Properties

Label 1008.6.a.bi.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(2\)
Coefficient field: \(\Q(\sqrt{193}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(7.44622\) 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)
 
\(f(q)\) \(=\) \(q-90.4622 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-90.4622 q^{5} +49.0000 q^{7} -552.494 q^{11} -593.172 q^{13} +1422.19 q^{17} -318.997 q^{19} +659.954 q^{23} +5058.41 q^{25} +8185.27 q^{29} +9598.03 q^{31} -4432.65 q^{35} +5180.56 q^{37} +2192.46 q^{41} -7458.29 q^{43} -19561.8 q^{47} +2401.00 q^{49} -36569.6 q^{53} +49979.9 q^{55} +16361.7 q^{59} -10893.1 q^{61} +53659.6 q^{65} -8035.91 q^{67} +55983.3 q^{71} -77752.5 q^{73} -27072.2 q^{77} +3208.43 q^{79} +76626.9 q^{83} -128655. q^{85} +84288.6 q^{89} -29065.4 q^{91} +28857.2 q^{95} +101273. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 42 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 42 q^{5} + 98 q^{7} - 716 q^{11} - 714 q^{13} + 1344 q^{17} + 1946 q^{19} - 1792 q^{23} + 4282 q^{25} + 1200 q^{29} + 6804 q^{31} - 2058 q^{35} + 14640 q^{37} - 7896 q^{41} - 524 q^{43} - 18396 q^{47} + 4802 q^{49} - 45132 q^{53} + 42056 q^{55} + 22582 q^{59} - 52822 q^{61} + 47804 q^{65} - 9848 q^{67} - 840 q^{71} - 122052 q^{73} - 35084 q^{77} - 31704 q^{79} + 36974 q^{83} - 132444 q^{85} + 210588 q^{89} - 34986 q^{91} + 138624 q^{95} - 44240 q^{97}+O(q^{100}) \) 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
\(5\) −90.4622 −1.61824 −0.809119 0.587645i \(-0.800055\pi\)
−0.809119 + 0.587645i \(0.800055\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −552.494 −1.37672 −0.688361 0.725369i \(-0.741669\pi\)
−0.688361 + 0.725369i \(0.741669\pi\)
\(12\) 0 0
\(13\) −593.172 −0.973469 −0.486734 0.873550i \(-0.661812\pi\)
−0.486734 + 0.873550i \(0.661812\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1422.19 1.19354 0.596769 0.802413i \(-0.296451\pi\)
0.596769 + 0.802413i \(0.296451\pi\)
\(18\) 0 0
\(19\) −318.997 −0.202723 −0.101361 0.994850i \(-0.532320\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 659.954 0.260132 0.130066 0.991505i \(-0.458481\pi\)
0.130066 + 0.991505i \(0.458481\pi\)
\(24\) 0 0
\(25\) 5058.41 1.61869
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8185.27 1.80733 0.903667 0.428237i \(-0.140865\pi\)
0.903667 + 0.428237i \(0.140865\pi\)
\(30\) 0 0
\(31\) 9598.03 1.79382 0.896908 0.442217i \(-0.145808\pi\)
0.896908 + 0.442217i \(0.145808\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4432.65 −0.611636
\(36\) 0 0
\(37\) 5180.56 0.622118 0.311059 0.950391i \(-0.399316\pi\)
0.311059 + 0.950391i \(0.399316\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2192.46 0.203691 0.101846 0.994800i \(-0.467525\pi\)
0.101846 + 0.994800i \(0.467525\pi\)
\(42\) 0 0
\(43\) −7458.29 −0.615131 −0.307566 0.951527i \(-0.599514\pi\)
−0.307566 + 0.951527i \(0.599514\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −19561.8 −1.29171 −0.645853 0.763462i \(-0.723498\pi\)
−0.645853 + 0.763462i \(0.723498\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −36569.6 −1.78826 −0.894129 0.447809i \(-0.852205\pi\)
−0.894129 + 0.447809i \(0.852205\pi\)
\(54\) 0 0
\(55\) 49979.9 2.22786
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 16361.7 0.611927 0.305963 0.952043i \(-0.401021\pi\)
0.305963 + 0.952043i \(0.401021\pi\)
\(60\) 0 0
\(61\) −10893.1 −0.374825 −0.187412 0.982281i \(-0.560010\pi\)
−0.187412 + 0.982281i \(0.560010\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 53659.6 1.57530
\(66\) 0 0
\(67\) −8035.91 −0.218700 −0.109350 0.994003i \(-0.534877\pi\)
−0.109350 + 0.994003i \(0.534877\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 55983.3 1.31799 0.658996 0.752146i \(-0.270981\pi\)
0.658996 + 0.752146i \(0.270981\pi\)
\(72\) 0 0
\(73\) −77752.5 −1.70768 −0.853841 0.520533i \(-0.825733\pi\)
−0.853841 + 0.520533i \(0.825733\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −27072.2 −0.520352
\(78\) 0 0
\(79\) 3208.43 0.0578396 0.0289198 0.999582i \(-0.490793\pi\)
