Properties

Label 9576.2.a.bc.1.1
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(76.4647449756\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.61803 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-3.61803 q^{5} +1.00000 q^{7} +5.85410 q^{11} +5.23607 q^{13} +2.47214 q^{17} -1.00000 q^{19} +5.70820 q^{23} +8.09017 q^{25} +0.854102 q^{29} +4.47214 q^{31} -3.61803 q^{35} -0.0901699 q^{37} +6.09017 q^{41} +6.85410 q^{43} +11.8541 q^{47} +1.00000 q^{49} +3.38197 q^{53} -21.1803 q^{55} -4.09017 q^{59} -7.85410 q^{61} -18.9443 q^{65} -14.9443 q^{67} -13.5623 q^{71} +8.76393 q^{73} +5.85410 q^{77} -6.85410 q^{79} -4.00000 q^{83} -8.94427 q^{85} -1.09017 q^{89} +5.23607 q^{91} +3.61803 q^{95} -3.56231 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 5 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 5 q^{5} + 2 q^{7} + 5 q^{11} + 6 q^{13} - 4 q^{17} - 2 q^{19} - 2 q^{23} + 5 q^{25} - 5 q^{29} - 5 q^{35} + 11 q^{37} + q^{41} + 7 q^{43} + 17 q^{47} + 2 q^{49} + 9 q^{53} - 20 q^{55} + 3 q^{59} - 9 q^{61} - 20 q^{65} - 12 q^{67} - 7 q^{71} + 22 q^{73} + 5 q^{77} - 7 q^{79} - 8 q^{83} + 9 q^{89} + 6 q^{91} + 5 q^{95} + 13 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.85410 1.76508 0.882539 0.470239i \(-0.155832\pi\)
0.882539 + 0.470239i \(0.155832\pi\)
\(12\) 0 0
\(13\) 5.23607 1.45222 0.726112 0.687576i \(-0.241325\pi\)
0.726112 + 0.687576i \(0.241325\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.47214 0.599581 0.299791 0.954005i \(-0.403083\pi\)
0.299791 + 0.954005i \(0.403083\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.70820 1.19024 0.595121 0.803636i \(-0.297104\pi\)
0.595121 + 0.803636i \(0.297104\pi\)
\(24\) 0 0
\(25\) 8.09017 1.61803
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.854102 0.158603 0.0793014 0.996851i \(-0.474731\pi\)
0.0793014 + 0.996851i \(0.474731\pi\)
\(30\) 0 0
\(31\) 4.47214 0.803219 0.401610 0.915811i \(-0.368451\pi\)
0.401610 + 0.915811i \(0.368451\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.61803 −0.611559
\(36\) 0 0
\(37\) −0.0901699 −0.0148238 −0.00741192 0.999973i \(-0.502359\pi\)
−0.00741192 + 0.999973i \(0.502359\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.09017 0.951125 0.475562 0.879682i \(-0.342245\pi\)
0.475562 + 0.879682i \(0.342245\pi\)
\(42\) 0 0
\(43\) 6.85410 1.04524 0.522620 0.852566i \(-0.324955\pi\)
0.522620 + 0.852566i \(0.324955\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.8541 1.72910 0.864549 0.502548i \(-0.167604\pi\)
0.864549 + 0.502548i \(0.167604\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.38197 0.464549 0.232274 0.972650i \(-0.425383\pi\)
0.232274 + 0.972650i \(0.425383\pi\)
\(54\) 0 0
\(55\) −21.1803 −2.85596
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.09017 −0.532495 −0.266247 0.963905i \(-0.585784\pi\)
−0.266247 + 0.963905i \(0.585784\pi\)
\(60\) 0 0
\(61\) −7.85410 −1.00561 −0.502807 0.864398i \(-0.667699\pi\)
−0.502807 + 0.864398i \(0.667699\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −18.9443 −2.34975
\(66\) 0 0
\(67\) −14.9443 −1.82573 −0.912867 0.408258i \(-0.866136\pi\)
−0.912867 + 0.408258i \(0.866136\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13.5623 −1.60955 −0.804775 0.593580i \(-0.797714\pi\)
−0.804775 + 0.593580i \(0.797714\pi\)
\(72\) 0 0
\(73\) 8.76393 1.02574 0.512870 0.858466i \(-0.328582\pi\)
0.512870 + 0.858466i \(0.328582\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.85410 0.667137
\(78\) 0 0
\(79\) −6.85410 −0.771147 −0.385573 0.922677i \(-0.625996\pi\)
−0.385573 + 0.922677i \(0.625996\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −8.94427 −0.970143
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.09017 −0.115558 −0.0577789 0.998329i \(-0.518402\pi\)
−0.0577789 + 0.998329i \(0.518402\pi\)
