Properties

Label 1008.6.a.e.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
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)
 
\(f(q)\) \(=\) \(q-74.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-74.0000 q^{5} -49.0000 q^{7} +216.000 q^{11} -186.000 q^{13} -1078.00 q^{17} +908.000 q^{19} -2236.00 q^{23} +2351.00 q^{25} -5366.00 q^{29} +536.000 q^{31} +3626.00 q^{35} +3798.00 q^{37} -18598.0 q^{41} -15308.0 q^{43} +23480.0 q^{47} +2401.00 q^{49} -9062.00 q^{53} -15984.0 q^{55} -49284.0 q^{59} +17806.0 q^{61} +13764.0 q^{65} -24876.0 q^{67} +3468.00 q^{71} -32414.0 q^{73} -10584.0 q^{77} -25384.0 q^{79} -67284.0 q^{83} +79772.0 q^{85} +698.000 q^{89} +9114.00 q^{91} -67192.0 q^{95} +154906. q^{97} +O(q^{100})\)

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
\(5\) −74.0000 −1.32375 −0.661876 0.749613i \(-0.730240\pi\)
−0.661876 + 0.749613i \(0.730240\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 216.000 0.538235 0.269118 0.963107i \(-0.413268\pi\)
0.269118 + 0.963107i \(0.413268\pi\)
\(12\) 0 0
\(13\) −186.000 −0.305249 −0.152625 0.988284i \(-0.548773\pi\)
−0.152625 + 0.988284i \(0.548773\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1078.00 −0.904683 −0.452342 0.891845i \(-0.649411\pi\)
−0.452342 + 0.891845i \(0.649411\pi\)
\(18\) 0 0
\(19\) 908.000 0.577035 0.288517 0.957475i \(-0.406838\pi\)
0.288517 + 0.957475i \(0.406838\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2236.00 −0.881358 −0.440679 0.897665i \(-0.645262\pi\)
−0.440679 + 0.897665i \(0.645262\pi\)
\(24\) 0 0
\(25\) 2351.00 0.752320
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5366.00 −1.18483 −0.592414 0.805633i \(-0.701825\pi\)
−0.592414 + 0.805633i \(0.701825\pi\)
\(30\) 0 0
\(31\) 536.000 0.100175 0.0500876 0.998745i \(-0.484050\pi\)
0.0500876 + 0.998745i \(0.484050\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3626.00 0.500331
\(36\) 0 0
\(37\) 3798.00 0.456090 0.228045 0.973651i \(-0.426767\pi\)
0.228045 + 0.973651i \(0.426767\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −18598.0 −1.72785 −0.863926 0.503619i \(-0.832002\pi\)
−0.863926 + 0.503619i \(0.832002\pi\)
\(42\) 0 0
\(43\) −15308.0 −1.26255 −0.631273 0.775561i \(-0.717467\pi\)
−0.631273 + 0.775561i \(0.717467\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 23480.0 1.55043 0.775217 0.631695i \(-0.217640\pi\)
0.775217 + 0.631695i \(0.217640\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9062.00 −0.443133 −0.221567 0.975145i \(-0.571117\pi\)
−0.221567 + 0.975145i \(0.571117\pi\)
\(54\) 0 0
\(55\) −15984.0 −0.712490
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −49284.0 −1.84321 −0.921607 0.388124i \(-0.873123\pi\)
−0.921607 + 0.388124i \(0.873123\pi\)
\(60\) 0 0
\(61\) 17806.0 0.612691 0.306346 0.951920i \(-0.400894\pi\)
0.306346 + 0.951920i \(0.400894\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13764.0 0.404074
\(66\) 0 0
\(67\) −24876.0 −0.677008 −0.338504 0.940965i \(-0.609921\pi\)
−0.338504 + 0.940965i \(0.609921\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3468.00 0.0816457 0.0408228 0.999166i \(-0.487002\pi\)
0.0408228 + 0.999166i \(0.487002\pi\)
\(72\) 0 0
\(73\) −32414.0 −0.711911 −0.355955 0.934503i \(-0.615844\pi\)
−0.355955 + 0.934503i \(0.615844\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10584.0 −0.203434
\(78\) 0 0
\(79\) −25384.0 −0.457607 −0.228803 0.973473i \(-0.573481\pi\)
−0.228803 + 0.973473i \(0.573481\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −67284.0 −1.07205 −0.536027 0.844201i \(-0.680075\pi\)
−0.536027 + 0.844201i \(0.680075\pi\)
\(84\) 0 0
\(85\) 79772.0 1.19758
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 698.000 0.00934072 0.00467036 0.999989i \(-0.498513\pi\)
0.00467036 + 0.999989i \(0.498513\pi\)
\(90\) 0 0
\(91\) 9114.00 0.115373
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −67192.0 −0.763851
\(96\) 0 0
