Properties

Label 588.6.a.l.1.2
Level $588$
Weight $6$
Character 588.1
Self dual yes
Analytic conductor $94.306$
Analytic rank $1$
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] = [588,6,Mod(1,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("588.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 588.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: \(94.3056860500\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{7081}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1770 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-41.5743\) of defining polynomial
Character \(\chi\) \(=\) 588.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{3} +65.5743 q^{5} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} +65.5743 q^{5} +81.0000 q^{9} -245.574 q^{11} +434.872 q^{13} +590.169 q^{15} -1102.30 q^{17} -2877.29 q^{19} -4229.43 q^{23} +1174.99 q^{25} +729.000 q^{27} +4969.60 q^{29} -8782.65 q^{31} -2210.17 q^{33} -2440.06 q^{37} +3913.85 q^{39} -3668.55 q^{41} -7198.06 q^{43} +5311.52 q^{45} +3273.32 q^{47} -9920.68 q^{51} -3021.67 q^{53} -16103.4 q^{55} -25895.6 q^{57} -51487.5 q^{59} -13313.3 q^{61} +28516.4 q^{65} +30895.7 q^{67} -38064.9 q^{69} -41882.8 q^{71} +34617.3 q^{73} +10574.9 q^{75} +77543.5 q^{79} +6561.00 q^{81} +100908. q^{83} -72282.4 q^{85} +44726.4 q^{87} +40783.7 q^{89} -79043.8 q^{93} -188676. q^{95} +140147. q^{97} -19891.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 18 q^{3} + 47 q^{5} + 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 18 q^{3} + 47 q^{5} + 162 q^{9} - 407 q^{11} + 449 q^{13} + 423 q^{15} - 1868 q^{17} - 1463 q^{19} - 44 q^{23} - 1605 q^{25} + 1458 q^{27} + 767 q^{29} - 11170 q^{31} - 3663 q^{33} - 3113 q^{37} + 4041 q^{39} - 7842 q^{41} - 12629 q^{43} + 3807 q^{45} + 9576 q^{47} - 16812 q^{51} + 13395 q^{53} - 13105 q^{55} - 13167 q^{57} - 47521 q^{59} - 63652 q^{61} + 28254 q^{65} + 44541 q^{67} - 396 q^{69} - 125840 q^{71} + 6039 q^{73} - 14445 q^{75} + 17588 q^{79} + 13122 q^{81} + 39325 q^{83} - 58060 q^{85} + 6903 q^{87} + 83082 q^{89} - 100530 q^{93} - 214946 q^{95} + 184785 q^{97} - 32967 q^{99}+O(q^{100}) \) 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
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) 65.5743 1.17303 0.586515 0.809939i \(-0.300500\pi\)
0.586515 + 0.809939i \(0.300500\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −245.574 −0.611929 −0.305965 0.952043i \(-0.598979\pi\)
−0.305965 + 0.952043i \(0.598979\pi\)
\(12\) 0 0
\(13\) 434.872 0.713679 0.356839 0.934166i \(-0.383854\pi\)
0.356839 + 0.934166i \(0.383854\pi\)
\(14\) 0 0
\(15\) 590.169 0.677249
\(16\) 0 0
\(17\) −1102.30 −0.925074 −0.462537 0.886600i \(-0.653061\pi\)
−0.462537 + 0.886600i \(0.653061\pi\)
\(18\) 0 0
\(19\) −2877.29 −1.82852 −0.914260 0.405127i \(-0.867227\pi\)
−0.914260 + 0.405127i \(0.867227\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4229.43 −1.66710 −0.833552 0.552441i \(-0.813696\pi\)
−0.833552 + 0.552441i \(0.813696\pi\)
\(24\) 0 0
\(25\) 1174.99 0.375998
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 4969.60 1.09730 0.548652 0.836051i \(-0.315141\pi\)
0.548652 + 0.836051i \(0.315141\pi\)
\(30\) 0 0
\(31\) −8782.65 −1.64143 −0.820713 0.571341i \(-0.806424\pi\)
−0.820713 + 0.571341i \(0.806424\pi\)
\(32\) 0 0
\(33\) −2210.17 −0.353298
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2440.06 −0.293019 −0.146510 0.989209i \(-0.546804\pi\)
−0.146510 + 0.989209i \(0.546804\pi\)
\(38\) 0 0
\(39\) 3913.85 0.412043
\(40\) 0 0
\(41\) −3668.55 −0.340828 −0.170414 0.985373i \(-0.554511\pi\)
−0.170414 + 0.985373i \(0.554511\pi\)
\(42\) 0 0
\(43\) −7198.06 −0.593669 −0.296835 0.954929i \(-0.595931\pi\)
−0.296835 + 0.954929i \(0.595931\pi\)
\(44\) 0 0
\(45\) 5311.52 0.391010
\(46\) 0 0
\(47\) 3273.32 0.216145 0.108072 0.994143i \(-0.465532\pi\)
0.108072 + 0.994143i \(0.465532\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −9920.68 −0.534092
\(52\) 0 0
\(53\) −3021.67 −0.147760 −0.0738801 0.997267i \(-0.523538\pi\)
−0.0738801 + 0.997267i \(0.523538\pi\)
\(54\) 0 0
\(55\) −16103.4 −0.717811
\(56\) 0 0
\(57\) −25895.6 −1.05570
\(58\) 0 0
\(59\) −51487.5 −1.92562 −0.962812 0.270171i \(-0.912920\pi\)
−0.962812 + 0.270171i \(0.912920\pi\)
\(60\) 0 0