\(90\) 0 0
\(91\) 5.23607 0.548889
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.61803 0.371202
\(96\) 0 0
\(97\) −3.56231 −0.361697 −0.180849 0.983511i \(-0.557884\pi\)
−0.180849 + 0.983511i \(0.557884\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.9443 1.08900 0.544498 0.838762i \(-0.316720\pi\)
0.544498 + 0.838762i \(0.316720\pi\)
\(102\) 0 0
\(103\) 13.7082 1.35071 0.675355 0.737493i \(-0.263991\pi\)
0.675355 + 0.737493i \(0.263991\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.1803 −1.17752 −0.588759 0.808309i \(-0.700383\pi\)
−0.588759 + 0.808309i \(0.700383\pi\)
\(108\) 0 0
\(109\) 9.56231 0.915903 0.457951 0.888977i \(-0.348583\pi\)
0.457951 + 0.888977i \(0.348583\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.9443 −1.59398 −0.796992 0.603991i \(-0.793576\pi\)
−0.796992 + 0.603991i \(0.793576\pi\)
\(114\) 0 0
\(115\) −20.6525 −1.92585
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.47214 0.226620
\(120\) 0 0
\(121\) 23.2705 2.11550
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) 2.14590 0.190418 0.0952088 0.995457i \(-0.469648\pi\)
0.0952088 + 0.995457i \(0.469648\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 22.1803 1.93791 0.968953 0.247246i \(-0.0795257\pi\)
0.968953 + 0.247246i \(0.0795257\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.5623 −1.58588 −0.792942 0.609297i \(-0.791452\pi\)
−0.792942 + 0.609297i \(0.791452\pi\)
\(138\) 0 0
\(139\) −2.47214 −0.209684 −0.104842 0.994489i \(-0.533434\pi\)
−0.104842 + 0.994489i \(0.533434\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 30.6525 2.56329
\(144\) 0 0
\(145\) −3.09017 −0.256625
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.94427 0.732743 0.366372 0.930469i \(-0.380600\pi\)
0.366372 + 0.930469i \(0.380600\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −16.1803 −1.29964
\(156\) 0 0
\(157\) 18.6180 1.48588 0.742940 0.669358i \(-0.233431\pi\)
0.742940 + 0.669358i \(0.233431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.70820 0.449869
\(162\) 0 0
\(163\) 1.56231 0.122369 0.0611846 0.998126i \(-0.480512\pi\)
0.0611846 + 0.998126i \(0.480512\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) 14.4164 1.10895
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.180340 −0.0137110 −0.00685549 0.999977i \(-0.502182\pi\)
−0.00685549 + 0.999977i \(0.502182\pi\)
\(174\) 0 0
\(175\) 8.09017 0.611559
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −21.1246 −1.57893 −0.789464 0.613797i \(-0.789641\pi\)
−0.789464 + 0.613797i \(0.789641\pi\)
\(180\) 0 0
\(181\) −7.23607 −0.537853 −0.268926 0.963161i \(-0.586669\pi\)
−0.268926 + 0.963161i \(0.586669\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.326238 0.0239855
\(186\) 0 0
\(187\) 14.4721 1.05831
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.70820 −0.123601 −0.0618006 0.998089i \(-0.519684\pi\)
−0.0618006 + 0.998089i \(0.519684\pi\)
\(192\) 0 0
\(193\) 7.23607 0.520864 0.260432 0.965492i \(-0.416135\pi\)
0.260432 + 0.965492i \(0.416135\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 1.03444 0.0733296 0.0366648 0.999328i \(-0.488327\pi\)
0.0366648 + 0.999328i \(0.488327\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.854102 0.0599462
\(204\) 0 0
\(205\) −22.0344 −1.53895
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.85410 −0.404937
\(210\) 0 0
\(211\) −13.8885 −0.956127 −0.478063 0.878325i \(-0.658661\pi\)
−0.478063 + 0.878325i \(0.658661\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −24.7984 −1.69124
\(216\) 0 0
\(217\) 4.47214 0.303588
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.9443 0.870726
\(222\) 0 0
\(223\) 2.18034 0.146006 0.0730032 0.997332i \(-0.476742\pi\)
0.0730032 + 0.997332i \(0.476742\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.9443 0.859142 0.429571 0.903033i \(-0.358665\pi\)
