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Properties

Label 252.6.a.b.1.1
Level $252$
Weight $6$
Character 252.1
Self dual yes
Analytic conductor $40.417$
Analytic rank $0$
Dimension $1$
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] = [252,6,Mod(1,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, 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("252.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 252.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: \(40.4167225929\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
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 1.1
Character \(\chi\) \(=\) 252.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.00000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-6.00000 q^{5} +49.0000 q^{7} +108.000 q^{11} -346.000 q^{13} +1398.00 q^{17} -1012.00 q^{19} +1536.00 q^{23} -3089.00 q^{25} +3762.00 q^{29} -736.000 q^{31} -294.000 q^{35} +2054.00 q^{37} +15534.0 q^{41} +11036.0 q^{43} -4560.00 q^{47} +2401.00 q^{49} +7962.00 q^{53} -648.000 q^{55} +7020.00 q^{59} +26870.0 q^{61} +2076.00 q^{65} +52148.0 q^{67} +2544.00 q^{71} -9766.00 q^{73} +5292.00 q^{77} +68672.0 q^{79} +61668.0 q^{83} -8388.00 q^{85} +41454.0 q^{89} -16954.0 q^{91} +6072.00 q^{95} -111262. q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −6.00000 −0.107331 −0.0536656 − 0.998559i \(-0.517091\pi\)
−0.0536656 + 0.998559i \(0.517091\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 108.000 0.269118 0.134559 − 0.990906i \(-0.457038\pi\)
0.134559 + 0.990906i \(0.457038\pi\)
\(12\) 0 0
\(13\) −346.000 −0.567829 −0.283915 − 0.958850i \(-0.591633\pi\)
−0.283915 + 0.958850i \(0.591633\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1398.00 1.17323 0.586617 − 0.809864i \(-0.300459\pi\)
0.586617 + 0.809864i \(0.300459\pi\)
\(18\) 0 0
\(19\) −1012.00 −0.643127 −0.321563 − 0.946888i \(-0.604208\pi\)
−0.321563 + 0.946888i \(0.604208\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1536.00 0.605441 0.302720 − 0.953079i \(-0.402105\pi\)
0.302720 + 0.953079i \(0.402105\pi\)
\(24\) 0 0
\(25\) −3089.00 −0.988480
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3762.00 0.830661 0.415330 − 0.909671i \(-0.363666\pi\)
0.415330 + 0.909671i \(0.363666\pi\)
\(30\) 0 0
\(31\) −736.000 −0.137554 −0.0687771 − 0.997632i \(-0.521910\pi\)
−0.0687771 + 0.997632i \(0.521910\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −294.000 −0.0405674
\(36\) 0 0
\(37\) 2054.00 0.246659 0.123329 − 0.992366i \(-0.460643\pi\)
0.123329 + 0.992366i \(0.460643\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 15534.0 1.44319 0.721595 − 0.692315i \(-0.243409\pi\)
0.721595 + 0.692315i \(0.243409\pi\)
\(42\) 0 0
\(43\) 11036.0 0.910208 0.455104 − 0.890438i \(-0.349602\pi\)
0.455104 + 0.890438i \(0.349602\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4560.00 −0.301107 −0.150553 − 0.988602i \(-0.548106\pi\)
−0.150553 + 0.988602i \(0.548106\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7962.00 0.389343 0.194672 − 0.980868i \(-0.437636\pi\)
0.194672 + 0.980868i \(0.437636\pi\)
\(54\) 0 0
\(55\) −648.000 −0.0288847
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7020.00 0.262547 0.131274 − 0.991346i \(-0.458093\pi\)
0.131274 + 0.991346i \(0.458093\pi\)
\(60\) 0 0
\(61\) 26870.0 0.924577 0.462288 − 0.886730i \(-0.347028\pi\)
0.462288 + 0.886730i \(0.347028\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2076.00 0.0609458
\(66\) 0 0
\(67\) 52148.0 1.41922 0.709612 − 0.704593i \(-0.248870\pi\)
0.709612 + 0.704593i \(0.248870\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2544.00 0.0598923 0.0299462 − 0.999552i \(-0.490466\pi\)
0.0299462 + 0.999552i \(0.490466\pi\)
\(72\) 0 0
\(73\) −9766.00 −0.214491 −0.107246 − 0.994233i \(-0.534203\pi\)
−0.107246 + 0.994233i \(0.534203\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5292.00 0.101717
\(78\) 0 0
\(79\) 68672.0 1.23798 0.618988 − 0.785401i \(-0.287543\pi\)
0.618988 + 0.785401i \(0.287543\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 61668.0 0.982573 0.491286 − 0.870998i \(-0.336527\pi\)