0.0289198 + 0.999582i \(0.490793\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 76626.9 1.22092 0.610458 0.792049i \(-0.290985\pi\)
0.610458 + 0.792049i \(0.290985\pi\)
\(84\) 0 0
\(85\) −128655. −1.93143
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 84288.6 1.12796 0.563980 0.825788i \(-0.309269\pi\)
0.563980 + 0.825788i \(0.309269\pi\)
\(90\) 0 0
\(91\) −29065.4 −0.367937
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 28857.2 0.328054
\(96\) 0 0
\(97\) 101273. 1.09286 0.546428 0.837506i \(-0.315987\pi\)
0.546428 + 0.837506i \(0.315987\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −77456.5 −0.755535 −0.377767 0.925901i \(-0.623308\pi\)
−0.377767 + 0.925901i \(0.623308\pi\)
\(102\) 0 0
\(103\) 56716.9 0.526768 0.263384 0.964691i \(-0.415161\pi\)
0.263384 + 0.964691i \(0.415161\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −38699.2 −0.326770 −0.163385 0.986562i \(-0.552241\pi\)
−0.163385 + 0.986562i \(0.552241\pi\)
\(108\) 0 0
\(109\) −16595.3 −0.133788 −0.0668941 0.997760i \(-0.521309\pi\)
−0.0668941 + 0.997760i \(0.521309\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 76723.9 0.565242 0.282621 0.959232i \(-0.408796\pi\)
0.282621 + 0.959232i \(0.408796\pi\)
\(114\) 0 0
\(115\) −59700.9 −0.420955
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 69687.4 0.451115
\(120\) 0 0
\(121\) 144199. 0.895361
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −174901. −1.00119
\(126\) 0 0
\(127\) −68539.3 −0.377077 −0.188539 0.982066i \(-0.560375\pi\)
−0.188539 + 0.982066i \(0.560375\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 95936.2 0.488432 0.244216 0.969721i \(-0.421469\pi\)
0.244216 + 0.969721i \(0.421469\pi\)
\(132\) 0 0
\(133\) −15630.9 −0.0766221
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −291295. −1.32597 −0.662983 0.748635i \(-0.730710\pi\)
−0.662983 + 0.748635i \(0.730710\pi\)
\(138\) 0 0
\(139\) 281554. 1.23602 0.618009 0.786171i \(-0.287939\pi\)
0.618009 + 0.786171i \(0.287939\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 327724. 1.34019
\(144\) 0 0
\(145\) −740458. −2.92469
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 128283. 0.473372 0.236686 0.971586i \(-0.423939\pi\)
0.236686 + 0.971586i \(0.423939\pi\)
\(150\) 0 0
\(151\) −19017.7 −0.0678760 −0.0339380 0.999424i \(-0.510805\pi\)
−0.0339380 + 0.999424i \(0.510805\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −868259. −2.90282
\(156\) 0 0
\(157\) −272988. −0.883883 −0.441941 0.897044i \(-0.645710\pi\)
−0.441941 + 0.897044i \(0.645710\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 32337.7 0.0983207
\(162\) 0 0
\(163\) −315849. −0.931131 −0.465565 0.885013i \(-0.654149\pi\)
−0.465565 + 0.885013i \(0.654149\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −588655. −1.63331 −0.816657 0.577123i \(-0.804175\pi\)
−0.816657 + 0.577123i \(0.804175\pi\)
\(168\) 0 0
\(169\) −19440.5 −0.0523590
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −718256. −1.82458 −0.912292 0.409540i \(-0.865689\pi\)
−0.912292 + 0.409540i \(0.865689\pi\)
\(174\) 0 0
\(175\) 247862. 0.611808
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 53637.2 0.125122 0.0625610 0.998041i \(-0.480073\pi\)
0.0625610 + 0.998041i \(0.480073\pi\)
\(180\) 0 0
\(181\) −392213. −0.889867 −0.444934 0.895564i \(-0.646773\pi\)
−0.444934 + 0.895564i \(0.646773\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −468645. −1.00673
\(186\) 0 0
\(187\) −785753. −1.64317
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 395509. 0.784463 0.392232 0.919866i \(-0.371703\pi\)
0.392232 + 0.919866i \(0.371703\pi\)
\(192\) 0 0
\(193\) −562892. −1.08776 −0.543878 0.839164i \(-0.683045\pi\)
−0.543878 + 0.839164i \(0.683045\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −402202. −0.738378 −0.369189 0.929354i \(-0.620365\pi\)
−0.369189 + 0.929354i \(0.620365\pi\)
\(198\) 0 0
\(199\) 455975. 0.816222 0.408111 0.912932i \(-0.366188\pi\)
0.408111 + 0.912932i \(0.366188\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 401078. 0.683108
\(204\) 0 0
\(205\) −198335. −0.329621
