Properties

Label 1008.6.a.bo.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: \(\Q(\sqrt{5569}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1392 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-36.8129\) 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)
 
\(f(q)\) \(=\) \(q-71.6257 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-71.6257 q^{5} +49.0000 q^{7} -567.380 q^{11} +831.754 q^{13} -888.374 q^{17} -2915.02 q^{19} +3102.37 q^{23} +2005.25 q^{25} -8271.03 q^{29} +7029.05 q^{31} -3509.66 q^{35} -10141.9 q^{37} -3095.65 q^{41} -15026.2 q^{43} +19895.4 q^{47} +2401.00 q^{49} +9206.42 q^{53} +40639.0 q^{55} -10301.3 q^{59} -22599.2 q^{61} -59575.0 q^{65} -6419.09 q^{67} -61279.0 q^{71} -29707.1 q^{73} -27801.6 q^{77} +15630.8 q^{79} +1668.23 q^{83} +63630.5 q^{85} -75833.3 q^{89} +40756.0 q^{91} +208790. q^{95} -98013.9 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} + 98 q^{7} - 90 q^{11} + 768 q^{13} - 1926 q^{17} - 2248 q^{19} + 6354 q^{23} + 4906 q^{25} - 10572 q^{29} + 3312 q^{31} + 294 q^{35} + 2104 q^{37} - 1266 q^{41} + 5768 q^{43} + 15612 q^{47} + 4802 q^{49} - 16512 q^{53} + 77696 q^{55} - 13140 q^{59} - 5796 q^{61} - 64524 q^{65} + 56116 q^{67} + 11022 q^{71} - 85384 q^{73} - 4410 q^{77} + 19620 q^{79} - 44424 q^{83} - 16916 q^{85} - 211218 q^{89} + 37632 q^{91} + 260568 q^{95} + 44864 q^{97}+O(q^{100}) \) 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
\(5\) −71.6257 −1.28128 −0.640640 0.767841i \(-0.721331\pi\)
−0.640640 + 0.767841i \(0.721331\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −567.380 −1.41381 −0.706907 0.707306i \(-0.749910\pi\)
−0.706907 + 0.707306i \(0.749910\pi\)
\(12\) 0 0
\(13\) 831.754 1.36501 0.682506 0.730880i \(-0.260890\pi\)
0.682506 + 0.730880i \(0.260890\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −888.374 −0.745545 −0.372772 0.927923i \(-0.621593\pi\)
−0.372772 + 0.927923i \(0.621593\pi\)
\(18\) 0 0
\(19\) −2915.02 −1.85250 −0.926248 0.376915i \(-0.876985\pi\)
−0.926248 + 0.376915i \(0.876985\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3102.37 1.22285 0.611427 0.791301i \(-0.290596\pi\)
0.611427 + 0.791301i \(0.290596\pi\)
\(24\) 0 0
\(25\) 2005.25 0.641679
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −8271.03 −1.82627 −0.913134 0.407659i \(-0.866345\pi\)
−0.913134 + 0.407659i \(0.866345\pi\)
\(30\) 0 0
\(31\) 7029.05 1.31369 0.656845 0.754026i \(-0.271891\pi\)
0.656845 + 0.754026i \(0.271891\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3509.66 −0.484278
\(36\) 0 0
\(37\) −10141.9 −1.21790 −0.608952 0.793207i \(-0.708410\pi\)
−0.608952 + 0.793207i \(0.708410\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3095.65 −0.287602 −0.143801 0.989607i \(-0.545933\pi\)
−0.143801 + 0.989607i \(0.545933\pi\)
\(42\) 0 0
\(43\) −15026.2 −1.23930 −0.619651 0.784877i \(-0.712726\pi\)
−0.619651 + 0.784877i \(0.712726\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 19895.4 1.31373 0.656867 0.754007i \(-0.271881\pi\)
0.656867 + 0.754007i \(0.271881\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9206.42 0.450196 0.225098 0.974336i \(-0.427730\pi\)
0.225098 + 0.974336i \(0.427730\pi\)
\(54\) 0 0
\(55\) 40639.0 1.81149
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10301.3 −0.385267 −0.192633 0.981271i \(-0.561703\pi\)
−0.192633 + 0.981271i \(0.561703\pi\)
\(60\) 0 0
\(61\) −22599.2 −0.777622 −0.388811 0.921318i \(-0.627114\pi\)
−0.388811 + 0.921318i \(0.627114\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −59575.0 −1.74896
\(66\) 0 0
\(67\) −6419.09 −0.174697 −0.0873487 0.996178i \(-0.527839\pi\)
−0.0873487 + 0.996178i \(0.527839\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −61279.0 −1.44267 −0.721333 0.692588i \(-0.756470\pi\)
−0.721333 + 0.692588i \(0.756470\pi\)
\(72\) 0 0
\(73\) −29707.1 −0.652459 −0.326230 0.945291i \(-0.605778\pi\)
−0.326230 + 0.945291i \(0.605778\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −27801.6 −0.534372
\(78\) 0 0
\(79\) 15630.8 0.281782 0.140891 0.990025i \(-0.455003\pi\)