0.491286 + 0.870998i \(0.336527\pi\)
\(84\) 0 0
\(85\) −8388.00 −0.125925
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 41454.0 0.554742 0.277371 − 0.960763i \(-0.410537\pi\)
0.277371 + 0.960763i \(0.410537\pi\)
\(90\) 0 0
\(91\) −16954.0 −0.214619
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6072.00 0.0690276
\(96\) 0 0
\(97\) −111262. −1.20065 −0.600327 − 0.799755i \(-0.704963\pi\)
−0.600327 + 0.799755i \(0.704963\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 180426. 1.75993 0.879966 − 0.475037i \(-0.157565\pi\)
0.879966 + 0.475037i \(0.157565\pi\)
\(102\) 0 0
\(103\) 35912.0 0.333539 0.166769 − 0.985996i \(-0.446666\pi\)
0.166769 + 0.985996i \(0.446666\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 30492.0 0.257470 0.128735 − 0.991679i \(-0.458908\pi\)
0.128735 + 0.991679i \(0.458908\pi\)
\(108\) 0 0
\(109\) 82382.0 0.664150 0.332075 − 0.943253i \(-0.392251\pi\)
0.332075 + 0.943253i \(0.392251\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 160398. 1.18169 0.590844 − 0.806786i \(-0.298795\pi\)
0.590844 + 0.806786i \(0.298795\pi\)
\(114\) 0 0
\(115\) −9216.00 −0.0649827
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 68502.0 0.443441
\(120\) 0 0
\(121\) −149387. −0.927576
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 37284.0 0.213426
\(126\) 0 0
\(127\) −80896.0 −0.445059 −0.222530 − 0.974926i \(-0.571431\pi\)
−0.222530 + 0.974926i \(0.571431\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −173676. −0.884223 −0.442111 − 0.896960i \(-0.645770\pi\)
−0.442111 + 0.896960i \(0.645770\pi\)
\(132\) 0 0
\(133\) −49588.0 −0.243079
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −390426. −1.77720 −0.888602 − 0.458679i \(-0.848323\pi\)
−0.888602 + 0.458679i \(0.848323\pi\)
\(138\) 0 0
\(139\) 83204.0 0.365264 0.182632 − 0.983181i \(-0.441538\pi\)
0.182632 + 0.983181i \(0.441538\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −37368.0 −0.152813
\(144\) 0 0
\(145\) −22572.0 −0.0891559
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −140358. −0.517931 −0.258965 − 0.965887i \(-0.583382\pi\)
−0.258965 + 0.965887i \(0.583382\pi\)
\(150\) 0 0
\(151\) 320360. 1.14339 0.571697 − 0.820465i \(-0.306285\pi\)
0.571697 + 0.820465i \(0.306285\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4416.00 0.0147639
\(156\) 0 0
\(157\) −158266. −0.512435 −0.256217 − 0.966619i \(-0.582476\pi\)
−0.256217 + 0.966619i \(0.582476\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 75264.0 0.228835
\(162\) 0 0
\(163\) 345476. 1.01847 0.509236 − 0.860627i \(-0.329928\pi\)
0.509236 + 0.860627i \(0.329928\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20568.0 0.0570691 0.0285345 − 0.999593i \(-0.490916\pi\)
0.0285345 + 0.999593i \(0.490916\pi\)
\(168\) 0 0
\(169\) −251577. −0.677570
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −732558. −1.86092 −0.930458 − 0.366399i \(-0.880591\pi\)
−0.930458 + 0.366399i \(0.880591\pi\)
\(174\) 0 0
\(175\) −151361. −0.373610
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −572220. −1.33484 −0.667422 − 0.744680i \(-0.732602\pi\)
−0.667422 + 0.744680i \(0.732602\pi\)
\(180\) 0 0
\(181\) −352402. −0.799543 −0.399772 − 0.916615i \(-0.630911\pi\)
−0.399772 + 0.916615i \(0.630911\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12324.0 −0.0264742
\(186\) 0 0
\(187\) 150984. 0.315738
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18456.0 0.0366062 0.0183031 − 0.999832i \(-0.494174\pi\)
0.0183031 + 0.999832i \(0.494174\pi\)
\(192\) 0 0
\(193\) 832322. 1.60841 0.804207 − 0.594349i \(-0.202590\pi\)
0.804207 + 0.594349i \(0.202590\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −612438. −1.12434 −0.562169 − 0.827023i \(-0.690033\pi\)
−0.562169 + 0.827023i \(0.690033\pi\)
\(198\) 0 0
\(199\) −501352. −0.897450 −0.448725 − 0.893670i \(-0.648122\pi\)
−0.448725 + 0.893670i \(0.648122\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 184338. 0.313960
\(204\) 0 0
\(205\) −93204.0 −0.154899
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −109296. −0.173077