\(61\) −13313.3 −0.458101 −0.229050 0.973415i \(-0.573562\pi\)
−0.229050 + 0.973415i \(0.573562\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 28516.4 0.837166
\(66\) 0 0
\(67\) 30895.7 0.840837 0.420418 0.907330i \(-0.361883\pi\)
0.420418 + 0.907330i \(0.361883\pi\)
\(68\) 0 0
\(69\) −38064.9 −0.962503
\(70\) 0 0
\(71\) −41882.8 −0.986030 −0.493015 0.870021i \(-0.664105\pi\)
−0.493015 + 0.870021i \(0.664105\pi\)
\(72\) 0 0
\(73\) 34617.3 0.760302 0.380151 0.924924i \(-0.375872\pi\)
0.380151 + 0.924924i \(0.375872\pi\)
\(74\) 0 0
\(75\) 10574.9 0.217083
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 77543.5 1.39790 0.698952 0.715168i \(-0.253650\pi\)
0.698952 + 0.715168i \(0.253650\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) 100908. 1.60779 0.803897 0.594768i \(-0.202756\pi\)
0.803897 + 0.594768i \(0.202756\pi\)
\(84\) 0 0
\(85\) −72282.4 −1.08514
\(86\) 0 0
\(87\) 44726.4 0.633528
\(88\) 0 0
\(89\) 40783.7 0.545772 0.272886 0.962046i \(-0.412022\pi\)
0.272886 + 0.962046i \(0.412022\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −79043.8 −0.947678
\(94\) 0 0
\(95\) −188676. −2.14491
\(96\) 0 0
\(97\) 140147. 1.51236 0.756178 0.654366i \(-0.227064\pi\)
0.756178 + 0.654366i \(0.227064\pi\)
\(98\) 0 0
\(99\) −19891.5 −0.203976
\(100\) 0 0
\(101\) 8576.45 0.0836574 0.0418287 0.999125i \(-0.486682\pi\)
0.0418287 + 0.999125i \(0.486682\pi\)
\(102\) 0 0
\(103\) −35260.1 −0.327485 −0.163742 0.986503i \(-0.552357\pi\)
−0.163742 + 0.986503i \(0.552357\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −192629. −1.62653 −0.813264 0.581895i \(-0.802311\pi\)
−0.813264 + 0.581895i \(0.802311\pi\)
\(108\) 0 0
\(109\) 123292. 0.993961 0.496980 0.867762i \(-0.334442\pi\)
0.496980 + 0.867762i \(0.334442\pi\)
\(110\) 0 0
\(111\) −21960.6 −0.169175
\(112\) 0 0
\(113\) 28400.9 0.209236 0.104618 0.994512i \(-0.466638\pi\)
0.104618 + 0.994512i \(0.466638\pi\)
\(114\) 0 0
\(115\) −277342. −1.95556
\(116\) 0 0
\(117\) 35224.6 0.237893
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −100744. −0.625542
\(122\) 0 0
\(123\) −33017.0 −0.196777
\(124\) 0 0
\(125\) −127870. −0.731973
\(126\) 0 0
\(127\) −47198.8 −0.259670 −0.129835 0.991536i \(-0.541445\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(128\) 0 0
\(129\) −64782.6 −0.342755
\(130\) 0 0
\(131\) 79809.3 0.406327 0.203163 0.979145i \(-0.434878\pi\)
0.203163 + 0.979145i \(0.434878\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 47803.7 0.225750
\(136\) 0 0
\(137\) −86064.3 −0.391761 −0.195881 0.980628i \(-0.562757\pi\)
−0.195881 + 0.980628i \(0.562757\pi\)
\(138\) 0 0
\(139\) 270587. 1.18787 0.593935 0.804513i \(-0.297573\pi\)
0.593935 + 0.804513i \(0.297573\pi\)
\(140\) 0 0
\(141\) 29459.9 0.124791
\(142\) 0 0
\(143\) −106793. −0.436721
\(144\) 0 0
\(145\) 325878. 1.28717
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −172548. −0.636713 −0.318356 0.947971i \(-0.603131\pi\)
−0.318356 + 0.947971i \(0.603131\pi\)
\(150\) 0 0
\(151\) −17899.5 −0.0638849 −0.0319425 0.999490i \(-0.510169\pi\)
−0.0319425 + 0.999490i \(0.510169\pi\)
\(152\) 0 0
\(153\) −89286.1 −0.308358
\(154\) 0 0
\(155\) −575916. −1.92544
\(156\) 0 0
\(157\) −179019. −0.579628 −0.289814 0.957083i \(-0.593593\pi\)
−0.289814 + 0.957083i \(0.593593\pi\)
\(158\) 0 0
\(159\) −27195.1 −0.0853094
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −237289. −0.699534 −0.349767 0.936837i \(-0.613739\pi\)
−0.349767 + 0.936837i \(0.613739\pi\)
\(164\) 0 0
\(165\) −144930. −0.414428
\(166\) 0 0
\(167\) −94040.0 −0.260928 −0.130464 0.991453i \(-0.541647\pi\)
−0.130464 + 0.991453i \(0.541647\pi\)
\(168\) 0 0
\(169\) −182180. −0.490663
\(170\) 0 0
\(171\) −233061. −0.609507
\(172\) 0 0
\(173\) 488713. 1.24148 0.620739 0.784017i \(-0.286833\pi\)
0.620739 + 0.784017i \(0.286833\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −463387. −1.11176
\(178\) 0 0
\(179\) 812996. 1.89651 0.948257 0.317505i \(-0.102845\pi\)
0.948257 + 0.317505i \(0.102845\pi\)
\(180\) 0 0
\(181\) −332961. −0.755434 −0.377717 0.925921i \(-0.623291\pi\)
−0.377717 + 0.925921i \(0.623291\pi\)
\(182\) 0 0
\(183\) −119820. −0.264484
\(184\) 0 0
\(185\) −160005. −0.343720
\(186\) 0 0
\(187\) 270696. 0.566080
