Properties

Label 1008.6.a.bp.1.1
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 1.1
Root \(33.2147\) 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)
 
\(f(q)\) \(=\) \(q-60.4294 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-60.4294 q^{5} -49.0000 q^{7} +223.288 q^{11} +250.859 q^{13} +421.016 q^{17} -1108.59 q^{19} -825.027 q^{23} +526.706 q^{25} +108.891 q^{29} -619.978 q^{31} +2961.04 q^{35} +2915.45 q^{37} -5979.32 q^{41} -11597.3 q^{43} -1582.12 q^{47} +2401.00 q^{49} -18758.5 q^{53} -13493.2 q^{55} +5580.03 q^{59} -18078.2 q^{61} -15159.2 q^{65} -43584.0 q^{67} +31720.9 q^{71} -67066.5 q^{73} -10941.1 q^{77} +573.208 q^{79} +122476. q^{83} -25441.7 q^{85} +33797.4 q^{89} -12292.1 q^{91} +66991.2 q^{95} -129727. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 10 q^{5} - 98 q^{7}+O(q^{10}) \) 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
\(5\) −60.4294 −1.08099 −0.540497 0.841346i \(-0.681764\pi\)
−0.540497 + 0.841346i \(0.681764\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 223.288 0.556396 0.278198 0.960524i \(-0.410263\pi\)
0.278198 + 0.960524i \(0.410263\pi\)
\(12\) 0 0
\(13\) 250.859 0.411690 0.205845 0.978585i \(-0.434006\pi\)
0.205845 + 0.978585i \(0.434006\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 421.016 0.353327 0.176663 0.984271i \(-0.443470\pi\)
0.176663 + 0.984271i \(0.443470\pi\)
\(18\) 0 0
\(19\) −1108.59 −0.704508 −0.352254 0.935904i \(-0.614585\pi\)
−0.352254 + 0.935904i \(0.614585\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −825.027 −0.325199 −0.162599 0.986692i \(-0.551988\pi\)
−0.162599 + 0.986692i \(0.551988\pi\)
\(24\) 0 0
\(25\) 526.706 0.168546
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 108.891 0.0240436 0.0120218 0.999928i \(-0.496173\pi\)
0.0120218 + 0.999928i \(0.496173\pi\)
\(30\) 0 0
\(31\) −619.978 −0.115870 −0.0579352 0.998320i \(-0.518452\pi\)
−0.0579352 + 0.998320i \(0.518452\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2961.04 0.408577
\(36\) 0 0
\(37\) 2915.45 0.350107 0.175053 0.984559i \(-0.443990\pi\)
0.175053 + 0.984559i \(0.443990\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5979.32 −0.555510 −0.277755 0.960652i \(-0.589590\pi\)
−0.277755 + 0.960652i \(0.589590\pi\)
\(42\) 0 0
\(43\) −11597.3 −0.956499 −0.478249 0.878224i \(-0.658728\pi\)
−0.478249 + 0.878224i \(0.658728\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1582.12 −0.104471 −0.0522354 0.998635i \(-0.516635\pi\)
−0.0522354 + 0.998635i \(0.516635\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −18758.5 −0.917292 −0.458646 0.888619i \(-0.651665\pi\)
−0.458646 + 0.888619i \(0.651665\pi\)
\(54\) 0 0
\(55\) −13493.2 −0.601460
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5580.03 0.208692 0.104346 0.994541i \(-0.466725\pi\)
0.104346 + 0.994541i \(0.466725\pi\)
\(60\) 0 0
\(61\) −18078.2 −0.622059 −0.311029 0.950400i \(-0.600674\pi\)
−0.311029 + 0.950400i \(0.600674\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −15159.2 −0.445035
\(66\) 0 0
\(67\) −43584.0 −1.18615 −0.593076 0.805146i \(-0.702087\pi\)
−0.593076 + 0.805146i \(0.702087\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 31720.9 0.746793 0.373396 0.927672i \(-0.378193\pi\)
0.373396 + 0.927672i \(0.378193\pi\)
\(72\) 0 0
\(73\) −67066.5 −1.47299 −0.736493 0.676445i \(-0.763520\pi\)
−0.736493 + 0.676445i \(0.763520\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10941.1 −0.210298
\(78\) 0 0
\(79\) 573.208 0.0103334 0.00516672 0.999987i \(-0.498355\pi\)
0.00516672 + 0.999987i \(0.498355\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 122476. 1.95145 0.975723 0.219010i \(-0.0702826\pi\)
0.975723 + 0.219010i \(0.0702826\pi\)
\(84\) 0 0
\(85\) −25441.7 −0.381944
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 33797.4 0.452281 0.226141 0.974095i \(-0.427389\pi\)
0.226141 + 0.974095i \(0.427389\pi\)
\(90\) 0 0
\(91\) −12292.1 −0.155604
