Properties

Label 184.2.a.d.1.1
Level $184$
Weight $2$
Character 184.1
Self dual yes
Analytic conductor $1.469$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [184,2,Mod(1,184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(184, 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("184.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.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: \(1.46924739719\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 184.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -2.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} -2.00000 q^{7} +6.00000 q^{9} -5.00000 q^{13} -6.00000 q^{17} +6.00000 q^{19} -6.00000 q^{21} +1.00000 q^{23} -5.00000 q^{25} +9.00000 q^{27} +9.00000 q^{29} +3.00000 q^{31} -8.00000 q^{37} -15.0000 q^{39} +3.00000 q^{41} -8.00000 q^{43} +7.00000 q^{47} -3.00000 q^{49} -18.0000 q^{51} -2.00000 q^{53} +18.0000 q^{57} +4.00000 q^{59} -10.0000 q^{61} -12.0000 q^{63} +8.00000 q^{67} +3.00000 q^{69} +7.00000 q^{71} +9.00000 q^{73} -15.0000 q^{75} -6.00000 q^{79} +9.00000 q^{81} -14.0000 q^{83} +27.0000 q^{87} +16.0000 q^{89} +10.0000 q^{91} +9.00000 q^{93} +6.00000 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) −6.00000 −1.30931
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) −15.0000 −2.40192
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.00000 1.02105 0.510527 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −18.0000 −2.52050
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 18.0000 2.38416
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −12.0000 −1.51186
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 0 0
\(75\) −15.0000 −1.73205
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 27.0000 2.89470
\(88\) 0 0
\(89\) 16.0000 1.69600 0.847998 0.529999i \(-0.177808\pi\)
0.847998 + 0.529999i \(0.177808\pi\)
\(90\) 0 0
\(91\) 10.0000 1.04828
\(92\) 0 0
\(93\) 9.00000 0.933257
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.0000 1.35343 0.676716 0.736245i \(-0.263403\pi\)
0.676716 + 0.736245i \(0.263403\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −24.0000 −2.27798
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −30.0000 −2.77350
\(118\) 0 0
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 9.00000 0.811503
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0 0
\(129\) −24.0000 −2.11308
\(130\) 0 0
\(131\) −9.00000 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.00000 0.341743 0.170872 0.985293i \(-0.445342\pi\)
0.170872 + 0.985293i \(0.445342\pi\)
\(138\) 0 0
\(139\) −23.0000 −1.95083 −0.975417 0.220366i \(-0.929275\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 21.0000 1.76852
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −9.00000 −0.742307
\(148\) 0 0
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 7.00000 0.569652 0.284826 0.958579i \(-0.408064\pi\)
0.284826 + 0.958579i \(0.408064\pi\)
\(152\) 0 0
\(153\) −36.0000 −2.91043
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) −2.00000 −0.157622
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.00000 0.309529 0.154765 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 36.0000 2.75299
\(172\) 0 0
\(173\) −10.0000 −0.760286 −0.380143 0.924928i \(-0.624125\pi\)
−0.380143 + 0.924928i \(0.624125\pi\)
\(174\) 0 0
\(175\) 10.0000 0.755929
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −30.0000 −2.21766
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −18.0000 −1.30931
\(190\) 0 0
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −27.0000 −1.92367 −0.961835 0.273629i \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 24.0000 1.69283
\(202\) 0 0
\(203\) −18.0000 −1.26335
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 21.0000 1.43890
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 0 0
\(219\) 27.0000 1.82449
\(220\) 0 0
\(221\) 30.0000 2.01802
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) −30.0000 −2.00000
\(226\) 0 0
\(227\) −10.0000 −0.663723 −0.331862 0.943328i \(-0.607677\pi\)
