Properties

Label 1008.6.a.bk.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{91}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 91 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 252)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(9.53939\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q+57.2364 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+57.2364 q^{5} -49.0000 q^{7} +515.127 q^{11} -670.000 q^{13} -973.018 q^{17} -284.000 q^{19} +1774.33 q^{23} +151.000 q^{25} +6868.36 q^{29} -1532.00 q^{31} -2804.58 q^{35} -15118.0 q^{37} +5322.98 q^{41} +10996.0 q^{43} +19345.9 q^{47} +2401.00 q^{49} +23466.9 q^{53} +29484.0 q^{55} +23695.8 q^{59} -14602.0 q^{61} -38348.4 q^{65} +36628.0 q^{67} -67939.5 q^{71} -54802.0 q^{73} -25241.2 q^{77} +31768.0 q^{79} +74178.3 q^{83} -55692.0 q^{85} -858.545 q^{89} +32830.0 q^{91} -16255.1 q^{95} +14126.0 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 98 q^{7} - 1340 q^{13} - 568 q^{19} + 302 q^{25} - 3064 q^{31} - 30236 q^{37} + 21992 q^{43} + 4802 q^{49} + 58968 q^{55} - 29204 q^{61} + 73256 q^{67} - 109604 q^{73} + 63536 q^{79} - 111384 q^{85} + 65660 q^{91} + 28252 q^{97}+O(q^{100}) \) 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
\(5\) 57.2364 1.02387 0.511937 0.859023i \(-0.328928\pi\)
0.511937 + 0.859023i \(0.328928\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 515.127 1.28361 0.641804 0.766868i \(-0.278186\pi\)
0.641804 + 0.766868i \(0.278186\pi\)
\(12\) 0 0
\(13\) −670.000 −1.09955 −0.549777 0.835312i \(-0.685287\pi\)
−0.549777 + 0.835312i \(0.685287\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −973.018 −0.816580 −0.408290 0.912852i \(-0.633875\pi\)
−0.408290 + 0.912852i \(0.633875\pi\)
\(18\) 0 0
\(19\) −284.000 −0.180482 −0.0902411 0.995920i \(-0.528764\pi\)
−0.0902411 + 0.995920i \(0.528764\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1774.33 0.699381 0.349691 0.936865i \(-0.386287\pi\)
0.349691 + 0.936865i \(0.386287\pi\)
\(24\) 0 0
\(25\) 151.000 0.0483200
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6868.36 1.51656 0.758278 0.651932i \(-0.226041\pi\)
0.758278 + 0.651932i \(0.226041\pi\)
\(30\) 0 0
\(31\) −1532.00 −0.286322 −0.143161 0.989699i \(-0.545727\pi\)
−0.143161 + 0.989699i \(0.545727\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2804.58 −0.386988
\(36\) 0 0
\(37\) −15118.0 −1.81547 −0.907737 0.419540i \(-0.862192\pi\)
−0.907737 + 0.419540i \(0.862192\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5322.98 0.494533 0.247266 0.968948i \(-0.420468\pi\)
0.247266 + 0.968948i \(0.420468\pi\)
\(42\) 0 0
\(43\) 10996.0 0.906909 0.453454 0.891279i \(-0.350191\pi\)
0.453454 + 0.891279i \(0.350191\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 19345.9 1.27745 0.638725 0.769435i \(-0.279462\pi\)
0.638725 + 0.769435i \(0.279462\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 23466.9 1.14754 0.573768 0.819018i \(-0.305481\pi\)
0.573768 + 0.819018i \(0.305481\pi\)
\(54\) 0 0
\(55\) 29484.0 1.31426
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 23695.8 0.886221 0.443111 0.896467i \(-0.353875\pi\)
0.443111 + 0.896467i \(0.353875\pi\)
\(60\) 0 0
\(61\) −14602.0 −0.502444 −0.251222 0.967929i \(-0.580832\pi\)
−0.251222 + 0.967929i \(0.580832\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −38348.4 −1.12581
\(66\) 0 0
\(67\) 36628.0 0.996842 0.498421 0.866935i \(-0.333913\pi\)
0.498421 + 0.866935i \(0.333913\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −67939.5 −1.59947 −0.799736 0.600351i \(-0.795027\pi\)
−0.799736 + 0.600351i \(0.795027\pi\)
\(72\) 0 0
\(73\) −54802.0 −1.20362 −0.601810 0.798639i \(-0.705553\pi\)
−0.601810 + 0.798639i \(0.705553\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −25241.2 −0.485159
\(78\) 0 0
\(79\) 31768.0 0.572693 0.286347 0.958126i \(-0.407559\pi\)
0.286347 + 0.958126i \(0.407559\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 74178.3 1.18190 0.590951 0.806707i \(-0.298753\pi\)