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 66991.2 0.761568
\(96\) 0 0
\(97\) −129727. −1.39991 −0.699957 0.714185i \(-0.746797\pi\)
−0.699957 + 0.714185i \(0.746797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 103066. 1.00534 0.502669 0.864479i \(-0.332352\pi\)
0.502669 + 0.864479i \(0.332352\pi\)
\(102\) 0 0
\(103\) 71765.5 0.666534 0.333267 0.942832i \(-0.391849\pi\)
0.333267 + 0.942832i \(0.391849\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 45455.2 0.383817 0.191908 0.981413i \(-0.438532\pi\)
0.191908 + 0.981413i \(0.438532\pi\)
\(108\) 0 0
\(109\) −109659. −0.884055 −0.442027 0.897002i \(-0.645741\pi\)
−0.442027 + 0.897002i \(0.645741\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 145332. 1.07069 0.535346 0.844633i \(-0.320181\pi\)
0.535346 + 0.844633i \(0.320181\pi\)
\(114\) 0 0
\(115\) 49855.9 0.351537
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −20629.8 −0.133545
\(120\) 0 0
\(121\) −111193. −0.690424
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 157013. 0.898796
\(126\) 0 0
\(127\) 343214. 1.88824 0.944118 0.329607i \(-0.106916\pi\)
0.944118 + 0.329607i \(0.106916\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −174199. −0.886886 −0.443443 0.896303i \(-0.646243\pi\)
−0.443443 + 0.896303i \(0.646243\pi\)
\(132\) 0 0
\(133\) 54320.8 0.266279
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 185466. 0.844233 0.422116 0.906542i \(-0.361287\pi\)
0.422116 + 0.906542i \(0.361287\pi\)
\(138\) 0 0
\(139\) 176438. 0.774561 0.387281 0.921962i \(-0.373414\pi\)
0.387281 + 0.921962i \(0.373414\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 56013.8 0.229063
\(144\) 0 0
\(145\) −6580.24 −0.0259909
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −321086. −1.18483 −0.592415 0.805633i \(-0.701825\pi\)
−0.592415 + 0.805633i \(0.701825\pi\)
\(150\) 0 0
\(151\) −52542.0 −0.187527 −0.0937635 0.995594i \(-0.529890\pi\)
−0.0937635 + 0.995594i \(0.529890\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 37464.9 0.125255
\(156\) 0 0
\(157\) 234894. 0.760541 0.380270 0.924875i \(-0.375831\pi\)
0.380270 + 0.924875i \(0.375831\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 40426.3 0.122914
\(162\) 0 0
\(163\) 345270. 1.01786 0.508932 0.860807i \(-0.330041\pi\)
0.508932 + 0.860807i \(0.330041\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 578981. 1.60647 0.803236 0.595661i \(-0.203110\pi\)
0.803236 + 0.595661i \(0.203110\pi\)
\(168\) 0 0
\(169\) −308363. −0.830511
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −19465.6 −0.0494483 −0.0247242 0.999694i \(-0.507871\pi\)
−0.0247242 + 0.999694i \(0.507871\pi\)
\(174\) 0 0
\(175\) −25808.6 −0.0637044
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 32668.8 0.0762080 0.0381040 0.999274i \(-0.487868\pi\)
0.0381040 + 0.999274i \(0.487868\pi\)
\(180\) 0 0
\(181\) −97510.7 −0.221236 −0.110618 0.993863i \(-0.535283\pi\)
−0.110618 + 0.993863i \(0.535283\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −176178. −0.378463
\(186\) 0 0
\(187\) 94007.9 0.196590
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 902748. 1.79054 0.895268 0.445527i \(-0.146984\pi\)
0.895268 + 0.445527i \(0.146984\pi\)
\(192\) 0 0
\(193\) −732102. −1.41475 −0.707373 0.706841i \(-0.750120\pi\)
−0.707373 + 0.706841i \(0.750120\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 263442. 0.483636 0.241818 0.970322i \(-0.422256\pi\)
0.241818 + 0.970322i \(0.422256\pi\)
\(198\) 0 0
\(199\) 274562. 0.491481 0.245741 0.969336i \(-0.420969\pi\)
0.245741 + 0.969336i \(0.420969\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5335.68 −0.00908761
\(204\) 0 0
\(205\) 361326. 0.600503
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −247534. −0.391985
\(210\) 0 0
\(211\) 971643. 1.50245 0.751226 0.660045i \(-0.229463\pi\)
0.751226 + 0.660045i \(0.229463\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 700815. 1.03397
\(216\) 0 0
\(217\) 30378.9 0.0437949
