Properties

Label 9216.2.a.bt.1.2
Level $9216$
Weight $2$
Character 9216.1
Self dual yes
Analytic conductor $73.590$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9216,2,Mod(1,9216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9216.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9216 = 2^{10} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9216.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: \(73.5901305028\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.8.10070523904.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} - 8x^{6} + 24x^{5} + 30x^{4} - 16x^{3} - 20x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 144)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.305093\) of defining polynomial
Character \(\chi\) \(=\) 9216.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.36028 q^{5} +3.64575 q^{7} +O(q^{10})\) \(q-3.36028 q^{5} +3.64575 q^{7} -1.19038 q^{11} +3.74166 q^{13} +3.06871 q^{17} +2.32744 q^{19} +7.82087 q^{23} +6.29150 q^{25} +0.979531 q^{29} +0.354249 q^{31} -12.2508 q^{35} -6.57008 q^{37} +6.43560 q^{41} +7.98430 q^{43} -11.1878 q^{47} +6.29150 q^{49} +7.70010 q^{53} +4.00000 q^{55} -11.0604 q^{59} +6.57008 q^{61} -12.5730 q^{65} -5.65685 q^{67} +3.36689 q^{71} +7.29150 q^{73} -4.33981 q^{77} +4.35425 q^{79} -1.19038 q^{83} -10.3117 q^{85} -9.50432 q^{89} +13.6412 q^{91} -7.82087 q^{95} +10.5830 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{7} + 8 q^{25} + 24 q^{31} + 8 q^{49} + 32 q^{55} + 16 q^{73} + 56 q^{79}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.36028 −1.50276 −0.751382 0.659867i \(-0.770612\pi\)
−0.751382 + 0.659867i \(0.770612\pi\)
\(6\) 0 0
\(7\) 3.64575 1.37796 0.688982 0.724778i \(-0.258058\pi\)
0.688982 + 0.724778i \(0.258058\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.19038 −0.358912 −0.179456 0.983766i \(-0.557434\pi\)
−0.179456 + 0.983766i \(0.557434\pi\)
\(12\) 0 0
\(13\) 3.74166 1.03775 0.518875 0.854850i \(-0.326351\pi\)
0.518875 + 0.854850i \(0.326351\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.06871 0.744272 0.372136 0.928178i \(-0.378625\pi\)
0.372136 + 0.928178i \(0.378625\pi\)
\(18\) 0 0
\(19\) 2.32744 0.533952 0.266976 0.963703i \(-0.413976\pi\)
0.266976 + 0.963703i \(0.413976\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.82087 1.63076 0.815382 0.578923i \(-0.196527\pi\)
0.815382 + 0.578923i \(0.196527\pi\)
\(24\) 0 0
\(25\) 6.29150 1.25830
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.979531 0.181894 0.0909472 0.995856i \(-0.471011\pi\)
0.0909472 + 0.995856i \(0.471011\pi\)
\(30\) 0 0
\(31\) 0.354249 0.0636249 0.0318125 0.999494i \(-0.489872\pi\)
0.0318125 + 0.999494i \(0.489872\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −12.2508 −2.07076
\(36\) 0 0
\(37\) −6.57008 −1.08012 −0.540058 0.841628i \(-0.681598\pi\)
−0.540058 + 0.841628i \(0.681598\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.43560 1.00507 0.502536 0.864556i \(-0.332400\pi\)
0.502536 + 0.864556i \(0.332400\pi\)
\(42\) 0 0
\(43\) 7.98430 1.21759 0.608797 0.793326i \(-0.291652\pi\)
0.608797 + 0.793326i \(0.291652\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.1878 −1.63190 −0.815951 0.578121i \(-0.803786\pi\)
−0.815951 + 0.578121i \(0.803786\pi\)
\(48\) 0 0
\(49\) 6.29150 0.898786
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.70010 1.05769 0.528845 0.848719i \(-0.322625\pi\)
0.528845 + 0.848719i \(0.322625\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.0604 −1.43994 −0.719969 0.694006i \(-0.755844\pi\)
−0.719969 + 0.694006i \(0.755844\pi\)
\(60\) 0 0
\(61\) 6.57008 0.841213 0.420607 0.907243i \(-0.361817\pi\)
0.420607 + 0.907243i \(0.361817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.5730 −1.55949
\(66\) 0 0
\(67\) −5.65685 −0.691095 −0.345547 0.938401i \(-0.612307\pi\)
−0.345547 + 0.938401i \(0.612307\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.36689 0.399577 0.199788 0.979839i \(-0.435975\pi\)
0.199788 + 0.979839i \(0.435975\pi\)
\(72\) 0 0
\(73\) 7.29150 0.853406 0.426703 0.904392i \(-0.359675\pi\)
