Properties

Label 1008.6.a.bp.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(\Q(\sqrt{4281}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1070 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-32.2147\) 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)
 
\(f(q)\) \(=\) \(q+70.4294 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+70.4294 q^{5} -49.0000 q^{7} -169.288 q^{11} -10.8587 q^{13} -2327.02 q^{17} +1508.59 q^{19} +3755.03 q^{23} +1835.29 q^{25} -5648.89 q^{29} -4284.02 q^{31} -3451.04 q^{35} +36.5543 q^{37} -90.6792 q^{41} +8293.26 q^{43} +18570.1 q^{47} +2401.00 q^{49} +11862.5 q^{53} -11922.8 q^{55} +48240.0 q^{59} +22226.2 q^{61} -764.771 q^{65} +10068.0 q^{67} +41797.1 q^{71} +67194.5 q^{73} +8295.11 q^{77} -58313.2 q^{79} -99460.2 q^{83} -163890. q^{85} +107733. q^{89} +532.076 q^{91} +106249. q^{95} -96488.9 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 10 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 10 q^{5} - 98 q^{7} + 54 q^{11} + 240 q^{13} - 1906 q^{17} + 400 q^{19} + 2930 q^{23} + 2362 q^{25} - 5540 q^{29} - 4904 q^{31} - 490 q^{35} + 2952 q^{37} - 6070 q^{41} - 3304 q^{43} + 16988 q^{47} + 4802 q^{49} - 6896 q^{53} - 25416 q^{55} + 53820 q^{59} + 4148 q^{61} - 15924 q^{65} - 33516 q^{67} + 73518 q^{71} + 128 q^{73} - 2646 q^{77} - 57740 q^{79} + 23016 q^{83} - 189332 q^{85} + 141530 q^{89} - 11760 q^{91} + 173240 q^{95} - 226216 q^{97}+O(q^{100}) \) 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
\(5\) 70.4294 1.25988 0.629939 0.776644i \(-0.283080\pi\)
0.629939 + 0.776644i \(0.283080\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −169.288 −0.421837 −0.210918 0.977504i \(-0.567645\pi\)
−0.210918 + 0.977504i \(0.567645\pi\)
\(12\) 0 0
\(13\) −10.8587 −0.0178205 −0.00891024 0.999960i \(-0.502836\pi\)
−0.00891024 + 0.999960i \(0.502836\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2327.02 −1.95289 −0.976444 0.215773i \(-0.930773\pi\)
−0.976444 + 0.215773i \(0.930773\pi\)
\(18\) 0 0
\(19\) 1508.59 0.958708 0.479354 0.877622i \(-0.340871\pi\)
0.479354 + 0.877622i \(0.340871\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3755.03 1.48011 0.740054 0.672547i \(-0.234800\pi\)
0.740054 + 0.672547i \(0.234800\pi\)
\(24\) 0 0
\(25\) 1835.29 0.587294
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5648.89 −1.24729 −0.623646 0.781707i \(-0.714349\pi\)
−0.623646 + 0.781707i \(0.714349\pi\)
\(30\) 0 0
\(31\) −4284.02 −0.800659 −0.400329 0.916371i \(-0.631104\pi\)
−0.400329 + 0.916371i \(0.631104\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3451.04 −0.476189
\(36\) 0 0
\(37\) 36.5543 0.00438969 0.00219484 0.999998i \(-0.499301\pi\)
0.00219484 + 0.999998i \(0.499301\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −90.6792 −0.00842458 −0.00421229 0.999991i \(-0.501341\pi\)
−0.00421229 + 0.999991i \(0.501341\pi\)
\(42\) 0 0
\(43\) 8293.26 0.683997 0.341999 0.939700i \(-0.388896\pi\)
0.341999 + 0.939700i \(0.388896\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 18570.1 1.22622 0.613112 0.789996i \(-0.289917\pi\)
0.613112 + 0.789996i \(0.289917\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11862.5 0.580077 0.290038 0.957015i \(-0.406332\pi\)
0.290038 + 0.957015i \(0.406332\pi\)
\(54\) 0 0
\(55\) −11922.8 −0.531463
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 48240.0 1.80417 0.902084 0.431560i \(-0.142037\pi\)
0.902084 + 0.431560i \(0.142037\pi\)
\(60\) 0 0
\(61\) 22226.2 0.764789 0.382394 0.923999i \(-0.375100\pi\)
0.382394 + 0.923999i \(0.375100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −764.771 −0.0224516
\(66\) 0 0
\(67\) 10068.0 0.274004 0.137002 0.990571i \(-0.456253\pi\)
0.137002 + 0.990571i \(0.456253\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 41797.1 0.984011 0.492005 0.870592i \(-0.336264\pi\)
0.492005 + 0.870592i \(0.336264\pi\)
\(72\) 0 0
\(73\) 67194.5 1.47580 0.737899 0.674912i \(-0.235818\pi\)
0.737899 + 0.674912i \(0.235818\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8295.11 0.159439
