Properties

Label 297.2.g.a.197.2
Level $297$
Weight $2$
Character 297.197
Analytic conductor $2.372$
Analytic rank $0$
Dimension $4$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(98,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.98");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.g (of order \(6\), degree \(2\), not minimal)

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: no
Analytic conductor: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label 197.2
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 297.197
Dual form 297.2.g.a.98.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{4} +(3.68614 - 2.12819i) q^{5} +(-2.87228 - 1.65831i) q^{11} +(-2.00000 + 3.46410i) q^{16} +(7.37228 + 4.25639i) q^{20} +(-2.87228 + 1.65831i) q^{23} +(6.55842 - 11.3595i) q^{25} +(5.55842 + 9.62747i) q^{31} -5.11684 q^{37} -6.63325i q^{44} +(-6.12772 - 3.53784i) q^{47} +(-3.50000 - 6.06218i) q^{49} +1.43710i q^{53} -14.1168 q^{55} +(-9.81386 + 5.66603i) q^{59} -8.00000 q^{64} +(1.05842 + 1.83324i) q^{67} -5.69349i q^{71} +17.0256i q^{80} +16.5831i q^{89} +(-5.74456 - 3.31662i) q^{92} +(8.55842 - 14.8236i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} + 9 q^{5} - 8 q^{16} + 18 q^{20} + 9 q^{25} + 5 q^{31} + 14 q^{37} - 36 q^{47} - 14 q^{49} - 22 q^{55} - 45 q^{59} - 32 q^{64} - 13 q^{67} + 17 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 3.68614 2.12819i 1.64849 0.951757i 0.670820 0.741620i \(-0.265942\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.87228 1.65831i −0.866025 0.500000i
\(12\) 0 0
\(13\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 7.37228 + 4.25639i 1.64849 + 0.951757i
\(21\) 0 0
\(22\) 0 0
\(23\) −2.87228 + 1.65831i −0.598912 + 0.345782i −0.768613 0.639713i \(-0.779053\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 0 0
\(25\) 6.55842 11.3595i 1.31168 2.27190i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 5.55842 + 9.62747i 0.998322 + 1.72914i 0.549309 + 0.835619i \(0.314891\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.11684 −0.841204 −0.420602 0.907245i \(-0.638181\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 6.63325i 1.00000i
\(45\) 0 0
\(46\) 0 0
\(47\) −6.12772 3.53784i −0.893820 0.516047i −0.0186297 0.999826i \(-0.505930\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.43710i 0.197400i 0.995117 + 0.0987002i \(0.0314685\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) −14.1168 −1.90351
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.81386 + 5.66603i −1.27766 + 0.737655i −0.976417 0.215894i \(-0.930733\pi\)
−0.301239 + 0.953549i \(0.597400\pi\)
\(60\) 0 0
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.05842 + 1.83324i 0.129307 + 0.223966i 0.923408 0.383819i \(-0.125391\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.69349i 0.675692i −0.941201 0.337846i \(-0.890302\pi\)
0.941201 0.337846i \(-0.109698\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 17.0256i 1.90351i
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.5831i 1.75781i 0.476999 + 0.878904i \(0.341725\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.74456 3.31662i −0.598912 0.345782i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.55842 14.8236i 0.868976 1.50511i 0.00593185 0.999982i \(-0.498112\pi\)
0.863044 0.505128i \(-0.168555\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 26.2337 2.62337
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −9.61684 16.6569i −0.947576 1.64125i −0.750510 0.660859i \(-0.770192\pi\)
−0.197066 0.980390i \(-0.563141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.1861 9.92242i 1.61674 0.933423i 0.628979 0.777422i \(-0.283473\pi\)
0.987757 0.156001i \(-0.0498603\pi\)
\(114\) 0 0
\(115\) −7.05842 + 12.2255i −0.658201 + 1.14004i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) −11.1168 + 19.2549i −0.998322 + 1.72914i
\(125\) 34.5484i 3.09011i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.3030 7.10313i −1.05111 0.606861i −0.128154 0.991754i \(-0.540905\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 0 0