0.426703 + 0.904392i \(0.359675\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.33981 −0.494568
\(78\) 0 0
\(79\) 4.35425 0.489891 0.244946 0.969537i \(-0.421230\pi\)
0.244946 + 0.969537i \(0.421230\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.19038 −0.130661 −0.0653304 0.997864i \(-0.520810\pi\)
−0.0653304 + 0.997864i \(0.520810\pi\)
\(84\) 0 0
\(85\) −10.3117 −1.11847
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.50432 −1.00746 −0.503728 0.863862i \(-0.668039\pi\)
−0.503728 + 0.863862i \(0.668039\pi\)
\(90\) 0 0
\(91\) 13.6412 1.42998
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.82087 −0.802404
\(96\) 0 0
\(97\) 10.5830 1.07454 0.537271 0.843410i \(-0.319455\pi\)
0.537271 + 0.843410i \(0.319455\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.36028 −0.334361 −0.167180 0.985926i \(-0.553466\pi\)
−0.167180 + 0.985926i \(0.553466\pi\)
\(102\) 0 0
\(103\) 1.06275 0.104715 0.0523577 0.998628i \(-0.483326\pi\)
0.0523577 + 0.998628i \(0.483326\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.4411 −1.29940 −0.649702 0.760189i \(-0.725106\pi\)
−0.649702 + 0.760189i \(0.725106\pi\)
\(108\) 0 0
\(109\) 1.91520 0.183443 0.0917213 0.995785i \(-0.470763\pi\)
0.0917213 + 0.995785i \(0.470763\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −26.2803 −2.45065
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 11.1878 1.02558
\(120\) 0 0
\(121\) −9.58301 −0.871182
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.33981 −0.388165
\(126\) 0 0
\(127\) 14.9373 1.32547 0.662733 0.748855i \(-0.269396\pi\)
0.662733 + 0.748855i \(0.269396\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.38075 −0.208007 −0.104004 0.994577i \(-0.533165\pi\)
−0.104004 + 0.994577i \(0.533165\pi\)
\(132\) 0 0
\(133\) 8.48528 0.735767
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.9399 −1.36184 −0.680920 0.732358i \(-0.738420\pi\)
−0.680920 + 0.732358i \(0.738420\pi\)
\(138\) 0 0
\(139\) −9.30978 −0.789645 −0.394822 0.918757i \(-0.629194\pi\)
−0.394822 + 0.918757i \(0.629194\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.45398 −0.372460
\(144\) 0 0
\(145\) −3.29150 −0.273344
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.31935 −0.435778 −0.217889 0.975974i \(-0.569917\pi\)
−0.217889 + 0.975974i \(0.569917\pi\)
\(150\) 0 0
\(151\) 15.6458 1.27323 0.636617 0.771180i \(-0.280333\pi\)
0.636617 + 0.771180i \(0.280333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.19038 −0.0956133
\(156\) 0 0
\(157\) −1.91520 −0.152849 −0.0764247 0.997075i \(-0.524350\pi\)
−0.0764247 + 0.997075i \(0.524350\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 28.5129 2.24714
\(162\) 0 0
\(163\) −8.98626 −0.703859 −0.351929 0.936027i \(-0.614474\pi\)
−0.351929 + 0.936027i \(0.614474\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.45398 0.344659 0.172330 0.985039i \(-0.444871\pi\)
0.172330 + 0.985039i \(0.444871\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.70010 0.585428 0.292714 0.956200i \(-0.405442\pi\)
0.292714 + 0.956200i \(0.405442\pi\)
\(174\) 0 0
\(175\) 22.9373 1.73389
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −13.4411 −1.00464 −0.502319 0.864683i \(-0.667520\pi\)
−0.502319 + 0.864683i \(0.667520\pi\)
\(180\) 0 0
\(181\) 6.57008 0.488351 0.244175 0.969731i \(-0.421483\pi\)
0.244175 + 0.969731i \(0.421483\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 22.0773 1.62316
\(186\) 0 0
\(187\) −3.65292 −0.267128
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.1878 −0.809518 −0.404759 0.914423i \(-0.632645\pi\)
−0.404759 + 0.914423i \(0.632645\pi\)
\(192\) 0 0
\(193\) −19.8745 −1.43060 −0.715299 0.698818i \(-0.753710\pi\)
−0.715299 + 0.698818i \(0.753710\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.4616 0.887852 0.443926 0.896063i \(-0.353585\pi\)
0.443926 + 0.896063i \(0.353585\pi\)
\(198\) 0 0
\(199\) 8.35425 0.592217 0.296108 0.955154i \(-0.404311\pi\)
0.296108 + 0.955154i \(0.404311\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.57113 0.250644
\(204\) 0 0
\(205\) −21.6255 −1.51039
