Properties

Label 882.6.a.s.1.1
Level $882$
Weight $6$
Character 882.1
Self dual yes
Analytic conductor $141.459$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,6,Mod(1,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("882.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 882.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: \(141.458529075\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 882.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +16.0000 q^{4} +26.0000 q^{5} +64.0000 q^{8} +O(q^{10})\) \(q+4.00000 q^{2} +16.0000 q^{4} +26.0000 q^{5} +64.0000 q^{8} +104.000 q^{10} -664.000 q^{11} -318.000 q^{13} +256.000 q^{16} +1582.00 q^{17} -236.000 q^{19} +416.000 q^{20} -2656.00 q^{22} -2212.00 q^{23} -2449.00 q^{25} -1272.00 q^{26} +4954.00 q^{29} +7128.00 q^{31} +1024.00 q^{32} +6328.00 q^{34} +4358.00 q^{37} -944.000 q^{38} +1664.00 q^{40} +10542.0 q^{41} -8452.00 q^{43} -10624.0 q^{44} -8848.00 q^{46} +5352.00 q^{47} -9796.00 q^{50} -5088.00 q^{52} +33354.0 q^{53} -17264.0 q^{55} +19816.0 q^{58} -15436.0 q^{59} +36762.0 q^{61} +28512.0 q^{62} +4096.00 q^{64} -8268.00 q^{65} +40972.0 q^{67} +25312.0 q^{68} +9092.00 q^{71} +73454.0 q^{73} +17432.0 q^{74} -3776.00 q^{76} +89400.0 q^{79} +6656.00 q^{80} +42168.0 q^{82} -6428.00 q^{83} +41132.0 q^{85} -33808.0 q^{86} -42496.0 q^{88} -122658. q^{89} -35392.0 q^{92} +21408.0 q^{94} -6136.00 q^{95} -21370.0 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) 0 0
\(4\) 16.0000 0.500000
\(5\) 26.0000 0.465102 0.232551 0.972584i \(-0.425293\pi\)
0.232551 + 0.972584i \(0.425293\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) 0 0
\(10\) 104.000 0.328877
\(11\) −664.000 −1.65457 −0.827287 0.561779i \(-0.810117\pi\)
−0.827287 + 0.561779i \(0.810117\pi\)
\(12\) 0 0
\(13\) −318.000 −0.521878 −0.260939 0.965355i \(-0.584032\pi\)
−0.260939 + 0.965355i \(0.584032\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 1582.00 1.32765 0.663826 0.747887i \(-0.268932\pi\)
0.663826 + 0.747887i \(0.268932\pi\)
\(18\) 0 0
\(19\) −236.000 −0.149978 −0.0749891 0.997184i \(-0.523892\pi\)
−0.0749891 + 0.997184i \(0.523892\pi\)
\(20\) 416.000 0.232551
\(21\) 0 0
\(22\) −2656.00 −1.16996
\(23\) −2212.00 −0.871898 −0.435949 0.899971i \(-0.643587\pi\)
−0.435949 + 0.899971i \(0.643587\pi\)
\(24\) 0 0
\(25\) −2449.00 −0.783680
\(26\) −1272.00 −0.369023
\(27\) 0 0
\(28\) 0 0
\(29\) 4954.00 1.09386 0.546929 0.837179i \(-0.315797\pi\)
0.546929 + 0.837179i \(0.315797\pi\)
\(30\) 0 0
\(31\) 7128.00 1.33218 0.666091 0.745871i \(-0.267966\pi\)
0.666091 + 0.745871i \(0.267966\pi\)
\(32\) 1024.00 0.176777
\(33\) 0 0
\(34\) 6328.00 0.938792
\(35\) 0 0
\(36\) 0 0
\(37\) 4358.00 0.523339 0.261669 0.965158i \(-0.415727\pi\)
0.261669 + 0.965158i \(0.415727\pi\)
\(38\) −944.000 −0.106051
\(39\) 0 0
\(40\) 1664.00 0.164438
\(41\) 10542.0 0.979407 0.489704 0.871889i \(-0.337105\pi\)
0.489704 + 0.871889i \(0.337105\pi\)
\(42\) 0 0
\(43\) −8452.00 −0.697089 −0.348545 0.937292i \(-0.613324\pi\)
−0.348545 + 0.937292i \(0.613324\pi\)
\(44\) −10624.0 −0.827287
\(45\) 0 0
\(46\) −8848.00 −0.616525
\(47\) 5352.00 0.353404 0.176702 0.984264i \(-0.443457\pi\)
0.176702 + 0.984264i \(0.443457\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −9796.00 −0.554145
\(51\) 0 0
\(52\) −5088.00 −0.260939
\(53\) 33354.0 1.63102 0.815508 0.578746i \(-0.196458\pi\)
0.815508 + 0.578746i \(0.196458\pi\)
\(54\) 0 0
\(55\) −17264.0 −0.769546
\(56\) 0 0
\(57\) 0 0
\(58\) 19816.0 0.773475
\(59\) −15436.0 −0.577304 −0.288652 0.957434i \(-0.593207\pi\)
−0.288652 + 0.957434i \(0.593207\pi\)
\(60\) 0 0
\(61\) 36762.0 1.26495 0.632477 0.774579i \(-0.282038\pi\)
0.632477 + 0.774579i \(0.282038\pi\)
\(62\) 28512.0 0.941995
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −8268.00 −0.242726
\(66\) 0 0
\(67\) 40972.0 1.11506 0.557532 0.830155i \(-0.311748\pi\)
0.557532 + 0.830155i \(0.311748\pi\)
\(68\) 25312.0 0.663826
\(69\) 0 0
\(70\) 0 0
\(71\) 9092.00 0.214049 0.107025 0.994256i \(-0.465868\pi\)
0.107025 + 0.994256i \(0.465868\pi\)
\(72\) 0 0
\(73\) 73454.0 1.61327 0.806637 0.591047i \(-0.201285\pi\)
0.806637 + 0.591047i \(0.201285\pi\)
\(74\) 17432.0 0.370056
\(75\) 0 0
\(76\) −3776.00 −0.0749891
\(77\) 0 0
\(78\) 0 0
\(79\) 89400.0 1.61165 0.805823 0.592156i \(-0.201723\pi\)
0.805823 + 0.592156i \(0.201723\pi\)
\(80\) 6656.00 0.116276
\(81\) 0 0
\(82\) 42168.0 0.692546
\(83\) −6428.00 −0.102419 −0.0512095 0.998688i \(-0.516308\pi\)
