Properties

Label 2736.2.a.bc.1.2
Level $2736$
Weight $2$
Character 2736.1
Self dual yes
Analytic conductor $21.847$
Analytic rank $0$
Dimension $3$
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] = [2736,2,Mod(1,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("2736.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.892.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 8x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1368)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.31955\) of defining polynomial
Character \(\chi\) \(=\) 2736.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.319551 q^{5} +2.61968 q^{7} +O(q^{10})\) \(q+0.319551 q^{5} +2.61968 q^{7} -4.31955 q^{11} +6.51757 q^{13} -4.19802 q^{17} +1.00000 q^{19} +0.639102 q^{23} -4.89789 q^{25} +7.87847 q^{29} +6.00000 q^{31} +0.837122 q^{35} +4.00000 q^{37} +12.5176 q^{41} +1.38032 q^{43} -7.55892 q^{47} -0.137255 q^{49} +13.1567 q^{53} -1.38032 q^{55} -13.0351 q^{59} -5.89789 q^{61} +2.08270 q^{65} -11.7569 q^{67} +11.7569 q^{71} +15.1373 q^{73} -11.3159 q^{77} -0.517571 q^{79} -11.8785 q^{83} -1.34148 q^{85} -3.87847 q^{89} +17.0740 q^{91} +0.319551 q^{95} +11.2782 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{5} + 2 q^{7} - 10 q^{11} - 4 q^{13} + 8 q^{17} + 3 q^{19} - 4 q^{23} + 3 q^{25} + 6 q^{29} + 18 q^{31} - 24 q^{35} + 12 q^{37} + 14 q^{41} + 10 q^{43} - 8 q^{47} + 29 q^{49} + 10 q^{53} - 10 q^{55} + 8 q^{59} + 24 q^{65} + 16 q^{73} + 16 q^{77} + 22 q^{79} - 18 q^{83} - 10 q^{85} + 6 q^{89} + 4 q^{91} - 2 q^{95} + 22 q^{97}+O(q^{100}) \) 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
\(5\) 0.319551 0.142907 0.0714537 0.997444i \(-0.477236\pi\)
0.0714537 + 0.997444i \(0.477236\pi\)
\(6\) 0 0
\(7\) 2.61968 0.990148 0.495074 0.868851i \(-0.335141\pi\)
0.495074 + 0.868851i \(0.335141\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.31955 −1.30239 −0.651197 0.758909i \(-0.725733\pi\)
−0.651197 + 0.758909i \(0.725733\pi\)
\(12\) 0 0
\(13\) 6.51757 1.80765 0.903825 0.427903i \(-0.140748\pi\)
0.903825 + 0.427903i \(0.140748\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.19802 −1.01817 −0.509085 0.860716i \(-0.670016\pi\)
−0.509085 + 0.860716i \(0.670016\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.639102 0.133262 0.0666309 0.997778i \(-0.478775\pi\)
0.0666309 + 0.997778i \(0.478775\pi\)
\(24\) 0 0
\(25\) −4.89789 −0.979577
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.87847 1.46300 0.731498 0.681844i \(-0.238822\pi\)
0.731498 + 0.681844i \(0.238822\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.837122 0.141499
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 12.5176 1.95492 0.977458 0.211129i \(-0.0677142\pi\)
0.977458 + 0.211129i \(0.0677142\pi\)
\(42\) 0 0
\(43\) 1.38032 0.210496 0.105248 0.994446i \(-0.466436\pi\)
0.105248 + 0.994446i \(0.466436\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.55892 −1.10258 −0.551291 0.834313i \(-0.685865\pi\)
−0.551291 + 0.834313i \(0.685865\pi\)
\(48\) 0 0
\(49\) −0.137255 −0.0196079
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13.1567 1.80721 0.903604 0.428369i \(-0.140912\pi\)
0.903604 + 0.428369i \(0.140912\pi\)
\(54\) 0 0
\(55\) −1.38032 −0.186122
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −13.0351 −1.69703 −0.848516 0.529171i \(-0.822503\pi\)
−0.848516 + 0.529171i \(0.822503\pi\)
\(60\) 0 0
\(61\) −5.89789 −0.755147 −0.377574 0.925980i \(-0.623241\pi\)
−0.377574 + 0.925980i \(0.623241\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.08270 0.258327
\(66\) 0 0
\(67\) −11.7569 −1.43634 −0.718169 0.695868i \(-0.755020\pi\)
−0.718169 + 0.695868i \(0.755020\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.7569 1.39529 0.697646 0.716443i \(-0.254231\pi\)
0.697646 + 0.716443i \(0.254231\pi\)
\(72\) 0 0
\(73\) 15.1373 1.77168 0.885841 0.463989i \(-0.153582\pi\)