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 105616. 0.145461
\(222\) 0 0
\(223\) −568728. −0.765848 −0.382924 0.923780i \(-0.625083\pi\)
−0.382924 + 0.923780i \(0.625083\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −684405. −0.881553 −0.440777 0.897617i \(-0.645297\pi\)
−0.440777 + 0.897617i \(0.645297\pi\)
\(228\) 0 0
\(229\) 1.09639e6 1.38158 0.690789 0.723057i \(-0.257263\pi\)
0.690789 + 0.723057i \(0.257263\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.27250e6 −1.53556 −0.767781 0.640713i \(-0.778639\pi\)
−0.767781 + 0.640713i \(0.778639\pi\)
\(234\) 0 0
\(235\) 95606.5 0.112932
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 175673. 0.198934 0.0994672 0.995041i \(-0.468286\pi\)
0.0994672 + 0.995041i \(0.468286\pi\)
\(240\) 0 0
\(241\) 826268. 0.916386 0.458193 0.888853i \(-0.348497\pi\)
0.458193 + 0.888853i \(0.348497\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −145091. −0.154428
\(246\) 0 0
\(247\) −278099. −0.290039
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 465653. 0.466528 0.233264 0.972413i \(-0.425059\pi\)
0.233264 + 0.972413i \(0.425059\pi\)
\(252\) 0 0
\(253\) −184219. −0.180939
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −718036. −0.678130 −0.339065 0.940763i \(-0.610111\pi\)
−0.339065 + 0.940763i \(0.610111\pi\)
\(258\) 0 0
\(259\) −142857. −0.132328
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −567991. −0.506351 −0.253176 0.967420i \(-0.581475\pi\)
−0.253176 + 0.967420i \(0.581475\pi\)
\(264\) 0 0
\(265\) 1.13356e6 0.991587
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.83327e6 1.54470 0.772351 0.635196i \(-0.219081\pi\)
0.772351 + 0.635196i \(0.219081\pi\)
\(270\) 0 0
\(271\) −553812. −0.458078 −0.229039 0.973417i \(-0.573558\pi\)
−0.229039 + 0.973417i \(0.573558\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 117607. 0.0937783
\(276\) 0 0
\(277\) 716241. 0.560867 0.280433 0.959873i \(-0.409522\pi\)
0.280433 + 0.959873i \(0.409522\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.33310e6 1.00716 0.503580 0.863949i \(-0.332016\pi\)
0.503580 + 0.863949i \(0.332016\pi\)
\(282\) 0 0
\(283\) 2.19183e6 1.62682 0.813412 0.581687i \(-0.197607\pi\)
0.813412 + 0.581687i \(0.197607\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 292987. 0.209963
\(288\) 0 0
\(289\) −1.24260e6 −0.875160
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −377872. −0.257144 −0.128572 0.991700i \(-0.541039\pi\)
−0.128572 + 0.991700i \(0.541039\pi\)
\(294\) 0 0
\(295\) −337198. −0.225595
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −206965. −0.133881
\(300\) 0 0
\(301\) 568266. 0.361522
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.09246e6 0.672441
\(306\) 0 0
\(307\) 991109. 0.600172 0.300086 0.953912i \(-0.402985\pi\)
0.300086 + 0.953912i \(0.402985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.82208e6 −1.65451 −0.827254 0.561828i \(-0.810098\pi\)
−0.827254 + 0.561828i \(0.810098\pi\)
\(312\) 0 0
\(313\) 2.05787e6 1.18729 0.593646 0.804726i \(-0.297688\pi\)
0.593646 + 0.804726i \(0.297688\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.81756e6 1.57480 0.787398 0.616444i \(-0.211427\pi\)
0.787398 + 0.616444i \(0.211427\pi\)
\(318\) 0 0
\(319\) 24314.2 0.0133777
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −466733. −0.248922
\(324\) 0 0
\(325\) 132129. 0.0693888
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 77523.9 0.0394862
\(330\) 0 0
\(331\) −1.01009e6 −0.506748 −0.253374 0.967368i \(-0.581540\pi\)
−0.253374 + 0.967368i \(0.581540\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.63375e6 1.28222
\(336\) 0 0
\(337\) −2.67521e6 −1.28317 −0.641584 0.767053i \(-0.721722\pi\)
−0.641584 + 0.767053i \(0.721722\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −138434. −0.0644697
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.83765e6 −0.819292 −0.409646 0.912245i \(-0.634348\pi\)