0.590951 + 0.806707i \(0.298753\pi\)
\(84\) 0 0
\(85\) −55692.0 −0.836076
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −858.545 −0.0114892 −0.00574458 0.999983i \(-0.501829\pi\)
−0.00574458 + 0.999983i \(0.501829\pi\)
\(90\) 0 0
\(91\) 32830.0 0.415592
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −16255.1 −0.184791
\(96\) 0 0
\(97\) 14126.0 0.152437 0.0762184 0.997091i \(-0.475715\pi\)
0.0762184 + 0.997091i \(0.475715\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 177604. 1.73241 0.866204 0.499690i \(-0.166553\pi\)
0.866204 + 0.499690i \(0.166553\pi\)
\(102\) 0 0
\(103\) 128356. 1.19213 0.596064 0.802937i \(-0.296730\pi\)
0.596064 + 0.802937i \(0.296730\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −74350.0 −0.627800 −0.313900 0.949456i \(-0.601636\pi\)
−0.313900 + 0.949456i \(0.601636\pi\)
\(108\) 0 0
\(109\) −103918. −0.837769 −0.418885 0.908039i \(-0.637579\pi\)
−0.418885 + 0.908039i \(0.637579\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 96157.1 0.708411 0.354205 0.935168i \(-0.384751\pi\)
0.354205 + 0.935168i \(0.384751\pi\)
\(114\) 0 0
\(115\) 101556. 0.716079
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 47677.9 0.308638
\(120\) 0 0
\(121\) 104305. 0.647652
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −170221. −0.974401
\(126\) 0 0
\(127\) −127112. −0.699322 −0.349661 0.936876i \(-0.613703\pi\)
−0.349661 + 0.936876i \(0.613703\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 328537. 1.67265 0.836326 0.548232i \(-0.184699\pi\)
0.836326 + 0.548232i \(0.184699\pi\)
\(132\) 0 0
\(133\) 13916.0 0.0682159
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −176631. −0.804019 −0.402010 0.915635i \(-0.631688\pi\)
−0.402010 + 0.915635i \(0.631688\pi\)
\(138\) 0 0
\(139\) 55792.0 0.244926 0.122463 0.992473i \(-0.460921\pi\)
0.122463 + 0.992473i \(0.460921\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −345135. −1.41140
\(144\) 0 0
\(145\) 393120. 1.55276
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −261570. −0.965211 −0.482606 0.875838i \(-0.660310\pi\)
−0.482606 + 0.875838i \(0.660310\pi\)
\(150\) 0 0
\(151\) −149288. −0.532822 −0.266411 0.963859i \(-0.585838\pi\)
−0.266411 + 0.963859i \(0.585838\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −87686.1 −0.293158
\(156\) 0 0
\(157\) 299222. 0.968823 0.484411 0.874840i \(-0.339034\pi\)
0.484411 + 0.874840i \(0.339034\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −86942.0 −0.264341
\(162\) 0 0
\(163\) 336220. 0.991185 0.495592 0.868555i \(-0.334951\pi\)
0.495592 + 0.868555i \(0.334951\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −262257. −0.727672 −0.363836 0.931463i \(-0.618533\pi\)
−0.363836 + 0.931463i \(0.618533\pi\)
\(168\) 0 0
\(169\) 77607.0 0.209018
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 541857. 1.37648 0.688239 0.725484i \(-0.258384\pi\)
0.688239 + 0.725484i \(0.258384\pi\)
\(174\) 0 0
\(175\) −7399.00 −0.0182632
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −296542. −0.691756 −0.345878 0.938279i \(-0.612419\pi\)
−0.345878 + 0.938279i \(0.612419\pi\)
\(180\) 0 0
\(181\) 587522. 1.33299 0.666496 0.745508i \(-0.267793\pi\)
0.666496 + 0.745508i \(0.267793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −865299. −1.85882
\(186\) 0 0
\(187\) −501228. −1.04817
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −188136. −0.373154 −0.186577 0.982440i \(-0.559739\pi\)
−0.186577 + 0.982440i \(0.559739\pi\)
\(192\) 0 0
\(193\) 403022. 0.778817 0.389409 0.921065i \(-0.372679\pi\)
0.389409 + 0.921065i \(0.372679\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 254702. 0.467591 0.233796 0.972286i \(-0.424885\pi\)
0.233796 + 0.972286i \(0.424885\pi\)
\(198\) 0 0
\(199\) −353360. −0.632535 −0.316268 0.948670i \(-0.602430\pi\)
−0.316268 + 0.948670i \(0.602430\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −336550. −0.573204
\(204\) 0 0
\(205\) 304668. 0.506340