0.885841 + 0.463989i \(0.153582\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.3159 −1.28956
\(78\) 0 0
\(79\) −0.517571 −0.0582313 −0.0291157 0.999576i \(-0.509269\pi\)
−0.0291157 + 0.999576i \(0.509269\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −11.8785 −1.30383 −0.651916 0.758291i \(-0.726034\pi\)
−0.651916 + 0.758291i \(0.726034\pi\)
\(84\) 0 0
\(85\) −1.34148 −0.145504
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.87847 −0.411117 −0.205558 0.978645i \(-0.565901\pi\)
−0.205558 + 0.978645i \(0.565901\pi\)
\(90\) 0 0
\(91\) 17.0740 1.78984
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.319551 0.0327852
\(96\) 0 0
\(97\) 11.2782 1.14513 0.572564 0.819860i \(-0.305949\pi\)
0.572564 + 0.819860i \(0.305949\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.51757 −0.449515 −0.224758 0.974415i \(-0.572159\pi\)
−0.224758 + 0.974415i \(0.572159\pi\)
\(102\) 0 0
\(103\) 19.0351 1.87559 0.937794 0.347192i \(-0.112865\pi\)
0.937794 + 0.347192i \(0.112865\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.11784 0.688107 0.344054 0.938950i \(-0.388200\pi\)
0.344054 + 0.938950i \(0.388200\pi\)
\(108\) 0 0
\(109\) −5.27820 −0.505560 −0.252780 0.967524i \(-0.581345\pi\)
−0.252780 + 0.967524i \(0.581345\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.39973 −0.131676 −0.0658379 0.997830i \(-0.520972\pi\)
−0.0658379 + 0.997830i \(0.520972\pi\)
\(114\) 0 0
\(115\) 0.204225 0.0190441
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.9975 −1.00814
\(120\) 0 0
\(121\) 7.65852 0.696229
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.16288 −0.282896
\(126\) 0 0
\(127\) 9.75694 0.865788 0.432894 0.901445i \(-0.357492\pi\)
0.432894 + 0.901445i \(0.357492\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 19.4374 1.69825 0.849126 0.528190i \(-0.177129\pi\)
0.849126 + 0.528190i \(0.177129\pi\)
\(132\) 0 0
\(133\) 2.61968 0.227155
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.9198 0.932943 0.466471 0.884536i \(-0.345525\pi\)
0.466471 + 0.884536i \(0.345525\pi\)
\(138\) 0 0
\(139\) 6.61968 0.561474 0.280737 0.959785i \(-0.409421\pi\)
0.280737 + 0.959785i \(0.409421\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −28.1530 −2.35427
\(144\) 0 0
\(145\) 2.51757 0.209073
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.958652 −0.0785359 −0.0392679 0.999229i \(-0.512503\pi\)
−0.0392679 + 0.999229i \(0.512503\pi\)
\(150\) 0 0
\(151\) −0.517571 −0.0421194 −0.0210597 0.999778i \(-0.506704\pi\)
−0.0210597 + 0.999778i \(0.506704\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.91730 0.154002
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.67424 0.131949
\(162\) 0 0
\(163\) −17.0351 −1.33430 −0.667148 0.744925i \(-0.732485\pi\)
−0.667148 + 0.744925i \(0.732485\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.6391 0.978043 0.489022 0.872272i \(-0.337354\pi\)
0.489022 + 0.872272i \(0.337354\pi\)
\(168\) 0 0
\(169\) 29.4787 2.26760
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.60027 0.197695 0.0988473 0.995103i \(-0.468484\pi\)
0.0988473 + 0.995103i \(0.468484\pi\)
\(174\) 0 0
\(175\) −12.8309 −0.969926
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −19.1178 −1.42893 −0.714467 0.699669i \(-0.753331\pi\)
−0.714467 + 0.699669i \(0.753331\pi\)
\(180\) 0 0
\(181\) −22.2745 −1.65565 −0.827826 0.560985i \(-0.810422\pi\)
−0.827826 + 0.560985i \(0.810422\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.27820 0.0939754
\(186\) 0 0
\(187\) 18.1336 1.32606
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.55892 0.546944 0.273472 0.961880i \(-0.411828\pi\)
0.273472 + 0.961880i \(0.411828\pi\)
\(192\) 0 0
\(193\) −0.517571 −0.0372556 −0.0186278 0.999826i \(-0.505930\pi\)
−0.0186278 + 0.999826i \(0.505930\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.4824 0.818089 0.409045 0.912514i \(-0.365862\pi\)
0.409045 + 0.912514i \(0.365862\pi\)
\(198\) 0 0
