Properties

Label 44.6.a.a.1.1
Level $44$
Weight $6$
Character 44.1
Self dual yes
Analytic conductor $7.057$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [44,6,Mod(1,44)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(44, 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("44.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 44.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: \(7.05688807177\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 44.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.00000 q^{3} -79.0000 q^{5} -50.0000 q^{7} -194.000 q^{9} +O(q^{10})\) \(q+7.00000 q^{3} -79.0000 q^{5} -50.0000 q^{7} -194.000 q^{9} +121.000 q^{11} -380.000 q^{13} -553.000 q^{15} -1154.00 q^{17} -1824.00 q^{19} -350.000 q^{21} +3591.00 q^{23} +3116.00 q^{25} -3059.00 q^{27} +8032.00 q^{29} -2945.00 q^{31} +847.000 q^{33} +3950.00 q^{35} +6979.00 q^{37} -2660.00 q^{39} -520.000 q^{41} -2486.00 q^{43} +15326.0 q^{45} -6920.00 q^{47} -14307.0 q^{49} -8078.00 q^{51} -13718.0 q^{53} -9559.00 q^{55} -12768.0 q^{57} -31779.0 q^{59} +34156.0 q^{61} +9700.00 q^{63} +30020.0 q^{65} -61503.0 q^{67} +25137.0 q^{69} -14971.0 q^{71} -36444.0 q^{73} +21812.0 q^{75} -6050.00 q^{77} -28538.0 q^{79} +25729.0 q^{81} +77482.0 q^{83} +91166.0 q^{85} +56224.0 q^{87} +36271.0 q^{89} +19000.0 q^{91} -20615.0 q^{93} +144096. q^{95} -49799.0 q^{97} -23474.0 q^{99} +O(q^{100})\)

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
\(3\) 7.00000 0.449050 0.224525 0.974468i \(-0.427917\pi\)
0.224525 + 0.974468i \(0.427917\pi\)
\(4\) 0 0
\(5\) −79.0000 −1.41319 −0.706597 0.707616i \(-0.749771\pi\)
−0.706597 + 0.707616i \(0.749771\pi\)
\(6\) 0 0
\(7\) −50.0000 −0.385678 −0.192839 0.981230i \(-0.561770\pi\)
−0.192839 + 0.981230i \(0.561770\pi\)
\(8\) 0 0
\(9\) −194.000 −0.798354
\(10\) 0 0
\(11\) 121.000 0.301511
\(12\) 0 0
\(13\) −380.000 −0.623627 −0.311814 0.950143i \(-0.600936\pi\)
−0.311814 + 0.950143i \(0.600936\pi\)
\(14\) 0 0
\(15\) −553.000 −0.634595
\(16\) 0 0
\(17\) −1154.00 −0.968464 −0.484232 0.874940i \(-0.660901\pi\)
−0.484232 + 0.874940i \(0.660901\pi\)
\(18\) 0 0
\(19\) −1824.00 −1.15915 −0.579577 0.814918i \(-0.696782\pi\)
−0.579577 + 0.814918i \(0.696782\pi\)
\(20\) 0 0
\(21\) −350.000 −0.173189
\(22\) 0 0
\(23\) 3591.00 1.41545 0.707727 0.706486i \(-0.249721\pi\)
0.707727 + 0.706486i \(0.249721\pi\)
\(24\) 0 0
\(25\) 3116.00 0.997120
\(26\) 0 0
\(27\) −3059.00 −0.807551
\(28\) 0 0
\(29\) 8032.00 1.77349 0.886745 0.462259i \(-0.152961\pi\)
0.886745 + 0.462259i \(0.152961\pi\)
\(30\) 0 0
\(31\) −2945.00 −0.550403 −0.275202 0.961387i \(-0.588745\pi\)
−0.275202 + 0.961387i \(0.588745\pi\)
\(32\) 0 0
\(33\) 847.000 0.135394
\(34\) 0 0
\(35\) 3950.00 0.545038
\(36\) 0 0
\(37\) 6979.00 0.838087 0.419043 0.907966i \(-0.362366\pi\)
0.419043 + 0.907966i \(0.362366\pi\)
\(38\) 0 0
\(39\) −2660.00 −0.280040
\(40\) 0 0
\(41\) −520.000 −0.0483107 −0.0241554 0.999708i \(-0.507690\pi\)
−0.0241554 + 0.999708i \(0.507690\pi\)
\(42\) 0 0
\(43\) −2486.00 −0.205036 −0.102518 0.994731i \(-0.532690\pi\)
−0.102518 + 0.994731i \(0.532690\pi\)
\(44\) 0 0
\(45\) 15326.0 1.12823
\(46\) 0 0
\(47\) −6920.00 −0.456942 −0.228471 0.973551i \(-0.573373\pi\)
−0.228471 + 0.973551i \(0.573373\pi\)
\(48\) 0 0
\(49\) −14307.0 −0.851252
\(50\) 0 0
\(51\) −8078.00 −0.434889
\(52\) 0 0
\(53\) −13718.0 −0.670812 −0.335406 0.942074i \(-0.608874\pi\)
−0.335406 + 0.942074i \(0.608874\pi\)
\(54\) 0 0
\(55\) −9559.00 −0.426094
\(56\) 0 0
\(57\) −12768.0 −0.520518
\(58\) 0 0
\(59\) −31779.0 −1.18853 −0.594265 0.804269i \(-0.702557\pi\)
−0.594265 + 0.804269i \(0.702557\pi\)
\(60\) 0 0
\(61\) 34156.0 1.17528 0.587641 0.809121i \(-0.300057\pi\)
0.587641 + 0.809121i \(0.300057\pi\)
\(62\) 0 0
\(63\) 9700.00 0.307908
\(64\) 0 0
\(65\) 30020.0 0.881307
\(66\) 0 0
\(67\) −61503.0 −1.67382 −0.836911 0.547339i \(-0.815641\pi\)
−0.836911 + 0.547339i \(0.815641\pi\)
\(68\) 0 0
\(69\) 25137.0 0.635610
\(70\) 0 0
\(71\) −14971.0 −0.352456 −0.176228 0.984349i \(-0.556390\pi\)
−0.176228 + 0.984349i \(0.556390\pi\)
\(72\) 0 0
\(73\) −36444.0 −0.800422 −0.400211 0.916423i \(-0.631063\pi\)
−0.400211 + 0.916423i \(0.631063\pi\)
\(74\) 0 0
\(75\) 21812.0 0.447757
\(76\) 0 0
\(77\) −6050.00 −0.116286
