Properties

Label 432.6.a.p.1.1
Level $432$
Weight $6$
Character 432.1
Self dual yes
Analytic conductor $69.286$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,6,Mod(1,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, 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("432.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.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: \(69.2858101592\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 108)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.44949\) of defining polynomial
Character \(\chi\) \(=\) 432.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-88.1816 q^{5} -29.0000 q^{7} +O(q^{10})\) \(q-88.1816 q^{5} -29.0000 q^{7} +88.1816 q^{11} +329.000 q^{13} +2204.54 q^{17} -1799.00 q^{19} +3615.45 q^{23} +4651.00 q^{25} -1410.91 q^{29} -5228.00 q^{31} +2557.27 q^{35} +8783.00 q^{37} +15520.0 q^{41} -19976.0 q^{43} -10846.3 q^{47} -15966.0 q^{49} -29452.7 q^{53} -7776.00 q^{55} +5731.81 q^{59} -1069.00 q^{61} -29011.8 q^{65} +62077.0 q^{67} -46383.5 q^{71} -48079.0 q^{73} -2557.27 q^{77} -49979.0 q^{79} -57670.8 q^{83} -194400. q^{85} +87917.1 q^{89} -9541.00 q^{91} +158639. q^{95} +12917.0 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 58 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 58 q^{7} + 658 q^{13} - 3598 q^{19} + 9302 q^{25} - 10456 q^{31} + 17566 q^{37} - 39952 q^{43} - 31932 q^{49} - 15552 q^{55} - 2138 q^{61} + 124154 q^{67} - 96158 q^{73} - 99958 q^{79} - 388800 q^{85} - 19082 q^{91} + 25834 q^{97}+O(q^{100}) \) 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
\(5\) −88.1816 −1.57744 −0.788720 0.614752i \(-0.789256\pi\)
−0.788720 + 0.614752i \(0.789256\pi\)
\(6\) 0 0
\(7\) −29.0000 −0.223693 −0.111847 0.993725i \(-0.535677\pi\)
−0.111847 + 0.993725i \(0.535677\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 88.1816 0.219734 0.109867 0.993946i \(-0.464958\pi\)
0.109867 + 0.993946i \(0.464958\pi\)
\(12\) 0 0
\(13\) 329.000 0.539930 0.269965 0.962870i \(-0.412988\pi\)
0.269965 + 0.962870i \(0.412988\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2204.54 1.85010 0.925051 0.379842i \(-0.124022\pi\)
0.925051 + 0.379842i \(0.124022\pi\)
\(18\) 0 0
\(19\) −1799.00 −1.14327 −0.571633 0.820510i \(-0.693690\pi\)
−0.571633 + 0.820510i \(0.693690\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3615.45 1.42509 0.712545 0.701626i \(-0.247542\pi\)
0.712545 + 0.701626i \(0.247542\pi\)
\(24\) 0 0
\(25\) 4651.00 1.48832
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1410.91 −0.311532 −0.155766 0.987794i \(-0.549785\pi\)
−0.155766 + 0.987794i \(0.549785\pi\)
\(30\) 0 0
\(31\) −5228.00 −0.977083 −0.488541 0.872541i \(-0.662471\pi\)
−0.488541 + 0.872541i \(0.662471\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2557.27 0.352863
\(36\) 0 0
\(37\) 8783.00 1.05472 0.527362 0.849641i \(-0.323181\pi\)
0.527362 + 0.849641i \(0.323181\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 15520.0 1.44189 0.720943 0.692994i \(-0.243709\pi\)
0.720943 + 0.692994i \(0.243709\pi\)
\(42\) 0 0
\(43\) −19976.0 −1.64755 −0.823773 0.566920i \(-0.808135\pi\)
−0.823773 + 0.566920i \(0.808135\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10846.3 −0.716207 −0.358104 0.933682i \(-0.616577\pi\)
−0.358104 + 0.933682i \(0.616577\pi\)
\(48\) 0 0
\(49\) −15966.0 −0.949961
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −29452.7 −1.44024 −0.720120 0.693849i \(-0.755913\pi\)
−0.720120 + 0.693849i \(0.755913\pi\)
\(54\) 0 0
\(55\) −7776.00 −0.346617
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5731.81 0.214369 0.107184 0.994239i \(-0.465816\pi\)
0.107184 + 0.994239i \(0.465816\pi\)
\(60\) 0 0
\(61\) −1069.00 −0.0367835 −0.0183918 0.999831i \(-0.505855\pi\)
−0.0183918 + 0.999831i \(0.505855\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −29011.8 −0.851708
\(66\) 0 0
\(67\) 62077.0 1.68944 0.844722 0.535206i \(-0.179766\pi\)
0.844722 + 0.535206i \(0.179766\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −46383.5 −1.09199 −0.545994 0.837789i \(-0.683848\pi\)