−0.331862 + 0.943328i \(0.607677\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −18.0000 −1.16923
\(238\) 0 0
\(239\) −13.0000 −0.840900 −0.420450 0.907316i \(-0.638128\pi\)
−0.420450 + 0.907316i \(0.638128\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −30.0000 −1.90885
\(248\) 0 0
\(249\) −42.0000 −2.66164
\(250\) 0 0
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.0000 −0.810918 −0.405459 0.914113i \(-0.632888\pi\)
−0.405459 + 0.914113i \(0.632888\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) 54.0000 3.34252
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 48.0000 2.93755
\(268\) 0 0
\(269\) 5.00000 0.304855 0.152428 0.988315i \(-0.451291\pi\)
0.152428 + 0.988315i \(0.451291\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 30.0000 1.81568
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −23.0000 −1.38194 −0.690968 0.722885i \(-0.742815\pi\)
−0.690968 + 0.722885i \(0.742815\pi\)
\(278\) 0 0
\(279\) 18.0000 1.07763
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 18.0000 1.05518
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.00000 −0.289157
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 0 0
\(303\) 18.0000 1.03407
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 42.0000 2.38930
\(310\) 0 0
\(311\) −17.0000 −0.963982 −0.481991 0.876176i \(-0.660086\pi\)
−0.481991 + 0.876176i \(0.660086\pi\)
\(312\) 0 0
\(313\) −20.0000 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 42.0000 2.34421
\(322\) 0 0
\(323\) −36.0000 −2.00309
\(324\) 0 0
\(325\) 25.0000 1.38675
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.0000 −0.771845
\(330\) 0 0
\(331\) −19.0000 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) 0 0
\(333\) −48.0000 −2.63038
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) −7.00000 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 0 0
\(351\) −45.0000 −2.40192
\(352\) 0 0
\(353\) −11.0000 −0.585471 −0.292735 0.956193i \(-0.594566\pi\)
−0.292735 + 0.956193i \(0.594566\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 36.0000 1.90532
\(358\) 0 0
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) −33.0000 −1.73205
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −45.0000 −2.31762
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 15.0000 0.768473
\(382\) 0 0
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −48.0000 −2.43998
\(388\) 0 0
\(389\) −4.00000 −0.202808 −0.101404 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) 0 0
\(393\) −27.0000 −1.36197
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 31.0000 1.55585 0.777923 0.628360i \(-0.216273\pi\)
0.777923 + 0.628360i \(0.216273\pi\)
\(398\) 0 0
\(399\) −36.0000 −1.80225
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) −15.0000 −0.747203
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 25.0000 1.23617 0.618085 0.786111i \(-0.287909\pi\)
0.618085 + 0.786111i \(0.287909\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 0 0
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −69.0000 −3.37894
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 42.0000 2.04211
\(424\) 0 0
\(425\) 30.0000 1.45521
\(426\) 0 0
\(427\) 20.0000 0.967868
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000 0.287019
\(438\) 0 0
\(439\) 5.00000 0.238637 0.119318 0.992856i \(-0.461929\pi\)
0.119318 + 0.992856i \(0.461929\pi\)
\(440\) 0 0
\(441\) −18.0000 −0.857143
\(442\) 0 0
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 42.0000 1.98653
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 21.0000 0.986666
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 0 0
\(459\) −54.0000 −2.52050
\(460\) 0 0
\(461\) 1.00000 0.0465746 0.0232873 0.999729i \(-0.492587\pi\)
0.0232873 + 0.999729i \(0.492587\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 36.0000 1.65879
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −30.0000 −1.37649
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) 38.0000 1.73626 0.868132 0.496333i \(-0.165321\pi\)
0.868132 + 0.496333i \(0.165321\pi\)
