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Properties

Label 576.6.a.o.1.1
Level $576$
Weight $6$
Character 576.1
Self dual yes
Analytic conductor $92.381$
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] = [576,6,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(92.3810802123\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-14.0000 q^{5} -100.000 q^{7} +O(q^{10})\) \(q-14.0000 q^{5} -100.000 q^{7} -220.000 q^{11} +818.000 q^{13} +774.000 q^{17} -1436.00 q^{19} +192.000 q^{23} -2929.00 q^{25} -7022.00 q^{29} -1436.00 q^{31} +1400.00 q^{35} +3410.00 q^{37} +7838.00 q^{41} -16036.0 q^{43} +22712.0 q^{47} -6807.00 q^{49} +27578.0 q^{53} +3080.00 q^{55} +28828.0 q^{59} -12438.0 q^{61} -11452.0 q^{65} -70948.0 q^{67} +58832.0 q^{71} +79386.0 q^{73} +22000.0 q^{77} +46948.0 q^{79} -67284.0 q^{83} -10836.0 q^{85} -16106.0 q^{89} -81800.0 q^{91} +20104.0 q^{95} -4238.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −14.0000 −0.250440 −0.125220 − 0.992129i \(-0.539964\pi\)
−0.125220 + 0.992129i \(0.539964\pi\)
\(6\) 0 0
\(7\) −100.000 −0.771356 −0.385678 − 0.922633i \(-0.626032\pi\)
−0.385678 + 0.922633i \(0.626032\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −220.000 −0.548202 −0.274101 − 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) 818.000 1.34244 0.671220 − 0.741258i \(-0.265771\pi\)
0.671220 + 0.741258i \(0.265771\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 774.000 0.649559 0.324780 − 0.945790i \(-0.394710\pi\)
0.324780 + 0.945790i \(0.394710\pi\)
\(18\) 0 0
\(19\) −1436.00 −0.912579 −0.456289 − 0.889831i \(-0.650822\pi\)
−0.456289 + 0.889831i \(0.650822\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 192.000 0.0756801 0.0378400 − 0.999284i \(-0.487952\pi\)
0.0378400 + 0.999284i \(0.487952\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7022.00 −1.55048 −0.775239 − 0.631668i \(-0.782371\pi\)
−0.775239 + 0.631668i \(0.782371\pi\)
\(30\) 0 0
\(31\) −1436.00 −0.268380 −0.134190 − 0.990956i \(-0.542843\pi\)
−0.134190 + 0.990956i \(0.542843\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1400.00 0.193178
\(36\) 0 0
\(37\) 3410.00 0.409496 0.204748 − 0.978815i \(-0.434362\pi\)
0.204748 + 0.978815i \(0.434362\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7838.00 0.728192 0.364096 − 0.931362i \(-0.381378\pi\)
0.364096 + 0.931362i \(0.381378\pi\)
\(42\) 0 0
\(43\) −16036.0 −1.32259 −0.661295 − 0.750126i \(-0.729993\pi\)
−0.661295 + 0.750126i \(0.729993\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 22712.0 1.49972 0.749861 − 0.661595i \(-0.230120\pi\)
0.749861 + 0.661595i \(0.230120\pi\)
\(48\) 0 0
\(49\) −6807.00 −0.405010
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 27578.0 1.34857 0.674284 − 0.738472i \(-0.264452\pi\)
0.674284 + 0.738472i \(0.264452\pi\)
\(54\) 0 0
\(55\) 3080.00 0.137292
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 28828.0 1.07816 0.539082 − 0.842254i \(-0.318771\pi\)
0.539082 + 0.842254i \(0.318771\pi\)
\(60\) 0 0
\(61\) −12438.0 −0.427982 −0.213991 − 0.976836i \(-0.568646\pi\)
−0.213991 + 0.976836i \(0.568646\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −11452.0 −0.336200
\(66\) 0 0
\(67\) −70948.0 −1.93087 −0.965435 − 0.260643i \(-0.916065\pi\)
−0.965435 + 0.260643i \(0.916065\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 58832.0 1.38506 0.692529 − 0.721390i \(-0.256497\pi\)
0.692529 + 0.721390i \(0.256497\pi\)
\(72\) 0 0
\(73\) 79386.0 1.74356 0.871780 − 0.489898i \(-0.162966\pi\)
0.871780 + 0.489898i \(0.162966\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 22000.0 0.422859
\(78\) 0 0
\(79\) 46948.0 0.846349 0.423174 − 0.906048i \(-0.360916\pi\)
0.423174 + 0.906048i \(0.360916\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −67284.0 −1.07205 −0.536027 − 0.844201i \(-0.680075\pi\)
−0.536027 + 0.844201i \(0.680075\pi\)
\(84\) 0 0
\(85\) −10836.0 −0.162675
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −16106.0 −0.215532 −0.107766 − 0.994176i \(-0.534370\pi\)
−0.107766 + 0.994176i \(0.534370\pi\)