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −146296. −0.231669
\(210\) 0 0
\(211\) −616292. −0.952973 −0.476486 0.879182i \(-0.658090\pi\)
−0.476486 + 0.879182i \(0.658090\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 629371. 0.928561
\(216\) 0 0
\(217\) 75068.0 0.108219
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 651922. 0.897873
\(222\) 0 0
\(223\) 328216. 0.441975 0.220987 0.975277i \(-0.429072\pi\)
0.220987 + 0.975277i \(0.429072\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 550270. 0.708780 0.354390 0.935098i \(-0.384689\pi\)
0.354390 + 0.935098i \(0.384689\pi\)
\(228\) 0 0
\(229\) 1.24299e6 1.56631 0.783155 0.621827i \(-0.213609\pi\)
0.783155 + 0.621827i \(0.213609\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 172968. 0.208726 0.104363 0.994539i \(-0.466720\pi\)
0.104363 + 0.994539i \(0.466720\pi\)
\(234\) 0 0
\(235\) 1.10729e6 1.30795
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.35278e6 1.53191 0.765954 0.642895i \(-0.222267\pi\)
0.765954 + 0.642895i \(0.222267\pi\)
\(240\) 0 0
\(241\) −605290. −0.671307 −0.335653 0.941986i \(-0.608957\pi\)
−0.335653 + 0.941986i \(0.608957\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 137424. 0.146268
\(246\) 0 0
\(247\) 190280. 0.198450
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −606820. −0.607961 −0.303980 0.952678i \(-0.598316\pi\)
−0.303980 + 0.952678i \(0.598316\pi\)
\(252\) 0 0
\(253\) 914004. 0.897732
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.29314e6 1.22127 0.610637 0.791911i \(-0.290914\pi\)
0.610637 + 0.791911i \(0.290914\pi\)
\(258\) 0 0
\(259\) 740782. 0.686185
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.53456e6 1.36803 0.684015 0.729468i \(-0.260232\pi\)
0.684015 + 0.729468i \(0.260232\pi\)
\(264\) 0 0
\(265\) 1.34316e6 1.17493
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −430131. −0.362427 −0.181213 0.983444i \(-0.558002\pi\)
−0.181213 + 0.983444i \(0.558002\pi\)
\(270\) 0 0
\(271\) 769804. 0.636732 0.318366 0.947968i \(-0.396866\pi\)
0.318366 + 0.947968i \(0.396866\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 77784.2 0.0620240
\(276\) 0 0
\(277\) −391066. −0.306232 −0.153116 0.988208i \(-0.548931\pi\)
−0.153116 + 0.988208i \(0.548931\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.18559e6 −0.895716 −0.447858 0.894105i \(-0.647813\pi\)
−0.447858 + 0.894105i \(0.647813\pi\)
\(282\) 0 0
\(283\) 2.02464e6 1.50274 0.751368 0.659884i \(-0.229394\pi\)
0.751368 + 0.659884i \(0.229394\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −260826. −0.186916
\(288\) 0 0
\(289\) −473093. −0.333198
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.16874e6 1.47584 0.737919 0.674889i \(-0.235808\pi\)
0.737919 + 0.674889i \(0.235808\pi\)
\(294\) 0 0
\(295\) 1.35626e6 0.907380
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.18880e6 −0.769007
\(300\) 0 0
\(301\) −538804. −0.342779
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −835765. −0.514440
\(306\) 0 0
\(307\) 743164. 0.450027 0.225014 0.974356i \(-0.427757\pi\)
0.225014 + 0.974356i \(0.427757\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.81546e6 −1.65062 −0.825311 0.564678i \(-0.809000\pi\)
−0.825311 + 0.564678i \(0.809000\pi\)
\(312\) 0 0
\(313\) 1.86240e6 1.07452 0.537258 0.843418i \(-0.319460\pi\)
0.537258 + 0.843418i \(0.319460\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.64234e6 0.917941 0.458971 0.888451i \(-0.348218\pi\)
0.458971 + 0.888451i \(0.348218\pi\)
\(318\) 0 0
\(319\) 3.53808e6 1.94666
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 276337. 0.147378
\(324\) 0 0
\(325\) −101170. −0.0531304
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −947948. −0.482831
\(330\) 0 0
\(331\) 3.80969e6 1.91126 0.955630 0.294569i \(-0.0951760\pi\)
0.955630 + 0.294569i \(0.0951760\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.09645e6 1.02064
\(336\) 0 0
\(337\) 2.19707e6 1.05383 0.526913 0.849919i \(-0.323349\pi\)