−0.545994 + 0.837789i \(0.683848\pi\)
\(72\) 0 0
\(73\) −48079.0 −1.05596 −0.527981 0.849256i \(-0.677051\pi\)
−0.527981 + 0.849256i \(0.677051\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2557.27 −0.0491529
\(78\) 0 0
\(79\) −49979.0 −0.900990 −0.450495 0.892779i \(-0.648752\pi\)
−0.450495 + 0.892779i \(0.648752\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −57670.8 −0.918884 −0.459442 0.888208i \(-0.651951\pi\)
−0.459442 + 0.888208i \(0.651951\pi\)
\(84\) 0 0
\(85\) −194400. −2.91843
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 87917.1 1.17652 0.588259 0.808673i \(-0.299814\pi\)
0.588259 + 0.808673i \(0.299814\pi\)
\(90\) 0 0
\(91\) −9541.00 −0.120779
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 158639. 1.80343
\(96\) 0 0
\(97\) 12917.0 0.139390 0.0696951 0.997568i \(-0.477797\pi\)
0.0696951 + 0.997568i \(0.477797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −112872. −1.10099 −0.550497 0.834837i \(-0.685562\pi\)
−0.550497 + 0.834837i \(0.685562\pi\)
\(102\) 0 0
\(103\) 77503.0 0.719823 0.359911 0.932987i \(-0.382807\pi\)
0.359911 + 0.932987i \(0.382807\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 111726. 0.943399 0.471699 0.881759i \(-0.343641\pi\)
0.471699 + 0.881759i \(0.343641\pi\)
\(108\) 0 0
\(109\) −17710.0 −0.142775 −0.0713875 0.997449i \(-0.522743\pi\)
−0.0713875 + 0.997449i \(0.522743\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 251582. 1.85346 0.926731 0.375725i \(-0.122606\pi\)
0.926731 + 0.375725i \(0.122606\pi\)
\(114\) 0 0
\(115\) −318816. −2.24800
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −63931.7 −0.413855
\(120\) 0 0
\(121\) −153275. −0.951717
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −134565. −0.770296
\(126\) 0 0
\(127\) −269444. −1.48238 −0.741189 0.671296i \(-0.765738\pi\)
−0.741189 + 0.671296i \(0.765738\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −154141. −0.784768 −0.392384 0.919801i \(-0.628350\pi\)
−0.392384 + 0.919801i \(0.628350\pi\)
\(132\) 0 0
\(133\) 52171.0 0.255741
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 271864. 1.23751 0.618757 0.785582i \(-0.287636\pi\)
0.618757 + 0.785582i \(0.287636\pi\)
\(138\) 0 0
\(139\) −182705. −0.802072 −0.401036 0.916062i \(-0.631350\pi\)
−0.401036 + 0.916062i \(0.631350\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 29011.8 0.118641
\(144\) 0 0
\(145\) 124416. 0.491424
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −347259. −1.28141 −0.640705 0.767787i \(-0.721358\pi\)
−0.640705 + 0.767787i \(0.721358\pi\)
\(150\) 0 0
\(151\) −434351. −1.55024 −0.775119 0.631815i \(-0.782310\pi\)
−0.775119 + 0.631815i \(0.782310\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 461014. 1.54129
\(156\) 0 0
\(157\) −22978.0 −0.0743983 −0.0371992 0.999308i \(-0.511844\pi\)
−0.0371992 + 0.999308i \(0.511844\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −104848. −0.318783
\(162\) 0 0
\(163\) −109961. −0.324168 −0.162084 0.986777i \(-0.551821\pi\)
−0.162084 + 0.986777i \(0.551821\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −307137. −0.852198 −0.426099 0.904677i \(-0.640112\pi\)
−0.426099 + 0.904677i \(0.640112\pi\)
\(168\) 0 0
\(169\) −263052. −0.708476
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4232.72 0.0107524 0.00537618 0.999986i \(-0.498289\pi\)
0.00537618 + 0.999986i \(0.498289\pi\)
\(174\) 0 0
\(175\) −134879. −0.332927
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −831906. −1.94062 −0.970312 0.241856i \(-0.922244\pi\)
−0.970312 + 0.241856i \(0.922244\pi\)
\(180\) 0 0
\(181\) −327187. −0.742334 −0.371167 0.928566i \(-0.621042\pi\)
−0.371167 + 0.928566i \(0.621042\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −774499. −1.66376
\(186\) 0 0
\(187\) 194400. 0.406530
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −468862. −0.929954 −0.464977 0.885323i \(-0.653937\pi\)
−0.464977 + 0.885323i \(0.653937\pi\)
\(192\) 0 0
\(193\) 152231. 0.294178 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 653514. 1.19975 0.599873 0.800095i \(-0.295218\pi\)