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −144288. −0.286185 −0.143092 0.989709i \(-0.545705\pi\)
−0.143092 + 0.989709i \(0.545705\pi\)
\(192\) 0 0
\(193\) −894619. −1.72880 −0.864400 0.502804i \(-0.832302\pi\)
−0.864400 + 0.502804i \(0.832302\pi\)
\(194\) 0 0
\(195\) 256648. 0.483338
\(196\) 0 0
\(197\) −599462. −1.10052 −0.550258 0.834995i \(-0.685470\pi\)
−0.550258 + 0.834995i \(0.685470\pi\)
\(198\) 0 0
\(199\) −778259. −1.39313 −0.696564 0.717494i \(-0.745289\pi\)
−0.696564 + 0.717494i \(0.745289\pi\)
\(200\) 0 0
\(201\) 278062. 0.485457
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −240563. −0.399801
\(206\) 0 0
\(207\) −342584. −0.555701
\(208\) 0 0
\(209\) 706589. 1.11893
\(210\) 0 0
\(211\) −810532. −1.25333 −0.626663 0.779291i \(-0.715580\pi\)
−0.626663 + 0.779291i \(0.715580\pi\)
\(212\) 0 0
\(213\) −376945. −0.569285
\(214\) 0 0
\(215\) −472008. −0.696391
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 311556. 0.438961
\(220\) 0 0
\(221\) −479358. −0.660206
\(222\) 0 0
\(223\) 220486. 0.296905 0.148453 0.988920i \(-0.452571\pi\)
0.148453 + 0.988920i \(0.452571\pi\)
\(224\) 0 0
\(225\) 95174.5 0.125333
\(226\) 0 0
\(227\) 1.34378e6 1.73087 0.865433 0.501025i \(-0.167044\pi\)
0.865433 + 0.501025i \(0.167044\pi\)
\(228\) 0 0
\(229\) −1.04258e6 −1.31378 −0.656889 0.753987i \(-0.728128\pi\)
−0.656889 + 0.753987i \(0.728128\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 632511. 0.763270 0.381635 0.924313i \(-0.375361\pi\)
0.381635 + 0.924313i \(0.375361\pi\)
\(234\) 0 0
\(235\) 214646. 0.253544
\(236\) 0 0
\(237\) 697891. 0.807081
\(238\) 0 0
\(239\) −684919. −0.775612 −0.387806 0.921741i \(-0.626767\pi\)
−0.387806 + 0.921741i \(0.626767\pi\)
\(240\) 0 0
\(241\) −7732.88 −0.00857628 −0.00428814 0.999991i \(-0.501365\pi\)
−0.00428814 + 0.999991i \(0.501365\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.25125e6 −1.30498
\(248\) 0 0
\(249\) 908172. 0.928261
\(250\) 0 0
\(251\) 1.09614e6 1.09820 0.549098 0.835758i \(-0.314971\pi\)
0.549098 + 0.835758i \(0.314971\pi\)
\(252\) 0 0
\(253\) 1.03864e6 1.02015
\(254\) 0 0
\(255\) −650542. −0.626505
\(256\) 0 0
\(257\) 714920. 0.675188 0.337594 0.941292i \(-0.390387\pi\)
0.337594 + 0.941292i \(0.390387\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 402538. 0.365768
\(262\) 0 0
\(263\) −596513. −0.531778 −0.265889 0.964004i \(-0.585665\pi\)
−0.265889 + 0.964004i \(0.585665\pi\)
\(264\) 0 0
\(265\) −198144. −0.173327
\(266\) 0 0
\(267\) 367053. 0.315102
\(268\) 0 0
\(269\) −2.03308e6 −1.71306 −0.856531 0.516096i \(-0.827385\pi\)
−0.856531 + 0.516096i \(0.827385\pi\)
\(270\) 0 0
\(271\) 1.79455e6 1.48434 0.742170 0.670212i \(-0.233797\pi\)
0.742170 + 0.670212i \(0.233797\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −288548. −0.230084
\(276\) 0 0
\(277\) 423580. 0.331693 0.165846 0.986152i \(-0.446964\pi\)
0.165846 + 0.986152i \(0.446964\pi\)
\(278\) 0 0
\(279\) −711395. −0.547142
\(280\) 0 0
\(281\) −1.63799e6 −1.23750 −0.618749 0.785589i \(-0.712360\pi\)
−0.618749 + 0.785589i \(0.712360\pi\)
\(282\) 0 0
\(283\) −294035. −0.218240 −0.109120 0.994029i \(-0.534803\pi\)
−0.109120 + 0.994029i \(0.534803\pi\)
\(284\) 0 0
\(285\) −1.69809e6 −1.23836
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −204798. −0.144238
\(290\) 0 0
\(291\) 1.26132e6 0.873159
\(292\) 0 0
\(293\) −356961. −0.242913 −0.121457 0.992597i \(-0.538757\pi\)
−0.121457 + 0.992597i \(0.538757\pi\)
\(294\) 0 0
\(295\) −3.37626e6 −2.25881
\(296\) 0 0
\(297\) −179024. −0.117766
\(298\) 0 0
\(299\) −1.83926e6 −1.18978
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 77188.1 0.0482996
\(304\) 0 0
\(305\) −873010. −0.537365
\(306\) 0 0
\(307\) −2.04097e6 −1.23592 −0.617960 0.786210i \(-0.712041\pi\)
−0.617960 + 0.786210i \(0.712041\pi\)
\(308\) 0 0
\(309\) −317341. −0.189073
\(310\) 0 0
\(311\) 2.04674e6 1.19994 0.599972 0.800021i \(-0.295178\pi\)
0.599972 + 0.800021i \(0.295178\pi\)
\(312\) 0 0
\(313\) 638545. 0.368409 0.184205 0.982888i \(-0.441029\pi\)
0.184205 + 0.982888i \(0.441029\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.49909e6 1.95572 0.977860 0.209260i \(-0.0671056\pi\)
0.977860 + 0.209260i \(0.0671056\pi\)
\(318\) 0 0
\(319\) −1.22041e6 −0.671472
\(320\) 0 0
\(321\) −1.73366e6 −0.939076
\(322\) 0 0
\(323\) 3.17163e6 1.69152