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 176244. 0.279093
\(210\) 0 0
\(211\) 1.18264e6 1.82871 0.914356 0.404911i \(-0.132698\pi\)
0.914356 + 0.404911i \(0.132698\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 674693. 0.995429
\(216\) 0 0
\(217\) 470303. 0.677999
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −843604. −1.16187
\(222\) 0 0
\(223\) −931112. −1.25383 −0.626917 0.779086i \(-0.715683\pi\)
−0.626917 + 0.779086i \(0.715683\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 192653. 0.248149 0.124074 0.992273i \(-0.460404\pi\)
0.124074 + 0.992273i \(0.460404\pi\)
\(228\) 0 0
\(229\) −783934. −0.987850 −0.493925 0.869505i \(-0.664438\pi\)
−0.493925 + 0.869505i \(0.664438\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.39976e6 1.68914 0.844568 0.535448i \(-0.179857\pi\)
0.844568 + 0.535448i \(0.179857\pi\)
\(234\) 0 0
\(235\) 1.76960e6 2.09029
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −643631. −0.728857 −0.364429 0.931231i \(-0.618736\pi\)
−0.364429 + 0.931231i \(0.618736\pi\)
\(240\) 0 0
\(241\) −58756.4 −0.0651647 −0.0325824 0.999469i \(-0.510373\pi\)
−0.0325824 + 0.999469i \(0.510373\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −217200. −0.231177
\(246\) 0 0
\(247\) 189220. 0.197344
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −641680. −0.642886 −0.321443 0.946929i \(-0.604168\pi\)
−0.321443 + 0.946929i \(0.604168\pi\)
\(252\) 0 0
\(253\) −364621. −0.358129
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −810671. −0.765617 −0.382809 0.923828i \(-0.625043\pi\)
−0.382809 + 0.923828i \(0.625043\pi\)
\(258\) 0 0
\(259\) 253848. 0.235138
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.04061e6 −1.81916 −0.909581 0.415526i \(-0.863597\pi\)
−0.909581 + 0.415526i \(0.863597\pi\)
\(264\) 0 0
\(265\) 3.30817e6 2.89383
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.28300e6 1.08105 0.540524 0.841328i \(-0.318226\pi\)
0.540524 + 0.841328i \(0.318226\pi\)
\(270\) 0 0
\(271\) 22511.3 0.0186199 0.00930994 0.999957i \(-0.497037\pi\)
0.00930994 + 0.999957i \(0.497037\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.79474e6 −2.22849
\(276\) 0 0
\(277\) 368210. 0.288334 0.144167 0.989553i \(-0.453950\pi\)
0.144167 + 0.989553i \(0.453950\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.03709e6 −1.53902 −0.769511 0.638634i \(-0.779500\pi\)
−0.769511 + 0.638634i \(0.779500\pi\)
\(282\) 0 0
\(283\) 656410. 0.487202 0.243601 0.969876i \(-0.421671\pi\)
0.243601 + 0.969876i \(0.421671\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 107431. 0.0769880
\(288\) 0 0
\(289\) 602773. 0.424531
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 962295. 0.654846 0.327423 0.944878i \(-0.393820\pi\)
0.327423 + 0.944878i \(0.393820\pi\)
\(294\) 0 0
\(295\) −1.48012e6 −0.990243
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −391466. −0.253230
\(300\) 0 0
\(301\) −365456. −0.232498
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 985418. 0.606556
\(306\) 0 0
\(307\) 296468. 0.179528 0.0897638 0.995963i \(-0.471389\pi\)
0.0897638 + 0.995963i \(0.471389\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.12063e6 0.656996 0.328498 0.944505i \(-0.393458\pi\)
0.328498 + 0.944505i \(0.393458\pi\)
\(312\) 0 0
\(313\) 1.74908e6 1.00913 0.504567 0.863373i \(-0.331652\pi\)
0.504567 + 0.863373i \(0.331652\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.17498e6 −1.77457 −0.887284 0.461223i \(-0.847411\pi\)
−0.887284 + 0.461223i \(0.847411\pi\)
\(318\) 0 0
\(319\) −4.52232e6 −2.48819
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −453675. −0.241957
\(324\) 0 0
\(325\) −3.00051e6 −1.57575
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −958526. −0.488219
\(330\) 0 0
\(331\) −878405. −0.440681 −0.220341 0.975423i \(-0.570717\pi\)
−0.220341 + 0.975423i \(0.570717\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 726946. 0.353908
\(336\) 0 0
\(337\) 2.05261e6 0.984536 0.492268 0.870444i \(-0.336168\pi\)
0.492268 + 0.870444i \(0.336168\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.30286e6 −2.46958