\(90\) 0 0
\(91\) −81800.0 −1.03550
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 20104.0 0.228546
\(96\) 0 0
\(97\) −4238.00 −0.0457332 −0.0228666 − 0.999739i \(-0.507279\pi\)
−0.0228666 + 0.999739i \(0.507279\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 51690.0 0.504200 0.252100 − 0.967701i \(-0.418879\pi\)
0.252100 + 0.967701i \(0.418879\pi\)
\(102\) 0 0
\(103\) 63828.0 0.592814 0.296407 − 0.955062i \(-0.404212\pi\)
0.296407 + 0.955062i \(0.404212\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3428.00 −0.0289455 −0.0144728 − 0.999895i \(-0.504607\pi\)
−0.0144728 + 0.999895i \(0.504607\pi\)
\(108\) 0 0
\(109\) 153250. 1.23548 0.617738 − 0.786384i \(-0.288049\pi\)
0.617738 + 0.786384i \(0.288049\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 263870. 1.94399 0.971995 − 0.235003i \(-0.0755099\pi\)
0.971995 + 0.235003i \(0.0755099\pi\)
\(114\) 0 0
\(115\) −2688.00 −0.0189533
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −77400.0 −0.501041
\(120\) 0 0
\(121\) −112651. −0.699474
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 84756.0 0.485172
\(126\) 0 0
\(127\) 297484. 1.63664 0.818322 − 0.574760i \(-0.194905\pi\)
0.818322 + 0.574760i \(0.194905\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −277468. −1.41265 −0.706325 − 0.707888i \(-0.749648\pi\)
−0.706325 + 0.707888i \(0.749648\pi\)
\(132\) 0 0
\(133\) 143600. 0.703923
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 290958. 1.32443 0.662215 − 0.749314i \(-0.269617\pi\)
0.662215 + 0.749314i \(0.269617\pi\)
\(138\) 0 0
\(139\) 10100.0 0.0443388 0.0221694 − 0.999754i \(-0.492943\pi\)
0.0221694 + 0.999754i \(0.492943\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −179960. −0.735929
\(144\) 0 0
\(145\) 98308.0 0.388301
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 96450.0 0.355907 0.177954 − 0.984039i \(-0.443052\pi\)
0.177954 + 0.984039i \(0.443052\pi\)
\(150\) 0 0
\(151\) −210900. −0.752721 −0.376361 − 0.926473i \(-0.622825\pi\)
−0.376361 + 0.926473i \(0.622825\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 20104.0 0.0672130
\(156\) 0 0
\(157\) −130310. −0.421919 −0.210959 − 0.977495i \(-0.567659\pi\)
−0.210959 + 0.977495i \(0.567659\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −19200.0 −0.0583763
\(162\) 0 0
\(163\) 633700. 1.86816 0.934081 − 0.357060i \(-0.116221\pi\)
0.934081 + 0.357060i \(0.116221\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 133880. 0.371471 0.185735 − 0.982600i \(-0.440533\pi\)
0.185735 + 0.982600i \(0.440533\pi\)
\(168\) 0 0
\(169\) 297831. 0.802145
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 373578. 0.949000 0.474500 − 0.880256i \(-0.342629\pi\)
0.474500 + 0.880256i \(0.342629\pi\)
\(174\) 0 0
\(175\) 292900. 0.722977
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 130836. 0.305207 0.152604 − 0.988287i \(-0.451234\pi\)
0.152604 + 0.988287i \(0.451234\pi\)
\(180\) 0 0
\(181\) 214426. 0.486498 0.243249 − 0.969964i \(-0.421787\pi\)
0.243249 + 0.969964i \(0.421787\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −47740.0 −0.102554
\(186\) 0 0
\(187\) −170280. −0.356090
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −466176. −0.924627 −0.462313 − 0.886717i \(-0.652980\pi\)
−0.462313 + 0.886717i \(0.652980\pi\)
\(192\) 0 0
\(193\) 584850. 1.13019 0.565095 − 0.825026i \(-0.308840\pi\)
0.565095 + 0.825026i \(0.308840\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 771418. 1.41620 0.708099 − 0.706113i \(-0.249553\pi\)
0.708099 + 0.706113i \(0.249553\pi\)
\(198\) 0 0
\(199\) −704540. −1.26117 −0.630584 − 0.776121i \(-0.717185\pi\)
−0.630584 + 0.776121i \(0.717185\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 702200. 1.19597
\(204\) 0 0
\(205\) −109732. −0.182368
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 315920. 0.500278
\(210\) 0 0
\(211\) 790732. 1.22271 0.611355 − 0.791357i \(-0.290625\pi\)
0.611355 + 0.791357i \(0.290625\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 224504. 0.331229
\(216\) 0 0
\(217\) 143600. 0.207017
