Properties

Label 9576.2.a.bh.1.1
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.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: \(76.4647449756\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{7}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.64575\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.64575 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-3.64575 q^{5} +1.00000 q^{7} -2.00000 q^{11} -4.00000 q^{13} +0.354249 q^{17} +1.00000 q^{19} +6.00000 q^{23} +8.29150 q^{25} -5.64575 q^{29} +1.29150 q^{31} -3.64575 q^{35} +5.29150 q^{37} +8.58301 q^{41} -2.00000 q^{43} -2.35425 q^{47} +1.00000 q^{49} +8.93725 q^{53} +7.29150 q^{55} -14.5830 q^{59} +2.70850 q^{61} +14.5830 q^{65} +14.5830 q^{67} -0.354249 q^{71} -9.29150 q^{73} -2.00000 q^{77} +11.2915 q^{79} -16.9373 q^{83} -1.29150 q^{85} -6.00000 q^{89} -4.00000 q^{91} -3.64575 q^{95} +16.5830 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 2 q^{7} - 4 q^{11} - 8 q^{13} + 6 q^{17} + 2 q^{19} + 12 q^{23} + 6 q^{25} - 6 q^{29} - 8 q^{31} - 2 q^{35} - 4 q^{41} - 4 q^{43} - 10 q^{47} + 2 q^{49} + 2 q^{53} + 4 q^{55} - 8 q^{59} + 16 q^{61} + 8 q^{65} + 8 q^{67} - 6 q^{71} - 8 q^{73} - 4 q^{77} + 12 q^{79} - 18 q^{83} + 8 q^{85} - 12 q^{89} - 8 q^{91} - 2 q^{95} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.64575 −1.63043 −0.815215 0.579159i \(-0.803381\pi\)
−0.815215 + 0.579159i \(0.803381\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.354249 0.0859179 0.0429590 0.999077i \(-0.486322\pi\)
0.0429590 + 0.999077i \(0.486322\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 8.29150 1.65830
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.64575 −1.04839 −0.524195 0.851598i \(-0.675634\pi\)
−0.524195 + 0.851598i \(0.675634\pi\)
\(30\) 0 0
\(31\) 1.29150 0.231961 0.115980 0.993252i \(-0.462999\pi\)
0.115980 + 0.993252i \(0.462999\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.64575 −0.616244
\(36\) 0 0
\(37\) 5.29150 0.869918 0.434959 0.900450i \(-0.356763\pi\)
0.434959 + 0.900450i \(0.356763\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.58301 1.34044 0.670220 0.742162i \(-0.266200\pi\)
0.670220 + 0.742162i \(0.266200\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.35425 −0.343402 −0.171701 0.985149i \(-0.554926\pi\)
−0.171701 + 0.985149i \(0.554926\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.93725 1.22763 0.613813 0.789451i \(-0.289635\pi\)
0.613813 + 0.789451i \(0.289635\pi\)
\(54\) 0 0
\(55\) 7.29150 0.983186
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −14.5830 −1.89855 −0.949273 0.314454i \(-0.898179\pi\)
−0.949273 + 0.314454i \(0.898179\pi\)
\(60\) 0 0
\(61\) 2.70850 0.346788 0.173394 0.984853i \(-0.444527\pi\)
0.173394 + 0.984853i \(0.444527\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14.5830 1.80880
\(66\) 0 0
\(67\) 14.5830 1.78160 0.890799 0.454398i \(-0.150146\pi\)
0.890799 + 0.454398i \(0.150146\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.354249 −0.0420416 −0.0210208 0.999779i \(-0.506692\pi\)
−0.0210208 + 0.999779i \(0.506692\pi\)
\(72\) 0 0
\(73\) −9.29150 −1.08749 −0.543744 0.839251i \(-0.682994\pi\)
−0.543744 + 0.839251i \(0.682994\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 11.2915 1.27039 0.635197 0.772350i \(-0.280919\pi\)
0.635197 + 0.772350i \(0.280919\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −16.9373 −1.85911 −0.929553 0.368690i \(-0.879807\pi\)
−0.929553 + 0.368690i \(0.879807\pi\)
\(84\) 0 0
\(85\) −1.29150 −0.140083