\(78\) 0 0
\(79\) −28538.0 −0.514465 −0.257232 0.966350i \(-0.582811\pi\)
−0.257232 + 0.966350i \(0.582811\pi\)
\(80\) 0 0
\(81\) 25729.0 0.435723
\(82\) 0 0
\(83\) 77482.0 1.23454 0.617271 0.786751i \(-0.288238\pi\)
0.617271 + 0.786751i \(0.288238\pi\)
\(84\) 0 0
\(85\) 91166.0 1.36863
\(86\) 0 0
\(87\) 56224.0 0.796386
\(88\) 0 0
\(89\) 36271.0 0.485383 0.242691 0.970104i \(-0.421970\pi\)
0.242691 + 0.970104i \(0.421970\pi\)
\(90\) 0 0
\(91\) 19000.0 0.240519
\(92\) 0 0
\(93\) −20615.0 −0.247159
\(94\) 0 0
\(95\) 144096. 1.63811
\(96\) 0 0
\(97\) −49799.0 −0.537392 −0.268696 0.963225i \(-0.586593\pi\)
−0.268696 + 0.963225i \(0.586593\pi\)
\(98\) 0 0
\(99\) −23474.0 −0.240713
\(100\) 0 0
\(101\) −153406. −1.49637 −0.748185 0.663490i \(-0.769074\pi\)
−0.748185 + 0.663490i \(0.769074\pi\)
\(102\) 0 0
\(103\) −134720. −1.25124 −0.625618 0.780130i \(-0.715153\pi\)
−0.625618 + 0.780130i \(0.715153\pi\)
\(104\) 0 0
\(105\) 27650.0 0.244750
\(106\) 0 0
\(107\) 169218. 1.42885 0.714426 0.699711i \(-0.246688\pi\)
0.714426 + 0.699711i \(0.246688\pi\)
\(108\) 0 0
\(109\) −233206. −1.88007 −0.940034 0.341081i \(-0.889207\pi\)
−0.940034 + 0.341081i \(0.889207\pi\)
\(110\) 0 0
\(111\) 48853.0 0.376343
\(112\) 0 0
\(113\) 94329.0 0.694943 0.347471 0.937691i \(-0.387040\pi\)
0.347471 + 0.937691i \(0.387040\pi\)
\(114\) 0 0
\(115\) −283689. −2.00031
\(116\) 0 0
\(117\) 73720.0 0.497875
\(118\) 0 0
\(119\) 57700.0 0.373515
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) 0 0
\(123\) −3640.00 −0.0216939
\(124\) 0 0
\(125\) 711.000 0.00407000
\(126\) 0 0
\(127\) −259480. −1.42756 −0.713780 0.700370i \(-0.753019\pi\)
−0.713780 + 0.700370i \(0.753019\pi\)
\(128\) 0 0
\(129\) −17402.0 −0.0920714
\(130\) 0 0
\(131\) −85410.0 −0.434841 −0.217420 0.976078i \(-0.569764\pi\)
−0.217420 + 0.976078i \(0.569764\pi\)
\(132\) 0 0
\(133\) 91200.0 0.447060
\(134\) 0 0
\(135\) 241661. 1.14123
\(136\) 0 0
\(137\) −427703. −1.94689 −0.973444 0.228926i \(-0.926479\pi\)
−0.973444 + 0.228926i \(0.926479\pi\)
\(138\) 0 0
\(139\) 309690. 1.35953 0.679767 0.733428i \(-0.262081\pi\)
0.679767 + 0.733428i \(0.262081\pi\)
\(140\) 0 0
\(141\) −48440.0 −0.205190
\(142\) 0 0
\(143\) −45980.0 −0.188031
\(144\) 0 0
\(145\) −634528. −2.50629
\(146\) 0 0
\(147\) −100149. −0.382255
\(148\) 0 0
\(149\) 449846. 1.65996 0.829981 0.557792i \(-0.188351\pi\)
0.829981 + 0.557792i \(0.188351\pi\)
\(150\) 0 0
\(151\) 405074. 1.44575 0.722873 0.690981i \(-0.242821\pi\)
0.722873 + 0.690981i \(0.242821\pi\)
\(152\) 0 0
\(153\) 223876. 0.773177
\(154\) 0 0
\(155\) 232655. 0.777827
\(156\) 0 0
\(157\) 339321. 1.09866 0.549328 0.835607i \(-0.314884\pi\)
0.549328 + 0.835607i \(0.314884\pi\)
\(158\) 0 0
\(159\) −96026.0 −0.301228
\(160\) 0 0
\(161\) −179550. −0.545910
\(162\) 0 0
\(163\) 271396. 0.800082 0.400041 0.916497i \(-0.368996\pi\)
0.400041 + 0.916497i \(0.368996\pi\)
\(164\) 0 0
\(165\) −66913.0 −0.191338
\(166\) 0 0
\(167\) 72468.0 0.201074 0.100537 0.994933i \(-0.467944\pi\)
0.100537 + 0.994933i \(0.467944\pi\)
\(168\) 0 0
\(169\) −226893. −0.611089
\(170\) 0 0
\(171\) 353856. 0.925414
\(172\) 0 0
\(173\) 479226. 1.21738 0.608689 0.793409i \(-0.291696\pi\)
0.608689 + 0.793409i \(0.291696\pi\)
\(174\) 0 0
\(175\) −155800. −0.384567
\(176\) 0 0
\(177\) −222453. −0.533710
\(178\) 0 0
\(179\) −40935.0 −0.0954910 −0.0477455 0.998860i \(-0.515204\pi\)
−0.0477455 + 0.998860i \(0.515204\pi\)
\(180\) 0 0
\(181\) −90169.0 −0.204579 −0.102289 0.994755i \(-0.532617\pi\)
−0.102289 + 0.994755i \(0.532617\pi\)
\(182\) 0 0
\(183\) 239092. 0.527761
\(184\) 0 0
\(185\) −551341. −1.18438
\(186\) 0 0
\(187\) −139634. −0.292003
\(188\) 0 0
\(189\) 152950. 0.311455
\(190\) 0 0
\(191\) −260375. −0.516435 −0.258218 0.966087i \(-0.583135\pi\)
−0.258218 + 0.966087i \(0.583135\pi\)
\(192\) 0 0
\(193\) 524324. 1.01323 0.506613 0.862173i \(-0.330897\pi\)
0.506613 + 0.862173i \(0.330897\pi\)
\(194\) 0 0
\(195\) 210140. 0.395751
\(196\) 0 0
\(197\) 759582. 1.39447 0.697235 0.716843i \(-0.254413\pi\)
0.697235 + 0.716843i \(0.254413\pi\)
\(198\) 0 0
\(199\) −882736. −1.58015 −0.790075 0.613011i \(-0.789958\pi\)
−0.790075 + 0.613011i \(0.789958\pi\)
\(200\) 0 0
\(201\) −430521. −0.751630
\(202\) 0 0
\(203\) −401600. −0.683996
\(204\) 0 0