0.429571 + 0.903033i \(0.358665\pi\)
\(228\) 0 0
\(229\) −9.32624 −0.616295 −0.308148 0.951339i \(-0.599709\pi\)
−0.308148 + 0.951339i \(0.599709\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.1459 0.664680 0.332340 0.943160i \(-0.392162\pi\)
0.332340 + 0.943160i \(0.392162\pi\)
\(234\) 0 0
\(235\) −42.8885 −2.79774
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.29180 0.536352 0.268176 0.963370i \(-0.413579\pi\)
0.268176 + 0.963370i \(0.413579\pi\)
\(240\) 0 0
\(241\) 4.56231 0.293884 0.146942 0.989145i \(-0.453057\pi\)
0.146942 + 0.989145i \(0.453057\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.61803 −0.231148
\(246\) 0 0
\(247\) −5.23607 −0.333163
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −29.2361 −1.84536 −0.922682 0.385562i \(-0.874008\pi\)
−0.922682 + 0.385562i \(0.874008\pi\)
\(252\) 0 0
\(253\) 33.4164 2.10087
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.67376 0.166785 0.0833923 0.996517i \(-0.473425\pi\)
0.0833923 + 0.996517i \(0.473425\pi\)
\(258\) 0 0
\(259\) −0.0901699 −0.00560289
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 25.2361 1.55612 0.778061 0.628188i \(-0.216203\pi\)
0.778061 + 0.628188i \(0.216203\pi\)
\(264\) 0 0
\(265\) −12.2361 −0.751656
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.4164 1.79355 0.896775 0.442487i \(-0.145904\pi\)
0.896775 + 0.442487i \(0.145904\pi\)
\(270\) 0 0
\(271\) 16.8541 1.02381 0.511907 0.859041i \(-0.328939\pi\)
0.511907 + 0.859041i \(0.328939\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 47.3607 2.85596
\(276\) 0 0
\(277\) −18.2918 −1.09905 −0.549524 0.835478i \(-0.685191\pi\)
−0.549524 + 0.835478i \(0.685191\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 17.8885 1.06714 0.533571 0.845756i \(-0.320850\pi\)
0.533571 + 0.845756i \(0.320850\pi\)
\(282\) 0 0
\(283\) 5.52786 0.328597 0.164299 0.986411i \(-0.447464\pi\)
0.164299 + 0.986411i \(0.447464\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.09017 0.359491
\(288\) 0 0
\(289\) −10.8885 −0.640503
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.23607 −0.305894 −0.152947 0.988234i \(-0.548876\pi\)
−0.152947 + 0.988234i \(0.548876\pi\)
\(294\) 0 0
\(295\) 14.7984 0.861595
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 29.8885 1.72850
\(300\) 0 0
\(301\) 6.85410 0.395064
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 28.4164 1.62712
\(306\) 0 0
\(307\) 3.90983 0.223146 0.111573 0.993756i \(-0.464411\pi\)
0.111573 + 0.993756i \(0.464411\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −25.4508 −1.44319 −0.721593 0.692318i \(-0.756590\pi\)
−0.721593 + 0.692318i \(0.756590\pi\)
\(312\) 0 0
\(313\) −8.00000 −0.452187 −0.226093 0.974106i \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.67376 0.431001 0.215501 0.976504i \(-0.430862\pi\)
0.215501 + 0.976504i \(0.430862\pi\)
\(318\) 0 0
\(319\) 5.00000 0.279946
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.47214 −0.137553
\(324\) 0 0
\(325\) 42.3607 2.34975
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.8541 0.653538
\(330\) 0 0
\(331\) −27.3050 −1.50082 −0.750408 0.660975i \(-0.770143\pi\)
−0.750408 + 0.660975i \(0.770143\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 54.0689 2.95410
\(336\) 0 0
\(337\) −9.23607 −0.503121 −0.251560 0.967842i \(-0.580944\pi\)
−0.251560 + 0.967842i \(0.580944\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 26.1803 1.41774
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.47214 0.132711 0.0663556 0.997796i \(-0.478863\pi\)
0.0663556 + 0.997796i \(0.478863\pi\)
\(348\) 0 0
\(349\) −15.8885 −0.850494 −0.425247 0.905077i \(-0.639813\pi\)
−0.425247 + 0.905077i \(0.639813\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.3607 1.29659 0.648294 0.761390i \(-0.275483\pi\)