−0.409646 + 0.912245i \(0.634348\pi\)
\(348\) 0 0
\(349\) 2.95781e6 1.29989 0.649944 0.759982i \(-0.274792\pi\)
0.649944 + 0.759982i \(0.274792\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.14752e6 0.490143 0.245072 0.969505i \(-0.421189\pi\)
0.245072 + 0.969505i \(0.421189\pi\)
\(354\) 0 0
\(355\) −1.91688e6 −0.807278
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.59542e6 1.06285 0.531425 0.847105i \(-0.321657\pi\)
0.531425 + 0.847105i \(0.321657\pi\)
\(360\) 0 0
\(361\) −1.24713e6 −0.503669
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.05279e6 1.59229
\(366\) 0 0
\(367\) 1.52216e6 0.589923 0.294962 0.955509i \(-0.404693\pi\)
0.294962 + 0.955509i \(0.404693\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 919165. 0.346704
\(372\) 0 0
\(373\) 189339. 0.0704641 0.0352321 0.999379i \(-0.488783\pi\)
0.0352321 + 0.999379i \(0.488783\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 27316.4 0.00989850
\(378\) 0 0
\(379\) 3.85160e6 1.37735 0.688674 0.725071i \(-0.258193\pi\)
0.688674 + 0.725071i \(0.258193\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.06452e6 0.719155 0.359578 0.933115i \(-0.382921\pi\)
0.359578 + 0.933115i \(0.382921\pi\)
\(384\) 0 0
\(385\) 661164. 0.227330
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21136.8 0.00708214 0.00354107 0.999994i \(-0.498873\pi\)
0.00354107 + 0.999994i \(0.498873\pi\)
\(390\) 0 0
\(391\) −347350. −0.114901
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −34638.6 −0.0111704
\(396\) 0 0
\(397\) 1.03128e6 0.328397 0.164198 0.986427i \(-0.447496\pi\)
0.164198 + 0.986427i \(0.447496\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.16597e6 0.362098 0.181049 0.983474i \(-0.442051\pi\)
0.181049 + 0.983474i \(0.442051\pi\)
\(402\) 0 0
\(403\) −155527. −0.0477027
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 650984. 0.194798
\(408\) 0 0
\(409\) 5.71350e6 1.68886 0.844430 0.535666i \(-0.179939\pi\)
0.844430 + 0.535666i \(0.179939\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −273422. −0.0788783
\(414\) 0 0
\(415\) −7.40116e6 −2.10950
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.79548e6 0.499627 0.249814 0.968294i \(-0.419631\pi\)
0.249814 + 0.968294i \(0.419631\pi\)
\(420\) 0 0
\(421\) −532453. −0.146412 −0.0732059 0.997317i \(-0.523323\pi\)
−0.0732059 + 0.997317i \(0.523323\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 221752. 0.0595519
\(426\) 0 0
\(427\) 885834. 0.235116
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.52516e6 0.654781 0.327390 0.944889i \(-0.393831\pi\)
0.327390 + 0.944889i \(0.393831\pi\)
\(432\) 0 0
\(433\) 1.97787e6 0.506964 0.253482 0.967340i \(-0.418424\pi\)
0.253482 + 0.967340i \(0.418424\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 914615. 0.229105
\(438\) 0 0
\(439\) −5.79298e6 −1.43463 −0.717317 0.696747i \(-0.754630\pi\)
−0.717317 + 0.696747i \(0.754630\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.45828e6 0.595143 0.297572 0.954699i \(-0.403823\pi\)
0.297572 + 0.954699i \(0.403823\pi\)
\(444\) 0 0
\(445\) −2.04236e6 −0.488913
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.38166e6 1.25980 0.629899 0.776677i \(-0.283096\pi\)
0.629899 + 0.776677i \(0.283096\pi\)
\(450\) 0 0
\(451\) −1.33511e6 −0.309084
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 742802. 0.168207
\(456\) 0 0
\(457\) 3.78914e6 0.848691 0.424346 0.905500i \(-0.360504\pi\)
0.424346 + 0.905500i \(0.360504\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.52631e6 0.772801 0.386400 0.922331i \(-0.373718\pi\)
0.386400 + 0.922331i \(0.373718\pi\)
\(462\) 0 0
\(463\) −796762. −0.172733 −0.0863666 0.996263i \(-0.527526\pi\)
−0.0863666 + 0.996263i \(0.527526\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −379675. −0.0805601 −0.0402801 0.999188i \(-0.512825\pi\)
−0.0402801 + 0.999188i \(0.512825\pi\)
\(468\) 0 0
\(469\) 2.13562e6 0.448323
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.58953e6 −0.532192