\(205\) 41080.0 0.0682725
\(206\) 0 0
\(207\) −696654. −1.13003
\(208\) 0 0
\(209\) −220704. −0.349498
\(210\) 0 0
\(211\) −1.15285e6 −1.78266 −0.891328 0.453360i \(-0.850225\pi\)
−0.891328 + 0.453360i \(0.850225\pi\)
\(212\) 0 0
\(213\) −104797. −0.158270
\(214\) 0 0
\(215\) 196394. 0.289756
\(216\) 0 0
\(217\) 147250. 0.212278
\(218\) 0 0
\(219\) −255108. −0.359430
\(220\) 0 0
\(221\) 438520. 0.603961
\(222\) 0 0
\(223\) −65893.0 −0.0887314 −0.0443657 0.999015i \(-0.514127\pi\)
−0.0443657 + 0.999015i \(0.514127\pi\)
\(224\) 0 0
\(225\) −604504. −0.796055
\(226\) 0 0
\(227\) −314526. −0.405128 −0.202564 0.979269i \(-0.564927\pi\)
−0.202564 + 0.979269i \(0.564927\pi\)
\(228\) 0 0
\(229\) 1.03846e6 1.30859 0.654293 0.756241i \(-0.272966\pi\)
0.654293 + 0.756241i \(0.272966\pi\)
\(230\) 0 0
\(231\) −42350.0 −0.0522184
\(232\) 0 0
\(233\) 509976. 0.615403 0.307702 0.951483i \(-0.400440\pi\)
0.307702 + 0.951483i \(0.400440\pi\)
\(234\) 0 0
\(235\) 546680. 0.645749
\(236\) 0 0
\(237\) −199766. −0.231021
\(238\) 0 0
\(239\) −444494. −0.503351 −0.251676 0.967812i \(-0.580982\pi\)
−0.251676 + 0.967812i \(0.580982\pi\)
\(240\) 0 0
\(241\) −283464. −0.314380 −0.157190 0.987568i \(-0.550244\pi\)
−0.157190 + 0.987568i \(0.550244\pi\)
\(242\) 0 0
\(243\) 923440. 1.00321
\(244\) 0 0
\(245\) 1.13025e6 1.20299
\(246\) 0 0
\(247\) 693120. 0.722880
\(248\) 0 0
\(249\) 542374. 0.554371
\(250\) 0 0
\(251\) −773807. −0.775262 −0.387631 0.921815i \(-0.626706\pi\)
−0.387631 + 0.921815i \(0.626706\pi\)
\(252\) 0 0
\(253\) 434511. 0.426775
\(254\) 0 0
\(255\) 638162. 0.614583
\(256\) 0 0
\(257\) −387714. −0.366167 −0.183083 0.983097i \(-0.558608\pi\)
−0.183083 + 0.983097i \(0.558608\pi\)
\(258\) 0 0
\(259\) −348950. −0.323232
\(260\) 0 0
\(261\) −1.55821e6 −1.41587
\(262\) 0 0
\(263\) −197602. −0.176158 −0.0880789 0.996113i \(-0.528073\pi\)
−0.0880789 + 0.996113i \(0.528073\pi\)
\(264\) 0 0
\(265\) 1.08372e6 0.947989
\(266\) 0 0
\(267\) 253897. 0.217961
\(268\) 0 0
\(269\) −262694. −0.221345 −0.110672 0.993857i \(-0.535300\pi\)
−0.110672 + 0.993857i \(0.535300\pi\)
\(270\) 0 0
\(271\) −159068. −0.131571 −0.0657854 0.997834i \(-0.520955\pi\)
−0.0657854 + 0.997834i \(0.520955\pi\)
\(272\) 0 0
\(273\) 133000. 0.108005
\(274\) 0 0
\(275\) 377036. 0.300643
\(276\) 0 0
\(277\) 1.29385e6 1.01318 0.506589 0.862188i \(-0.330906\pi\)
0.506589 + 0.862188i \(0.330906\pi\)
\(278\) 0 0
\(279\) 571330. 0.439417
\(280\) 0 0
\(281\) −1.78114e6 −1.34565 −0.672824 0.739802i \(-0.734919\pi\)
−0.672824 + 0.739802i \(0.734919\pi\)
\(282\) 0 0
\(283\) 1.98279e6 1.47167 0.735835 0.677161i \(-0.236790\pi\)
0.735835 + 0.677161i \(0.236790\pi\)
\(284\) 0 0
\(285\) 1.00867e6 0.735593
\(286\) 0 0
\(287\) 26000.0 0.0186324
\(288\) 0 0
\(289\) −88141.0 −0.0620774
\(290\) 0 0
\(291\) −348593. −0.241316
\(292\) 0 0
\(293\) 578360. 0.393577 0.196788 0.980446i \(-0.436949\pi\)
0.196788 + 0.980446i \(0.436949\pi\)
\(294\) 0 0
\(295\) 2.51054e6 1.67962
\(296\) 0 0
\(297\) −370139. −0.243486
\(298\) 0 0
\(299\) −1.36458e6 −0.882716
\(300\) 0 0
\(301\) 124300. 0.0790779
\(302\) 0 0
\(303\) −1.07384e6 −0.671945
\(304\) 0 0
\(305\) −2.69832e6 −1.66090
\(306\) 0 0
\(307\) −3.07602e6 −1.86270 −0.931352 0.364120i \(-0.881370\pi\)
−0.931352 + 0.364120i \(0.881370\pi\)
\(308\) 0 0
\(309\) −943040. −0.561868
\(310\) 0 0
\(311\) −3.13757e6 −1.83947 −0.919735 0.392540i \(-0.871597\pi\)
−0.919735 + 0.392540i \(0.871597\pi\)
\(312\) 0 0
\(313\) 2.61784e6 1.51037 0.755183 0.655514i \(-0.227548\pi\)
0.755183 + 0.655514i \(0.227548\pi\)
\(314\) 0 0
\(315\) −766300. −0.435133
\(316\) 0 0
\(317\) −2.49220e6 −1.39294 −0.696472 0.717584i \(-0.745248\pi\)
−0.696472 + 0.717584i \(0.745248\pi\)
\(318\) 0 0
\(319\) 971872. 0.534727
\(320\) 0 0
\(321\) 1.18453e6 0.641626
\(322\) 0 0
\(323\) 2.10490e6 1.12260
\(324\) 0 0
\(325\) −1.18408e6 −0.621831
\(326\) 0 0
\(327\) −1.63244e6 −0.844245
\(328\) 0 0
\(329\) 346000. 0.176233
\(330\) 0 0
\(331\) −2.70125e6 −1.35517 −0.677586 0.735443i \(-0.736974\pi\)
−0.677586 + 0.735443i \(0.736974\pi\)
\(332\) 0 0
\(333\) −1.35393e6 −0.669090
\(334\) 0 0
\(335\) 4.85874e6 2.36544
\(336\) 0 0
\(337\) −1.42610e6 −0.684031 −0.342016 0.939694i \(-0.611110\pi\)
−0.342016 + 0.939694i \(0.611110\pi\)