0.648294 + 0.761390i \(0.275483\pi\)
\(354\) 0 0
\(355\) 49.0689 2.60431
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.7639 0.673655 0.336827 0.941566i \(-0.390646\pi\)
0.336827 + 0.941566i \(0.390646\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −31.7082 −1.65968
\(366\) 0 0
\(367\) 5.67376 0.296168 0.148084 0.988975i \(-0.452689\pi\)
0.148084 + 0.988975i \(0.452689\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.38197 0.175583
\(372\) 0 0
\(373\) 9.03444 0.467786 0.233893 0.972262i \(-0.424854\pi\)
0.233893 + 0.972262i \(0.424854\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.47214 0.230327
\(378\) 0 0
\(379\) 35.1246 1.80423 0.902115 0.431496i \(-0.142014\pi\)
0.902115 + 0.431496i \(0.142014\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −26.0689 −1.33206 −0.666029 0.745926i \(-0.732007\pi\)
−0.666029 + 0.745926i \(0.732007\pi\)
\(384\) 0 0
\(385\) −21.1803 −1.07945
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −30.3607 −1.53935 −0.769674 0.638437i \(-0.779581\pi\)
−0.769674 + 0.638437i \(0.779581\pi\)
\(390\) 0 0
\(391\) 14.1115 0.713647
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 24.7984 1.24774
\(396\) 0 0
\(397\) 36.5066 1.83221 0.916106 0.400935i \(-0.131315\pi\)
0.916106 + 0.400935i \(0.131315\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.88854 −0.493810 −0.246905 0.969040i \(-0.579414\pi\)
−0.246905 + 0.969040i \(0.579414\pi\)
\(402\) 0 0
\(403\) 23.4164 1.16645
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.527864 −0.0261652
\(408\) 0 0
\(409\) −9.09017 −0.449480 −0.224740 0.974419i \(-0.572153\pi\)
−0.224740 + 0.974419i \(0.572153\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.09017 −0.201264
\(414\) 0 0
\(415\) 14.4721 0.710409
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.4721 −1.39095 −0.695477 0.718548i \(-0.744807\pi\)
−0.695477 + 0.718548i \(0.744807\pi\)
\(420\) 0 0
\(421\) −20.4721 −0.997751 −0.498875 0.866674i \(-0.666253\pi\)
−0.498875 + 0.866674i \(0.666253\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 20.0000 0.970143
\(426\) 0 0
\(427\) −7.85410 −0.380087
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 23.0902 1.11221 0.556107 0.831111i \(-0.312294\pi\)
0.556107 + 0.831111i \(0.312294\pi\)
\(432\) 0 0
\(433\) −18.2705 −0.878025 −0.439012 0.898481i \(-0.644672\pi\)
−0.439012 + 0.898481i \(0.644672\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.70820 −0.273060
\(438\) 0 0
\(439\) −23.3050 −1.11228 −0.556142 0.831087i \(-0.687719\pi\)
−0.556142 + 0.831087i \(0.687719\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.27051 0.297921 0.148960 0.988843i \(-0.452407\pi\)
0.148960 + 0.988843i \(0.452407\pi\)
\(444\) 0 0
\(445\) 3.94427 0.186976
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −26.1803 −1.23553 −0.617763 0.786364i \(-0.711961\pi\)
−0.617763 + 0.786364i \(0.711961\pi\)
\(450\) 0 0
\(451\) 35.6525 1.67881
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −18.9443 −0.888121
\(456\) 0 0
\(457\) 29.2705 1.36922 0.684608 0.728911i \(-0.259973\pi\)
0.684608 + 0.728911i \(0.259973\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −26.0344 −1.21254 −0.606272 0.795257i \(-0.707336\pi\)
−0.606272 + 0.795257i \(0.707336\pi\)
\(462\) 0 0
\(463\) 5.23607 0.243341 0.121670 0.992571i \(-0.461175\pi\)
0.121670 + 0.992571i \(0.461175\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.18034 0.193443 0.0967215 0.995311i \(-0.469164\pi\)
0.0967215 + 0.995311i \(0.469164\pi\)
\(468\) 0 0
\(469\) −14.9443 −0.690062
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 40.1246 1.84493
\(474\) 0 0
\(475\) −8.09017 −0.371202
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 37.3951 1.70863 0.854313 0.519758i \(-0.173978\pi\)