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.77053 −0.191642
\(210\) 0 0
\(211\) 9.30978 0.640911 0.320456 0.947264i \(-0.396164\pi\)
0.320456 + 0.947264i \(0.396164\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −26.8295 −1.82976
\(216\) 0 0
\(217\) 1.29150 0.0876729
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 11.4821 0.772368
\(222\) 0 0
\(223\) 19.6458 1.31558 0.657788 0.753203i \(-0.271492\pi\)
0.657788 + 0.753203i \(0.271492\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 25.6919 1.70523 0.852615 0.522539i \(-0.175015\pi\)
0.852615 + 0.522539i \(0.175015\pi\)
\(228\) 0 0
\(229\) −2.91716 −0.192772 −0.0963858 0.995344i \(-0.530728\pi\)
−0.0963858 + 0.995344i \(0.530728\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.7792 1.42680 0.713400 0.700757i \(-0.247154\pi\)
0.713400 + 0.700757i \(0.247154\pi\)
\(234\) 0 0
\(235\) 37.5940 2.45237
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 23.4626 1.51767 0.758835 0.651283i \(-0.225769\pi\)
0.758835 + 0.651283i \(0.225769\pi\)
\(240\) 0 0
\(241\) −9.29150 −0.598518 −0.299259 0.954172i \(-0.596740\pi\)
−0.299259 + 0.954172i \(0.596740\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −21.1412 −1.35066
\(246\) 0 0
\(247\) 8.70850 0.554108
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.5496 1.17084 0.585421 0.810729i \(-0.300929\pi\)
0.585421 + 0.810729i \(0.300929\pi\)
\(252\) 0 0
\(253\) −9.30978 −0.585301
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −16.2381 −1.01290 −0.506452 0.862268i \(-0.669043\pi\)
−0.506452 + 0.862268i \(0.669043\pi\)
\(258\) 0 0
\(259\) −23.9529 −1.48836
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 15.6417 0.964511 0.482256 0.876031i \(-0.339818\pi\)
0.482256 + 0.876031i \(0.339818\pi\)
\(264\) 0 0
\(265\) −25.8745 −1.58946
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.0399 0.734086 0.367043 0.930204i \(-0.380370\pi\)
0.367043 + 0.930204i \(0.380370\pi\)
\(270\) 0 0
\(271\) 11.6458 0.707429 0.353715 0.935353i \(-0.384918\pi\)
0.353715 + 0.935353i \(0.384918\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.48925 −0.451619
\(276\) 0 0
\(277\) 29.0200 1.74364 0.871822 0.489822i \(-0.162938\pi\)
0.871822 + 0.489822i \(0.162938\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.50432 −0.566980 −0.283490 0.958975i \(-0.591492\pi\)
−0.283490 + 0.958975i \(0.591492\pi\)
\(282\) 0 0
\(283\) 26.2803 1.56220 0.781102 0.624403i \(-0.214658\pi\)
0.781102 + 0.624403i \(0.214658\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.4626 1.38495
\(288\) 0 0
\(289\) −7.58301 −0.446059
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.1412 1.23508 0.617542 0.786538i \(-0.288129\pi\)
0.617542 + 0.786538i \(0.288129\pi\)
\(294\) 0 0
\(295\) 37.1660 2.16389
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 29.2630 1.69232
\(300\) 0 0
\(301\) 29.1088 1.67780
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −22.0773 −1.26415
\(306\) 0 0
\(307\) −28.2843 −1.61427 −0.807134 0.590368i \(-0.798983\pi\)
−0.807134 + 0.590368i \(0.798983\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.6417 −0.886962 −0.443481 0.896284i \(-0.646257\pi\)
−0.443481 + 0.896284i \(0.646257\pi\)
\(312\) 0 0
\(313\) 1.29150 0.0730000 0.0365000 0.999334i \(-0.488379\pi\)
0.0365000 + 0.999334i \(0.488379\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.36028 −0.188732 −0.0943662 0.995538i \(-0.530082\pi\)
−0.0943662 + 0.995538i \(0.530082\pi\)
\(318\) 0 0
\(319\) −1.16601 −0.0652841
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.14226 0.397406
\(324\) 0 0
\(325\) 23.5406 1.30580
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −40.7878 −2.24870
\(330\) 0 0
\(331\) 11.3137 0.621858 0.310929 0.950433i \(-0.399360\pi\)
0.310929 + 0.950433i \(0.399360\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 19.0086 1.03855
\(336\) 0 0
\(337\) −15.2915 −0.832981 −0.416491 0.909140i \(-0.636740\pi\)
−0.416491 + 0.909140i \(0.636740\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.421689 −0.0228357
\(342\) 0 0