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 476182. 0.212300 0.106150 0.994350i \(-0.466148\pi\)
0.106150 + 0.994350i \(0.466148\pi\)
\(348\) 0 0
\(349\) 351681. 0.154556 0.0772780 0.997010i \(-0.475377\pi\)
0.0772780 + 0.997010i \(0.475377\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.73722e6 0.742023 0.371011 0.928628i \(-0.379011\pi\)
0.371011 + 0.928628i \(0.379011\pi\)
\(354\) 0 0
\(355\) −5.06438e6 −2.13282
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.69731e6 −0.695063 −0.347531 0.937668i \(-0.612980\pi\)
−0.347531 + 0.937668i \(0.612980\pi\)
\(360\) 0 0
\(361\) −2.37434e6 −0.958903
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.03366e6 2.76344
\(366\) 0 0
\(367\) 1.11920e6 0.433752 0.216876 0.976199i \(-0.430413\pi\)
0.216876 + 0.976199i \(0.430413\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.79191e6 −0.675898
\(372\) 0 0
\(373\) −837822. −0.311803 −0.155901 0.987773i \(-0.549828\pi\)
−0.155901 + 0.987773i \(0.549828\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.85527e6 −1.75938
\(378\) 0 0
\(379\) 1.94713e6 0.696300 0.348150 0.937439i \(-0.386810\pi\)
0.348150 + 0.937439i \(0.386810\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −202063. −0.0703866 −0.0351933 0.999381i \(-0.511205\pi\)
−0.0351933 + 0.999381i \(0.511205\pi\)
\(384\) 0 0
\(385\) 2.44901e6 0.842053
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.23741e6 −1.08473 −0.542367 0.840141i \(-0.682472\pi\)
−0.542367 + 0.840141i \(0.682472\pi\)
\(390\) 0 0
\(391\) 938581. 0.310477
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −290242. −0.0935982
\(396\) 0 0
\(397\) 823921. 0.262367 0.131183 0.991358i \(-0.458122\pi\)
0.131183 + 0.991358i \(0.458122\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.39337e6 −0.743273 −0.371637 0.928378i \(-0.621203\pi\)
−0.371637 + 0.928378i \(0.621203\pi\)
\(402\) 0 0
\(403\) −5.69328e6 −1.74622
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.86223e6 −0.856483
\(408\) 0 0
\(409\) −581801. −0.171975 −0.0859876 0.996296i \(-0.527405\pi\)
−0.0859876 + 0.996296i \(0.527405\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 801725. 0.231287
\(414\) 0 0
\(415\) −6.93184e6 −1.97573
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.11898e6 0.867915 0.433957 0.900933i \(-0.357117\pi\)
0.433957 + 0.900933i \(0.357117\pi\)
\(420\) 0 0
\(421\) −1.14481e6 −0.314796 −0.157398 0.987535i \(-0.550311\pi\)
−0.157398 + 0.987535i \(0.550311\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 7.19403e6 1.93197
\(426\) 0 0
\(427\) −533764. −0.141671
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.31012e6 −1.11762 −0.558812 0.829294i \(-0.688743\pi\)
−0.558812 + 0.829294i \(0.688743\pi\)
\(432\) 0 0
\(433\) −2.79301e6 −0.715901 −0.357950 0.933741i \(-0.616524\pi\)
−0.357950 + 0.933741i \(0.616524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −210523. −0.0527347
\(438\) 0 0
\(439\) −252467. −0.0625236 −0.0312618 0.999511i \(-0.509953\pi\)
−0.0312618 + 0.999511i \(0.509953\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.43282e6 −0.831077 −0.415539 0.909576i \(-0.636407\pi\)
−0.415539 + 0.909576i \(0.636407\pi\)
\(444\) 0 0
\(445\) −7.62494e6 −1.82531
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.68031e6 0.393345 0.196673 0.980469i \(-0.436986\pi\)
0.196673 + 0.980469i \(0.436986\pi\)
\(450\) 0 0
\(451\) −1.21132e6 −0.280426
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.62932e6 0.595409
\(456\) 0 0
\(457\) −2.94585e6 −0.659812 −0.329906 0.944014i \(-0.607017\pi\)
−0.329906 + 0.944014i \(0.607017\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.91583e6 0.419860 0.209930 0.977716i \(-0.432676\pi\)
0.209930 + 0.977716i \(0.432676\pi\)
\(462\) 0 0
\(463\) 3.75401e6 0.813847 0.406924 0.913462i \(-0.366602\pi\)
0.406924 + 0.913462i \(0.366602\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.10594e6 −0.446842 −0.223421 0.974722i \(-0.571722\pi\)
−0.223421 + 0.974722i \(0.571722\pi\)
\(468\) 0 0