0.599873 + 0.800095i \(0.295218\pi\)
\(198\) 0 0
\(199\) 645895. 1.15619 0.578095 0.815969i \(-0.303796\pi\)
0.578095 + 0.815969i \(0.303796\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 40916.3 0.0696877
\(204\) 0 0
\(205\) −1.36858e6 −2.27449
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −158639. −0.251214
\(210\) 0 0
\(211\) −169637. −0.262310 −0.131155 0.991362i \(-0.541869\pi\)
−0.131155 + 0.991362i \(0.541869\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.76152e6 2.59891
\(216\) 0 0
\(217\) 151612. 0.218567
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 725294. 0.998926
\(222\) 0 0
\(223\) 691276. 0.930871 0.465435 0.885082i \(-0.345898\pi\)
0.465435 + 0.885082i \(0.345898\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 989927. 1.27508 0.637542 0.770416i \(-0.279951\pi\)
0.637542 + 0.770416i \(0.279951\pi\)
\(228\) 0 0
\(229\) 352250. 0.443877 0.221938 0.975061i \(-0.428762\pi\)
0.221938 + 0.975061i \(0.428762\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −381297. −0.460123 −0.230062 0.973176i \(-0.573893\pi\)
−0.230062 + 0.973176i \(0.573893\pi\)
\(234\) 0 0
\(235\) 956448. 1.12977
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −785698. −0.889736 −0.444868 0.895596i \(-0.646749\pi\)
−0.444868 + 0.895596i \(0.646749\pi\)
\(240\) 0 0
\(241\) −1.20262e6 −1.33379 −0.666894 0.745152i \(-0.732377\pi\)
−0.666894 + 0.745152i \(0.732377\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.40791e6 1.49851
\(246\) 0 0
\(247\) −591871. −0.617284
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −416570. −0.417353 −0.208677 0.977985i \(-0.566916\pi\)
−0.208677 + 0.977985i \(0.566916\pi\)
\(252\) 0 0
\(253\) 318816. 0.313140
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 44972.6 0.0424732 0.0212366 0.999774i \(-0.493240\pi\)
0.0212366 + 0.999774i \(0.493240\pi\)
\(258\) 0 0
\(259\) −254707. −0.235935
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −515157. −0.459251 −0.229626 0.973279i \(-0.573750\pi\)
−0.229626 + 0.973279i \(0.573750\pi\)
\(264\) 0 0
\(265\) 2.59718e6 2.27189
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −197439. −0.166361 −0.0831805 0.996534i \(-0.526508\pi\)
−0.0831805 + 0.996534i \(0.526508\pi\)
\(270\) 0 0
\(271\) 1.01499e6 0.839530 0.419765 0.907633i \(-0.362112\pi\)
0.419765 + 0.907633i \(0.362112\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 410133. 0.327034
\(276\) 0 0
\(277\) −379318. −0.297033 −0.148516 0.988910i \(-0.547450\pi\)
−0.148516 + 0.988910i \(0.547450\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −955889. −0.722174 −0.361087 0.932532i \(-0.617594\pi\)
−0.361087 + 0.932532i \(0.617594\pi\)
\(282\) 0 0
\(283\) −662912. −0.492028 −0.246014 0.969266i \(-0.579121\pi\)
−0.246014 + 0.969266i \(0.579121\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −450079. −0.322540
\(288\) 0 0
\(289\) 3.44014e6 2.42288
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −447522. −0.304541 −0.152270 0.988339i \(-0.548658\pi\)
−0.152270 + 0.988339i \(0.548658\pi\)
\(294\) 0 0
\(295\) −505440. −0.338154
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.18948e6 0.769449
\(300\) 0 0
\(301\) 579304. 0.368545
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 94266.2 0.0580238
\(306\) 0 0
\(307\) 1.17362e6 0.710690 0.355345 0.934735i \(-0.384363\pi\)
0.355345 + 0.934735i \(0.384363\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.41221e6 1.41421 0.707105 0.707109i \(-0.250001\pi\)
0.707105 + 0.707109i \(0.250001\pi\)
\(312\) 0 0
\(313\) 1.72967e6 0.997934 0.498967 0.866621i \(-0.333713\pi\)
0.498967 + 0.866621i \(0.333713\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.17476e6 −0.656598 −0.328299 0.944574i \(-0.606475\pi\)
−0.328299 + 0.944574i \(0.606475\pi\)
\(318\) 0 0
\(319\) −124416. −0.0684541
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.96597e6 −2.11516
\(324\) 0 0
\(325\) 1.53018e6 0.803589
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 314544. 0.160211
\(330\) 0 0
\(331\) −451001. −0.226260 −0.113130 0.993580i \(-0.536088\pi\)
