Properties

Label 1008.6.a.x.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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] = [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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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)
 
\(f(q)\) \(=\) \(q+54.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+54.0000 q^{5} -49.0000 q^{7} +216.000 q^{11} +998.000 q^{13} -1302.00 q^{17} -884.000 q^{19} -2268.00 q^{23} -209.000 q^{25} +1482.00 q^{29} -8360.00 q^{31} -2646.00 q^{35} -4714.00 q^{37} +9786.00 q^{41} -19436.0 q^{43} +22200.0 q^{47} +2401.00 q^{49} -26790.0 q^{53} +11664.0 q^{55} +28092.0 q^{59} -38866.0 q^{61} +53892.0 q^{65} -23948.0 q^{67} -20628.0 q^{71} +290.000 q^{73} -10584.0 q^{77} +99544.0 q^{79} +19308.0 q^{83} -70308.0 q^{85} -36390.0 q^{89} -48902.0 q^{91} -47736.0 q^{95} -79078.0 q^{97} +O(q^{100})\)

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
\(5\) 54.0000 0.965981 0.482991 0.875625i \(-0.339550\pi\)
0.482991 + 0.875625i \(0.339550\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 216.000 0.538235 0.269118 0.963107i \(-0.413268\pi\)
0.269118 + 0.963107i \(0.413268\pi\)
\(12\) 0 0
\(13\) 998.000 1.63784 0.818921 0.573906i \(-0.194572\pi\)
0.818921 + 0.573906i \(0.194572\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1302.00 −1.09267 −0.546335 0.837567i \(-0.683977\pi\)
−0.546335 + 0.837567i \(0.683977\pi\)
\(18\) 0 0
\(19\) −884.000 −0.561783 −0.280891 0.959740i \(-0.590630\pi\)
−0.280891 + 0.959740i \(0.590630\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2268.00 −0.893971 −0.446986 0.894541i \(-0.647502\pi\)
−0.446986 + 0.894541i \(0.647502\pi\)
\(24\) 0 0
\(25\) −209.000 −0.0668800
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1482.00 0.327230 0.163615 0.986524i \(-0.447685\pi\)
0.163615 + 0.986524i \(0.447685\pi\)
\(30\) 0 0
\(31\) −8360.00 −1.56244 −0.781218 0.624259i \(-0.785401\pi\)
−0.781218 + 0.624259i \(0.785401\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2646.00 −0.365107
\(36\) 0 0
\(37\) −4714.00 −0.566090 −0.283045 0.959107i \(-0.591345\pi\)
−0.283045 + 0.959107i \(0.591345\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9786.00 0.909171 0.454585 0.890703i \(-0.349787\pi\)
0.454585 + 0.890703i \(0.349787\pi\)
\(42\) 0 0
\(43\) −19436.0 −1.60301 −0.801504 0.597989i \(-0.795967\pi\)
−0.801504 + 0.597989i \(0.795967\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 22200.0 1.46591 0.732957 0.680275i \(-0.238140\pi\)
0.732957 + 0.680275i \(0.238140\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −26790.0 −1.31004 −0.655018 0.755614i \(-0.727339\pi\)
−0.655018 + 0.755614i \(0.727339\pi\)
\(54\) 0 0
\(55\) 11664.0 0.519925
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 28092.0 1.05064 0.525318 0.850906i \(-0.323946\pi\)
0.525318 + 0.850906i \(0.323946\pi\)
\(60\) 0 0
\(61\) −38866.0 −1.33735 −0.668675 0.743555i \(-0.733138\pi\)
−0.668675 + 0.743555i \(0.733138\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 53892.0 1.58213
\(66\) 0 0
\(67\) −23948.0 −0.651752 −0.325876 0.945413i \(-0.605659\pi\)
−0.325876 + 0.945413i \(0.605659\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −20628.0 −0.485636 −0.242818 0.970072i \(-0.578072\pi\)
−0.242818 + 0.970072i \(0.578072\pi\)
\(72\) 0 0
\(73\) 290.000 0.00636929 0.00318464 0.999995i \(-0.498986\pi\)
0.00318464 + 0.999995i \(0.498986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10584.0 −0.203434
\(78\) 0 0
\(79\) 99544.0 1.79452 0.897258 0.441506i \(-0.145556\pi\)
0.897258 + 0.441506i \(0.145556\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 19308.0 0.307639 0.153820 0.988099i \(-0.450842\pi\)
0.153820 + 0.988099i \(0.450842\pi\)
\(84\) 0 0
\(85\) −70308.0 −1.05550
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −36390.0 −0.486975 −0.243488 0.969904i \(-0.578292\pi\)
−0.243488 + 0.969904i \(0.578292\pi\)
\(90\) 0 0
\(91\) −48902.0 −0.619046