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 633132. 0.871994
\(222\) 0 0
\(223\) −1.22890e6 −1.65483 −0.827417 − 0.561588i \(-0.810191\pi\)
−0.827417 + 0.561588i \(0.810191\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −367572. −0.473454 −0.236727 − 0.971576i \(-0.576075\pi\)
−0.236727 + 0.971576i \(0.576075\pi\)
\(228\) 0 0
\(229\) 513754. 0.647391 0.323695 − 0.946161i \(-0.395075\pi\)
0.323695 + 0.946161i \(0.395075\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.10717e6 1.33606 0.668030 − 0.744134i \(-0.267138\pi\)
0.668030 + 0.744134i \(0.267138\pi\)
\(234\) 0 0
\(235\) −317968. −0.375590
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −886656. −1.00406 −0.502031 − 0.864850i \(-0.667414\pi\)
−0.502031 + 0.864850i \(0.667414\pi\)
\(240\) 0 0
\(241\) −250958. −0.278329 −0.139164 − 0.990269i \(-0.544442\pi\)
−0.139164 + 0.990269i \(0.544442\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 95298.0 0.101431
\(246\) 0 0
\(247\) −1.17465e6 −1.22508
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.14076e6 1.14290 0.571450 − 0.820637i \(-0.306381\pi\)
0.571450 + 0.820637i \(0.306381\pi\)
\(252\) 0 0
\(253\) −42240.0 −0.0414880
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 726014. 0.685665 0.342833 − 0.939396i \(-0.388614\pi\)
0.342833 + 0.939396i \(0.388614\pi\)
\(258\) 0 0
\(259\) −341000. −0.315868
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.09052e6 1.86365 0.931826 − 0.362905i \(-0.118215\pi\)
0.931826 + 0.362905i \(0.118215\pi\)
\(264\) 0 0
\(265\) −386092. −0.337735
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.05059e6 −1.72782 −0.863909 − 0.503647i \(-0.831991\pi\)
−0.863909 + 0.503647i \(0.831991\pi\)
\(270\) 0 0
\(271\) 544044. 0.449998 0.224999 − 0.974359i \(-0.427762\pi\)
0.224999 + 0.974359i \(0.427762\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 644380. 0.513819
\(276\) 0 0
\(277\) 697082. 0.545864 0.272932 − 0.962033i \(-0.412007\pi\)
0.272932 + 0.962033i \(0.412007\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −583002. −0.440458 −0.220229 − 0.975448i \(-0.570680\pi\)
−0.220229 + 0.975448i \(0.570680\pi\)
\(282\) 0 0
\(283\) −890812. −0.661180 −0.330590 − 0.943774i \(-0.607248\pi\)
−0.330590 + 0.943774i \(0.607248\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −783800. −0.561695
\(288\) 0 0
\(289\) −820781. −0.578073
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 514794. 0.350320 0.175160 − 0.984540i \(-0.443956\pi\)
0.175160 + 0.984540i \(0.443956\pi\)
\(294\) 0 0
\(295\) −403592. −0.270015
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 157056. 0.101596
\(300\) 0 0
\(301\) 1.60360e6 1.02019
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 174132. 0.107184
\(306\) 0 0
\(307\) 1.15326e6 0.698363 0.349182 − 0.937055i \(-0.386460\pi\)
0.349182 + 0.937055i \(0.386460\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 783000. 0.459051 0.229525 − 0.973303i \(-0.426283\pi\)
0.229525 + 0.973303i \(0.426283\pi\)
\(312\) 0 0
\(313\) −205718. −0.118689 −0.0593446 − 0.998238i \(-0.518901\pi\)
−0.0593446 + 0.998238i \(0.518901\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 515874. 0.288334 0.144167 − 0.989553i \(-0.453950\pi\)
0.144167 + 0.989553i \(0.453950\pi\)
\(318\) 0 0
\(319\) 1.54484e6 0.849976
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.11146e6 −0.592774
\(324\) 0 0
\(325\) −2.39592e6 −1.25824
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.27120e6 −1.15682
\(330\) 0 0
\(331\) −641212. −0.321686 −0.160843 − 0.986980i \(-0.551421\pi\)
−0.160843 + 0.986980i \(0.551421\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 993272. 0.483566
\(336\) 0 0
\(337\) 2.41978e6 1.16065 0.580324 − 0.814385i \(-0.302926\pi\)
0.580324 + 0.814385i \(0.302926\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 315920. 0.147127
\(342\) 0 0
\(343\) 2.36140e6 1.08376
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.60123e6 −0.713887 −0.356944 − 0.934126i \(-0.616181\pi\)
−0.356944 + 0.934126i \(0.616181\pi\)
\(348\) 0 0