\(210\) 0 0
\(211\) −556588. −0.860652 −0.430326 − 0.902673i \(-0.641601\pi\)
−0.430326 + 0.902673i \(0.641601\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −66216.0 −0.0976938
\(216\) 0 0
\(217\) −36064.0 −0.0519906
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −483708. −0.666197
\(222\) 0 0
\(223\) −1.25680e6 −1.69240 −0.846202 − 0.532862i \(-0.821116\pi\)
−0.846202 + 0.532862i \(0.821116\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 700932. 0.902841 0.451420 − 0.892311i \(-0.350917\pi\)
0.451420 + 0.892311i \(0.350917\pi\)
\(228\) 0 0
\(229\) 153374. 0.193269 0.0966347 − 0.995320i \(-0.469192\pi\)
0.0966347 + 0.995320i \(0.469192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −154266. −0.186157 −0.0930787 − 0.995659i \(-0.529671\pi\)
−0.0930787 + 0.995659i \(0.529671\pi\)
\(234\) 0 0
\(235\) 27360.0 0.0323181
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 926376. 1.04904 0.524521 − 0.851398i \(-0.324245\pi\)
0.524521 + 0.851398i \(0.324245\pi\)
\(240\) 0 0
\(241\) −1.05662e6 −1.17186 −0.585932 − 0.810360i \(-0.699271\pi\)
−0.585932 + 0.810360i \(0.699271\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −14406.0 −0.0153330
\(246\) 0 0
\(247\) 350152. 0.365186
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.45984e6 1.46258 0.731290 − 0.682066i \(-0.238919\pi\)
0.731290 + 0.682066i \(0.238919\pi\)
\(252\) 0 0
\(253\) 165888. 0.162935
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.57142e6 −1.48409 −0.742043 − 0.670353i \(-0.766143\pi\)
−0.742043 + 0.670353i \(0.766143\pi\)
\(258\) 0 0
\(259\) 100646. 0.0932282
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.46275e6 1.30401 0.652006 − 0.758214i \(-0.273928\pi\)
0.652006 + 0.758214i \(0.273928\pi\)
\(264\) 0 0
\(265\) −47772.0 −0.0417887
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 230850. 0.194513 0.0972566 − 0.995259i \(-0.468993\pi\)
0.0972566 + 0.995259i \(0.468993\pi\)
\(270\) 0 0
\(271\) −574432. −0.475133 −0.237567 − 0.971371i \(-0.576350\pi\)
−0.237567 + 0.971371i \(0.576350\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −333612. −0.266017
\(276\) 0 0
\(277\) 510950. 0.400110 0.200055 − 0.979785i \(-0.435888\pi\)
0.200055 + 0.979785i \(0.435888\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −931146. −0.703480 −0.351740 − 0.936098i \(-0.614410\pi\)
−0.351740 + 0.936098i \(0.614410\pi\)
\(282\) 0 0
\(283\) 2.15560e6 1.59994 0.799969 − 0.600042i \(-0.204849\pi\)
0.799969 + 0.600042i \(0.204849\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 761166. 0.545475
\(288\) 0 0
\(289\) 534547. 0.376479
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −962070. −0.654693 −0.327346 − 0.944904i \(-0.606154\pi\)
−0.327346 + 0.944904i \(0.606154\pi\)
\(294\) 0 0
\(295\) −42120.0 −0.0281795
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −531456. −0.343787
\(300\) 0 0
\(301\) 540764. 0.344026
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −161220. −0.0992360
\(306\) 0 0
\(307\) 1.71988e6 1.04149 0.520743 − 0.853714i \(-0.325655\pi\)
0.520743 + 0.853714i \(0.325655\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.38121e6 1.39604 0.698018 − 0.716081i \(-0.254066\pi\)
0.698018 + 0.716081i \(0.254066\pi\)
\(312\) 0 0
\(313\) −293494. −0.169332 −0.0846659 − 0.996409i \(-0.526982\pi\)
−0.0846659 + 0.996409i \(0.526982\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.94642e6 1.08790 0.543949 − 0.839118i \(-0.316929\pi\)
0.543949 + 0.839118i \(0.316929\pi\)
\(318\) 0 0
\(319\) 406296. 0.223545
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.41478e6 −0.754538
\(324\) 0 0
\(325\) 1.06879e6 0.561288
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −223440. −0.113808
\(330\) 0 0
\(331\) 1.25184e6 0.628026 0.314013 − 0.949419i \(-0.398326\pi\)
0.314013 + 0.949419i \(0.398326\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −312888. −0.152327
\(336\) 0 0
\(337\) 297458. 0.142676 0.0713380 − 0.997452i \(-0.477273\pi\)
0.0713380 + 0.997452i \(0.477273\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −79488.0 −0.0370182