0.854313 + 0.519758i \(0.173978\pi\)
\(480\) 0 0
\(481\) −0.472136 −0.0215275
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.8885 0.585239
\(486\) 0 0
\(487\) 17.1459 0.776955 0.388477 0.921458i \(-0.373001\pi\)
0.388477 + 0.921458i \(0.373001\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.88854 0.265746 0.132873 0.991133i \(-0.457580\pi\)
0.132873 + 0.991133i \(0.457580\pi\)
\(492\) 0 0
\(493\) 2.11146 0.0950952
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.5623 −0.608353
\(498\) 0 0
\(499\) 31.0344 1.38929 0.694646 0.719352i \(-0.255561\pi\)
0.694646 + 0.719352i \(0.255561\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.14590 0.318620 0.159310 0.987229i \(-0.449073\pi\)
0.159310 + 0.987229i \(0.449073\pi\)
\(504\) 0 0
\(505\) −39.5967 −1.76203
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.76393 −0.211158 −0.105579 0.994411i \(-0.533670\pi\)
−0.105579 + 0.994411i \(0.533670\pi\)
\(510\) 0 0
\(511\) 8.76393 0.387694
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −49.5967 −2.18549
\(516\) 0 0
\(517\) 69.3951 3.05199
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −23.3050 −1.02101 −0.510504 0.859875i \(-0.670541\pi\)
−0.510504 + 0.859875i \(0.670541\pi\)
\(522\) 0 0
\(523\) 33.8885 1.48184 0.740921 0.671592i \(-0.234389\pi\)
0.740921 + 0.671592i \(0.234389\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.0557 0.481595
\(528\) 0 0
\(529\) 9.58359 0.416678
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 31.8885 1.38125
\(534\) 0 0
\(535\) 44.0689 1.90526
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.85410 0.252154
\(540\) 0 0
\(541\) 13.7082 0.589362 0.294681 0.955596i \(-0.404787\pi\)
0.294681 + 0.955596i \(0.404787\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −34.5967 −1.48196
\(546\) 0 0
\(547\) −25.7082 −1.09920 −0.549602 0.835427i \(-0.685221\pi\)
−0.549602 + 0.835427i \(0.685221\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.854102 −0.0363860
\(552\) 0 0
\(553\) −6.85410 −0.291466
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.81966 −0.0771015 −0.0385507 0.999257i \(-0.512274\pi\)
−0.0385507 + 0.999257i \(0.512274\pi\)
\(558\) 0 0
\(559\) 35.8885 1.51792
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20.7984 −0.876547 −0.438273 0.898842i \(-0.644410\pi\)
−0.438273 + 0.898842i \(0.644410\pi\)
\(564\) 0 0
\(565\) 61.3050 2.57912
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.7082 −0.574678 −0.287339 0.957829i \(-0.592771\pi\)
−0.287339 + 0.957829i \(0.592771\pi\)
\(570\) 0 0
\(571\) 34.2148 1.43184 0.715922 0.698180i \(-0.246007\pi\)
0.715922 + 0.698180i \(0.246007\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 46.1803 1.92585
\(576\) 0 0
\(577\) −18.9443 −0.788660 −0.394330 0.918969i \(-0.629023\pi\)
−0.394330 + 0.918969i \(0.629023\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.00000 −0.165948
\(582\) 0 0
\(583\) 19.7984 0.819965
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −21.1246 −0.871906 −0.435953 0.899969i \(-0.643589\pi\)
−0.435953 + 0.899969i \(0.643589\pi\)
\(588\) 0 0
\(589\) −4.47214 −0.184271
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.1246 0.538963 0.269482 0.963006i \(-0.413148\pi\)
0.269482 + 0.963006i \(0.413148\pi\)
\(594\) 0 0
\(595\) −8.94427 −0.366679
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 42.7984 1.74869 0.874347 0.485301i \(-0.161290\pi\)
0.874347 + 0.485301i \(0.161290\pi\)
\(600\) 0 0
\(601\) 7.88854 0.321780 0.160890 0.986972i \(-0.448563\pi\)
0.160890 + 0.986972i \(0.448563\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −84.1935 −3.42295
\(606\) 0 0
\(607\) 9.23607 0.374880 0.187440 0.982276i \(-0.439981\pi\)
0.187440 + 0.982276i \(0.439981\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 62.0689 2.51104