\(349\) −2.41356e6 −1.06070 −0.530352 − 0.847778i \(-0.677940\pi\)
−0.530352 + 0.847778i \(0.677940\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 581902. 0.248550 0.124275 − 0.992248i \(-0.460340\pi\)
0.124275 + 0.992248i \(0.460340\pi\)
\(354\) 0 0
\(355\) −823648. −0.346873
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.45614e6 −1.00581 −0.502907 − 0.864341i \(-0.667736\pi\)
−0.502907 + 0.864341i \(0.667736\pi\)
\(360\) 0 0
\(361\) −414003. −0.167200
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.11140e6 −0.436656
\(366\) 0 0
\(367\) 3.74831e6 1.45268 0.726340 − 0.687335i \(-0.241220\pi\)
0.726340 + 0.687335i \(0.241220\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.75780e6 −1.04023
\(372\) 0 0
\(373\) −1.63989e6 −0.610297 −0.305149 − 0.952305i \(-0.598706\pi\)
−0.305149 + 0.952305i \(0.598706\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.74400e6 −2.08142
\(378\) 0 0
\(379\) −1.67642e6 −0.599494 −0.299747 − 0.954019i \(-0.596902\pi\)
−0.299747 + 0.954019i \(0.596902\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −464416. −0.161775 −0.0808873 − 0.996723i \(-0.525775\pi\)
−0.0808873 + 0.996723i \(0.525775\pi\)
\(384\) 0 0
\(385\) −308000. −0.105901
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.35377e6 −0.453599 −0.226800 − 0.973941i \(-0.572826\pi\)
−0.226800 + 0.973941i \(0.572826\pi\)
\(390\) 0 0
\(391\) 148608. 0.0491587
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −657272. −0.211959
\(396\) 0 0
\(397\) −1.44535e6 −0.460253 −0.230127 − 0.973161i \(-0.573914\pi\)
−0.230127 + 0.973161i \(0.573914\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 554614. 0.172238 0.0861192 − 0.996285i \(-0.472553\pi\)
0.0861192 + 0.996285i \(0.472553\pi\)
\(402\) 0 0
\(403\) −1.17465e6 −0.360284
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −750200. −0.224487
\(408\) 0 0
\(409\) −3.96815e6 −1.17295 −0.586475 − 0.809967i \(-0.699485\pi\)
−0.586475 + 0.809967i \(0.699485\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.88280e6 −0.831648
\(414\) 0 0
\(415\) 941976. 0.268485
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.95621e6 −1.10089 −0.550446 − 0.834871i \(-0.685542\pi\)
−0.550446 + 0.834871i \(0.685542\pi\)
\(420\) 0 0
\(421\) 2.47057e6 0.679347 0.339674 − 0.940543i \(-0.389683\pi\)
0.339674 + 0.940543i \(0.389683\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.26705e6 −0.608819
\(426\) 0 0
\(427\) 1.24380e6 0.330127
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 197928. 0.0513232 0.0256616 − 0.999671i \(-0.491831\pi\)
0.0256616 + 0.999671i \(0.491831\pi\)
\(432\) 0 0
\(433\) −2.22817e6 −0.571123 −0.285561 − 0.958360i \(-0.592180\pi\)
−0.285561 + 0.958360i \(0.592180\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −275712. −0.0690641
\(438\) 0 0
\(439\) 4.72212e6 1.16943 0.584717 − 0.811238i \(-0.301206\pi\)
0.584717 + 0.811238i \(0.301206\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.30366e6 −0.799809 −0.399904 − 0.916557i \(-0.630957\pi\)
−0.399904 + 0.916557i \(0.630957\pi\)
\(444\) 0 0
\(445\) 225484. 0.0539779
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.08543e6 0.488180 0.244090 − 0.969753i \(-0.421511\pi\)
0.244090 + 0.969753i \(0.421511\pi\)
\(450\) 0 0
\(451\) −1.72436e6 −0.399196
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.14520e6 0.259330
\(456\) 0 0
\(457\) −1.04724e6 −0.234561 −0.117280 − 0.993099i \(-0.537418\pi\)
−0.117280 + 0.993099i \(0.537418\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.15929e6 −1.78813 −0.894067 − 0.447934i \(-0.852160\pi\)
−0.894067 + 0.447934i \(0.852160\pi\)
\(462\) 0 0
\(463\) −1.65324e6 −0.358412 −0.179206 − 0.983812i \(-0.557353\pi\)
−0.179206 + 0.983812i \(0.557353\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.64288e6 1.83386 0.916930 − 0.399049i \(-0.130660\pi\)
0.916930 + 0.399049i \(0.130660\pi\)
\(468\) 0 0
\(469\) 7.09480e6 1.48939
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.52792e6 0.725047
\(474\) 0 0
\(475\) 4.20604e6 0.855342