\(199\) 1.38032 0.0978480 0.0489240 0.998803i \(-0.484421\pi\)
0.0489240 + 0.998803i \(0.484421\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 20.6391 1.44858
\(204\) 0 0
\(205\) 4.00000 0.279372
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.31955 −0.298790
\(210\) 0 0
\(211\) −2.72180 −0.187376 −0.0936881 0.995602i \(-0.529866\pi\)
−0.0936881 + 0.995602i \(0.529866\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.441081 0.0300815
\(216\) 0 0
\(217\) 15.7181 1.06701
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −27.3609 −1.84049
\(222\) 0 0
\(223\) 9.79577 0.655974 0.327987 0.944682i \(-0.393630\pi\)
0.327987 + 0.944682i \(0.393630\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.6391 0.838887 0.419443 0.907782i \(-0.362225\pi\)
0.419443 + 0.907782i \(0.362225\pi\)
\(228\) 0 0
\(229\) −11.1373 −0.735971 −0.367985 0.929832i \(-0.619952\pi\)
−0.367985 + 0.929832i \(0.619952\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.8723 −1.43290 −0.716450 0.697639i \(-0.754234\pi\)
−0.716450 + 0.697639i \(0.754234\pi\)
\(234\) 0 0
\(235\) −2.41546 −0.157567
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.8723 1.67354 0.836769 0.547556i \(-0.184442\pi\)
0.836769 + 0.547556i \(0.184442\pi\)
\(240\) 0 0
\(241\) 9.79577 0.631001 0.315501 0.948925i \(-0.397828\pi\)
0.315501 + 0.948925i \(0.397828\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.0438601 −0.00280212
\(246\) 0 0
\(247\) 6.51757 0.414703
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.28441 0.207310 0.103655 0.994613i \(-0.466946\pi\)
0.103655 + 0.994613i \(0.466946\pi\)
\(252\) 0 0
\(253\) −2.76063 −0.173559
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.5176 −0.780825 −0.390412 0.920640i \(-0.627668\pi\)
−0.390412 + 0.920640i \(0.627668\pi\)
\(258\) 0 0
\(259\) 10.4787 0.651117
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.1980 −1.49211 −0.746057 0.665882i \(-0.768055\pi\)
−0.746057 + 0.665882i \(0.768055\pi\)
\(264\) 0 0
\(265\) 4.20423 0.258264
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 11.8785 0.724243 0.362122 0.932131i \(-0.382053\pi\)
0.362122 + 0.932131i \(0.382053\pi\)
\(270\) 0 0
\(271\) 6.55641 0.398273 0.199137 0.979972i \(-0.436186\pi\)
0.199137 + 0.979972i \(0.436186\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.1567 1.27580
\(276\) 0 0
\(277\) −16.6585 −1.00091 −0.500457 0.865762i \(-0.666835\pi\)
−0.500457 + 0.865762i \(0.666835\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.3572 −0.617859 −0.308930 0.951085i \(-0.599971\pi\)
−0.308930 + 0.951085i \(0.599971\pi\)
\(282\) 0 0
\(283\) 30.4155 1.80801 0.904006 0.427520i \(-0.140613\pi\)
0.904006 + 0.427520i \(0.140613\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 32.7921 1.93566
\(288\) 0 0
\(289\) 0.623376 0.0366692
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 12.2745 0.717085 0.358542 0.933513i \(-0.383274\pi\)
0.358542 + 0.933513i \(0.383274\pi\)
\(294\) 0 0
\(295\) −4.16539 −0.242518
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.16539 0.240891
\(300\) 0 0
\(301\) 3.61599 0.208422
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.88467 −0.107916
\(306\) 0 0
\(307\) −2.72180 −0.155341 −0.0776706 0.996979i \(-0.524748\pi\)
−0.0776706 + 0.996979i \(0.524748\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.837122 −0.0474688 −0.0237344 0.999718i \(-0.507556\pi\)
−0.0237344 + 0.999718i \(0.507556\pi\)
\(312\) 0 0
\(313\) 12.5564 0.709730 0.354865 0.934918i \(-0.384527\pi\)
0.354865 + 0.934918i \(0.384527\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.517571 0.0290697 0.0145349 0.999894i \(-0.495373\pi\)
0.0145349 + 0.999894i \(0.495373\pi\)
\(318\) 0 0
\(319\) −34.0315 −1.90540
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.19802 −0.233584
\(324\) 0 0
\(325\) −31.9223 −1.77073
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −19.8020 −1.09172
\(330\) 0 0
