.694202i \(0.755757\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.06596e6 0.496427
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.29114e6 −1.46731 −0.733656 0.679521i \(-0.762188\pi\)
−0.733656 + 0.679521i \(0.762188\pi\)
\(348\) 0 0
\(349\) −2.96059e6 −1.30111 −0.650557 0.759458i \(-0.725464\pi\)
−0.650557 + 0.759458i \(0.725464\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.65899e6 0.708611 0.354306 0.935130i \(-0.384717\pi\)
0.354306 + 0.935130i \(0.384717\pi\)
\(354\) 0 0
\(355\) 476476. 0.200664
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.33841e6 −0.957603 −0.478801 0.877923i \(-0.658929\pi\)
−0.478801 + 0.877923i \(0.658929\pi\)
\(360\) 0 0
\(361\) −129075. −0.0521284
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −945932. −0.371645
\(366\) 0 0
\(367\) 1.77875e6 0.689367 0.344683 0.938719i \(-0.387986\pi\)
0.344683 + 0.938719i \(0.387986\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 372204. 0.140393
\(372\) 0 0
\(373\) −1.38079e6 −0.513874 −0.256937 0.966428i \(-0.582713\pi\)
−0.256937 + 0.966428i \(0.582713\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.32451e6 1.56705
\(378\) 0 0
\(379\) −4.18575e6 −1.49684 −0.748419 0.663226i \(-0.769187\pi\)
−0.748419 + 0.663226i \(0.769187\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 586216. 0.204202 0.102101 0.994774i \(-0.467443\pi\)
0.102101 + 0.994774i \(0.467443\pi\)
\(384\) 0 0
\(385\) 598780. 0.205881
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.50212e6 −0.503304 −0.251652 0.967818i \(-0.580974\pi\)
−0.251652 + 0.967818i \(0.580974\pi\)
\(390\) 0 0
\(391\) 434300. 0.143664
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 774384. 0.249726
\(396\) 0 0
\(397\) −2.01988e6 −0.643205 −0.321603 0.946875i \(-0.604222\pi\)
−0.321603 + 0.946875i \(0.604222\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.67558e6 −0.830916 −0.415458 0.909612i \(-0.636379\pi\)
−0.415458 + 0.909612i \(0.636379\pi\)
\(402\) 0 0
\(403\) −1.45606e6 −0.446597
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.49978e6 1.34650
\(408\) 0 0
\(409\) −1.32378e6 −0.391297 −0.195649 0.980674i \(-0.562681\pi\)
−0.195649 + 0.980674i \(0.562681\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 926492. 0.267280
\(414\) 0 0
\(415\) −734240. −0.209275
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 451212. 0.125558 0.0627792 0.998027i \(-0.480004\pi\)
0.0627792 + 0.998027i \(0.480004\pi\)
\(420\) 0 0
\(421\) −3.88005e6 −1.06692 −0.533460 0.845825i \(-0.679109\pi\)
−0.533460 + 0.845825i \(0.679109\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.47349e6 −0.664260
\(426\) 0 0
\(427\) −1.80134e6 −0.478107
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.31469e6 −1.37811 −0.689056 0.724708i \(-0.741975\pi\)
−0.689056 + 0.724708i \(0.741975\pi\)
\(432\) 0 0
\(433\) 2.68951e6 0.689373 0.344686 0.938718i \(-0.387985\pi\)
0.344686 + 0.938718i \(0.387985\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −658760. −0.165015
\(438\) 0 0
\(439\) 643392. 0.159336 0.0796681 0.996821i \(-0.474614\pi\)
0.0796681 + 0.996821i \(0.474614\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.53601e6 0.613961 0.306981 0.951716i \(-0.400681\pi\)
0.306981 + 0.951716i \(0.400681\pi\)
\(444\) 0 0
\(445\) 1.97480e6 0.472742