\(338\) 0 0
\(339\) 660303. 0.312064
\(340\) 0 0
\(341\) −356345. −0.165953
\(342\) 0 0
\(343\) 1.55570e6 0.713987
\(344\) 0 0
\(345\) −1.98582e6 −0.898241
\(346\) 0 0
\(347\) 2.86374e6 1.27676 0.638381 0.769721i \(-0.279604\pi\)
0.638381 + 0.769721i \(0.279604\pi\)
\(348\) 0 0
\(349\) 296350. 0.130239 0.0651195 0.997877i \(-0.479257\pi\)
0.0651195 + 0.997877i \(0.479257\pi\)
\(350\) 0 0
\(351\) 1.16242e6 0.503611
\(352\) 0 0
\(353\) −2.12114e6 −0.906010 −0.453005 0.891508i \(-0.649648\pi\)
−0.453005 + 0.891508i \(0.649648\pi\)
\(354\) 0 0
\(355\) 1.18271e6 0.498089
\(356\) 0 0
\(357\) 403900. 0.167727
\(358\) 0 0
\(359\) −3.47512e6 −1.42310 −0.711548 0.702638i \(-0.752006\pi\)
−0.711548 + 0.702638i \(0.752006\pi\)
\(360\) 0 0
\(361\) 850877. 0.343636
\(362\) 0 0
\(363\) 102487. 0.0408227
\(364\) 0 0
\(365\) 2.87908e6 1.13115
\(366\) 0 0
\(367\) 1.56190e6 0.605322 0.302661 0.953098i \(-0.402125\pi\)
0.302661 + 0.953098i \(0.402125\pi\)
\(368\) 0 0
\(369\) 100880. 0.0385691
\(370\) 0 0
\(371\) 685900. 0.258718
\(372\) 0 0
\(373\) 1.93773e6 0.721144 0.360572 0.932731i \(-0.382581\pi\)
0.360572 + 0.932731i \(0.382581\pi\)
\(374\) 0 0
\(375\) 4977.00 0.00182764
\(376\) 0 0
\(377\) −3.05216e6 −1.10600
\(378\) 0 0
\(379\) 3.07495e6 1.09961 0.549806 0.835292i \(-0.314702\pi\)
0.549806 + 0.835292i \(0.314702\pi\)
\(380\) 0 0
\(381\) −1.81636e6 −0.641046
\(382\) 0 0
\(383\) 4.31553e6 1.50327 0.751635 0.659579i \(-0.229266\pi\)
0.751635 + 0.659579i \(0.229266\pi\)
\(384\) 0 0
\(385\) 477950. 0.164335
\(386\) 0 0
\(387\) 482284. 0.163691
\(388\) 0 0
\(389\) 2.36251e6 0.791590 0.395795 0.918339i \(-0.370469\pi\)
0.395795 + 0.918339i \(0.370469\pi\)
\(390\) 0 0
\(391\) −4.14401e6 −1.37082
\(392\) 0 0
\(393\) −597870. −0.195265
\(394\) 0 0
\(395\) 2.25450e6 0.727039
\(396\) 0 0
\(397\) 1.77598e6 0.565539 0.282769 0.959188i \(-0.408747\pi\)
0.282769 + 0.959188i \(0.408747\pi\)
\(398\) 0 0
\(399\) 638400. 0.200752
\(400\) 0 0
\(401\) 1.56967e6 0.487468 0.243734 0.969842i \(-0.421628\pi\)
0.243734 + 0.969842i \(0.421628\pi\)
\(402\) 0 0
\(403\) 1.11910e6 0.343247
\(404\) 0 0
\(405\) −2.03259e6 −0.615761
\(406\) 0 0
\(407\) 844459. 0.252693
\(408\) 0 0
\(409\) 1.29485e6 0.382746 0.191373 0.981517i \(-0.438706\pi\)
0.191373 + 0.981517i \(0.438706\pi\)
\(410\) 0 0
\(411\) −2.99392e6 −0.874250
\(412\) 0 0
\(413\) 1.58895e6 0.458390
\(414\) 0 0
\(415\) −6.12108e6 −1.74465
\(416\) 0 0
\(417\) 2.16783e6 0.610499
\(418\) 0 0
\(419\) 272916. 0.0759441 0.0379720 0.999279i \(-0.487910\pi\)
0.0379720 + 0.999279i \(0.487910\pi\)
\(420\) 0 0
\(421\) −2.61801e6 −0.719890 −0.359945 0.932974i \(-0.617205\pi\)
−0.359945 + 0.932974i \(0.617205\pi\)
\(422\) 0 0
\(423\) 1.34248e6 0.364802
\(424\) 0 0
\(425\) −3.59586e6 −0.965675
\(426\) 0 0
\(427\) −1.70780e6 −0.453281
\(428\) 0 0
\(429\) −321860. −0.0844352
\(430\) 0 0
\(431\) 2.81037e6 0.728735 0.364368 0.931255i \(-0.381285\pi\)
0.364368 + 0.931255i \(0.381285\pi\)
\(432\) 0 0
\(433\) 5.98509e6 1.53409 0.767046 0.641593i \(-0.221726\pi\)
0.767046 + 0.641593i \(0.221726\pi\)
\(434\) 0 0
\(435\) −4.44170e6 −1.12545
\(436\) 0 0
\(437\) −6.54998e6 −1.64073
\(438\) 0 0
\(439\) −7.50486e6 −1.85858 −0.929290 0.369352i \(-0.879580\pi\)
−0.929290 + 0.369352i \(0.879580\pi\)
\(440\) 0 0
\(441\) 2.77556e6 0.679601
\(442\) 0 0
\(443\) 1.56806e6 0.379624 0.189812 0.981820i \(-0.439212\pi\)
0.189812 + 0.981820i \(0.439212\pi\)
\(444\) 0 0
\(445\) −2.86541e6 −0.685941
\(446\) 0 0
\(447\) 3.14892e6 0.745406
\(448\) 0 0
\(449\) −4.04044e6 −0.945831 −0.472915 0.881108i \(-0.656798\pi\)
−0.472915 + 0.881108i \(0.656798\pi\)
\(450\) 0 0
\(451\) −62920.0 −0.0145662
\(452\) 0 0
\(453\) 2.83552e6 0.649213
\(454\) 0 0
\(455\) −1.50100e6 −0.339901
\(456\) 0 0
\(457\) 2.21132e6 0.495291 0.247645 0.968851i \(-0.420343\pi\)
0.247645 + 0.968851i \(0.420343\pi\)
\(458\) 0 0
\(459\) 3.53009e6 0.782084
\(460\) 0 0
\(461\) −3.56735e6 −0.781795 −0.390898 0.920434i \(-0.627835\pi\)
−0.390898 + 0.920434i \(0.627835\pi\)
\(462\) 0 0
\(463\) 747757. 0.162109 0.0810547 0.996710i \(-0.474171\pi\)
0.0810547 + 0.996710i \(0.474171\pi\)
\(464\) 0 0
\(465\) 1.62858e6 0.349283
\(466\) 0 0
\(467\) −5.44511e6 −1.15535 −0.577676 0.816266i \(-0.696040\pi\)
−0.577676 + 0.816266i \(0.696040\pi\)