\(97\) 154906. 1.67163 0.835813 0.549015i \(-0.184997\pi\)
0.835813 + 0.549015i \(0.184997\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −23538.0 −0.229597 −0.114798 0.993389i \(-0.536622\pi\)
−0.114798 + 0.993389i \(0.536622\pi\)
\(102\) 0 0
\(103\) −16464.0 −0.152912 −0.0764561 0.997073i \(-0.524361\pi\)
−0.0764561 + 0.997073i \(0.524361\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −113640. −0.959559 −0.479780 0.877389i \(-0.659283\pi\)
−0.479780 + 0.877389i \(0.659283\pi\)
\(108\) 0 0
\(109\) 107374. 0.865631 0.432816 0.901482i \(-0.357520\pi\)
0.432816 + 0.901482i \(0.357520\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 86766.0 0.639225 0.319612 0.947548i \(-0.396447\pi\)
0.319612 + 0.947548i \(0.396447\pi\)
\(114\) 0 0
\(115\) 165464. 1.16670
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 52822.0 0.341938
\(120\) 0 0
\(121\) −114395. −0.710303
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 57276.0 0.327867
\(126\) 0 0
\(127\) 98056.0 0.539467 0.269733 0.962935i \(-0.413064\pi\)
0.269733 + 0.962935i \(0.413064\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 160604. 0.817670 0.408835 0.912608i \(-0.365935\pi\)
0.408835 + 0.912608i \(0.365935\pi\)
\(132\) 0 0
\(133\) −44492.0 −0.218099
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 99694.0 0.453803 0.226902 0.973918i \(-0.427140\pi\)
0.226902 + 0.973918i \(0.427140\pi\)
\(138\) 0 0
\(139\) 110508. 0.485128 0.242564 0.970135i \(-0.422011\pi\)
0.242564 + 0.970135i \(0.422011\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −40176.0 −0.164296
\(144\) 0 0
\(145\) 397084. 1.56842
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 277562. 1.02422 0.512111 0.858919i \(-0.328864\pi\)
0.512111 + 0.858919i \(0.328864\pi\)
\(150\) 0 0
\(151\) 372872. 1.33081 0.665407 0.746481i \(-0.268258\pi\)
0.665407 + 0.746481i \(0.268258\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −39664.0 −0.132607
\(156\) 0 0
\(157\) 532638. 1.72458 0.862289 0.506416i \(-0.169030\pi\)
0.862289 + 0.506416i \(0.169030\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 109564. 0.333122
\(162\) 0 0
\(163\) −545164. −1.60716 −0.803578 0.595199i \(-0.797073\pi\)
−0.803578 + 0.595199i \(0.797073\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −304176. −0.843983 −0.421992 0.906600i \(-0.638669\pi\)
−0.421992 + 0.906600i \(0.638669\pi\)
\(168\) 0 0
\(169\) −336697. −0.906823
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −108506. −0.275638 −0.137819 0.990457i \(-0.544009\pi\)
−0.137819 + 0.990457i \(0.544009\pi\)
\(174\) 0 0
\(175\) −115199. −0.284350
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 62072.0 0.144798 0.0723991 0.997376i \(-0.476934\pi\)
0.0723991 + 0.997376i \(0.476934\pi\)
\(180\) 0 0
\(181\) 762734. 1.73052 0.865260 0.501323i \(-0.167153\pi\)
0.865260 + 0.501323i \(0.167153\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −281052. −0.603750
\(186\) 0 0
\(187\) −232848. −0.486932
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −371036. −0.735923 −0.367962 0.929841i \(-0.619944\pi\)
−0.367962 + 0.929841i \(0.619944\pi\)
\(192\) 0 0
\(193\) −375534. −0.725698 −0.362849 0.931848i \(-0.618196\pi\)
−0.362849 + 0.931848i \(0.618196\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.07803e6 1.97908 0.989541 0.144254i \(-0.0460782\pi\)
0.989541 + 0.144254i \(0.0460782\pi\)
\(198\) 0 0
\(199\) 60280.0 0.107905 0.0539524 0.998544i \(-0.482818\pi\)
0.0539524 + 0.998544i \(0.482818\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 262934. 0.447823
\(204\) 0 0
\(205\) 1.37625e6 2.28725
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 196128. 0.310580
\(210\) 0 0
\(211\) −766436. −1.18514 −0.592570 0.805519i \(-0.701887\pi\)
−0.592570 + 0.805519i \(0.701887\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.13279e6 1.67130
\(216\) 0 0
\(217\) −26264.0 −0.0378627
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 200508. 0.276154