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.79178e6 1.12171 0.560856 0.827913i \(-0.310472\pi\)
0.560856 + 0.827913i \(0.310472\pi\)
\(450\) 0 0
\(451\) −6.77082e6 −1.56747
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −817908. −0.185215
\(456\) 0 0
\(457\) 6.39833e6 1.43310 0.716549 0.697537i \(-0.245721\pi\)
0.716549 + 0.697537i \(0.245721\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.59151e6 −1.88286 −0.941428 0.337214i \(-0.890516\pi\)
−0.941428 + 0.337214i \(0.890516\pi\)
\(462\) 0 0
\(463\) 1.66558e6 0.361089 0.180544 0.983567i \(-0.442214\pi\)
0.180544 + 0.983567i \(0.442214\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.88124e6 1.67225 0.836127 0.548536i \(-0.184815\pi\)
0.836127 + 0.548536i \(0.184815\pi\)
\(468\) 0 0
\(469\) 1.80261e6 0.378417
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.58156e6 −0.941587
\(474\) 0 0
\(475\) 3.75187e6 0.762981
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.25396e6 0.448857 0.224429 0.974491i \(-0.427948\pi\)
0.224429 + 0.974491i \(0.427948\pi\)
\(480\) 0 0
\(481\) −6.14651e6 −1.21134
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.09794e6 0.404985
\(486\) 0 0
\(487\) −6.29194e6 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 460542. 0.0862116 0.0431058 0.999071i \(-0.486275\pi\)
0.0431058 + 0.999071i \(0.486275\pi\)
\(492\) 0 0
\(493\) 6.80336e6 1.26068
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −897974. −0.163070
\(498\) 0 0
\(499\) −9.33924e6 −1.67904 −0.839519 0.543331i \(-0.817163\pi\)
−0.839519 + 0.543331i \(0.817163\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.89982e6 0.511036 0.255518 0.966804i \(-0.417754\pi\)
0.255518 + 0.966804i \(0.417754\pi\)
\(504\) 0 0
\(505\) −813956. −0.142028
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.97477e6 0.337849 0.168925 0.985629i \(-0.445971\pi\)
0.168925 + 0.985629i \(0.445971\pi\)
\(510\) 0 0
\(511\) 1.78272e6 0.302016
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.67561e6 0.444533
\(516\) 0 0
\(517\) 7.99188e6 1.31499
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.31576e6 −0.696567 −0.348283 0.937389i \(-0.613235\pi\)
−0.348283 + 0.937389i \(0.613235\pi\)
\(522\) 0 0
\(523\) 1.01477e7 1.62223 0.811116 0.584885i \(-0.198860\pi\)
0.811116 + 0.584885i \(0.198860\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.29068e6 −0.359284
\(528\) 0 0
\(529\) −6.25144e6 −0.971273
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.24865e6 1.41013
\(534\) 0 0
\(535\) −4.48453e6 −0.677380
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.12847e6 −0.167309
\(540\) 0 0
\(541\) −1.57718e6 −0.231679 −0.115840 0.993268i \(-0.536956\pi\)
−0.115840 + 0.993268i \(0.536956\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.52222e6 0.507955
\(546\) 0 0
\(547\) 6.24229e6 0.892022 0.446011 0.895027i \(-0.352844\pi\)
0.446011 + 0.895027i \(0.352844\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.03196e7 −1.44804
\(552\) 0 0
\(553\) −1.45942e6 −0.202939
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.36277e6 −1.14212 −0.571061 0.820908i \(-0.693468\pi\)
−0.571061 + 0.820908i \(0.693468\pi\)
\(558\) 0 0
\(559\) 6.25822e6 0.847073
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.91051e6 −1.31773 −0.658863 0.752263i \(-0.728962\pi\)
−0.658863 + 0.752263i \(0.728962\pi\)