\(468\) 0 0
\(469\) 3.07515e6 0.645556
\(470\) 0 0
\(471\) 2.37525e6 0.493352
\(472\) 0 0
\(473\) −300806. −0.0618207
\(474\) 0 0
\(475\) −5.68358e6 −1.15581
\(476\) 0 0
\(477\) 2.66129e6 0.535546
\(478\) 0 0
\(479\) −6.22046e6 −1.23875 −0.619375 0.785095i \(-0.712614\pi\)
−0.619375 + 0.785095i \(0.712614\pi\)
\(480\) 0 0
\(481\) −2.65202e6 −0.522654
\(482\) 0 0
\(483\) −1.25685e6 −0.245141
\(484\) 0 0
\(485\) 3.93412e6 0.759440
\(486\) 0 0
\(487\) −3.34398e6 −0.638913 −0.319457 0.947601i \(-0.603500\pi\)
−0.319457 + 0.947601i \(0.603500\pi\)
\(488\) 0 0
\(489\) 1.89977e6 0.359277
\(490\) 0 0
\(491\) 5.58646e6 1.04576 0.522881 0.852406i \(-0.324857\pi\)
0.522881 + 0.852406i \(0.324857\pi\)
\(492\) 0 0
\(493\) −9.26893e6 −1.71756
\(494\) 0 0
\(495\) 1.85445e6 0.340174
\(496\) 0 0
\(497\) 748550. 0.135935
\(498\) 0 0
\(499\) −8.29348e6 −1.49103 −0.745514 0.666490i \(-0.767796\pi\)
−0.745514 + 0.666490i \(0.767796\pi\)
\(500\) 0 0
\(501\) 507276. 0.0902922
\(502\) 0 0
\(503\) 5.29951e6 0.933933 0.466967 0.884275i \(-0.345347\pi\)
0.466967 + 0.884275i \(0.345347\pi\)
\(504\) 0 0
\(505\) 1.21191e7 2.11466
\(506\) 0 0
\(507\) −1.58825e6 −0.274410
\(508\) 0 0
\(509\) 24415.0 0.00417698 0.00208849 0.999998i \(-0.499335\pi\)
0.00208849 + 0.999998i \(0.499335\pi\)
\(510\) 0 0
\(511\) 1.82220e6 0.308705
\(512\) 0 0
\(513\) 5.57962e6 0.936076
\(514\) 0 0
\(515\) 1.06429e7 1.76824
\(516\) 0 0
\(517\) −837320. −0.137773
\(518\) 0 0
\(519\) 3.35458e6 0.546663
\(520\) 0 0
\(521\) 4.76275e6 0.768712 0.384356 0.923185i \(-0.374424\pi\)
0.384356 + 0.923185i \(0.374424\pi\)
\(522\) 0 0
\(523\) 735248. 0.117538 0.0587692 0.998272i \(-0.481282\pi\)
0.0587692 + 0.998272i \(0.481282\pi\)
\(524\) 0 0
\(525\) −1.09060e6 −0.172690
\(526\) 0 0
\(527\) 3.39853e6 0.533046
\(528\) 0 0
\(529\) 6.45894e6 1.00351
\(530\) 0 0
\(531\) 6.16513e6 0.948868
\(532\) 0 0
\(533\) 197600. 0.0301279
\(534\) 0 0
\(535\) −1.33682e7 −2.01925
\(536\) 0 0
\(537\) −286545. −0.0428802
\(538\) 0 0
\(539\) −1.73115e6 −0.256662
\(540\) 0 0
\(541\) −3.19649e6 −0.469548 −0.234774 0.972050i \(-0.575435\pi\)
−0.234774 + 0.972050i \(0.575435\pi\)
\(542\) 0 0
\(543\) −631183. −0.0918662
\(544\) 0 0
\(545\) 1.84233e7 2.65690
\(546\) 0 0
\(547\) 8.85902e6 1.26595 0.632976 0.774171i \(-0.281833\pi\)
0.632976 + 0.774171i \(0.281833\pi\)
\(548\) 0 0
\(549\) −6.62626e6 −0.938292
\(550\) 0 0
\(551\) −1.46504e7 −2.05575
\(552\) 0 0
\(553\) 1.42690e6 0.198418
\(554\) 0 0
\(555\) −3.85939e6 −0.531846
\(556\) 0 0
\(557\) −1.74512e6 −0.238335 −0.119167 0.992874i \(-0.538023\pi\)
−0.119167 + 0.992874i \(0.538023\pi\)
\(558\) 0 0
\(559\) 944680. 0.127866
\(560\) 0 0
\(561\) −977438. −0.131124
\(562\) 0 0
\(563\) −1.32333e7 −1.75953 −0.879764 0.475410i \(-0.842300\pi\)
−0.879764 + 0.475410i \(0.842300\pi\)
\(564\) 0 0
\(565\) −7.45199e6 −0.982090
\(566\) 0 0
\(567\) −1.28645e6 −0.168049
\(568\) 0 0
\(569\) 1.04156e7 1.34867 0.674335 0.738426i \(-0.264430\pi\)
0.674335 + 0.738426i \(0.264430\pi\)
\(570\) 0 0
\(571\) −2.48163e6 −0.318527 −0.159264 0.987236i \(-0.550912\pi\)
−0.159264 + 0.987236i \(0.550912\pi\)
\(572\) 0 0
\(573\) −1.82262e6 −0.231905
\(574\) 0 0
\(575\) 1.11896e7 1.41138
\(576\) 0 0
\(577\) −1.31244e7 −1.64112 −0.820562 0.571557i \(-0.806339\pi\)
−0.820562 + 0.571557i \(0.806339\pi\)
\(578\) 0 0
\(579\) 3.67027e6 0.454989
\(580\) 0 0
\(581\) −3.87410e6 −0.476135
\(582\) 0 0
\(583\) −1.65988e6 −0.202258
\(584\) 0 0
\(585\) −5.82388e6 −0.703595
\(586\) 0 0
\(587\) −4.86010e6 −0.582170 −0.291085 0.956697i \(-0.594016\pi\)
−0.291085 + 0.956697i \(0.594016\pi\)
\(588\) 0 0
\(589\) 5.37168e6 0.638002
\(590\) 0 0
\(591\) 5.31707e6 0.626187
\(592\) 0 0
\(593\) −1.58559e6 −0.185163 −0.0925814 0.995705i \(-0.529512\pi\)
−0.0925814 + 0.995705i \(0.529512\pi\)
\(594\) 0 0
\(595\) −4.55830e6 −0.527850
\(596\) 0 0
\(597\) −6.17915e6 −0.709566
\(598\) 0 0
\(599\) 9.04294e6 1.02978 0.514888 0.857258i \(-0.327834\pi\)
0.514888 + 0.857258i \(0.327834\pi\)
\(600\) 0 0
\(601\) 729186. 0.0823478 0.0411739 0.999152i \(-0.486890\pi\)
0.0411739 + 0.999152i \(0.486890\pi\)
\(602\) 0 0
\(603\) 1.19316e7 1.33630
\(604\) 0 0
\(605\) −1.15664e6 −0.128472
\(606\) 0 0
\(607\) −3.91130e6 −0.430873 −0.215437 0.976518i \(-0.569117\pi\)