\(78\) 0 0
\(79\) −58313.2 −1.05123 −0.525617 0.850721i \(-0.676165\pi\)
−0.525617 + 0.850721i \(0.676165\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −99460.2 −1.58473 −0.792363 0.610050i \(-0.791149\pi\)
−0.792363 + 0.610050i \(0.791149\pi\)
\(84\) 0 0
\(85\) −163890. −2.46040
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 107733. 1.44169 0.720845 0.693096i \(-0.243754\pi\)
0.720845 + 0.693096i \(0.243754\pi\)
\(90\) 0 0
\(91\) 532.076 0.00673551
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 106249. 1.20786
\(96\) 0 0
\(97\) −96488.9 −1.04123 −0.520617 0.853790i \(-0.674298\pi\)
−0.520617 + 0.853790i \(0.674298\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −53571.9 −0.522557 −0.261279 0.965263i \(-0.584144\pi\)
−0.261279 + 0.965263i \(0.584144\pi\)
\(102\) 0 0
\(103\) 111547. 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 59718.8 0.504257 0.252128 0.967694i \(-0.418869\pi\)
0.252128 + 0.967694i \(0.418869\pi\)
\(108\) 0 0
\(109\) −82440.7 −0.664623 −0.332312 0.943170i \(-0.607829\pi\)
−0.332312 + 0.943170i \(0.607829\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 204480. 1.50645 0.753225 0.657763i \(-0.228497\pi\)
0.753225 + 0.657763i \(0.228497\pi\)
\(114\) 0 0
\(115\) 264464. 1.86476
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 114024. 0.738122
\(120\) 0 0
\(121\) −132393. −0.822054
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −90833.2 −0.519960
\(126\) 0 0
\(127\) −120810. −0.664654 −0.332327 0.943164i \(-0.607834\pi\)
−0.332327 + 0.943164i \(0.607834\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 260775. 1.32766 0.663832 0.747882i \(-0.268929\pi\)
0.663832 + 0.747882i \(0.268929\pi\)
\(132\) 0 0
\(133\) −73920.8 −0.362358
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2185.69 −0.00994918 −0.00497459 0.999988i \(-0.501583\pi\)
−0.00497459 + 0.999988i \(0.501583\pi\)
\(138\) 0 0
\(139\) −4670.22 −0.0205022 −0.0102511 0.999947i \(-0.503263\pi\)
−0.0102511 + 0.999947i \(0.503263\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1838.25 0.00751734
\(144\) 0 0
\(145\) −397848. −1.57144
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 214126. 0.790140 0.395070 0.918651i \(-0.370720\pi\)
0.395070 + 0.918651i \(0.370720\pi\)
\(150\) 0 0
\(151\) 373534. 1.33318 0.666588 0.745426i \(-0.267754\pi\)
0.666588 + 0.745426i \(0.267754\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −301721. −1.00873
\(156\) 0 0
\(157\) −320994. −1.03932 −0.519658 0.854374i \(-0.673941\pi\)
−0.519658 + 0.854374i \(0.673941\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −183996. −0.559428
\(162\) 0 0
\(163\) −297770. −0.877833 −0.438916 0.898528i \(-0.644638\pi\)
−0.438916 + 0.898528i \(0.644638\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 108151. 0.300082 0.150041 0.988680i \(-0.452059\pi\)
0.150041 + 0.988680i \(0.452059\pi\)
\(168\) 0 0
\(169\) −371175. −0.999682
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −453000. −1.15076 −0.575378 0.817888i \(-0.695145\pi\)
−0.575378 + 0.817888i \(0.695145\pi\)
\(174\) 0 0
\(175\) −89929.4 −0.221976
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 307341. 0.716949 0.358474 0.933540i \(-0.383297\pi\)
0.358474 + 0.933540i \(0.383297\pi\)
\(180\) 0 0
\(181\) 258687. 0.586918 0.293459 0.955972i \(-0.405194\pi\)
0.293459 + 0.955972i \(0.405194\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2574.49 0.00553048
\(186\) 0 0
\(187\) 393936. 0.823800
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −122006. −0.241991 −0.120995 0.992653i \(-0.538609\pi\)
−0.120995 + 0.992653i \(0.538609\pi\)
\(192\) 0 0
\(193\) 873534. 1.68806 0.844028 0.536300i \(-0.180178\pi\)
0.844028 + 0.536300i \(0.180178\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 286734. 0.526398 0.263199 0.964742i \(-0.415222\pi\)
0.263199 + 0.964742i \(0.415222\pi\)
\(198\) 0 0
\(199\) 488646. 0.874706 0.437353 0.899290i \(-0.355916\pi\)