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.40657e6 1.51878 0.759388 − 0.650638i \(-0.225498\pi\)
0.759388 + 0.650638i \(0.225498\pi\)
\(348\) 0 0
\(349\) −420826. −0.184943 −0.0924717 − 0.995715i \(-0.529477\pi\)
−0.0924717 + 0.995715i \(0.529477\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.39435e6 −0.595571 −0.297786 − 0.954633i \(-0.596248\pi\)
−0.297786 + 0.954633i \(0.596248\pi\)
\(354\) 0 0
\(355\) −15264.0 −0.00642832
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.55037e6 1.45391 0.726955 − 0.686686i \(-0.240935\pi\)
0.726955 + 0.686686i \(0.240935\pi\)
\(360\) 0 0
\(361\) −1.45196e6 −0.586388
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 58596.0 0.0230216
\(366\) 0 0
\(367\) −391696. −0.151804 −0.0759021 − 0.997115i \(-0.524184\pi\)
−0.0759021 + 0.997115i \(0.524184\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 390138. 0.147158
\(372\) 0 0
\(373\) −163834. −0.0609722 −0.0304861 − 0.999535i \(-0.509706\pi\)
−0.0304861 + 0.999535i \(0.509706\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.30165e6 −0.471674
\(378\) 0 0
\(379\) 206156. 0.0737221 0.0368611 − 0.999320i \(-0.488264\pi\)
0.0368611 + 0.999320i \(0.488264\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −484176. −0.168658 −0.0843289 − 0.996438i \(-0.526875\pi\)
−0.0843289 + 0.996438i \(0.526875\pi\)
\(384\) 0 0
\(385\) −31752.0 −0.0109174
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.17479e6 1.39882 0.699409 − 0.714722i \(-0.253447\pi\)
0.699409 + 0.714722i \(0.253447\pi\)
\(390\) 0 0
\(391\) 2.14733e6 0.710324
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −412032. −0.132873
\(396\) 0 0
\(397\) −4.39998e6 −1.40112 −0.700558 − 0.713595i \(-0.747066\pi\)
−0.700558 + 0.713595i \(0.747066\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.45917e6 1.69537 0.847687 − 0.530497i \(-0.177995\pi\)
0.847687 + 0.530497i \(0.177995\pi\)
\(402\) 0 0
\(403\) 254656. 0.0781072
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 221832. 0.0663801
\(408\) 0 0
\(409\) 2.18307e6 0.645295 0.322648 − 0.946519i \(-0.395427\pi\)
0.322648 + 0.946519i \(0.395427\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 343980. 0.0992334
\(414\) 0 0
\(415\) −370008. −0.105461
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.44561e6 −1.51535 −0.757673 − 0.652635i \(-0.773664\pi\)
−0.757673 + 0.652635i \(0.773664\pi\)
\(420\) 0 0
\(421\) −4.83054e6 −1.32828 −0.664141 − 0.747607i \(-0.731203\pi\)
−0.664141 + 0.747607i \(0.731203\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.31842e6 −1.15972
\(426\) 0 0
\(427\) 1.31663e6 0.349457
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.58182e6 1.96598 0.982992 − 0.183647i \(-0.0587904\pi\)
0.982992 + 0.183647i \(0.0587904\pi\)
\(432\) 0 0
\(433\) −99838.0 −0.0255903 −0.0127952 − 0.999918i \(-0.504073\pi\)
−0.0127952 + 0.999918i \(0.504073\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.55443e6 −0.389375
\(438\) 0 0
\(439\) −7.77690e6 −1.92595 −0.962976 − 0.269587i \(-0.913113\pi\)
−0.962976 + 0.269587i \(0.913113\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.15488e6 −0.763790 −0.381895 − 0.924206i \(-0.624728\pi\)
−0.381895 + 0.924206i \(0.624728\pi\)
\(444\) 0 0
\(445\) −248724. −0.0595412
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.91450e6 −1.15044 −0.575219 − 0.817999i \(-0.695083\pi\)
−0.575219 + 0.817999i \(0.695083\pi\)
\(450\) 0 0
\(451\) 1.67767e6 0.388388
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 101724. 0.0230354
\(456\) 0 0
\(457\) −5.77001e6 −1.29237 −0.646183 − 0.763182i \(-0.723636\pi\)
−0.646183 + 0.763182i \(0.723636\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.65272e6 −0.362198 −0.181099 − 0.983465i \(-0.557965\pi\)
−0.181099 + 0.983465i \(0.557965\pi\)
\(462\) 0 0
\(463\) 7.69146e6 1.66746 0.833731 − 0.552170i \(-0.186200\pi\)
0.833731 + 0.552170i \(0.186200\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.95880e6 −1.05217 −0.526083 − 0.850433i \(-0.676340\pi\)
−0.526083 + 0.850433i \(0.676340\pi\)