−0.113130 + 0.993580i \(0.536088\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.47405e6 −2.66500
\(336\) 0 0
\(337\) 2.17937e6 1.04534 0.522669 0.852536i \(-0.324936\pi\)
0.522669 + 0.852536i \(0.324936\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −461014. −0.214698
\(342\) 0 0
\(343\) 950417. 0.436193
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −381474. −0.170075 −0.0850376 0.996378i \(-0.527101\pi\)
−0.0850376 + 0.996378i \(0.527101\pi\)
\(348\) 0 0
\(349\) −2.29596e6 −1.00902 −0.504511 0.863405i \(-0.668327\pi\)
−0.504511 + 0.863405i \(0.668327\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.24103e6 −1.38435 −0.692175 0.721730i \(-0.743347\pi\)
−0.692175 + 0.721730i \(0.743347\pi\)
\(354\) 0 0
\(355\) 4.09018e6 1.72255
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.15044e6 1.69965 0.849823 0.527068i \(-0.176709\pi\)
0.849823 + 0.527068i \(0.176709\pi\)
\(360\) 0 0
\(361\) 760302. 0.307056
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.23968e6 1.66572
\(366\) 0 0
\(367\) −3.39911e6 −1.31735 −0.658674 0.752429i \(-0.728882\pi\)
−0.658674 + 0.752429i \(0.728882\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 854127. 0.322172
\(372\) 0 0
\(373\) −3.14494e6 −1.17041 −0.585207 0.810884i \(-0.698987\pi\)
−0.585207 + 0.810884i \(0.698987\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −464188. −0.168206
\(378\) 0 0
\(379\) 2.76635e6 0.989257 0.494628 0.869105i \(-0.335304\pi\)
0.494628 + 0.869105i \(0.335304\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.24898e6 0.783411 0.391705 0.920091i \(-0.371885\pi\)
0.391705 + 0.920091i \(0.371885\pi\)
\(384\) 0 0
\(385\) 225504. 0.0775358
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −555985. −0.186290 −0.0931449 0.995653i \(-0.529692\pi\)
−0.0931449 + 0.995653i \(0.529692\pi\)
\(390\) 0 0
\(391\) 7.97040e6 2.63656
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.40723e6 1.42126
\(396\) 0 0
\(397\) 836174. 0.266269 0.133134 0.991098i \(-0.457496\pi\)
0.133134 + 0.991098i \(0.457496\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.01283e6 0.625096 0.312548 0.949902i \(-0.398817\pi\)
0.312548 + 0.949902i \(0.398817\pi\)
\(402\) 0 0
\(403\) −1.72001e6 −0.527556
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 774499. 0.231758
\(408\) 0 0
\(409\) −1.37271e6 −0.405762 −0.202881 0.979203i \(-0.565030\pi\)
−0.202881 + 0.979203i \(0.565030\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −166222. −0.0479528
\(414\) 0 0
\(415\) 5.08550e6 1.44949
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.54305e6 −0.985921 −0.492961 0.870052i \(-0.664085\pi\)
−0.492961 + 0.870052i \(0.664085\pi\)
\(420\) 0 0
\(421\) −3.48884e6 −0.959347 −0.479673 0.877447i \(-0.659245\pi\)
−0.479673 + 0.877447i \(0.659245\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.02533e7 2.75354
\(426\) 0 0
\(427\) 31001.0 0.00822822
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.43754e6 −1.40997 −0.704985 0.709223i \(-0.749046\pi\)
−0.704985 + 0.709223i \(0.749046\pi\)
\(432\) 0 0
\(433\) 4.96023e6 1.27140 0.635699 0.771937i \(-0.280712\pi\)
0.635699 + 0.771937i \(0.280712\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.50419e6 −1.62926
\(438\) 0 0
\(439\) −5.75071e6 −1.42416 −0.712082 0.702096i \(-0.752248\pi\)
−0.712082 + 0.702096i \(0.752248\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.63110e6 1.36328 0.681639 0.731689i \(-0.261268\pi\)
0.681639 + 0.731689i \(0.261268\pi\)
\(444\) 0 0
\(445\) −7.75267e6 −1.85589
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.45310e6 0.808340 0.404170 0.914684i \(-0.367560\pi\)
0.404170 + 0.914684i \(0.367560\pi\)
\(450\) 0 0
\(451\) 1.36858e6 0.316831
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 841341. 0.190521
\(456\) 0 0
\(457\) 1.96799e6 0.440791 0.220395 0.975411i \(-0.429265\pi\)
0.220395 + 0.975411i \(0.429265\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.63329e6 −1.45371 −0.726853 0.686793i \(-0.759018\pi\)
−0.726853 + 0.686793i \(0.759018\pi\)
\(462\) 0 0