\(343\) −2.58301 −0.139469
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.19038 0.0639027 0.0319514 0.999489i \(-0.489828\pi\)
0.0319514 + 0.999489i \(0.489828\pi\)
\(348\) 0 0
\(349\) −32.8504 −1.75844 −0.879221 0.476413i \(-0.841937\pi\)
−0.879221 + 0.476413i \(0.841937\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 28.5129 1.51759 0.758796 0.651329i \(-0.225788\pi\)
0.758796 + 0.651329i \(0.225788\pi\)
\(354\) 0 0
\(355\) −11.3137 −0.600469
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −19.0086 −1.00324 −0.501619 0.865089i \(-0.667262\pi\)
−0.501619 + 0.865089i \(0.667262\pi\)
\(360\) 0 0
\(361\) −13.5830 −0.714895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −24.5015 −1.28247
\(366\) 0 0
\(367\) −12.8118 −0.668769 −0.334384 0.942437i \(-0.608528\pi\)
−0.334384 + 0.942437i \(0.608528\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 28.0726 1.45746
\(372\) 0 0
\(373\) −5.56812 −0.288306 −0.144153 0.989555i \(-0.546046\pi\)
−0.144153 + 0.989555i \(0.546046\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.66507 0.188761
\(378\) 0 0
\(379\) 19.2980 0.991272 0.495636 0.868530i \(-0.334935\pi\)
0.495636 + 0.868530i \(0.334935\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.1878 0.571668 0.285834 0.958279i \(-0.407729\pi\)
0.285834 + 0.958279i \(0.407729\pi\)
\(384\) 0 0
\(385\) 14.5830 0.743219
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −10.5025 −0.532500 −0.266250 0.963904i \(-0.585785\pi\)
−0.266250 + 0.963904i \(0.585785\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −14.6315 −0.736191
\(396\) 0 0
\(397\) −33.8524 −1.69900 −0.849501 0.527586i \(-0.823097\pi\)
−0.849501 + 0.527586i \(0.823097\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.20614 0.459733 0.229866 0.973222i \(-0.426171\pi\)
0.229866 + 0.973222i \(0.426171\pi\)
\(402\) 0 0
\(403\) 1.32548 0.0660267
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.82087 0.387666
\(408\) 0 0
\(409\) −17.1660 −0.848805 −0.424402 0.905474i \(-0.639516\pi\)
−0.424402 + 0.905474i \(0.639516\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −40.3234 −1.98418
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.5496 0.906209 0.453104 0.891457i \(-0.350316\pi\)
0.453104 + 0.891457i \(0.350316\pi\)
\(420\) 0 0
\(421\) −23.5406 −1.14730 −0.573650 0.819100i \(-0.694473\pi\)
−0.573650 + 0.819100i \(0.694473\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 19.3068 0.936518
\(426\) 0 0
\(427\) 23.9529 1.15916
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.08709 −0.0523632 −0.0261816 0.999657i \(-0.508335\pi\)
−0.0261816 + 0.999657i \(0.508335\pi\)
\(432\) 0 0
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.2026 0.870750
\(438\) 0 0
\(439\) 37.5203 1.79074 0.895372 0.445319i \(-0.146910\pi\)
0.895372 + 0.445319i \(0.146910\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 32.8341 1.56000 0.779999 0.625781i \(-0.215220\pi\)
0.779999 + 0.625781i \(0.215220\pi\)
\(444\) 0 0
\(445\) 31.9372 1.51397
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −37.7191 −1.78007 −0.890037 0.455889i \(-0.849322\pi\)
−0.890037 + 0.455889i \(0.849322\pi\)
\(450\) 0 0
\(451\) −7.66079 −0.360732
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −45.8381 −2.14892
\(456\) 0 0
\(457\) 26.5830 1.24350 0.621750 0.783216i \(-0.286422\pi\)
0.621750 + 0.783216i \(0.286422\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.4616 −0.580395 −0.290197 0.956967i \(-0.593721\pi\)
−0.290197 + 0.956967i \(0.593721\pi\)
\(462\) 0 0
\(463\) 30.9373 1.43778 0.718888 0.695126i \(-0.244651\pi\)
0.718888 + 0.695126i \(0.244651\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.1689 0.748207 0.374103 0.927387i \(-0.377951\pi\)
0.374103 + 0.927387i \(0.377951\pi\)
\(468\) 0 0
\(469\) −20.6235 −0.952304
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.50432 −0.437009
\(474\) 0 0
\(475\) 14.6431 0.671872
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.2748 −0.560852 −0.280426 0.959876i \(-0.590476\pi\)
−0.280426 + 0.959876i \(0.590476\pi\)
\(480\) 0 0
\(481\) −24.5830 −1.12089