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.64575 −0.374046
\(96\) 0 0
\(97\) 16.5830 1.68375 0.841875 0.539673i \(-0.181452\pi\)
0.841875 + 0.539673i \(0.181452\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.35425 −0.433264 −0.216632 0.976253i \(-0.569507\pi\)
−0.216632 + 0.976253i \(0.569507\pi\)
\(102\) 0 0
\(103\) −2.58301 −0.254511 −0.127256 0.991870i \(-0.540617\pi\)
−0.127256 + 0.991870i \(0.540617\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.64575 −0.352448 −0.176224 0.984350i \(-0.556388\pi\)
−0.176224 + 0.984350i \(0.556388\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.9373 1.59332 0.796661 0.604426i \(-0.206597\pi\)
0.796661 + 0.604426i \(0.206597\pi\)
\(114\) 0 0
\(115\) −21.8745 −2.03981
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.354249 0.0324739
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16.9373 1.47981 0.739907 0.672709i \(-0.234869\pi\)
0.739907 + 0.672709i \(0.234869\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −22.5830 −1.92940 −0.964698 0.263358i \(-0.915170\pi\)
−0.964698 + 0.263358i \(0.915170\pi\)
\(138\) 0 0
\(139\) −0.708497 −0.0600940 −0.0300470 0.999548i \(-0.509566\pi\)
−0.0300470 + 0.999548i \(0.509566\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 20.5830 1.70933
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.2915 −1.25273 −0.626364 0.779530i \(-0.715458\pi\)
−0.626364 + 0.779530i \(0.715458\pi\)
\(150\) 0 0
\(151\) 19.2915 1.56992 0.784960 0.619546i \(-0.212683\pi\)
0.784960 + 0.619546i \(0.212683\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.70850 −0.378196
\(156\) 0 0
\(157\) 11.8745 0.947689 0.473844 0.880609i \(-0.342866\pi\)
0.473844 + 0.880609i \(0.342866\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) −12.5830 −0.985577 −0.492789 0.870149i \(-0.664022\pi\)
−0.492789 + 0.870149i \(0.664022\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.2915 −1.18329 −0.591646 0.806198i \(-0.701522\pi\)
−0.591646 + 0.806198i \(0.701522\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −14.0000 −1.06440 −0.532200 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 0 0
\(175\) 8.29150 0.626779
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −25.5203 −1.90747 −0.953737 0.300643i \(-0.902799\pi\)
−0.953737 + 0.300643i \(0.902799\pi\)
\(180\) 0 0
\(181\) 16.5830 1.23261 0.616303 0.787509i \(-0.288630\pi\)
0.616303 + 0.787509i \(0.288630\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −19.2915 −1.41834
\(186\) 0 0
\(187\) −0.708497 −0.0518105
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) 0 0
\(193\) −25.2915 −1.82052 −0.910261 0.414035i \(-0.864119\pi\)
−0.910261 + 0.414035i \(0.864119\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.41699 0.385945 0.192972 0.981204i \(-0.438187\pi\)
0.192972 + 0.981204i \(0.438187\pi\)
\(198\) 0 0
\(199\) 1.41699 0.100448 0.0502240 0.998738i \(-0.484006\pi\)
0.0502240 + 0.998738i \(0.484006\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.64575 −0.396254
\(204\) 0 0
\(205\) −31.2915 −2.18549
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −1.41699 −0.0975499 −0.0487750 0.998810i \(-0.515532\pi\)
−0.0487750 + 0.998810i \(0.515532\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.29150 0.497276
\(216\) 0 0
\(217\) 1.29150 0.0876729
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.41699 −0.0953174
\(222\) 0 0
\(223\) −5.29150 −0.354345 −0.177173 0.984180i \(-0.556695\pi\)