\(469\) −393759. −0.0826607
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.12066e6 0.846864
\(474\) 0 0
\(475\) −1.61362e6 −0.328146
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −274926. −0.0547491 −0.0273745 0.999625i \(-0.508715\pi\)
−0.0273745 + 0.999625i \(0.508715\pi\)
\(480\) 0 0
\(481\) −3.07296e6 −0.605612
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9.16135e6 −1.76850
\(486\) 0 0
\(487\) −7.67128e6 −1.46570 −0.732851 0.680389i \(-0.761811\pi\)
−0.732851 + 0.680389i \(0.761811\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.42352e6 −0.453673 −0.226837 0.973933i \(-0.572838\pi\)
−0.226837 + 0.973933i \(0.572838\pi\)
\(492\) 0 0
\(493\) 1.16410e7 2.15712
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.74318e6 0.498154
\(498\) 0 0
\(499\) 8.22317e6 1.47839 0.739193 0.673494i \(-0.235207\pi\)
0.739193 + 0.673494i \(0.235207\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.98186e6 0.525493 0.262746 0.964865i \(-0.415372\pi\)
0.262746 + 0.964865i \(0.415372\pi\)
\(504\) 0 0
\(505\) 7.00689e6 1.22263
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.26867e6 1.07246 0.536230 0.844072i \(-0.319848\pi\)
0.536230 + 0.844072i \(0.319848\pi\)
\(510\) 0 0
\(511\) −3.80987e6 −0.645443
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.13073e6 −0.852435
\(516\) 0 0
\(517\) 1.08078e7 1.77832
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.12134e6 0.665188 0.332594 0.943070i \(-0.392076\pi\)
0.332594 + 0.943070i \(0.392076\pi\)
\(522\) 0 0
\(523\) 4.70469e6 0.752102 0.376051 0.926599i \(-0.377282\pi\)
0.376051 + 0.926599i \(0.377282\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.36502e7 2.14099
\(528\) 0 0
\(529\) −6.00080e6 −0.932331
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.30051e6 −0.198287
\(534\) 0 0
\(535\) 3.50081e6 0.528791
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.32654e6 −0.196674
\(540\) 0 0
\(541\) 4.47840e6 0.657855 0.328927 0.944355i \(-0.393313\pi\)
0.328927 + 0.944355i \(0.393313\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.50124e6 0.216501
\(546\) 0 0
\(547\) 6.49187e6 0.927687 0.463843 0.885917i \(-0.346470\pi\)
0.463843 + 0.885917i \(0.346470\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.61108e6 −0.366388
\(552\) 0 0
\(553\) 157213. 0.0218613
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.50858e6 0.342602 0.171301 0.985219i \(-0.445203\pi\)
0.171301 + 0.985219i \(0.445203\pi\)
\(558\) 0 0
\(559\) 4.42404e6 0.598811
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.52702e6 −0.468961 −0.234480 0.972121i \(-0.575339\pi\)
−0.234480 + 0.972121i \(0.575339\pi\)
\(564\) 0 0
\(565\) −6.94061e6 −0.914696
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.75283e6 −1.26284 −0.631422 0.775439i \(-0.717529\pi\)
−0.631422 + 0.775439i \(0.717529\pi\)
\(570\) 0 0
\(571\) −1.70085e6 −0.218312 −0.109156 0.994025i \(-0.534815\pi\)
−0.109156 + 0.994025i \(0.534815\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.33832e6 0.421074
\(576\) 0 0
\(577\) −1.17066e7 −1.46383 −0.731914 0.681397i \(-0.761373\pi\)
−0.731914 + 0.681397i \(0.761373\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.75472e6 0.461463
\(582\) 0 0
\(583\) 2.02045e7 2.46193
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.75683e6 −0.450015 −0.225007 0.974357i \(-0.572241\pi\)
−0.225007 + 0.974357i \(0.572241\pi\)
\(588\) 0 0
\(589\) −3.06175e6 −0.363648
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.64338e6 −1.00936 −0.504681 0.863306i \(-0.668390\pi\)
−0.504681 + 0.863306i \(0.668390\pi\)
\(594\) 0 0
\(595\) −6.30408e6 −0.730011
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.31930e6 1.06125 0.530623 0.847608i \(-0.321958\pi\)
0.530623 + 0.847608i \(0.321958\pi\)
\(600\) 0 0
\(601\) 910438. 0.102817 0.0514084 0.998678i \(-0.483629\pi\)
0.0514084 + 0.998678i \(0.483629\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.30445e7 −1.44891
\(606\) 0 0
\(607\) −5.70173e6 −0.628109 −0.314054 0.949405i \(-0.601687\pi\)
−0.314054 + 0.949405i \(0.601687\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.16035e7 1.25743