\(222\) 0 0
\(223\) −300768. −0.405013 −0.202507 0.979281i \(-0.564909\pi\)
−0.202507 + 0.979281i \(0.564909\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.20016e6 1.54588 0.772940 0.634479i \(-0.218785\pi\)
0.772940 + 0.634479i \(0.218785\pi\)
\(228\) 0 0
\(229\) −217330. −0.273861 −0.136931 0.990581i \(-0.543724\pi\)
−0.136931 + 0.990581i \(0.543724\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 612526. 0.739154 0.369577 0.929200i \(-0.379503\pi\)
0.369577 + 0.929200i \(0.379503\pi\)
\(234\) 0 0
\(235\) −1.73752e6 −2.05239
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −668164. −0.756638 −0.378319 0.925675i \(-0.623498\pi\)
−0.378319 + 0.925675i \(0.623498\pi\)
\(240\) 0 0
\(241\) −972038. −1.07805 −0.539027 0.842288i \(-0.681208\pi\)
−0.539027 + 0.842288i \(0.681208\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −177674. −0.189107
\(246\) 0 0
\(247\) −168888. −0.176139
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.73264e6 1.73589 0.867947 0.496657i \(-0.165439\pi\)
0.867947 + 0.496657i \(0.165439\pi\)
\(252\) 0 0
\(253\) −482976. −0.474378
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −514542. −0.485946 −0.242973 0.970033i \(-0.578123\pi\)
−0.242973 + 0.970033i \(0.578123\pi\)
\(258\) 0 0
\(259\) −186102. −0.172386
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 682836. 0.608733 0.304367 0.952555i \(-0.401555\pi\)
0.304367 + 0.952555i \(0.401555\pi\)
\(264\) 0 0
\(265\) 670588. 0.586599
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.05574e6 0.889564 0.444782 0.895639i \(-0.353281\pi\)
0.444782 + 0.895639i \(0.353281\pi\)
\(270\) 0 0
\(271\) −241400. −0.199671 −0.0998353 0.995004i \(-0.531832\pi\)
−0.0998353 + 0.995004i \(0.531832\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 507816. 0.404925
\(276\) 0 0
\(277\) −2.27139e6 −1.77865 −0.889327 0.457272i \(-0.848827\pi\)
−0.889327 + 0.457272i \(0.848827\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.91293e6 1.44521 0.722607 0.691259i \(-0.242944\pi\)
0.722607 + 0.691259i \(0.242944\pi\)
\(282\) 0 0
\(283\) 2.28975e6 1.69950 0.849751 0.527185i \(-0.176752\pi\)
0.849751 + 0.527185i \(0.176752\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 911302. 0.653067
\(288\) 0 0
\(289\) −257773. −0.181549
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.11253e6 0.757079 0.378539 0.925585i \(-0.376426\pi\)
0.378539 + 0.925585i \(0.376426\pi\)
\(294\) 0 0
\(295\) 3.64702e6 2.43996
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 415896. 0.269034
\(300\) 0 0
\(301\) 750092. 0.477198
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.31764e6 −0.811052
\(306\) 0 0
\(307\) −615988. −0.373015 −0.186508 0.982454i \(-0.559717\pi\)
−0.186508 + 0.982454i \(0.559717\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −891408. −0.522607 −0.261304 0.965257i \(-0.584152\pi\)
−0.261304 + 0.965257i \(0.584152\pi\)
\(312\) 0 0
\(313\) −1.65852e6 −0.956884 −0.478442 0.878119i \(-0.658798\pi\)
−0.478442 + 0.878119i \(0.658798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −816798. −0.456527 −0.228264 0.973599i \(-0.573305\pi\)
−0.228264 + 0.973599i \(0.573305\pi\)
\(318\) 0 0
\(319\) −1.15906e6 −0.637717
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −978824. −0.522033
\(324\) 0 0
\(325\) −437286. −0.229645
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.15052e6 −0.586009
\(330\) 0 0
\(331\) 1.78008e6 0.893039 0.446520 0.894774i \(-0.352663\pi\)
0.446520 + 0.894774i \(0.352663\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.84082e6 0.896190
\(336\) 0 0
\(337\) 1.30551e6 0.626187 0.313094 0.949722i \(-0.398635\pi\)
0.313094 + 0.949722i \(0.398635\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 115776. 0.0539179
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.32307e6 0.589875 0.294937 0.955517i \(-0.404701\pi\)
0.294937 + 0.955517i \(0.404701\pi\)
\(348\) 0 0