\(474\) 0 0
\(475\) −583900. −0.118742
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.56975e6 1.30831 0.654154 0.756361i \(-0.273025\pi\)
0.654154 + 0.756361i \(0.273025\pi\)
\(480\) 0 0
\(481\) 731365. 0.144136
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.83932e6 1.51330
\(486\) 0 0
\(487\) −2.12335e6 −0.405695 −0.202848 0.979210i \(-0.565020\pi\)
−0.202848 + 0.979210i \(0.565020\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.10257e6 −1.32957 −0.664786 0.747034i \(-0.731477\pi\)
−0.664786 + 0.747034i \(0.731477\pi\)
\(492\) 0 0
\(493\) 45845.1 0.00849524
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.55433e6 −0.282261
\(498\) 0 0
\(499\) −7.99824e6 −1.43795 −0.718974 0.695037i \(-0.755388\pi\)
−0.718974 + 0.695037i \(0.755388\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.18840e6 0.738123 0.369061 0.929405i \(-0.379679\pi\)
0.369061 + 0.929405i \(0.379679\pi\)
\(504\) 0 0
\(505\) −6.22821e6 −1.08676
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.27264e6 −1.07314 −0.536569 0.843856i \(-0.680280\pi\)
−0.536569 + 0.843856i \(0.680280\pi\)
\(510\) 0 0
\(511\) 3.28626e6 0.556736
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.33674e6 −0.720519
\(516\) 0 0
\(517\) −353269. −0.0581271
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.98236e6 −0.642756 −0.321378 0.946951i \(-0.604146\pi\)
−0.321378 + 0.946951i \(0.604146\pi\)
\(522\) 0 0
\(523\) 3.36876e6 0.538537 0.269269 0.963065i \(-0.413218\pi\)
0.269269 + 0.963065i \(0.413218\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −261021. −0.0409401
\(528\) 0 0
\(529\) −5.75567e6 −0.894246
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.49996e6 −0.228698
\(534\) 0 0
\(535\) −2.74683e6 −0.414903
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 536115. 0.0794851
\(540\) 0 0
\(541\) −1.14977e6 −0.168895 −0.0844474 0.996428i \(-0.526912\pi\)
−0.0844474 + 0.996428i \(0.526912\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6.62664e6 0.955657
\(546\) 0 0
\(547\) 9.25175e6 1.32207 0.661037 0.750353i \(-0.270117\pi\)
0.661037 + 0.750353i \(0.270117\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −120716. −0.0169389
\(552\) 0 0
\(553\) −28087.2 −0.00390567
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.35893e7 −1.85591 −0.927956 0.372689i \(-0.878436\pi\)
−0.927956 + 0.372689i \(0.878436\pi\)
\(558\) 0 0
\(559\) −2.90927e6 −0.393781
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.04604e6 −0.803897 −0.401948 0.915662i \(-0.631667\pi\)
−0.401948 + 0.915662i \(0.631667\pi\)
\(564\) 0 0
\(565\) −8.78231e6 −1.15741
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 902424. 0.116850 0.0584252 0.998292i \(-0.481392\pi\)
0.0584252 + 0.998292i \(0.481392\pi\)
\(570\) 0 0
\(571\) 7.88210e6 1.01170 0.505850 0.862621i \(-0.331179\pi\)
0.505850 + 0.862621i \(0.331179\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −434547. −0.0548110
\(576\) 0 0
\(577\) 7.49480e6 0.937174 0.468587 0.883417i \(-0.344763\pi\)
0.468587 + 0.883417i \(0.344763\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.00133e6 −0.737577
\(582\) 0 0
\(583\) −4.18854e6 −0.510377
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.89570e6 0.586435 0.293218 0.956046i \(-0.405274\pi\)
0.293218 + 0.956046i \(0.405274\pi\)
\(588\) 0 0
\(589\) 687300. 0.0816315
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.31116e7 −1.53116 −0.765578 0.643343i \(-0.777547\pi\)
−0.765578 + 0.643343i \(0.777547\pi\)
\(594\) 0 0
\(595\) 1.24665e6 0.144361
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.35593e6 −0.268284 −0.134142 0.990962i \(-0.542828\pi\)
−0.134142 + 0.990962i \(0.542828\pi\)
\(600\) 0 0
\(601\) −9.69333e6 −1.09468 −0.547339 0.836911i \(-0.684359\pi\)
−0.547339 + 0.836911i \(0.684359\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.71935e6 0.746343
\(606\) 0 0
\(607\) 6.67081e6 0.734864 0.367432 0.930050i \(-0.380237\pi\)