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −47736.0 −0.542671
\(96\) 0 0
\(97\) −79078.0 −0.853348 −0.426674 0.904405i \(-0.640315\pi\)
−0.426674 + 0.904405i \(0.640315\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −184626. −1.80090 −0.900450 0.434960i \(-0.856762\pi\)
−0.900450 + 0.434960i \(0.856762\pi\)
\(102\) 0 0
\(103\) −64592.0 −0.599909 −0.299955 0.953953i \(-0.596972\pi\)
−0.299955 + 0.953953i \(0.596972\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 149592. 1.26313 0.631566 0.775322i \(-0.282412\pi\)
0.631566 + 0.775322i \(0.282412\pi\)
\(108\) 0 0
\(109\) −63826.0 −0.514555 −0.257277 0.966338i \(-0.582825\pi\)
−0.257277 + 0.966338i \(0.582825\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 71022.0 0.523235 0.261618 0.965172i \(-0.415744\pi\)
0.261618 + 0.965172i \(0.415744\pi\)
\(114\) 0 0
\(115\) −122472. −0.863559
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 63798.0 0.412990
\(120\) 0 0
\(121\) −114395. −0.710303
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −180036. −1.03059
\(126\) 0 0
\(127\) −269624. −1.48337 −0.741685 0.670749i \(-0.765973\pi\)
−0.741685 + 0.670749i \(0.765973\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 81180.0 0.413305 0.206653 0.978414i \(-0.433743\pi\)
0.206653 + 0.978414i \(0.433743\pi\)
\(132\) 0 0
\(133\) 43316.0 0.212334
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 260910. 1.18765 0.593826 0.804593i \(-0.297617\pi\)
0.593826 + 0.804593i \(0.297617\pi\)
\(138\) 0 0
\(139\) 297964. 1.30806 0.654029 0.756470i \(-0.273078\pi\)
0.654029 + 0.756470i \(0.273078\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 215568. 0.881544
\(144\) 0 0
\(145\) 80028.0 0.316098
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 398970. 1.47223 0.736113 0.676859i \(-0.236659\pi\)
0.736113 + 0.676859i \(0.236659\pi\)
\(150\) 0 0
\(151\) 224968. 0.802931 0.401466 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −451440. −1.50928
\(156\) 0 0
\(157\) −233218. −0.755115 −0.377557 0.925986i \(-0.623236\pi\)
−0.377557 + 0.925986i \(0.623236\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 111132. 0.337889
\(162\) 0 0
\(163\) −466220. −1.37443 −0.687214 0.726455i \(-0.741166\pi\)
−0.687214 + 0.726455i \(0.741166\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −100848. −0.279818 −0.139909 0.990164i \(-0.544681\pi\)
−0.139909 + 0.990164i \(0.544681\pi\)
\(168\) 0 0
\(169\) 624711. 1.68253
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 668838. 1.69905 0.849524 0.527550i \(-0.176889\pi\)
0.849524 + 0.527550i \(0.176889\pi\)
\(174\) 0 0
\(175\) 10241.0 0.0252783
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −614856. −1.43430 −0.717151 0.696917i \(-0.754554\pi\)
−0.717151 + 0.696917i \(0.754554\pi\)
\(180\) 0 0
\(181\) 540686. 1.22673 0.613365 0.789800i \(-0.289816\pi\)
0.613365 + 0.789800i \(0.289816\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −254556. −0.546832
\(186\) 0 0
\(187\) −281232. −0.588113
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −41916.0 −0.0831374 −0.0415687 0.999136i \(-0.513236\pi\)
−0.0415687 + 0.999136i \(0.513236\pi\)
\(192\) 0 0
\(193\) −533998. −1.03192 −0.515960 0.856612i \(-0.672565\pi\)
−0.515960 + 0.856612i \(0.672565\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −824886. −1.51436 −0.757179 0.653208i \(-0.773423\pi\)
−0.757179 + 0.653208i \(0.773423\pi\)
\(198\) 0 0
\(199\) 399544. 0.715207 0.357604 0.933873i \(-0.383594\pi\)
0.357604 + 0.933873i \(0.383594\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −72618.0 −0.123681
\(204\) 0 0
\(205\) 528444. 0.878242
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −190944. −0.302371
\(210\) 0 0
\(211\) −868868. −1.34353 −0.671765 0.740764i \(-0.734464\pi\)
−0.671765 + 0.740764i \(0.734464\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.04954e6 −1.54848
\(216\) 0 0
\(217\) 409640. 0.590545
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.29940e6 −1.78962
\(222\) 0 0
\(223\) 626656. 0.843853 0.421927 0.906630i \(-0.361354\pi\)