\(324\) 0 0
\(325\) 510972. 0.268342
\(326\) 0 0
\(327\) 1.10963e6 0.573864
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.94179e6 −1.47585 −0.737923 0.674885i \(-0.764193\pi\)
−0.737923 + 0.674885i \(0.764193\pi\)
\(332\) 0 0
\(333\) −197645. −0.0976731
\(334\) 0 0
\(335\) 2.02597e6 0.986326
\(336\) 0 0
\(337\) 2.77854e6 1.33273 0.666364 0.745627i \(-0.267850\pi\)
0.666364 + 0.745627i \(0.267850\pi\)
\(338\) 0 0
\(339\) 255608. 0.120802
\(340\) 0 0
\(341\) 2.15679e6 1.00444
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.49608e6 −1.12904
\(346\) 0 0
\(347\) −172004. −0.0766857 −0.0383429 0.999265i \(-0.512208\pi\)
−0.0383429 + 0.999265i \(0.512208\pi\)
\(348\) 0 0
\(349\) −3.88321e6 −1.70658 −0.853290 0.521436i \(-0.825397\pi\)
−0.853290 + 0.521436i \(0.825397\pi\)
\(350\) 0 0
\(351\) 317021. 0.137348
\(352\) 0 0
\(353\) −770935. −0.329292 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(354\) 0 0
\(355\) −2.74644e6 −1.15664
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.14033e6 1.28600 0.642998 0.765868i \(-0.277691\pi\)
0.642998 + 0.765868i \(0.277691\pi\)
\(360\) 0 0
\(361\) 5.80271e6 2.34349
\(362\) 0 0
\(363\) −906698. −0.361157
\(364\) 0 0
\(365\) 2.27001e6 0.891857
\(366\) 0 0
\(367\) −365684. −0.141723 −0.0708615 0.997486i \(-0.522575\pi\)
−0.0708615 + 0.997486i \(0.522575\pi\)
\(368\) 0 0
\(369\) −297153. −0.113609
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −154260. −0.0574091 −0.0287045 0.999588i \(-0.509138\pi\)
−0.0287045 + 0.999588i \(0.509138\pi\)
\(374\) 0 0
\(375\) −1.15083e6 −0.422605
\(376\) 0 0
\(377\) 2.16114e6 0.783122
\(378\) 0 0
\(379\) 4.06013e6 1.45192 0.725959 0.687738i \(-0.241396\pi\)
0.725959 + 0.687738i \(0.241396\pi\)
\(380\) 0 0
\(381\) −424789. −0.149920
\(382\) 0 0
\(383\) 2.04303e6 0.711669 0.355834 0.934549i \(-0.384197\pi\)
0.355834 + 0.934549i \(0.384197\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −583043. −0.197890
\(388\) 0 0
\(389\) −2.12366e6 −0.711560 −0.355780 0.934570i \(-0.615785\pi\)
−0.355780 + 0.934570i \(0.615785\pi\)
\(390\) 0 0
\(391\) 4.66209e6 1.54219
\(392\) 0 0
\(393\) 718284. 0.234593
\(394\) 0 0
\(395\) 5.08486e6 1.63978
\(396\) 0 0
\(397\) −3.66364e6 −1.16664 −0.583319 0.812243i \(-0.698246\pi\)
−0.583319 + 0.812243i \(0.698246\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −64089.7 −0.0199034 −0.00995170 0.999950i \(-0.503168\pi\)
−0.00995170 + 0.999950i \(0.503168\pi\)
\(402\) 0 0
\(403\) −3.81933e6 −1.17145
\(404\) 0 0
\(405\) 430233. 0.130337
\(406\) 0 0
\(407\) 599216. 0.179307
\(408\) 0 0
\(409\) 2.02574e6 0.598790 0.299395 0.954129i \(-0.403215\pi\)
0.299395 + 0.954129i \(0.403215\pi\)
\(410\) 0 0
\(411\) −774579. −0.226184
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.61698e6 1.88599
\(416\) 0 0
\(417\) 2.43528e6 0.685818
\(418\) 0 0
\(419\) 2.38986e6 0.665025 0.332513 0.943099i \(-0.392104\pi\)
0.332513 + 0.943099i \(0.392104\pi\)
\(420\) 0 0
\(421\) 3.46875e6 0.953822 0.476911 0.878952i \(-0.341756\pi\)
0.476911 + 0.878952i \(0.341756\pi\)
\(422\) 0 0
\(423\) 265139. 0.0720482
\(424\) 0 0
\(425\) −1.29519e6 −0.347826
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −961140. −0.252141
\(430\) 0 0
\(431\) −1.60440e6 −0.416025 −0.208013 0.978126i \(-0.566700\pi\)
−0.208013 + 0.978126i \(0.566700\pi\)
\(432\) 0 0
\(433\) 741661. 0.190102 0.0950508 0.995472i \(-0.469699\pi\)
0.0950508 + 0.995472i \(0.469699\pi\)
\(434\) 0 0
\(435\) 2.93291e6 0.743147
\(436\) 0 0
\(437\) 1.21693e7 3.04833
\(438\) 0 0
\(439\) 2.86787e6 0.710230 0.355115 0.934823i \(-0.384442\pi\)
0.355115 + 0.934823i \(0.384442\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −178298. −0.0431655 −0.0215827 0.999767i \(-0.506871\pi\)
−0.0215827 + 0.999767i \(0.506871\pi\)
\(444\) 0 0
\(445\) 2.67436e6 0.640207
\(446\) 0 0
\(447\) −1.55293e6 −0.367606
\(448\) 0 0
\(449\) −2.77890e6 −0.650515 −0.325258 0.945625i \(-0.605451\pi\)
−0.325258 + 0.945625i \(0.605451\pi\)
\(450\) 0 0
\(451\) 900903. 0.208563
\(452\) 0 0
\(453\) −161095. −0.0368840
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.41339e6 1.43647 0.718236 0.695800i \(-0.244950\pi\)
0.718236 + 0.695800i \(0.244950\pi\)
\(458\) 0 0
\(459\) −803575. −0.178031
\(460\) 0 0
\(461\) −6.88393e6 −1.50864 −0.754318 0.656510i \(-0.772032\pi\)