\(612\) 0 0
\(613\) 16.9443 0.684373 0.342186 0.939632i \(-0.388833\pi\)
0.342186 + 0.939632i \(0.388833\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −31.9098 −1.28464 −0.642321 0.766436i \(-0.722028\pi\)
−0.642321 + 0.766436i \(0.722028\pi\)
\(618\) 0 0
\(619\) 18.2918 0.735209 0.367605 0.929982i \(-0.380178\pi\)
0.367605 + 0.929982i \(0.380178\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.09017 −0.0436767
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.222912 −0.00888810
\(630\) 0 0
\(631\) 40.3607 1.60673 0.803367 0.595485i \(-0.203040\pi\)
0.803367 + 0.595485i \(0.203040\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.76393 −0.308102
\(636\) 0 0
\(637\) 5.23607 0.207461
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22.6525 0.894719 0.447360 0.894354i \(-0.352364\pi\)
0.447360 + 0.894354i \(0.352364\pi\)
\(642\) 0 0
\(643\) 37.5279 1.47995 0.739977 0.672632i \(-0.234836\pi\)
0.739977 + 0.672632i \(0.234836\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.2705 0.796916 0.398458 0.917187i \(-0.369545\pi\)
0.398458 + 0.917187i \(0.369545\pi\)
\(648\) 0 0
\(649\) −23.9443 −0.939895
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 32.6525 1.27779 0.638895 0.769294i \(-0.279392\pi\)
0.638895 + 0.769294i \(0.279392\pi\)
\(654\) 0 0
\(655\) −80.2492 −3.13560
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.94427 0.348419 0.174210 0.984709i \(-0.444263\pi\)
0.174210 + 0.984709i \(0.444263\pi\)
\(660\) 0 0
\(661\) −16.8328 −0.654721 −0.327360 0.944900i \(-0.606159\pi\)
−0.327360 + 0.944900i \(0.606159\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.61803 0.140301
\(666\) 0 0
\(667\) 4.87539 0.188776
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −45.9787 −1.77499
\(672\) 0 0
\(673\) −25.2361 −0.972779 −0.486389 0.873742i \(-0.661686\pi\)
−0.486389 + 0.873742i \(0.661686\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) −3.56231 −0.136709
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23.8885 −0.914070 −0.457035 0.889449i \(-0.651089\pi\)
−0.457035 + 0.889449i \(0.651089\pi\)
\(684\) 0 0
\(685\) 67.1591 2.56602
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 17.7082 0.674629
\(690\) 0 0
\(691\) −38.6525 −1.47041 −0.735205 0.677845i \(-0.762914\pi\)
−0.735205 + 0.677845i \(0.762914\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.94427 0.339276
\(696\) 0 0
\(697\) 15.0557 0.570276
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −39.2361 −1.48193 −0.740963 0.671546i \(-0.765631\pi\)
−0.740963 + 0.671546i \(0.765631\pi\)
\(702\) 0 0
\(703\) 0.0901699 0.00340082
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.9443 0.411602
\(708\) 0 0
\(709\) 18.1803 0.682777 0.341388 0.939922i \(-0.389103\pi\)
0.341388 + 0.939922i \(0.389103\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 25.5279 0.956026
\(714\) 0 0
\(715\) −110.902 −4.14749
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −25.8885 −0.965480 −0.482740 0.875764i \(-0.660358\pi\)
−0.482740 + 0.875764i \(0.660358\pi\)
\(720\) 0 0
\(721\) 13.7082 0.510520
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.90983 0.256625
\(726\) 0 0
\(727\) 15.5623 0.577174 0.288587 0.957454i \(-0.406815\pi\)
0.288587 + 0.957454i \(0.406815\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.9443 0.626707
\(732\) 0 0
\(733\) −27.4377 −1.01343 −0.506717 0.862112i \(-0.669141\pi\)
−0.506717 + 0.862112i \(0.669141\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −87.4853 −3.22256
\(738\) 0 0
\(739\) −32.5623 −1.19782 −0.598912 0.800815i \(-0.704400\pi\)
−0.598912 + 0.800815i \(0.704400\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.79837 −0.139349 −0.0696744 0.997570i \(-0.522196\pi\)
−0.0696744 + 0.997570i \(0.522196\pi\)