\(349\) −139330. −0.0612324 −0.0306162 0.999531i \(-0.509747\pi\)
−0.0306162 + 0.999531i \(0.509747\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.75783e6 1.17796 0.588981 0.808147i \(-0.299529\pi\)
0.588981 + 0.808147i \(0.299529\pi\)
\(354\) 0 0
\(355\) −256632. −0.108079
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.47218e6 −1.01238 −0.506190 0.862422i \(-0.668947\pi\)
−0.506190 + 0.862422i \(0.668947\pi\)
\(360\) 0 0
\(361\) −1.65163e6 −0.667031
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.39864e6 0.942393
\(366\) 0 0
\(367\) 3.89637e6 1.51006 0.755031 0.655689i \(-0.227622\pi\)
0.755031 + 0.655689i \(0.227622\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 444038. 0.167489
\(372\) 0 0
\(373\) 2.54231e6 0.946142 0.473071 0.881024i \(-0.343145\pi\)
0.473071 + 0.881024i \(0.343145\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 998076. 0.361668
\(378\) 0 0
\(379\) 4.60420e6 1.64648 0.823239 0.567695i \(-0.192165\pi\)
0.823239 + 0.567695i \(0.192165\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −128640. −0.0448104 −0.0224052 0.999749i \(-0.507132\pi\)
−0.0224052 + 0.999749i \(0.507132\pi\)
\(384\) 0 0
\(385\) 783216. 0.269296
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.82077e6 1.95032 0.975161 0.221496i \(-0.0710940\pi\)
0.975161 + 0.221496i \(0.0710940\pi\)
\(390\) 0 0
\(391\) 2.41041e6 0.797349
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.87842e6 0.605758
\(396\) 0 0
\(397\) 2.10091e6 0.669008 0.334504 0.942394i \(-0.391431\pi\)
0.334504 + 0.942394i \(0.391431\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.58388e6 −1.73410 −0.867052 0.498217i \(-0.833988\pi\)
−0.867052 + 0.498217i \(0.833988\pi\)
\(402\) 0 0
\(403\) −99696.0 −0.0305784
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 820368. 0.245484
\(408\) 0 0
\(409\) −4.96822e6 −1.46856 −0.734282 0.678845i \(-0.762481\pi\)
−0.734282 + 0.678845i \(0.762481\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.41492e6 0.696670
\(414\) 0 0
\(415\) 4.97902e6 1.41913
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.41098e6 1.22744 0.613720 0.789524i \(-0.289673\pi\)
0.613720 + 0.789524i \(0.289673\pi\)
\(420\) 0 0
\(421\) −2.69671e6 −0.741532 −0.370766 0.928726i \(-0.620905\pi\)
−0.370766 + 0.928726i \(0.620905\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.53438e6 −0.680611
\(426\) 0 0
\(427\) −872494. −0.231576
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.11504e6 −1.32634 −0.663171 0.748468i \(-0.730790\pi\)
−0.663171 + 0.748468i \(0.730790\pi\)
\(432\) 0 0
\(433\) 6.40472e6 1.64165 0.820825 0.571180i \(-0.193514\pi\)
0.820825 + 0.571180i \(0.193514\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.03029e6 −0.508574
\(438\) 0 0
\(439\) −3.67092e6 −0.909104 −0.454552 0.890720i \(-0.650201\pi\)
−0.454552 + 0.890720i \(0.650201\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.91509e6 1.18993 0.594966 0.803751i \(-0.297166\pi\)
0.594966 + 0.803751i \(0.297166\pi\)
\(444\) 0 0
\(445\) −51652.0 −0.0123648
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.10147e6 −0.491936 −0.245968 0.969278i \(-0.579106\pi\)
−0.245968 + 0.969278i \(0.579106\pi\)
\(450\) 0 0
\(451\) −4.01717e6 −0.929991
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −674436. −0.152726
\(456\) 0 0
\(457\) 3.00356e6 0.672738 0.336369 0.941730i \(-0.390801\pi\)
0.336369 + 0.941730i \(0.390801\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.49454e6 −0.765839 −0.382919 0.923782i \(-0.625081\pi\)
−0.382919 + 0.923782i \(0.625081\pi\)
\(462\) 0 0
\(463\) 6.61804e6 1.43475 0.717376 0.696686i \(-0.245343\pi\)
0.717376 + 0.696686i \(0.245343\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.86853e6 1.66956 0.834779 0.550585i \(-0.185595\pi\)
0.834779 + 0.550585i \(0.185595\pi\)
\(468\) 0 0
\(469\) 1.21892e6 0.255885
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.30653e6 −0.679547
\(474\) 0 0