0.526913 + 0.849919i \(0.323349\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −789175. −0.367525
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.02493e6 0.456953 0.228476 0.973549i \(-0.426626\pi\)
0.228476 + 0.973549i \(0.426626\pi\)
\(348\) 0 0
\(349\) −2.16719e6 −0.952429 −0.476215 0.879329i \(-0.657991\pi\)
−0.476215 + 0.879329i \(0.657991\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −582494. −0.248803 −0.124401 0.992232i \(-0.539701\pi\)
−0.124401 + 0.992232i \(0.539701\pi\)
\(354\) 0 0
\(355\) −3.88861e6 −1.63766
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −203704. −0.0834188 −0.0417094 0.999130i \(-0.513280\pi\)
−0.0417094 + 0.999130i \(0.513280\pi\)
\(360\) 0 0
\(361\) −2.39544e6 −0.967426
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.13667e6 −1.23236
\(366\) 0 0
\(367\) 4.08011e6 1.58127 0.790637 0.612286i \(-0.209750\pi\)
0.790637 + 0.612286i \(0.209750\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.14988e6 −0.433728
\(372\) 0 0
\(373\) −3.40643e6 −1.26773 −0.633865 0.773444i \(-0.718533\pi\)
−0.633865 + 0.773444i \(0.718533\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.60180e6 −1.66753
\(378\) 0 0
\(379\) 1.35617e6 0.484972 0.242486 0.970155i \(-0.422037\pi\)
0.242486 + 0.970155i \(0.422037\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.20219e6 0.418771 0.209386 0.977833i \(-0.432854\pi\)
0.209386 + 0.977833i \(0.432854\pi\)
\(384\) 0 0
\(385\) −1.44472e6 −0.496742
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.21103e6 1.74602 0.873010 0.487702i \(-0.162165\pi\)
0.873010 + 0.487702i \(0.162165\pi\)
\(390\) 0 0
\(391\) −1.72645e6 −0.571101
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.81828e6 0.586366
\(396\) 0 0
\(397\) 4.05383e6 1.29089 0.645445 0.763807i \(-0.276672\pi\)
0.645445 + 0.763807i \(0.276672\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −468079. −0.145364 −0.0726822 0.997355i \(-0.523156\pi\)
−0.0726822 + 0.997355i \(0.523156\pi\)
\(402\) 0 0
\(403\) 1.02644e6 0.314826
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.78769e6 −2.33036
\(408\) 0 0
\(409\) 3.46254e6 1.02350 0.511749 0.859135i \(-0.328998\pi\)
0.511749 + 0.859135i \(0.328998\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.16110e6 −0.334960
\(414\) 0 0
\(415\) 4.24570e6 1.21012
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.91747e6 −1.92492 −0.962459 0.271427i \(-0.912505\pi\)
−0.962459 + 0.271427i \(0.912505\pi\)
\(420\) 0 0
\(421\) 3.57661e6 0.983483 0.491741 0.870741i \(-0.336361\pi\)
0.491741 + 0.870741i \(0.336361\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −146926. −0.0394571
\(426\) 0 0
\(427\) 715498. 0.189906
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.99921e6 0.518400 0.259200 0.965824i \(-0.416541\pi\)
0.259200 + 0.965824i \(0.416541\pi\)
\(432\) 0 0
\(433\) 4.79321e6 1.22859 0.614295 0.789077i \(-0.289441\pi\)
0.614295 + 0.789077i \(0.289441\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −503909. −0.126226
\(438\) 0 0
\(439\) −6.94501e6 −1.71993 −0.859966 0.510351i \(-0.829516\pi\)
−0.859966 + 0.510351i \(0.829516\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.09496e6 1.71767 0.858837 0.512249i \(-0.171188\pi\)
0.858837 + 0.512249i \(0.171188\pi\)
\(444\) 0 0
\(445\) −49140.0 −0.0117635
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.71016e6 1.57079 0.785393 0.618997i \(-0.212461\pi\)
0.785393 + 0.618997i \(0.212461\pi\)
\(450\) 0 0
\(451\) 2.74201e6 0.634787
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.87907e6 0.425514
\(456\) 0 0
\(457\) 164054. 0.0367448 0.0183724 0.999831i \(-0.494152\pi\)
0.0183724 + 0.999831i \(0.494152\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.64173e6 −1.23640 −0.618201 0.786020i \(-0.712138\pi\)
−0.618201 + 0.786020i \(0.712138\pi\)
\(462\) 0 0
\(463\) −7.50483e6 −1.62700 −0.813502 0.581562i \(-0.802442\pi\)
−0.813502 + 0.581562i \(0.802442\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.83446e6 0.601420 0.300710 0.953716i \(-0.402776\pi\)