0.421927 + 0.906630i \(0.361354\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −450396. −0.580136 −0.290068 0.957006i \(-0.593678\pi\)
−0.290068 + 0.957006i \(0.593678\pi\)
\(228\) 0 0
\(229\) −1.06453e6 −1.34143 −0.670717 0.741714i \(-0.734013\pi\)
−0.670717 + 0.741714i \(0.734013\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.43618e6 −1.73308 −0.866540 0.499108i \(-0.833661\pi\)
−0.866540 + 0.499108i \(0.833661\pi\)
\(234\) 0 0
\(235\) 1.19880e6 1.41605
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −997860. −1.12999 −0.564995 0.825094i \(-0.691122\pi\)
−0.564995 + 0.825094i \(0.691122\pi\)
\(240\) 0 0
\(241\) −227974. −0.252838 −0.126419 0.991977i \(-0.540348\pi\)
−0.126419 + 0.991977i \(0.540348\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 129654. 0.137997
\(246\) 0 0
\(247\) −882232. −0.920111
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.51657e6 1.51942 0.759712 0.650260i \(-0.225340\pi\)
0.759712 + 0.650260i \(0.225340\pi\)
\(252\) 0 0
\(253\) −489888. −0.481167
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −455886. −0.430550 −0.215275 0.976553i \(-0.569065\pi\)
−0.215275 + 0.976553i \(0.569065\pi\)
\(258\) 0 0
\(259\) 230986. 0.213962
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −752652. −0.670973 −0.335486 0.942045i \(-0.608901\pi\)
−0.335486 + 0.942045i \(0.608901\pi\)
\(264\) 0 0
\(265\) −1.44666e6 −1.26547
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −143682. −0.121066 −0.0605329 0.998166i \(-0.519280\pi\)
−0.0605329 + 0.998166i \(0.519280\pi\)
\(270\) 0 0
\(271\) −757496. −0.626552 −0.313276 0.949662i \(-0.601426\pi\)
−0.313276 + 0.949662i \(0.601426\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −45144.0 −0.0359972
\(276\) 0 0
\(277\) −1.16214e6 −0.910035 −0.455018 0.890482i \(-0.650367\pi\)
−0.455018 + 0.890482i \(0.650367\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 414366. 0.313053 0.156527 0.987674i \(-0.449970\pi\)
0.156527 + 0.987674i \(0.449970\pi\)
\(282\) 0 0
\(283\) −120428. −0.0893843 −0.0446922 0.999001i \(-0.514231\pi\)
−0.0446922 + 0.999001i \(0.514231\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −479514. −0.343634
\(288\) 0 0
\(289\) 275347. 0.193926
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.20159e6 −1.49819 −0.749094 0.662463i \(-0.769511\pi\)
−0.749094 + 0.662463i \(0.769511\pi\)
\(294\) 0 0
\(295\) 1.51697e6 1.01490
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.26346e6 −1.46418
\(300\) 0 0
\(301\) 952364. 0.605880
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.09876e6 −1.29186
\(306\) 0 0
\(307\) −110900. −0.0671561 −0.0335781 0.999436i \(-0.510690\pi\)
−0.0335781 + 0.999436i \(0.510690\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −910608. −0.533864 −0.266932 0.963715i \(-0.586010\pi\)
−0.266932 + 0.963715i \(0.586010\pi\)
\(312\) 0 0
\(313\) 3.12247e6 1.80152 0.900758 0.434322i \(-0.143012\pi\)
0.900758 + 0.434322i \(0.143012\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.76688e6 1.54647 0.773237 0.634117i \(-0.218636\pi\)
0.773237 + 0.634117i \(0.218636\pi\)
\(318\) 0 0
\(319\) 320112. 0.176127
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.15097e6 0.613842
\(324\) 0 0
\(325\) −208582. −0.109539
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.08780e6 −0.554063
\(330\) 0 0
\(331\) −3.22257e6 −1.61671 −0.808356 0.588694i \(-0.799642\pi\)
−0.808356 + 0.588694i \(0.799642\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.29319e6 −0.629580
\(336\) 0 0
\(337\) 1.63306e6 0.783298 0.391649 0.920115i \(-0.371905\pi\)
0.391649 + 0.920115i \(0.371905\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.80576e6 −0.840958
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.03642e6 0.462073 0.231036 0.972945i \(-0.425788\pi\)
0.231036 + 0.972945i \(0.425788\pi\)
\(348\) 0 0
\(349\) −4.22999e6 −1.85898 −0.929491 0.368844i \(-0.879754\pi\)