\(475\) 2.13471e6 0.434115
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.70513e6 1.13613 0.568063 0.822985i \(-0.307693\pi\)
0.568063 + 0.822985i \(0.307693\pi\)
\(480\) 0 0
\(481\) −706428. −0.139221
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.14630e7 −2.21282
\(486\) 0 0
\(487\) 1.40170e6 0.267814 0.133907 0.990994i \(-0.457248\pi\)
0.133907 + 0.990994i \(0.457248\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.85330e6 −1.28291 −0.641454 0.767161i \(-0.721669\pi\)
−0.641454 + 0.767161i \(0.721669\pi\)
\(492\) 0 0
\(493\) 5.78455e6 1.07189
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −169932. −0.0308592
\(498\) 0 0
\(499\) 699596. 0.125775 0.0628877 0.998021i \(-0.479969\pi\)
0.0628877 + 0.998021i \(0.479969\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6.28585e6 −1.10776 −0.553878 0.832598i \(-0.686853\pi\)
−0.553878 + 0.832598i \(0.686853\pi\)
\(504\) 0 0
\(505\) 1.74181e6 0.303929
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.58181e6 −0.783867 −0.391934 0.919993i \(-0.628194\pi\)
−0.391934 + 0.919993i \(0.628194\pi\)
\(510\) 0 0
\(511\) 1.58829e6 0.269077
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.21834e6 0.202418
\(516\) 0 0
\(517\) 5.07168e6 0.834498
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.12576e7 1.81699 0.908493 0.417900i \(-0.137234\pi\)
0.908493 + 0.417900i \(0.137234\pi\)
\(522\) 0 0
\(523\) −8.20312e6 −1.31137 −0.655685 0.755035i \(-0.727620\pi\)
−0.655685 + 0.755035i \(0.727620\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −577808. −0.0906269
\(528\) 0 0
\(529\) −1.43665e6 −0.223209
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.45923e6 0.527426
\(534\) 0 0
\(535\) 8.40936e6 1.27022
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 518616. 0.0768907
\(540\) 0 0
\(541\) −8.20335e6 −1.20503 −0.602515 0.798108i \(-0.705835\pi\)
−0.602515 + 0.798108i \(0.705835\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.94568e6 −1.14588
\(546\) 0 0
\(547\) −1.21740e7 −1.73967 −0.869833 0.493346i \(-0.835774\pi\)
−0.869833 + 0.493346i \(0.835774\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.87233e6 −0.683687
\(552\) 0 0
\(553\) 1.24382e6 0.172959
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.31330e6 0.862220 0.431110 0.902299i \(-0.358122\pi\)
0.431110 + 0.902299i \(0.358122\pi\)
\(558\) 0 0
\(559\) 2.84729e6 0.385391
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −692588. −0.0920882 −0.0460441 0.998939i \(-0.514661\pi\)
−0.0460441 + 0.998939i \(0.514661\pi\)
\(564\) 0 0
\(565\) −6.42068e6 −0.846175
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.25329e6 0.291768 0.145884 0.989302i \(-0.453397\pi\)
0.145884 + 0.989302i \(0.453397\pi\)
\(570\) 0 0
\(571\) −1.11830e7 −1.43538 −0.717690 0.696363i \(-0.754800\pi\)
−0.717690 + 0.696363i \(0.754800\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.25684e6 −0.663063
\(576\) 0 0
\(577\) −9.00373e6 −1.12586 −0.562928 0.826506i \(-0.690325\pi\)
−0.562928 + 0.826506i \(0.690325\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.29692e6 0.405198
\(582\) 0 0
\(583\) −1.95739e6 −0.238510
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.98821e6 −0.357945 −0.178972 0.983854i \(-0.557277\pi\)
−0.178972 + 0.983854i \(0.557277\pi\)
\(588\) 0 0
\(589\) 486688. 0.0578046
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.32321e7 1.54522 0.772611 0.634880i \(-0.218951\pi\)
0.772611 + 0.634880i \(0.218951\pi\)
\(594\) 0 0
\(595\) −3.90883e6 −0.452641
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.03034e7 −1.17331 −0.586657 0.809836i \(-0.699556\pi\)
−0.586657 + 0.809836i \(0.699556\pi\)
\(600\) 0 0
\(601\) 1.18785e7 1.34145 0.670725 0.741706i \(-0.265983\pi\)
0.670725 + 0.741706i \(0.265983\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.46523e6 0.940265
\(606\) 0 0
\(607\) −1.21813e7 −1.34190 −0.670951 0.741502i \(-0.734114\pi\)