−0.0512095 + 0.998688i \(0.516308\pi\)
\(84\) 0 0
\(85\) 41132.0 0.617494
\(86\) −33808.0 −0.492916
\(87\) 0 0
\(88\) −42496.0 −0.584980
\(89\) −122658. −1.64142 −0.820712 0.571342i \(-0.806423\pi\)
−0.820712 + 0.571342i \(0.806423\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −35392.0 −0.435949
\(93\) 0 0
\(94\) 21408.0 0.249894
\(95\) −6136.00 −0.0697552
\(96\) 0 0
\(97\) −21370.0 −0.230608 −0.115304 0.993330i \(-0.536784\pi\)
−0.115304 + 0.993330i \(0.536784\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −39184.0 −0.391840
\(101\) −36814.0 −0.359095 −0.179548 0.983749i \(-0.557463\pi\)
−0.179548 + 0.983749i \(0.557463\pi\)
\(102\) 0 0
\(103\) −104528. −0.970822 −0.485411 0.874286i \(-0.661330\pi\)
−0.485411 + 0.874286i \(0.661330\pi\)
\(104\) −20352.0 −0.184512
\(105\) 0 0
\(106\) 133416. 1.15330
\(107\) −214440. −1.81070 −0.905350 0.424667i \(-0.860391\pi\)
−0.905350 + 0.424667i \(0.860391\pi\)
\(108\) 0 0
\(109\) 28798.0 0.232165 0.116082 0.993240i \(-0.462966\pi\)
0.116082 + 0.993240i \(0.462966\pi\)
\(110\) −69056.0 −0.544151
\(111\) 0 0
\(112\) 0 0
\(113\) 56014.0 0.412668 0.206334 0.978482i \(-0.433847\pi\)
0.206334 + 0.978482i \(0.433847\pi\)
\(114\) 0 0
\(115\) −57512.0 −0.405521
\(116\) 79264.0 0.546929
\(117\) 0 0
\(118\) −61744.0 −0.408216
\(119\) 0 0
\(120\) 0 0
\(121\) 279845. 1.73762
\(122\) 147048. 0.894457
\(123\) 0 0
\(124\) 114048. 0.666091
\(125\) −144924. −0.829593
\(126\) 0 0
\(127\) 185400. 1.02000 0.510000 0.860174i \(-0.329645\pi\)
0.510000 + 0.860174i \(0.329645\pi\)
\(128\) 16384.0 0.0883883
\(129\) 0 0
\(130\) −33072.0 −0.171634
\(131\) 64532.0 0.328547 0.164273 0.986415i \(-0.447472\pi\)
0.164273 + 0.986415i \(0.447472\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 163888. 0.788470
\(135\) 0 0
\(136\) 101248. 0.469396
\(137\) −152930. −0.696131 −0.348066 0.937470i \(-0.613161\pi\)
−0.348066 + 0.937470i \(0.613161\pi\)
\(138\) 0 0
\(139\) 343460. 1.50778 0.753892 0.656998i \(-0.228174\pi\)
0.753892 + 0.656998i \(0.228174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 36368.0 0.151356
\(143\) 211152. 0.863486
\(144\) 0 0
\(145\) 128804. 0.508756
\(146\) 293816. 1.14076
\(147\) 0 0
\(148\) 69728.0 0.261669
\(149\) 174858. 0.645238 0.322619 0.946529i \(-0.395437\pi\)
0.322619 + 0.946529i \(0.395437\pi\)
\(150\) 0 0
\(151\) −452552. −1.61520 −0.807600 0.589731i \(-0.799234\pi\)
−0.807600 + 0.589731i \(0.799234\pi\)
\(152\) −15104.0 −0.0530253
\(153\) 0 0
\(154\) 0 0
\(155\) 185328. 0.619601
\(156\) 0 0
\(157\) 499066. 1.61588 0.807940 0.589265i \(-0.200583\pi\)
0.807940 + 0.589265i \(0.200583\pi\)
\(158\) 357600. 1.13961
\(159\) 0 0
\(160\) 26624.0 0.0822192
\(161\) 0 0
\(162\) 0 0
\(163\) −475588. −1.40204 −0.701022 0.713139i \(-0.747273\pi\)
−0.701022 + 0.713139i \(0.747273\pi\)
\(164\) 168672. 0.489704
\(165\) 0 0
\(166\) −25712.0 −0.0724212
\(167\) 120224. 0.333580 0.166790 0.985992i \(-0.446660\pi\)
0.166790 + 0.985992i \(0.446660\pi\)
\(168\) 0 0
\(169\) −270169. −0.727644
\(170\) 164528. 0.436634
\(171\) 0 0
\(172\) −135232. −0.348545
\(173\) 508874. 1.29269 0.646346 0.763045i \(-0.276296\pi\)
0.646346 + 0.763045i \(0.276296\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −169984. −0.413644
\(177\) 0 0
\(178\) −490632. −1.16066
\(179\) −487560. −1.13735 −0.568677 0.822561i \(-0.692544\pi\)
−0.568677 + 0.822561i \(0.692544\pi\)
\(180\) 0 0
\(181\) 544410. 1.23518 0.617589 0.786501i \(-0.288109\pi\)
0.617589 + 0.786501i \(0.288109\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −141568. −0.308262
\(185\) 113308. 0.243406
\(186\) 0 0
\(187\) −1.05045e6 −2.19670
\(188\) 85632.0 0.176702
\(189\) 0 0
\(190\) −24544.0 −0.0493243
\(191\) −376404. −0.746570 −0.373285 0.927717i \(-0.621769\pi\)
−0.373285 + 0.927717i \(0.621769\pi\)
\(192\) 0 0
\(193\) 844946. 1.63281 0.816405 0.577480i \(-0.195964\pi\)
0.816405 + 0.577480i \(0.195964\pi\)
\(194\) −85480.0 −0.163065
\(195\) 0 0
\(196\) 0 0
\(197\) 492794. 0.904690 0.452345 0.891843i \(-0.350588\pi\)
0.452345 + 0.891843i \(0.350588\pi\)
\(198\) 0 0
\(199\) 914776. 1.63750 0.818751 0.574148i \(-0.194667\pi\)
0.818751 + 0.574148i \(0.194667\pi\)
\(200\) −156736. −0.277073
\(201\) 0 0
\(202\) −147256. −0.253919
\(203\) 0 0
\(204\) 0 0
\(205\) 274092. 0.455524
\(206\) −418112. −0.686475
\(207\) 0 0
\(208\) −81408.0 −0.130469
\(209\) 156704. 0.248150
\(210\) 0 0
\(211\) 311780. 0.482106 0.241053 0.970512i \(-0.422507\pi\)
0.241053 + 0.970512i \(0.422507\pi\)