\(612\) 0 0
\(613\) 1.61327e7 1.73403 0.867016 0.498280i \(-0.166035\pi\)
0.867016 + 0.498280i \(0.166035\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.53575e6 0.585415 0.292708 0.956202i \(-0.405444\pi\)
0.292708 + 0.956202i \(0.405444\pi\)
\(618\) 0 0
\(619\) 1.88448e7 1.97681 0.988407 0.151828i \(-0.0485161\pi\)
0.988407 + 0.151828i \(0.0485161\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.13014e6 0.426329
\(624\) 0 0
\(625\) 14378.1 0.00147232
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.36776e6 0.742521
\(630\) 0 0
\(631\) −2.63269e6 −0.263224 −0.131612 0.991301i \(-0.542015\pi\)
−0.131612 + 0.991301i \(0.542015\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.20021e6 0.610200
\(636\) 0 0
\(637\) −1.42420e6 −0.139067
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.42939e7 −1.37406 −0.687028 0.726631i \(-0.741085\pi\)
−0.687028 + 0.726631i \(0.741085\pi\)
\(642\) 0 0
\(643\) 1.63874e7 1.56308 0.781542 0.623853i \(-0.214434\pi\)
0.781542 + 0.623853i \(0.214434\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.19303e7 1.12045 0.560224 0.828341i \(-0.310715\pi\)
0.560224 + 0.828341i \(0.310715\pi\)
\(648\) 0 0
\(649\) −9.03977e6 −0.842453
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.47862e6 −0.319245 −0.159622 0.987178i \(-0.551028\pi\)
−0.159622 + 0.987178i \(0.551028\pi\)
\(654\) 0 0
\(655\) −8.67860e6 −0.790399
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.09397e7 1.87826 0.939131 0.343560i \(-0.111633\pi\)
0.939131 + 0.343560i \(0.111633\pi\)
\(660\) 0 0
\(661\) −1.02566e7 −0.913059 −0.456530 0.889708i \(-0.650908\pi\)
−0.456530 + 0.889708i \(0.650908\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.41400e6 0.123993
\(666\) 0 0
\(667\) 5.40190e6 0.470145
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.01840e6 0.516029
\(672\) 0 0
\(673\) 716398. 0.0609701 0.0304851 0.999535i \(-0.490295\pi\)
0.0304851 + 0.999535i \(0.490295\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −945625. −0.0792953 −0.0396476 0.999214i \(-0.512624\pi\)
−0.0396476 + 0.999214i \(0.512624\pi\)
\(678\) 0 0
\(679\) 4.96236e6 0.413061
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.56992e6 0.292824 0.146412 0.989224i \(-0.453227\pi\)
0.146412 + 0.989224i \(0.453227\pi\)
\(684\) 0 0
\(685\) 2.63512e7 2.14573
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.16920e7 1.74081
\(690\) 0 0
\(691\) −9.67811e6 −0.771073 −0.385536 0.922693i \(-0.625984\pi\)
−0.385536 + 0.922693i \(0.625984\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.54700e7 −2.00017
\(696\) 0 0
\(697\) 3.11810e6 0.243113
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.52404e7 −1.94000 −0.970000 0.243105i \(-0.921834\pi\)
−0.970000 + 0.243105i \(0.921834\pi\)
\(702\) 0 0
\(703\) −1.65259e6 −0.126118
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.79537e6 −0.285565
\(708\) 0 0
\(709\) −1.74744e7 −1.30553 −0.652765 0.757560i \(-0.726391\pi\)
−0.652765 + 0.757560i \(0.726391\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.33426e6 0.466629
\(714\) 0 0
\(715\) −2.96466e7 −2.16875
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.73361e6 −0.702185 −0.351093 0.936341i \(-0.614190\pi\)
−0.351093 + 0.936341i \(0.614190\pi\)
\(720\) 0 0
\(721\) 2.77913e6 0.199100
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.14045e7 2.92552
\(726\) 0 0
\(727\) 1.60454e7 1.12594 0.562971 0.826477i \(-0.309658\pi\)
0.562971 + 0.826477i \(0.309658\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.06071e7 −0.734182
\(732\) 0 0
\(733\) 1.04534e7 0.718615 0.359307 0.933219i \(-0.383013\pi\)
0.359307 + 0.933219i \(0.383013\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.43979e6 0.301088
\(738\) 0 0
\(739\) 7.47638e6 0.503594 0.251797 0.967780i \(-0.418978\pi\)
0.251797 + 0.967780i \(0.418978\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.33998e7 −0.890483 −0.445241 0.895411i \(-0.646882\pi\)
−0.445241 + 0.895411i \(0.646882\pi\)
\(744\) 0 0
\(745\) −1.16047e7 −0.766028