−0.929491 + 0.368844i \(0.879754\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −238806. −0.102002 −0.0510010 0.998699i \(-0.516241\pi\)
−0.0510010 + 0.998699i \(0.516241\pi\)
\(354\) 0 0
\(355\) −1.11391e6 −0.469116
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.66428e6 −1.09105 −0.545523 0.838096i \(-0.683669\pi\)
−0.545523 + 0.838096i \(0.683669\pi\)
\(360\) 0 0
\(361\) −1.69464e6 −0.684400
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15660.0 0.00615261
\(366\) 0 0
\(367\) 1.71083e6 0.663044 0.331522 0.943448i \(-0.392438\pi\)
0.331522 + 0.943448i \(0.392438\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.31271e6 0.495147
\(372\) 0 0
\(373\) −3.96649e6 −1.47616 −0.738081 0.674712i \(-0.764268\pi\)
−0.738081 + 0.674712i \(0.764268\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.47904e6 0.535951
\(378\) 0 0
\(379\) −828668. −0.296335 −0.148167 0.988962i \(-0.547337\pi\)
−0.148167 + 0.988962i \(0.547337\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.55686e6 −0.890657 −0.445329 0.895367i \(-0.646913\pi\)
−0.445329 + 0.895367i \(0.646913\pi\)
\(384\) 0 0
\(385\) −571536. −0.196513
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.91785e6 −0.977664 −0.488832 0.872378i \(-0.662577\pi\)
−0.488832 + 0.872378i \(0.662577\pi\)
\(390\) 0 0
\(391\) 2.95294e6 0.976815
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5.37538e6 1.73347
\(396\) 0 0
\(397\) 2.50715e6 0.798370 0.399185 0.916870i \(-0.369293\pi\)
0.399185 + 0.916870i \(0.369293\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −990666. −0.307657 −0.153828 0.988098i \(-0.549160\pi\)
−0.153828 + 0.988098i \(0.549160\pi\)
\(402\) 0 0
\(403\) −8.34328e6 −2.55902
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.01822e6 −0.304689
\(408\) 0 0
\(409\) 4.51824e6 1.33555 0.667777 0.744362i \(-0.267246\pi\)
0.667777 + 0.744362i \(0.267246\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.37651e6 −0.397103
\(414\) 0 0
\(415\) 1.04263e6 0.297174
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 605220. 0.168414 0.0842070 0.996448i \(-0.473164\pi\)
0.0842070 + 0.996448i \(0.473164\pi\)
\(420\) 0 0
\(421\) 4.49893e6 1.23710 0.618549 0.785746i \(-0.287721\pi\)
0.618549 + 0.785746i \(0.287721\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 272118. 0.0730777
\(426\) 0 0
\(427\) 1.90443e6 0.505471
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.37594e6 1.39400 0.696998 0.717074i \(-0.254519\pi\)
0.696998 + 0.717074i \(0.254519\pi\)
\(432\) 0 0
\(433\) −1.98561e6 −0.508950 −0.254475 0.967079i \(-0.581903\pi\)
−0.254475 + 0.967079i \(0.581903\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.00491e6 0.502217
\(438\) 0 0
\(439\) −3.38727e6 −0.838859 −0.419429 0.907788i \(-0.637770\pi\)
−0.419429 + 0.907788i \(0.637770\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.14094e6 0.518318 0.259159 0.965835i \(-0.416555\pi\)
0.259159 + 0.965835i \(0.416555\pi\)
\(444\) 0 0
\(445\) −1.96506e6 −0.470409
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.97808e6 1.63350 0.816752 0.576990i \(-0.195773\pi\)
0.816752 + 0.576990i \(0.195773\pi\)
\(450\) 0 0
\(451\) 2.11378e6 0.489348
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.64071e6 −0.597987
\(456\) 0 0
\(457\) −5.17999e6 −1.16021 −0.580107 0.814540i \(-0.696989\pi\)
−0.580107 + 0.814540i \(0.696989\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7.83001e6 1.71597 0.857985 0.513674i \(-0.171716\pi\)
0.857985 + 0.513674i \(0.171716\pi\)
\(462\) 0 0
\(463\) −165320. −0.0358404 −0.0179202 0.999839i \(-0.505704\pi\)
−0.0179202 + 0.999839i \(0.505704\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.79329e6 −0.380504 −0.190252 0.981735i \(-0.560930\pi\)
−0.190252 + 0.981735i \(0.560930\pi\)
\(468\) 0 0
\(469\) 1.17345e6 0.246339
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.19818e6 −0.862795
\(474\) 0 0
\(475\) 184756. 0.0375720
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.59657e6 −1.31365 −0.656824 0.754044i \(-0.728101\pi\)
−0.656824 + 0.754044i \(0.728101\pi\)
\(480\) 0 0