\(212\) 533664. 0.815508
\(213\) 0 0
\(214\) −857760. −1.28036
\(215\) −219752. −0.324218
\(216\) 0 0
\(217\) 0 0
\(218\) 115192. 0.164165
\(219\) 0 0
\(220\) −276224. −0.384773
\(221\) −503076. −0.692872
\(222\) 0 0
\(223\) 1.28776e6 1.73409 0.867047 0.498226i \(-0.166015\pi\)
0.867047 + 0.498226i \(0.166015\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 224056. 0.291800
\(227\) 1.28905e6 1.66037 0.830187 0.557485i \(-0.188234\pi\)
0.830187 + 0.557485i \(0.188234\pi\)
\(228\) 0 0
\(229\) −678214. −0.854630 −0.427315 0.904103i \(-0.640540\pi\)
−0.427315 + 0.904103i \(0.640540\pi\)
\(230\) −230048. −0.286747
\(231\) 0 0
\(232\) 317056. 0.386737
\(233\) 1.11731e6 1.34829 0.674146 0.738598i \(-0.264512\pi\)
0.674146 + 0.738598i \(0.264512\pi\)
\(234\) 0 0
\(235\) 139152. 0.164369
\(236\) −246976. −0.288652
\(237\) 0 0
\(238\) 0 0
\(239\) 1.26196e6 1.42906 0.714528 0.699606i \(-0.246641\pi\)
0.714528 + 0.699606i \(0.246641\pi\)
\(240\) 0 0
\(241\) −948218. −1.05164 −0.525818 0.850597i \(-0.676241\pi\)
−0.525818 + 0.850597i \(0.676241\pi\)
\(242\) 1.11938e6 1.22868
\(243\) 0 0
\(244\) 588192. 0.632477
\(245\) 0 0
\(246\) 0 0
\(247\) 75048.0 0.0782703
\(248\) 456192. 0.470997
\(249\) 0 0
\(250\) −579696. −0.586611
\(251\) −486396. −0.487310 −0.243655 0.969862i \(-0.578347\pi\)
−0.243655 + 0.969862i \(0.578347\pi\)
\(252\) 0 0
\(253\) 1.46877e6 1.44262
\(254\) 741600. 0.721249
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −1.03910e6 −0.981349 −0.490675 0.871343i \(-0.663250\pi\)
−0.490675 + 0.871343i \(0.663250\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −132288. −0.121363
\(261\) 0 0
\(262\) 258128. 0.232317
\(263\) −1.35104e6 −1.20443 −0.602213 0.798335i \(-0.705714\pi\)
−0.602213 + 0.798335i \(0.705714\pi\)
\(264\) 0 0
\(265\) 867204. 0.758589
\(266\) 0 0
\(267\) 0 0
\(268\) 655552. 0.557532
\(269\) −1.11811e6 −0.942115 −0.471057 0.882103i \(-0.656128\pi\)
−0.471057 + 0.882103i \(0.656128\pi\)
\(270\) 0 0
\(271\) 190104. 0.157242 0.0786209 0.996905i \(-0.474948\pi\)
0.0786209 + 0.996905i \(0.474948\pi\)
\(272\) 404992. 0.331913
\(273\) 0 0
\(274\) −611720. −0.492239
\(275\) 1.62614e6 1.29666
\(276\) 0 0
\(277\) −200506. −0.157010 −0.0785051 0.996914i \(-0.525015\pi\)
−0.0785051 + 0.996914i \(0.525015\pi\)
\(278\) 1.37384e6 1.06616
\(279\) 0 0
\(280\) 0 0
\(281\) −1.09237e6 −0.825285 −0.412643 0.910893i \(-0.635394\pi\)
−0.412643 + 0.910893i \(0.635394\pi\)
\(282\) 0 0
\(283\) −1.81258e6 −1.34534 −0.672669 0.739944i \(-0.734852\pi\)
−0.672669 + 0.739944i \(0.734852\pi\)
\(284\) 145472. 0.107025
\(285\) 0 0
\(286\) 844608. 0.610577
\(287\) 0 0
\(288\) 0 0
\(289\) 1.08287e6 0.762659
\(290\) 515216. 0.359745
\(291\) 0 0
\(292\) 1.17526e6 0.806637
\(293\) 2.10031e6 1.42927 0.714634 0.699499i \(-0.246593\pi\)
0.714634 + 0.699499i \(0.246593\pi\)
\(294\) 0 0
\(295\) −401336. −0.268505
\(296\) 278912. 0.185028
\(297\) 0 0
\(298\) 699432. 0.456252
\(299\) 703416. 0.455024
\(300\) 0 0
\(301\) 0 0
\(302\) −1.81021e6 −1.14212
\(303\) 0 0
\(304\) −60416.0 −0.0374945
\(305\) 955812. 0.588333
\(306\) 0 0
\(307\) 1.64104e6 0.993743 0.496872 0.867824i \(-0.334482\pi\)
0.496872 + 0.867824i \(0.334482\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 741312. 0.438124
\(311\) −945232. −0.554163 −0.277081 0.960846i \(-0.589367\pi\)
−0.277081 + 0.960846i \(0.589367\pi\)
\(312\) 0 0
\(313\) −415354. −0.239639 −0.119820 0.992796i \(-0.538232\pi\)
−0.119820 + 0.992796i \(0.538232\pi\)
\(314\) 1.99626e6 1.14260
\(315\) 0 0
\(316\) 1.43040e6 0.805823
\(317\) −1.18481e6 −0.662220 −0.331110 0.943592i \(-0.607423\pi\)
−0.331110 + 0.943592i \(0.607423\pi\)
\(318\) 0 0
\(319\) −3.28946e6 −1.80987
\(320\) 106496. 0.0581378
\(321\) 0 0
\(322\) 0 0
\(323\) −373352. −0.199119
\(324\) 0 0
\(325\) 778782. 0.408985
\(326\) −1.90235e6 −0.991395
\(327\) 0 0
\(328\) 674688. 0.346273
\(329\) 0 0
\(330\) 0 0
\(331\) 1.37155e6 0.688083 0.344042 0.938954i \(-0.388204\pi\)
0.344042 + 0.938954i \(0.388204\pi\)
\(332\) −102848. −0.0512095
\(333\) 0 0
\(334\) 480896. 0.235877
\(335\) 1.06527e6 0.518619
\(336\) 0 0
\(337\) 963522. 0.462154 0.231077 0.972935i \(-0.425775\pi\)
0.231077 + 0.972935i \(0.425775\pi\)
\(338\) −1.08068e6 −0.514522
\(339\) 0 0
\(340\) 658112. 0.308747
\(341\) −4.73299e6 −2.20419
\(342\) 0 0
\(343\) 0 0
\(344\) −540928. −0.246458
\(345\) 0 0
\(346\) 2.03550e6 0.914071
\(347\) −2.57731e6 −1.14906 −0.574531 0.818483i \(-0.694815\pi\)