0.437353 + 0.899290i \(0.355916\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 276796. 0.471432
\(204\) 0 0
\(205\) −6386.48 −0.0106139
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −255386. −0.404418
\(210\) 0 0
\(211\) 203765. 0.315081 0.157541 0.987513i \(-0.449643\pi\)
0.157541 + 0.987513i \(0.449643\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 584089. 0.861753
\(216\) 0 0
\(217\) 209917. 0.302621
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 25268.4 0.0348014
\(222\) 0 0
\(223\) −120144. −0.161786 −0.0808929 0.996723i \(-0.525777\pi\)
−0.0808929 + 0.996723i \(0.525777\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −487855. −0.628386 −0.314193 0.949359i \(-0.601734\pi\)
−0.314193 + 0.949359i \(0.601734\pi\)
\(228\) 0 0
\(229\) 1.13748e6 1.43336 0.716678 0.697405i \(-0.245662\pi\)
0.716678 + 0.697405i \(0.245662\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.15703e6 1.39622 0.698109 0.715992i \(-0.254025\pi\)
0.698109 + 0.715992i \(0.254025\pi\)
\(234\) 0 0
\(235\) 1.30788e6 1.54489
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 835593. 0.946237 0.473119 0.880999i \(-0.343128\pi\)
0.473119 + 0.880999i \(0.343128\pi\)
\(240\) 0 0
\(241\) 353868. 0.392463 0.196232 0.980558i \(-0.437130\pi\)
0.196232 + 0.980558i \(0.437130\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 169101. 0.179983
\(246\) 0 0
\(247\) −16381.3 −0.0170846
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 983591. 0.985440 0.492720 0.870188i \(-0.336003\pi\)
0.492720 + 0.870188i \(0.336003\pi\)
\(252\) 0 0
\(253\) −635681. −0.624364
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.25338e6 −1.18372 −0.591861 0.806040i \(-0.701606\pi\)
−0.591861 + 0.806040i \(0.701606\pi\)
\(258\) 0 0
\(259\) −1791.16 −0.00165915
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.15241e6 1.02735 0.513673 0.857986i \(-0.328284\pi\)
0.513673 + 0.857986i \(0.328284\pi\)
\(264\) 0 0
\(265\) 835466. 0.730826
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.60138e6 −1.34932 −0.674659 0.738129i \(-0.735709\pi\)
−0.674659 + 0.738129i \(0.735709\pi\)
\(270\) 0 0
\(271\) −1.82052e6 −1.50582 −0.752910 0.658123i \(-0.771351\pi\)
−0.752910 + 0.658123i \(0.771351\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −310693. −0.247742
\(276\) 0 0
\(277\) −1.30239e6 −1.01986 −0.509929 0.860216i \(-0.670328\pi\)
−0.509929 + 0.860216i \(0.670328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.56996e6 1.18610 0.593052 0.805164i \(-0.297923\pi\)
0.593052 + 0.805164i \(0.297923\pi\)
\(282\) 0 0
\(283\) 1.19887e6 0.889831 0.444915 0.895573i \(-0.353234\pi\)
0.444915 + 0.895573i \(0.353234\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4443.28 0.00318419
\(288\) 0 0
\(289\) 3.99515e6 2.81377
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.93610e6 1.31753 0.658763 0.752350i \(-0.271080\pi\)
0.658763 + 0.752350i \(0.271080\pi\)
\(294\) 0 0
\(295\) 3.39751e6 2.27303
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −40774.7 −0.0263763
\(300\) 0 0
\(301\) −406370. −0.258527
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.56538e6 0.963541
\(306\) 0 0
\(307\) −977005. −0.591631 −0.295816 0.955245i \(-0.595591\pi\)
−0.295816 + 0.955245i \(0.595591\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 416145. 0.243974 0.121987 0.992532i \(-0.461073\pi\)
0.121987 + 0.992532i \(0.461073\pi\)
\(312\) 0 0
\(313\) 2.35309e6 1.35762 0.678809 0.734315i \(-0.262496\pi\)
0.678809 + 0.734315i \(0.262496\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −420149. −0.234831 −0.117415 0.993083i \(-0.537461\pi\)
−0.117415 + 0.993083i \(0.537461\pi\)
\(318\) 0 0
\(319\) 956290. 0.526154
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.51051e6 −1.87225
\(324\) 0 0
\(325\) −19928.9 −0.0104659
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −909936. −0.463469
\(330\) 0 0
\(331\) 2.26504e6 1.13633 0.568166 0.822914i \(-0.307653\pi\)
0.568166 + 0.822914i \(0.307653\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 709085. 0.345212