0.300710 + 0.953716i \(0.402776\pi\)
\(468\) 0 0
\(469\) −1.79477e6 −0.376771
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.66434e6 1.16412
\(474\) 0 0
\(475\) −42884.0 −0.00872090
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.12012e6 −0.223061 −0.111531 0.993761i \(-0.535575\pi\)
−0.111531 + 0.993761i \(0.535575\pi\)
\(480\) 0 0
\(481\) 1.01291e7 1.99621
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 808521. 0.156076
\(486\) 0 0
\(487\) 9.75086e6 1.86303 0.931516 0.363700i \(-0.118487\pi\)
0.931516 + 0.363700i \(0.118487\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.08277e6 −0.389887 −0.194943 0.980815i \(-0.562452\pi\)
−0.194943 + 0.980815i \(0.562452\pi\)
\(492\) 0 0
\(493\) −6.68304e6 −1.23839
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.32904e6 0.604544
\(498\) 0 0
\(499\) −7.75963e6 −1.39505 −0.697525 0.716561i \(-0.745715\pi\)
−0.697525 + 0.716561i \(0.745715\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.56697e6 −0.628607 −0.314304 0.949323i \(-0.601771\pi\)
−0.314304 + 0.949323i \(0.601771\pi\)
\(504\) 0 0
\(505\) 1.01654e7 1.77377
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.86105e6 −1.51597 −0.757985 0.652272i \(-0.773816\pi\)
−0.757985 + 0.652272i \(0.773816\pi\)
\(510\) 0 0
\(511\) 2.68530e6 0.454925
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.34663e6 1.22059
\(516\) 0 0
\(517\) 9.96559e6 1.63975
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.43039e6 0.230867 0.115433 0.993315i \(-0.463174\pi\)
0.115433 + 0.993315i \(0.463174\pi\)
\(522\) 0 0
\(523\) −1.08653e7 −1.73694 −0.868472 0.495737i \(-0.834898\pi\)
−0.868472 + 0.495737i \(0.834898\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.49066e6 0.233805
\(528\) 0 0
\(529\) −3.28811e6 −0.510866
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.56640e6 −0.543766
\(534\) 0 0
\(535\) −4.25552e6 −0.642789
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.23682e6 0.183373
\(540\) 0 0
\(541\) −6.46621e6 −0.949854 −0.474927 0.880025i \(-0.657525\pi\)
−0.474927 + 0.880025i \(0.657525\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.94789e6 −0.857771
\(546\) 0 0
\(547\) −153932. −0.0219969 −0.0109984 0.999940i \(-0.503501\pi\)
−0.0109984 + 0.999940i \(0.503501\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.95061e6 −0.273711
\(552\) 0 0
\(553\) −1.55663e6 −0.216458
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.26625e6 0.446079 0.223039 0.974809i \(-0.428402\pi\)
0.223039 + 0.974809i \(0.428402\pi\)
\(558\) 0 0
\(559\) −7.36732e6 −0.997195
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.21209e6 −0.825975 −0.412987 0.910737i \(-0.635515\pi\)
−0.412987 + 0.910737i \(0.635515\pi\)
\(564\) 0 0
\(565\) 5.50368e6 0.725324
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.00375e6 0.777395 0.388698 0.921365i \(-0.372925\pi\)
0.388698 + 0.921365i \(0.372925\pi\)
\(570\) 0 0
\(571\) −5.08418e6 −0.652575 −0.326288 0.945271i \(-0.605798\pi\)
−0.326288 + 0.945271i \(0.605798\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 267923. 0.0337941
\(576\) 0 0
\(577\) −4.96896e6 −0.621335 −0.310667 0.950519i \(-0.600553\pi\)
−0.310667 + 0.950519i \(0.600553\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.63474e6 −0.446717
\(582\) 0 0
\(583\) 1.20884e7 1.47299
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.18769e6 1.10055 0.550277 0.834982i \(-0.314522\pi\)
0.550277 + 0.834982i \(0.314522\pi\)
\(588\) 0 0
\(589\) 435088. 0.0516760
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.35521e7 1.58260 0.791300 0.611428i \(-0.209405\pi\)
0.791300 + 0.611428i \(0.209405\pi\)
\(594\) 0 0
\(595\) 2.72891e6 0.316007
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.97161e6 0.566148 0.283074 0.959098i \(-0.408646\pi\)
0.283074 + 0.959098i \(0.408646\pi\)
\(600\) 0 0
\(601\) −5.49055e6 −0.620054 −0.310027 0.950728i \(-0.600338\pi\)