−0.574531 + 0.818483i \(0.694815\pi\)
\(348\) 0 0
\(349\) 3.06751e6 1.34810 0.674051 0.738684i \(-0.264553\pi\)
0.674051 + 0.738684i \(0.264553\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −679936. −0.292490
\(353\) −3.10144e6 −1.32473 −0.662364 0.749182i \(-0.730447\pi\)
−0.662364 + 0.749182i \(0.730447\pi\)
\(354\) 0 0
\(355\) 236392. 0.0995547
\(356\) −1.96253e6 −0.820712
\(357\) 0 0
\(358\) −1.95024e6 −0.804230
\(359\) 327508. 0.134118 0.0670588 0.997749i \(-0.478638\pi\)
0.0670588 + 0.997749i \(0.478638\pi\)
\(360\) 0 0
\(361\) −2.42040e6 −0.977507
\(362\) 2.17764e6 0.873403
\(363\) 0 0
\(364\) 0 0
\(365\) 1.90980e6 0.750337
\(366\) 0 0
\(367\) 2.86739e6 1.11128 0.555638 0.831424i \(-0.312474\pi\)
0.555638 + 0.831424i \(0.312474\pi\)
\(368\) −566272. −0.217974
\(369\) 0 0
\(370\) 453232. 0.172114
\(371\) 0 0
\(372\) 0 0
\(373\) 3.58029e6 1.33244 0.666218 0.745757i \(-0.267912\pi\)
0.666218 + 0.745757i \(0.267912\pi\)
\(374\) −4.20179e6 −1.55330
\(375\) 0 0
\(376\) 342528. 0.124947
\(377\) −1.57537e6 −0.570860
\(378\) 0 0
\(379\) 1.64235e6 0.587310 0.293655 0.955912i \(-0.405128\pi\)
0.293655 + 0.955912i \(0.405128\pi\)
\(380\) −98176.0 −0.0348776
\(381\) 0 0
\(382\) −1.50562e6 −0.527905
\(383\) −2.05698e6 −0.716527 −0.358263 0.933621i \(-0.616631\pi\)
−0.358263 + 0.933621i \(0.616631\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.37978e6 1.15457
\(387\) 0 0
\(388\) −341920. −0.115304
\(389\) −616142. −0.206446 −0.103223 0.994658i \(-0.532916\pi\)
−0.103223 + 0.994658i \(0.532916\pi\)
\(390\) 0 0
\(391\) −3.49938e6 −1.15758
\(392\) 0 0
\(393\) 0 0
\(394\) 1.97118e6 0.639713
\(395\) 2.32440e6 0.749580
\(396\) 0 0
\(397\) −2.19212e6 −0.698052 −0.349026 0.937113i \(-0.613487\pi\)
−0.349026 + 0.937113i \(0.613487\pi\)
\(398\) 3.65910e6 1.15789
\(399\) 0 0
\(400\) −626944. −0.195920
\(401\) −3.28454e6 −1.02003 −0.510015 0.860165i \(-0.670360\pi\)
−0.510015 + 0.860165i \(0.670360\pi\)
\(402\) 0 0
\(403\) −2.26670e6 −0.695236
\(404\) −589024. −0.179548
\(405\) 0 0
\(406\) 0 0
\(407\) −2.89371e6 −0.865903
\(408\) 0 0
\(409\) 3.61219e6 1.06773 0.533866 0.845569i \(-0.320739\pi\)
0.533866 + 0.845569i \(0.320739\pi\)
\(410\) 1.09637e6 0.322104
\(411\) 0 0
\(412\) −1.67245e6 −0.485411
\(413\) 0 0
\(414\) 0 0
\(415\) −167128. −0.0476353
\(416\) −325632. −0.0922558
\(417\) 0 0
\(418\) 626816. 0.175469
\(419\) 5.41489e6 1.50680 0.753398 0.657564i \(-0.228413\pi\)
0.753398 + 0.657564i \(0.228413\pi\)
\(420\) 0 0
\(421\) 3.60629e6 0.991644 0.495822 0.868424i \(-0.334867\pi\)
0.495822 + 0.868424i \(0.334867\pi\)
\(422\) 1.24712e6 0.340900
\(423\) 0 0
\(424\) 2.13466e6 0.576651
\(425\) −3.87432e6 −1.04045
\(426\) 0 0
\(427\) 0 0
\(428\) −3.43104e6 −0.905350
\(429\) 0 0
\(430\) −879008. −0.229257
\(431\) 2.78214e6 0.721416 0.360708 0.932679i \(-0.382535\pi\)
0.360708 + 0.932679i \(0.382535\pi\)
\(432\) 0 0
\(433\) −6.27619e6 −1.60871 −0.804353 0.594152i \(-0.797488\pi\)
−0.804353 + 0.594152i \(0.797488\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 460768. 0.116082
\(437\) 522032. 0.130766
\(438\) 0 0
\(439\) −641592. −0.158890 −0.0794452 0.996839i \(-0.525315\pi\)
−0.0794452 + 0.996839i \(0.525315\pi\)
\(440\) −1.10490e6 −0.272076
\(441\) 0 0
\(442\) −2.01230e6 −0.489934
\(443\) −6.05546e6 −1.46601 −0.733006 0.680222i \(-0.761883\pi\)
−0.733006 + 0.680222i \(0.761883\pi\)
\(444\) 0 0
\(445\) −3.18911e6 −0.763430
\(446\) 5.15104e6 1.22619
\(447\) 0 0
\(448\) 0 0
\(449\) 5.16681e6 1.20950 0.604752 0.796414i \(-0.293272\pi\)
0.604752 + 0.796414i \(0.293272\pi\)
\(450\) 0 0
\(451\) −6.99989e6 −1.62050
\(452\) 896224. 0.206334
\(453\) 0 0
\(454\) 5.15621e6 1.17406
\(455\) 0 0
\(456\) 0 0
\(457\) −227798. −0.0510222 −0.0255111 0.999675i \(-0.508121\pi\)
−0.0255111 + 0.999675i \(0.508121\pi\)
\(458\) −2.71286e6 −0.604315
\(459\) 0 0
\(460\) −920192. −0.202761
\(461\) 585146. 0.128237 0.0641183 0.997942i \(-0.479577\pi\)
0.0641183 + 0.997942i \(0.479577\pi\)
\(462\) 0 0
\(463\) −3.41454e6 −0.740251 −0.370126 0.928982i \(-0.620685\pi\)
−0.370126 + 0.928982i \(0.620685\pi\)
\(464\) 1.26822e6 0.273465
\(465\) 0 0
\(466\) 4.46924e6 0.953386
\(467\) 716300. 0.151986 0.0759929 0.997108i \(-0.475787\pi\)
0.0759929 + 0.997108i \(0.475787\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 556608. 0.116226
\(471\) 0 0
\(472\) −987904. −0.204108
\(473\) 5.61213e6 1.15339
\(474\) 0 0
\(475\) 577964. 0.117535
\(476\) 0 0
\(477\) 0 0
\(478\) 5.04782e6 1.01050