\(336\) 0 0
\(337\) −312951. −0.150107 −0.0750537 0.997179i \(-0.523913\pi\)
−0.0750537 + 0.997179i \(0.523913\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 725234. 0.337747
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.26857e6 −1.01141 −0.505706 0.862706i \(-0.668768\pi\)
−0.505706 + 0.862706i \(0.668768\pi\)
\(348\) 0 0
\(349\) −1.85308e6 −0.814388 −0.407194 0.913342i \(-0.633493\pi\)
−0.407194 + 0.913342i \(0.633493\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.81453e6 1.20218 0.601089 0.799182i \(-0.294734\pi\)
0.601089 + 0.799182i \(0.294734\pi\)
\(354\) 0 0
\(355\) 2.94374e6 1.23973
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.07160e6 0.848339 0.424169 0.905583i \(-0.360566\pi\)
0.424169 + 0.905583i \(0.360566\pi\)
\(360\) 0 0
\(361\) −200264. −0.0808789
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.73247e6 1.85933
\(366\) 0 0
\(367\) −3.90586e6 −1.51374 −0.756870 0.653566i \(-0.773272\pi\)
−0.756870 + 0.653566i \(0.773272\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −581261. −0.219248
\(372\) 0 0
\(373\) 1.26552e6 0.470974 0.235487 0.971877i \(-0.424331\pi\)
0.235487 + 0.971877i \(0.424331\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 61339.6 0.0222274
\(378\) 0 0
\(379\) −2.73373e6 −0.977592 −0.488796 0.872398i \(-0.662564\pi\)
−0.488796 + 0.872398i \(0.662564\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.59033e6 1.25066 0.625328 0.780362i \(-0.284965\pi\)
0.625328 + 0.780362i \(0.284965\pi\)
\(384\) 0 0
\(385\) 584220. 0.200874
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.58625e6 1.20162 0.600809 0.799392i \(-0.294845\pi\)
0.600809 + 0.799392i \(0.294845\pi\)
\(390\) 0 0
\(391\) −8.73801e6 −2.89048
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.10696e6 −1.32443
\(396\) 0 0
\(397\) 5.23550e6 1.66718 0.833590 0.552384i \(-0.186282\pi\)
0.833590 + 0.552384i \(0.186282\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.97474e6 1.54493 0.772467 0.635055i \(-0.219023\pi\)
0.772467 + 0.635055i \(0.219023\pi\)
\(402\) 0 0
\(403\) 46518.9 0.0142681
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6188.20 −0.00185173
\(408\) 0 0
\(409\) −3.04069e6 −0.898801 −0.449401 0.893330i \(-0.648362\pi\)
−0.449401 + 0.893330i \(0.648362\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.36376e6 −0.681911
\(414\) 0 0
\(415\) −7.00492e6 −1.99656
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.25931e6 1.46350 0.731752 0.681571i \(-0.238703\pi\)
0.731752 + 0.681571i \(0.238703\pi\)
\(420\) 0 0
\(421\) −6.51872e6 −1.79249 −0.896245 0.443559i \(-0.853716\pi\)
−0.896245 + 0.443559i \(0.853716\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.27076e6 −1.14692
\(426\) 0 0
\(427\) −1.08909e6 −0.289063
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.19867e6 0.570120 0.285060 0.958510i \(-0.407986\pi\)
0.285060 + 0.958510i \(0.407986\pi\)
\(432\) 0 0
\(433\) −899455. −0.230547 −0.115274 0.993334i \(-0.536774\pi\)
−0.115274 + 0.993334i \(0.536774\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.66479e6 1.41899
\(438\) 0 0
\(439\) −3.76938e6 −0.933489 −0.466744 0.884392i \(-0.654573\pi\)
−0.466744 + 0.884392i \(0.654573\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.23892e6 1.51043 0.755214 0.655479i \(-0.227533\pi\)
0.755214 + 0.655479i \(0.227533\pi\)
\(444\) 0 0
\(445\) 7.58754e6 1.81636
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.09379e6 −0.724228 −0.362114 0.932134i \(-0.617945\pi\)
−0.362114 + 0.932134i \(0.617945\pi\)
\(450\) 0 0
\(451\) 15350.9 0.00355380
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 37473.8 0.00848593
\(456\) 0 0
\(457\) −5.90697e6 −1.32304 −0.661522 0.749926i \(-0.730089\pi\)
−0.661522 + 0.749926i \(0.730089\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.80920e6 −0.396491 −0.198245 0.980152i \(-0.563524\pi\)
−0.198245 + 0.980152i \(0.563524\pi\)
\(462\) 0 0
\(463\) 1.75786e6 0.381094 0.190547 0.981678i \(-0.438974\pi\)