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −35.5619 −1.61478
\(486\) 0 0
\(487\) −18.2288 −0.826024 −0.413012 0.910726i \(-0.635523\pi\)
−0.413012 + 0.910726i \(0.635523\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19.7400 0.890854 0.445427 0.895318i \(-0.353052\pi\)
0.445427 + 0.895318i \(0.353052\pi\)
\(492\) 0 0
\(493\) 3.00590 0.135379
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.2748 0.550602
\(498\) 0 0
\(499\) −14.9666 −0.669998 −0.334999 0.942218i \(-0.608736\pi\)
−0.334999 + 0.942218i \(0.608736\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −25.7424 −1.14780 −0.573899 0.818926i \(-0.694570\pi\)
−0.573899 + 0.818926i \(0.694570\pi\)
\(504\) 0 0
\(505\) 11.2915 0.502465
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 38.5005 1.70650 0.853252 0.521499i \(-0.174627\pi\)
0.853252 + 0.521499i \(0.174627\pi\)
\(510\) 0 0
\(511\) 26.5830 1.17596
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.57113 −0.157363
\(516\) 0 0
\(517\) 13.3176 0.585709
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.7105 0.819720 0.409860 0.912148i \(-0.365578\pi\)
0.409860 + 0.912148i \(0.365578\pi\)
\(522\) 0 0
\(523\) 4.33138 0.189398 0.0946989 0.995506i \(-0.469811\pi\)
0.0946989 + 0.995506i \(0.469811\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.08709 0.0473543
\(528\) 0 0
\(529\) 38.1660 1.65939
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0798 1.04301
\(534\) 0 0
\(535\) 45.1660 1.95270
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7.48925 −0.322585
\(540\) 0 0
\(541\) 12.0495 0.518047 0.259024 0.965871i \(-0.416599\pi\)
0.259024 + 0.965871i \(0.416599\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.43560 −0.275671
\(546\) 0 0
\(547\) 1.32548 0.0566733 0.0283367 0.999598i \(-0.490979\pi\)
0.0283367 + 0.999598i \(0.490979\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.27980 0.0971229
\(552\) 0 0
\(553\) 15.8745 0.675053
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 35.0041 1.48317 0.741585 0.670859i \(-0.234075\pi\)
0.741585 + 0.670859i \(0.234075\pi\)
\(558\) 0 0
\(559\) 29.8745 1.26356
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.3111 0.982447 0.491224 0.871033i \(-0.336550\pi\)
0.491224 + 0.871033i \(0.336550\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.9767 0.502088 0.251044 0.967976i \(-0.419226\pi\)
0.251044 + 0.967976i \(0.419226\pi\)
\(570\) 0 0
\(571\) 5.65685 0.236732 0.118366 0.992970i \(-0.462234\pi\)
0.118366 + 0.992970i \(0.462234\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 49.2050 2.05199
\(576\) 0 0
\(577\) 35.0405 1.45876 0.729378 0.684111i \(-0.239810\pi\)
0.729378 + 0.684111i \(0.239810\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.33981 −0.180046
\(582\) 0 0
\(583\) −9.16601 −0.379617
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26.8823 1.10955 0.554775 0.832000i \(-0.312804\pi\)
0.554775 + 0.832000i \(0.312804\pi\)
\(588\) 0 0
\(589\) 0.824494 0.0339727
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12.2748 0.504068 0.252034 0.967718i \(-0.418901\pi\)
0.252034 + 0.967718i \(0.418901\pi\)
\(594\) 0 0
\(595\) −37.5940 −1.54121
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 30.1964 1.23379 0.616896 0.787045i \(-0.288390\pi\)
0.616896 + 0.787045i \(0.288390\pi\)
\(600\) 0 0
\(601\) −7.29150 −0.297427 −0.148713 0.988880i \(-0.547513\pi\)
−0.148713 + 0.988880i \(0.547513\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 32.2016 1.30918
\(606\) 0 0
\(607\) 44.1033 1.79010 0.895048 0.445970i \(-0.147141\pi\)
0.895048 + 0.445970i \(0.147141\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −41.8608 −1.69351
\(612\) 0 0
\(613\) −30.1995 −1.21975 −0.609873 0.792500i \(-0.708779\pi\)
−0.609873 + 0.792500i \(0.708779\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 25.7424 1.03635 0.518175 0.855274i \(-0.326611\pi\)
0.518175 + 0.855274i \(0.326611\pi\)
\(618\) 0 0
\(619\) −29.9333 −1.20312 −0.601560 0.798828i \(-0.705454\pi\)
−0.601560 + 0.798828i \(0.705454\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −34.6504 −1.38824