\(331\) −18.3133 −1.00659 −0.503296 0.864114i \(-0.667880\pi\)
−0.503296 + 0.864114i \(0.667880\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.75694 −0.205264
\(336\) 0 0
\(337\) −3.27820 −0.178575 −0.0892876 0.996006i \(-0.528459\pi\)
−0.0892876 + 0.996006i \(0.528459\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −25.9173 −1.40350
\(342\) 0 0
\(343\) −18.6974 −1.00956
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.5978 −0.729966 −0.364983 0.931014i \(-0.618925\pi\)
−0.364983 + 0.931014i \(0.618925\pi\)
\(348\) 0 0
\(349\) 16.1724 0.865689 0.432844 0.901469i \(-0.357510\pi\)
0.432844 + 0.901469i \(0.357510\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.47874 −0.344828 −0.172414 0.985025i \(-0.555157\pi\)
−0.172414 + 0.985025i \(0.555157\pi\)
\(354\) 0 0
\(355\) 3.75694 0.199398
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.67676 −0.352386 −0.176193 0.984356i \(-0.556378\pi\)
−0.176193 + 0.984356i \(0.556378\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.83712 0.253187
\(366\) 0 0
\(367\) −25.0351 −1.30682 −0.653412 0.757003i \(-0.726663\pi\)
−0.653412 + 0.757003i \(0.726663\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 34.4663 1.78940
\(372\) 0 0
\(373\) 14.5564 0.753702 0.376851 0.926274i \(-0.377007\pi\)
0.376851 + 0.926274i \(0.377007\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 51.3485 2.64458
\(378\) 0 0
\(379\) 1.23937 0.0636621 0.0318310 0.999493i \(-0.489866\pi\)
0.0318310 + 0.999493i \(0.489866\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.67424 0.0855499 0.0427749 0.999085i \(-0.486380\pi\)
0.0427749 + 0.999085i \(0.486380\pi\)
\(384\) 0 0
\(385\) −3.61599 −0.184288
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −26.6329 −1.35034 −0.675171 0.737661i \(-0.735930\pi\)
−0.675171 + 0.737661i \(0.735930\pi\)
\(390\) 0 0
\(391\) −2.68296 −0.135683
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.165390 −0.00832169
\(396\) 0 0
\(397\) −17.8979 −0.898269 −0.449135 0.893464i \(-0.648268\pi\)
−0.449135 + 0.893464i \(0.648268\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −33.7958 −1.68768 −0.843840 0.536595i \(-0.819710\pi\)
−0.843840 + 0.536595i \(0.819710\pi\)
\(402\) 0 0
\(403\) 39.1054 1.94798
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −17.2782 −0.856449
\(408\) 0 0
\(409\) −21.5139 −1.06379 −0.531896 0.846809i \(-0.678520\pi\)
−0.531896 + 0.846809i \(0.678520\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −34.1480 −1.68031
\(414\) 0 0
\(415\) −3.79577 −0.186327
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.6003 −0.517857 −0.258928 0.965897i \(-0.583369\pi\)
−0.258928 + 0.965897i \(0.583369\pi\)
\(420\) 0 0
\(421\) −23.7181 −1.15595 −0.577975 0.816055i \(-0.696157\pi\)
−0.577975 + 0.816055i \(0.696157\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 20.5614 0.997376
\(426\) 0 0
\(427\) −15.4506 −0.747707
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 19.3609 0.932582 0.466291 0.884631i \(-0.345590\pi\)
0.466291 + 0.884631i \(0.345590\pi\)
\(432\) 0 0
\(433\) −13.7569 −0.661116 −0.330558 0.943786i \(-0.607237\pi\)
−0.330558 + 0.943786i \(0.607237\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.639102 0.0305724
\(438\) 0 0
\(439\) −20.2357 −0.965796 −0.482898 0.875677i \(-0.660416\pi\)
−0.482898 + 0.875677i \(0.660416\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.87596 −0.326687 −0.163343 0.986569i \(-0.552228\pi\)
−0.163343 + 0.986569i \(0.552228\pi\)
\(444\) 0 0
\(445\) −1.23937 −0.0587517
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.76063 0.224668 0.112334 0.993670i \(-0.464167\pi\)
0.112334 + 0.993670i \(0.464167\pi\)
\(450\) 0 0
\(451\) −54.0703 −2.54607
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.45600 0.255781
\(456\) 0 0
\(457\) 5.82022 0.272258 0.136129 0.990691i \(-0.456534\pi\)