\(468\) 0 0
\(469\) 2.55525e6 0.536416
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.19189e6 0.244953
\(474\) 0 0
\(475\) 3.12607e6 0.635718
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.46899e6 0.292537 0.146268 − 0.989245i \(-0.453274\pi\)
0.146268 + 0.989245i \(0.453274\pi\)
\(480\) 0 0
\(481\) −710684. −0.140060
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 667572. 0.128868
\(486\) 0 0
\(487\) −6.46679e6 −1.23557 −0.617784 − 0.786348i \(-0.711969\pi\)
−0.617784 + 0.786348i \(0.711969\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.94479e6 −1.67443 −0.837214 − 0.546876i \(-0.815817\pi\)
−0.837214 + 0.546876i \(0.815817\pi\)
\(492\) 0 0
\(493\) 5.25928e6 0.974560
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 124656. 0.0226372
\(498\) 0 0
\(499\) 1.05052e7 1.88866 0.944329 − 0.329004i \(-0.106713\pi\)
0.944329 + 0.329004i \(0.106713\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.97993e6 −1.40630 −0.703152 − 0.711040i \(-0.748225\pi\)
−0.703152 + 0.711040i \(0.748225\pi\)
\(504\) 0 0
\(505\) −1.08256e6 −0.188896
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.13425e6 −1.39163 −0.695814 − 0.718222i \(-0.744956\pi\)
−0.695814 + 0.718222i \(0.744956\pi\)
\(510\) 0 0
\(511\) −478534. −0.0810701
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −215472. −0.0357992
\(516\) 0 0
\(517\) −492480. −0.0810331
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.76800e6 −0.285357 −0.142678 − 0.989769i \(-0.545571\pi\)
−0.142678 + 0.989769i \(0.545571\pi\)
\(522\) 0 0
\(523\) −4.07211e6 −0.650976 −0.325488 − 0.945546i \(-0.605529\pi\)
−0.325488 + 0.945546i \(0.605529\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.02893e6 −0.161383
\(528\) 0 0
\(529\) −4.07705e6 −0.633442
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.37476e6 −0.819486
\(534\) 0 0
\(535\) −182952. −0.0276346
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 259308. 0.0384454
\(540\) 0 0
\(541\) −4.60904e6 −0.677045 −0.338522 − 0.940958i \(-0.609927\pi\)
−0.338522 + 0.940958i \(0.609927\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −494292. −0.0712840
\(546\) 0 0
\(547\) −5.81091e6 −0.830378 −0.415189 − 0.909735i \(-0.636285\pi\)
−0.415189 + 0.909735i \(0.636285\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.80714e6 −0.534220
\(552\) 0 0
\(553\) 3.36493e6 0.467911
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.59949e6 1.31102 0.655511 − 0.755185i \(-0.272453\pi\)
0.655511 + 0.755185i \(0.272453\pi\)
\(558\) 0 0
\(559\) −3.81846e6 −0.516843
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.21152e6 0.427012 0.213506 − 0.976942i \(-0.431512\pi\)
0.213506 + 0.976942i \(0.431512\pi\)
\(564\) 0 0
\(565\) −962388. −0.126832
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.23573e6 1.19589 0.597944 − 0.801538i \(-0.295984\pi\)
0.597944 + 0.801538i \(0.295984\pi\)
\(570\) 0 0
\(571\) 2.81683e6 0.361551 0.180776 − 0.983524i \(-0.442139\pi\)
0.180776 + 0.983524i \(0.442139\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.74470e6 −0.598466
\(576\) 0 0
\(577\) 4.13415e6 0.516947 0.258474 − 0.966018i \(-0.416780\pi\)
0.258474 + 0.966018i \(0.416780\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.02173e6 0.371378
\(582\) 0 0
\(583\) 859896. 0.104779
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.38155e6 0.524847 0.262423 − 0.964953i \(-0.415478\pi\)
0.262423 + 0.964953i \(0.415478\pi\)
\(588\) 0 0
\(589\) 744832. 0.0884647
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.22971e7 −1.43604 −0.718020 − 0.696023i \(-0.754951\pi\)
−0.718020 + 0.696023i \(0.754951\pi\)
\(594\) 0 0
\(595\) −411012. −0.0475951
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.20928e6 1.04872 0.524359 − 0.851497i \(-0.324305\pi\)
0.524359 + 0.851497i \(0.324305\pi\)
\(600\) 0 0
\(601\) −1.63394e7 −1.84522 −0.922612 − 0.385730i \(-0.873950\pi\)
−0.922612 + 0.385730i \(0.873950\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 896322. 0.0995579
\(606\) 0 0
\(607\) −3.73082e6 −0.410991 −0.205495 − 0.978658i \(-0.565881\pi\)