−0.310027 + 0.950728i \(0.600338\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.97004e6 0.663115
\(606\) 0 0
\(607\) −1.76305e7 −1.94220 −0.971098 0.238682i \(-0.923285\pi\)
−0.971098 + 0.238682i \(0.923285\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.29617e7 −1.40463
\(612\) 0 0
\(613\) −1.47183e7 −1.58200 −0.791002 0.611813i \(-0.790441\pi\)
−0.791002 + 0.611813i \(0.790441\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.00355e6 −0.740637 −0.370319 0.928905i \(-0.620752\pi\)
−0.370319 + 0.928905i \(0.620752\pi\)
\(618\) 0 0
\(619\) 6.85036e6 0.718599 0.359300 0.933222i \(-0.383016\pi\)
0.359300 + 0.933222i \(0.383016\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 42068.7 0.00434249
\(624\) 0 0
\(625\) −1.02147e7 −1.04599
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.47101e7 1.48248
\(630\) 0 0
\(631\) −1.36802e7 −1.36779 −0.683894 0.729581i \(-0.739715\pi\)
−0.683894 + 0.729581i \(0.739715\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.27543e6 −0.716018
\(636\) 0 0
\(637\) −1.60867e6 −0.157079
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.90471e6 0.183098 0.0915491 0.995801i \(-0.470818\pi\)
0.0915491 + 0.995801i \(0.470818\pi\)
\(642\) 0 0
\(643\) 5.19569e6 0.495583 0.247791 0.968813i \(-0.420295\pi\)
0.247791 + 0.968813i \(0.420295\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.37749e6 0.880696 0.440348 0.897827i \(-0.354855\pi\)
0.440348 + 0.897827i \(0.354855\pi\)
\(648\) 0 0
\(649\) 1.22064e7 1.13756
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.31149e7 −1.20360 −0.601800 0.798647i \(-0.705550\pi\)
−0.601800 + 0.798647i \(0.705550\pi\)
\(654\) 0 0
\(655\) 1.88042e7 1.71259
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.62527e7 1.45784 0.728922 0.684597i \(-0.240022\pi\)
0.728922 + 0.684597i \(0.240022\pi\)
\(660\) 0 0
\(661\) −4.31300e6 −0.383951 −0.191976 0.981400i \(-0.561489\pi\)
−0.191976 + 0.981400i \(0.561489\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 796501. 0.0698445
\(666\) 0 0
\(667\) 1.21867e7 1.06065
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.52189e6 −0.644942
\(672\) 0 0
\(673\) −1.61027e7 −1.37044 −0.685220 0.728336i \(-0.740294\pi\)
−0.685220 + 0.728336i \(0.740294\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.02526e6 0.337538 0.168769 0.985656i \(-0.446021\pi\)
0.168769 + 0.985656i \(0.446021\pi\)
\(678\) 0 0
\(679\) −692174. −0.0576157
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.70526e6 0.467976 0.233988 0.972239i \(-0.424822\pi\)
0.233988 + 0.972239i \(0.424822\pi\)
\(684\) 0 0
\(685\) −1.01097e7 −0.823215
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.57228e7 −1.26178
\(690\) 0 0
\(691\) 610648. 0.0486515 0.0243257 0.999704i \(-0.492256\pi\)
0.0243257 + 0.999704i \(0.492256\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.19333e6 0.250774
\(696\) 0 0
\(697\) −5.17936e6 −0.403826
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.55440e7 −1.19473 −0.597363 0.801971i \(-0.703785\pi\)
−0.597363 + 0.801971i \(0.703785\pi\)
\(702\) 0 0
\(703\) 4.29351e6 0.327661
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.70262e6 −0.654789
\(708\) 0 0
\(709\) −2.53702e7 −1.89543 −0.947717 0.319111i \(-0.896616\pi\)
−0.947717 + 0.319111i \(0.896616\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.71827e6 −0.200248
\(714\) 0 0
\(715\) −1.97543e7 −1.44509
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.71869e7 1.23987 0.619935 0.784653i \(-0.287159\pi\)
0.619935 + 0.784653i \(0.287159\pi\)
\(720\) 0 0
\(721\) −6.28944e6 −0.450582
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.03712e6 0.0732799
\(726\) 0 0
\(727\) −3.03580e6 −0.213028 −0.106514 0.994311i \(-0.533969\pi\)
−0.106514 + 0.994311i \(0.533969\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.06993e7 −0.740563
\(732\) 0 0
\(733\) 3.64299e6 0.250436 0.125218 0.992129i \(-0.460037\pi\)
0.125218 + 0.992129i \(0.460037\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.88681e7 1.27955
\(738\) 0 0