0.140891 + 0.990025i \(0.455003\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1668.23 0.0265804 0.0132902 0.999912i \(-0.495769\pi\)
0.0132902 + 0.999912i \(0.495769\pi\)
\(84\) 0 0
\(85\) 63630.5 0.955252
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −75833.3 −1.01481 −0.507405 0.861707i \(-0.669395\pi\)
−0.507405 + 0.861707i \(0.669395\pi\)
\(90\) 0 0
\(91\) 40756.0 0.515926
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 208790. 2.37357
\(96\) 0 0
\(97\) −98013.9 −1.05769 −0.528845 0.848718i \(-0.677375\pi\)
−0.528845 + 0.848718i \(0.677375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −54466.9 −0.531287 −0.265644 0.964071i \(-0.585584\pi\)
−0.265644 + 0.964071i \(0.585584\pi\)
\(102\) 0 0
\(103\) 178867. 1.66126 0.830631 0.556823i \(-0.187980\pi\)
0.830631 + 0.556823i \(0.187980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6591.90 −0.0556610 −0.0278305 0.999613i \(-0.508860\pi\)
−0.0278305 + 0.999613i \(0.508860\pi\)
\(108\) 0 0
\(109\) 177946. 1.43457 0.717285 0.696780i \(-0.245385\pi\)
0.717285 + 0.696780i \(0.245385\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −101861. −0.750432 −0.375216 0.926937i \(-0.622431\pi\)
−0.375216 + 0.926937i \(0.622431\pi\)
\(114\) 0 0
\(115\) −222210. −1.56682
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −43530.3 −0.281789
\(120\) 0 0
\(121\) 160869. 0.998871
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 80203.2 0.459110
\(126\) 0 0
\(127\) 153984. 0.847163 0.423581 0.905858i \(-0.360773\pi\)
0.423581 + 0.905858i \(0.360773\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 245130. 1.24801 0.624005 0.781420i \(-0.285504\pi\)
0.624005 + 0.781420i \(0.285504\pi\)
\(132\) 0 0
\(133\) −142836. −0.700178
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −85541.3 −0.389381 −0.194690 0.980865i \(-0.562370\pi\)
−0.194690 + 0.980865i \(0.562370\pi\)
\(138\) 0 0
\(139\) 195746. 0.859320 0.429660 0.902991i \(-0.358633\pi\)
0.429660 + 0.902991i \(0.358633\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −471921. −1.92987
\(144\) 0 0
\(145\) 592419. 2.33996
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 276266. 1.01944 0.509720 0.860340i \(-0.329749\pi\)
0.509720 + 0.860340i \(0.329749\pi\)
\(150\) 0 0
\(151\) −281649. −1.00523 −0.502616 0.864510i \(-0.667629\pi\)
−0.502616 + 0.864510i \(0.667629\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −503461. −1.68320
\(156\) 0 0
\(157\) −455344. −1.47432 −0.737158 0.675720i \(-0.763833\pi\)
−0.737158 + 0.675720i \(0.763833\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 152016. 0.462195
\(162\) 0 0
\(163\) 375179. 1.10604 0.553018 0.833169i \(-0.313476\pi\)
0.553018 + 0.833169i \(0.313476\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 279742. 0.776186 0.388093 0.921620i \(-0.373134\pi\)
0.388093 + 0.921620i \(0.373134\pi\)
\(168\) 0 0
\(169\) 320522. 0.863260
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 162065. 0.411693 0.205847 0.978584i \(-0.434005\pi\)
0.205847 + 0.978584i \(0.434005\pi\)
\(174\) 0 0
\(175\) 98257.0 0.242532
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −153376. −0.357787 −0.178894 0.983868i \(-0.557252\pi\)
−0.178894 + 0.983868i \(0.557252\pi\)
\(180\) 0 0
\(181\) −323034. −0.732911 −0.366456 0.930435i \(-0.619429\pi\)
−0.366456 + 0.930435i \(0.619429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 726418. 1.56048
\(186\) 0 0
\(187\) 504046. 1.05406
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 654819. 1.29879 0.649394 0.760453i \(-0.275023\pi\)
0.649394 + 0.760453i \(0.275023\pi\)
\(192\) 0 0
\(193\) 776059. 1.49969 0.749845 0.661613i \(-0.230128\pi\)
0.749845 + 0.661613i \(0.230128\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 399284. 0.733020 0.366510 0.930414i \(-0.380553\pi\)
0.366510 + 0.930414i \(0.380553\pi\)
\(198\) 0 0
\(199\) −9524.77 −0.0170499 −0.00852495 0.999964i \(-0.502714\pi\)
−0.00852495 + 0.999964i \(0.502714\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −405280. −0.690265