\(139\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −5.11684 8.86263i −0.420602 0.728504i
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 40.9783 + 23.6588i 3.29145 + 1.90032i
\(156\) 0 0
\(157\) 10.0584 + 17.4217i 0.802749 + 1.39040i 0.917800 + 0.397043i \(0.129964\pi\)
−0.115050 + 0.993360i \(0.536703\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 25.2337 1.97645 0.988227 0.152992i \(-0.0488907\pi\)
0.988227 + 0.152992i \(0.0488907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) −6.50000 + 11.2583i −0.500000 + 0.866025i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 11.4891 6.63325i 0.866025 0.500000i
\(177\) 0 0
\(178\) 0 0
\(179\) 9.89497i 0.739585i 0.929114 + 0.369792i \(0.120571\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 3.88316 0.288633 0.144316 0.989532i \(-0.453902\pi\)
0.144316 + 0.989532i \(0.453902\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −18.8614 + 10.8896i −1.38672 + 0.800622i
\(186\) 0 0
\(187\) 0 0
\(188\) 14.1514i 1.03209i
\(189\) 0 0
\(190\) 0 0
\(191\) 1.19702 + 0.691097i 0.0866130 + 0.0500060i 0.542681 0.839939i \(-0.317409\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(192\) 0 0
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 7.00000 12.1244i 0.500000 0.866025i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 7.23369 0.512783 0.256391 0.966573i \(-0.417466\pi\)
0.256391 + 0.966573i \(0.417466\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −2.48913 + 1.43710i −0.170954 + 0.0987002i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −14.1168 24.4511i −0.951757 1.64849i
\(221\) 0 0
\(222\) 0 0
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) −2.50000 4.33013i −0.165205 0.286143i 0.771523 0.636201i \(-0.219495\pi\)
−0.936728 + 0.350058i \(0.886162\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) −30.1168 −1.96461
\(236\) −19.6277 11.3321i −1.27766 0.737655i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −25.8030 14.8974i −1.64849 0.951757i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5831i 1.04672i 0.852112 + 0.523359i \(0.175321\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) 11.0000 0.691564
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 22.9783 13.2665i 1.43334 0.827541i 0.435970 0.899961i \(-0.356405\pi\)
0.997374 + 0.0724199i \(0.0230722\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 3.05842 + 5.29734i 0.187877 + 0.325413i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.11684 + 3.66648i −0.129307 + 0.223966i
\(269\) 32.6140i 1.98851i 0.107031 + 0.994256i \(0.465866\pi\)
−0.107031 + 0.994256i \(0.534134\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −37.6753 + 21.7518i −2.27190 + 1.31168i
\(276\) 0 0
\(277\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(282\) 0 0
\(283\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(284\) 9.86141 5.69349i 0.585167 0.337846i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) −24.1168 + 41.7716i −1.40414 + 2.43204i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 23.3614 13.4877i 1.32470 0.764818i 0.340229 0.940343i \(-0.389495\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.1060 + 11.6082i 1.12926 + 0.651981i 0.943750 0.330661i \(-0.107272\pi\)
0.185514 + 0.982642i \(0.440605\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −29.4891 + 17.0256i −1.64849 + 0.951757i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.0584 22.6179i 0.717756 1.24319i −0.244131 0.969742i \(-0.578503\pi\)
0.961887 0.273447i \(-0.0881639\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.80298 + 4.50506i 0.426323 + 0.246137i
\(336\) 0 0
\(337\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.8704i 1.99664i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −31.5951 18.2414i −1.68164 0.970894i −0.960574 0.278024i \(-0.910320\pi\)
−0.721063 0.692869i \(-0.756346\pi\)
\(354\) 0 0
\(355\) −12.1168 20.9870i −0.643095 1.11387i