\(739\) −8.20260e6 −0.552510 −0.276255 0.961084i \(-0.589093\pi\)
−0.276255 + 0.961084i \(0.589093\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.44384e7 −0.959504 −0.479752 0.877404i \(-0.659273\pi\)
−0.479752 + 0.877404i \(0.659273\pi\)
\(744\) 0 0
\(745\) −1.49713e7 −0.988256
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.64315e6 0.237286
\(750\) 0 0
\(751\) −8.34049e6 −0.539624 −0.269812 0.962913i \(-0.586962\pi\)
−0.269812 + 0.962913i \(0.586962\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.54470e6 −0.545544
\(756\) 0 0
\(757\) −2.78547e7 −1.76668 −0.883342 0.468729i \(-0.844712\pi\)
−0.883342 + 0.468729i \(0.844712\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.79193e6 −0.174760 −0.0873802 0.996175i \(-0.527850\pi\)
−0.0873802 + 0.996175i \(0.527850\pi\)
\(762\) 0 0
\(763\) 5.09198e6 0.316647
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.58762e7 −0.974448
\(768\) 0 0
\(769\) 2.56309e7 1.56296 0.781481 0.623929i \(-0.214465\pi\)
0.781481 + 0.623929i \(0.214465\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.07212e7 −1.24729 −0.623644 0.781709i \(-0.714348\pi\)
−0.623644 + 0.781709i \(0.714348\pi\)
\(774\) 0 0
\(775\) −231332. −0.0138351
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.51173e6 −0.0892544
\(780\) 0 0
\(781\) −3.49975e7 −2.05310
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.71264e7 0.991954
\(786\) 0 0
\(787\) 2.42099e6 0.139334 0.0696669 0.997570i \(-0.477806\pi\)
0.0696669 + 0.997570i \(0.477806\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.71170e6 −0.267754
\(792\) 0 0
\(793\) 9.78334e6 0.552464
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.82162e7 1.01581 0.507905 0.861413i \(-0.330420\pi\)
0.507905 + 0.861413i \(0.330420\pi\)
\(798\) 0 0
\(799\) −1.88239e7 −1.04314
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.82300e7 −1.54498
\(804\) 0 0
\(805\) −4.97624e6 −0.270652
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.25647e7 −1.74935 −0.874674 0.484711i \(-0.838925\pi\)
−0.874674 + 0.484711i \(0.838925\pi\)
\(810\) 0 0
\(811\) 1.52243e7 0.812801 0.406401 0.913695i \(-0.366784\pi\)
0.406401 + 0.913695i \(0.366784\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.92440e7 1.01485
\(816\) 0 0
\(817\) −3.12286e6 −0.163681
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.47838e7 −1.80102 −0.900511 0.434833i \(-0.856807\pi\)
−0.900511 + 0.434833i \(0.856807\pi\)
\(822\) 0 0
\(823\) 4.15043e6 0.213596 0.106798 0.994281i \(-0.465940\pi\)
0.106798 + 0.994281i \(0.465940\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.23139e7 0.626082 0.313041 0.949740i \(-0.398652\pi\)
0.313041 + 0.949740i \(0.398652\pi\)
\(828\) 0 0
\(829\) −2.50392e7 −1.26542 −0.632710 0.774389i \(-0.718058\pi\)
−0.632710 + 0.774389i \(0.718058\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.33622e6 −0.116654
\(834\) 0 0
\(835\) −1.50106e7 −0.745045
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6.76247e6 0.331666 0.165833 0.986154i \(-0.446969\pi\)
0.165833 + 0.986154i \(0.446969\pi\)
\(840\) 0 0
\(841\) 2.66633e7 1.29994
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.44194e6 0.214009
\(846\) 0 0
\(847\) −5.11094e6 −0.244789
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.68243e7 −1.26971
\(852\) 0 0
\(853\) −601162. −0.0282891 −0.0141445 0.999900i \(-0.504502\pi\)
−0.0141445 + 0.999900i \(0.504502\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.81694e7 0.845062 0.422531 0.906349i \(-0.361142\pi\)
0.422531 + 0.906349i \(0.361142\pi\)
\(858\) 0 0
\(859\) −4.04414e7 −1.87001 −0.935004 0.354636i \(-0.884605\pi\)
−0.935004 + 0.354636i \(0.884605\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8.66358e6 −0.395977 −0.197989 0.980204i \(-0.563441\pi\)
−0.197989 + 0.980204i \(0.563441\pi\)
\(864\) 0 0
\(865\) 3.10139e7 1.40934
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.63646e7 0.735114
\(870\) 0 0
\(871\) −2.45408e7 −1.09608