\(204\) 0 0
\(205\) 221728. 0.368499
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.65392e6 2.61908
\(210\) 0 0
\(211\) 481254. 0.744164 0.372082 0.928200i \(-0.378644\pi\)
0.372082 + 0.928200i \(0.378644\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.07626e6 1.58789
\(216\) 0 0
\(217\) 344424. 0.496528
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −738909. −1.01768
\(222\) 0 0
\(223\) −765559. −1.03090 −0.515450 0.856919i \(-0.672375\pi\)
−0.515450 + 0.856919i \(0.672375\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 657810. 0.847297 0.423649 0.905827i \(-0.360749\pi\)
0.423649 + 0.905827i \(0.360749\pi\)
\(228\) 0 0
\(229\) 499749. 0.629743 0.314871 0.949134i \(-0.398039\pi\)
0.314871 + 0.949134i \(0.398039\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 480588. 0.579940 0.289970 0.957036i \(-0.406355\pi\)
0.289970 + 0.957036i \(0.406355\pi\)
\(234\) 0 0
\(235\) −1.42502e6 −1.68326
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 869603. 0.984751 0.492376 0.870383i \(-0.336129\pi\)
0.492376 + 0.870383i \(0.336129\pi\)
\(240\) 0 0
\(241\) −671527. −0.744768 −0.372384 0.928079i \(-0.621460\pi\)
−0.372384 + 0.928079i \(0.621460\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −171973. −0.183040
\(246\) 0 0
\(247\) −2.42458e6 −2.52868
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −405312. −0.406074 −0.203037 0.979171i \(-0.565081\pi\)
−0.203037 + 0.979171i \(0.565081\pi\)
\(252\) 0 0
\(253\) −1.76023e6 −1.72889
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 837649. 0.791096 0.395548 0.918445i \(-0.370555\pi\)
0.395548 + 0.918445i \(0.370555\pi\)
\(258\) 0 0
\(259\) −496951. −0.460325
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 629562. 0.561241 0.280620 0.959819i \(-0.409460\pi\)
0.280620 + 0.959819i \(0.409460\pi\)
\(264\) 0 0
\(265\) −659417. −0.576827
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 319041. 0.268822 0.134411 0.990926i \(-0.457086\pi\)
0.134411 + 0.990926i \(0.457086\pi\)
\(270\) 0 0
\(271\) −715999. −0.592229 −0.296114 0.955153i \(-0.595691\pi\)
−0.296114 + 0.955153i \(0.595691\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.13774e6 −0.907214
\(276\) 0 0
\(277\) −869625. −0.680977 −0.340489 0.940249i \(-0.610592\pi\)
−0.340489 + 0.940249i \(0.610592\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.58664e6 −1.19870 −0.599351 0.800486i \(-0.704575\pi\)
−0.599351 + 0.800486i \(0.704575\pi\)
\(282\) 0 0
\(283\) 1.60231e6 1.18927 0.594636 0.803995i \(-0.297296\pi\)
0.594636 + 0.803995i \(0.297296\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −151687. −0.108703
\(288\) 0 0
\(289\) −630648. −0.444163
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.18717e6 −0.807874 −0.403937 0.914787i \(-0.632359\pi\)
−0.403937 + 0.914787i \(0.632359\pi\)
\(294\) 0 0
\(295\) 737837. 0.493635
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.58041e6 1.66921
\(300\) 0 0
\(301\) −736283. −0.468412
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.61868e6 0.996351
\(306\) 0 0
\(307\) 2.24511e6 1.35954 0.679769 0.733426i \(-0.262080\pi\)
0.679769 + 0.733426i \(0.262080\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 562022. 0.329498 0.164749 0.986336i \(-0.447319\pi\)
0.164749 + 0.986336i \(0.447319\pi\)
\(312\) 0 0
\(313\) 320869. 0.185126 0.0925629 0.995707i \(-0.470494\pi\)
0.0925629 + 0.995707i \(0.470494\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.18659e6 1.22213 0.611067 0.791579i \(-0.290741\pi\)
0.611067 + 0.791579i \(0.290741\pi\)
\(318\) 0 0
\(319\) 4.69282e6 2.58200
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.58963e6 1.38112
\(324\) 0 0
\(325\) 1.66787e6 0.875899
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 974873. 0.496545
\(330\) 0 0
\(331\) −211399. −0.106056 −0.0530278 0.998593i \(-0.516887\pi\)
−0.0530278 + 0.998593i \(0.516887\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 459772. 0.223836
\(336\) 0 0
\(337\) −1.37707e6 −0.660511 −0.330256 0.943892i \(-0.607135\pi\)