−0.215437 + 0.976518i \(0.569117\pi\)
\(608\) 0 0
\(609\) −2.81120e6 −0.307149
\(610\) 0 0
\(611\) 2.62960e6 0.284962
\(612\) 0 0
\(613\) −5.52184e6 −0.593516 −0.296758 0.954953i \(-0.595906\pi\)
−0.296758 + 0.954953i \(0.595906\pi\)
\(614\) 0 0
\(615\) 287560. 0.0306578
\(616\) 0 0
\(617\) −4.88539e6 −0.516638 −0.258319 0.966060i \(-0.583169\pi\)
−0.258319 + 0.966060i \(0.583169\pi\)
\(618\) 0 0
\(619\) −4.11150e6 −0.431295 −0.215647 0.976471i \(-0.569186\pi\)
−0.215647 + 0.976471i \(0.569186\pi\)
\(620\) 0 0
\(621\) −1.09849e7 −1.14305
\(622\) 0 0
\(623\) −1.81355e6 −0.187202
\(624\) 0 0
\(625\) −9.79367e6 −1.00287
\(626\) 0 0
\(627\) −1.54493e6 −0.156942
\(628\) 0 0
\(629\) −8.05377e6 −0.811657
\(630\) 0 0
\(631\) 8.24910e6 0.824771 0.412385 0.911009i \(-0.364696\pi\)
0.412385 + 0.911009i \(0.364696\pi\)
\(632\) 0 0
\(633\) −8.06996e6 −0.800502
\(634\) 0 0
\(635\) 2.04989e7 2.01742
\(636\) 0 0
\(637\) 5.43666e6 0.530864
\(638\) 0 0
\(639\) 2.90437e6 0.281385
\(640\) 0 0
\(641\) −4.29330e6 −0.412711 −0.206355 0.978477i \(-0.566160\pi\)
−0.206355 + 0.978477i \(0.566160\pi\)
\(642\) 0 0
\(643\) −1.63045e7 −1.55518 −0.777588 0.628774i \(-0.783557\pi\)
−0.777588 + 0.628774i \(0.783557\pi\)
\(644\) 0 0
\(645\) 1.37476e6 0.130115
\(646\) 0 0
\(647\) 4.42624e6 0.415695 0.207847 0.978161i \(-0.433354\pi\)
0.207847 + 0.978161i \(0.433354\pi\)
\(648\) 0 0
\(649\) −3.84526e6 −0.358355
\(650\) 0 0
\(651\) 1.03075e6 0.0953237
\(652\) 0 0
\(653\) −6.27529e6 −0.575905 −0.287952 0.957645i \(-0.592975\pi\)
−0.287952 + 0.957645i \(0.592975\pi\)
\(654\) 0 0
\(655\) 6.74739e6 0.614515
\(656\) 0 0
\(657\) 7.07014e6 0.639020
\(658\) 0 0
\(659\) −1.09748e7 −0.984422 −0.492211 0.870476i \(-0.663811\pi\)
−0.492211 + 0.870476i \(0.663811\pi\)
\(660\) 0 0
\(661\) 2.02025e7 1.79846 0.899229 0.437478i \(-0.144128\pi\)
0.899229 + 0.437478i \(0.144128\pi\)
\(662\) 0 0
\(663\) 3.06964e6 0.271209
\(664\) 0 0
\(665\) −7.20480e6 −0.631783
\(666\) 0 0
\(667\) 2.88429e7 2.51029
\(668\) 0 0
\(669\) −461251. −0.0398448
\(670\) 0 0
\(671\) 4.13288e6 0.354361
\(672\) 0 0
\(673\) 1.14233e7 0.972200 0.486100 0.873903i \(-0.338419\pi\)
0.486100 + 0.873903i \(0.338419\pi\)
\(674\) 0 0
\(675\) −9.53184e6 −0.805225
\(676\) 0 0
\(677\) −2.43918e6 −0.204537 −0.102268 0.994757i \(-0.532610\pi\)
−0.102268 + 0.994757i \(0.532610\pi\)
\(678\) 0 0
\(679\) 2.48995e6 0.207260
\(680\) 0 0
\(681\) −2.20168e6 −0.181923
\(682\) 0 0
\(683\) 1.01384e6 0.0831606 0.0415803 0.999135i \(-0.486761\pi\)
0.0415803 + 0.999135i \(0.486761\pi\)
\(684\) 0 0
\(685\) 3.37885e7 2.75133
\(686\) 0 0
\(687\) 7.26924e6 0.587621
\(688\) 0 0
\(689\) 5.21284e6 0.418337
\(690\) 0 0
\(691\) −8.03186e6 −0.639913 −0.319957 0.947432i \(-0.603668\pi\)
−0.319957 + 0.947432i \(0.603668\pi\)
\(692\) 0 0
\(693\) 1.17370e6 0.0928376
\(694\) 0 0
\(695\) −2.44655e7 −1.92129
\(696\) 0 0
\(697\) 600080. 0.0467872
\(698\) 0 0
\(699\) 3.56983e6 0.276347
\(700\) 0 0
\(701\) −259806. −0.0199689 −0.00998445 0.999950i \(-0.503178\pi\)
−0.00998445 + 0.999950i \(0.503178\pi\)
\(702\) 0 0
\(703\) −1.27297e7 −0.971471
\(704\) 0 0
\(705\) 3.82676e6 0.289974
\(706\) 0 0
\(707\) 7.67030e6 0.577117
\(708\) 0 0
\(709\) −1.92848e7 −1.44079 −0.720393 0.693566i \(-0.756039\pi\)
−0.720393 + 0.693566i \(0.756039\pi\)
\(710\) 0 0
\(711\) 5.53637e6 0.410725
\(712\) 0 0
\(713\) −1.05755e7 −0.779071
\(714\) 0 0
\(715\) 3.63242e6 0.265724
\(716\) 0 0
\(717\) −3.11146e6 −0.226030
\(718\) 0 0
\(719\) 926119. 0.0668105 0.0334052 0.999442i \(-0.489365\pi\)
0.0334052 + 0.999442i \(0.489365\pi\)
\(720\) 0 0
\(721\) 6.73600e6 0.482574
\(722\) 0 0
\(723\) −1.98425e6 −0.141173
\(724\) 0 0
\(725\) 2.50277e7 1.76838
\(726\) 0 0
\(727\) 2.02599e7 1.42168 0.710840 0.703354i \(-0.248315\pi\)
0.710840 + 0.703354i \(0.248315\pi\)
\(728\) 0 0
\(729\) 211933. 0.0147700
\(730\) 0 0
\(731\) 2.86884e6 0.198570
\(732\) 0 0
\(733\) 1.10982e7 0.762944 0.381472 0.924380i \(-0.375417\pi\)
0.381472 + 0.924380i \(0.375417\pi\)
\(734\) 0 0
\(735\) 7.91177e6 0.540201
\(736\) 0 0
\(737\) −7.44186e6 −0.504676
\(738\) 0 0
\(739\) 624962. 0.0420962 0.0210481 0.999778i \(-0.493300\pi\)
0.0210481 + 0.999778i \(0.493300\pi\)
\(740\) 0 0
\(741\) 4.85184e6 0.324609
\(742\) 0 0