\(624\) 0 0
\(625\) −16.8745 −0.674980
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20.1617 −0.803900
\(630\) 0 0
\(631\) −18.2288 −0.725675 −0.362838 0.931852i \(-0.618192\pi\)
−0.362838 + 0.931852i \(0.618192\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −50.1934 −1.99186
\(636\) 0 0
\(637\) 23.5406 0.932714
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.20614 −0.363621 −0.181810 0.983334i \(-0.558196\pi\)
−0.181810 + 0.983334i \(0.558196\pi\)
\(642\) 0 0
\(643\) −2.32744 −0.0917854 −0.0458927 0.998946i \(-0.514613\pi\)
−0.0458927 + 0.998946i \(0.514613\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.82087 −0.307470 −0.153735 0.988112i \(-0.549130\pi\)
−0.153735 + 0.988112i \(0.549130\pi\)
\(648\) 0 0
\(649\) 13.1660 0.516811
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.5025 0.410996 0.205498 0.978658i \(-0.434119\pi\)
0.205498 + 0.978658i \(0.434119\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 34.0245 1.32541 0.662704 0.748882i \(-0.269409\pi\)
0.662704 + 0.748882i \(0.269409\pi\)
\(660\) 0 0
\(661\) −41.3357 −1.60777 −0.803886 0.594783i \(-0.797238\pi\)
−0.803886 + 0.594783i \(0.797238\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −28.5129 −1.10568
\(666\) 0 0
\(667\) 7.66079 0.296627
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.82087 −0.301921
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.12179 0.312146 0.156073 0.987746i \(-0.450117\pi\)
0.156073 + 0.987746i \(0.450117\pi\)
\(678\) 0 0
\(679\) 38.5830 1.48068
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −50.1934 −1.92060 −0.960299 0.278974i \(-0.910006\pi\)
−0.960299 + 0.278974i \(0.910006\pi\)
\(684\) 0 0
\(685\) 53.5626 2.04652
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 28.8111 1.09762
\(690\) 0 0
\(691\) 2.32744 0.0885401 0.0442701 0.999020i \(-0.485904\pi\)
0.0442701 + 0.999020i \(0.485904\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 31.2835 1.18665
\(696\) 0 0
\(697\) 19.7490 0.748047
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23.5220 −0.888413 −0.444206 0.895924i \(-0.646514\pi\)
−0.444206 + 0.895924i \(0.646514\pi\)
\(702\) 0 0
\(703\) −15.2915 −0.576730
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.2508 −0.460737
\(708\) 0 0
\(709\) 49.8210 1.87107 0.935533 0.353239i \(-0.114920\pi\)
0.935533 + 0.353239i \(0.114920\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.77053 0.103757
\(714\) 0 0
\(715\) 14.9666 0.559720
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10.1007 −0.376692 −0.188346 0.982103i \(-0.560313\pi\)
−0.188346 + 0.982103i \(0.560313\pi\)
\(720\) 0 0
\(721\) 3.87451 0.144294
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.16272 0.228878
\(726\) 0 0
\(727\) −35.3948 −1.31272 −0.656360 0.754448i \(-0.727905\pi\)
−0.656360 + 0.754448i \(0.727905\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 24.5015 0.906221
\(732\) 0 0
\(733\) −10.4005 −0.384150 −0.192075 0.981380i \(-0.561522\pi\)
−0.192075 + 0.981380i \(0.561522\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.73378 0.248042
\(738\) 0 0
\(739\) −46.9038 −1.72538 −0.862692 0.505729i \(-0.831224\pi\)
−0.862692 + 0.505729i \(0.831224\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.5547 0.533958 0.266979 0.963702i \(-0.413974\pi\)
0.266979 + 0.963702i \(0.413974\pi\)
\(744\) 0 0
\(745\) 17.8745 0.654871
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −49.0030 −1.79053
\(750\) 0 0
\(751\) −2.93725 −0.107182 −0.0535910 0.998563i \(-0.517067\pi\)
−0.0535910 + 0.998563i \(0.517067\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −52.5742 −1.91337
\(756\) 0 0
\(757\) 27.1936 0.988367 0.494184 0.869358i \(-0.335467\pi\)
0.494184 + 0.869358i \(0.335467\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.43560 −0.233290 −0.116645 0.993174i \(-0.537214\pi\)
−0.116645 + 0.993174i \(0.537214\pi\)
\(762\) 0 0
\(763\) 6.98233 0.252777
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −41.3842 −1.49430
\(768\) 0 0
\(769\) 6.70850 0.241915 0.120957 0.992658i \(-0.461404\pi\)