−0.330256 + 0.943892i \(0.607135\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.98814e6 −1.85731
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.62901e6 −0.726273 −0.363136 0.931736i \(-0.618294\pi\)
−0.363136 + 0.931736i \(0.618294\pi\)
\(348\) 0 0
\(349\) 3.30453e6 1.45227 0.726133 0.687554i \(-0.241316\pi\)
0.726133 + 0.687554i \(0.241316\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.46031e6 1.05088 0.525440 0.850831i \(-0.323901\pi\)
0.525440 + 0.850831i \(0.323901\pi\)
\(354\) 0 0
\(355\) 4.38916e6 1.84846
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.00216e6 1.63892 0.819462 0.573134i \(-0.194272\pi\)
0.819462 + 0.573134i \(0.194272\pi\)
\(360\) 0 0
\(361\) 6.02123e6 2.43174
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.12779e6 0.835983
\(366\) 0 0
\(367\) −4.74112e6 −1.83745 −0.918725 0.394897i \(-0.870780\pi\)
−0.918725 + 0.394897i \(0.870780\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 451115. 0.170158
\(372\) 0 0
\(373\) −3.18391e6 −1.18492 −0.592460 0.805600i \(-0.701843\pi\)
−0.592460 + 0.805600i \(0.701843\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.87946e6 −2.49288
\(378\) 0 0
\(379\) −980638. −0.350680 −0.175340 0.984508i \(-0.556102\pi\)
−0.175340 + 0.984508i \(0.556102\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 42711.2 0.0148780 0.00743901 0.999972i \(-0.497632\pi\)
0.00743901 + 0.999972i \(0.497632\pi\)
\(384\) 0 0
\(385\) 1.99131e6 0.684680
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.96471e6 1.66349 0.831744 0.555159i \(-0.187343\pi\)
0.831744 + 0.555159i \(0.187343\pi\)
\(390\) 0 0
\(391\) −2.75607e6 −0.911692
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.11957e6 −0.361042
\(396\) 0 0
\(397\) −2.38304e6 −0.758848 −0.379424 0.925223i \(-0.623878\pi\)
−0.379424 + 0.925223i \(0.623878\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.53716e6 1.40904 0.704520 0.709684i \(-0.251162\pi\)
0.704520 + 0.709684i \(0.251162\pi\)
\(402\) 0 0
\(403\) 5.84645e6 1.79320
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.75429e6 1.72189
\(408\) 0 0
\(409\) 1.20350e6 0.355746 0.177873 0.984053i \(-0.443078\pi\)
0.177873 + 0.984053i \(0.443078\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −504763. −0.145617
\(414\) 0 0
\(415\) −119489. −0.0340570
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.44364e6 1.23653 0.618264 0.785970i \(-0.287836\pi\)
0.618264 + 0.785970i \(0.287836\pi\)
\(420\) 0 0
\(421\) 4.10480e6 1.12872 0.564361 0.825528i \(-0.309123\pi\)
0.564361 + 0.825528i \(0.309123\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.78141e6 −0.478400
\(426\) 0 0
\(427\) −1.10736e6 −0.293913
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.92814e6 −0.499971 −0.249986 0.968250i \(-0.580426\pi\)
−0.249986 + 0.968250i \(0.580426\pi\)
\(432\) 0 0
\(433\) −4.07929e6 −1.04560 −0.522799 0.852456i \(-0.675112\pi\)
−0.522799 + 0.852456i \(0.675112\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.04348e6 −2.26533
\(438\) 0 0
\(439\) 5.79028e6 1.43396 0.716982 0.697091i \(-0.245523\pi\)
0.716982 + 0.697091i \(0.245523\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.95039e6 −0.472184 −0.236092 0.971731i \(-0.575867\pi\)
−0.236092 + 0.971731i \(0.575867\pi\)
\(444\) 0 0
\(445\) 5.43162e6 1.30026
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 422170. 0.0988260 0.0494130 0.998778i \(-0.484265\pi\)
0.0494130 + 0.998778i \(0.484265\pi\)
\(450\) 0 0
\(451\) 1.75641e6 0.406616
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.91918e6 −0.661046
\(456\) 0 0
\(457\) 4.28191e6 0.959063 0.479532 0.877525i \(-0.340807\pi\)
0.479532 + 0.877525i \(0.340807\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.33830e6 1.16990 0.584952 0.811068i \(-0.301113\pi\)
0.584952 + 0.811068i \(0.301113\pi\)
\(462\) 0 0
\(463\) −3.36278e6 −0.729030 −0.364515 0.931198i \(-0.618765\pi\)
−0.364515 + 0.931198i \(0.618765\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.26556e6 −1.11725 −0.558627 0.829419i \(-0.688672\pi\)