\(463\) 1.62568e6 0.352439 0.176219 0.984351i \(-0.443613\pi\)
0.176219 + 0.984351i \(0.443613\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.48346e6 −0.526944 −0.263472 0.964667i \(-0.584868\pi\)
−0.263472 + 0.964667i \(0.584868\pi\)
\(468\) 0 0
\(469\) −1.80023e6 −0.377917
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.76152e6 −0.362021
\(474\) 0 0
\(475\) −8.36715e6 −1.70155
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.59626e6 0.317882 0.158941 0.987288i \(-0.449192\pi\)
0.158941 + 0.987288i \(0.449192\pi\)
\(480\) 0 0
\(481\) 2.88961e6 0.569477
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.13904e6 −0.219880
\(486\) 0 0
\(487\) −7.95245e6 −1.51942 −0.759712 0.650260i \(-0.774660\pi\)
−0.759712 + 0.650260i \(0.774660\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.05595e6 0.384866 0.192433 0.981310i \(-0.438362\pi\)
0.192433 + 0.981310i \(0.438362\pi\)
\(492\) 0 0
\(493\) −3.11040e6 −0.576367
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.34512e6 0.244270
\(498\) 0 0
\(499\) −4.93539e6 −0.887300 −0.443650 0.896200i \(-0.646317\pi\)
−0.443650 + 0.896200i \(0.646317\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 836755. 0.147461 0.0737307 0.997278i \(-0.476509\pi\)
0.0737307 + 0.997278i \(0.476509\pi\)
\(504\) 0 0
\(505\) 9.95328e6 1.73675
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.90156e6 −1.00965 −0.504826 0.863221i \(-0.668443\pi\)
−0.504826 + 0.863221i \(0.668443\pi\)
\(510\) 0 0
\(511\) 1.39429e6 0.236212
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.83434e6 −1.13548
\(516\) 0 0
\(517\) −956448. −0.157375
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 163577. 0.0264014 0.0132007 0.999913i \(-0.495798\pi\)
0.0132007 + 0.999913i \(0.495798\pi\)
\(522\) 0 0
\(523\) 2.95232e6 0.471965 0.235983 0.971757i \(-0.424169\pi\)
0.235983 + 0.971757i \(0.424169\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.15253e7 −1.80770
\(528\) 0 0
\(529\) 6.63511e6 1.03088
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.10607e6 0.778518
\(534\) 0 0
\(535\) −9.85219e6 −1.48816
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.40791e6 −0.208738
\(540\) 0 0
\(541\) −9.58390e6 −1.40783 −0.703913 0.710286i \(-0.748566\pi\)
−0.703913 + 0.710286i \(0.748566\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.56170e6 0.225219
\(546\) 0 0
\(547\) −1.21781e7 −1.74025 −0.870127 0.492827i \(-0.835964\pi\)
−0.870127 + 0.492827i \(0.835964\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.53822e6 0.356164
\(552\) 0 0
\(553\) 1.44939e6 0.201545
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.32679e6 −0.727491 −0.363745 0.931498i \(-0.618502\pi\)
−0.363745 + 0.931498i \(0.618502\pi\)
\(558\) 0 0
\(559\) −6.57210e6 −0.889559
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.23899e6 −1.09548 −0.547738 0.836650i \(-0.684511\pi\)
−0.547738 + 0.836650i \(0.684511\pi\)
\(564\) 0 0
\(565\) −2.21849e7 −2.92373
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.42410e6 −0.961309 −0.480655 0.876910i \(-0.659601\pi\)
−0.480655 + 0.876910i \(0.659601\pi\)
\(570\) 0 0
\(571\) 288553. 0.0370370 0.0185185 0.999829i \(-0.494105\pi\)
0.0185185 + 0.999829i \(0.494105\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.68154e7 2.12099
\(576\) 0 0
\(577\) 933299. 0.116703 0.0583514 0.998296i \(-0.481416\pi\)
0.0583514 + 0.998296i \(0.481416\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.67245e6 0.205548
\(582\) 0 0
\(583\) −2.59718e6 −0.316469
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.15424e6 0.976761 0.488381 0.872631i \(-0.337588\pi\)
0.488381 + 0.872631i \(0.337588\pi\)
\(588\) 0 0
\(589\) 9.40517e6 1.11707
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.18214e6 −0.254828 −0.127414 0.991850i \(-0.540668\pi\)
−0.127414 + 0.991850i \(0.540668\pi\)
\(594\) 0 0
\(595\) 5.63760e6 0.652833
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.85991e6 0.325675 0.162838 0.986653i \(-0.447935\pi\)
0.162838 + 0.986653i \(0.447935\pi\)
\(600\) 0 0
\(601\) −1.52613e7 −1.72347 −0.861737 0.507355i \(-0.830623\pi\)