\(744\) 0 0
\(745\) −32.3607 −1.18560
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.1803 −0.445060
\(750\) 0 0
\(751\) 13.9098 0.507577 0.253788 0.967260i \(-0.418323\pi\)
0.253788 + 0.967260i \(0.418323\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 72.3607 2.63347
\(756\) 0 0
\(757\) 21.5279 0.782444 0.391222 0.920296i \(-0.372053\pi\)
0.391222 + 0.920296i \(0.372053\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10.9443 0.396730 0.198365 0.980128i \(-0.436437\pi\)
0.198365 + 0.980128i \(0.436437\pi\)
\(762\) 0 0
\(763\) 9.56231 0.346179
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −21.4164 −0.773302
\(768\) 0 0
\(769\) 30.6525 1.10536 0.552678 0.833395i \(-0.313606\pi\)
0.552678 + 0.833395i \(0.313606\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 37.7082 1.35627 0.678135 0.734937i \(-0.262789\pi\)
0.678135 + 0.734937i \(0.262789\pi\)
\(774\) 0 0
\(775\) 36.1803 1.29964
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.09017 −0.218203
\(780\) 0 0
\(781\) −79.3951 −2.84098
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −67.3607 −2.40421
\(786\) 0 0
\(787\) −28.6738 −1.02211 −0.511055 0.859548i \(-0.670745\pi\)
−0.511055 + 0.859548i \(0.670745\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −16.9443 −0.602469
\(792\) 0 0
\(793\) −41.1246 −1.46038
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −49.7082 −1.76075 −0.880377 0.474274i \(-0.842711\pi\)
−0.880377 + 0.474274i \(0.842711\pi\)
\(798\) 0 0
\(799\) 29.3050 1.03673
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 51.3050 1.81051
\(804\) 0 0
\(805\) −20.6525 −0.727904
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −9.03444 −0.317634 −0.158817 0.987308i \(-0.550768\pi\)
−0.158817 + 0.987308i \(0.550768\pi\)
\(810\) 0 0
\(811\) −5.45085 −0.191405 −0.0957026 0.995410i \(-0.530510\pi\)
−0.0957026 + 0.995410i \(0.530510\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.65248 −0.197998
\(816\) 0 0
\(817\) −6.85410 −0.239795
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33.4164 −1.16624 −0.583120 0.812386i \(-0.698168\pi\)
−0.583120 + 0.812386i \(0.698168\pi\)
\(822\) 0 0
\(823\) −29.4164 −1.02539 −0.512696 0.858570i \(-0.671353\pi\)
−0.512696 + 0.858570i \(0.671353\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18.0689 −0.628317 −0.314158 0.949371i \(-0.601722\pi\)
−0.314158 + 0.949371i \(0.601722\pi\)
\(828\) 0 0
\(829\) −31.4164 −1.09114 −0.545568 0.838066i \(-0.683686\pi\)
−0.545568 + 0.838066i \(0.683686\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.47214 0.0856544
\(834\) 0 0
\(835\) −7.23607 −0.250414
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 21.0557 0.726924 0.363462 0.931609i \(-0.381595\pi\)
0.363462 + 0.931609i \(0.381595\pi\)
\(840\) 0 0
\(841\) −28.2705 −0.974845
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −52.1591 −1.79433
\(846\) 0 0
\(847\) 23.2705 0.799584
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −0.514708 −0.0176440
\(852\) 0 0
\(853\) 1.90983 0.0653913 0.0326957 0.999465i \(-0.489591\pi\)
0.0326957 + 0.999465i \(0.489591\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −50.0000 −1.70797 −0.853984 0.520300i \(-0.825820\pi\)
−0.853984 + 0.520300i \(0.825820\pi\)
\(858\) 0 0
\(859\) −7.59675 −0.259198 −0.129599 0.991567i \(-0.541369\pi\)
−0.129599 + 0.991567i \(0.541369\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −6.27051 −0.213451 −0.106725 0.994289i \(-0.534037\pi\)
−0.106725 + 0.994289i \(0.534037\pi\)
\(864\) 0 0
\(865\) 0.652476 0.0221848
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −40.1246 −1.36113
\(870\) 0 0
\(871\) −78.2492 −2.65137
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −11.1803 −0.377964
\(876\) 0 0
\(877\) −34.4377 −1.16288 −0.581439 0.813590i \(-0.697510\pi\)