−0.177173 + 0.984180i \(0.556695\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.7085 −0.843493 −0.421746 0.906714i \(-0.638583\pi\)
−0.421746 + 0.906714i \(0.638583\pi\)
\(228\) 0 0
\(229\) −8.58301 −0.567181 −0.283590 0.958945i \(-0.591526\pi\)
−0.283590 + 0.958945i \(0.591526\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.2915 1.00178 0.500890 0.865511i \(-0.333006\pi\)
0.500890 + 0.865511i \(0.333006\pi\)
\(234\) 0 0
\(235\) 8.58301 0.559894
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.70850 −0.175198 −0.0875991 0.996156i \(-0.527919\pi\)
−0.0875991 + 0.996156i \(0.527919\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.64575 −0.232919
\(246\) 0 0
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.35425 −0.148599 −0.0742994 0.997236i \(-0.523672\pi\)
−0.0742994 + 0.997236i \(0.523672\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.2915 −0.829101 −0.414551 0.910026i \(-0.636061\pi\)
−0.414551 + 0.910026i \(0.636061\pi\)
\(258\) 0 0
\(259\) 5.29150 0.328798
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.70850 −0.167013 −0.0835066 0.996507i \(-0.526612\pi\)
−0.0835066 + 0.996507i \(0.526612\pi\)
\(264\) 0 0
\(265\) −32.5830 −2.00156
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.4575 1.36926 0.684629 0.728891i \(-0.259964\pi\)
0.684629 + 0.728891i \(0.259964\pi\)
\(270\) 0 0
\(271\) 4.70850 0.286021 0.143010 0.989721i \(-0.454322\pi\)
0.143010 + 0.989721i \(0.454322\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.5830 −0.999993
\(276\) 0 0
\(277\) −29.8745 −1.79499 −0.897493 0.441030i \(-0.854613\pi\)
−0.897493 + 0.441030i \(0.854613\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.06275 0.421328 0.210664 0.977559i \(-0.432437\pi\)
0.210664 + 0.977559i \(0.432437\pi\)
\(282\) 0 0
\(283\) 8.00000 0.475551 0.237775 0.971320i \(-0.423582\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.58301 0.506639
\(288\) 0 0
\(289\) −16.8745 −0.992618
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.41699 −0.199623 −0.0998115 0.995006i \(-0.531824\pi\)
−0.0998115 + 0.995006i \(0.531824\pi\)
\(294\) 0 0
\(295\) 53.1660 3.09544
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9.87451 −0.565413
\(306\) 0 0
\(307\) −23.8745 −1.36259 −0.681295 0.732009i \(-0.738583\pi\)
−0.681295 + 0.732009i \(0.738583\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.3542 0.813955 0.406977 0.913438i \(-0.366583\pi\)
0.406977 + 0.913438i \(0.366583\pi\)
\(312\) 0 0
\(313\) 17.2915 0.977374 0.488687 0.872459i \(-0.337476\pi\)
0.488687 + 0.872459i \(0.337476\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.93725 0.277304 0.138652 0.990341i \(-0.455723\pi\)
0.138652 + 0.990341i \(0.455723\pi\)
\(318\) 0 0
\(319\) 11.2915 0.632203
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.354249 0.0197109
\(324\) 0 0
\(325\) −33.1660 −1.83972
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.35425 −0.129794
\(330\) 0 0
\(331\) −24.4575 −1.34431 −0.672153 0.740412i \(-0.734630\pi\)
−0.672153 + 0.740412i \(0.734630\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −53.1660 −2.90477
\(336\) 0 0
\(337\) 12.5830 0.685440 0.342720 0.939438i \(-0.388652\pi\)
0.342720 + 0.939438i \(0.388652\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.58301 −0.139878
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.8745 1.06692 0.533460 0.845825i \(-0.320892\pi\)
0.533460 + 0.845825i \(0.320892\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.6458 1.04564 0.522819 0.852444i \(-0.324880\pi\)
0.522819 + 0.852444i \(0.324880\pi\)
\(354\) 0 0