0.136129 + 0.990691i \(0.456534\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0413 0.700545 0.350273 0.936648i \(-0.386089\pi\)
0.350273 + 0.936648i \(0.386089\pi\)
\(462\) 0 0
\(463\) 27.6548 1.28523 0.642614 0.766190i \(-0.277850\pi\)
0.642614 + 0.766190i \(0.277850\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −34.9513 −1.61735 −0.808676 0.588254i \(-0.799815\pi\)
−0.808676 + 0.588254i \(0.799815\pi\)
\(468\) 0 0
\(469\) −30.7995 −1.42219
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.96234 −0.274149
\(474\) 0 0
\(475\) −4.89789 −0.224730
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.67424 0.442028 0.221014 0.975271i \(-0.429063\pi\)
0.221014 + 0.975271i \(0.429063\pi\)
\(480\) 0 0
\(481\) 26.0703 1.18870
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.60396 0.163647
\(486\) 0 0
\(487\) −20.5176 −0.929740 −0.464870 0.885379i \(-0.653899\pi\)
−0.464870 + 0.885379i \(0.653899\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −36.9136 −1.66589 −0.832944 0.553357i \(-0.813346\pi\)
−0.832944 + 0.553357i \(0.813346\pi\)
\(492\) 0 0
\(493\) −33.0740 −1.48958
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 30.7995 1.38154
\(498\) 0 0
\(499\) −9.17609 −0.410778 −0.205389 0.978680i \(-0.565846\pi\)
−0.205389 + 0.978680i \(0.565846\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 32.1530 1.43363 0.716815 0.697263i \(-0.245599\pi\)
0.716815 + 0.697263i \(0.245599\pi\)
\(504\) 0 0
\(505\) −1.44359 −0.0642391
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.9136 −0.749683 −0.374841 0.927089i \(-0.622303\pi\)
−0.374841 + 0.927089i \(0.622303\pi\)
\(510\) 0 0
\(511\) 39.6548 1.75423
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.08270 0.268036
\(516\) 0 0
\(517\) 32.6511 1.43600
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0388 0.439809 0.219905 0.975521i \(-0.429425\pi\)
0.219905 + 0.975521i \(0.429425\pi\)
\(522\) 0 0
\(523\) −34.2745 −1.49872 −0.749360 0.662163i \(-0.769639\pi\)
−0.749360 + 0.662163i \(0.769639\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −25.1881 −1.09721
\(528\) 0 0
\(529\) −22.5915 −0.982241
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 81.5842 3.53380
\(534\) 0 0
\(535\) 2.27451 0.0983357
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.592882 0.0255372
\(540\) 0 0
\(541\) −28.1724 −1.21123 −0.605613 0.795759i \(-0.707072\pi\)
−0.605613 + 0.795759i \(0.707072\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.68665 −0.0722483
\(546\) 0 0
\(547\) 7.55271 0.322931 0.161465 0.986878i \(-0.448378\pi\)
0.161465 + 0.986878i \(0.448378\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.87847 0.335634
\(552\) 0 0
\(553\) −1.35587 −0.0576576
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23.4374 0.993074 0.496537 0.868016i \(-0.334605\pi\)
0.496537 + 0.868016i \(0.334605\pi\)
\(558\) 0 0
\(559\) 8.99631 0.380503
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 34.3133 1.44614 0.723068 0.690777i \(-0.242732\pi\)
0.723068 + 0.690777i \(0.242732\pi\)
\(564\) 0 0
\(565\) −0.447286 −0.0188175
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23.8785 −1.00104 −0.500519 0.865726i \(-0.666857\pi\)
−0.500519 + 0.865726i \(0.666857\pi\)
\(570\) 0 0
\(571\) 9.03514 0.378109 0.189054 0.981967i \(-0.439458\pi\)
0.189054 + 0.981967i \(0.439458\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.13025 −0.130540
\(576\) 0 0
\(577\) −18.8554 −0.784959 −0.392479 0.919761i \(-0.628383\pi\)
−0.392479 + 0.919761i \(0.628383\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −31.1178 −1.29099
\(582\) 0 0
\(583\) −56.8309 −2.35370
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.68045 −0.151908 −0.0759542 0.997111i \(-0.524200\pi\)
−0.0759542 + 0.997111i \(0.524200\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −23.5139 −0.965599 −0.482800 0.875731i \(-0.660380\pi\)
−0.482800 + 0.875731i \(0.660380\pi\)
\(594\) 0 0
\(595\) −3.51426 −0.144070