0.190547 + 0.981678i \(0.438974\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −368945. −0.0782833 −0.0391417 0.999234i \(-0.512462\pi\)
−0.0391417 + 0.999234i \(0.512462\pi\)
\(468\) 0 0
\(469\) −493334. −0.103564
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.40395e6 −0.288535
\(474\) 0 0
\(475\) 2.76870e6 0.563043
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.53603e6 −1.50074 −0.750368 0.661021i \(-0.770123\pi\)
−0.750368 + 0.661021i \(0.770123\pi\)
\(480\) 0 0
\(481\) −396.932 −7.82264e−5 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.79565e6 −1.31183
\(486\) 0 0
\(487\) 5.60411e6 1.07074 0.535371 0.844617i \(-0.320172\pi\)
0.535371 + 0.844617i \(0.320172\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.77047e6 −0.331425 −0.165713 0.986174i \(-0.552992\pi\)
−0.165713 + 0.986174i \(0.552992\pi\)
\(492\) 0 0
\(493\) 1.31451e7 2.43582
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.04806e6 −0.371921
\(498\) 0 0
\(499\) −5.51873e6 −0.992174 −0.496087 0.868273i \(-0.665230\pi\)
−0.496087 + 0.868273i \(0.665230\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.25678e6 1.27886 0.639431 0.768848i \(-0.279170\pi\)
0.639431 + 0.768848i \(0.279170\pi\)
\(504\) 0 0
\(505\) −3.77304e6 −0.658359
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.80322e6 1.67716 0.838580 0.544779i \(-0.183386\pi\)
0.838580 + 0.544779i \(0.183386\pi\)
\(510\) 0 0
\(511\) −3.29253e6 −0.557799
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.85615e6 1.30524
\(516\) 0 0
\(517\) −3.14370e6 −0.517267
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −391729. −0.0632254 −0.0316127 0.999500i \(-0.510064\pi\)
−0.0316127 + 0.999500i \(0.510064\pi\)
\(522\) 0 0
\(523\) 7.78131e6 1.24394 0.621969 0.783042i \(-0.286333\pi\)
0.621969 + 0.783042i \(0.286333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.96899e6 1.56360
\(528\) 0 0
\(529\) 7.66389e6 1.19072
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 984.658 0.000150130 0
\(534\) 0 0
\(535\) 4.20596e6 0.635302
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −406461. −0.0602624
\(540\) 0 0
\(541\) −7.05542e6 −1.03641 −0.518203 0.855258i \(-0.673399\pi\)
−0.518203 + 0.855258i \(0.673399\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.80624e6 −0.837344
\(546\) 0 0
\(547\) 1.81191e6 0.258922 0.129461 0.991585i \(-0.458675\pi\)
0.129461 + 0.991585i \(0.458675\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8.52184e6 −1.19579
\(552\) 0 0
\(553\) 2.85735e6 0.397329
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.06385e6 0.555009 0.277504 0.960724i \(-0.410493\pi\)
0.277504 + 0.960724i \(0.410493\pi\)
\(558\) 0 0
\(559\) −90054.1 −0.0121892
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.44664e6 −0.325312 −0.162656 0.986683i \(-0.552006\pi\)
−0.162656 + 0.986683i \(0.552006\pi\)
\(564\) 0 0
\(565\) 1.44014e7 1.89794
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.04615e6 0.394431 0.197215 0.980360i \(-0.436810\pi\)
0.197215 + 0.980360i \(0.436810\pi\)
\(570\) 0 0
\(571\) 1.24745e7 1.60115 0.800574 0.599234i \(-0.204528\pi\)
0.800574 + 0.599234i \(0.204528\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.89158e6 0.869259
\(576\) 0 0
\(577\) −8.47677e6 −1.05996 −0.529982 0.848009i \(-0.677801\pi\)
−0.529982 + 0.848009i \(0.677801\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.87355e6 0.598970
\(582\) 0 0
\(583\) −2.00817e6 −0.244698
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.44764e7 −1.73406 −0.867030 0.498256i \(-0.833974\pi\)
−0.867030 + 0.498256i \(0.833974\pi\)
\(588\) 0 0
\(589\) −6.46282e6 −0.767598
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.37231e6 0.627371 0.313686 0.949527i \(-0.398436\pi\)
0.313686 + 0.949527i \(0.398436\pi\)
\(594\) 0 0
\(595\) 8.03062e6 0.929944
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.96968e6 −1.13531 −0.567655 0.823267i \(-0.692149\pi\)
−0.567655 + 0.823267i \(0.692149\pi\)
\(600\) 0 0