\(355\) 1.29150 0.0685458
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 32.5830 1.71967 0.859833 0.510576i \(-0.170568\pi\)
0.859833 + 0.510576i \(0.170568\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 33.8745 1.77307
\(366\) 0 0
\(367\) −17.1660 −0.896058 −0.448029 0.894019i \(-0.647874\pi\)
−0.448029 + 0.894019i \(0.647874\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.93725 0.463999
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 22.5830 1.16308
\(378\) 0 0
\(379\) 7.29150 0.374539 0.187270 0.982309i \(-0.440036\pi\)
0.187270 + 0.982309i \(0.440036\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.12549 0.108608 0.0543038 0.998524i \(-0.482706\pi\)
0.0543038 + 0.998524i \(0.482706\pi\)
\(384\) 0 0
\(385\) 7.29150 0.371609
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.8745 1.10908 0.554541 0.832157i \(-0.312894\pi\)
0.554541 + 0.832157i \(0.312894\pi\)
\(390\) 0 0
\(391\) 2.12549 0.107491
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −41.1660 −2.07129
\(396\) 0 0
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.6458 −0.681436 −0.340718 0.940165i \(-0.610670\pi\)
−0.340718 + 0.940165i \(0.610670\pi\)
\(402\) 0 0
\(403\) −5.16601 −0.257337
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.5830 −0.524580
\(408\) 0 0
\(409\) −13.1660 −0.651017 −0.325509 0.945539i \(-0.605536\pi\)
−0.325509 + 0.945539i \(0.605536\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14.5830 −0.717583
\(414\) 0 0
\(415\) 61.7490 3.03114
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.06275 −0.345038 −0.172519 0.985006i \(-0.555191\pi\)
−0.172519 + 0.985006i \(0.555191\pi\)
\(420\) 0 0
\(421\) 19.8745 0.968624 0.484312 0.874895i \(-0.339070\pi\)
0.484312 + 0.874895i \(0.339070\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.93725 0.142478
\(426\) 0 0
\(427\) 2.70850 0.131073
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.0627 −0.629210 −0.314605 0.949223i \(-0.601872\pi\)
−0.314605 + 0.949223i \(0.601872\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000 0.287019
\(438\) 0 0
\(439\) −35.8745 −1.71220 −0.856098 0.516813i \(-0.827118\pi\)
−0.856098 + 0.516813i \(0.827118\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −21.2915 −1.01159 −0.505795 0.862654i \(-0.668801\pi\)
−0.505795 + 0.862654i \(0.668801\pi\)
\(444\) 0 0
\(445\) 21.8745 1.03695
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9.64575 −0.455211 −0.227606 0.973753i \(-0.573090\pi\)
−0.227606 + 0.973753i \(0.573090\pi\)
\(450\) 0 0
\(451\) −17.1660 −0.808316
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 14.5830 0.683662
\(456\) 0 0
\(457\) −33.8745 −1.58458 −0.792291 0.610143i \(-0.791112\pi\)
−0.792291 + 0.610143i \(0.791112\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.9373 −0.509399 −0.254699 0.967020i \(-0.581977\pi\)
−0.254699 + 0.967020i \(0.581977\pi\)
\(462\) 0 0
\(463\) −29.1660 −1.35546 −0.677730 0.735311i \(-0.737036\pi\)
−0.677730 + 0.735311i \(0.737036\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.22876 −0.380781 −0.190391 0.981708i \(-0.560975\pi\)
−0.190391 + 0.981708i \(0.560975\pi\)
\(468\) 0 0
\(469\) 14.5830 0.673381
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) 8.29150 0.380440
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −20.2288 −0.924275 −0.462138 0.886808i \(-0.652917\pi\)
−0.462138 + 0.886808i \(0.652917\pi\)
\(480\) 0 0
\(481\) −21.1660 −0.965087
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −60.4575 −2.74523
\(486\) 0 0