\(480\) 0 0
\(481\) 40.0000 1.82384
\(482\) 0 0
\(483\) −6.00000 −0.273009
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 17.0000 0.770344 0.385172 0.922845i \(-0.374142\pi\)
0.385172 + 0.922845i \(0.374142\pi\)
\(488\) 0 0
\(489\) −33.0000 −1.49231
\(490\) 0 0
\(491\) −7.00000 −0.315906 −0.157953 0.987447i \(-0.550489\pi\)
−0.157953 + 0.987447i \(0.550489\pi\)
\(492\) 0 0
\(493\) −54.0000 −2.43204
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.0000 −0.627986
\(498\) 0 0
\(499\) −1.00000 −0.0447661 −0.0223831 0.999749i \(-0.507125\pi\)
−0.0223831 + 0.999749i \(0.507125\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) 10.0000 0.445878 0.222939 0.974832i \(-0.428435\pi\)
0.222939 + 0.974832i \(0.428435\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 36.0000 1.59882
\(508\) 0 0
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) −18.0000 −0.796273
\(512\) 0 0
\(513\) 54.0000 2.38416
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −30.0000 −1.31685
\(520\) 0 0
\(521\) 8.00000 0.350486 0.175243 0.984525i \(-0.443929\pi\)
0.175243 + 0.984525i \(0.443929\pi\)
\(522\) 0 0
\(523\) 18.0000 0.787085 0.393543 0.919306i \(-0.371249\pi\)
0.393543 + 0.919306i \(0.371249\pi\)
\(524\) 0 0
\(525\) 30.0000 1.30931
\(526\) 0 0
\(527\) −18.0000 −0.784092
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 24.0000 1.04151
\(532\) 0 0
\(533\) −15.0000 −0.649722
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.00000 −0.388379
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −43.0000 −1.84871 −0.924357 0.381528i \(-0.875398\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) 0 0
\(549\) −60.0000 −2.56074
\(550\) 0 0
\(551\) 54.0000 2.30048
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.00000 0.338971 0.169485 0.985533i \(-0.445789\pi\)
0.169485 + 0.985533i \(0.445789\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 44.0000 1.85438 0.927189 0.374593i \(-0.122217\pi\)
0.927189 + 0.374593i \(0.122217\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −18.0000 −0.755929
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) 0 0
\(573\) −48.0000 −2.00523
\(574\) 0 0
\(575\) −5.00000 −0.208514
\(576\) 0 0
\(577\) 33.0000 1.37381 0.686904 0.726748i \(-0.258969\pi\)
0.686904 + 0.726748i \(0.258969\pi\)
\(578\) 0 0
\(579\) −21.0000 −0.872730
\(580\) 0 0
\(581\) 28.0000 1.16164
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.0000 0.619116 0.309558 0.950881i \(-0.399819\pi\)
0.309558 + 0.950881i \(0.399819\pi\)
\(588\) 0 0
\(589\) 18.0000 0.741677
\(590\) 0 0
\(591\) −81.0000 −3.33189
\(592\) 0 0
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 60.0000 2.45564
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 13.0000 0.530281 0.265141 0.964210i \(-0.414582\pi\)
0.265141 + 0.964210i \(0.414582\pi\)
\(602\) 0 0
\(603\) 48.0000 1.95471
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 40.0000 1.62355 0.811775 0.583970i \(-0.198502\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(608\) 0 0
\(609\) −54.0000 −2.18819
\(610\) 0 0
\(611\) −35.0000 −1.41595
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 9.00000 0.361158
\(622\) 0 0
\(623\) −32.0000 −1.28205
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 0 0
\(633\) 24.0000 0.953914
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 15.0000 0.594322
\(638\) 0 0
\(639\) 42.0000 1.66149
\(640\) 0 0
\(641\) −40.0000 −1.57991 −0.789953 0.613168i \(-0.789895\pi\)
−0.789953 + 0.613168i \(0.789895\pi\)
\(642\) 0 0
\(643\) −44.0000 −1.73519 −0.867595 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −33.0000 −1.29736 −0.648682 0.761060i \(-0.724679\pi\)
−0.648682 + 0.761060i \(0.724679\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −18.0000 −0.705476
\(652\) 0 0
\(653\) 39.0000 1.52619 0.763094 0.646288i \(-0.223679\pi\)
0.763094 + 0.646288i \(0.223679\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 54.0000 2.10674
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) 0 0
\(661\) −42.0000 −1.63361 −0.816805 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) 0 0