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.67209e6 1.72697 0.863485 − 0.504374i \(-0.168277\pi\)
0.863485 + 0.504374i \(0.168277\pi\)
\(480\) 0 0
\(481\) 2.78938e6 0.549724
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 59332.0 0.0114534
\(486\) 0 0
\(487\) −4.93066e6 −0.942069 −0.471034 − 0.882115i \(-0.656119\pi\)
−0.471034 + 0.882115i \(0.656119\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.59340e6 1.42145 0.710727 − 0.703468i \(-0.248366\pi\)
0.710727 + 0.703468i \(0.248366\pi\)
\(492\) 0 0
\(493\) −5.43503e6 −1.00713
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.88320e6 −1.06837
\(498\) 0 0
\(499\) −1.56008e6 −0.280477 −0.140238 − 0.990118i \(-0.544787\pi\)
−0.140238 + 0.990118i \(0.544787\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8.79648e6 −1.55020 −0.775102 − 0.631836i \(-0.782302\pi\)
−0.775102 + 0.631836i \(0.782302\pi\)
\(504\) 0 0
\(505\) −723660. −0.126272
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.17251e6 −1.39817 −0.699087 − 0.715037i \(-0.746410\pi\)
−0.699087 + 0.715037i \(0.746410\pi\)
\(510\) 0 0
\(511\) −7.93860e6 −1.34491
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −893592. −0.148464
\(516\) 0 0
\(517\) −4.99664e6 −0.822151
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.66202e6 −1.23666 −0.618328 − 0.785920i \(-0.712190\pi\)
−0.618328 + 0.785920i \(0.712190\pi\)
\(522\) 0 0
\(523\) −691092. −0.110479 −0.0552397 − 0.998473i \(-0.517592\pi\)
−0.0552397 + 0.998473i \(0.517592\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.11146e6 −0.174329
\(528\) 0 0
\(529\) −6.39948e6 −0.994273
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.41148e6 0.977554
\(534\) 0 0
\(535\) 47992.0 0.00724911
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.49754e6 0.222027
\(540\) 0 0
\(541\) −5.26056e6 −0.772749 −0.386375 − 0.922342i \(-0.626273\pi\)
−0.386375 + 0.922342i \(0.626273\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.14550e6 −0.309412
\(546\) 0 0
\(547\) −2.98897e6 −0.427124 −0.213562 − 0.976930i \(-0.568506\pi\)
−0.213562 + 0.976930i \(0.568506\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.00836e7 1.41493
\(552\) 0 0
\(553\) −4.69480e6 −0.652836
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.72780e6 0.782258 0.391129 − 0.920336i \(-0.372085\pi\)
0.391129 + 0.920336i \(0.372085\pi\)
\(558\) 0 0
\(559\) −1.31174e7 −1.77550
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.01894e7 1.35480 0.677401 − 0.735614i \(-0.263106\pi\)
0.677401 + 0.735614i \(0.263106\pi\)
\(564\) 0 0
\(565\) −3.69418e6 −0.486852
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 994190. 0.128733 0.0643663 − 0.997926i \(-0.479497\pi\)
0.0643663 + 0.997926i \(0.479497\pi\)
\(570\) 0 0
\(571\) 7.46040e6 0.957573 0.478787 − 0.877931i \(-0.341077\pi\)
0.478787 + 0.877931i \(0.341077\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −562368. −0.0709334
\(576\) 0 0
\(577\) 1.42449e7 1.78123 0.890614 − 0.454761i \(-0.150275\pi\)
0.890614 + 0.454761i \(0.150275\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.72840e6 0.826935
\(582\) 0 0
\(583\) −6.06716e6 −0.739289
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.50084e7 −1.79779 −0.898895 − 0.438165i \(-0.855629\pi\)
−0.898895 + 0.438165i \(0.855629\pi\)
\(588\) 0 0
\(589\) 2.06210e6 0.244918
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.45853e6 1.10455 0.552277 − 0.833661i \(-0.313759\pi\)
0.552277 + 0.833661i \(0.313759\pi\)
\(594\) 0 0
\(595\) 1.08360e6 0.125481
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.38815e7 −1.58077 −0.790387 − 0.612607i \(-0.790121\pi\)
−0.790387 + 0.612607i \(0.790121\pi\)
\(600\) 0 0
\(601\) 2.83787e6 0.320484 0.160242 − 0.987078i \(-0.448773\pi\)
0.160242 + 0.987078i \(0.448773\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.57711e6 0.175176
\(606\) 0 0
\(607\) −5.38418e6 −0.593127 −0.296564 − 0.955013i \(-0.595841\pi\)
−0.296564 + 0.955013i \(0.595841\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.85784e7 2.01329
\(612\) 0 0