\(487\) 35.7490 1.61994 0.809971 0.586470i \(-0.199483\pi\)
0.809971 + 0.586470i \(0.199483\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.29150 −0.419320 −0.209660 0.977774i \(-0.567236\pi\)
−0.209660 + 0.977774i \(0.567236\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.354249 −0.0158902
\(498\) 0 0
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 23.5203 1.04872 0.524358 0.851498i \(-0.324305\pi\)
0.524358 + 0.851498i \(0.324305\pi\)
\(504\) 0 0
\(505\) 15.8745 0.706406
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −21.2915 −0.943729 −0.471865 0.881671i \(-0.656419\pi\)
−0.471865 + 0.881671i \(0.656419\pi\)
\(510\) 0 0
\(511\) −9.29150 −0.411032
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.41699 0.414962
\(516\) 0 0
\(517\) 4.70850 0.207079
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.8745 0.695475 0.347737 0.937592i \(-0.386950\pi\)
0.347737 + 0.937592i \(0.386950\pi\)
\(522\) 0 0
\(523\) 23.8745 1.04396 0.521980 0.852958i \(-0.325194\pi\)
0.521980 + 0.852958i \(0.325194\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.457513 0.0199296
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −34.3320 −1.48708
\(534\) 0 0
\(535\) 13.2915 0.574642
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 15.1660 0.652038 0.326019 0.945363i \(-0.394293\pi\)
0.326019 + 0.945363i \(0.394293\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −36.4575 −1.56167
\(546\) 0 0
\(547\) 15.2915 0.653817 0.326909 0.945056i \(-0.393993\pi\)
0.326909 + 0.945056i \(0.393993\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.64575 −0.240517
\(552\) 0 0
\(553\) 11.2915 0.480164
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.87451 0.418396 0.209198 0.977873i \(-0.432915\pi\)
0.209198 + 0.977873i \(0.432915\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21.8745 0.921901 0.460950 0.887426i \(-0.347509\pi\)
0.460950 + 0.887426i \(0.347509\pi\)
\(564\) 0 0
\(565\) −61.7490 −2.59780
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.3542 −0.769450 −0.384725 0.923031i \(-0.625704\pi\)
−0.384725 + 0.923031i \(0.625704\pi\)
\(570\) 0 0
\(571\) 39.7490 1.66344 0.831722 0.555192i \(-0.187355\pi\)
0.831722 + 0.555192i \(0.187355\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 49.7490 2.07468
\(576\) 0 0
\(577\) −41.0405 −1.70854 −0.854270 0.519830i \(-0.825995\pi\)
−0.854270 + 0.519830i \(0.825995\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.9373 −0.702676
\(582\) 0 0
\(583\) −17.8745 −0.740286
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.9373 −0.699075 −0.349538 0.936922i \(-0.613661\pi\)
−0.349538 + 0.936922i \(0.613661\pi\)
\(588\) 0 0
\(589\) 1.29150 0.0532154
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −31.6458 −1.29954 −0.649768 0.760133i \(-0.725134\pi\)
−0.649768 + 0.760133i \(0.725134\pi\)
\(594\) 0 0
\(595\) −1.29150 −0.0529464
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.5203 −1.53304 −0.766518 0.642223i \(-0.778012\pi\)
−0.766518 + 0.642223i \(0.778012\pi\)
\(600\) 0 0
\(601\) −44.3320 −1.80834 −0.904170 0.427172i \(-0.859510\pi\)
−0.904170 + 0.427172i \(0.859510\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 25.5203 1.03755
\(606\) 0 0
\(607\) 1.41699 0.0575140 0.0287570 0.999586i \(-0.490845\pi\)
0.0287570 + 0.999586i \(0.490845\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.41699 0.380971
\(612\) 0 0
\(613\) −31.2915 −1.26385 −0.631926 0.775029i \(-0.717735\pi\)