\(564\) 0 0
\(565\) 3.52643e6 0.464745
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.44344e6 0.963814 0.481907 0.876222i \(-0.339944\pi\)
0.481907 + 0.876222i \(0.339944\pi\)
\(570\) 0 0
\(571\) 4.08068e6 0.523773 0.261886 0.965099i \(-0.415655\pi\)
0.261886 + 0.965099i \(0.415655\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.05307e6 −0.132827
\(576\) 0 0
\(577\) 5.65712e6 0.707385 0.353693 0.935362i \(-0.384926\pi\)
0.353693 + 0.935362i \(0.384926\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.38376e6 0.170067
\(582\) 0 0
\(583\) −3.57012e6 −0.435022
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.38451e7 1.65845 0.829223 0.558917i \(-0.188783\pi\)
0.829223 + 0.558917i \(0.188783\pi\)
\(588\) 0 0
\(589\) 3.47458e6 0.412680
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.22720e7 1.43311 0.716553 0.697533i \(-0.245719\pi\)
0.716553 + 0.697533i \(0.245719\pi\)
\(594\) 0 0
\(595\) −1.28674e6 −0.149004
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −920118. −0.104780 −0.0523898 0.998627i \(-0.516684\pi\)
−0.0523898 + 0.998627i \(0.516684\pi\)
\(600\) 0 0
\(601\) −1.30680e7 −1.47579 −0.737893 0.674917i \(-0.764179\pi\)
−0.737893 + 0.674917i \(0.764179\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.55607e6 −0.172839
\(606\) 0 0
\(607\) −6.07692e6 −0.669440 −0.334720 0.942318i \(-0.608642\pi\)
−0.334720 + 0.942318i \(0.608642\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.09166e7 −1.18300
\(612\) 0 0
\(613\) 1.40826e7 1.51367 0.756835 0.653606i \(-0.226745\pi\)
0.756835 + 0.653606i \(0.226745\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.45617e6 −0.365496 −0.182748 0.983160i \(-0.558499\pi\)
−0.182748 + 0.983160i \(0.558499\pi\)
\(618\) 0 0
\(619\) −1.29450e6 −0.135793 −0.0678964 0.997692i \(-0.521629\pi\)
−0.0678964 + 0.997692i \(0.521629\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.72175e6 −0.384173
\(624\) 0 0
\(625\) 3.88510e6 0.397834
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.66974e6 −0.974514
\(630\) 0 0
\(631\) 1.51131e7 1.51106 0.755529 0.655116i \(-0.227380\pi\)
0.755529 + 0.655116i \(0.227380\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.17538e6 −0.706172
\(636\) 0 0
\(637\) 1.54144e6 0.150515
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.22343e6 0.213736 0.106868 0.994273i \(-0.465918\pi\)
0.106868 + 0.994273i \(0.465918\pi\)
\(642\) 0 0
\(643\) −2.02821e6 −0.193458 −0.0967288 0.995311i \(-0.530838\pi\)
−0.0967288 + 0.995311i \(0.530838\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.31471e7 1.23472 0.617360 0.786681i \(-0.288202\pi\)
0.617360 + 0.786681i \(0.288202\pi\)
\(648\) 0 0
\(649\) −8.88676e6 −0.828193
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.07280e7 0.984550 0.492275 0.870440i \(-0.336165\pi\)
0.492275 + 0.870440i \(0.336165\pi\)
\(654\) 0 0
\(655\) 1.31269e6 0.119552
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.71881e7 −1.54176 −0.770878 0.636983i \(-0.780182\pi\)
−0.770878 + 0.636983i \(0.780182\pi\)
\(660\) 0 0
\(661\) 1.48793e7 1.32459 0.662293 0.749245i \(-0.269583\pi\)
0.662293 + 0.749245i \(0.269583\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.95177e6 0.171149
\(666\) 0 0
\(667\) 2.89648e6 0.252090
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.72781e7 1.48146