\(743\) 46436.0 0.00308591 0.00154295 0.999999i \(-0.499509\pi\)
0.00154295 + 0.999999i \(0.499509\pi\)
\(744\) 0 0
\(745\) −3.55378e7 −2.34585
\(746\) 0 0
\(747\) −1.50315e7 −0.985601
\(748\) 0 0
\(749\) −8.46090e6 −0.551077
\(750\) 0 0
\(751\) −6.12144e6 −0.396053 −0.198027 0.980197i \(-0.563453\pi\)
−0.198027 + 0.980197i \(0.563453\pi\)
\(752\) 0 0
\(753\) −5.41665e6 −0.348131
\(754\) 0 0
\(755\) −3.20008e7 −2.04312
\(756\) 0 0
\(757\) −3.26458e6 −0.207056 −0.103528 0.994627i \(-0.533013\pi\)
−0.103528 + 0.994627i \(0.533013\pi\)
\(758\) 0 0
\(759\) 3.04158e6 0.191644
\(760\) 0 0
\(761\) 1.60311e7 1.00346 0.501732 0.865023i \(-0.332696\pi\)
0.501732 + 0.865023i \(0.332696\pi\)
\(762\) 0 0
\(763\) 1.16603e7 0.725101
\(764\) 0 0
\(765\) −1.76862e7 −1.09265
\(766\) 0 0
\(767\) 1.20760e7 0.741200
\(768\) 0 0
\(769\) 2.64617e7 1.61362 0.806811 0.590810i \(-0.201192\pi\)
0.806811 + 0.590810i \(0.201192\pi\)
\(770\) 0 0
\(771\) −2.71400e6 −0.164427
\(772\) 0 0
\(773\) −2.63836e7 −1.58813 −0.794063 0.607836i \(-0.792038\pi\)
−0.794063 + 0.607836i \(0.792038\pi\)
\(774\) 0 0
\(775\) −9.17662e6 −0.548818
\(776\) 0 0
\(777\) −2.44265e6 −0.145147
\(778\) 0 0
\(779\) 948480. 0.0559995
\(780\) 0 0
\(781\) −1.81149e6 −0.106269
\(782\) 0 0
\(783\) −2.45699e7 −1.43218
\(784\) 0 0
\(785\) −2.68064e7 −1.55261
\(786\) 0 0
\(787\) −5.68115e6 −0.326964 −0.163482 0.986546i \(-0.552273\pi\)
−0.163482 + 0.986546i \(0.552273\pi\)
\(788\) 0 0
\(789\) −1.38321e6 −0.0791037
\(790\) 0 0
\(791\) −4.71645e6 −0.268024
\(792\) 0 0
\(793\) −1.29793e7 −0.732939
\(794\) 0 0
\(795\) 7.58605e6 0.425695
\(796\) 0 0
\(797\) 9.99383e6 0.557296 0.278648 0.960393i \(-0.410114\pi\)
0.278648 + 0.960393i \(0.410114\pi\)
\(798\) 0 0
\(799\) 7.98568e6 0.442532
\(800\) 0 0
\(801\) −7.03657e6 −0.387507
\(802\) 0 0
\(803\) −4.40972e6 −0.241336
\(804\) 0 0
\(805\) 1.41844e7 0.771477
\(806\) 0 0
\(807\) −1.83886e6 −0.0993950
\(808\) 0 0
\(809\) 2.32455e7 1.24873 0.624364 0.781134i \(-0.285358\pi\)
0.624364 + 0.781134i \(0.285358\pi\)
\(810\) 0 0
\(811\) 1.27367e7 0.679991 0.339995 0.940427i \(-0.389574\pi\)
0.339995 + 0.940427i \(0.389574\pi\)
\(812\) 0 0
\(813\) −1.11348e6 −0.0590819
\(814\) 0 0
\(815\) −2.14403e7 −1.13067
\(816\) 0 0
\(817\) 4.53446e6 0.237668
\(818\) 0 0
\(819\) −3.68600e6 −0.192020
\(820\) 0 0
\(821\) −7.85748e6 −0.406842 −0.203421 0.979091i \(-0.565206\pi\)
−0.203421 + 0.979091i \(0.565206\pi\)
\(822\) 0 0
\(823\) −1.09499e7 −0.563524 −0.281762 0.959484i \(-0.590919\pi\)
−0.281762 + 0.959484i \(0.590919\pi\)
\(824\) 0 0
\(825\) 2.63925e6 0.135004
\(826\) 0 0
\(827\) 2.20638e7 1.12180 0.560901 0.827883i \(-0.310455\pi\)
0.560901 + 0.827883i \(0.310455\pi\)
\(828\) 0 0
\(829\) 7.05255e6 0.356418 0.178209 0.983993i \(-0.442970\pi\)
0.178209 + 0.983993i \(0.442970\pi\)
\(830\) 0 0
\(831\) 9.05698e6 0.454968
\(832\) 0 0
\(833\) 1.65103e7 0.824407
\(834\) 0 0
\(835\) −5.72497e6 −0.284156
\(836\) 0 0
\(837\) 9.00876e6 0.444479
\(838\) 0 0
\(839\) −2.26195e7 −1.10937 −0.554686 0.832060i \(-0.687162\pi\)
−0.554686 + 0.832060i \(0.687162\pi\)
\(840\) 0 0
\(841\) 4.40019e7 2.14527
\(842\) 0 0
\(843\) −1.24680e7 −0.604264
\(844\) 0 0
\(845\) 1.79245e7 0.863588
\(846\) 0 0
\(847\) −732050. −0.0350616
\(848\) 0 0
\(849\) 1.38795e7 0.660853
\(850\) 0 0
\(851\) 2.50616e7 1.18627
\(852\) 0 0
\(853\) 9.46645e6 0.445466 0.222733 0.974880i \(-0.428502\pi\)
0.222733 + 0.974880i \(0.428502\pi\)
\(854\) 0 0
\(855\) −2.79546e7 −1.30779
\(856\) 0 0
\(857\) 941480. 0.0437884 0.0218942 0.999760i \(-0.493030\pi\)
0.0218942 + 0.999760i \(0.493030\pi\)
\(858\) 0 0
\(859\) −806423. −0.0372889 −0.0186445 0.999826i \(-0.505935\pi\)
−0.0186445 + 0.999826i \(0.505935\pi\)
\(860\) 0 0
\(861\) 182000. 0.00836688
\(862\) 0 0
\(863\) 1.19485e7 0.546119 0.273059 0.961997i \(-0.411964\pi\)
0.273059 + 0.961997i \(0.411964\pi\)
\(864\) 0 0
\(865\) −3.78589e7 −1.72039
\(866\) 0 0
\(867\) −616987. −0.0278759
\(868\) 0 0
\(869\) −3.45310e6 −0.155117
\(870\) 0 0
\(871\) 2.33711e7 1.04384
\(872\) 0 0
\(873\) 9.66101e6 0.429029
\(874\) 0 0
\(875\) −35550.0 −0.00156971
\(876\) 0 0
\(877\) 7.84853e6 0.344580 0.172290 0.985046i \(-0.444883\pi\)
0.172290 + 0.985046i \(0.444883\pi\)
\(878\) 0 0
\(879\) 4.04852e6 0.176736
\(880\) 0 0