−0.631926 + 0.775029i \(0.717735\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.16601 0.207976 0.103988 0.994579i \(-0.466840\pi\)
0.103988 + 0.994579i \(0.466840\pi\)
\(618\) 0 0
\(619\) −37.8745 −1.52231 −0.761153 0.648573i \(-0.775366\pi\)
−0.761153 + 0.648573i \(0.775366\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) 2.29150 0.0916601
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.87451 0.0747415
\(630\) 0 0
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14.5830 0.578709
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.35425 −0.250978 −0.125489 0.992095i \(-0.540050\pi\)
−0.125489 + 0.992095i \(0.540050\pi\)
\(642\) 0 0
\(643\) 21.1660 0.834706 0.417353 0.908744i \(-0.362958\pi\)
0.417353 + 0.908744i \(0.362958\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.22876 0.166250 0.0831248 0.996539i \(-0.473510\pi\)
0.0831248 + 0.996539i \(0.473510\pi\)
\(648\) 0 0
\(649\) 29.1660 1.14487
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −37.1660 −1.45442 −0.727209 0.686416i \(-0.759183\pi\)
−0.727209 + 0.686416i \(0.759183\pi\)
\(654\) 0 0
\(655\) −61.7490 −2.41273
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −5.06275 −0.197217 −0.0986083 0.995126i \(-0.531439\pi\)
−0.0986083 + 0.995126i \(0.531439\pi\)
\(660\) 0 0
\(661\) −34.5830 −1.34512 −0.672562 0.740041i \(-0.734806\pi\)
−0.672562 + 0.740041i \(0.734806\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.64575 −0.141376
\(666\) 0 0
\(667\) −33.8745 −1.31163
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.41699 −0.209121
\(672\) 0 0
\(673\) −22.4575 −0.865674 −0.432837 0.901472i \(-0.642487\pi\)
−0.432837 + 0.901472i \(0.642487\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.4575 1.17058 0.585289 0.810825i \(-0.300981\pi\)
0.585289 + 0.810825i \(0.300981\pi\)
\(678\) 0 0
\(679\) 16.5830 0.636397
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24.1033 −0.922286 −0.461143 0.887326i \(-0.652560\pi\)
−0.461143 + 0.887326i \(0.652560\pi\)
\(684\) 0 0
\(685\) 82.3320 3.14574
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −35.7490 −1.36193
\(690\) 0 0
\(691\) −47.2915 −1.79905 −0.899527 0.436866i \(-0.856089\pi\)
−0.899527 + 0.436866i \(0.856089\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.58301 0.0979790
\(696\) 0 0
\(697\) 3.04052 0.115168
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −17.1660 −0.648351 −0.324176 0.945997i \(-0.605087\pi\)
−0.324176 + 0.945997i \(0.605087\pi\)
\(702\) 0 0
\(703\) 5.29150 0.199573
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.35425 −0.163758
\(708\) 0 0
\(709\) −43.0405 −1.61642 −0.808210 0.588894i \(-0.799564\pi\)
−0.808210 + 0.588894i \(0.799564\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.74902 0.290203
\(714\) 0 0
\(715\) −29.1660 −1.09075
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −40.9373 −1.52670 −0.763351 0.645984i \(-0.776447\pi\)
−0.763351 + 0.645984i \(0.776447\pi\)
\(720\) 0 0
\(721\) −2.58301 −0.0961961
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −46.8118 −1.73855
\(726\) 0 0
\(727\) −10.1255 −0.375534 −0.187767 0.982214i \(-0.560125\pi\)
−0.187767 + 0.982214i \(0.560125\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.708497 −0.0262047
\(732\) 0 0
\(733\) −19.8745 −0.734082 −0.367041 0.930205i \(-0.619629\pi\)
−0.367041 + 0.930205i \(0.619629\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −29.1660 −1.07434
\(738\) 0 0
\(739\) 26.0000 0.956425 0.478213 0.878244i \(-0.341285\pi\)
0.478213 + 0.878244i \(0.341285\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 28.3542 1.04022 0.520108 0.854100i \(-0.325892\pi\)