−0.861737 + 0.507355i \(0.830623\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.35160e7 1.50128
\(606\) 0 0
\(607\) −2.37356e6 −0.261474 −0.130737 0.991417i \(-0.541734\pi\)
−0.130737 + 0.991417i \(0.541734\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.56845e6 −0.386702
\(612\) 0 0
\(613\) −4.21002e6 −0.452515 −0.226258 0.974068i \(-0.572649\pi\)
−0.226258 + 0.974068i \(0.572649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.19579e6 −0.337960 −0.168980 0.985619i \(-0.554047\pi\)
−0.168980 + 0.985619i \(0.554047\pi\)
\(618\) 0 0
\(619\) 1.30206e7 1.36586 0.682930 0.730484i \(-0.260706\pi\)
0.682930 + 0.730484i \(0.260706\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.54960e6 −0.263179
\(624\) 0 0
\(625\) −2.66820e6 −0.273224
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.93625e7 1.95135
\(630\) 0 0
\(631\) 1.44185e7 1.44161 0.720803 0.693140i \(-0.243773\pi\)
0.720803 + 0.693140i \(0.243773\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.37600e7 2.33837
\(636\) 0 0
\(637\) −5.25281e6 −0.512913
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.40822e6 −0.327629 −0.163815 0.986491i \(-0.552380\pi\)
−0.163815 + 0.986491i \(0.552380\pi\)
\(642\) 0 0
\(643\) −1.43017e7 −1.36414 −0.682070 0.731287i \(-0.738920\pi\)
−0.682070 + 0.731287i \(0.738920\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.59891e7 −1.50163 −0.750815 0.660512i \(-0.770339\pi\)
−0.750815 + 0.660512i \(0.770339\pi\)
\(648\) 0 0
\(649\) 505440. 0.0471040
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.83032e7 1.67974 0.839872 0.542785i \(-0.182630\pi\)
0.839872 + 0.542785i \(0.182630\pi\)
\(654\) 0 0
\(655\) 1.35924e7 1.23793
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.82724e6 −0.432997 −0.216499 0.976283i \(-0.569464\pi\)
−0.216499 + 0.976283i \(0.569464\pi\)
\(660\) 0 0
\(661\) −1.45127e7 −1.29195 −0.645973 0.763360i \(-0.723548\pi\)
−0.645973 + 0.763360i \(0.723548\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.60052e6 −0.403416
\(666\) 0 0
\(667\) −5.10106e6 −0.443962
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −94266.2 −0.00808257
\(672\) 0 0
\(673\) −5.23273e6 −0.445339 −0.222670 0.974894i \(-0.571477\pi\)
−0.222670 + 0.974894i \(0.571477\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.31889e6 −0.278305 −0.139153 0.990271i \(-0.544438\pi\)
−0.139153 + 0.990271i \(0.544438\pi\)
\(678\) 0 0
\(679\) −374593. −0.0311807
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 350257. 0.0287300 0.0143650 0.999897i \(-0.495427\pi\)
0.0143650 + 0.999897i \(0.495427\pi\)
\(684\) 0 0
\(685\) −2.39734e7 −1.95211
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.68993e6 −0.777629
\(690\) 0 0
\(691\) 9.62745e6 0.767037 0.383518 0.923533i \(-0.374712\pi\)
0.383518 + 0.923533i \(0.374712\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.61112e7 1.26522
\(696\) 0 0
\(697\) 3.42144e7 2.66764
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.75325e7 −1.34756 −0.673782 0.738930i \(-0.735332\pi\)
−0.673782 + 0.738930i \(0.735332\pi\)
\(702\) 0 0
\(703\) −1.58006e7 −1.20583
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.27330e6 0.246285
\(708\) 0 0
\(709\) 5.32158e6 0.397581 0.198790 0.980042i \(-0.436299\pi\)
0.198790 + 0.980042i \(0.436299\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.89016e7 −1.39243
\(714\) 0 0
\(715\) −2.55830e6 −0.187149
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.74700e7 −1.26029 −0.630146 0.776477i \(-0.717005\pi\)
−0.630146 + 0.776477i \(0.717005\pi\)
\(720\) 0 0
\(721\) −2.24759e6 −0.161019
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.56212e6 −0.463660
\(726\) 0 0
\(727\) 5.86973e6 0.411891 0.205945 0.978563i \(-0.433973\pi\)
0.205945 + 0.978563i \(0.433973\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.40379e7 −3.04813
\(732\) 0 0
\(733\) −5.60294e6 −0.385173 −0.192587 0.981280i \(-0.561688\pi\)
−0.192587 + 0.981280i \(0.561688\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.47405e6 0.371227
\(738\) 0 0