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.89626e6 −0.123507
\(750\) 0 0
\(751\) −9.13903e6 −0.591290 −0.295645 0.955298i \(-0.595535\pi\)
−0.295645 + 0.955298i \(0.595535\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.72039e6 0.109840
\(756\) 0 0
\(757\) −1.16376e7 −0.738117 −0.369059 0.929406i \(-0.620320\pi\)
−0.369059 + 0.929406i \(0.620320\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.07072e6 0.505186 0.252593 0.967573i \(-0.418717\pi\)
0.252593 + 0.967573i \(0.418717\pi\)
\(762\) 0 0
\(763\) −813167. −0.0505672
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.70532e6 −0.595692
\(768\) 0 0
\(769\) −1.30085e7 −0.793255 −0.396628 0.917980i \(-0.629820\pi\)
−0.396628 + 0.917980i \(0.629820\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.37637e7 −1.43043 −0.715214 0.698906i \(-0.753671\pi\)
−0.715214 + 0.698906i \(0.753671\pi\)
\(774\) 0 0
\(775\) 4.85508e7 2.90364
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −699389. −0.0412929
\(780\) 0 0
\(781\) −3.09305e7 −1.81451
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.46951e7 1.43033
\(786\) 0 0
\(787\) 2.84940e7 1.63989 0.819947 0.572439i \(-0.194003\pi\)
0.819947 + 0.572439i \(0.194003\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.75947e6 0.213641
\(792\) 0 0
\(793\) 6.46150e6 0.364880
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.43450e7 −0.799938 −0.399969 0.916529i \(-0.630979\pi\)
−0.399969 + 0.916529i \(0.630979\pi\)
\(798\) 0 0
\(799\) −2.78206e7 −1.54170
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.29578e7 2.35100
\(804\) 0 0
\(805\) −2.92534e6 −0.159106
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3.59284e6 0.193004 0.0965020 0.995333i \(-0.469235\pi\)
0.0965020 + 0.995333i \(0.469235\pi\)
\(810\) 0 0
\(811\) −3.52968e7 −1.88445 −0.942223 0.334988i \(-0.891268\pi\)
−0.942223 + 0.334988i \(0.891268\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.85724e7 1.50679
\(816\) 0 0
\(817\) 2.37917e6 0.124701
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.04558e7 −0.541378 −0.270689 0.962667i \(-0.587252\pi\)
−0.270689 + 0.962667i \(0.587252\pi\)
\(822\) 0 0
\(823\) −4.99190e6 −0.256901 −0.128451 0.991716i \(-0.541000\pi\)
−0.128451 + 0.991716i \(0.541000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.06198e7 −1.04839 −0.524193 0.851599i \(-0.675633\pi\)
−0.524193 + 0.851599i \(0.675633\pi\)
\(828\) 0 0
\(829\) −506843. −0.0256146 −0.0128073 0.999918i \(-0.504077\pi\)
−0.0128073 + 0.999918i \(0.504077\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.41468e6 0.170505
\(834\) 0 0
\(835\) 5.32511e7 2.64309
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −4.41851e6 −0.216706 −0.108353 0.994112i \(-0.534558\pi\)
−0.108353 + 0.994112i \(0.534558\pi\)
\(840\) 0 0
\(841\) 4.64876e7 2.26645
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.75863e6 0.0847292
\(846\) 0 0
\(847\) 7.06574e6 0.338415
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.41893e6 0.161833
\(852\) 0 0
\(853\) −1.11737e7 −0.525806 −0.262903 0.964822i \(-0.584680\pi\)
−0.262903 + 0.964822i \(0.584680\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.12308e7 −0.987448 −0.493724 0.869619i \(-0.664365\pi\)
−0.493724 + 0.869619i \(0.664365\pi\)
\(858\) 0 0
\(859\) −3.64229e7 −1.68419 −0.842096 0.539328i \(-0.818678\pi\)
−0.842096 + 0.539328i \(0.818678\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.53298e7 −1.15772 −0.578861 0.815426i \(-0.696503\pi\)
−0.578861 + 0.815426i \(0.696503\pi\)
\(864\) 0 0
\(865\) 6.49750e7 2.95261
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.77264e6 −0.0796290
\(870\) 0 0
\(871\) 4.76667e6 0.212897
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.57014e6 −0.378415
\(876\) 0 0
\(877\) −577138. −0.0253385 −0.0126692 0.999920i \(-0.504033\pi\)
−0.0126692 + 0.999920i \(0.504033\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.15071e7 0.933561 0.466781 0.884373i \(-0.345414\pi\)
0.466781 + 0.884373i \(0.345414\pi\)
\(882\) 0 0
\(883\) 3.71948e6 0.160539 0.0802695 0.996773i \(-0.474422\pi\)