\(663\) 90.0000 3.49531
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 0.348481
\(668\) 0 0
\(669\) 24.0000 0.927894
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −5.00000 −0.192736 −0.0963679 0.995346i \(-0.530723\pi\)
−0.0963679 + 0.995346i \(0.530723\pi\)
\(674\) 0 0
\(675\) −45.0000 −1.73205
\(676\) 0 0
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 0 0
\(679\) −12.0000 −0.460518
\(680\) 0 0
\(681\) −30.0000 −1.14960
\(682\) 0 0
\(683\) 29.0000 1.10965 0.554827 0.831966i \(-0.312784\pi\)
0.554827 + 0.831966i \(0.312784\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −60.0000 −2.28914
\(688\) 0 0
\(689\) 10.0000 0.380970
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0000 −0.681799
\(698\) 0 0
\(699\) 45.0000 1.70206
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) −48.0000 −1.81035
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −36.0000 −1.35011
\(712\) 0 0
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −39.0000 −1.45648
\(718\) 0 0
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) −28.0000 −1.04277
\(722\) 0 0
\(723\) −12.0000 −0.446285
\(724\) 0 0
\(725\) −45.0000 −1.67126
\(726\) 0 0
\(727\) −36.0000 −1.33517 −0.667583 0.744535i \(-0.732671\pi\)
−0.667583 + 0.744535i \(0.732671\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 48.0000 1.77534
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 29.0000 1.06678 0.533391 0.845869i \(-0.320917\pi\)
0.533391 + 0.845869i \(0.320917\pi\)
\(740\) 0 0
\(741\) −90.0000 −3.30623
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −84.0000 −3.07340
\(748\) 0 0
\(749\) −28.0000 −1.02310
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 0 0
\(753\) 30.0000 1.09326
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −12.0000 −0.436147 −0.218074 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 41.0000 1.48625 0.743124 0.669153i \(-0.233343\pi\)
0.743124 + 0.669153i \(0.233343\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −20.0000 −0.722158
\(768\) 0 0
\(769\) −28.0000 −1.00971 −0.504853 0.863205i \(-0.668453\pi\)
−0.504853 + 0.863205i \(0.668453\pi\)
\(770\) 0 0
\(771\) −39.0000 −1.40455
\(772\) 0 0
\(773\) 8.00000 0.287740 0.143870 0.989597i \(-0.454045\pi\)
0.143870 + 0.989597i \(0.454045\pi\)
\(774\) 0 0
\(775\) −15.0000 −0.538816
\(776\) 0 0
\(777\) 48.0000 1.72199
\(778\) 0 0
\(779\) 18.0000 0.644917
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 81.0000 2.89470
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 40.0000 1.42585 0.712923 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) 0 0
\(789\) 18.0000 0.640817
\(790\) 0 0
\(791\) −4.00000 −0.142224
\(792\) 0 0
\(793\) 50.0000 1.77555
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −42.0000 −1.48585
\(800\) 0 0
\(801\) 96.0000 3.39199
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 15.0000 0.528025
\(808\) 0 0
\(809\) 2.00000 0.0703163 0.0351581 0.999382i \(-0.488807\pi\)
0.0351581 + 0.999382i \(0.488807\pi\)
\(810\) 0 0
\(811\) −5.00000 −0.175574 −0.0877869 0.996139i \(-0.527979\pi\)
−0.0877869 + 0.996139i \(0.527979\pi\)
\(812\) 0 0
\(813\) −24.0000 −0.841717
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −48.0000 −1.67931
\(818\) 0 0
\(819\) 60.0000 2.09657
\(820\) 0 0
\(821\) −54.0000 −1.88461 −0.942306 0.334751i \(-0.891348\pi\)
−0.942306 + 0.334751i \(0.891348\pi\)
\(822\) 0 0
\(823\) −57.0000 −1.98690 −0.993448 0.114289i \(-0.963541\pi\)
−0.993448 + 0.114289i \(0.963541\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) 54.0000 1.87550 0.937749 0.347314i \(-0.112906\pi\)
0.937749 + 0.347314i \(0.112906\pi\)
\(830\) 0 0
\(831\) −69.0000 −2.39358
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 27.0000 0.933257
\(838\) 0 0
\(839\) 30.0000 1.03572 0.517858 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 0 0
\(843\) −54.0000 −1.85986
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 22.0000 0.755929
\(848\) 0 0
\(849\) 12.0000 0.411839
\(850\) 0 0
\(851\) −8.00000 −0.274236