\(613\) 8.47139e6 0.910550 0.455275 − 0.890351i \(-0.349541\pi\)
0.455275 + 0.890351i \(0.349541\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50297e7 −1.58942 −0.794708 − 0.606992i \(-0.792376\pi\)
−0.794708 + 0.606992i \(0.792376\pi\)
\(618\) 0 0
\(619\) 1.24601e7 1.30706 0.653530 − 0.756901i \(-0.273287\pi\)
0.653530 + 0.756901i \(0.273287\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.61060e6 0.166252
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.63934e6 0.265992
\(630\) 0 0
\(631\) 1.24849e7 1.24828 0.624138 − 0.781314i \(-0.285450\pi\)
0.624138 + 0.781314i \(0.285450\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.16478e6 −0.409881
\(636\) 0 0
\(637\) −5.56813e6 −0.543701
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.85191e7 1.78022 0.890112 − 0.455742i \(-0.150626\pi\)
0.890112 + 0.455742i \(0.150626\pi\)
\(642\) 0 0
\(643\) −5.22232e6 −0.498122 −0.249061 − 0.968488i \(-0.580122\pi\)
−0.249061 + 0.968488i \(0.580122\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.94424e6 −0.464343 −0.232171 − 0.972675i \(-0.574583\pi\)
−0.232171 + 0.972675i \(0.574583\pi\)
\(648\) 0 0
\(649\) −6.34216e6 −0.591052
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.20663e6 −0.753151 −0.376575 − 0.926386i \(-0.622898\pi\)
−0.376575 + 0.926386i \(0.622898\pi\)
\(654\) 0 0
\(655\) 3.88455e6 0.353784
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.46992e7 −1.31850 −0.659250 − 0.751924i \(-0.729126\pi\)
−0.659250 + 0.751924i \(0.729126\pi\)
\(660\) 0 0
\(661\) 1.27866e7 1.13828 0.569141 − 0.822240i \(-0.307276\pi\)
0.569141 + 0.822240i \(0.307276\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.01040e6 −0.176290
\(666\) 0 0
\(667\) −1.34822e6 −0.117340
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.73636e6 0.234621
\(672\) 0 0
\(673\) −7.86969e6 −0.669762 −0.334881 − 0.942261i \(-0.608696\pi\)
−0.334881 + 0.942261i \(0.608696\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.88522e6 0.577359 0.288680 − 0.957426i \(-0.406784\pi\)
0.288680 + 0.957426i \(0.406784\pi\)
\(678\) 0 0
\(679\) 423800. 0.0352766
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.00604e6 0.492647 0.246324 − 0.969188i \(-0.420777\pi\)
0.246324 + 0.969188i \(0.420777\pi\)
\(684\) 0 0
\(685\) −4.07341e6 −0.331690
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.25588e7 1.81037
\(690\) 0 0
\(691\) 8.58485e6 0.683971 0.341986 − 0.939705i \(-0.388901\pi\)
0.341986 + 0.939705i \(0.388901\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −141400. −0.0111042
\(696\) 0 0
\(697\) 6.06661e6 0.473003
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.39556e7 −1.07263 −0.536317 − 0.844016i \(-0.680185\pi\)
−0.536317 + 0.844016i \(0.680185\pi\)
\(702\) 0 0
\(703\) −4.89676e6 −0.373698
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.16900e6 −0.388918
\(708\) 0 0
\(709\) 1.61567e7 1.20709 0.603543 − 0.797331i \(-0.293755\pi\)
0.603543 + 0.797331i \(0.293755\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −275712. −0.0203110
\(714\) 0 0
\(715\) 2.51944e6 0.184306
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.03861e7 −1.47066 −0.735330 − 0.677709i \(-0.762973\pi\)
−0.735330 + 0.677709i \(0.762973\pi\)
\(720\) 0 0
\(721\) −6.38280e6 −0.457270
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.05674e7 1.45323
\(726\) 0 0
\(727\) 2.27446e7 1.59604 0.798018 − 0.602634i \(-0.205882\pi\)
0.798018 + 0.602634i \(0.205882\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.24119e7 −0.859100
\(732\) 0 0
\(733\) 2.67512e7 1.83901 0.919503 − 0.393082i \(-0.128591\pi\)
0.919503 + 0.393082i \(0.128591\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.56086e7 1.05851
\(738\) 0 0
\(739\) 8.28027e6 0.557742 0.278871 − 0.960329i \(-0.410040\pi\)
0.278871 + 0.960329i \(0.410040\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.79877e7 1.19537 0.597686 − 0.801730i \(-0.296087\pi\)
0.597686 + 0.801730i \(0.296087\pi\)
\(744\) 0 0
\(745\) −1.35030e6 −0.0891332
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 342800. 0.0223273