\(479\) 5.24092e6 1.04368 0.521842 0.853042i \(-0.325245\pi\)
0.521842 + 0.853042i \(0.325245\pi\)
\(480\) 0 0
\(481\) −1.38584e6 −0.273119
\(482\) −3.79287e6 −0.743619
\(483\) 0 0
\(484\) 4.47752e6 0.868809
\(485\) −555620. −0.107256
\(486\) 0 0
\(487\) 1.11702e6 0.213421 0.106710 0.994290i \(-0.465968\pi\)
0.106710 + 0.994290i \(0.465968\pi\)
\(488\) 2.35277e6 0.447229
\(489\) 0 0
\(490\) 0 0
\(491\) −1.34458e6 −0.251699 −0.125850 0.992049i \(-0.540166\pi\)
−0.125850 + 0.992049i \(0.540166\pi\)
\(492\) 0 0
\(493\) 7.83723e6 1.45226
\(494\) 300192. 0.0553454
\(495\) 0 0
\(496\) 1.82477e6 0.333045
\(497\) 0 0
\(498\) 0 0
\(499\) −6.54648e6 −1.17695 −0.588473 0.808517i \(-0.700271\pi\)
−0.588473 + 0.808517i \(0.700271\pi\)
\(500\) −2.31878e6 −0.414797
\(501\) 0 0
\(502\) −1.94558e6 −0.344580
\(503\) −8.22050e6 −1.44870 −0.724350 0.689432i \(-0.757860\pi\)
−0.724350 + 0.689432i \(0.757860\pi\)
\(504\) 0 0
\(505\) −957164. −0.167016
\(506\) 5.87507e6 1.02009
\(507\) 0 0
\(508\) 2.96640e6 0.510000
\(509\) −5.11045e6 −0.874308 −0.437154 0.899387i \(-0.644013\pi\)
−0.437154 + 0.899387i \(0.644013\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) −4.15639e6 −0.693919
\(515\) −2.71773e6 −0.451531
\(516\) 0 0
\(517\) −3.55373e6 −0.584733
\(518\) 0 0
\(519\) 0 0
\(520\) −529152. −0.0858168
\(521\) 9.69999e6 1.56559 0.782793 0.622282i \(-0.213794\pi\)
0.782793 + 0.622282i \(0.213794\pi\)
\(522\) 0 0
\(523\) 3.17295e6 0.507234 0.253617 0.967305i \(-0.418380\pi\)
0.253617 + 0.967305i \(0.418380\pi\)
\(524\) 1.03251e6 0.164273
\(525\) 0 0
\(526\) −5.40418e6 −0.851658
\(527\) 1.12765e7 1.76867
\(528\) 0 0
\(529\) −1.54340e6 −0.239794
\(530\) 3.46882e6 0.536403
\(531\) 0 0
\(532\) 0 0
\(533\) −3.35236e6 −0.511131
\(534\) 0 0
\(535\) −5.57544e6 −0.842160
\(536\) 2.62221e6 0.394235
\(537\) 0 0
\(538\) −4.47244e6 −0.666176
\(539\) 0 0
\(540\) 0 0
\(541\) −6.62575e6 −0.973289 −0.486644 0.873600i \(-0.661779\pi\)
−0.486644 + 0.873600i \(0.661779\pi\)
\(542\) 760416. 0.111187
\(543\) 0 0
\(544\) 1.61997e6 0.234698
\(545\) 748748. 0.107980
\(546\) 0 0
\(547\) 3.84707e6 0.549745 0.274873 0.961481i \(-0.411364\pi\)
0.274873 + 0.961481i \(0.411364\pi\)
\(548\) −2.44688e6 −0.348066
\(549\) 0 0
\(550\) 6.50454e6 0.916875
\(551\) −1.16914e6 −0.164055
\(552\) 0 0
\(553\) 0 0
\(554\) −802024. −0.111023
\(555\) 0 0
\(556\) 5.49536e6 0.753892
\(557\) −5.00176e6 −0.683101 −0.341550 0.939863i \(-0.610952\pi\)
−0.341550 + 0.939863i \(0.610952\pi\)
\(558\) 0 0
\(559\) 2.68774e6 0.363795
\(560\) 0 0
\(561\) 0 0
\(562\) −4.36948e6 −0.583565
\(563\) 2.27772e6 0.302852 0.151426 0.988469i \(-0.451614\pi\)
0.151426 + 0.988469i \(0.451614\pi\)
\(564\) 0 0
\(565\) 1.45636e6 0.191933
\(566\) −7.25032e6 −0.951297
\(567\) 0 0
\(568\) 581888. 0.0756778
\(569\) −8.86979e6 −1.14850 −0.574252 0.818678i \(-0.694707\pi\)
−0.574252 + 0.818678i \(0.694707\pi\)
\(570\) 0 0
\(571\) 1.40102e7 1.79826 0.899132 0.437678i \(-0.144199\pi\)
0.899132 + 0.437678i \(0.144199\pi\)
\(572\) 3.37843e6 0.431743
\(573\) 0 0
\(574\) 0 0
\(575\) 5.41719e6 0.683289
\(576\) 0 0
\(577\) −8.75327e6 −1.09454 −0.547269 0.836957i \(-0.684332\pi\)
−0.547269 + 0.836957i \(0.684332\pi\)
\(578\) 4.33147e6 0.539281
\(579\) 0 0
\(580\) 2.06086e6 0.254378
\(581\) 0 0
\(582\) 0 0
\(583\) −2.21471e7 −2.69864
\(584\) 4.70106e6 0.570379
\(585\) 0 0
\(586\) 8.40122e6 1.01064
\(587\) −1.06117e7 −1.27113 −0.635564 0.772048i \(-0.719232\pi\)
−0.635564 + 0.772048i \(0.719232\pi\)
\(588\) 0 0
\(589\) −1.68221e6 −0.199798
\(590\) −1.60534e6 −0.189862
\(591\) 0 0
\(592\) 1.11565e6 0.130835
\(593\) 1.88552e6 0.220188 0.110094 0.993921i \(-0.464885\pi\)
0.110094 + 0.993921i \(0.464885\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.79773e6 0.322619
\(597\) 0 0
\(598\) 2.81366e6 0.321751
\(599\) −1.27256e7 −1.44915 −0.724573 0.689198i \(-0.757963\pi\)
−0.724573 + 0.689198i \(0.757963\pi\)
\(600\) 0 0
\(601\) −7.18846e6 −0.811801 −0.405900 0.913917i \(-0.633042\pi\)
−0.405900 + 0.913917i \(0.633042\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −7.24083e6 −0.807600
\(605\) 7.27597e6 0.808170
\(606\) 0 0
\(607\) −1.08494e7 −1.19519 −0.597593 0.801800i \(-0.703876\pi\)
−0.597593 + 0.801800i \(0.703876\pi\)
\(608\) −241664. −0.0265126
\(609\) 0 0
\(610\) 3.82325e6 0.416014
\(611\) −1.70194e6 −0.184434
\(612\) 0 0
\(613\) −4.90511e6 −0.527227 −0.263614 0.964628i \(-0.584914\pi\)
−0.263614 + 0.964628i \(0.584914\pi\)
\(614\) 6.56418e6 0.702683