−0.670951 + 0.741502i \(0.734114\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.36728e6 −0.473269
\(612\) 0 0
\(613\) −5.67204e6 −0.609661 −0.304830 0.952407i \(-0.598600\pi\)
−0.304830 + 0.952407i \(0.598600\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.31301e6 −0.773363 −0.386681 0.922213i \(-0.626379\pi\)
−0.386681 + 0.922213i \(0.626379\pi\)
\(618\) 0 0
\(619\) −2.30831e6 −0.242140 −0.121070 0.992644i \(-0.538633\pi\)
−0.121070 + 0.992644i \(0.538633\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −34202.0 −0.00353046
\(624\) 0 0
\(625\) −1.15853e7 −1.18633
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.09424e6 −0.412617
\(630\) 0 0
\(631\) −1.10468e7 −1.10449 −0.552244 0.833682i \(-0.686228\pi\)
−0.552244 + 0.833682i \(0.686228\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.25614e6 −0.714121
\(636\) 0 0
\(637\) −446586. −0.0436070
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.48945e6 0.335437 0.167719 0.985835i \(-0.446360\pi\)
0.167719 + 0.985835i \(0.446360\pi\)
\(642\) 0 0
\(643\) 5.66155e6 0.540017 0.270009 0.962858i \(-0.412973\pi\)
0.270009 + 0.962858i \(0.412973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.18746e6 −0.205437 −0.102718 0.994710i \(-0.532754\pi\)
−0.102718 + 0.994710i \(0.532754\pi\)
\(648\) 0 0
\(649\) −1.06453e7 −0.992083
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.36706e6 −0.767874 −0.383937 0.923359i \(-0.625432\pi\)
−0.383937 + 0.923359i \(0.625432\pi\)
\(654\) 0 0
\(655\) −1.18847e7 −1.08239
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 662336. 0.0594107 0.0297054 0.999559i \(-0.490543\pi\)
0.0297054 + 0.999559i \(0.490543\pi\)
\(660\) 0 0
\(661\) −1.00537e7 −0.894995 −0.447497 0.894285i \(-0.647685\pi\)
−0.447497 + 0.894285i \(0.647685\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.29241e6 0.288708
\(666\) 0 0
\(667\) 1.19984e7 1.04426
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.84610e6 0.329772
\(672\) 0 0
\(673\) 1.73547e7 1.47699 0.738497 0.674257i \(-0.235536\pi\)
0.738497 + 0.674257i \(0.235536\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.18052e7 0.989923 0.494962 0.868915i \(-0.335182\pi\)
0.494962 + 0.868915i \(0.335182\pi\)
\(678\) 0 0
\(679\) −7.59039e6 −0.631815
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.03419e6 0.166855 0.0834277 0.996514i \(-0.473413\pi\)
0.0834277 + 0.996514i \(0.473413\pi\)
\(684\) 0 0
\(685\) −7.37736e6 −0.600723
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.68553e6 0.135266
\(690\) 0 0
\(691\) 6.80453e6 0.542130 0.271065 0.962561i \(-0.412624\pi\)
0.271065 + 0.962561i \(0.412624\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.17759e6 −0.642190
\(696\) 0 0
\(697\) 2.00486e7 1.56316
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.05452e7 0.810512 0.405256 0.914203i \(-0.367182\pi\)
0.405256 + 0.914203i \(0.367182\pi\)
\(702\) 0 0
\(703\) 3.44858e6 0.263180
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.15336e6 0.0867795
\(708\) 0 0
\(709\) 2.31218e7 1.72745 0.863725 0.503964i \(-0.168125\pi\)
0.863725 + 0.503964i \(0.168125\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.19850e6 −0.0882903
\(714\) 0 0
\(715\) 2.97302e6 0.217487
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.12905e7 0.814497 0.407249 0.913317i \(-0.366488\pi\)
0.407249 + 0.913317i \(0.366488\pi\)
\(720\) 0 0
\(721\) 806736. 0.0577954
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.26155e7 −0.891371
\(726\) 0 0
\(727\) −1.10545e7 −0.775719 −0.387859 0.921719i \(-0.626785\pi\)
−0.387859 + 0.921719i \(0.626785\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.65020e7 1.14220
\(732\) 0 0
\(733\) −9.39718e6 −0.646007 −0.323004 0.946398i \(-0.604693\pi\)
−0.323004 + 0.946398i \(0.604693\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.37322e6 −0.364389
\(738\) 0 0
\(739\) −1.69963e7 −1.14484 −0.572418 0.819962i \(-0.693995\pi\)