\(750\) 0 0
\(751\) 1.78553e7 1.15523 0.577615 − 0.816310i \(-0.303984\pi\)
0.577615 + 0.816310i \(0.303984\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.95260e6 0.188511
\(756\) 0 0
\(757\) −1.74527e7 −1.10693 −0.553467 − 0.832871i \(-0.686696\pi\)
−0.553467 + 0.832871i \(0.686696\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.20819e6 −0.200816 −0.100408 − 0.994946i \(-0.532015\pi\)
−0.100408 + 0.994946i \(0.532015\pi\)
\(762\) 0 0
\(763\) −1.53250e7 −0.952992
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.35813e7 1.44737
\(768\) 0 0
\(769\) 1.87050e7 1.14062 0.570311 − 0.821429i \(-0.306823\pi\)
0.570311 + 0.821429i \(0.306823\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.06368e7 1.24221 0.621104 − 0.783728i \(-0.286685\pi\)
0.621104 + 0.783728i \(0.286685\pi\)
\(774\) 0 0
\(775\) 4.20604e6 0.251547
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.12554e7 −0.664532
\(780\) 0 0
\(781\) −1.29430e7 −0.759292
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.82434e6 0.105665
\(786\) 0 0
\(787\) −2.28794e7 −1.31676 −0.658382 − 0.752684i \(-0.728759\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.63870e7 −1.49951
\(792\) 0 0
\(793\) −1.01743e7 −0.574541
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.66035e7 0.925880 0.462940 − 0.886390i \(-0.346795\pi\)
0.462940 + 0.886390i \(0.346795\pi\)
\(798\) 0 0
\(799\) 1.75791e7 0.974158
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.74649e7 −0.955824
\(804\) 0 0
\(805\) 268800. 0.0146197
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.78923e7 1.49835 0.749174 − 0.662374i \(-0.230451\pi\)
0.749174 + 0.662374i \(0.230451\pi\)
\(810\) 0 0
\(811\) −1.33062e7 −0.710401 −0.355200 − 0.934790i \(-0.615587\pi\)
−0.355200 + 0.934790i \(0.615587\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.87180e6 −0.467862
\(816\) 0 0
\(817\) 2.30277e7 1.20697
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.27230e7 1.17654 0.588272 − 0.808663i \(-0.299808\pi\)
0.588272 + 0.808663i \(0.299808\pi\)
\(822\) 0 0
\(823\) 1.29782e6 0.0667905 0.0333953 − 0.999442i \(-0.489368\pi\)
0.0333953 + 0.999442i \(0.489368\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.28396e7 0.652810 0.326405 − 0.945230i \(-0.394163\pi\)
0.326405 + 0.945230i \(0.394163\pi\)
\(828\) 0 0
\(829\) −6.98277e6 −0.352891 −0.176446 − 0.984310i \(-0.556460\pi\)
−0.176446 + 0.984310i \(0.556460\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.26862e6 −0.263078
\(834\) 0 0
\(835\) −1.87432e6 −0.0930310
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.63449e7 1.78254 0.891268 − 0.453478i \(-0.149817\pi\)
0.891268 + 0.453478i \(0.149817\pi\)
\(840\) 0 0
\(841\) 2.87973e7 1.40398
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.16963e6 −0.200889
\(846\) 0 0
\(847\) 1.12651e7 0.539544
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 654720. 0.0309907
\(852\) 0 0
\(853\) −4.31369e6 −0.202991 −0.101495 − 0.994836i \(-0.532363\pi\)
−0.101495 + 0.994836i \(0.532363\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.74751e7 −1.74297 −0.871486 − 0.490420i \(-0.836844\pi\)
−0.871486 + 0.490420i \(0.836844\pi\)
\(858\) 0 0
\(859\) −2.42986e6 −0.112357 −0.0561783 − 0.998421i \(-0.517892\pi\)
−0.0561783 + 0.998421i \(0.517892\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.34998e6 0.335938 0.167969 − 0.985792i \(-0.446279\pi\)
0.167969 + 0.985792i \(0.446279\pi\)
\(864\) 0 0
\(865\) −5.23009e6 −0.237667
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.03286e7 −0.463970
\(870\) 0 0
\(871\) −5.80355e7 −2.59208
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.47560e6 −0.374240
\(876\) 0 0
\(877\) −1.06809e7 −0.468932 −0.234466 − 0.972124i \(-0.575334\pi\)
−0.234466 + 0.972124i \(0.575334\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.18750e7 −0.515460 −0.257730 − 0.966217i \(-0.582974\pi\)
−0.257730 + 0.966217i \(0.582974\pi\)
\(882\) 0 0
\(883\) −8.59380e6 −0.370923 −0.185461 − 0.982652i \(-0.559378\pi\)