\(601\) −6.79612e6 −0.767493 −0.383747 0.923438i \(-0.625366\pi\)
−0.383747 + 0.923438i \(0.625366\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.32432e6 −1.03569
\(606\) 0 0
\(607\) −3.73507e6 −0.411459 −0.205730 0.978609i \(-0.565957\pi\)
−0.205730 + 0.978609i \(0.565957\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −201647. −0.0218519
\(612\) 0 0
\(613\) −6.64420e6 −0.714153 −0.357076 0.934075i \(-0.616226\pi\)
−0.357076 + 0.934075i \(0.616226\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.85062e6 −0.512961 −0.256480 0.966549i \(-0.582563\pi\)
−0.256480 + 0.966549i \(0.582563\pi\)
\(618\) 0 0
\(619\) −1.73039e7 −1.81517 −0.907585 0.419868i \(-0.862077\pi\)
−0.907585 + 0.419868i \(0.862077\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.27890e6 −0.544908
\(624\) 0 0
\(625\) −1.21326e7 −1.24238
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −85062.4 −0.00857257
\(630\) 0 0
\(631\) 1.41085e7 1.41061 0.705306 0.708903i \(-0.250810\pi\)
0.705306 + 0.708903i \(0.250810\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.50860e6 −0.837383
\(636\) 0 0
\(637\) −26071.7 −0.00254578
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.48183e7 −1.42447 −0.712234 0.701942i \(-0.752316\pi\)
−0.712234 + 0.701942i \(0.752316\pi\)
\(642\) 0 0
\(643\) 1.36121e7 1.29837 0.649186 0.760630i \(-0.275110\pi\)
0.649186 + 0.760630i \(0.275110\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.95253e6 0.277289 0.138645 0.990342i \(-0.455725\pi\)
0.138645 + 0.990342i \(0.455725\pi\)
\(648\) 0 0
\(649\) −8.16645e6 −0.761065
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.25557e6 0.849416 0.424708 0.905330i \(-0.360377\pi\)
0.424708 + 0.905330i \(0.360377\pi\)
\(654\) 0 0
\(655\) 1.83662e7 1.67269
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.38161e6 −0.751820 −0.375910 0.926656i \(-0.622670\pi\)
−0.375910 + 0.926656i \(0.622670\pi\)
\(660\) 0 0
\(661\) 1.42353e7 1.26725 0.633624 0.773641i \(-0.281567\pi\)
0.633624 + 0.773641i \(0.281567\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.20619e6 −0.456527
\(666\) 0 0
\(667\) −2.12117e7 −1.84613
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.76264e6 −0.322616
\(672\) 0 0
\(673\) −1.22312e7 −1.04095 −0.520477 0.853876i \(-0.674246\pi\)
−0.520477 + 0.853876i \(0.674246\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.73520e7 −1.45505 −0.727524 0.686082i \(-0.759329\pi\)
−0.727524 + 0.686082i \(0.759329\pi\)
\(678\) 0 0
\(679\) 4.72796e6 0.393549
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.12597e7 −0.923584 −0.461792 0.886988i \(-0.652793\pi\)
−0.461792 + 0.886988i \(0.652793\pi\)
\(684\) 0 0
\(685\) −153937. −0.0125348
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −128811. −0.0103372
\(690\) 0 0
\(691\) 1.39801e7 1.11382 0.556912 0.830572i \(-0.311986\pi\)
0.556912 + 0.830572i \(0.311986\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −328921. −0.0258303
\(696\) 0 0
\(697\) 211012. 0.0164522
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9.27004e6 −0.712503 −0.356251 0.934390i \(-0.615945\pi\)
−0.356251 + 0.934390i \(0.615945\pi\)
\(702\) 0 0
\(703\) 55145.3 0.00420843
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.62502e6 0.197508
\(708\) 0 0
\(709\) −6.26469e6 −0.468041 −0.234021 0.972232i \(-0.575188\pi\)
−0.234021 + 0.972232i \(0.575188\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.60866e7 −1.18506
\(714\) 0 0
\(715\) 129467. 0.00947093
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.98860e6 0.143458 0.0717289 0.997424i \(-0.477148\pi\)
0.0717289 + 0.997424i \(0.477148\pi\)
\(720\) 0 0
\(721\) −5.46578e6 −0.391574
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.03674e7 −0.732527
\(726\) 0 0
\(727\) 6.79449e6 0.476783 0.238392 0.971169i \(-0.423380\pi\)
0.238392 + 0.971169i \(0.423380\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.92986e7 −1.33577
\(732\) 0 0
\(733\) −1.08090e7 −0.743064 −0.371532 0.928420i \(-0.621167\pi\)