−0.558627 + 0.829419i \(0.688672\pi\)
\(468\) 0 0
\(469\) −314535. −0.0660294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.52555e6 1.75214
\(474\) 0 0
\(475\) −5.84533e6 −1.18871
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.27654e6 −1.05078 −0.525388 0.850863i \(-0.676080\pi\)
−0.525388 + 0.850863i \(0.676080\pi\)
\(480\) 0 0
\(481\) −8.43554e6 −1.66246
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.02032e6 1.35520
\(486\) 0 0
\(487\) 3.72209e6 0.711155 0.355578 0.934647i \(-0.384284\pi\)
0.355578 + 0.934647i \(0.384284\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.19917e6 −0.973263 −0.486631 0.873607i \(-0.661775\pi\)
−0.486631 + 0.873607i \(0.661775\pi\)
\(492\) 0 0
\(493\) 7.34777e6 1.36156
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.00267e6 −0.545277
\(498\) 0 0
\(499\) 5.32512e6 0.957366 0.478683 0.877988i \(-0.341114\pi\)
0.478683 + 0.877988i \(0.341114\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.26899e6 −0.752324 −0.376162 0.926554i \(-0.622756\pi\)
−0.376162 + 0.926554i \(0.622756\pi\)
\(504\) 0 0
\(505\) 3.90123e6 0.680728
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.07761e7 −1.84361 −0.921805 0.387655i \(-0.873285\pi\)
−0.921805 + 0.387655i \(0.873285\pi\)
\(510\) 0 0
\(511\) −1.45565e6 −0.246606
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.28115e7 −2.12854
\(516\) 0 0
\(517\) −1.12882e7 −1.85738
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.57993e6 1.06201 0.531003 0.847370i \(-0.321815\pi\)
0.531003 + 0.847370i \(0.321815\pi\)
\(522\) 0 0
\(523\) 4.93301e6 0.788602 0.394301 0.918981i \(-0.370987\pi\)
0.394301 + 0.918981i \(0.370987\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.24443e6 −0.979414
\(528\) 0 0
\(529\) 3.18838e6 0.495372
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.57482e6 −0.392581
\(534\) 0 0
\(535\) 472149. 0.0713173
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.36228e6 −0.201973
\(540\) 0 0
\(541\) 8.39789e6 1.23361 0.616804 0.787117i \(-0.288427\pi\)
0.616804 + 0.787117i \(0.288427\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.27455e7 −1.83808
\(546\) 0 0
\(547\) −7.34611e6 −1.04976 −0.524879 0.851177i \(-0.675890\pi\)
−0.524879 + 0.851177i \(0.675890\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.41102e7 3.38315
\(552\) 0 0
\(553\) 765910. 0.106504
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.36793e7 1.86821 0.934107 0.356994i \(-0.116198\pi\)
0.934107 + 0.356994i \(0.116198\pi\)
\(558\) 0 0
\(559\) −1.24981e7 −1.69166
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.35081e7 −1.79607 −0.898037 0.439920i \(-0.855007\pi\)
−0.898037 + 0.439920i \(0.855007\pi\)
\(564\) 0 0
\(565\) 7.29586e6 0.961513
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.31087e7 1.69738 0.848692 0.528888i \(-0.177391\pi\)
0.848692 + 0.528888i \(0.177391\pi\)
\(570\) 0 0
\(571\) 2.25105e6 0.288931 0.144466 0.989510i \(-0.453854\pi\)
0.144466 + 0.989510i \(0.453854\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.22102e6 0.784679
\(576\) 0 0
\(577\) 3.93495e6 0.492039 0.246020 0.969265i \(-0.420877\pi\)
0.246020 + 0.969265i \(0.420877\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 81743.5 0.0100465
\(582\) 0 0
\(583\) −5.22354e6 −0.636493
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.57017e6 0.307869 0.153935 0.988081i \(-0.450806\pi\)
0.153935 + 0.988081i \(0.450806\pi\)
\(588\) 0 0
\(589\) −2.04898e7 −2.43360
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.17677e6 −0.137422 −0.0687111 0.997637i \(-0.521889\pi\)
−0.0687111 + 0.997637i \(0.521889\pi\)
\(594\) 0 0
\(595\) 3.11789e6 0.361051
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.31387e6 1.06063 0.530314 0.847801i \(-0.322074\pi\)
0.530314 + 0.847801i \(0.322074\pi\)
\(600\) 0 0
\(601\) −9.65552e6 −1.09041 −0.545205 0.838303i \(-0.683548\pi\)
−0.545205 + 0.838303i \(0.683548\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.15224e7 −1.27983
\(606\) 0 0
\(607\) −1.42813e6 −0.157325 −0.0786625 0.996901i \(-0.525065\pi\)