−0.185461 + 0.982652i \(0.559378\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.10692e7 −0.472397 −0.236199 − 0.971705i \(-0.575902\pi\)
−0.236199 + 0.971705i \(0.575902\pi\)
\(888\) 0 0
\(889\) −2.97484e7 −1.26244
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.26144e7 −1.36861
\(894\) 0 0
\(895\) −1.83170e6 −0.0764360
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.00836e7 0.416118
\(900\) 0 0
\(901\) 2.13454e7 0.875975
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.00196e6 −0.121838
\(906\) 0 0
\(907\) −3.73654e7 −1.50818 −0.754088 − 0.656774i \(-0.771921\pi\)
−0.754088 + 0.656774i \(0.771921\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.15898e7 1.26110 0.630551 − 0.776148i \(-0.282829\pi\)
0.630551 + 0.776148i \(0.282829\pi\)
\(912\) 0 0
\(913\) 1.48025e7 0.587703
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.77468e7 1.08966
\(918\) 0 0
\(919\) 3.45760e7 1.35047 0.675237 − 0.737601i \(-0.264042\pi\)
0.675237 + 0.737601i \(0.264042\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.81246e7 1.85936
\(924\) 0 0
\(925\) −9.98789e6 −0.383813
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.19448e7 1.21440 0.607198 − 0.794550i \(-0.292293\pi\)
0.607198 + 0.794550i \(0.292293\pi\)
\(930\) 0 0
\(931\) 9.77485e6 0.369603
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.38392e6 0.0891790
\(936\) 0 0
\(937\) −4.33625e6 −0.161349 −0.0806743 − 0.996741i \(-0.525707\pi\)
−0.0806743 + 0.996741i \(0.525707\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.46316e6 −0.0538663 −0.0269332 − 0.999637i \(-0.508574\pi\)
−0.0269332 + 0.999637i \(0.508574\pi\)
\(942\) 0 0
\(943\) 1.50490e6 0.0551096
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.39115e7 −1.22878 −0.614388 − 0.789004i \(-0.710597\pi\)
−0.614388 + 0.789004i \(0.710597\pi\)
\(948\) 0 0
\(949\) 6.49377e7 2.34062
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −7.49099e6 −0.267182 −0.133591 − 0.991037i \(-0.542651\pi\)
−0.133591 + 0.991037i \(0.542651\pi\)
\(954\) 0 0
\(955\) 6.52646e6 0.231563
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2.90958e7 −1.02161
\(960\) 0 0
\(961\) −2.65671e7 −0.927972
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8.18790e6 −0.283044
\(966\) 0 0
\(967\) −4.52251e7 −1.55530 −0.777649 − 0.628699i \(-0.783588\pi\)
−0.777649 + 0.628699i \(0.783588\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.70782e7 1.60240 0.801202 − 0.598394i \(-0.204194\pi\)
0.801202 + 0.598394i \(0.204194\pi\)
\(972\) 0 0
\(973\) −1.01000e6 −0.0342010
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.50439e7 1.50973 0.754865 − 0.655880i \(-0.227702\pi\)
0.754865 + 0.655880i \(0.227702\pi\)
\(978\) 0 0
\(979\) 3.54332e6 0.118155
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.65491e7 1.20640 0.603202 − 0.797588i \(-0.293891\pi\)
0.603202 + 0.797588i \(0.293891\pi\)
\(984\) 0 0
\(985\) −1.07999e7 −0.354672
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.07891e6 −0.100094
\(990\) 0 0
\(991\) −3.80715e7 −1.23145 −0.615724 − 0.787962i \(-0.711136\pi\)
−0.615724 + 0.787962i \(0.711136\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9.86356e6 0.315846
\(996\) 0 0
\(997\) −5.19349e7 −1.65471 −0.827354 − 0.561681i \(-0.810155\pi\)
−0.827354 + 0.561681i \(0.810155\pi\)
\(998\) 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 576.6.a.o.1.1 1
3.2 odd 2 192.6.a.e.1.1 1
4.3 odd 2 576.6.a.p.1.1 1
8.3 odd 2 288.6.a.g.1.1 1
8.5 even 2 288.6.a.f.1.1 1
12.11 even 2 192.6.a.m.1.1 1
24.5 odd 2 96.6.a.e.1.1 yes 1
24.11 even 2 96.6.a.b.1.1 ✓ 1
48.5 odd 4 768.6.d.l.385.2 2
48.11 even 4 768.6.d.g.385.1 2
48.29 odd 4 768.6.d.l.385.1 2
48.35 even 4 768.6.d.g.385.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.6.a.b.1.1 ✓ 1 24.11 even 2
96.6.a.e.1.1 yes 1 24.5 odd 2
192.6.a.e.1.1 1 3.2 odd 2
192.6.a.m.1.1 1 12.11 even 2
288.6.a.f.1.1 1 8.5 even 2
288.6.a.g.1.1 1 8.3 odd 2
576.6.a.o.1.1 1 1.1 even 1 trivial
576.6.a.p.1.1 1 4.3 odd 2
768.6.d.g.385.1 2 48.11 even 4
768.6.d.g.385.2 2 48.35 even 4
768.6.d.l.385.1 2 48.29 odd 4
768.6.d.l.385.2 2 48.5 odd 4