−0.371532 + 0.928420i \(0.621167\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.70440e6 −0.115585
\(738\) 0 0
\(739\) 5.71735e6 0.385109 0.192554 0.981286i \(-0.438323\pi\)
0.192554 + 0.981286i \(0.438323\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.73241e7 1.15127 0.575636 0.817706i \(-0.304754\pi\)
0.575636 + 0.817706i \(0.304754\pi\)
\(744\) 0 0
\(745\) 1.50808e7 0.995480
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.92622e6 −0.190591
\(750\) 0 0
\(751\) −6.62606e6 −0.428702 −0.214351 0.976757i \(-0.568764\pi\)
−0.214351 + 0.976757i \(0.568764\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.63078e7 1.67964
\(756\) 0 0
\(757\) 7.48660e6 0.474837 0.237419 0.971407i \(-0.423699\pi\)
0.237419 + 0.971407i \(0.423699\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.15179e7 −1.34691 −0.673453 0.739230i \(-0.735190\pi\)
−0.673453 + 0.739230i \(0.735190\pi\)
\(762\) 0 0
\(763\) 4.03959e6 0.251204
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −523823. −0.0321512
\(768\) 0 0
\(769\) −2.82284e7 −1.72136 −0.860678 0.509149i \(-0.829960\pi\)
−0.860678 + 0.509149i \(0.829960\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8.55229e6 −0.514794 −0.257397 0.966306i \(-0.582865\pi\)
−0.257397 + 0.966306i \(0.582865\pi\)
\(774\) 0 0
\(775\) −7.86244e6 −0.470222
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −136797. −0.00807671
\(780\) 0 0
\(781\) −7.07574e6 −0.415092
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.26074e7 −1.30941
\(786\) 0 0
\(787\) −1.02638e7 −0.590707 −0.295354 0.955388i \(-0.595437\pi\)
−0.295354 + 0.955388i \(0.595437\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.00195e7 −0.569385
\(792\) 0 0
\(793\) −241348. −0.0136289
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.90512e7 1.62001 0.810007 0.586421i \(-0.199464\pi\)
0.810007 + 0.586421i \(0.199464\pi\)
\(798\) 0 0
\(799\) −4.32130e7 −2.39468
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.13752e7 −0.622546
\(804\) 0 0
\(805\) −1.29587e7 −0.704812
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.64973e7 −1.96060 −0.980302 0.197506i \(-0.936716\pi\)
−0.980302 + 0.197506i \(0.936716\pi\)
\(810\) 0 0
\(811\) −1.27111e7 −0.678625 −0.339313 0.940674i \(-0.610194\pi\)
−0.339313 + 0.940674i \(0.610194\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.09717e7 −1.10596
\(816\) 0 0
\(817\) 1.25111e7 0.655753
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.48113e7 1.80245 0.901224 0.433353i \(-0.142670\pi\)
0.901224 + 0.433353i \(0.142670\pi\)
\(822\) 0 0
\(823\) −2.50392e7 −1.28861 −0.644303 0.764770i \(-0.722853\pi\)
−0.644303 + 0.764770i \(0.722853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.90538e7 0.968766 0.484383 0.874856i \(-0.339044\pi\)
0.484383 + 0.874856i \(0.339044\pi\)
\(828\) 0 0
\(829\) 2.85861e7 1.44467 0.722336 0.691542i \(-0.243068\pi\)
0.722336 + 0.691542i \(0.243068\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.58717e6 −0.278984
\(834\) 0 0
\(835\) 7.61702e6 0.378067
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 8.79713e6 0.431456 0.215728 0.976454i \(-0.430788\pi\)
0.215728 + 0.976454i \(0.430788\pi\)
\(840\) 0 0
\(841\) 1.13988e7 0.555738
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.61416e7 −1.25948
\(846\) 0 0
\(847\) 6.48724e6 0.310707
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 137262. 0.00649722
\(852\) 0 0
\(853\) 3.29937e6 0.155260 0.0776298 0.996982i \(-0.475265\pi\)
0.0776298 + 0.996982i \(0.475265\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −7.79857e6 −0.362713 −0.181356 0.983417i \(-0.558049\pi\)
−0.181356 + 0.983417i \(0.558049\pi\)
\(858\) 0 0
\(859\) −1.03989e7 −0.480845 −0.240422 0.970668i \(-0.577286\pi\)
−0.240422 + 0.970668i \(0.577286\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.47008e7 −1.12898 −0.564488 0.825442i \(-0.690926\pi\)
−0.564488 + 0.825442i \(0.690926\pi\)
\(864\) 0 0
\(865\) −3.19045e7 −1.44981
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 9.87173e6 0.443449
\(870\) 0 0