\(481\) −4.70457e6 −0.927166
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.27021e6 −0.824319
\(486\) 0 0
\(487\) 5.97393e6 1.14140 0.570700 0.821159i \(-0.306672\pi\)
0.570700 + 0.821159i \(0.306672\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 381264. 0.0713710 0.0356855 0.999363i \(-0.488639\pi\)
0.0356855 + 0.999363i \(0.488639\pi\)
\(492\) 0 0
\(493\) −1.92956e6 −0.357554
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.01077e6 0.183553
\(498\) 0 0
\(499\) −1.54351e6 −0.277497 −0.138748 0.990328i \(-0.544308\pi\)
−0.138748 + 0.990328i \(0.544308\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.02300e6 −0.708974 −0.354487 0.935061i \(-0.615344\pi\)
−0.354487 + 0.935061i \(0.615344\pi\)
\(504\) 0 0
\(505\) −9.96980e6 −1.73964
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.94715e6 0.333123 0.166562 0.986031i \(-0.446734\pi\)
0.166562 + 0.986031i \(0.446734\pi\)
\(510\) 0 0
\(511\) −14210.0 −0.00240736
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.48797e6 −0.579501
\(516\) 0 0
\(517\) 4.79520e6 0.789006
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.38569e6 −1.19206 −0.596028 0.802963i \(-0.703255\pi\)
−0.596028 + 0.802963i \(0.703255\pi\)
\(522\) 0 0
\(523\) 329740. 0.0527130 0.0263565 0.999653i \(-0.491610\pi\)
0.0263565 + 0.999653i \(0.491610\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.08847e7 1.70722
\(528\) 0 0
\(529\) −1.29252e6 −0.200816
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.76643e6 1.48908
\(534\) 0 0
\(535\) 8.07797e6 1.22016
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 518616. 0.0768907
\(540\) 0 0
\(541\) 87086.0 0.0127925 0.00639625 0.999980i \(-0.497964\pi\)
0.00639625 + 0.999980i \(0.497964\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.44660e6 −0.497050
\(546\) 0 0
\(547\) −6.91531e6 −0.988196 −0.494098 0.869406i \(-0.664502\pi\)
−0.494098 + 0.869406i \(0.664502\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.31009e6 −0.183832
\(552\) 0 0
\(553\) −4.87766e6 −0.678263
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.52258e6 0.207942 0.103971 0.994580i \(-0.466845\pi\)
0.103971 + 0.994580i \(0.466845\pi\)
\(558\) 0 0
\(559\) −1.93971e7 −2.62548
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.86462e6 −1.04570 −0.522850 0.852425i \(-0.675131\pi\)
−0.522850 + 0.852425i \(0.675131\pi\)
\(564\) 0 0
\(565\) 3.83519e6 0.505435
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.46321e6 0.189464 0.0947321 0.995503i \(-0.469801\pi\)
0.0947321 + 0.995503i \(0.469801\pi\)
\(570\) 0 0
\(571\) −9.19855e6 −1.18067 −0.590336 0.807158i \(-0.701005\pi\)
−0.590336 + 0.807158i \(0.701005\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 474012. 0.0597888
\(576\) 0 0
\(577\) 3.28939e6 0.411317 0.205658 0.978624i \(-0.434066\pi\)
0.205658 + 0.978624i \(0.434066\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −946092. −0.116277
\(582\) 0 0
\(583\) −5.78664e6 −0.705107
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.12929e6 0.614416 0.307208 0.951642i \(-0.400605\pi\)
0.307208 + 0.951642i \(0.400605\pi\)
\(588\) 0 0
\(589\) 7.39024e6 0.877749
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.75433e6 0.321647 0.160823 0.986983i \(-0.448585\pi\)
0.160823 + 0.986983i \(0.448585\pi\)
\(594\) 0 0
\(595\) 3.44509e6 0.398941
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.88616e6 −1.12580 −0.562899 0.826525i \(-0.690314\pi\)
−0.562899 + 0.826525i \(0.690314\pi\)
\(600\) 0 0
\(601\) 1.37039e7 1.54760 0.773798 0.633433i \(-0.218355\pi\)
0.773798 + 0.633433i \(0.218355\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.17733e6 −0.686139
\(606\) 0 0
\(607\) 7.85310e6 0.865107 0.432553 0.901608i \(-0.357613\pi\)
0.432553 + 0.901608i \(0.357613\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.21556e7 2.40094
\(612\) 0 0
\(613\) 1.46977e7 1.57978 0.789892 0.613246i \(-0.210136\pi\)
0.789892 + 0.613246i \(0.210136\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.28370e6 −0.664511 −0.332256 0.943189i \(-0.607810\pi\)