−0.205495 + 0.978658i \(0.565881\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.57776e6 0.170977
\(612\) 0 0
\(613\) 1.46503e7 1.57469 0.787346 − 0.616511i \(-0.211455\pi\)
0.787346 + 0.616511i \(0.211455\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.33527e6 0.458462 0.229231 − 0.973372i \(-0.426379\pi\)
0.229231 + 0.973372i \(0.426379\pi\)
\(618\) 0 0
\(619\) −1.79095e7 −1.87869 −0.939346 − 0.342970i \(-0.888567\pi\)
−0.939346 + 0.342970i \(0.888567\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.03125e6 0.209673
\(624\) 0 0
\(625\) 9.42942e6 0.965573
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.87149e6 0.289388
\(630\) 0 0
\(631\) −7.13615e6 −0.713495 −0.356747 − 0.934201i \(-0.616114\pi\)
−0.356747 + 0.934201i \(0.616114\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 485376. 0.0477688
\(636\) 0 0
\(637\) −830746. −0.0811185
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.47025e6 0.237463 0.118732 − 0.992926i \(-0.462117\pi\)
0.118732 + 0.992926i \(0.462117\pi\)
\(642\) 0 0
\(643\) 1.13717e7 1.08467 0.542337 − 0.840161i \(-0.317540\pi\)
0.542337 + 0.840161i \(0.317540\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.69812e7 1.59480 0.797402 − 0.603449i \(-0.206207\pi\)
0.797402 + 0.603449i \(0.206207\pi\)
\(648\) 0 0
\(649\) 758160. 0.0706560
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.56724e7 1.43831 0.719157 − 0.694847i \(-0.244528\pi\)
0.719157 + 0.694847i \(0.244528\pi\)
\(654\) 0 0
\(655\) 1.04206e6 0.0949047
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.85424e6 −0.256021 −0.128011 − 0.991773i \(-0.540859\pi\)
−0.128011 + 0.991773i \(0.540859\pi\)
\(660\) 0 0
\(661\) 1.56396e7 1.39226 0.696131 − 0.717915i \(-0.254903\pi\)
0.696131 + 0.717915i \(0.254903\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 297528. 0.0260900
\(666\) 0 0
\(667\) 5.77843e6 0.502916
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.90196e6 0.248820
\(672\) 0 0
\(673\) −3.01209e6 −0.256349 −0.128174 − 0.991752i \(-0.540912\pi\)
−0.128174 + 0.991752i \(0.540912\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.98733e6 −0.753632 −0.376816 − 0.926288i \(-0.622981\pi\)
−0.376816 + 0.926288i \(0.622981\pi\)
\(678\) 0 0
\(679\) −5.45184e6 −0.453804
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.13932e6 −0.585605 −0.292803 − 0.956173i \(-0.594588\pi\)
−0.292803 + 0.956173i \(0.594588\pi\)
\(684\) 0 0
\(685\) 2.34256e6 0.190750
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.75485e6 −0.221080
\(690\) 0 0
\(691\) −1.55104e7 −1.23575 −0.617873 − 0.786278i \(-0.712005\pi\)
−0.617873 + 0.786278i \(0.712005\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −499224. −0.0392043
\(696\) 0 0
\(697\) 2.17165e7 1.69320
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.22948e7 1.71359 0.856797 − 0.515654i \(-0.172451\pi\)
0.856797 + 0.515654i \(0.172451\pi\)
\(702\) 0 0
\(703\) −2.07865e6 −0.158633
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.84087e6 0.665191
\(708\) 0 0
\(709\) 2534.00 0.000189318 0 9.46588e−5 − 1.00000i \(-0.499970\pi\)
9.46588e−5 1.00000i \(0.499970\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.13050e6 −0.0832809
\(714\) 0 0
\(715\) 224208. 0.0164016
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.66728e7 −1.20278 −0.601390 − 0.798955i \(-0.705386\pi\)
−0.601390 + 0.798955i \(0.705386\pi\)
\(720\) 0 0
\(721\) 1.75969e6 0.126066
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.16208e7 −0.821092
\(726\) 0 0
\(727\) −940648. −0.0660072 −0.0330036 − 0.999455i \(-0.510507\pi\)
−0.0330036 + 0.999455i \(0.510507\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.54283e7 1.06789
\(732\) 0 0
\(733\) 2.76783e7 1.90274 0.951369 − 0.308053i \(-0.0996773\pi\)
0.951369 + 0.308053i \(0.0996773\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.63198e6 0.381938
\(738\) 0 0
\(739\) 1.00351e7 0.675947 0.337973 − 0.941156i \(-0.390259\pi\)
0.337973 + 0.941156i \(0.390259\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.67202e7 −1.11114 −0.555572 − 0.831469i \(-0.687501\pi\)