0.120957 + 0.992658i \(0.461404\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −20.7195 −0.745230 −0.372615 0.927986i \(-0.621539\pi\)
−0.372615 + 0.927986i \(0.621539\pi\)
\(774\) 0 0
\(775\) 2.22876 0.0800593
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14.9785 0.536661
\(780\) 0 0
\(781\) −4.00787 −0.143413
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.43560 0.229697
\(786\) 0 0
\(787\) −28.6078 −1.01976 −0.509879 0.860246i \(-0.670310\pi\)
−0.509879 + 0.860246i \(0.670310\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 24.5830 0.872968
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20.7195 −0.733924 −0.366962 0.930236i \(-0.619602\pi\)
−0.366962 + 0.930236i \(0.619602\pi\)
\(798\) 0 0
\(799\) −34.3320 −1.21458
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8.67963 −0.306297
\(804\) 0 0
\(805\) −95.8116 −3.37691
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −44.4529 −1.56288 −0.781440 0.623981i \(-0.785514\pi\)
−0.781440 + 0.623981i \(0.785514\pi\)
\(810\) 0 0
\(811\) 14.6431 0.514189 0.257095 0.966386i \(-0.417235\pi\)
0.257095 + 0.966386i \(0.417235\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 30.1964 1.05773
\(816\) 0 0
\(817\) 18.5830 0.650137
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 43.6837 1.52457 0.762285 0.647241i \(-0.224077\pi\)
0.762285 + 0.647241i \(0.224077\pi\)
\(822\) 0 0
\(823\) 5.77124 0.201173 0.100586 0.994928i \(-0.467928\pi\)
0.100586 + 0.994928i \(0.467928\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11.0604 −0.384607 −0.192304 0.981335i \(-0.561596\pi\)
−0.192304 + 0.981335i \(0.561596\pi\)
\(828\) 0 0
\(829\) 13.2289 0.459459 0.229729 0.973255i \(-0.426216\pi\)
0.229729 + 0.973255i \(0.426216\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 19.3068 0.668941
\(834\) 0 0
\(835\) −14.9666 −0.517942
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 40.1914 1.38756 0.693781 0.720186i \(-0.255943\pi\)
0.693781 + 0.720186i \(0.255943\pi\)
\(840\) 0 0
\(841\) −28.0405 −0.966914
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.36028 −0.115597
\(846\) 0 0
\(847\) −34.9373 −1.20046
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −51.3838 −1.76141
\(852\) 0 0
\(853\) −5.56812 −0.190649 −0.0953244 0.995446i \(-0.530389\pi\)
−0.0953244 + 0.995446i \(0.530389\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15.9399 0.544497 0.272249 0.962227i \(-0.412233\pi\)
0.272249 + 0.962227i \(0.412233\pi\)
\(858\) 0 0
\(859\) −45.5783 −1.55511 −0.777557 0.628813i \(-0.783541\pi\)
−0.777557 + 0.628813i \(0.783541\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 13.3619 0.454846 0.227423 0.973796i \(-0.426970\pi\)
0.227423 + 0.973796i \(0.426970\pi\)
\(864\) 0 0
\(865\) −25.8745 −0.879760
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.18319 −0.175828
\(870\) 0 0
\(871\) −21.1660 −0.717183
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −15.8219 −0.534877
\(876\) 0 0
\(877\) 8.57402 0.289524 0.144762 0.989467i \(-0.453758\pi\)
0.144762 + 0.989467i \(0.453758\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −40.7878 −1.37418 −0.687088 0.726574i \(-0.741111\pi\)
−0.687088 + 0.726574i \(0.741111\pi\)
\(882\) 0 0
\(883\) 47.2273 1.58933 0.794663 0.607051i \(-0.207648\pi\)
0.794663 + 0.607051i \(0.207648\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 19.0086 0.638247 0.319124 0.947713i \(-0.396611\pi\)
0.319124 + 0.947713i \(0.396611\pi\)
\(888\) 0 0
\(889\) 54.4575 1.82645
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −26.0389 −0.871358
\(894\) 0 0
\(895\) 45.1660 1.50973
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.346998 0.0115730
\(900\) 0 0
\(901\) 23.6294 0.787209
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −22.0773 −0.733876
\(906\) 0 0
\(907\) 59.5430 1.97709 0.988547 0.150916i \(-0.0482224\pi\)
0.988547 + 0.150916i \(0.0482224\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −45.8381 −1.51869 −0.759343 0.650691i \(-0.774479\pi\)
−0.759343 + 0.650691i \(0.774479\pi\)
\(912\) 0 0