\(615\) 0 0
\(616\) 0 0
\(617\) −2.58445e6 −0.273310 −0.136655 0.990619i \(-0.543635\pi\)
−0.136655 + 0.990619i \(0.543635\pi\)
\(618\) 0 0
\(619\) 4.99336e6 0.523801 0.261901 0.965095i \(-0.415651\pi\)
0.261901 + 0.965095i \(0.415651\pi\)
\(620\) 2.96525e6 0.309800
\(621\) 0 0
\(622\) −3.78093e6 −0.391852
\(623\) 0 0
\(624\) 0 0
\(625\) 3.88510e6 0.397834
\(626\) −1.66142e6 −0.169450
\(627\) 0 0
\(628\) 7.98506e6 0.807940
\(629\) 6.89436e6 0.694812
\(630\) 0 0
\(631\) −1.18219e7 −1.18199 −0.590997 0.806674i \(-0.701265\pi\)
−0.590997 + 0.806674i \(0.701265\pi\)
\(632\) 5.72160e6 0.569803
\(633\) 0 0
\(634\) −4.73926e6 −0.468260
\(635\) 4.82040e6 0.474404
\(636\) 0 0
\(637\) 0 0
\(638\) −1.31578e7 −1.27977
\(639\) 0 0
\(640\) 425984. 0.0411096
\(641\) 5.47007e6 0.525833 0.262916 0.964819i \(-0.415316\pi\)
0.262916 + 0.964819i \(0.415316\pi\)
\(642\) 0 0
\(643\) −9.64934e6 −0.920386 −0.460193 0.887819i \(-0.652220\pi\)
−0.460193 + 0.887819i \(0.652220\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.49341e6 −0.140798
\(647\) 292368. 0.0274580 0.0137290 0.999906i \(-0.495630\pi\)
0.0137290 + 0.999906i \(0.495630\pi\)
\(648\) 0 0
\(649\) 1.02495e7 0.955193
\(650\) 3.11513e6 0.289196
\(651\) 0 0
\(652\) −7.60941e6 −0.701022
\(653\) −6.94081e6 −0.636982 −0.318491 0.947926i \(-0.603176\pi\)
−0.318491 + 0.947926i \(0.603176\pi\)
\(654\) 0 0
\(655\) 1.67783e6 0.152808
\(656\) 2.69875e6 0.244852
\(657\) 0 0
\(658\) 0 0
\(659\) 1.32912e7 1.19221 0.596104 0.802908i \(-0.296715\pi\)
0.596104 + 0.802908i \(0.296715\pi\)
\(660\) 0 0
\(661\) −2.05219e6 −0.182690 −0.0913448 0.995819i \(-0.529117\pi\)
−0.0913448 + 0.995819i \(0.529117\pi\)
\(662\) 5.48619e6 0.486548
\(663\) 0 0
\(664\) −411392. −0.0362106
\(665\) 0 0
\(666\) 0 0
\(667\) −1.09582e7 −0.953732
\(668\) 1.92358e6 0.166790
\(669\) 0 0
\(670\) 4.26109e6 0.366719
\(671\) −2.44100e7 −2.09296
\(672\) 0 0
\(673\) −1.57039e7 −1.33650 −0.668252 0.743935i \(-0.732957\pi\)
−0.668252 + 0.743935i \(0.732957\pi\)
\(674\) 3.85409e6 0.326792
\(675\) 0 0
\(676\) −4.32270e6 −0.363822
\(677\) −969534. −0.0813002 −0.0406501 0.999173i \(-0.512943\pi\)
−0.0406501 + 0.999173i \(0.512943\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.63245e6 0.218317
\(681\) 0 0
\(682\) −1.89320e7 −1.55860
\(683\) 1.49908e7 1.22962 0.614812 0.788673i \(-0.289232\pi\)
0.614812 + 0.788673i \(0.289232\pi\)
\(684\) 0 0
\(685\) −3.97618e6 −0.323772
\(686\) 0 0
\(687\) 0 0
\(688\) −2.16371e6 −0.174272
\(689\) −1.06066e7 −0.851191
\(690\) 0 0
\(691\) 7.16038e6 0.570481 0.285240 0.958456i \(-0.407927\pi\)
0.285240 + 0.958456i \(0.407927\pi\)
\(692\) 8.14198e6 0.646346
\(693\) 0 0
\(694\) −1.03092e7 −0.812509
\(695\) 8.92996e6 0.701274
\(696\) 0 0
\(697\) 1.66774e7 1.30031
\(698\) 1.22701e7 0.953253
\(699\) 0 0
\(700\) 0 0
\(701\) 91834.0 0.00705844 0.00352922 0.999994i \(-0.498877\pi\)
0.00352922 + 0.999994i \(0.498877\pi\)
\(702\) 0 0
\(703\) −1.02849e6 −0.0784894
\(704\) −2.71974e6 −0.206822
\(705\) 0 0
\(706\) −1.24058e7 −0.936725
\(707\) 0 0
\(708\) 0 0
\(709\) 2.20981e7 1.65097 0.825487 0.564422i \(-0.190901\pi\)
0.825487 + 0.564422i \(0.190901\pi\)
\(710\) 945568. 0.0703958
\(711\) 0 0
\(712\) −7.85011e6 −0.580331
\(713\) −1.57671e7 −1.16153
\(714\) 0 0
\(715\) 5.48995e6 0.401609
\(716\) −7.80096e6 −0.568677
\(717\) 0 0
\(718\) 1.31003e6 0.0948355
\(719\) 1.58388e7 1.14262 0.571308 0.820736i \(-0.306436\pi\)
0.571308 + 0.820736i \(0.306436\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.68161e6 −0.691202
\(723\) 0 0
\(724\) 8.71056e6 0.617589
\(725\) −1.21323e7 −0.857235
\(726\) 0 0
\(727\) −6.31418e6 −0.443078 −0.221539 0.975151i \(-0.571108\pi\)
−0.221539 + 0.975151i \(0.571108\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.63922e6 0.530569
\(731\) −1.33711e7 −0.925492
\(732\) 0 0
\(733\) −6.93003e6 −0.476404 −0.238202 0.971216i \(-0.576558\pi\)
−0.238202 + 0.971216i \(0.576558\pi\)
\(734\) 1.14696e7 0.785791
\(735\) 0 0
\(736\) −2.26509e6 −0.154131
\(737\) −2.72054e7 −1.84496
\(738\) 0 0
\(739\) 1.42331e7 0.958714 0.479357 0.877620i \(-0.340870\pi\)
0.479357 + 0.877620i \(0.340870\pi\)
\(740\) 1.81293e6 0.121703
\(741\) 0 0
\(742\) 0 0
\(743\) 5.94460e6 0.395048 0.197524 0.980298i \(-0.436710\pi\)
0.197524 + 0.980298i \(0.436710\pi\)
\(744\) 0 0
\(745\) 4.54631e6 0.300102
\(746\) 1.43212e7 0.942175
\(747\) 0 0
\(748\) −1.68072e7 −1.09835
\(749\) 0 0
\(750\) 0 0
\(751\) −682752. −0.0441736 −0.0220868 0.999756i \(-0.507031\pi\)