−0.754318 + 0.656510i \(0.772032\pi\)
\(462\) 0 0
\(463\) 6.70530e6 1.45367 0.726835 0.686812i \(-0.240991\pi\)
0.726835 + 0.686812i \(0.240991\pi\)
\(464\) 0 0
\(465\) −5.18325e6 −1.11165
\(466\) 0 0
\(467\) −3.25673e6 −0.691017 −0.345509 0.938416i \(-0.612294\pi\)
−0.345509 + 0.938416i \(0.612294\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.61117e6 −0.334648
\(472\) 0 0
\(473\) 1.76766e6 0.363283
\(474\) 0 0
\(475\) −3.38080e6 −0.687520
\(476\) 0 0
\(477\) −244755. −0.0492534
\(478\) 0 0
\(479\) 9.35832e6 1.86363 0.931814 0.362936i \(-0.118226\pi\)
0.931814 + 0.362936i \(0.118226\pi\)
\(480\) 0 0
\(481\) −1.06111e6 −0.209122
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.19004e6 1.77404
\(486\) 0 0
\(487\) −2.62940e6 −0.502382 −0.251191 0.967938i \(-0.580822\pi\)
−0.251191 + 0.967938i \(0.580822\pi\)
\(488\) 0 0
\(489\) −2.13560e6 −0.403876
\(490\) 0 0
\(491\) −4.81856e6 −0.902015 −0.451008 0.892520i \(-0.648935\pi\)
−0.451008 + 0.892520i \(0.648935\pi\)
\(492\) 0 0
\(493\) −5.47798e6 −1.01509
\(494\) 0 0
\(495\) −1.30437e6 −0.239270
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4.19098e6 −0.753467 −0.376733 0.926322i \(-0.622953\pi\)
−0.376733 + 0.926322i \(0.622953\pi\)
\(500\) 0 0
\(501\) −846360. −0.150647
\(502\) 0 0
\(503\) −1.75338e6 −0.308999 −0.154500 0.987993i \(-0.549377\pi\)
−0.154500 + 0.987993i \(0.549377\pi\)
\(504\) 0 0
\(505\) 562395. 0.0981326
\(506\) 0 0
\(507\) −1.63962e6 −0.283284
\(508\) 0 0
\(509\) 5.61846e6 0.961221 0.480610 0.876934i \(-0.340415\pi\)
0.480610 + 0.876934i \(0.340415\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.09755e6 −0.351899
\(514\) 0 0
\(515\) −2.31216e6 −0.384149
\(516\) 0 0
\(517\) −803844. −0.132265
\(518\) 0 0
\(519\) 4.39842e6 0.716768
\(520\) 0 0
\(521\) 1.10718e7 1.78700 0.893498 0.449068i \(-0.148244\pi\)
0.893498 + 0.449068i \(0.148244\pi\)
\(522\) 0 0
\(523\) −7.59788e6 −1.21461 −0.607307 0.794467i \(-0.707750\pi\)
−0.607307 + 0.794467i \(0.707750\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.68109e6 1.51844
\(528\) 0 0
\(529\) 1.14518e7 1.77924
\(530\) 0 0
\(531\) −4.17049e6 −0.641875
\(532\) 0 0
\(533\) −1.59535e6 −0.243242
\(534\) 0 0
\(535\) −1.26315e7 −1.90796
\(536\) 0 0
\(537\) 7.31697e6 1.09495
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −3.35079e6 −0.492214 −0.246107 0.969243i \(-0.579151\pi\)
−0.246107 + 0.969243i \(0.579151\pi\)
\(542\) 0 0
\(543\) −2.99665e6 −0.436150
\(544\) 0 0
\(545\) 8.08480e6 1.16595
\(546\) 0 0
\(547\) −1.00856e7 −1.44123 −0.720615 0.693335i \(-0.756140\pi\)
−0.720615 + 0.693335i \(0.756140\pi\)
\(548\) 0 0
\(549\) −1.07838e6 −0.152700
\(550\) 0 0
\(551\) −1.42990e7 −2.00644
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.44005e6 −0.198447
\(556\) 0 0
\(557\) 1.35667e7 1.85284 0.926419 0.376495i \(-0.122871\pi\)
0.926419 + 0.376495i \(0.122871\pi\)
\(558\) 0 0
\(559\) −3.13023e6 −0.423689
\(560\) 0 0
\(561\) 2.43626e6 0.326826
\(562\) 0 0
\(563\) −3.96988e6 −0.527845 −0.263922 0.964544i \(-0.585016\pi\)
−0.263922 + 0.964544i \(0.585016\pi\)
\(564\) 0 0
\(565\) 1.86237e6 0.245440
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.17449e6 −0.540534 −0.270267 0.962785i \(-0.587112\pi\)
−0.270267 + 0.962785i \(0.587112\pi\)
\(570\) 0 0
\(571\) 3.85666e6 0.495018 0.247509 0.968886i \(-0.420388\pi\)
0.247509 + 0.968886i \(0.420388\pi\)
\(572\) 0 0
\(573\) −1.29859e6 −0.165229
\(574\) 0 0
\(575\) −4.96956e6 −0.626828
\(576\) 0 0
\(577\) −2.24575e6 −0.280817 −0.140408 0.990094i \(-0.544842\pi\)
−0.140408 + 0.990094i \(0.544842\pi\)
\(578\) 0 0
\(579\) −8.05157e6 −0.998123
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 742045. 0.0904188
\(584\) 0 0
\(585\) 2.30983e6 0.279055
\(586\) 0 0
\(587\) 6.40082e6 0.766726 0.383363 0.923598i \(-0.374766\pi\)
0.383363 + 0.923598i \(0.374766\pi\)
\(588\) 0 0
\(589\) 2.52702e7 3.00138
\(590\) 0 0
\(591\) −5.39516e6 −0.635383
\(592\) 0 0
\(593\) 1.11206e7 1.29865 0.649325 0.760511i \(-0.275051\pi\)
0.649325 + 0.760511i \(0.275051\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.00433e6 −0.804323
\(598\) 0 0
\(599\) −1.31341e7 −1.49567 −0.747833 0.663887i \(-0.768905\pi\)
−0.747833 + 0.663887i \(0.768905\pi\)
\(600\) 0 0