−0.572418 + 0.819962i \(0.693995\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.70520e6 0.312684 0.156342 0.987703i \(-0.450030\pi\)
0.156342 + 0.987703i \(0.450030\pi\)
\(744\) 0 0
\(745\) −2.05396e7 −1.35582
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.56836e6 0.362679
\(750\) 0 0
\(751\) 8.00214e6 0.517734 0.258867 0.965913i \(-0.416651\pi\)
0.258867 + 0.965913i \(0.416651\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.75925e7 −1.76167
\(756\) 0 0
\(757\) 2.00466e7 1.27146 0.635729 0.771912i \(-0.280700\pi\)
0.635729 + 0.771912i \(0.280700\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.39759e6 −0.588240 −0.294120 0.955768i \(-0.595027\pi\)
−0.294120 + 0.955768i \(0.595027\pi\)
\(762\) 0 0
\(763\) −5.26133e6 −0.327178
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.16682e6 0.562640
\(768\) 0 0
\(769\) 8.43805e6 0.514548 0.257274 0.966338i \(-0.417176\pi\)
0.257274 + 0.966338i \(0.417176\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.59390e7 −1.56137 −0.780684 0.624926i \(-0.785129\pi\)
−0.780684 + 0.624926i \(0.785129\pi\)
\(774\) 0 0
\(775\) 1.26014e6 0.0753639
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.68870e7 −0.997031
\(780\) 0 0
\(781\) 749088. 0.0439446
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.94152e7 −2.28291
\(786\) 0 0
\(787\) −2.77502e7 −1.59709 −0.798544 0.601936i \(-0.794396\pi\)
−0.798544 + 0.601936i \(0.794396\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.25153e6 −0.241604
\(792\) 0 0
\(793\) −3.31192e6 −0.187024
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.66947e7 1.48860 0.744301 0.667844i \(-0.232783\pi\)
0.744301 + 0.667844i \(0.232783\pi\)
\(798\) 0 0
\(799\) −2.53114e7 −1.40265
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7.00142e6 −0.383175
\(804\) 0 0
\(805\) −8.10774e6 −0.440971
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.62003e6 −0.140745 −0.0703727 0.997521i \(-0.522419\pi\)
−0.0703727 + 0.997521i \(0.522419\pi\)
\(810\) 0 0
\(811\) 1.86925e7 0.997965 0.498983 0.866612i \(-0.333707\pi\)
0.498983 + 0.866612i \(0.333707\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.03421e7 2.12748
\(816\) 0 0
\(817\) −1.38997e7 −0.728533
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.31881e6 −0.378950 −0.189475 0.981886i \(-0.560679\pi\)
−0.189475 + 0.981886i \(0.560679\pi\)
\(822\) 0 0
\(823\) −1.28122e7 −0.659362 −0.329681 0.944092i \(-0.606941\pi\)
−0.329681 + 0.944092i \(0.606941\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8.71034e6 −0.442865 −0.221433 0.975176i \(-0.571073\pi\)
−0.221433 + 0.975176i \(0.571073\pi\)
\(828\) 0 0
\(829\) −2.02190e7 −1.02182 −0.510909 0.859635i \(-0.670691\pi\)
−0.510909 + 0.859635i \(0.670691\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.58828e6 −0.129240
\(834\) 0 0
\(835\) 2.25090e7 1.11722
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −8.72741e6 −0.428036 −0.214018 0.976830i \(-0.568655\pi\)
−0.214018 + 0.976830i \(0.568655\pi\)
\(840\) 0 0
\(841\) 8.28281e6 0.403820
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.49156e7 1.20041
\(846\) 0 0
\(847\) 5.60536e6 0.268469
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −8.49233e6 −0.401979
\(852\) 0 0
\(853\) 2.45049e7 1.15313 0.576567 0.817050i \(-0.304392\pi\)
0.576567 + 0.817050i \(0.304392\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.02514e7 −1.87210 −0.936050 0.351867i \(-0.885547\pi\)
−0.936050 + 0.351867i \(0.885547\pi\)
\(858\) 0 0
\(859\) 2.23124e7 1.03172 0.515862 0.856672i \(-0.327472\pi\)
0.515862 + 0.856672i \(0.327472\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.76747e7 −1.72196 −0.860980 0.508639i \(-0.830149\pi\)
−0.860980 + 0.508639i \(0.830149\pi\)
\(864\) 0 0
\(865\) 8.02944e6 0.364876
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.48294e6 −0.246300
\(870\) 0 0
\(871\) 4.62694e6 0.206656
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.80652e6 −0.123922