−0.332256 + 0.943189i \(0.607810\pi\)
\(618\) 0 0
\(619\) 2.26692e6 0.237799 0.118900 0.992906i \(-0.462063\pi\)
0.118900 + 0.992906i \(0.462063\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.78311e6 0.184059
\(624\) 0 0
\(625\) −9.06882e6 −0.928647
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.13763e6 0.618549
\(630\) 0 0
\(631\) 1.17477e7 1.17457 0.587285 0.809380i \(-0.300197\pi\)
0.587285 + 0.809380i \(0.300197\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.45597e7 −1.43291
\(636\) 0 0
\(637\) 2.39620e6 0.233978
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.93231e6 −0.570268 −0.285134 0.958488i \(-0.592038\pi\)
−0.285134 + 0.958488i \(0.592038\pi\)
\(642\) 0 0
\(643\) 6.94443e6 0.662383 0.331191 0.943564i \(-0.392549\pi\)
0.331191 + 0.943564i \(0.392549\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.97050e6 −0.466809 −0.233404 0.972380i \(-0.574987\pi\)
−0.233404 + 0.972380i \(0.574987\pi\)
\(648\) 0 0
\(649\) 6.06787e6 0.565490
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.83355e7 1.68271 0.841354 0.540484i \(-0.181759\pi\)
0.841354 + 0.540484i \(0.181759\pi\)
\(654\) 0 0
\(655\) 4.38372e6 0.399245
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.01402e6 0.808546 0.404273 0.914638i \(-0.367525\pi\)
0.404273 + 0.914638i \(0.367525\pi\)
\(660\) 0 0
\(661\) 699398. 0.0622617 0.0311308 0.999515i \(-0.490089\pi\)
0.0311308 + 0.999515i \(0.490089\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.33906e6 0.205111
\(666\) 0 0
\(667\) −3.36118e6 −0.292534
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.39506e6 −0.719809
\(672\) 0 0
\(673\) −5.80603e6 −0.494130 −0.247065 0.968999i \(-0.579466\pi\)
−0.247065 + 0.968999i \(0.579466\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −985074. −0.0826033 −0.0413016 0.999147i \(-0.513150\pi\)
−0.0413016 + 0.999147i \(0.513150\pi\)
\(678\) 0 0
\(679\) 3.87482e6 0.322535
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.88208e7 −1.54379 −0.771894 0.635752i \(-0.780690\pi\)
−0.771894 + 0.635752i \(0.780690\pi\)
\(684\) 0 0
\(685\) 1.40891e7 1.14725
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.67364e7 −2.14563
\(690\) 0 0
\(691\) 1.93385e7 1.54073 0.770366 0.637601i \(-0.220073\pi\)
0.770366 + 0.637601i \(0.220073\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.60901e7 1.26356
\(696\) 0 0
\(697\) −1.27414e7 −0.993423
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.41489e6 0.108750 0.0543748 0.998521i \(-0.482683\pi\)
0.0543748 + 0.998521i \(0.482683\pi\)
\(702\) 0 0
\(703\) 4.16718e6 0.318019
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.04667e6 0.680676
\(708\) 0 0
\(709\) −754906. −0.0563998 −0.0281999 0.999602i \(-0.508977\pi\)
−0.0281999 + 0.999602i \(0.508977\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.89605e7 1.39677
\(714\) 0 0
\(715\) 1.16407e7 0.851555
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.08854e6 0.0785279 0.0392639 0.999229i \(-0.487499\pi\)
0.0392639 + 0.999229i \(0.487499\pi\)
\(720\) 0 0
\(721\) 3.16501e6 0.226744
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −309738. −0.0218851
\(726\) 0 0
\(727\) 755392. 0.0530074 0.0265037 0.999649i \(-0.491563\pi\)
0.0265037 + 0.999649i \(0.491563\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.53057e7 1.75156
\(732\) 0 0
\(733\) 1.56369e6 0.107495 0.0537477 0.998555i \(-0.482883\pi\)
0.0537477 + 0.998555i \(0.482883\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.17277e6 −0.350796
\(738\) 0 0
\(739\) 1.05544e7 0.710922 0.355461 0.934691i \(-0.384324\pi\)
0.355461 + 0.934691i \(0.384324\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.73678e7 1.15418 0.577088 0.816682i \(-0.304189\pi\)
0.577088 + 0.816682i \(0.304189\pi\)
\(744\) 0 0
\(745\) 2.15444e7 1.42214
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7.33001e6 −0.477419
\(750\) 0 0
\(751\) 2.80181e7 1.81276 0.906378 0.422467i \(-0.138836\pi\)