−0.555572 + 0.831469i \(0.687501\pi\)
\(744\) 0 0
\(745\) 842148. 0.0555901
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.49411e6 0.0973145
\(750\) 0 0
\(751\) 9.81728e6 0.635172 0.317586 − 0.948229i \(-0.397128\pi\)
0.317586 + 0.948229i \(0.397128\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.92216e6 −0.122722
\(756\) 0 0
\(757\) −2.72948e6 −0.173117 −0.0865587 − 0.996247i \(-0.527587\pi\)
−0.0865587 + 0.996247i \(0.527587\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.78176e6 −0.174124 −0.0870619 − 0.996203i \(-0.527748\pi\)
−0.0870619 + 0.996203i \(0.527748\pi\)
\(762\) 0 0
\(763\) 4.03672e6 0.251025
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.42892e6 −0.149082
\(768\) 0 0
\(769\) 5.04331e6 0.307539 0.153769 − 0.988107i \(-0.450859\pi\)
0.153769 + 0.988107i \(0.450859\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.49824e7 0.901845 0.450923 − 0.892563i \(-0.351095\pi\)
0.450923 + 0.892563i \(0.351095\pi\)
\(774\) 0 0
\(775\) 2.27350e6 0.135969
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.57204e7 −0.928154
\(780\) 0 0
\(781\) 274752. 0.0161181
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 949596. 0.0550003
\(786\) 0 0
\(787\) 4.82851e6 0.277892 0.138946 − 0.990300i \(-0.455629\pi\)
0.138946 + 0.990300i \(0.455629\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.85950e6 0.446636
\(792\) 0 0
\(793\) −9.29702e6 −0.525002
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.22125e7 1.23866 0.619331 − 0.785130i \(-0.287404\pi\)
0.619331 + 0.785130i \(0.287404\pi\)
\(798\) 0 0
\(799\) −6.37488e6 −0.353269
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.05473e6 −0.0577234
\(804\) 0 0
\(805\) −451584. −0.0245612
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.34312e7 −0.721512 −0.360756 − 0.932660i \(-0.617481\pi\)
−0.360756 + 0.932660i \(0.617481\pi\)
\(810\) 0 0
\(811\) −1.99673e7 −1.06602 −0.533012 − 0.846107i \(-0.678940\pi\)
−0.533012 + 0.846107i \(0.678940\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.07286e6 −0.109314
\(816\) 0 0
\(817\) −1.11684e7 −0.585379
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.90063e7 1.50188 0.750939 − 0.660372i \(-0.229601\pi\)
0.750939 + 0.660372i \(0.229601\pi\)
\(822\) 0 0
\(823\) 2.38801e7 1.22896 0.614478 − 0.788934i \(-0.289366\pi\)
0.614478 + 0.788934i \(0.289366\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.58724e6 0.487450 0.243725 − 0.969844i \(-0.421631\pi\)
0.243725 + 0.969844i \(0.421631\pi\)
\(828\) 0 0
\(829\) −2.66835e7 −1.34852 −0.674260 − 0.738494i \(-0.735537\pi\)
−0.674260 + 0.738494i \(0.735537\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.35660e6 0.167605
\(834\) 0 0
\(835\) −123408. −0.00612530
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −5.41870e6 −0.265760 −0.132880 − 0.991132i \(-0.542423\pi\)
−0.132880 + 0.991132i \(0.542423\pi\)
\(840\) 0 0
\(841\) −6.35850e6 −0.310002
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.50946e6 0.0727244
\(846\) 0 0
\(847\) −7.31996e6 −0.350591
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.15494e6 0.149337
\(852\) 0 0
\(853\) −2.02323e7 −0.952079 −0.476040 − 0.879424i \(-0.657928\pi\)
−0.476040 + 0.879424i \(0.657928\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −7.16071e6 −0.333046 −0.166523 − 0.986038i \(-0.553254\pi\)
−0.166523 + 0.986038i \(0.553254\pi\)
\(858\) 0 0
\(859\) −1.24840e7 −0.577258 −0.288629 − 0.957441i \(-0.593199\pi\)
−0.288629 + 0.957441i \(0.593199\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.32731e7 −1.52078 −0.760391 − 0.649466i \(-0.774993\pi\)
−0.760391 + 0.649466i \(0.774993\pi\)
\(864\) 0 0
\(865\) 4.39535e6 0.199734
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7.41658e6 0.333161
\(870\) 0 0
\(871\) −1.80432e7 −0.805876
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.82692e6 0.0806675
\(876\) 0 0
\(877\) 4.10248e6 0.180114 0.0900570 − 0.995937i \(-0.471295\pi\)
0.0900570 + 0.995937i \(0.471295\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.99636e6 0.130063 0.0650315 − 0.997883i \(-0.479285\pi\)