\(739\) 5.56792e6 0.375044 0.187522 0.982260i \(-0.439954\pi\)
0.187522 + 0.982260i \(0.439954\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.78484e6 0.251522 0.125761 0.992061i \(-0.459863\pi\)
0.125761 + 0.992061i \(0.459863\pi\)
\(744\) 0 0
\(745\) 3.06219e7 2.02135
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.24006e6 −0.211032
\(750\) 0 0
\(751\) 6.76657e6 0.437793 0.218897 0.975748i \(-0.429754\pi\)
0.218897 + 0.975748i \(0.429754\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.83018e7 2.44541
\(756\) 0 0
\(757\) 2.46970e7 1.56640 0.783202 0.621768i \(-0.213585\pi\)
0.783202 + 0.621768i \(0.213585\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.00870e7 1.88329 0.941644 0.336611i \(-0.109281\pi\)
0.941644 + 0.336611i \(0.109281\pi\)
\(762\) 0 0
\(763\) 513590. 0.0319378
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.88576e6 0.115744
\(768\) 0 0
\(769\) 3.25118e6 0.198256 0.0991278 0.995075i \(-0.468395\pi\)
0.0991278 + 0.995075i \(0.468395\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.30628e6 0.199017 0.0995087 0.995037i \(-0.468273\pi\)
0.0995087 + 0.995037i \(0.468273\pi\)
\(774\) 0 0
\(775\) −2.43154e7 −1.45421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.79204e7 −1.64846
\(780\) 0 0
\(781\) −4.09018e6 −0.239946
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.02624e6 0.117359
\(786\) 0 0
\(787\) −1.70156e7 −0.979286 −0.489643 0.871923i \(-0.662873\pi\)
−0.489643 + 0.871923i \(0.662873\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.29588e6 −0.414607
\(792\) 0 0
\(793\) −351701. −0.0198605
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.31267e7 0.731999 0.365999 0.930615i \(-0.380727\pi\)
0.365999 + 0.930615i \(0.380727\pi\)
\(798\) 0 0
\(799\) −2.39112e7 −1.32506
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.23968e6 −0.232030
\(804\) 0 0
\(805\) 9.24566e6 0.502862
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.90313e7 −1.55954 −0.779768 0.626068i \(-0.784663\pi\)
−0.779768 + 0.626068i \(0.784663\pi\)
\(810\) 0 0
\(811\) 2.70345e7 1.44333 0.721666 0.692241i \(-0.243377\pi\)
0.721666 + 0.692241i \(0.243377\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.69654e6 0.511355
\(816\) 0 0
\(817\) 3.59368e7 1.88358
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.14836e7 −1.11237 −0.556185 0.831059i \(-0.687735\pi\)
−0.556185 + 0.831059i \(0.687735\pi\)
\(822\) 0 0
\(823\) 2.46282e7 1.26745 0.633727 0.773557i \(-0.281524\pi\)
0.633727 + 0.773557i \(0.281524\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5.10933e6 0.259777 0.129888 0.991529i \(-0.458538\pi\)
0.129888 + 0.991529i \(0.458538\pi\)
\(828\) 0 0
\(829\) 3.04805e7 1.54041 0.770205 0.637797i \(-0.220154\pi\)
0.770205 + 0.637797i \(0.220154\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.51977e7 −1.75753
\(834\) 0 0
\(835\) 2.70838e7 1.34429
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.36807e7 0.670969 0.335485 0.942046i \(-0.391100\pi\)
0.335485 + 0.942046i \(0.391100\pi\)
\(840\) 0 0
\(841\) −1.85205e7 −0.902948
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.31964e7 1.11758
\(846\) 0 0
\(847\) 4.44498e6 0.212893
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.17545e7 1.50308
\(852\) 0 0
\(853\) 3.44079e7 1.61914 0.809572 0.587020i \(-0.199699\pi\)
0.809572 + 0.587020i \(0.199699\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.73555e7 1.27231 0.636155 0.771561i \(-0.280524\pi\)
0.636155 + 0.771561i \(0.280524\pi\)
\(858\) 0 0
\(859\) 5.37818e6 0.248687 0.124343 0.992239i \(-0.460318\pi\)
0.124343 + 0.992239i \(0.460318\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.64604e7 −1.20940 −0.604699 0.796454i \(-0.706707\pi\)
−0.604699 + 0.796454i \(0.706707\pi\)
\(864\) 0 0
\(865\) −373248. −0.0169612
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4.40723e6 −0.197978
\(870\) 0 0
\(871\) 2.04233e7 0.912181
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.90239e6 0.172310
\(876\) 0 0
\(877\) −1.77108e7 −0.777571 −0.388785 0.921328i \(-0.627105\pi\)