\(881\) −1.73933e7 −0.754991 −0.377496 0.926011i \(-0.623215\pi\)
−0.377496 + 0.926011i \(0.623215\pi\)
\(882\) 0 0
\(883\) −4.31619e7 −1.86294 −0.931470 0.363818i \(-0.881473\pi\)
−0.931470 + 0.363818i \(0.881473\pi\)
\(884\) 0 0
\(885\) 1.75738e7 0.754236
\(886\) 0 0
\(887\) −9.25652e6 −0.395038 −0.197519 0.980299i \(-0.563288\pi\)
−0.197519 + 0.980299i \(0.563288\pi\)
\(888\) 0 0
\(889\) 1.29740e7 0.550579
\(890\) 0 0
\(891\) 3.11321e6 0.131375
\(892\) 0 0
\(893\) 1.26221e7 0.529666
\(894\) 0 0
\(895\) 3.23386e6 0.134947
\(896\) 0 0
\(897\) −9.55206e6 −0.396384
\(898\) 0 0
\(899\) −2.36542e7 −0.976135
\(900\) 0 0
\(901\) 1.58306e7 0.649658
\(902\) 0 0
\(903\) 870100. 0.0355099
\(904\) 0 0
\(905\) 7.12335e6 0.289110
\(906\) 0 0
\(907\) 4.47293e7 1.80540 0.902700 0.430270i \(-0.141582\pi\)
0.902700 + 0.430270i \(0.141582\pi\)
\(908\) 0 0
\(909\) 2.97608e7 1.19463
\(910\) 0 0
\(911\) 2.57577e7 1.02828 0.514139 0.857707i \(-0.328112\pi\)
0.514139 + 0.857707i \(0.328112\pi\)
\(912\) 0 0
\(913\) 9.37532e6 0.372228
\(914\) 0 0
\(915\) −1.88883e7 −0.745829
\(916\) 0 0
\(917\) 4.27050e6 0.167709
\(918\) 0 0
\(919\) −3.63488e7 −1.41972 −0.709858 0.704344i \(-0.751241\pi\)
−0.709858 + 0.704344i \(0.751241\pi\)
\(920\) 0 0
\(921\) −2.15322e7 −0.836447
\(922\) 0 0
\(923\) 5.68898e6 0.219801
\(924\) 0 0
\(925\) 2.17466e7 0.835673
\(926\) 0 0
\(927\) 2.61357e7 0.998929
\(928\) 0 0
\(929\) −3.96617e6 −0.150776 −0.0753880 0.997154i \(-0.524020\pi\)
−0.0753880 + 0.997154i \(0.524020\pi\)
\(930\) 0 0
\(931\) 2.60960e7 0.986732
\(932\) 0 0
\(933\) −2.19630e7 −0.826014
\(934\) 0 0
\(935\) 1.10311e7 0.412657
\(936\) 0 0
\(937\) −3.50528e7 −1.30429 −0.652145 0.758094i \(-0.726131\pi\)
−0.652145 + 0.758094i \(0.726131\pi\)
\(938\) 0 0
\(939\) 1.83249e7 0.678230
\(940\) 0 0
\(941\) −1.40738e7 −0.518130 −0.259065 0.965860i \(-0.583414\pi\)
−0.259065 + 0.965860i \(0.583414\pi\)
\(942\) 0 0
\(943\) −1.86732e6 −0.0683816
\(944\) 0 0
\(945\) −1.20830e7 −0.440146
\(946\) 0 0
\(947\) −3.73759e7 −1.35431 −0.677153 0.735842i \(-0.736786\pi\)
−0.677153 + 0.735842i \(0.736786\pi\)
\(948\) 0 0
\(949\) 1.38487e7 0.499165
\(950\) 0 0
\(951\) −1.74454e7 −0.625502
\(952\) 0 0
\(953\) −3.18424e7 −1.13572 −0.567862 0.823124i \(-0.692229\pi\)
−0.567862 + 0.823124i \(0.692229\pi\)
\(954\) 0 0
\(955\) 2.05696e7 0.729824
\(956\) 0 0
\(957\) 6.80310e6 0.240119
\(958\) 0 0
\(959\) 2.13852e7 0.750872
\(960\) 0 0
\(961\) −1.99561e7 −0.697056
\(962\) 0 0
\(963\) −3.28283e7 −1.14073
\(964\) 0 0
\(965\) −4.14216e7 −1.43189
\(966\) 0 0
\(967\) −3.16276e7 −1.08768 −0.543838 0.839190i \(-0.683029\pi\)
−0.543838 + 0.839190i \(0.683029\pi\)
\(968\) 0 0
\(969\) 1.47343e7 0.504103
\(970\) 0 0
\(971\) −2.73412e7 −0.930614 −0.465307 0.885149i \(-0.654056\pi\)
−0.465307 + 0.885149i \(0.654056\pi\)
\(972\) 0 0
\(973\) −1.54845e7 −0.524343
\(974\) 0 0
\(975\) −8.28856e6 −0.279234
\(976\) 0 0
\(977\) −5.81630e6 −0.194944 −0.0974721 0.995238i \(-0.531076\pi\)
−0.0974721 + 0.995238i \(0.531076\pi\)
\(978\) 0 0
\(979\) 4.38879e6 0.146348
\(980\) 0 0
\(981\) 4.52420e7 1.50096
\(982\) 0 0
\(983\) −3.81817e7 −1.26029 −0.630146 0.776476i \(-0.717005\pi\)
−0.630146 + 0.776476i \(0.717005\pi\)
\(984\) 0 0
\(985\) −6.00070e7 −1.97066
\(986\) 0 0
\(987\) 2.42200e6 0.0791373
\(988\) 0 0
\(989\) −8.92723e6 −0.290219
\(990\) 0 0
\(991\) 5.44564e6 0.176143 0.0880714 0.996114i \(-0.471930\pi\)
0.0880714 + 0.996114i \(0.471930\pi\)
\(992\) 0 0
\(993\) −1.89087e7 −0.608541
\(994\) 0 0
\(995\) 6.97361e7 2.23306
\(996\) 0 0
\(997\) −3.77967e6 −0.120425 −0.0602125 0.998186i \(-0.519178\pi\)
−0.0602125 + 0.998186i \(0.519178\pi\)
\(998\) 0 0
\(999\) −2.13488e7 −0.676798
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 44.6.a.a.1.1 1
3.2 odd 2 396.6.a.e.1.1 1
4.3 odd 2 176.6.a.a.1.1 1
5.2 odd 4 1100.6.b.a.749.1 2
5.3 odd 4 1100.6.b.a.749.2 2
5.4 even 2 1100.6.a.a.1.1 1
8.3 odd 2 704.6.a.g.1.1 1
8.5 even 2 704.6.a.d.1.1 1
11.10 odd 2 484.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.6.a.a.1.1 1 1.1 even 1 trivial
176.6.a.a.1.1 1 4.3 odd 2
396.6.a.e.1.1 1 3.2 odd 2
484.6.a.b.1.1 1 11.10 odd 2
704.6.a.d.1.1 1 8.5 even 2
704.6.a.g.1.1 1 8.3 odd 2
1100.6.a.a.1.1 1 5.4 even 2
1100.6.b.a.749.1 2 5.2 odd 4
1100.6.b.a.749.2 2 5.3 odd 4