\(672\) 0 0
\(673\) −1.02649e7 −0.873611 −0.436806 0.899556i \(-0.643890\pi\)
−0.436806 + 0.899556i \(0.643890\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5.21750e6 0.437513 0.218756 0.975780i \(-0.429800\pi\)
0.218756 + 0.975780i \(0.429800\pi\)
\(678\) 0 0
\(679\) −3.95381e6 −0.329110
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.36733e7 1.12156 0.560780 0.827965i \(-0.310501\pi\)
0.560780 + 0.827965i \(0.310501\pi\)
\(684\) 0 0
\(685\) −3.56751e6 −0.290495
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.87663e6 0.391356
\(690\) 0 0
\(691\) 2.09599e7 1.66991 0.834956 0.550317i \(-0.185493\pi\)
0.834956 + 0.550317i \(0.185493\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 547040. 0.0429593
\(696\) 0 0
\(697\) 1.45501e7 1.13444
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.76672e6 0.520096 0.260048 0.965596i \(-0.416262\pi\)
0.260048 + 0.965596i \(0.416262\pi\)
\(702\) 0 0
\(703\) 1.46674e7 1.11934
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.53399e6 0.115418
\(708\) 0 0
\(709\) 1.52983e7 1.14295 0.571477 0.820618i \(-0.306371\pi\)
0.571477 + 0.820618i \(0.306371\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −975240. −0.0718435
\(714\) 0 0
\(715\) 7.84524e6 0.573906
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −932736. −0.0672878 −0.0336439 0.999434i \(-0.510711\pi\)
−0.0336439 + 0.999434i \(0.510711\pi\)
\(720\) 0 0
\(721\) −5.04249e6 −0.361249
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.64965e7 −1.16559
\(726\) 0 0
\(727\) 2.19675e7 1.54150 0.770751 0.637137i \(-0.219881\pi\)
0.770751 + 0.637137i \(0.219881\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.84548e6 0.681465
\(732\) 0 0
\(733\) −3.41626e6 −0.234850 −0.117425 0.993082i \(-0.537464\pi\)
−0.117425 + 0.993082i \(0.537464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.72904e7 −1.17256
\(738\) 0 0
\(739\) 2.00714e7 1.35197 0.675983 0.736917i \(-0.263719\pi\)
0.675983 + 0.736917i \(0.263719\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.87764e6 −0.257689 −0.128844 0.991665i \(-0.541127\pi\)
−0.128844 + 0.991665i \(0.541127\pi\)
\(744\) 0 0
\(745\) −6.25217e6 −0.412705
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.45162e6 0.550472
\(750\) 0 0
\(751\) −965112. −0.0624422 −0.0312211 0.999513i \(-0.509940\pi\)
−0.0312211 + 0.999513i \(0.509940\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.45125e6 0.539577
\(756\) 0 0
\(757\) 1.51809e6 0.0962848 0.0481424 0.998840i \(-0.484670\pi\)
0.0481424 + 0.998840i \(0.484670\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.78210e7 −1.74145 −0.870724 0.491772i \(-0.836349\pi\)
−0.870724 + 0.491772i \(0.836349\pi\)
\(762\) 0 0
\(763\) −6.63803e6 −0.412789
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.21389e7 0.745062
\(768\) 0 0
\(769\) 1.29011e7 0.786704 0.393352 0.919388i \(-0.371315\pi\)
0.393352 + 0.919388i \(0.371315\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.03741e7 −1.22640 −0.613198 0.789929i \(-0.710117\pi\)
−0.613198 + 0.789929i \(0.710117\pi\)
\(774\) 0 0
\(775\) 5.55433e6 0.332183
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.20700e7 −1.30304
\(780\) 0 0
\(781\) 8.61322e6 0.505287
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.39811e7 −0.809779
\(786\) 0 0