−0.0220868 + 0.999756i \(0.507031\pi\)
\(752\) 1.37011e6 0.0883510
\(753\) 0 0
\(754\) −6.30149e6 −0.403659
\(755\) −1.17664e7 −0.751233
\(756\) 0 0
\(757\) 1.46333e7 0.928116 0.464058 0.885805i \(-0.346393\pi\)
0.464058 + 0.885805i \(0.346393\pi\)
\(758\) 6.56939e6 0.415291
\(759\) 0 0
\(760\) −392704. −0.0246622
\(761\) −1.16367e7 −0.728399 −0.364200 0.931321i \(-0.618657\pi\)
−0.364200 + 0.931321i \(0.618657\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −6.02246e6 −0.373285
\(765\) 0 0
\(766\) −8.22790e6 −0.506661
\(767\) 4.90865e6 0.301282
\(768\) 0 0
\(769\) −1.91472e7 −1.16759 −0.583793 0.811902i \(-0.698432\pi\)
−0.583793 + 0.811902i \(0.698432\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.35191e7 0.816405
\(773\) −5.39261e6 −0.324601 −0.162301 0.986741i \(-0.551891\pi\)
−0.162301 + 0.986741i \(0.551891\pi\)
\(774\) 0 0
\(775\) −1.74565e7 −1.04400
\(776\) −1.36768e6 −0.0815324
\(777\) 0 0
\(778\) −2.46457e6 −0.145979
\(779\) −2.48791e6 −0.146890
\(780\) 0 0
\(781\) −6.03709e6 −0.354160
\(782\) −1.39975e7 −0.818530
\(783\) 0 0
\(784\) 0 0
\(785\) 1.29757e7 0.751549
\(786\) 0 0
\(787\) −3.04348e6 −0.175159 −0.0875796 0.996158i \(-0.527913\pi\)
−0.0875796 + 0.996158i \(0.527913\pi\)
\(788\) 7.88470e6 0.452345
\(789\) 0 0
\(790\) 9.29760e6 0.530033
\(791\) 0 0
\(792\) 0 0
\(793\) −1.16903e7 −0.660151
\(794\) −8.76847e6 −0.493597
\(795\) 0 0
\(796\) 1.46364e7 0.818751
\(797\) 2.29652e7 1.28063 0.640316 0.768111i \(-0.278803\pi\)
0.640316 + 0.768111i \(0.278803\pi\)
\(798\) 0 0
\(799\) 8.46686e6 0.469197
\(800\) −2.50778e6 −0.138536
\(801\) 0 0
\(802\) −1.31382e7 −0.721271
\(803\) −4.87735e7 −2.66928
\(804\) 0 0
\(805\) 0 0
\(806\) −9.06682e6 −0.491606
\(807\) 0 0
\(808\) −2.35610e6 −0.126959
\(809\) −1.90787e7 −1.02489 −0.512445 0.858720i \(-0.671260\pi\)
−0.512445 + 0.858720i \(0.671260\pi\)
\(810\) 0 0
\(811\) −1.09414e7 −0.584147 −0.292074 0.956396i \(-0.594345\pi\)
−0.292074 + 0.956396i \(0.594345\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.15748e7 −0.612286
\(815\) −1.23653e7 −0.652094
\(816\) 0 0
\(817\) 1.99467e6 0.104548
\(818\) 1.44488e7 0.755001
\(819\) 0 0
\(820\) 4.38547e6 0.227762
\(821\) −2.12594e7 −1.10076 −0.550380 0.834914i \(-0.685517\pi\)
−0.550380 + 0.834914i \(0.685517\pi\)
\(822\) 0 0
\(823\) −1.42256e7 −0.732103 −0.366052 0.930595i \(-0.619291\pi\)
−0.366052 + 0.930595i \(0.619291\pi\)
\(824\) −6.68979e6 −0.343237
\(825\) 0 0
\(826\) 0 0
\(827\) −2.76103e6 −0.140381 −0.0701904 0.997534i \(-0.522361\pi\)
−0.0701904 + 0.997534i \(0.522361\pi\)
\(828\) 0 0
\(829\) 3.82147e7 1.93127 0.965637 0.259895i \(-0.0836880\pi\)
0.965637 + 0.259895i \(0.0836880\pi\)
\(830\) −668512. −0.0336832
\(831\) 0 0
\(832\) −1.30253e6 −0.0652347
\(833\) 0 0
\(834\) 0 0
\(835\) 3.12582e6 0.155149
\(836\) 2.50726e6 0.124075
\(837\) 0 0
\(838\) 2.16596e7 1.06547
\(839\) 1.06044e7 0.520094 0.260047 0.965596i \(-0.416262\pi\)
0.260047 + 0.965596i \(0.416262\pi\)
\(840\) 0 0
\(841\) 4.03097e6 0.196526
\(842\) 1.44252e7 0.701198
\(843\) 0 0
\(844\) 4.98848e6 0.241053
\(845\) −7.02439e6 −0.338429
\(846\) 0 0
\(847\) 0 0
\(848\) 8.53862e6 0.407754
\(849\) 0 0
\(850\) −1.54973e7 −0.735712
\(851\) −9.63990e6 −0.456298
\(852\) 0 0
\(853\) 4.07009e7 1.91527 0.957637 0.287977i \(-0.0929826\pi\)
0.957637 + 0.287977i \(0.0929826\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.37242e7 −0.640179
\(857\) −3.10120e7 −1.44237 −0.721187 0.692741i \(-0.756403\pi\)
−0.721187 + 0.692741i \(0.756403\pi\)
\(858\) 0 0
\(859\) −1.09104e7 −0.504495 −0.252247 0.967663i \(-0.581170\pi\)
−0.252247 + 0.967663i \(0.581170\pi\)
\(860\) −3.51603e6 −0.162109
\(861\) 0 0
\(862\) 1.11286e7 0.510118
\(863\) −1.04089e7 −0.475751 −0.237875 0.971296i \(-0.576451\pi\)
−0.237875 + 0.971296i \(0.576451\pi\)
\(864\) 0 0
\(865\) 1.32307e7 0.601234
\(866\) −2.51048e7 −1.13753
\(867\) 0 0
\(868\) 0 0
\(869\) −5.93616e7 −2.66659
\(870\) 0 0
\(871\) −1.30291e7 −0.581928
\(872\) 1.84307e6 0.0820826
\(873\) 0 0
\(874\) 2.08813e6 0.0924652
\(875\) 0 0
\(876\) 0 0
\(877\) 1.64064e7 0.720299 0.360150 0.932895i \(-0.382726\pi\)
0.360150 + 0.932895i \(0.382726\pi\)
\(878\) −2.56637e6 −0.112352
\(879\) 0 0
\(880\) −4.41958e6 −0.192387
\(881\) 1.48577e7 0.644927 0.322464 0.946582i \(-0.395489\pi\)
0.322464 + 0.946582i \(0.395489\pi\)
\(882\) 0 0
\(883\) −2.72018e7 −1.17407 −0.587037 0.809560i \(-0.699706\pi\)
−0.587037 + 0.809560i \(0.699706\pi\)