\(601\) −7.88546e6 −0.890514 −0.445257 0.895403i \(-0.646888\pi\)
−0.445257 + 0.895403i \(0.646888\pi\)
\(602\) 0 0
\(603\) 2.50255e6 0.280279
\(604\) 0 0
\(605\) −6.60624e6 −0.733780
\(606\) 0 0
\(607\) −7.65934e6 −0.843762 −0.421881 0.906651i \(-0.638630\pi\)
−0.421881 + 0.906651i \(0.638630\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.42348e6 0.154258
\(612\) 0 0
\(613\) −1.52413e7 −1.63822 −0.819108 0.573639i \(-0.805531\pi\)
−0.819108 + 0.573639i \(0.805531\pi\)
\(614\) 0 0
\(615\) −2.16507e6 −0.230825
\(616\) 0 0
\(617\) 1.35844e7 1.43657 0.718285 0.695749i \(-0.244927\pi\)
0.718285 + 0.695749i \(0.244927\pi\)
\(618\) 0 0
\(619\) 6.37417e6 0.668647 0.334324 0.942458i \(-0.391492\pi\)
0.334324 + 0.942458i \(0.391492\pi\)
\(620\) 0 0
\(621\) −3.08326e6 −0.320834
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.20569e7 −1.23462
\(626\) 0 0
\(627\) 6.35930e6 0.646012
\(628\) 0 0
\(629\) 2.68967e6 0.271065
\(630\) 0 0
\(631\) −1.42736e7 −1.42712 −0.713561 0.700593i \(-0.752919\pi\)
−0.713561 + 0.700593i \(0.752919\pi\)
\(632\) 0 0
\(633\) −7.29479e6 −0.723608
\(634\) 0 0
\(635\) −3.09503e6 −0.304600
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −3.39251e6 −0.328677
\(640\) 0 0
\(641\) −9.26960e6 −0.891079 −0.445539 0.895262i \(-0.646988\pi\)
−0.445539 + 0.895262i \(0.646988\pi\)
\(642\) 0 0
\(643\) 1.17375e7 1.11956 0.559780 0.828641i \(-0.310885\pi\)
0.559780 + 0.828641i \(0.310885\pi\)
\(644\) 0 0
\(645\) −4.24807e6 −0.402062
\(646\) 0 0
\(647\) 1.02545e7 0.963059 0.481529 0.876430i \(-0.340082\pi\)
0.481529 + 0.876430i \(0.340082\pi\)
\(648\) 0 0
\(649\) 1.26440e7 1.17835
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.28977e6 0.760781 0.380391 0.924826i \(-0.375790\pi\)
0.380391 + 0.924826i \(0.375790\pi\)
\(654\) 0 0
\(655\) 5.23344e6 0.476633
\(656\) 0 0
\(657\) 2.80400e6 0.253434
\(658\) 0 0
\(659\) −2.06731e7 −1.85435 −0.927174 0.374631i \(-0.877770\pi\)
−0.927174 + 0.374631i \(0.877770\pi\)
\(660\) 0 0
\(661\) 194342. 0.0173007 0.00865035 0.999963i \(-0.497246\pi\)
0.00865035 + 0.999963i \(0.497246\pi\)
\(662\) 0 0
\(663\) −4.31422e6 −0.381170
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.10186e7 −1.82932
\(668\) 0 0
\(669\) 1.98437e6 0.171418
\(670\) 0 0
\(671\) 3.26940e6 0.280325
\(672\) 0 0
\(673\) −1.14437e7 −0.973929 −0.486965 0.873422i \(-0.661896\pi\)
−0.486965 + 0.873422i \(0.661896\pi\)
\(674\) 0 0
\(675\) 856571. 0.0723609
\(676\) 0 0
\(677\) 9.03738e6 0.757828 0.378914 0.925432i \(-0.376298\pi\)
0.378914 + 0.925432i \(0.376298\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.20940e7 0.999316
\(682\) 0 0
\(683\) −1.11842e7 −0.917392 −0.458696 0.888593i \(-0.651683\pi\)
−0.458696 + 0.888593i \(0.651683\pi\)
\(684\) 0 0
\(685\) −5.64361e6 −0.459548
\(686\) 0 0
\(687\) −9.38325e6 −0.758510
\(688\) 0 0
\(689\) −1.31404e6 −0.105453
\(690\) 0 0
\(691\) 5.66930e6 0.451684 0.225842 0.974164i \(-0.427487\pi\)
0.225842 + 0.974164i \(0.427487\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.77435e7 1.39341
\(696\) 0 0
\(697\) 4.04384e6 0.315291
\(698\) 0 0
\(699\) 5.69260e6 0.440674
\(700\) 0 0
\(701\) −1.31822e6 −0.101320 −0.0506599 0.998716i \(-0.516132\pi\)
−0.0506599 + 0.998716i \(0.516132\pi\)
\(702\) 0 0
\(703\) 7.02077e6 0.535792
\(704\) 0 0
\(705\) 1.93181e6 0.146384
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 8.26035e6 0.617139 0.308570 0.951202i \(-0.400150\pi\)
0.308570 + 0.951202i \(0.400150\pi\)
\(710\) 0 0
\(711\) 6.28102e6 0.465968
\(712\) 0 0
\(713\) 3.71456e7 2.73643
\(714\) 0 0
\(715\) −7.00290e6 −0.512287
\(716\) 0 0
\(717\) −6.16427e6 −0.447800
\(718\) 0 0
\(719\) 2.26743e7 1.63573 0.817865 0.575410i \(-0.195157\pi\)
0.817865 + 0.575410i \(0.195157\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −69596.0 −0.00495152
\(724\) 0 0
\(725\) 5.83925e6 0.412584
\(726\) 0 0
\(727\) −1.93477e7 −1.35767 −0.678833 0.734293i \(-0.737514\pi\)
−0.678833 + 0.734293i \(0.737514\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 7.93440e6 0.549188
\(732\) 0 0
\(733\) 1.48584e7 1.02144 0.510720 0.859747i \(-0.329379\pi\)
0.510720 + 0.859747i \(0.329379\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.58720e6 −0.514533
\(738\) 0 0
\(739\) −1.76818e7 −1.19101 −0.595504 0.803352i \(-0.703048\pi\)