\(356\) −28.7228 + 16.5831i −1.52231 + 0.878904i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.94158 + 8.55906i −0.257948 + 0.446780i −0.965692 0.259690i \(-0.916380\pi\)
0.707744 + 0.706469i \(0.249713\pi\)
\(368\) 13.2665i 0.691564i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.6861 17.7167i 1.56799 0.905279i 0.571585 0.820543i \(-0.306329\pi\)
0.996403 0.0847358i \(-0.0270046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 34.2337 1.73795
\(389\) 27.0475 + 15.6159i 1.37137 + 0.791758i 0.991100 0.133120i \(-0.0424994\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −35.4674 −1.78006 −0.890028 0.455905i \(-0.849316\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 26.2337 + 45.4381i 1.31168 + 2.27190i
\(401\) 11.0109 6.35713i 0.549857 0.317460i −0.199207 0.979957i \(-0.563837\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14.6970 + 8.48533i 0.728504 + 0.420602i
\(408\) 0 0
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 19.2337 33.3137i 0.947576 1.64125i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.63859 + 2.10074i −0.177757 + 0.102628i −0.586238 0.810139i \(-0.699392\pi\)
0.408481 + 0.912767i \(0.366058\pi\)
\(420\) 0 0
\(421\) 14.7337 25.5195i 0.718076 1.24374i −0.243685 0.969854i \(-0.578356\pi\)
0.961761 0.273890i \(-0.0883103\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.0475473 + 0.0274514i 0.00225904 + 0.00130426i 0.501129 0.865373i \(-0.332918\pi\)
−0.498870 + 0.866677i \(0.666252\pi\)
\(444\) 0 0
\(445\) 35.2921 + 61.1277i 1.67301 + 2.89773i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 25.4834i 1.20264i 0.799009 + 0.601319i \(0.205358\pi\)
−0.799009 + 0.601319i \(0.794642\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 34.3723 + 19.8448i 1.61674 + 0.933423i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −28.2337 −1.31640
\(461\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0 0
\(463\) 15.5000 + 26.8468i 0.720346 + 1.24768i 0.960861 + 0.277031i \(0.0893503\pi\)
−0.240515 + 0.970645i \(0.577316\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 24.1561i 1.11781i 0.829231 + 0.558906i \(0.188779\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −11.0000 + 19.0526i −0.500000 + 0.866025i
\(485\) 72.8559i 3.30822i
\(486\) 0 0
\(487\) 12.8832 0.583792 0.291896 0.956450i \(-0.405714\pi\)
0.291896 + 0.956450i \(0.405714\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −44.4674 −1.99664
\(497\) 0 0
\(498\) 0 0
\(499\) −18.6168 32.2453i −0.833404 1.44350i −0.895323 0.445418i \(-0.853055\pi\)
0.0619186 0.998081i \(-0.480278\pi\)
\(500\) 59.8397 34.5484i 2.67611 1.54505i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.87228 + 1.65831i −0.127312 + 0.0735034i −0.562303 0.826931i \(-0.690085\pi\)
0.434992 + 0.900434i \(0.356751\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −70.8981 40.9330i −3.12414 1.80372i
\(516\) 0 0
\(517\) 11.7337 + 20.3233i 0.516047 + 0.893820i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.56768i 0.375357i 0.982231 + 0.187678i \(0.0600963\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.00000 + 10.3923i −0.260870 + 0.451839i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 23.2164i 1.00000i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 28.4125i 1.21372i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 0 0
\(565\) 42.2337 73.1509i 1.77678 3.07748i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 43.5036i 1.81423i
\(576\) 0 0
\(577\) −32.1168 −1.33704 −0.668521 0.743693i \(-0.733072\pi\)
−0.668521 + 0.743693i \(0.733072\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.38316 4.12775i 0.0987002 0.170954i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −33.1277 19.1263i −1.36733 0.789427i −0.376741 0.926319i \(-0.622955\pi\)
−0.990586 + 0.136892i \(0.956289\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 10.2337 17.7253i 0.420602 0.728504i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −28.7228 + 16.5831i −1.17358 + 0.677568i −0.954521 0.298143i \(-0.903633\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 0 0