0.906378 + 0.422467i \(0.138836\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.21483e7 0.775617
\(756\) 0 0
\(757\) −1.01979e7 −0.646801 −0.323401 0.946262i \(-0.604826\pi\)
−0.323401 + 0.946262i \(0.604826\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.57535e6 −0.161204 −0.0806018 0.996746i \(-0.525684\pi\)
−0.0806018 + 0.996746i \(0.525684\pi\)
\(762\) 0 0
\(763\) 3.12747e6 0.194483
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.80358e7 1.72078
\(768\) 0 0
\(769\) 971234. 0.0592254 0.0296127 0.999561i \(-0.490573\pi\)
0.0296127 + 0.999561i \(0.490573\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.72921e7 1.04088 0.520439 0.853899i \(-0.325768\pi\)
0.520439 + 0.853899i \(0.325768\pi\)
\(774\) 0 0
\(775\) 1.74724e6 0.104496
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.65082e6 −0.510756
\(780\) 0 0
\(781\) −4.45565e6 −0.261387
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.25938e7 −0.729427
\(786\) 0 0
\(787\) 1.65515e7 0.952576 0.476288 0.879289i \(-0.341982\pi\)
0.476288 + 0.879289i \(0.341982\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.48008e6 −0.197764
\(792\) 0 0
\(793\) −3.87883e7 −2.19037
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.91057e6 −0.162305 −0.0811526 0.996702i \(-0.525860\pi\)
−0.0811526 + 0.996702i \(0.525860\pi\)
\(798\) 0 0
\(799\) −2.89044e7 −1.60176
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 62640.0 0.00342817
\(804\) 0 0
\(805\) 6.00113e6 0.326395
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.16252e7 0.624496 0.312248 0.950001i \(-0.398918\pi\)
0.312248 + 0.950001i \(0.398918\pi\)
\(810\) 0 0
\(811\) −3.09020e7 −1.64981 −0.824906 0.565270i \(-0.808772\pi\)
−0.824906 + 0.565270i \(0.808772\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.51759e7 −1.32767
\(816\) 0 0
\(817\) 1.71814e7 0.900542
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.22870e7 1.15397 0.576984 0.816755i \(-0.304229\pi\)
0.576984 + 0.816755i \(0.304229\pi\)
\(822\) 0 0
\(823\) 1.64895e7 0.848610 0.424305 0.905519i \(-0.360518\pi\)
0.424305 + 0.905519i \(0.360518\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.37457e7 −1.20732 −0.603658 0.797244i \(-0.706291\pi\)
−0.603658 + 0.797244i \(0.706291\pi\)
\(828\) 0 0
\(829\) 2.60865e7 1.31835 0.659173 0.751991i \(-0.270906\pi\)
0.659173 + 0.751991i \(0.270906\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.12610e6 −0.156096
\(834\) 0 0
\(835\) −5.44579e6 −0.270299
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.00872e7 0.494729 0.247365 0.968922i \(-0.420435\pi\)
0.247365 + 0.968922i \(0.420435\pi\)
\(840\) 0 0
\(841\) −1.83148e7 −0.892920
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.37344e7 1.62529
\(846\) 0 0
\(847\) 5.60536e6 0.268469
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.06914e7 0.506068
\(852\) 0 0
\(853\) −2.43630e7 −1.14646 −0.573229 0.819395i \(-0.694309\pi\)
−0.573229 + 0.819395i \(0.694309\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.45612e6 −0.114234 −0.0571172 0.998367i \(-0.518191\pi\)
−0.0571172 + 0.998367i \(0.518191\pi\)
\(858\) 0 0
\(859\) −8.62982e6 −0.399042 −0.199521 0.979894i \(-0.563939\pi\)
−0.199521 + 0.979894i \(0.563939\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.05199e7 0.480824 0.240412 0.970671i \(-0.422717\pi\)
0.240412 + 0.970671i \(0.422717\pi\)
\(864\) 0 0
\(865\) 3.61173e7 1.64125
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.15015e7 0.965872
\(870\) 0 0
\(871\) −2.39001e7 −1.06747
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.82176e6 0.389525
\(876\) 0 0
\(877\) −1.14540e7 −0.502872 −0.251436 0.967874i \(-0.580903\pi\)
−0.251436 + 0.967874i \(0.580903\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.18134e7 0.512786 0.256393 0.966573i \(-0.417466\pi\)
0.256393 + 0.966573i \(0.417466\pi\)
\(882\) 0 0
\(883\) −4.63221e6 −0.199934 −0.0999670 0.994991i \(-0.531874\pi\)
−0.0999670 + 0.994991i \(0.531874\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4.47728e7 1.91075 0.955377 0.295388i \(-0.0954490\pi\)