\(913\) 1.41699 0.0468957
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.67963 −0.286627
\(918\) 0 0
\(919\) 16.1033 0.531198 0.265599 0.964084i \(-0.414430\pi\)
0.265599 + 0.964084i \(0.414430\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 12.5978 0.414660
\(924\) 0 0
\(925\) −41.3357 −1.35911
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −19.3068 −0.633436 −0.316718 0.948520i \(-0.602581\pi\)
−0.316718 + 0.948520i \(0.602581\pi\)
\(930\) 0 0
\(931\) 14.6431 0.479909
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 12.2748 0.401430
\(936\) 0 0
\(937\) −11.1660 −0.364778 −0.182389 0.983226i \(-0.558383\pi\)
−0.182389 + 0.983226i \(0.558383\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 36.5414 1.19122 0.595608 0.803275i \(-0.296911\pi\)
0.595608 + 0.803275i \(0.296911\pi\)
\(942\) 0 0
\(943\) 50.3320 1.63904
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −13.4411 −0.436778 −0.218389 0.975862i \(-0.570080\pi\)
−0.218389 + 0.975862i \(0.570080\pi\)
\(948\) 0 0
\(949\) 27.2823 0.885621
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −24.8479 −0.804902 −0.402451 0.915442i \(-0.631842\pi\)
−0.402451 + 0.915442i \(0.631842\pi\)
\(954\) 0 0
\(955\) 37.5940 1.21651
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −58.1130 −1.87657
\(960\) 0 0
\(961\) −30.8745 −0.995952
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 66.7840 2.14985
\(966\) 0 0
\(967\) 23.3948 0.752325 0.376162 0.926554i \(-0.377243\pi\)
0.376162 + 0.926554i \(0.377243\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −43.0511 −1.38158 −0.690789 0.723057i \(-0.742736\pi\)
−0.690789 + 0.723057i \(0.742736\pi\)
\(972\) 0 0
\(973\) −33.9411 −1.08810
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −43.8565 −1.40309 −0.701547 0.712623i \(-0.747507\pi\)
−0.701547 + 0.712623i \(0.747507\pi\)
\(978\) 0 0
\(979\) 11.3137 0.361588
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6.73378 0.214774 0.107387 0.994217i \(-0.465752\pi\)
0.107387 + 0.994217i \(0.465752\pi\)
\(984\) 0 0
\(985\) −41.8745 −1.33423
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 62.4442 1.98561
\(990\) 0 0
\(991\) −18.9373 −0.601562 −0.300781 0.953693i \(-0.597247\pi\)
−0.300781 + 0.953693i \(0.597247\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −28.0726 −0.889963
\(996\) 0 0
\(997\) 0.735758 0.0233017 0.0116508 0.999932i \(-0.496291\pi\)
0.0116508 + 0.999932i \(0.496291\pi\)
\(998\) 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 9216.2.a.bt.1.2 8
3.2 odd 2 inner 9216.2.a.bt.1.8 8
4.3 odd 2 9216.2.a.bq.1.2 8
8.3 odd 2 9216.2.a.bq.1.7 8
8.5 even 2 inner 9216.2.a.bt.1.7 8
12.11 even 2 9216.2.a.bq.1.8 8
24.5 odd 2 inner 9216.2.a.bt.1.1 8
24.11 even 2 9216.2.a.bq.1.1 8
32.3 odd 8 144.2.k.c.109.3 yes 8
32.5 even 8 1152.2.k.d.865.1 8
32.11 odd 8 144.2.k.c.37.3 yes 8
32.13 even 8 1152.2.k.d.289.1 8
32.19 odd 8 1152.2.k.e.289.1 8
32.21 even 8 576.2.k.c.433.4 8
32.27 odd 8 1152.2.k.e.865.1 8
32.29 even 8 576.2.k.c.145.4 8
96.5 odd 8 1152.2.k.d.865.4 8
96.11 even 8 144.2.k.c.37.2 8
96.29 odd 8 576.2.k.c.145.1 8
96.35 even 8 144.2.k.c.109.2 yes 8
96.53 odd 8 576.2.k.c.433.1 8
96.59 even 8 1152.2.k.e.865.4 8
96.77 odd 8 1152.2.k.d.289.4 8
96.83 even 8 1152.2.k.e.289.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.k.c.37.2 8 96.11 even 8
144.2.k.c.37.3 yes 8 32.11 odd 8
144.2.k.c.109.2 yes 8 96.35 even 8
144.2.k.c.109.3 yes 8 32.3 odd 8
576.2.k.c.145.1 8 96.29 odd 8
576.2.k.c.145.4 8 32.29 even 8
576.2.k.c.433.1 8 96.53 odd 8
576.2.k.c.433.4 8 32.21 even 8
1152.2.k.d.289.1 8 32.13 even 8
1152.2.k.d.289.4 8 96.77 odd 8
1152.2.k.d.865.1 8 32.5 even 8
1152.2.k.d.865.4 8 96.5 odd 8
1152.2.k.e.289.1 8 32.19 odd 8
1152.2.k.e.289.4 8 96.83 even 8
1152.2.k.e.865.1 8 32.27 odd 8
1152.2.k.e.865.4 8 96.59 even 8
9216.2.a.bq.1.1 8 24.11 even 2
9216.2.a.bq.1.2 8 4.3 odd 2
9216.2.a.bq.1.7 8 8.3 odd 2
9216.2.a.bq.1.8 8 12.11 even 2
9216.2.a.bt.1.1 8 24.5 odd 2 inner
9216.2.a.bt.1.2 8 1.1 even 1 trivial
9216.2.a.bt.1.7 8 8.5 even 2 inner
9216.2.a.bt.1.8 8 3.2 odd 2 inner