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 40.5475 + 23.4101i 1.64849 + 0.951757i
\(606\) 0 0
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.9891 + 24.8198i −1.73068 + 0.999207i −0.845428 + 0.534089i \(0.820655\pi\)
−0.885249 + 0.465118i \(0.846012\pi\)
\(618\) 0 0
\(619\) −21.7921 + 37.7450i −0.875899 + 1.51710i −0.0200967 + 0.999798i \(0.506397\pi\)
−0.855802 + 0.517303i \(0.826936\pi\)
\(620\) 94.6352i 3.80064i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −40.7337 70.5528i −1.62935 2.82211i
\(626\) 0 0
\(627\) 0 0
\(628\) −20.1168 + 34.8434i −0.802749 + 1.39040i
\(629\) 0 0
\(630\) 0 0
\(631\) 46.5842 1.85449 0.927244 0.374457i \(-0.122171\pi\)
0.927244 + 0.374457i \(0.122171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.1060 + 11.6082i 0.794138 + 0.458496i 0.841417 0.540386i \(-0.181722\pi\)
−0.0472793 + 0.998882i \(0.515055\pi\)
\(642\) 0 0
\(643\) −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 43.1161i 1.69507i −0.530740 0.847535i \(-0.678086\pi\)
0.530740 0.847535i \(-0.321914\pi\)
\(648\) 0 0
\(649\) 37.5842 1.47531
\(650\) 0 0
\(651\) 0 0
\(652\) 25.2337 + 43.7060i 0.988227 + 1.71166i
\(653\) −36.8139 + 21.2545i −1.44064 + 0.831753i −0.997892 0.0648948i \(-0.979329\pi\)
−0.442746 + 0.896647i \(0.645995\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) −24.7921 42.9412i −0.964301 1.67022i −0.711481 0.702706i \(-0.751975\pi\)
−0.252821 0.967513i \(-0.581358\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −26.0000 −1.00000
\(677\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.0010i 1.68365i −0.539750 0.841825i \(-0.681481\pi\)
0.539750 0.841825i \(-0.318519\pi\)
\(684\) 0 0
\(685\) −60.4674 −2.31034
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −17.2921 + 29.9508i −0.657823 + 1.13938i 0.323355 + 0.946278i \(0.395189\pi\)
−0.981178 + 0.193105i \(0.938144\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 22.9783 + 13.2665i 0.866025 + 0.500000i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −26.2921 + 45.5393i −0.987421 + 1.71026i −0.356780 + 0.934188i \(0.616125\pi\)
−0.630641 + 0.776075i \(0.717208\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31.9307 18.4352i −1.19581 0.690404i
\(714\) 0 0
\(715\) 0 0
\(716\) −17.1386 + 9.89497i −0.640499 + 0.369792i
\(717\) 0 0
\(718\) 0 0
\(719\) 52.4589i 1.95639i −0.207700 0.978193i \(-0.566598\pi\)
0.207700 0.978193i \(-0.433402\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 3.88316 + 6.72582i 0.144316 + 0.249963i
\(725\) 0 0
\(726\) 0 0
\(727\) 17.5584 30.4121i 0.651206 1.12792i −0.331625 0.943411i \(-0.607597\pi\)
0.982831 0.184510i \(-0.0590699\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.02078i 0.258614i
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −37.7228 21.7793i −1.38672 0.800622i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −15.7921 27.3527i −0.576262 0.998116i −0.995903 0.0904254i \(-0.971177\pi\)
0.419641 0.907690i \(-0.362156\pi\)
\(752\) 24.5109 14.1514i 0.893820 0.516047i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −53.4674 −1.94330 −0.971652 0.236414i \(-0.924028\pi\)
−0.971652 + 0.236414i \(0.924028\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.76439i 0.100012i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.2665i 0.477163i −0.971123 0.238581i \(-0.923318\pi\)
0.971123 0.238581i \(-0.0766824\pi\)
\(774\) 0 0
\(775\) 145.818 5.23793
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −9.44158 + 16.3533i −0.337846 + 0.585167i
\(782\) 0 0
\(783\) 0 0
\(784\) 28.0000 1.00000
\(785\) 74.1535 + 42.8126i 2.64665 + 1.52805i
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 7.23369 + 12.5291i 0.256391 + 0.444083i
\(797\) −22.1644 + 12.7966i −0.785103 + 0.453279i −0.838236 0.545308i \(-0.816413\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 93.0149 53.7022i 3.25817 1.88111i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(822\) 0 0
\(823\) 24.5000 + 42.4352i 0.854016 + 1.47920i 0.877555 + 0.479477i \(0.159174\pi\)