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.34082e6 0.368289
\(876\) 0 0
\(877\) 1.30182e6 0.0571548 0.0285774 0.999592i \(-0.490902\pi\)
0.0285774 + 0.999592i \(0.490902\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.03826e7 −0.884749 −0.442374 0.896830i \(-0.645864\pi\)
−0.442374 + 0.896830i \(0.645864\pi\)
\(882\) 0 0
\(883\) 3.24432e6 0.140030 0.0700152 0.997546i \(-0.477695\pi\)
0.0700152 + 0.997546i \(0.477695\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.57482e7 1.09885 0.549425 0.835543i \(-0.314847\pi\)
0.549425 + 0.835543i \(0.314847\pi\)
\(888\) 0 0
\(889\) 6.22849e6 0.264319
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.49423e6 −0.230557
\(894\) 0 0
\(895\) −1.69730e7 −0.708272
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.05223e7 −0.434223
\(900\) 0 0
\(901\) −2.28337e7 −0.937054
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.36276e7 1.36482
\(906\) 0 0
\(907\) 2.75038e6 0.111013 0.0555066 0.998458i \(-0.482323\pi\)
0.0555066 + 0.998458i \(0.482323\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.07918e7 1.22925 0.614624 0.788820i \(-0.289308\pi\)
0.614624 + 0.788820i \(0.289308\pi\)
\(912\) 0 0
\(913\) 3.82113e7 1.51710
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.60983e7 −0.632203
\(918\) 0 0
\(919\) −1.55324e7 −0.606666 −0.303333 0.952885i \(-0.598099\pi\)
−0.303333 + 0.952885i \(0.598099\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.55195e7 1.75871
\(924\) 0 0
\(925\) −2.28282e6 −0.0877237
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4.23841e6 −0.161125 −0.0805626 0.996750i \(-0.525672\pi\)
−0.0805626 + 0.996750i \(0.525672\pi\)
\(930\) 0 0
\(931\) −681884. −0.0257832
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.86885e7 −1.07319
\(936\) 0 0
\(937\) 2.16194e7 0.804443 0.402222 0.915542i \(-0.368238\pi\)
0.402222 + 0.915542i \(0.368238\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.75669e7 1.75118 0.875590 0.483055i \(-0.160473\pi\)
0.875590 + 0.483055i \(0.160473\pi\)
\(942\) 0 0
\(943\) 9.44471e6 0.345867
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.54109e7 1.64545 0.822726 0.568438i \(-0.192452\pi\)
0.822726 + 0.568438i \(0.192452\pi\)
\(948\) 0 0
\(949\) 3.67173e7 1.32344
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.93139e7 1.04554 0.522772 0.852473i \(-0.324898\pi\)
0.522772 + 0.852473i \(0.324898\pi\)
\(954\) 0 0
\(955\) −1.07682e7 −0.382063
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 8.65494e6 0.303891
\(960\) 0 0
\(961\) −2.62821e7 −0.918020
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.30675e7 0.797411
\(966\) 0 0
\(967\) 1.45552e7 0.500557 0.250278 0.968174i \(-0.419478\pi\)
0.250278 + 0.968174i \(0.419478\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.70222e7 1.60050 0.800248 0.599669i \(-0.204701\pi\)
0.800248 + 0.599669i \(0.204701\pi\)
\(972\) 0 0
\(973\) −2.73381e6 −0.0925733
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.46666e7 −1.16192 −0.580958 0.813934i \(-0.697322\pi\)
−0.580958 + 0.813934i \(0.697322\pi\)
\(978\) 0 0
\(979\) −442260. −0.0147476
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.35848e7 −0.778482 −0.389241 0.921136i \(-0.627263\pi\)
−0.389241 + 0.921136i \(0.627263\pi\)
\(984\) 0 0
\(985\) 1.45782e7 0.478755
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.95105e7 0.634275
\(990\) 0 0
\(991\) −2.63456e7 −0.852166 −0.426083 0.904684i \(-0.640107\pi\)
−0.426083 + 0.904684i \(0.640107\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.02250e7 −0.647637
\(996\) 0 0
\(997\) 1.40009e7 0.446086 0.223043 0.974809i \(-0.428401\pi\)
0.223043 + 0.974809i \(0.428401\pi\)
\(998\) 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.bk.1.2 2
3.2 odd 2 inner 1008.6.a.bk.1.1 2
4.3 odd 2 252.6.a.g.1.2 yes 2
12.11 even 2 252.6.a.g.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.6.a.g.1.1 2 12.11 even 2
252.6.a.g.1.2 yes 2 4.3 odd 2
1008.6.a.bk.1.1 2 3.2 odd 2 inner
1008.6.a.bk.1.2 2 1.1 even 1 trivial