−0.388785 + 0.921328i \(0.627105\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.04035e7 1.31973 0.659864 0.751385i \(-0.270614\pi\)
0.659864 + 0.751385i \(0.270614\pi\)
\(882\) 0 0
\(883\) −2.93557e7 −1.26704 −0.633521 0.773726i \(-0.718391\pi\)
−0.633521 + 0.773726i \(0.718391\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.64563e6 −0.112907 −0.0564533 0.998405i \(-0.517979\pi\)
−0.0564533 + 0.998405i \(0.517979\pi\)
\(888\) 0 0
\(889\) 7.81388e6 0.331598
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.95126e7 0.818815
\(894\) 0 0
\(895\) 7.33588e7 3.06122
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.37622e6 0.304393
\(900\) 0 0
\(901\) −6.49296e7 −2.66459
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.88519e7 1.17099
\(906\) 0 0
\(907\) −2.07393e7 −0.837095 −0.418548 0.908195i \(-0.637461\pi\)
−0.418548 + 0.908195i \(0.637461\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.55091e7 1.81678 0.908390 0.418123i \(-0.137312\pi\)
0.908390 + 0.418123i \(0.137312\pi\)
\(912\) 0 0
\(913\) −5.08550e6 −0.201910
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.47010e6 0.175547
\(918\) 0 0
\(919\) −1.89012e7 −0.738247 −0.369123 0.929380i \(-0.620342\pi\)
−0.369123 + 0.929380i \(0.620342\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.52602e7 −0.589597
\(924\) 0 0
\(925\) 4.08497e7 1.56977
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.08391e7 1.17236 0.586181 0.810180i \(-0.300631\pi\)
0.586181 + 0.810180i \(0.300631\pi\)
\(930\) 0 0
\(931\) 2.87228e7 1.08606
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.71425e7 −0.641277
\(936\) 0 0
\(937\) −5.36296e6 −0.199552 −0.0997758 0.995010i \(-0.531813\pi\)
−0.0997758 + 0.995010i \(0.531813\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.76785e7 −1.38714 −0.693569 0.720390i \(-0.743963\pi\)
−0.693569 + 0.720390i \(0.743963\pi\)
\(942\) 0 0
\(943\) 5.61116e7 2.05482
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.96221e7 0.711001 0.355501 0.934676i \(-0.384310\pi\)
0.355501 + 0.934676i \(0.384310\pi\)
\(948\) 0 0
\(949\) −1.58180e7 −0.570146
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.36730e7 −0.487676 −0.243838 0.969816i \(-0.578407\pi\)
−0.243838 + 0.969816i \(0.578407\pi\)
\(954\) 0 0
\(955\) 4.13450e7 1.46695
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.88406e6 −0.276824
\(960\) 0 0
\(961\) −1.29717e6 −0.0453093
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.34240e7 −0.464048
\(966\) 0 0
\(967\) −3.63824e7 −1.25119 −0.625597 0.780146i \(-0.715145\pi\)
−0.625597 + 0.780146i \(0.715145\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 9.46886e6 0.322292 0.161146 0.986931i \(-0.448481\pi\)
0.161146 + 0.986931i \(0.448481\pi\)
\(972\) 0 0
\(973\) 5.29844e6 0.179418
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.59889e7 −1.20623 −0.603117 0.797653i \(-0.706075\pi\)
−0.603117 + 0.797653i \(0.706075\pi\)
\(978\) 0 0
\(979\) 7.75267e6 0.258520
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.60556e7 −0.860039 −0.430019 0.902820i \(-0.641493\pi\)
−0.430019 + 0.902820i \(0.641493\pi\)
\(984\) 0 0
\(985\) −5.76279e7 −1.89253
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.22222e7 −2.34790
\(990\) 0 0
\(991\) −1.92232e7 −0.621788 −0.310894 0.950445i \(-0.600628\pi\)
−0.310894 + 0.950445i \(0.600628\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.69561e7 −1.82382
\(996\) 0 0
\(997\) 2.93287e7 0.934448 0.467224 0.884139i \(-0.345254\pi\)
0.467224 + 0.884139i \(0.345254\pi\)
\(998\) 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 432.6.a.p.1.1 2
3.2 odd 2 inner 432.6.a.p.1.2 2
4.3 odd 2 108.6.a.d.1.1 2
12.11 even 2 108.6.a.d.1.2 yes 2
36.7 odd 6 324.6.e.e.109.2 4
36.11 even 6 324.6.e.e.109.1 4
36.23 even 6 324.6.e.e.217.1 4
36.31 odd 6 324.6.e.e.217.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.6.a.d.1.1 2 4.3 odd 2
108.6.a.d.1.2 yes 2 12.11 even 2
324.6.e.e.109.1 4 36.11 even 6
324.6.e.e.109.2 4 36.7 odd 6
324.6.e.e.217.1 4 36.23 even 6
324.6.e.e.217.2 4 36.31 odd 6
432.6.a.p.1.1 2 1.1 even 1 trivial
432.6.a.p.1.2 2 3.2 odd 2 inner