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.31335 0.257956 0.128978 0.991647i \(-0.458830\pi\)
0.128978 + 0.991647i \(0.458830\pi\)
\(600\) 0 0
\(601\) 19.4824 0.794705 0.397352 0.917666i \(-0.369929\pi\)
0.397352 + 0.917666i \(0.369929\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.44729 0.0994963
\(606\) 0 0
\(607\) 37.7569 1.53251 0.766253 0.642538i \(-0.222119\pi\)
0.766253 + 0.642538i \(0.222119\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −49.2658 −1.99308
\(612\) 0 0
\(613\) −4.65852 −0.188156 −0.0940779 0.995565i \(-0.529990\pi\)
−0.0940779 + 0.995565i \(0.529990\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −36.3510 −1.46344 −0.731718 0.681607i \(-0.761281\pi\)
−0.731718 + 0.681607i \(0.761281\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10.1604 −0.407066
\(624\) 0 0
\(625\) 23.4787 0.939149
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −16.7921 −0.669544
\(630\) 0 0
\(631\) −35.4506 −1.41127 −0.705633 0.708577i \(-0.749337\pi\)
−0.705633 + 0.708577i \(0.749337\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.11784 0.123728
\(636\) 0 0
\(637\) −0.894572 −0.0354442
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.8785 0.943143 0.471571 0.881828i \(-0.343687\pi\)
0.471571 + 0.881828i \(0.343687\pi\)
\(642\) 0 0
\(643\) 3.93672 0.155249 0.0776246 0.996983i \(-0.475266\pi\)
0.0776246 + 0.996983i \(0.475266\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.8020 −0.621240 −0.310620 0.950534i \(-0.600537\pi\)
−0.310620 + 0.950534i \(0.600537\pi\)
\(648\) 0 0
\(649\) 56.3060 2.21020
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 43.2720 1.69336 0.846682 0.532099i \(-0.178597\pi\)
0.846682 + 0.532099i \(0.178597\pi\)
\(654\) 0 0
\(655\) 6.21123 0.242693
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.8396 −0.850751 −0.425376 0.905017i \(-0.639858\pi\)
−0.425376 + 0.905017i \(0.639858\pi\)
\(660\) 0 0
\(661\) −9.03514 −0.351426 −0.175713 0.984441i \(-0.556223\pi\)
−0.175713 + 0.984441i \(0.556223\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.837122 0.0324622
\(666\) 0 0
\(667\) 5.03514 0.194962
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.4762 0.983499
\(672\) 0 0
\(673\) 9.96116 0.383975 0.191987 0.981397i \(-0.438507\pi\)
0.191987 + 0.981397i \(0.438507\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.35721 0.244327 0.122164 0.992510i \(-0.461017\pi\)
0.122164 + 0.992510i \(0.461017\pi\)
\(678\) 0 0
\(679\) 29.5453 1.13385
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 37.1881 1.42296 0.711482 0.702704i \(-0.248024\pi\)
0.711482 + 0.702704i \(0.248024\pi\)
\(684\) 0 0
\(685\) 3.48944 0.133325
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 85.7496 3.26680
\(690\) 0 0
\(691\) −32.8942 −1.25135 −0.625677 0.780082i \(-0.715177\pi\)
−0.625677 + 0.780082i \(0.715177\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.11533 0.0802389
\(696\) 0 0
\(697\) −52.5490 −1.99044
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 16.4399 0.620926 0.310463 0.950585i \(-0.399516\pi\)
0.310463 + 0.950585i \(0.399516\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11.8346 −0.445086
\(708\) 0 0
\(709\) −41.5139 −1.55909 −0.779543 0.626348i \(-0.784549\pi\)
−0.779543 + 0.626348i \(0.784549\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.83461 0.143607
\(714\) 0 0
\(715\) −8.99631 −0.336443
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32.8371 −1.22462 −0.612309 0.790619i \(-0.709759\pi\)
−0.612309 + 0.790619i \(0.709759\pi\)
\(720\) 0 0
\(721\) 49.8661 1.85711
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −38.5879 −1.43312
\(726\) 0 0
\(727\) −4.89419 −0.181516 −0.0907578 0.995873i \(-0.528929\pi\)
−0.0907578 + 0.995873i \(0.528929\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.79459 −0.214321
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 50.7847 1.87068
\(738\) 0 0