\(787\) 8.69990e6 0.500700 0.250350 0.968155i \(-0.419454\pi\)
0.250350 + 0.968155i \(0.419454\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.64597e6 −0.377674
\(792\) 0 0
\(793\) −2.36012e7 −1.33276
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.56281e7 −1.98677 −0.993383 0.114845i \(-0.963363\pi\)
−0.993383 + 0.114845i \(0.963363\pi\)
\(798\) 0 0
\(799\) −1.71740e7 −0.951712
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.70995e7 −0.935827
\(804\) 0 0
\(805\) −547820. −0.0297953
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.12912e7 1.14375 0.571873 0.820342i \(-0.306217\pi\)
0.571873 + 0.820342i \(0.306217\pi\)
\(810\) 0 0
\(811\) −1.83458e7 −0.979455 −0.489728 0.871875i \(-0.662904\pi\)
−0.489728 + 0.871875i \(0.662904\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.04974e7 0.553592
\(816\) 0 0
\(817\) −1.49339e7 −0.782743
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.50359e7 1.29630 0.648149 0.761514i \(-0.275544\pi\)
0.648149 + 0.761514i \(0.275544\pi\)
\(822\) 0 0
\(823\) −3.30923e6 −0.170305 −0.0851525 0.996368i \(-0.527138\pi\)
−0.0851525 + 0.996368i \(0.527138\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.25220e7 0.636664 0.318332 0.947979i \(-0.396877\pi\)
0.318332 + 0.947979i \(0.396877\pi\)
\(828\) 0 0
\(829\) 8.72677e6 0.441029 0.220515 0.975384i \(-0.429226\pi\)
0.220515 + 0.975384i \(0.429226\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.42501e6 0.121088
\(834\) 0 0
\(835\) 1.82627e7 0.906461
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.17349e7 −1.55644 −0.778221 0.627991i \(-0.783877\pi\)
−0.778221 + 0.627991i \(0.783877\pi\)
\(840\) 0 0
\(841\) 2.48625e7 1.21215
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.06265e6 −0.0511973
\(846\) 0 0
\(847\) 2.93260e6 0.140457
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.11682e6 −0.194867
\(852\) 0 0
\(853\) 3.40388e7 1.60178 0.800888 0.598814i \(-0.204361\pi\)
0.800888 + 0.598814i \(0.204361\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.84100e7 1.32135 0.660676 0.750671i \(-0.270270\pi\)
0.660676 + 0.750671i \(0.270270\pi\)
\(858\) 0 0
\(859\) −1.44582e7 −0.668545 −0.334272 0.942477i \(-0.608491\pi\)
−0.334272 + 0.942477i \(0.608491\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.46943e7 0.671619 0.335809 0.941930i \(-0.390990\pi\)
0.335809 + 0.941930i \(0.390990\pi\)
\(864\) 0 0
\(865\) 1.89001e7 0.858862
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.39985e7 0.628827
\(870\) 0 0
\(871\) 2.36179e7 1.05486
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 7.10128e6 0.313557
\(876\) 0 0
\(877\) 2.47228e7 1.08542 0.542711 0.839920i \(-0.317398\pi\)
0.542711 + 0.839920i \(0.317398\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.50211e6 −0.152016 −0.0760081 0.997107i \(-0.524217\pi\)
−0.0760081 + 0.997107i \(0.524217\pi\)
\(882\) 0 0
\(883\) 767908. 0.0331442 0.0165721 0.999863i \(-0.494725\pi\)
0.0165721 + 0.999863i \(0.494725\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.14209e7 0.487405 0.243703 0.969850i \(-0.421638\pi\)
0.243703 + 0.969850i \(0.421638\pi\)
\(888\) 0 0
\(889\) 1.35228e7 0.573869
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.60501e7 1.09315
\(894\) 0 0
\(895\) 1.87829e7 0.783798
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.52772e7 −0.630443