\(852\) 0 0
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 23.0000 0.785665 0.392833 0.919610i \(-0.371495\pi\)
0.392833 + 0.919610i \(0.371495\pi\)
\(858\) 0 0
\(859\) −17.0000 −0.580033 −0.290016 0.957022i \(-0.593661\pi\)
−0.290016 + 0.957022i \(0.593661\pi\)
\(860\) 0 0
\(861\) −18.0000 −0.613438
\(862\) 0 0
\(863\) 49.0000 1.66798 0.833990 0.551780i \(-0.186051\pi\)
0.833990 + 0.551780i \(0.186051\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 57.0000 1.93582
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −40.0000 −1.35535
\(872\) 0 0
\(873\) 36.0000 1.21842
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 0 0
\(879\) 36.0000 1.21425
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 27.0000 0.906571 0.453286 0.891365i \(-0.350252\pi\)
0.453286 + 0.891365i \(0.350252\pi\)
\(888\) 0 0
\(889\) −10.0000 −0.335389
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 42.0000 1.40548
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −15.0000 −0.500835
\(898\) 0 0
\(899\) 27.0000 0.900500
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) 0 0
\(903\) 48.0000 1.59734
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 0 0
\(909\) 36.0000 1.19404
\(910\) 0 0
\(911\) −50.0000 −1.65657 −0.828287 0.560304i \(-0.810684\pi\)
−0.828287 + 0.560304i \(0.810684\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18.0000 0.594412
\(918\) 0 0
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) −35.0000 −1.15204
\(924\) 0 0
\(925\) 40.0000 1.31519
\(926\) 0 0
\(927\) 84.0000 2.75892
\(928\) 0 0
\(929\) 7.00000 0.229663 0.114831 0.993385i \(-0.463367\pi\)
0.114831 + 0.993385i \(0.463367\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) 0 0
\(933\) −51.0000 −1.66967
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 4.00000 0.130674 0.0653372 0.997863i \(-0.479188\pi\)
0.0653372 + 0.997863i \(0.479188\pi\)
\(938\) 0 0
\(939\) −60.0000 −1.95803
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 0 0
\(943\) 3.00000 0.0976934
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7.00000 0.227469 0.113735 0.993511i \(-0.463719\pi\)
0.113735 + 0.993511i \(0.463719\pi\)
\(948\) 0 0
\(949\) −45.0000 −1.46076
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) 42.0000 1.36051 0.680257 0.732974i \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.00000 −0.258333
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 84.0000 2.70686
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −47.0000 −1.51142 −0.755709 0.654907i \(-0.772708\pi\)
−0.755709 + 0.654907i \(0.772708\pi\)
\(968\) 0 0
\(969\) −108.000 −3.46946
\(970\) 0 0
\(971\) −26.0000 −0.834380 −0.417190 0.908819i \(-0.636985\pi\)
−0.417190 + 0.908819i \(0.636985\pi\)
\(972\) 0 0
\(973\) 46.0000 1.47469
\(974\) 0 0
\(975\) 75.0000 2.40192
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −14.0000 −0.446531 −0.223265 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −42.0000 −1.33687
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −57.0000 −1.80884
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −50.0000 −1.58352 −0.791758 0.610835i \(-0.790834\pi\)
−0.791758 + 0.610835i \(0.790834\pi\)
\(998\) 0 0
\(999\) −72.0000 −2.27798
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 184.2.a.d.1.1 1
3.2 odd 2 1656.2.a.c.1.1 1
4.3 odd 2 368.2.a.a.1.1 1
5.2 odd 4 4600.2.e.a.4049.1 2
5.3 odd 4 4600.2.e.a.4049.2 2
5.4 even 2 4600.2.a.a.1.1 1
7.6 odd 2 9016.2.a.b.1.1 1
8.3 odd 2 1472.2.a.m.1.1 1
8.5 even 2 1472.2.a.a.1.1 1
12.11 even 2 3312.2.a.i.1.1 1
20.19 odd 2 9200.2.a.bj.1.1 1
23.22 odd 2 4232.2.a.j.1.1 1
92.91 even 2 8464.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.d.1.1 1 1.1 even 1 trivial
368.2.a.a.1.1 1 4.3 odd 2
1472.2.a.a.1.1 1 8.5 even 2
1472.2.a.m.1.1 1 8.3 odd 2
1656.2.a.c.1.1 1 3.2 odd 2
3312.2.a.i.1.1 1 12.11 even 2
4232.2.a.j.1.1 1 23.22 odd 2
4600.2.a.a.1.1 1 5.4 even 2
4600.2.e.a.4049.1 2 5.2 odd 4
4600.2.e.a.4049.2 2 5.3 odd 4
8464.2.a.b.1.1 1 92.91 even 2
9016.2.a.b.1.1 1 7.6 odd 2
9200.2.a.bj.1.1 1 20.19 odd 2