0.520108 + 0.854100i \(0.325892\pi\)
\(744\) 0 0
\(745\) 55.7490 2.04249
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.64575 −0.133213
\(750\) 0 0
\(751\) −8.45751 −0.308619 −0.154310 0.988023i \(-0.549315\pi\)
−0.154310 + 0.988023i \(0.549315\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −70.3320 −2.55964
\(756\) 0 0
\(757\) 32.3320 1.17513 0.587564 0.809178i \(-0.300087\pi\)
0.587564 + 0.809178i \(0.300087\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13.0627 −0.473524 −0.236762 0.971568i \(-0.576086\pi\)
−0.236762 + 0.971568i \(0.576086\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 58.3320 2.10625
\(768\) 0 0
\(769\) 30.4575 1.09833 0.549163 0.835715i \(-0.314947\pi\)
0.549163 + 0.835715i \(0.314947\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.58301 0.308709 0.154355 0.988016i \(-0.450670\pi\)
0.154355 + 0.988016i \(0.450670\pi\)
\(774\) 0 0
\(775\) 10.7085 0.384661
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.58301 0.307518
\(780\) 0 0
\(781\) 0.708497 0.0253520
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −43.2915 −1.54514
\(786\) 0 0
\(787\) 34.4575 1.22828 0.614139 0.789198i \(-0.289503\pi\)
0.614139 + 0.789198i \(0.289503\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 16.9373 0.602219
\(792\) 0 0
\(793\) −10.8340 −0.384726
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4.83399 0.171229 0.0856143 0.996328i \(-0.472715\pi\)
0.0856143 + 0.996328i \(0.472715\pi\)
\(798\) 0 0
\(799\) −0.833990 −0.0295044
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 18.5830 0.655780
\(804\) 0 0
\(805\) −21.8745 −0.770975
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 39.7490 1.39750 0.698750 0.715365i \(-0.253740\pi\)
0.698750 + 0.715365i \(0.253740\pi\)
\(810\) 0 0
\(811\) 50.3320 1.76740 0.883698 0.468057i \(-0.155046\pi\)
0.883698 + 0.468057i \(0.155046\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 45.8745 1.60691
\(816\) 0 0
\(817\) −2.00000 −0.0699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.29150 −0.114874 −0.0574371 0.998349i \(-0.518293\pi\)
−0.0574371 + 0.998349i \(0.518293\pi\)
\(822\) 0 0
\(823\) −4.58301 −0.159754 −0.0798768 0.996805i \(-0.525453\pi\)
−0.0798768 + 0.996805i \(0.525453\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 38.2288 1.32934 0.664672 0.747135i \(-0.268571\pi\)
0.664672 + 0.747135i \(0.268571\pi\)
\(828\) 0 0
\(829\) −7.16601 −0.248886 −0.124443 0.992227i \(-0.539714\pi\)
−0.124443 + 0.992227i \(0.539714\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.354249 0.0122740
\(834\) 0 0
\(835\) 55.7490 1.92927
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.41699 0.325111 0.162555 0.986699i \(-0.448026\pi\)
0.162555 + 0.986699i \(0.448026\pi\)
\(840\) 0 0
\(841\) 2.87451 0.0991210
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10.9373 −0.376253
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 31.7490 1.08834
\(852\) 0 0
\(853\) −31.4170 −1.07570 −0.537849 0.843041i \(-0.680763\pi\)
−0.537849 + 0.843041i \(0.680763\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −49.7490 −1.69939 −0.849697 0.527271i \(-0.823215\pi\)
−0.849697 + 0.527271i \(0.823215\pi\)
\(858\) 0 0
\(859\) −17.4170 −0.594260 −0.297130 0.954837i \(-0.596030\pi\)
−0.297130 + 0.954837i \(0.596030\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.2288 0.348191 0.174095 0.984729i \(-0.444300\pi\)
0.174095 + 0.984729i \(0.444300\pi\)
\(864\) 0 0