−0.0235383 + 0.999723i \(0.507493\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 28.5842 0.992771 0.496385 0.868102i \(-0.334660\pi\)
0.496385 + 0.868102i \(0.334660\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −31.5951 18.2414i −1.09078 0.629764i −0.156999 0.987599i \(-0.550182\pi\)
−0.933785 + 0.357834i \(0.883515\pi\)
\(840\) 0 0
\(841\) 14.5000 + 25.1147i 0.500000 + 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 55.3331i 1.90351i
\(846\) 0 0
\(847\) 0 0
\(848\) −4.97825 2.87419i −0.170954 0.0987002i
\(849\) 0 0
\(850\) 0 0
\(851\) 14.6970 8.48533i 0.503807 0.290873i
\(852\) 0 0
\(853\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(858\) 0 0
\(859\) −29.2921 50.7354i −0.999434 1.73107i −0.528853 0.848713i \(-0.677378\pi\)
−0.470581 0.882357i \(-0.655956\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 46.4327i 1.58059i 0.612727 + 0.790295i \(0.290072\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 28.2337 48.9022i 0.951757 1.64849i
\(881\) 41.0719i 1.38375i 0.722019 + 0.691873i \(0.243214\pi\)
−0.722019 + 0.691873i \(0.756786\pi\)
\(882\) 0 0
\(883\) −10.7663 −0.362315 −0.181158 0.983454i \(-0.557984\pi\)
−0.181158 + 0.983454i \(0.557984\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 2.00000 0.0669650
\(893\) 0 0
\(894\) 0 0
\(895\) 21.0584 + 36.4743i 0.703905 + 1.21920i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.3139 8.26411i 0.475809 0.274708i
\(906\) 0 0
\(907\) −4.00000 + 6.92820i −0.132818 + 0.230047i −0.924762 0.380547i \(-0.875736\pi\)
0.791944 + 0.610594i \(0.209069\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 47.8723 + 27.6391i 1.58608 + 0.915723i 0.993944 + 0.109885i \(0.0350482\pi\)
0.592135 + 0.805839i \(0.298285\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 5.00000 8.66025i 0.165205 0.286143i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −33.5584 + 58.1249i −1.10339 + 1.91113i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −45.4783 26.2569i −1.49209 0.861460i −0.492134 0.870519i \(-0.663783\pi\)
−0.999959 + 0.00905914i \(0.997116\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −30.1168 52.1639i −0.982303 1.70140i
\(941\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 45.3283i 1.47531i
\(945\) 0 0
\(946\) 0 0
\(947\) −52.8030 30.4858i −1.71587 0.990656i −0.926126 0.377215i \(-0.876882\pi\)
−0.789741 0.613441i \(-0.789785\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 5.88316 0.190374
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −46.2921 + 80.1803i −1.49329 + 2.58646i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 43.1161i 1.38366i −0.722059 0.691831i \(-0.756804\pi\)
0.722059 0.691831i \(-0.243196\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 48.8288 28.1913i 1.56217 0.901920i 0.565134 0.824999i \(-0.308824\pi\)
0.997037 0.0769208i \(-0.0245089\pi\)
\(978\) 0 0
\(979\) 27.5000 47.6314i 0.878904 1.52231i
\(980\) 59.5894i 1.90351i
\(981\) 0 0
\(982\) 0 0
\(983\) 54.0475 + 31.2044i 1.72385 + 0.995265i 0.910525 + 0.413453i \(0.135677\pi\)
0.813324 + 0.581811i \(0.197656\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 26.6644 15.3947i 0.845318 0.488045i
\(996\) 0 0
\(997\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 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 297.2.g.a.197.2 4
3.2 odd 2 99.2.g.a.65.1 yes 4
9.2 odd 6 891.2.d.a.890.1 4
9.4 even 3 99.2.g.a.32.1 4
9.5 odd 6 inner 297.2.g.a.98.2 4
9.7 even 3 891.2.d.a.890.4 4
11.10 odd 2 CM 297.2.g.a.197.2 4
33.32 even 2 99.2.g.a.65.1 yes 4
99.32 even 6 inner 297.2.g.a.98.2 4
99.43 odd 6 891.2.d.a.890.4 4
99.65 even 6 891.2.d.a.890.1 4
99.76 odd 6 99.2.g.a.32.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.g.a.32.1 4 9.4 even 3
99.2.g.a.32.1 4 99.76 odd 6
99.2.g.a.65.1 yes 4 3.2 odd 2
99.2.g.a.65.1 yes 4 33.32 even 2
297.2.g.a.98.2 4 9.5 odd 6 inner
297.2.g.a.98.2 4 99.32 even 6 inner
297.2.g.a.197.2 4 1.1 even 1 trivial
297.2.g.a.197.2 4 11.10 odd 2 CM
891.2.d.a.890.1 4 9.2 odd 6
891.2.d.a.890.1 4 99.65 even 6
891.2.d.a.890.4 4 9.7 even 3
891.2.d.a.890.4 4 99.43 odd 6