\(871\) −109326. −0.00488289
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4.45083e6 0.196526
\(876\) 0 0
\(877\) 2.47844e7 1.08813 0.544064 0.839044i \(-0.316885\pi\)
0.544064 + 0.839044i \(0.316885\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.77740e7 1.63966 0.819828 0.572610i \(-0.194069\pi\)
0.819828 + 0.572610i \(0.194069\pi\)
\(882\) 0 0
\(883\) −1.85386e7 −0.800158 −0.400079 0.916481i \(-0.631017\pi\)
−0.400079 + 0.916481i \(0.631017\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.45793e7 −1.90250 −0.951249 0.308425i \(-0.900198\pi\)
−0.951249 + 0.308425i \(0.900198\pi\)
\(888\) 0 0
\(889\) 5.91971e6 0.251215
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.80146e7 1.17559
\(894\) 0 0
\(895\) 2.16458e7 0.903269
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.42000e7 0.998655
\(900\) 0 0
\(901\) −2.76042e7 −1.13282
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.82191e7 0.739446
\(906\) 0 0
\(907\) −2.67809e7 −1.08095 −0.540477 0.841359i \(-0.681756\pi\)
−0.540477 + 0.841359i \(0.681756\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.02429e6 −0.200576 −0.100288 0.994958i \(-0.531976\pi\)
−0.100288 + 0.994958i \(0.531976\pi\)
\(912\) 0 0
\(913\) 1.68374e7 0.668496
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.27780e7 −0.501810
\(918\) 0 0
\(919\) 2.20858e7 0.862628 0.431314 0.902202i \(-0.358050\pi\)
0.431314 + 0.902202i \(0.358050\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −453862. −0.0175356
\(924\) 0 0
\(925\) 67087.8 0.00257804
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.40060e7 1.29276 0.646378 0.763017i \(-0.276283\pi\)
0.646378 + 0.763017i \(0.276283\pi\)
\(930\) 0 0
\(931\) 3.62212e6 0.136958
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.77447e7 1.03789
\(936\) 0 0
\(937\) 1.80468e7 0.671509 0.335754 0.941950i \(-0.391009\pi\)
0.335754 + 0.941950i \(0.391009\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.72299e7 0.634321 0.317161 0.948372i \(-0.397271\pi\)
0.317161 + 0.948372i \(0.397271\pi\)
\(942\) 0 0
\(943\) −340503. −0.0124693
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.27460e7 −0.461847 −0.230923 0.972972i \(-0.574175\pi\)
−0.230923 + 0.972972i \(0.574175\pi\)
\(948\) 0 0
\(949\) −729645. −0.0262994
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −4.67300e7 −1.66672 −0.833361 0.552729i \(-0.813586\pi\)
−0.833361 + 0.552729i \(0.813586\pi\)
\(954\) 0 0
\(955\) −8.59282e6 −0.304879
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 107099. 0.00376043
\(960\) 0 0
\(961\) −1.02763e7 −0.358946
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 6.15224e7 2.12674
\(966\) 0 0
\(967\) 4.33085e7 1.48939 0.744693 0.667408i \(-0.232596\pi\)
0.744693 + 0.667408i \(0.232596\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.38056e7 −0.810272 −0.405136 0.914256i \(-0.632776\pi\)
−0.405136 + 0.914256i \(0.632776\pi\)
\(972\) 0 0
\(973\) 228841. 0.00774910
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.55338e7 −0.855815 −0.427907 0.903823i \(-0.640749\pi\)
−0.427907 + 0.903823i \(0.640749\pi\)
\(978\) 0 0
\(979\) −1.82378e7 −0.608158
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8.83504e6 −0.291625 −0.145812 0.989312i \(-0.546580\pi\)
−0.145812 + 0.989312i \(0.546580\pi\)
\(984\) 0 0
\(985\) 2.01945e7 0.663198
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.11414e7 1.01239
\(990\) 0 0
\(991\) 2.34048e7 0.757045 0.378522 0.925592i \(-0.376432\pi\)
0.378522 + 0.925592i \(0.376432\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.44151e7 1.10202
\(996\) 0 0
\(997\) 4.81022e7 1.53259 0.766297 0.642487i \(-0.222097\pi\)
0.766297 + 0.642487i \(0.222097\pi\)
\(998\) 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.bp.1.2 2
3.2 odd 2 336.6.a.s.1.1 2
4.3 odd 2 504.6.a.p.1.2 2
12.11 even 2 168.6.a.i.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.i.1.1 2 12.11 even 2
336.6.a.s.1.1 2 3.2 odd 2
504.6.a.p.1.2 2 4.3 odd 2
1008.6.a.bp.1.2 2 1.1 even 1 trivial