0.0650315 + 0.997883i \(0.479285\pi\)
\(882\) 0 0
\(883\) −1.07514e7 −0.464049 −0.232024 − 0.972710i \(-0.574535\pi\)
−0.232024 + 0.972710i \(0.574535\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.04970e7 −0.874744 −0.437372 − 0.899281i \(-0.644091\pi\)
−0.437372 + 0.899281i \(0.644091\pi\)
\(888\) 0 0
\(889\) −3.96390e6 −0.168217
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.61472e6 0.193650
\(894\) 0 0
\(895\) 3.43332e6 0.143270
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.76883e6 −0.114261
\(900\) 0 0
\(901\) 1.11309e7 0.456791
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.11441e6 0.0858160
\(906\) 0 0
\(907\) −1.97520e7 −0.797245 −0.398623 − 0.917115i \(-0.630512\pi\)
−0.398623 + 0.917115i \(0.630512\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.48511e7 −0.992087 −0.496044 − 0.868298i \(-0.665214\pi\)
−0.496044 + 0.868298i \(0.665214\pi\)
\(912\) 0 0
\(913\) 6.66014e6 0.264428
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.51012e6 −0.334205
\(918\) 0 0
\(919\) 1.54864e7 0.604869 0.302435 − 0.953170i \(-0.402201\pi\)
0.302435 + 0.953170i \(0.402201\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −880224. −0.0340086
\(924\) 0 0
\(925\) −6.34481e6 −0.243817
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.73849e7 −0.660895 −0.330447 − 0.943824i \(-0.607200\pi\)
−0.330447 + 0.943824i \(0.607200\pi\)
\(930\) 0 0
\(931\) −2.42981e6 −0.0918752
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −905904. −0.0338886
\(936\) 0 0
\(937\) −2.72897e7 −1.01543 −0.507714 − 0.861526i \(-0.669509\pi\)
−0.507714 + 0.861526i \(0.669509\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.20400e7 0.443256 0.221628 − 0.975131i \(-0.428863\pi\)
0.221628 + 0.975131i \(0.428863\pi\)
\(942\) 0 0
\(943\) 2.38602e7 0.873766
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.82808e7 −1.38710 −0.693548 − 0.720411i \(-0.743953\pi\)
−0.693548 + 0.720411i \(0.743953\pi\)
\(948\) 0 0
\(949\) 3.37904e6 0.121794
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.83655e7 −0.655043 −0.327521 − 0.944844i \(-0.606213\pi\)
−0.327521 + 0.944844i \(0.606213\pi\)
\(954\) 0 0
\(955\) −110736. −0.00392899
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.91309e7 −0.671720
\(960\) 0 0
\(961\) −2.80875e7 −0.981079
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4.99393e6 −0.172633
\(966\) 0 0
\(967\) 1.83781e7 0.632024 0.316012 − 0.948755i \(-0.397656\pi\)
0.316012 + 0.948755i \(0.397656\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.90795e7 0.649411 0.324706 − 0.945815i \(-0.394735\pi\)
0.324706 + 0.945815i \(0.394735\pi\)
\(972\) 0 0
\(973\) 4.07700e6 0.138057
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.37407e7 −1.13088 −0.565442 − 0.824788i \(-0.691294\pi\)
−0.565442 + 0.824788i \(0.691294\pi\)
\(978\) 0 0
\(979\) 4.47703e6 0.149291
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.56535e7 −0.516689 −0.258344 − 0.966053i \(-0.583177\pi\)
−0.258344 + 0.966053i \(0.583177\pi\)
\(984\) 0 0
\(985\) 3.67463e6 0.120677
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.69513e7 0.551077
\(990\) 0 0
\(991\) −1.10122e7 −0.356198 −0.178099 − 0.984013i \(-0.556995\pi\)
−0.178099 + 0.984013i \(0.556995\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.00811e6 0.0963244
\(996\) 0 0
\(997\) 2.38356e7 0.759431 0.379716 − 0.925103i \(-0.376022\pi\)
0.379716 + 0.925103i \(0.376022\pi\)
\(998\) 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 252.6.a.b.1.1 1
3.2 odd 2 84.6.a.a.1.1 ✓ 1
4.3 odd 2 1008.6.a.o.1.1 1
12.11 even 2 336.6.a.n.1.1 1
21.2 odd 6 588.6.i.f.361.1 2
21.5 even 6 588.6.i.b.361.1 2
21.11 odd 6 588.6.i.f.373.1 2
21.17 even 6 588.6.i.b.373.1 2
21.20 even 2 588.6.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.a.1.1 ✓ 1 3.2 odd 2
252.6.a.b.1.1 1 1.1 even 1 trivial
336.6.a.n.1.1 1 12.11 even 2
588.6.a.e.1.1 1 21.20 even 2
588.6.i.b.361.1 2 21.5 even 6
588.6.i.b.373.1 2 21.17 even 6
588.6.i.f.361.1 2 21.2 odd 6
588.6.i.f.373.1 2 21.11 odd 6
1008.6.a.o.1.1 1 4.3 odd 2