−0.0786625 + 0.996901i \(0.525065\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.65481e7 1.79326
\(612\) 0 0
\(613\) −9.41130e6 −1.01158 −0.505788 0.862658i \(-0.668798\pi\)
−0.505788 + 0.862658i \(0.668798\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.68556e7 −1.78251 −0.891256 0.453501i \(-0.850175\pi\)
−0.891256 + 0.453501i \(0.850175\pi\)
\(618\) 0 0
\(619\) −1.07193e7 −1.12444 −0.562222 0.826986i \(-0.690053\pi\)
−0.562222 + 0.826986i \(0.690053\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.71583e6 −0.383562
\(624\) 0 0
\(625\) −1.20110e7 −1.22993
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.00977e6 0.908002
\(630\) 0 0
\(631\) −368207. −0.0368145 −0.0184073 0.999831i \(-0.505860\pi\)
−0.0184073 + 0.999831i \(0.505860\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.10292e7 −1.08545
\(636\) 0 0
\(637\) 1.99704e6 0.195002
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.43233e7 −1.37689 −0.688445 0.725289i \(-0.741706\pi\)
−0.688445 + 0.725289i \(0.741706\pi\)
\(642\) 0 0
\(643\) 7.65392e6 0.730056 0.365028 0.930996i \(-0.381059\pi\)
0.365028 + 0.930996i \(0.381059\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.84497e6 −0.830684 −0.415342 0.909665i \(-0.636338\pi\)
−0.415342 + 0.909665i \(0.636338\pi\)
\(648\) 0 0
\(649\) 5.84475e6 0.544696
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.22481e6 −0.479499 −0.239749 0.970835i \(-0.577065\pi\)
−0.239749 + 0.970835i \(0.577065\pi\)
\(654\) 0 0
\(655\) −1.75576e7 −1.59905
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.14374e6 0.640785 0.320392 0.947285i \(-0.396185\pi\)
0.320392 + 0.947285i \(0.396185\pi\)
\(660\) 0 0
\(661\) −1.05360e6 −0.0937934 −0.0468967 0.998900i \(-0.514933\pi\)
−0.0468967 + 0.998900i \(0.514933\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.02307e7 0.897123
\(666\) 0 0
\(667\) −2.56598e7 −2.23326
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.28223e7 1.09941
\(672\) 0 0
\(673\) −1.01967e7 −0.867802 −0.433901 0.900960i \(-0.642863\pi\)
−0.433901 + 0.900960i \(0.642863\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.65785e7 −1.39019 −0.695094 0.718919i \(-0.744637\pi\)
−0.695094 + 0.718919i \(0.744637\pi\)
\(678\) 0 0
\(679\) −4.80268e6 −0.399769
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.43664e6 −0.117841 −0.0589206 0.998263i \(-0.518766\pi\)
−0.0589206 + 0.998263i \(0.518766\pi\)
\(684\) 0 0
\(685\) 6.12696e6 0.498906
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.65748e6 0.614523
\(690\) 0 0
\(691\) 1.15592e7 0.920939 0.460469 0.887676i \(-0.347681\pi\)
0.460469 + 0.887676i \(0.347681\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.40204e7 −1.10103
\(696\) 0 0
\(697\) 2.75010e6 0.214420
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.28743e6 −0.636979 −0.318489 0.947926i \(-0.603176\pi\)
−0.318489 + 0.947926i \(0.603176\pi\)
\(702\) 0 0
\(703\) 2.95637e7 2.25616
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.66888e6 −0.200808
\(708\) 0 0
\(709\) −3.40586e6 −0.254455 −0.127228 0.991874i \(-0.540608\pi\)
−0.127228 + 0.991874i \(0.540608\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.18068e7 1.60645
\(714\) 0 0
\(715\) 3.38017e7 2.47271
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.81891e6 −0.131217 −0.0656083 0.997845i \(-0.520899\pi\)
−0.0656083 + 0.997845i \(0.520899\pi\)
\(720\) 0 0
\(721\) 8.76450e6 0.627898
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.65854e7 −1.17188
\(726\) 0 0
\(727\) −6.14132e6 −0.430949 −0.215474 0.976510i \(-0.569130\pi\)
−0.215474 + 0.976510i \(0.569130\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.33489e7 0.923955
\(732\) 0 0
\(733\) −7.62786e6 −0.524376 −0.262188 0.965017i \(-0.584444\pi\)
−0.262188 + 0.965017i \(0.584444\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.64206e6 0.246990
\(738\) 0 0
\(739\) −2.76967e7 −1.86560 −0.932798 0.360400i \(-0.882640\pi\)
−0.932798 + 0.360400i \(0.882640\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.10656e7 −0.735366 −0.367683 0.929951i \(-0.619849\pi\)