\(739\) −19.4506 −0.715502 −0.357751 0.933817i \(-0.616456\pi\)
−0.357751 + 0.933817i \(0.616456\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −23.5915 −0.865490 −0.432745 0.901516i \(-0.642455\pi\)
−0.432745 + 0.901516i \(0.642455\pi\)
\(744\) 0 0
\(745\) −0.306338 −0.0112234
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 18.6465 0.681328
\(750\) 0 0
\(751\) −4.76063 −0.173718 −0.0868590 0.996221i \(-0.527683\pi\)
−0.0868590 + 0.996221i \(0.527683\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.165390 −0.00601917
\(756\) 0 0
\(757\) −46.9330 −1.70581 −0.852905 0.522066i \(-0.825161\pi\)
−0.852905 + 0.522066i \(0.825161\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −33.3108 −1.20752 −0.603758 0.797167i \(-0.706331\pi\)
−0.603758 + 0.797167i \(0.706331\pi\)
\(762\) 0 0
\(763\) −13.8272 −0.500579
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −84.9575 −3.06764
\(768\) 0 0
\(769\) −14.9330 −0.538499 −0.269249 0.963070i \(-0.586776\pi\)
−0.269249 + 0.963070i \(0.586776\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −32.5176 −1.16958 −0.584788 0.811186i \(-0.698822\pi\)
−0.584788 + 0.811186i \(0.698822\pi\)
\(774\) 0 0
\(775\) −29.3873 −1.05562
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.5176 0.448489
\(780\) 0 0
\(781\) −50.7847 −1.81722
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.639102 0.0228105
\(786\) 0 0
\(787\) −14.5564 −0.518880 −0.259440 0.965759i \(-0.583538\pi\)
−0.259440 + 0.965759i \(0.583538\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.66686 −0.130379
\(792\) 0 0
\(793\) −38.4399 −1.36504
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −23.2394 −0.823181 −0.411590 0.911369i \(-0.635027\pi\)
−0.411590 + 0.911369i \(0.635027\pi\)
\(798\) 0 0
\(799\) 31.7325 1.12262
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −65.3861 −2.30743
\(804\) 0 0
\(805\) 0.535006 0.0188565
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 39.7896 1.39893 0.699463 0.714668i \(-0.253422\pi\)
0.699463 + 0.714668i \(0.253422\pi\)
\(810\) 0 0
\(811\) −39.4750 −1.38616 −0.693078 0.720862i \(-0.743746\pi\)
−0.693078 + 0.720862i \(0.743746\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.44359 −0.190681
\(816\) 0 0
\(817\) 1.38032 0.0482911
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −16.3196 −0.569556 −0.284778 0.958593i \(-0.591920\pi\)
−0.284778 + 0.958593i \(0.591920\pi\)
\(822\) 0 0
\(823\) −16.9719 −0.591602 −0.295801 0.955250i \(-0.595587\pi\)
−0.295801 + 0.955250i \(0.595587\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −25.1128 −0.873258 −0.436629 0.899642i \(-0.643828\pi\)
−0.436629 + 0.899642i \(0.643828\pi\)
\(828\) 0 0
\(829\) −35.5915 −1.23615 −0.618073 0.786121i \(-0.712086\pi\)
−0.618073 + 0.786121i \(0.712086\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.576201 0.0199642
\(834\) 0 0
\(835\) 4.03884 0.139770
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −29.8396 −1.03018 −0.515089 0.857137i \(-0.672241\pi\)
−0.515089 + 0.857137i \(0.672241\pi\)
\(840\) 0 0
\(841\) 33.0703 1.14035
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 9.41995 0.324056
\(846\) 0 0
\(847\) 20.0629 0.689369
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.55641 0.0876325
\(852\) 0 0
\(853\) 14.0777 0.482010 0.241005 0.970524i \(-0.422523\pi\)
0.241005 + 0.970524i \(0.422523\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 30.9963 1.05881 0.529407 0.848368i \(-0.322415\pi\)
0.529407 + 0.848368i \(0.322415\pi\)
\(858\) 0 0
\(859\) 43.2464 1.47555 0.737774 0.675048i \(-0.235877\pi\)
0.737774 + 0.675048i \(0.235877\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 12.9575 0.441077 0.220539 0.975378i \(-0.429218\pi\)
0.220539 + 0.975378i \(0.429218\pi\)
\(864\) 0 0
\(865\) 0.830917 0.0282520
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.23568 0.0758401
\(870\) 0 0
\(871\) −76.6267 −2.59640