0.367432 + 0.930050i \(0.380237\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −396889. −0.0430096
\(612\) 0 0
\(613\) −1.50616e6 −0.161890 −0.0809450 0.996719i \(-0.525794\pi\)
−0.0809450 + 0.996719i \(0.525794\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.85725e6 −0.936668 −0.468334 0.883551i \(-0.655146\pi\)
−0.468334 + 0.883551i \(0.655146\pi\)
\(618\) 0 0
\(619\) 9.88906e6 1.03736 0.518679 0.854969i \(-0.326424\pi\)
0.518679 + 0.854969i \(0.326424\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.65607e6 −0.170946
\(624\) 0 0
\(625\) −1.11342e7 −1.14014
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.22745e6 0.123702
\(630\) 0 0
\(631\) 2.79106e6 0.279059 0.139530 0.990218i \(-0.455441\pi\)
0.139530 + 0.990218i \(0.455441\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.07402e7 −2.04117
\(636\) 0 0
\(637\) 602312. 0.0588129
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.08308e6 −0.104116 −0.0520580 0.998644i \(-0.516578\pi\)
−0.0520580 + 0.998644i \(0.516578\pi\)
\(642\) 0 0
\(643\) 2.82572e6 0.269526 0.134763 0.990878i \(-0.456973\pi\)
0.134763 + 0.990878i \(0.456973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.40446e6 −0.883229 −0.441614 0.897205i \(-0.645594\pi\)
−0.441614 + 0.897205i \(0.645594\pi\)
\(648\) 0 0
\(649\) 1.24595e6 0.116116
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.47880e6 0.778128 0.389064 0.921211i \(-0.372798\pi\)
0.389064 + 0.921211i \(0.372798\pi\)
\(654\) 0 0
\(655\) 1.05267e7 0.958718
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.26349e6 0.741225 0.370612 0.928788i \(-0.379148\pi\)
0.370612 + 0.928788i \(0.379148\pi\)
\(660\) 0 0
\(661\) −3.04960e6 −0.271481 −0.135741 0.990744i \(-0.543341\pi\)
−0.135741 + 0.990744i \(0.543341\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.28257e6 −0.287846
\(666\) 0 0
\(667\) −89838.4 −0.00781893
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.03666e6 −0.346111
\(672\) 0 0
\(673\) −5.24989e6 −0.446799 −0.223400 0.974727i \(-0.571715\pi\)
−0.223400 + 0.974727i \(0.571715\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.89170e6 0.158628 0.0793141 0.996850i \(-0.474727\pi\)
0.0793141 + 0.996850i \(0.474727\pi\)
\(678\) 0 0
\(679\) 6.35663e6 0.529118
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.90302e6 0.402172 0.201086 0.979574i \(-0.435553\pi\)
0.201086 + 0.979574i \(0.435553\pi\)
\(684\) 0 0
\(685\) −1.12076e7 −0.912610
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.70572e6 −0.377640
\(690\) 0 0
\(691\) 8.83530e6 0.703925 0.351962 0.936014i \(-0.385515\pi\)
0.351962 + 0.936014i \(0.385515\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.06620e7 −0.837295
\(696\) 0 0
\(697\) −2.51739e6 −0.196277
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.02145e7 −1.55371 −0.776853 0.629682i \(-0.783185\pi\)
−0.776853 + 0.629682i \(0.783185\pi\)
\(702\) 0 0
\(703\) −3.23203e6 −0.246653
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.05023e6 −0.379982
\(708\) 0 0
\(709\) −1.29615e7 −0.968368 −0.484184 0.874966i \(-0.660883\pi\)
−0.484184 + 0.874966i \(0.660883\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 511499. 0.0376809
\(714\) 0 0
\(715\) −3.38487e6 −0.247615
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 729212. 0.0526055 0.0263028 0.999654i \(-0.491627\pi\)
0.0263028 + 0.999654i \(0.491627\pi\)
\(720\) 0 0
\(721\) −3.51651e6 −0.251926
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 57353.8 0.00405245
\(726\) 0 0
\(727\) 4.29143e6 0.301138 0.150569 0.988599i \(-0.451889\pi\)
0.150569 + 0.988599i \(0.451889\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.88264e6 −0.337957
\(732\) 0 0
\(733\) 1.90438e7 1.30916 0.654581 0.755992i \(-0.272845\pi\)
0.654581 + 0.755992i \(0.272845\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.73179e6 −0.659970
\(738\) 0 0
\(739\) −8.34081e6 −0.561820 −0.280910 0.959734i \(-0.590636\pi\)