\(876\) 0 0
\(877\) 2.44552e7 1.07367 0.536837 0.843686i \(-0.319619\pi\)
0.536837 + 0.843686i \(0.319619\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.92174e7 0.834169 0.417084 0.908868i \(-0.363052\pi\)
0.417084 + 0.908868i \(0.363052\pi\)
\(882\) 0 0
\(883\) −8.50546e6 −0.367110 −0.183555 0.983009i \(-0.558761\pi\)
−0.183555 + 0.983009i \(0.558761\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.50375e7 0.641753 0.320876 0.947121i \(-0.396023\pi\)
0.320876 + 0.947121i \(0.396023\pi\)
\(888\) 0 0
\(889\) −4.80474e6 −0.203899
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.13198e7 0.894654
\(894\) 0 0
\(895\) −4.59333e6 −0.191677
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.87618e6 −0.118691
\(900\) 0 0
\(901\) 9.76884e6 0.400895
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.64423e7 −2.29078
\(906\) 0 0
\(907\) 7.46525e6 0.301319 0.150659 0.988586i \(-0.451860\pi\)
0.150659 + 0.988586i \(0.451860\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.50368e7 −0.999500 −0.499750 0.866170i \(-0.666575\pi\)
−0.499750 + 0.866170i \(0.666575\pi\)
\(912\) 0 0
\(913\) −1.45333e7 −0.577017
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.86960e6 −0.309050
\(918\) 0 0
\(919\) −2.32108e6 −0.0906570 −0.0453285 0.998972i \(-0.514433\pi\)
−0.0453285 + 0.998972i \(0.514433\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −645048. −0.0249223
\(924\) 0 0
\(925\) 8.92910e6 0.343126
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.84131e7 −1.08014 −0.540069 0.841621i \(-0.681602\pi\)
−0.540069 + 0.841621i \(0.681602\pi\)
\(930\) 0 0
\(931\) 2.18011e6 0.0824335
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.72308e7 0.644578
\(936\) 0 0
\(937\) −1.92186e7 −0.715109 −0.357555 0.933892i \(-0.616389\pi\)
−0.357555 + 0.933892i \(0.616389\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.13365e6 −0.225811 −0.112905 0.993606i \(-0.536016\pi\)
−0.112905 + 0.993606i \(0.536016\pi\)
\(942\) 0 0
\(943\) 4.15851e7 1.52286
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.89945e7 −0.688260 −0.344130 0.938922i \(-0.611826\pi\)
−0.344130 + 0.938922i \(0.611826\pi\)
\(948\) 0 0
\(949\) 6.02900e6 0.217310
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 459686. 0.0163957 0.00819783 0.999966i \(-0.497391\pi\)
0.00819783 + 0.999966i \(0.497391\pi\)
\(954\) 0 0
\(955\) 2.74567e7 0.974180
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.88501e6 −0.171522
\(960\) 0 0
\(961\) −2.83419e7 −0.989965
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.77895e7 0.960644
\(966\) 0 0
\(967\) −3.31883e7 −1.14135 −0.570674 0.821177i \(-0.693318\pi\)
−0.570674 + 0.821177i \(0.693318\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −5.06987e7 −1.72564 −0.862818 0.505515i \(-0.831303\pi\)
−0.862818 + 0.505515i \(0.831303\pi\)
\(972\) 0 0
\(973\) −5.41489e6 −0.183361
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.67557e6 0.190228 0.0951138 0.995466i \(-0.469679\pi\)
0.0951138 + 0.995466i \(0.469679\pi\)
\(978\) 0 0
\(979\) 150768. 0.00502750
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.81000e7 0.597441 0.298720 0.954341i \(-0.403440\pi\)
0.298720 + 0.954341i \(0.403440\pi\)
\(984\) 0 0
\(985\) −7.97739e7 −2.61981
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.42287e7 1.11275
\(990\) 0 0
\(991\) 3.99088e7 1.29088 0.645439 0.763812i \(-0.276675\pi\)
0.645439 + 0.763812i \(0.276675\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.46072e6 −0.142839
\(996\) 0 0
\(997\) −3.19517e7 −1.01802 −0.509009 0.860761i \(-0.669988\pi\)
−0.509009 + 0.860761i \(0.669988\pi\)
\(998\) 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.e.1.1 1
3.2 odd 2 336.6.a.p.1.1 1
4.3 odd 2 504.6.a.a.1.1 1
12.11 even 2 168.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.c.1.1 1 12.11 even 2
336.6.a.p.1.1 1 3.2 odd 2
504.6.a.a.1.1 1 4.3 odd 2
1008.6.a.e.1.1 1 1.1 even 1 trivial