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.28574 −0.280109
\(876\) 0 0
\(877\) −11.7181 −0.395692 −0.197846 0.980233i \(-0.563395\pi\)
−0.197846 + 0.980233i \(0.563395\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −28.3510 −0.955169 −0.477585 0.878586i \(-0.658488\pi\)
−0.477585 + 0.878586i \(0.658488\pi\)
\(882\) 0 0
\(883\) −22.3378 −0.751726 −0.375863 0.926675i \(-0.622654\pi\)
−0.375863 + 0.926675i \(0.622654\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.5490 1.22720 0.613598 0.789619i \(-0.289722\pi\)
0.613598 + 0.789619i \(0.289722\pi\)
\(888\) 0 0
\(889\) 25.5601 0.857258
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7.55892 −0.252950
\(894\) 0 0
\(895\) −6.10912 −0.204205
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 47.2708 1.57657
\(900\) 0 0
\(901\) −55.2320 −1.84004
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.11784 −0.236605
\(906\) 0 0
\(907\) −47.3097 −1.57089 −0.785446 0.618931i \(-0.787566\pi\)
−0.785446 + 0.618931i \(0.787566\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 37.8396 1.25368 0.626842 0.779147i \(-0.284347\pi\)
0.626842 + 0.779147i \(0.284347\pi\)
\(912\) 0 0
\(913\) 51.3097 1.69810
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 50.9198 1.68152
\(918\) 0 0
\(919\) 43.5915 1.43795 0.718976 0.695035i \(-0.244611\pi\)
0.718976 + 0.695035i \(0.244611\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 76.6267 2.52220
\(924\) 0 0
\(925\) −19.5915 −0.644166
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −23.7569 −0.779440 −0.389720 0.920933i \(-0.627428\pi\)
−0.389720 + 0.920933i \(0.627428\pi\)
\(930\) 0 0
\(931\) −0.137255 −0.00449836
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 5.79459 0.189504
\(936\) 0 0
\(937\) −45.4894 −1.48608 −0.743038 0.669250i \(-0.766616\pi\)
−0.743038 + 0.669250i \(0.766616\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 48.7482 1.58915 0.794573 0.607168i \(-0.207695\pi\)
0.794573 + 0.607168i \(0.207695\pi\)
\(942\) 0 0
\(943\) 8.00000 0.260516
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.94876 0.193309 0.0966543 0.995318i \(-0.469186\pi\)
0.0966543 + 0.995318i \(0.469186\pi\)
\(948\) 0 0
\(949\) 98.6581 3.20258
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.4473 0.467993 0.233997 0.972237i \(-0.424819\pi\)
0.233997 + 0.972237i \(0.424819\pi\)
\(954\) 0 0
\(955\) 2.41546 0.0781624
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 28.6065 0.923751
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.165390 −0.00532410
\(966\) 0 0
\(967\) −18.0703 −0.581101 −0.290551 0.956860i \(-0.593838\pi\)
−0.290551 + 0.956860i \(0.593838\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40.0000 1.28366 0.641831 0.766846i \(-0.278175\pi\)
0.641831 + 0.766846i \(0.278175\pi\)
\(972\) 0 0
\(973\) 17.3415 0.555942
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −13.1567 −0.420919 −0.210460 0.977603i \(-0.567496\pi\)
−0.210460 + 0.977603i \(0.567496\pi\)
\(978\) 0 0
\(979\) 16.7532 0.535436
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6.23568 0.198887 0.0994436 0.995043i \(-0.468294\pi\)
0.0994436 + 0.995043i \(0.468294\pi\)
\(984\) 0 0
\(985\) 3.66922 0.116911
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.882162 0.0280511
\(990\) 0 0
\(991\) 47.8661 1.52052 0.760258 0.649622i \(-0.225073\pi\)
0.760258 + 0.649622i \(0.225073\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.441081 0.0139832
\(996\) 0 0
\(997\) 44.9256 1.42281 0.711405 0.702783i \(-0.248059\pi\)
0.711405 + 0.702783i \(0.248059\pi\)
\(998\) 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 2736.2.a.bc.1.2 3
3.2 odd 2 2736.2.a.be.1.2 3
4.3 odd 2 1368.2.a.m.1.2 3
12.11 even 2 1368.2.a.o.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.a.m.1.2 3 4.3 odd 2
1368.2.a.o.1.2 yes 3 12.11 even 2
2736.2.a.bc.1.2 3 1.1 even 1 trivial
2736.2.a.be.1.2 3 3.2 odd 2