−0.280910 + 0.959734i \(0.590636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.74448e6 0.248840 0.124420 0.992230i \(-0.460293\pi\)
0.124420 + 0.992230i \(0.460293\pi\)
\(744\) 0 0
\(745\) 1.94030e7 1.28079
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.22730e6 −0.145069
\(750\) 0 0
\(751\) −2.21978e6 −0.143619 −0.0718093 0.997418i \(-0.522877\pi\)
−0.0718093 + 0.997418i \(0.522877\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.17508e6 0.202715
\(756\) 0 0
\(757\) 9.31129e6 0.590568 0.295284 0.955409i \(-0.404586\pi\)
0.295284 + 0.955409i \(0.404586\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10299e7 −0.690417 −0.345208 0.938526i \(-0.612192\pi\)
−0.345208 + 0.938526i \(0.612192\pi\)
\(762\) 0 0
\(763\) 5.37331e6 0.334141
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.39980e6 0.0859167
\(768\) 0 0
\(769\) −1.70965e6 −0.104254 −0.0521269 0.998640i \(-0.516600\pi\)
−0.0521269 + 0.998640i \(0.516600\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8.60659e6 −0.518063 −0.259032 0.965869i \(-0.583403\pi\)
−0.259032 + 0.965869i \(0.583403\pi\)
\(774\) 0 0
\(775\) −326547. −0.0195295
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.62860e6 0.391361
\(780\) 0 0
\(781\) 7.08291e6 0.415512
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.41945e7 −0.822139
\(786\) 0 0
\(787\) −3.28977e7 −1.89334 −0.946669 0.322207i \(-0.895575\pi\)
−0.946669 + 0.322207i \(0.895575\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.12126e6 −0.404684
\(792\) 0 0
\(793\) −4.53508e6 −0.256096
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.93037e6 −0.442229 −0.221115 0.975248i \(-0.570970\pi\)
−0.221115 + 0.975248i \(0.570970\pi\)
\(798\) 0 0
\(799\) −666098. −0.0369123
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.49752e7 −0.819563
\(804\) 0 0
\(805\) −2.44294e6 −0.132869
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.63556e7 −0.878606 −0.439303 0.898339i \(-0.644774\pi\)
−0.439303 + 0.898339i \(0.644774\pi\)
\(810\) 0 0
\(811\) 1.61988e7 0.864827 0.432414 0.901675i \(-0.357662\pi\)
0.432414 + 0.901675i \(0.357662\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.08644e7 −1.10030
\(816\) 0 0
\(817\) 1.28566e7 0.673861
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.20722e7 1.14285 0.571424 0.820655i \(-0.306391\pi\)
0.571424 + 0.820655i \(0.306391\pi\)
\(822\) 0 0
\(823\) 3.09817e7 1.59443 0.797216 0.603695i \(-0.206305\pi\)
0.797216 + 0.603695i \(0.206305\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.50054e7 1.77980 0.889900 0.456156i \(-0.150774\pi\)
0.889900 + 0.456156i \(0.150774\pi\)
\(828\) 0 0
\(829\) 3.35460e7 1.69533 0.847664 0.530533i \(-0.178008\pi\)
0.847664 + 0.530533i \(0.178008\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.01086e6 0.0504753
\(834\) 0 0
\(835\) −3.49874e7 −1.73658
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.08801e6 0.102406 0.0512032 0.998688i \(-0.483694\pi\)
0.0512032 + 0.998688i \(0.483694\pi\)
\(840\) 0 0
\(841\) −2.04993e7 −0.999422
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.86342e7 0.897777
\(846\) 0 0
\(847\) 5.44848e6 0.260956
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.40532e6 −0.113854
\(852\) 0 0
\(853\) −2.68196e7 −1.26206 −0.631029 0.775759i \(-0.717367\pi\)
−0.631029 + 0.775759i \(0.717367\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.61592e7 −1.21667 −0.608335 0.793680i \(-0.708162\pi\)
−0.608335 + 0.793680i \(0.708162\pi\)
\(858\) 0 0
\(859\) −5.04313e6 −0.233194 −0.116597 0.993179i \(-0.537199\pi\)
−0.116597 + 0.993179i \(0.537199\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.20811e7 0.552177 0.276089 0.961132i \(-0.410962\pi\)
0.276089 + 0.961132i \(0.410962\pi\)
\(864\) 0 0
\(865\) 1.17629e6 0.0534533
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 127991. 0.00574948
\(870\) 0 0
\(871\) −1.09334e7 −0.488328
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −7.69365e6 −0.339713