\(865\) 51.0405 1.73543
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −22.5830 −0.766076
\(870\) 0 0
\(871\) −58.3320 −1.97651
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −12.0000 −0.405674
\(876\) 0 0
\(877\) 12.5830 0.424898 0.212449 0.977172i \(-0.431856\pi\)
0.212449 + 0.977172i \(0.431856\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 14.4797 0.487835 0.243917 0.969796i \(-0.421567\pi\)
0.243917 + 0.969796i \(0.421567\pi\)
\(882\) 0 0
\(883\) 41.1660 1.38535 0.692673 0.721252i \(-0.256433\pi\)
0.692673 + 0.721252i \(0.256433\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6.12549 −0.205674 −0.102837 0.994698i \(-0.532792\pi\)
−0.102837 + 0.994698i \(0.532792\pi\)
\(888\) 0 0
\(889\) −4.00000 −0.134156
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.35425 −0.0787819
\(894\) 0 0
\(895\) 93.0405 3.11000
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.29150 −0.243185
\(900\) 0 0
\(901\) 3.16601 0.105475
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −60.4575 −2.00968
\(906\) 0 0
\(907\) −25.1660 −0.835624 −0.417812 0.908534i \(-0.637203\pi\)
−0.417812 + 0.908534i \(0.637203\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 18.9373 0.627419 0.313710 0.949519i \(-0.398428\pi\)
0.313710 + 0.949519i \(0.398428\pi\)
\(912\) 0 0
\(913\) 33.8745 1.12108
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 16.9373 0.559317
\(918\) 0 0
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.41699 0.0466410
\(924\) 0 0
\(925\) 43.8745 1.44258
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −27.6458 −0.907028 −0.453514 0.891249i \(-0.649830\pi\)
−0.453514 + 0.891249i \(0.649830\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.58301 0.0844733
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.29150 −0.172498 −0.0862490 0.996274i \(-0.527488\pi\)
−0.0862490 + 0.996274i \(0.527488\pi\)
\(942\) 0 0
\(943\) 51.4980 1.67701
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.00000 0.194974 0.0974869 0.995237i \(-0.468920\pi\)
0.0974869 + 0.995237i \(0.468920\pi\)
\(948\) 0 0
\(949\) 37.1660 1.20646
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.5203 0.632323 0.316162 0.948705i \(-0.397606\pi\)
0.316162 + 0.948705i \(0.397606\pi\)
\(954\) 0 0
\(955\) 21.8745 0.707842
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −22.5830 −0.729243
\(960\) 0 0
\(961\) −29.3320 −0.946194
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 92.2065 2.96823
\(966\) 0 0
\(967\) 0.833990 0.0268193 0.0134096 0.999910i \(-0.495731\pi\)
0.0134096 + 0.999910i \(0.495731\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 5.41699 0.173840 0.0869198 0.996215i \(-0.472298\pi\)
0.0869198 + 0.996215i \(0.472298\pi\)
\(972\) 0 0
\(973\) −0.708497 −0.0227134
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −9.39477 −0.300565 −0.150283 0.988643i \(-0.548018\pi\)
−0.150283 + 0.988643i \(0.548018\pi\)
\(978\) 0 0
\(979\) 12.0000 0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 42.5830 1.35819 0.679093 0.734052i \(-0.262373\pi\)
0.679093 + 0.734052i \(0.262373\pi\)
\(984\) 0 0
\(985\) −19.7490 −0.629256
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.16601 −0.163774
\(996\) 0 0
\(997\) −23.8745 −0.756113 −0.378057 0.925782i \(-0.623408\pi\)
−0.378057 + 0.925782i \(0.623408\pi\)
\(998\) 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 9576.2.a.bh.1.1 2
3.2 odd 2 9576.2.a.bu.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bh.1.1 2 1.1 even 1 trivial
9576.2.a.bu.1.2 yes 2 3.2 odd 2