\(884\) −8.04922e6 −0.346436
\(885\) 0 0
\(886\) −2.42218e7 −1.03663
\(887\) 2.71242e7 1.15757 0.578785 0.815480i \(-0.303527\pi\)
0.578785 + 0.815480i \(0.303527\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1.27564e7 −0.539827
\(891\) 0 0
\(892\) 2.06042e7 0.867047
\(893\) −1.26307e6 −0.0530029
\(894\) 0 0
\(895\) −1.26766e7 −0.528986
\(896\) 0 0
\(897\) 0 0
\(898\) 2.06673e7 0.855248
\(899\) 3.53121e7 1.45722
\(900\) 0 0
\(901\) 5.27660e7 2.16542
\(902\) −2.79996e7 −1.14587
\(903\) 0 0
\(904\) 3.58490e6 0.145900
\(905\) 1.41547e7 0.574484
\(906\) 0 0
\(907\) −8.42269e6 −0.339964 −0.169982 0.985447i \(-0.554371\pi\)
−0.169982 + 0.985447i \(0.554371\pi\)
\(908\) 2.06248e7 0.830187
\(909\) 0 0
\(910\) 0 0
\(911\) −3.08637e7 −1.23212 −0.616060 0.787700i \(-0.711272\pi\)
−0.616060 + 0.787700i \(0.711272\pi\)
\(912\) 0 0
\(913\) 4.26819e6 0.169460
\(914\) −911192. −0.0360782
\(915\) 0 0
\(916\) −1.08514e7 −0.427315
\(917\) 0 0
\(918\) 0 0
\(919\) 4.93895e6 0.192906 0.0964531 0.995338i \(-0.469250\pi\)
0.0964531 + 0.995338i \(0.469250\pi\)
\(920\) −3.68077e6 −0.143373
\(921\) 0 0
\(922\) 2.34058e6 0.0906770
\(923\) −2.89126e6 −0.111707
\(924\) 0 0
\(925\) −1.06727e7 −0.410130
\(926\) −1.36581e7 −0.523437
\(927\) 0 0
\(928\) 5.07290e6 0.193369
\(929\) 5.62575e6 0.213866 0.106933 0.994266i \(-0.465897\pi\)
0.106933 + 0.994266i \(0.465897\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.78770e7 0.674146
\(933\) 0 0
\(934\) 2.86520e6 0.107470
\(935\) −2.73116e7 −1.02169
\(936\) 0 0
\(937\) −2.60073e7 −0.967714 −0.483857 0.875147i \(-0.660764\pi\)
−0.483857 + 0.875147i \(0.660764\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 2.22643e6 0.0821845
\(941\) 3.02160e6 0.111241 0.0556203 0.998452i \(-0.482286\pi\)
0.0556203 + 0.998452i \(0.482286\pi\)
\(942\) 0 0
\(943\) −2.33189e7 −0.853943
\(944\) −3.95162e6 −0.144326
\(945\) 0 0
\(946\) 2.24485e7 0.815567
\(947\) 3.48282e7 1.26199 0.630995 0.775787i \(-0.282647\pi\)
0.630995 + 0.775787i \(0.282647\pi\)
\(948\) 0 0
\(949\) −2.33584e7 −0.841932
\(950\) 2.31186e6 0.0831097
\(951\) 0 0
\(952\) 0 0
\(953\) 9.39009e6 0.334917 0.167459 0.985879i \(-0.446444\pi\)
0.167459 + 0.985879i \(0.446444\pi\)
\(954\) 0 0
\(955\) −9.78650e6 −0.347232
\(956\) 2.01913e7 0.714528
\(957\) 0 0
\(958\) 2.09637e7 0.737996
\(959\) 0 0
\(960\) 0 0
\(961\) 2.21792e7 0.774708
\(962\) −5.54338e6 −0.193124
\(963\) 0 0
\(964\) −1.51715e7 −0.525818
\(965\) 2.19686e7 0.759423
\(966\) 0 0
\(967\) 1.44768e7 0.497860 0.248930 0.968521i \(-0.419921\pi\)
0.248930 + 0.968521i \(0.419921\pi\)
\(968\) 1.79101e7 0.614340
\(969\) 0 0
\(970\) −2.22248e6 −0.0758418
\(971\) 9.24976e6 0.314834 0.157417 0.987532i \(-0.449683\pi\)
0.157417 + 0.987532i \(0.449683\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 4.46806e6 0.150911
\(975\) 0 0
\(976\) 9.41107e6 0.316238
\(977\) 4.97780e7 1.66840 0.834202 0.551459i \(-0.185929\pi\)
0.834202 + 0.551459i \(0.185929\pi\)
\(978\) 0 0
\(979\) 8.14449e7 2.71586
\(980\) 0 0
\(981\) 0 0
\(982\) −5.37830e6 −0.177978
\(983\) −8.95601e6 −0.295618 −0.147809 0.989016i \(-0.547222\pi\)
−0.147809 + 0.989016i \(0.547222\pi\)
\(984\) 0 0
\(985\) 1.28126e7 0.420773
\(986\) 3.13489e7 1.02690
\(987\) 0 0
\(988\) 1.20077e6 0.0391351
\(989\) 1.86958e7 0.607790
\(990\) 0 0
\(991\) 2.62400e7 0.848751 0.424376 0.905486i \(-0.360494\pi\)
0.424376 + 0.905486i \(0.360494\pi\)
\(992\) 7.29907e6 0.235499
\(993\) 0 0
\(994\) 0 0
\(995\) 2.37842e7 0.761606
\(996\) 0 0
\(997\) −2.80506e7 −0.893727 −0.446863 0.894602i \(-0.647459\pi\)
−0.446863 + 0.894602i \(0.647459\pi\)
\(998\) −2.61859e7 −0.832226
\(999\) 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 882.6.a.s.1.1 1
3.2 odd 2 294.6.a.b.1.1 1
7.6 odd 2 126.6.a.i.1.1 1
21.2 odd 6 294.6.e.p.67.1 2
21.5 even 6 294.6.e.i.67.1 2
21.11 odd 6 294.6.e.p.79.1 2
21.17 even 6 294.6.e.i.79.1 2
21.20 even 2 42.6.a.d.1.1 1
28.27 even 2 1008.6.a.j.1.1 1
84.83 odd 2 336.6.a.h.1.1 1
105.62 odd 4 1050.6.g.i.799.1 2
105.83 odd 4 1050.6.g.i.799.2 2
105.104 even 2 1050.6.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.d.1.1 1 21.20 even 2
126.6.a.i.1.1 1 7.6 odd 2
294.6.a.b.1.1 1 3.2 odd 2
294.6.e.i.67.1 2 21.5 even 6
294.6.e.i.79.1 2 21.17 even 6
294.6.e.p.67.1 2 21.2 odd 6
294.6.e.p.79.1 2 21.11 odd 6
336.6.a.h.1.1 1 84.83 odd 2
882.6.a.s.1.1 1 1.1 even 1 trivial
1008.6.a.j.1.1 1 28.27 even 2
1050.6.a.k.1.1 1 105.104 even 2
1050.6.g.i.799.1 2 105.62 odd 4
1050.6.g.i.799.2 2 105.83 odd 4