\(876\) 0 0
\(877\) −1.21596e7 −0.533852 −0.266926 0.963717i \(-0.586008\pi\)
−0.266926 + 0.963717i \(0.586008\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6.17663e6 −0.268109 −0.134055 0.990974i \(-0.542800\pi\)
−0.134055 + 0.990974i \(0.542800\pi\)
\(882\) 0 0
\(883\) −2.14118e7 −0.924167 −0.462084 0.886836i \(-0.652898\pi\)
−0.462084 + 0.886836i \(0.652898\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6.20130e6 −0.264651 −0.132326 0.991206i \(-0.542244\pi\)
−0.132326 + 0.991206i \(0.542244\pi\)
\(888\) 0 0
\(889\) −1.68175e7 −0.713686
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.75392e6 0.0736005
\(894\) 0 0
\(895\) −1.97415e6 −0.0823803
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −67510.3 −0.00278593
\(900\) 0 0
\(901\) −7.89762e6 −0.324104
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.89251e6 0.239155
\(906\) 0 0
\(907\) −2.99708e6 −0.120971 −0.0604854 0.998169i \(-0.519265\pi\)
−0.0604854 + 0.998169i \(0.519265\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.06294e7 0.424340 0.212170 0.977233i \(-0.431947\pi\)
0.212170 + 0.977233i \(0.431947\pi\)
\(912\) 0 0
\(913\) 2.73475e7 1.08578
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.53576e6 0.335211
\(918\) 0 0
\(919\) −3.83265e7 −1.49696 −0.748480 0.663158i \(-0.769216\pi\)
−0.748480 + 0.663158i \(0.769216\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 7.95747e6 0.307448
\(924\) 0 0
\(925\) 1.53558e6 0.0590091
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 5.57501e6 0.211937 0.105968 0.994369i \(-0.466206\pi\)
0.105968 + 0.994369i \(0.466206\pi\)
\(930\) 0 0
\(931\) −2.66172e6 −0.100644
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.68084e6 −0.212512
\(936\) 0 0
\(937\) −2.26728e7 −0.843636 −0.421818 0.906680i \(-0.638608\pi\)
−0.421818 + 0.906680i \(0.638608\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.75582e7 1.01456 0.507279 0.861782i \(-0.330651\pi\)
0.507279 + 0.861782i \(0.330651\pi\)
\(942\) 0 0
\(943\) 4.93310e6 0.180651
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.09071e7 0.757563 0.378781 0.925486i \(-0.376343\pi\)
0.378781 + 0.925486i \(0.376343\pi\)
\(948\) 0 0
\(949\) −1.68242e7 −0.606414
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.17506e7 −0.775781 −0.387890 0.921706i \(-0.626796\pi\)
−0.387890 + 0.921706i \(0.626796\pi\)
\(954\) 0 0
\(955\) −5.45525e7 −1.93556
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −9.08782e6 −0.319090
\(960\) 0 0
\(961\) −2.82448e7 −0.986574
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.42405e7 1.52933
\(966\) 0 0
\(967\) −5.24829e7 −1.80490 −0.902448 0.430799i \(-0.858232\pi\)
−0.902448 + 0.430799i \(0.858232\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.51330e7 −0.855454 −0.427727 0.903908i \(-0.640685\pi\)
−0.427727 + 0.903908i \(0.640685\pi\)
\(972\) 0 0
\(973\) −8.64547e6 −0.292757
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.17512e7 0.393864 0.196932 0.980417i \(-0.436902\pi\)
0.196932 + 0.980417i \(0.436902\pi\)
\(978\) 0 0
\(979\) 7.54656e6 0.251647
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.58466e7 −1.51329 −0.756647 0.653824i \(-0.773164\pi\)
−0.756647 + 0.653824i \(0.773164\pi\)
\(984\) 0 0
\(985\) −1.59196e7 −0.522807
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.56806e6 0.311052
\(990\) 0 0
\(991\) 3.24273e7 1.04888 0.524441 0.851447i \(-0.324274\pi\)
0.524441 + 0.851447i \(0.324274\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.65916e7 −0.531288
\(996\) 0 0
\(997\) 5.71398e7 1.82054 0.910272 0.414012i \(-0.135873\pi\)
0.910272 + 0.414012i \(0.135873\pi\)
\(998\) 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.1.1 2
3.2 odd 2 336.6.a.s.1.2 2
4.3 odd 2 504.6.a.p.1.1 2
12.11 even 2 168.6.a.i.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.i.1.2 2 12.11 even 2
336.6.a.s.1.2 2 3.2 odd 2
504.6.a.p.1.1 2 4.3 odd 2
1008.6.a.bp.1.1 2 1.1 even 1 trivial