−0.367683 + 0.929951i \(0.619849\pi\)
\(744\) 0 0
\(745\) −1.97878e7 −1.30619
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −323003. −0.0210379
\(750\) 0 0
\(751\) −2.77646e6 −0.179635 −0.0898176 0.995958i \(-0.528628\pi\)
−0.0898176 + 0.995958i \(0.528628\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.01733e7 1.28798
\(756\) 0 0
\(757\) −2.67284e7 −1.69525 −0.847624 0.530597i \(-0.821968\pi\)
−0.847624 + 0.530597i \(0.821968\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.43818e7 −1.52618 −0.763089 0.646294i \(-0.776318\pi\)
−0.763089 + 0.646294i \(0.776318\pi\)
\(762\) 0 0
\(763\) 8.71934e6 0.542216
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.56814e6 −0.525894
\(768\) 0 0
\(769\) −1.88874e7 −1.15174 −0.575872 0.817540i \(-0.695337\pi\)
−0.575872 + 0.817540i \(0.695337\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.11832e7 −0.673156 −0.336578 0.941656i \(-0.609270\pi\)
−0.336578 + 0.941656i \(0.609270\pi\)
\(774\) 0 0
\(775\) 1.40950e7 0.842966
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.02387e6 0.532782
\(780\) 0 0
\(781\) 3.47685e7 2.03966
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.26144e7 1.88901
\(786\) 0 0
\(787\) 1.23669e7 0.711742 0.355871 0.934535i \(-0.384184\pi\)
0.355871 + 0.934535i \(0.384184\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.99118e6 −0.283637
\(792\) 0 0
\(793\) −1.87970e7 −1.06146
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.24152e6 0.515345 0.257672 0.966232i \(-0.417044\pi\)
0.257672 + 0.966232i \(0.417044\pi\)
\(798\) 0 0
\(799\) −1.76745e7 −0.979447
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.68552e7 0.922456
\(804\) 0 0
\(805\) −1.08883e7 −0.592202
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.29668e7 −1.23376 −0.616878 0.787059i \(-0.711603\pi\)
−0.616878 + 0.787059i \(0.711603\pi\)
\(810\) 0 0
\(811\) −1.99916e6 −0.106732 −0.0533662 0.998575i \(-0.516995\pi\)
−0.0533662 + 0.998575i \(0.516995\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.68725e7 −1.41714
\(816\) 0 0
\(817\) 4.38016e7 2.29580
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.16393e7 1.12043 0.560215 0.828347i \(-0.310718\pi\)
0.560215 + 0.828347i \(0.310718\pi\)
\(822\) 0 0
\(823\) 2.68119e7 1.37984 0.689919 0.723887i \(-0.257646\pi\)
0.689919 + 0.723887i \(0.257646\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.76847e7 1.40759 0.703794 0.710404i \(-0.251488\pi\)
0.703794 + 0.710404i \(0.251488\pi\)
\(828\) 0 0
\(829\) 1.51184e7 0.764046 0.382023 0.924153i \(-0.375227\pi\)
0.382023 + 0.924153i \(0.375227\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.13299e6 −0.106506
\(834\) 0 0
\(835\) −2.00367e7 −0.994512
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.29436e7 −1.61572 −0.807859 0.589376i \(-0.799374\pi\)
−0.807859 + 0.589376i \(0.799374\pi\)
\(840\) 0 0
\(841\) 4.78988e7 2.33526
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.29577e7 −1.10608
\(846\) 0 0
\(847\) 7.88259e6 0.377538
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.14638e7 −1.48932
\(852\) 0 0
\(853\) 1.37677e7 0.647869 0.323935 0.946079i \(-0.394994\pi\)
0.323935 + 0.946079i \(0.394994\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.52437e7 −0.708986 −0.354493 0.935059i \(-0.615346\pi\)
−0.354493 + 0.935059i \(0.615346\pi\)
\(858\) 0 0
\(859\) −8.37545e6 −0.387280 −0.193640 0.981073i \(-0.562029\pi\)
−0.193640 + 0.981073i \(0.562029\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.92437e7 0.879550 0.439775 0.898108i \(-0.355058\pi\)
0.439775 + 0.898108i \(0.355058\pi\)
\(864\) 0 0
\(865\) −1.16080e7 −0.527495
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8.86861e6 −0.398388
\(870\) 0 0
\(871\) −5.33911e6 −0.238464
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.92996e6 0.173527
\(876\) 0 0
\(877\) −1.04613e7 −0.459290 −0.229645 0.973275i \(-0.573756\pi\)
−0.229645 + 0.973275i \(0.573756\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.71859e7 −1.18006 −0.590030 0.807381i \(-0.700884\pi\)