\(900\) 0 0
\(901\) 7.67196e6 0.314843
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.67064e6 0.351908
\(906\) 0 0
\(907\) 1.31900e7 0.532387 0.266194 0.963920i \(-0.414234\pi\)
0.266194 + 0.963920i \(0.414234\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.99072e7 −1.19393 −0.596965 0.802267i \(-0.703627\pi\)
−0.596965 + 0.802267i \(0.703627\pi\)
\(912\) 0 0
\(913\) −1.32728e7 −0.526970
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.47391e6 −0.0971540
\(918\) 0 0
\(919\) −2.53866e7 −0.991552 −0.495776 0.868450i \(-0.665116\pi\)
−0.495776 + 0.868450i \(0.665116\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.17653e7 −0.454568
\(924\) 0 0
\(925\) 2.34467e7 0.901006
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.29559e7 0.872680 0.436340 0.899782i \(-0.356274\pi\)
0.436340 + 0.899782i \(0.356274\pi\)
\(930\) 0 0
\(931\) −3.67833e6 −0.139084
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.23422e7 0.461704
\(936\) 0 0
\(937\) 1.16444e7 0.433280 0.216640 0.976252i \(-0.430490\pi\)
0.216640 + 0.976252i \(0.430490\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.04943e7 0.754500 0.377250 0.926111i \(-0.376870\pi\)
0.377250 + 0.926111i \(0.376870\pi\)
\(942\) 0 0
\(943\) 6.19458e6 0.226847
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.91160e7 1.05501 0.527505 0.849552i \(-0.323128\pi\)
0.527505 + 0.849552i \(0.323128\pi\)
\(948\) 0 0
\(949\) 2.33572e7 0.841891
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.20790e6 −0.185751 −0.0928753 0.995678i \(-0.529606\pi\)
−0.0928753 + 0.995678i \(0.529606\pi\)
\(954\) 0 0
\(955\) −1.73976e7 −0.617278
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.72339e6 0.236070
\(960\) 0 0
\(961\) −2.34853e7 −0.820329
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.99172e6 0.103419
\(966\) 0 0
\(967\) 4.28147e6 0.147240 0.0736202 0.997286i \(-0.476545\pi\)
0.0736202 + 0.997286i \(0.476545\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.20741e7 0.410966 0.205483 0.978661i \(-0.434124\pi\)
0.205483 + 0.978661i \(0.434124\pi\)
\(972\) 0 0
\(973\) −1.03096e6 −0.0349108
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.06568e7 0.357183 0.178591 0.983923i \(-0.442846\pi\)
0.178591 + 0.983923i \(0.442846\pi\)
\(978\) 0 0
\(979\) 3.56984e7 1.19040
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −3.55409e7 −1.17312 −0.586562 0.809904i \(-0.699519\pi\)
−0.586562 + 0.809904i \(0.699519\pi\)
\(984\) 0 0
\(985\) 5.54746e6 0.182181
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.19164e6 0.136268
\(990\) 0 0
\(991\) −2.83700e7 −0.917647 −0.458823 0.888527i \(-0.651729\pi\)
−0.458823 + 0.888527i \(0.651729\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.06777e7 0.662132
\(996\) 0 0
\(997\) −6.15275e6 −0.196034 −0.0980169 0.995185i \(-0.531250\pi\)
−0.0980169 + 0.995185i \(0.531250\pi\)
\(998\) 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 1008.6.a.i.1.1 1
3.2 odd 2 1008.6.a.r.1.1 1
4.3 odd 2 126.6.a.j.1.1 yes 1
12.11 even 2 126.6.a.d.1.1 1
28.27 even 2 882.6.a.u.1.1 1
84.83 odd 2 882.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.6.a.d.1.1 1 12.11 even 2
126.6.a.j.1.1 yes 1 4.3 odd 2
882.6.a.c.1.1 1 84.83 odd 2
882.6.a.u.1.1 1 28.27 even 2
1008.6.a.i.1.1 1 1.1 even 1 trivial
1008.6.a.r.1.1 1 3.2 odd 2