0.955377 + 0.295388i \(0.0954490\pi\)
\(888\) 0 0
\(889\) 1.32116e7 0.560661
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.96248e7 −0.823525
\(894\) 0 0
\(895\) −3.32022e7 −1.38551
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.23895e7 −0.511276
\(900\) 0 0
\(901\) 3.48806e7 1.43144
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.91970e7 1.18500
\(906\) 0 0
\(907\) 2.08357e7 0.840986 0.420493 0.907296i \(-0.361857\pi\)
0.420493 + 0.907296i \(0.361857\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 5.27869e6 0.210732 0.105366 0.994434i \(-0.466399\pi\)
0.105366 + 0.994434i \(0.466399\pi\)
\(912\) 0 0
\(913\) 4.17053e6 0.165582
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.97782e6 −0.156215
\(918\) 0 0
\(919\) −2.51286e7 −0.981477 −0.490738 0.871307i \(-0.663273\pi\)
−0.490738 + 0.871307i \(0.663273\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.05867e7 −0.795396
\(924\) 0 0
\(925\) 985226. 0.0378601
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.38042e7 −0.524774 −0.262387 0.964963i \(-0.584510\pi\)
−0.262387 + 0.964963i \(0.584510\pi\)
\(930\) 0 0
\(931\) −2.12248e6 −0.0802547
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.51865e7 −0.568106
\(936\) 0 0
\(937\) −4.73307e7 −1.76114 −0.880570 0.473915i \(-0.842840\pi\)
−0.880570 + 0.473915i \(0.842840\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.25570e7 1.19859 0.599295 0.800528i \(-0.295448\pi\)
0.599295 + 0.800528i \(0.295448\pi\)
\(942\) 0 0
\(943\) −2.21946e7 −0.812773
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.27117e6 −0.190999 −0.0954997 0.995429i \(-0.530445\pi\)
−0.0954997 + 0.995429i \(0.530445\pi\)
\(948\) 0 0
\(949\) 289420. 0.0104319
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −8.20579e6 −0.292677 −0.146338 0.989235i \(-0.546749\pi\)
−0.146338 + 0.989235i \(0.546749\pi\)
\(954\) 0 0
\(955\) −2.26346e6 −0.0803092
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.27846e7 −0.448890
\(960\) 0 0
\(961\) 4.12604e7 1.44120
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.88359e7 −0.996816
\(966\) 0 0
\(967\) 1.18118e7 0.406210 0.203105 0.979157i \(-0.434897\pi\)
0.203105 + 0.979157i \(0.434897\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.67702e7 −1.25155 −0.625774 0.780004i \(-0.715217\pi\)
−0.625774 + 0.780004i \(0.715217\pi\)
\(972\) 0 0
\(973\) −1.46002e7 −0.494399
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.85183e7 0.620674 0.310337 0.950627i \(-0.399558\pi\)
0.310337 + 0.950627i \(0.399558\pi\)
\(978\) 0 0
\(979\) −7.86024e6 −0.262107
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.72169e7 0.898370 0.449185 0.893439i \(-0.351714\pi\)
0.449185 + 0.893439i \(0.351714\pi\)
\(984\) 0 0
\(985\) −4.45438e7 −1.46284
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.40808e7 1.43304
\(990\) 0 0
\(991\) −1.63398e7 −0.528522 −0.264261 0.964451i \(-0.585128\pi\)
−0.264261 + 0.964451i \(0.585128\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.15754e7 0.690877
\(996\) 0 0
\(997\) −3.02062e7 −0.962406 −0.481203 0.876609i \(-0.659800\pi\)
−0.481203 + 0.876609i \(0.659800\pi\)
\(998\) 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.x.1.1 1
3.2 odd 2 336.6.a.j.1.1 1
4.3 odd 2 126.6.a.k.1.1 1
12.11 even 2 42.6.a.a.1.1 1
28.27 even 2 882.6.a.o.1.1 1
60.23 odd 4 1050.6.g.o.799.2 2
60.47 odd 4 1050.6.g.o.799.1 2
60.59 even 2 1050.6.a.n.1.1 1
84.11 even 6 294.6.e.r.79.1 2
84.23 even 6 294.6.e.r.67.1 2
84.47 odd 6 294.6.e.h.67.1 2
84.59 odd 6 294.6.e.h.79.1 2
84.83 odd 2 294.6.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.a.1.1 1 12.11 even 2
126.6.a.k.1.1 1 4.3 odd 2
294.6.a.h.1.1 1 84.83 odd 2
294.6.e.h.67.1 2 84.47 odd 6
294.6.e.h.79.1 2 84.59 odd 6
294.6.e.r.67.1 2 84.23 even 6
294.6.e.r.79.1 2 84.11 even 6
336.6.a.j.1.1 1 3.2 odd 2
882.6.a.o.1.1 1 28.27 even 2
1008.6.a.x.1.1 1 1.1 even 1 trivial
1050.6.a.n.1.1 1 60.59 even 2
1050.6.g.o.799.1 2 60.47 odd 4
1050.6.g.o.799.2 2 60.23 odd 4