−0.590030 + 0.807381i \(0.700884\pi\)
\(882\) 0 0
\(883\) −2.07191e7 −0.894272 −0.447136 0.894466i \(-0.647556\pi\)
−0.447136 + 0.894466i \(0.647556\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.29309e7 0.551850 0.275925 0.961179i \(-0.411016\pi\)
0.275925 + 0.961179i \(0.411016\pi\)
\(888\) 0 0
\(889\) 7.54523e6 0.320197
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.79953e7 −2.43369
\(894\) 0 0
\(895\) 1.09857e7 0.458426
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.81375e7 −2.39915
\(900\) 0 0
\(901\) −8.17875e6 −0.335641
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.31375e7 0.939065
\(906\) 0 0
\(907\) −3.43055e7 −1.38467 −0.692334 0.721578i \(-0.743417\pi\)
−0.692334 + 0.721578i \(0.743417\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.23945e7 −0.894017 −0.447009 0.894530i \(-0.647511\pi\)
−0.447009 + 0.894530i \(0.647511\pi\)
\(912\) 0 0
\(913\) −946523. −0.0375798
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.20114e7 0.471704
\(918\) 0 0
\(919\) −2.86863e7 −1.12043 −0.560216 0.828346i \(-0.689282\pi\)
−0.560216 + 0.828346i \(0.689282\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.09691e7 −1.96926
\(924\) 0 0
\(925\) −2.03369e7 −0.781503
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.36199e7 1.65823 0.829116 0.559076i \(-0.188844\pi\)
0.829116 + 0.559076i \(0.188844\pi\)
\(930\) 0 0
\(931\) −6.99896e6 −0.264642
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3.61027e7 −1.35055
\(936\) 0 0
\(937\) −2.15646e7 −0.802401 −0.401201 0.915990i \(-0.631407\pi\)
−0.401201 + 0.915990i \(0.631407\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.30720e7 0.481246 0.240623 0.970619i \(-0.422648\pi\)
0.240623 + 0.970619i \(0.422648\pi\)
\(942\) 0 0
\(943\) −9.60386e6 −0.351695
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.81492e6 −0.210702 −0.105351 0.994435i \(-0.533597\pi\)
−0.105351 + 0.994435i \(0.533597\pi\)
\(948\) 0 0
\(949\) −2.47090e7 −0.890615
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.70378e7 0.607689 0.303845 0.952722i \(-0.401730\pi\)
0.303845 + 0.952722i \(0.401730\pi\)
\(954\) 0 0
\(955\) −4.69019e7 −1.66411
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.19153e6 −0.147172
\(960\) 0 0
\(961\) 2.07784e7 0.725779
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.55858e7 −1.92152
\(966\) 0 0
\(967\) 3.39209e7 1.16654 0.583272 0.812277i \(-0.301772\pi\)
0.583272 + 0.812277i \(0.301772\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.89258e7 −1.32492 −0.662460 0.749097i \(-0.730487\pi\)
−0.662460 + 0.749097i \(0.730487\pi\)
\(972\) 0 0
\(973\) 9.59154e6 0.324793
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.06514e7 1.36251 0.681253 0.732048i \(-0.261435\pi\)
0.681253 + 0.732048i \(0.261435\pi\)
\(978\) 0 0
\(979\) 4.30263e7 1.43475
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.55210e7 0.512315 0.256158 0.966635i \(-0.417543\pi\)
0.256158 + 0.966635i \(0.417543\pi\)
\(984\) 0 0
\(985\) −2.85990e7 −0.939204
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.66168e7 −1.51549
\(990\) 0 0
\(991\) 1.73682e7 0.561784 0.280892 0.959739i \(-0.409370\pi\)
0.280892 + 0.959739i \(0.409370\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 682219. 0.0218457
\(996\) 0 0
\(997\) 2.42265e7 0.771885 0.385943 0.922523i \(-0.373876\pi\)
0.385943 + 0.922523i \(0.373876\pi\)
\(998\) 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.bo.1.1 2
3.2 odd 2 336.6.a.x.1.2 2
4.3 odd 2 252.6.a.h.1.1 2
12.11 even 2 84.6.a.c.1.2 2
84.11 even 6 588.6.i.l.373.1 4
84.23 even 6 588.6.i.l.361.1 4
84.47 odd 6 588.6.i.i.361.2 4
84.59 odd 6 588.6.i.i.373.2 4
84.83 odd 2 588.6.a.k.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.c.1.2 2 12.11 even 2
252.6.a.h.1.1 2 4.3 odd 2
336.6.a.x.1.2 2 3.2 odd 2
588.6.a.k.1.1 2 84.83 odd 2
588.6.i.i.361.2 4 84.47 odd 6
588.6.i.i.373.2 4 84.59 odd 6
588.6.i.l.361.1 4 84.23 even 6
588.6.i.l.373.1 4 84.11 even 6
1008.6.a.bo.1.1 2 1.1 even 1 trivial