0.0802695 + 0.996773i \(0.474422\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.81760e7 0.775694 0.387847 0.921724i \(-0.373219\pi\)
0.387847 + 0.921724i \(0.373219\pi\)
\(888\) 0 0
\(889\) −3.35842e6 −0.142522
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 6.24015e6 0.261858
\(894\) 0 0
\(895\) −4.85214e6 −0.202477
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.85625e7 3.24202
\(900\) 0 0
\(901\) −5.20090e7 −2.13435
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.54804e7 1.44002
\(906\) 0 0
\(907\) 1.35430e7 0.546635 0.273317 0.961924i \(-0.411879\pi\)
0.273317 + 0.961924i \(0.411879\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −412746. −0.0164773 −0.00823866 0.999966i \(-0.502622\pi\)
−0.00823866 + 0.999966i \(0.502622\pi\)
\(912\) 0 0
\(913\) −4.23359e7 −1.68086
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.70087e6 0.184610
\(918\) 0 0
\(919\) −2.79059e7 −1.08995 −0.544976 0.838452i \(-0.683461\pi\)
−0.544976 + 0.838452i \(0.683461\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.32077e7 −1.28302
\(924\) 0 0
\(925\) 2.62054e7 1.00702
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.94840e7 0.740695 0.370348 0.928893i \(-0.379239\pi\)
0.370348 + 0.928893i \(0.379239\pi\)
\(930\) 0 0
\(931\) −765912. −0.0289604
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.10809e7 2.65904
\(936\) 0 0
\(937\) −1.89631e7 −0.705602 −0.352801 0.935698i \(-0.614771\pi\)
−0.352801 + 0.935698i \(0.614771\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.30498e7 0.848579 0.424290 0.905526i \(-0.360524\pi\)
0.424290 + 0.905526i \(0.360524\pi\)
\(942\) 0 0
\(943\) 1.44692e6 0.0529866
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.49310e7 −1.26572 −0.632858 0.774268i \(-0.718118\pi\)
−0.632858 + 0.774268i \(0.718118\pi\)
\(948\) 0 0
\(949\) 4.61206e7 1.66238
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.74501e7 −0.979066 −0.489533 0.871985i \(-0.662833\pi\)
−0.489533 + 0.871985i \(0.662833\pi\)
\(954\) 0 0
\(955\) −3.57786e7 −1.26945
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.42735e7 −0.501168
\(960\) 0 0
\(961\) 6.34930e7 2.21778
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5.09204e7 1.76025
\(966\) 0 0
\(967\) 9.37608e6 0.322445 0.161222 0.986918i \(-0.448456\pi\)
0.161222 + 0.986918i \(0.448456\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7.23359e6 0.246210 0.123105 0.992394i \(-0.460715\pi\)
0.123105 + 0.992394i \(0.460715\pi\)
\(972\) 0 0
\(973\) 1.37962e7 0.467171
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.88022e7 0.965360 0.482680 0.875797i \(-0.339663\pi\)
0.482680 + 0.875797i \(0.339663\pi\)
\(978\) 0 0
\(979\) −4.65690e7 −1.55289
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5.21848e7 1.72250 0.861252 0.508178i \(-0.169681\pi\)
0.861252 + 0.508178i \(0.169681\pi\)
\(984\) 0 0
\(985\) 3.63841e7 1.19487
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.92212e6 −0.160015
\(990\) 0 0
\(991\) 3.89578e7 1.26012 0.630058 0.776548i \(-0.283031\pi\)
0.630058 + 0.776548i \(0.283031\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.12485e7 −1.32084
\(996\) 0 0
\(997\) −3.01716e7 −0.961305 −0.480652 0.876911i \(-0.659600\pi\)
−0.480652 + 0.876911i \(0.659600\pi\)
\(998\) 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.bi.1.1 2
3.2 odd 2 112.6.a.j.1.2 2
4.3 odd 2 504.6.a.m.1.1 2
12.11 even 2 56.6.a.d.1.1 2
21.20 even 2 784.6.a.q.1.1 2
24.5 odd 2 448.6.a.r.1.1 2
24.11 even 2 448.6.a.x.1.2 2
84.11 even 6 392.6.i.k.177.2 4
84.23 even 6 392.6.i.k.361.2 4
84.47 odd 6 392.6.i.h.361.1 4
84.59 odd 6 392.6.i.h.177.1 4
84.83 odd 2 392.6.a.e.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.d.1.1 2 12.11 even 2
112.6.a.j.1.2 2 3.2 odd 2
392.6.a.e.1.2 2 84.83 odd 2
392.6.i.h.177.1 4 84.59 odd 6
392.6.i.h.361.1 4 84.47 odd 6
392.6.i.k.177.2 4 84.11 even 6
392.6.i.k.361.2 4 84.23 even 6
448.6.a.r.1.1 2 24.5 odd 2
448.6.a.x.1.2 2 24.11 even 2
504.6.a.m.1.1 2 4.3 odd 2
784.6.a.q.1.1 2 21.20 even 2
1008.6.a.bi.1.1 2 1.1 even 1 trivial