−0.595504 + 0.803352i \(0.703048\pi\)
\(740\) 0 0
\(741\) −1.12613e7 −0.753428
\(742\) 0 0
\(743\) −8.28756e6 −0.550750 −0.275375 0.961337i \(-0.588802\pi\)
−0.275375 + 0.961337i \(0.588802\pi\)
\(744\) 0 0
\(745\) −1.13147e7 −0.746883
\(746\) 0 0
\(747\) 8.17355e6 0.535932
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.31365e7 −1.49691 −0.748457 0.663183i \(-0.769205\pi\)
−0.748457 + 0.663183i \(0.769205\pi\)
\(752\) 0 0
\(753\) 9.86523e6 0.634044
\(754\) 0 0
\(755\) −1.17375e6 −0.0749389
\(756\) 0 0
\(757\) −1.95475e7 −1.23980 −0.619900 0.784681i \(-0.712827\pi\)
−0.619900 + 0.784681i \(0.712827\pi\)
\(758\) 0 0
\(759\) 9.34776e6 0.588984
\(760\) 0 0
\(761\) 7.82465e6 0.489783 0.244891 0.969551i \(-0.421248\pi\)
0.244891 + 0.969551i \(0.421248\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −5.85488e6 −0.361713
\(766\) 0 0
\(767\) −2.23905e7 −1.37428
\(768\) 0 0
\(769\) −8.27325e6 −0.504499 −0.252250 0.967662i \(-0.581170\pi\)
−0.252250 + 0.967662i \(0.581170\pi\)
\(770\) 0 0
\(771\) 6.43428e6 0.389820
\(772\) 0 0
\(773\) −1.88369e7 −1.13386 −0.566931 0.823765i \(-0.691869\pi\)
−0.566931 + 0.823765i \(0.691869\pi\)
\(774\) 0 0
\(775\) −1.03196e7 −0.617173
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.05555e7 0.623211
\(780\) 0 0
\(781\) 1.02853e7 0.603381
\(782\) 0 0
\(783\) 3.62284e6 0.211176
\(784\) 0 0
\(785\) −1.17390e7 −0.679920
\(786\) 0 0
\(787\) −1.83947e7 −1.05866 −0.529329 0.848417i \(-0.677556\pi\)
−0.529329 + 0.848417i \(0.677556\pi\)
\(788\) 0 0
\(789\) −5.36861e6 −0.307022
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −5.78957e6 −0.326937
\(794\) 0 0
\(795\) −1.78330e6 −0.100070
\(796\) 0 0
\(797\) 3.70208e6 0.206443 0.103222 0.994658i \(-0.467085\pi\)
0.103222 + 0.994658i \(0.467085\pi\)
\(798\) 0 0
\(799\) −3.60818e6 −0.199950
\(800\) 0 0
\(801\) 3.30348e6 0.181924
\(802\) 0 0
\(803\) −8.50113e6 −0.465251
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.82977e7 −0.989037
\(808\) 0 0
\(809\) 1.21913e7 0.654903 0.327451 0.944868i \(-0.393810\pi\)
0.327451 + 0.944868i \(0.393810\pi\)
\(810\) 0 0
\(811\) −2.52433e6 −0.134770 −0.0673851 0.997727i \(-0.521466\pi\)
−0.0673851 + 0.997727i \(0.521466\pi\)
\(812\) 0 0
\(813\) 1.61510e7 0.856984
\(814\) 0 0
\(815\) −1.55601e7 −0.820574
\(816\) 0 0
\(817\) 2.07109e7 1.08554
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9.50051e6 −0.491914 −0.245957 0.969281i \(-0.579102\pi\)
−0.245957 + 0.969281i \(0.579102\pi\)
\(822\) 0 0
\(823\) −2.26336e7 −1.16481 −0.582403 0.812900i \(-0.697887\pi\)
−0.582403 + 0.812900i \(0.697887\pi\)
\(824\) 0 0
\(825\) −2.59694e6 −0.132839
\(826\) 0 0
\(827\) 1.09007e7 0.554230 0.277115 0.960837i \(-0.410622\pi\)
0.277115 + 0.960837i \(0.410622\pi\)
\(828\) 0 0
\(829\) −2.36120e7 −1.19329 −0.596647 0.802504i \(-0.703501\pi\)
−0.596647 + 0.802504i \(0.703501\pi\)
\(830\) 0 0
\(831\) 3.81222e6 0.191503
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −6.16661e6 −0.306077
\(836\) 0 0
\(837\) −6.40255e6 −0.315893
\(838\) 0 0
\(839\) 2.67438e7 1.31165 0.655826 0.754912i \(-0.272321\pi\)
0.655826 + 0.754912i \(0.272321\pi\)
\(840\) 0 0
\(841\) 4.18580e6 0.204075
\(842\) 0 0
\(843\) −1.47419e7 −0.714469
\(844\) 0 0
\(845\) −1.19463e7 −0.575562
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −2.64632e6 −0.126001
\(850\) 0 0
\(851\) 1.03201e7 0.488494
\(852\) 0 0
\(853\) 5.00667e6 0.235600 0.117800 0.993037i \(-0.462416\pi\)
0.117800 + 0.993037i \(0.462416\pi\)
\(854\) 0 0
\(855\) −1.52828e7 −0.714969
\(856\) 0 0
\(857\) 2.43624e7 1.13310 0.566549 0.824028i \(-0.308278\pi\)
0.566549 + 0.824028i \(0.308278\pi\)
\(858\) 0 0
\(859\) −2.99153e7 −1.38328 −0.691641 0.722241i \(-0.743112\pi\)
−0.691641 + 0.722241i \(0.743112\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.60103e7 −1.18883 −0.594414 0.804160i \(-0.702616\pi\)
−0.594414 + 0.804160i \(0.702616\pi\)
\(864\) 0 0
\(865\) 3.20471e7 1.45629
\(866\) 0 0
\(867\) −1.84318e6 −0.0832759
\(868\) 0 0
\(869\) −1.90427e7 −0.855419
\(870\) 0 0
\(871\) 1.34357e7 0.600087
\(872\) 0 0
\(873\) 1.13519e7 0.504119
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.01375e7 −0.884109 −0.442055 0.896988i \(-0.645750\pi\)
−0.442055 + 0.896988i \(0.645750\pi\)
\(878\) 0 0
\(879\) −3.21265e6 −0.140246
\(880\) 0 0
\(881\) −3.69393e7 −1.60343 −0.801713 0.597710i \(-0.796078\pi\)
−0.801713 + 0.597710i \(0.796078\pi\)
\(882\) 0 0
\(883\) 2.27031e7 0.979904 0.489952 0.871749i \(-0.337014\pi\)
0.489952 + 0.871749i \(0.337014\pi\)
\(884\) 0 0
\(885\) −3.03863e7 −1.30413
\(886\) 0 0
\(887\) −1.55979e7 −0.665666 −0.332833 0.942986i \(-0.608005\pi\)
−0.332833 + 0.942986i \(0.608005\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.61121e6 −0.0679921
\(892\) 0 0
\(893\) −9.41831e6 −0.395225
\(894\) 0 0
\(895\) 5.33117e7 2.22467
\(896\) 0 0
\(897\) −1.65533e7 −0.686918
\(898\) 0 0
\(899\) −4.36463e7 −1.80114
\(900\) 0 0
\(901\) 3.33078e6 0.136689
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.18337e7 −0.886146
\(906\) 0 0
\(907\) −1.93485e7 −0.780961 −0.390480 0.920611i \(-0.627691\pi\)
−0.390480 + 0.920611i \(0.627691\pi\)
\(908\) 0 0
\(909\) 694693. 0.0278858
\(910\) 0 0
\(911\) −3.84661e7 −1.53561 −0.767807 0.640682i \(-0.778652\pi\)
−0.767807 + 0.640682i \(0.778652\pi\)
\(912\) 0 0
\(913\) −2.47804e7 −0.983857
\(914\) 0 0
\(915\) −7.85709e6 −0.310248
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.95838e7 0.764905 0.382453 0.923975i \(-0.375080\pi\)
0.382453 + 0.923975i \(0.375080\pi\)
\(920\) 0 0
\(921\) −1.83687e7 −0.713558
\(922\) 0 0
\(923\) −1.82137e7 −0.703709
\(924\) 0 0
\(925\) −2.86706e6 −0.110175
\(926\) 0 0
\(927\) −2.85607e6 −0.109162
\(928\) 0 0
\(929\) −1.28256e7 −0.487572 −0.243786 0.969829i \(-0.578390\pi\)
−0.243786 + 0.969829i \(0.578390\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.84206e7 0.692789
\(934\) 0 0
\(935\) 1.77507e7 0.664028
\(936\) 0 0
\(937\) 5.60430e6 0.208532 0.104266 0.994549i \(-0.466751\pi\)
0.104266 + 0.994549i \(0.466751\pi\)
\(938\) 0 0
\(939\) 5.74690e6 0.212701
\(940\) 0 0
\(941\) 3.44348e7 1.26772 0.633861 0.773447i \(-0.281469\pi\)
0.633861 + 0.773447i \(0.281469\pi\)
\(942\) 0 0
\(943\) 1.55159e7 0.568196
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7.10626e6 −0.257493 −0.128747 0.991678i \(-0.541095\pi\)
−0.128747 + 0.991678i \(0.541095\pi\)
\(948\) 0 0
\(949\) 1.50541e7 0.542612
\(950\) 0 0
\(951\) 3.14918e7 1.12914
\(952\) 0 0
\(953\) 3.78058e7 1.34842 0.674212 0.738538i \(-0.264483\pi\)
0.674212 + 0.738538i \(0.264483\pi\)
\(954\) 0 0
\(955\) −9.46158e6 −0.335703
\(956\) 0 0
\(957\) −1.09837e7 −0.387675
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 4.85058e7 1.69428
\(962\) 0 0
\(963\) −1.56029e7 −0.542176
\(964\) 0 0
\(965\) −5.86641e7 −2.02793
\(966\) 0 0
\(967\) 1.33643e7 0.459601 0.229800 0.973238i \(-0.426193\pi\)
0.229800 + 0.973238i \(0.426193\pi\)
\(968\) 0 0
\(969\) 2.85447e7 0.976598
\(970\) 0 0
\(971\) 4.68668e7 1.59521 0.797604 0.603181i \(-0.206101\pi\)
0.797604 + 0.603181i \(0.206101\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 4.59874e6 0.154927
\(976\) 0 0
\(977\) 4.25939e7 1.42761 0.713807 0.700343i \(-0.246969\pi\)
0.713807 + 0.700343i \(0.246969\pi\)
\(978\) 0 0
\(979\) −1.00154e7 −0.333974
\(980\) 0 0
\(981\) 9.98667e6 0.331320
\(982\) 0 0
\(983\) 5.20577e7 1.71831 0.859154 0.511718i \(-0.170991\pi\)
0.859154 + 0.511718i \(0.170991\pi\)
\(984\) 0 0
\(985\) −3.93093e7 −1.29094
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.04437e7 0.989708
\(990\) 0 0
\(991\) 2.91535e7 0.942989 0.471495 0.881869i \(-0.343715\pi\)
0.471495 + 0.881869i \(0.343715\pi\)
\(992\) 0 0
\(993\) −2.64761e7 −0.852080
\(994\) 0 0
\(995\) −5.10338e7 −1.63418
\(996\) 0 0
\(997\) 8.99304e6 0.286529 0.143264 0.989684i \(-0.454240\pi\)
0.143264 + 0.989684i \(0.454240\pi\)
\(998\) 0 0
\(999\) −1.77880e6 −0.0563916
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 588.6.a.l.1.2 2
7.2 even 3 84.6.i.b.25.1 4
7.3 odd 6 588.6.i.m.373.2 4
7.4 even 3 84.6.i.b.37.1 yes 4
7.5 odd 6 588.6.i.m.361.2 4
7.6 odd 2 588.6.a.h.1.1 2
21.2 odd 6 252.6.k.e.109.2 4
21.11 odd 6 252.6.k.e.37.2 4
28.11 odd 6 336.6.q.g.289.1 4
28.23 odd 6 336.6.q.g.193.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.i.b.25.1 4 7.2 even 3
84.6.i.b.37.1 yes 4 7.4 even 3
252.6.k.e.37.2 4 21.11 odd 6
252.6.k.e.109.2 4 21.2 odd 6
336.6.q.g.193.1 4 28.23 odd 6
336.6.q.g.289.1 4 28.11 odd 6
588.6.a.h.1.1 2 7.6 odd 2
588.6.a.l.1.2 2 1.1 even 1 trivial
588.6.i.m.361.2 4 7.5 odd 6
588.6.i.m.373.2 4 7.3 odd 6