−0.581439 + 0.813590i \(0.697510\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −17.5967 −0.592849 −0.296425 0.955056i \(-0.595794\pi\)
−0.296425 + 0.955056i \(0.595794\pi\)
\(882\) 0 0
\(883\) −19.9656 −0.671895 −0.335947 0.941881i \(-0.609056\pi\)
−0.335947 + 0.941881i \(0.609056\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 17.4164 0.584786 0.292393 0.956298i \(-0.405549\pi\)
0.292393 + 0.956298i \(0.405549\pi\)
\(888\) 0 0
\(889\) 2.14590 0.0719711
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −11.8541 −0.396682
\(894\) 0 0
\(895\) 76.4296 2.55476
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.81966 0.127393
\(900\) 0 0
\(901\) 8.36068 0.278535
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 26.1803 0.870264
\(906\) 0 0
\(907\) 29.0132 0.963366 0.481683 0.876346i \(-0.340026\pi\)
0.481683 + 0.876346i \(0.340026\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 43.9787 1.45708 0.728540 0.685003i \(-0.240199\pi\)
0.728540 + 0.685003i \(0.240199\pi\)
\(912\) 0 0
\(913\) −23.4164 −0.774970
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 22.1803 0.732459
\(918\) 0 0
\(919\) 39.5967 1.30618 0.653088 0.757282i \(-0.273473\pi\)
0.653088 + 0.757282i \(0.273473\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −71.0132 −2.33743
\(924\) 0 0
\(925\) −0.729490 −0.0239855
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.76393 0.0906817 0.0453408 0.998972i \(-0.485563\pi\)
0.0453408 + 0.998972i \(0.485563\pi\)
\(930\) 0 0
\(931\) −1.00000 −0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −52.3607 −1.71238
\(936\) 0 0
\(937\) −25.8885 −0.845742 −0.422871 0.906190i \(-0.638978\pi\)
−0.422871 + 0.906190i \(0.638978\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 58.5410 1.90838 0.954191 0.299197i \(-0.0967188\pi\)
0.954191 + 0.299197i \(0.0967188\pi\)
\(942\) 0 0
\(943\) 34.7639 1.13207
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12.6869 −0.412269 −0.206135 0.978524i \(-0.566089\pi\)
−0.206135 + 0.978524i \(0.566089\pi\)
\(948\) 0 0
\(949\) 45.8885 1.48961
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.4721 1.18145 0.590724 0.806874i \(-0.298842\pi\)
0.590724 + 0.806874i \(0.298842\pi\)
\(954\) 0 0
\(955\) 6.18034 0.199991
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18.5623 −0.599408
\(960\) 0 0
\(961\) −11.0000 −0.354839
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −26.1803 −0.842775
\(966\) 0 0
\(967\) −15.4164 −0.495758 −0.247879 0.968791i \(-0.579734\pi\)
−0.247879 + 0.968791i \(0.579734\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.43769 0.142412 0.0712062 0.997462i \(-0.477315\pi\)
0.0712062 + 0.997462i \(0.477315\pi\)
\(972\) 0 0
\(973\) −2.47214 −0.0792530
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.06888 0.0661895 0.0330947 0.999452i \(-0.489464\pi\)
0.0330947 + 0.999452i \(0.489464\pi\)
\(978\) 0 0
\(979\) −6.38197 −0.203969
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 31.0557 0.990524 0.495262 0.868744i \(-0.335072\pi\)
0.495262 + 0.868744i \(0.335072\pi\)
\(984\) 0 0
\(985\) 65.1246 2.07504
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 39.1246 1.24409
\(990\) 0 0
\(991\) 23.6738 0.752022 0.376011 0.926615i \(-0.377296\pi\)
0.376011 + 0.926615i \(0.377296\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.74265 −0.118650
\(996\) 0 0
\(997\) −14.4508 −0.457663 −0.228832 0.973466i \(-0.573490\pi\)
−0.228832 + 0.973466i \(0.573490\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 9576.2.a.bc.1.1 2
3.2 odd 2 1064.2.a.e.1.2 2
12.11 even 2 2128.2.a.d.1.1 2
21.20 even 2 7448.2.a.y.1.1 2
24.5 odd 2 8512.2.a.e.1.1 2
24.11 even 2 8512.2.a.ba.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.a.e.1.2 2 3.2 odd 2
2128.2.a.d.1.1 2 12.11 even 2
7448.2.a.y.1.1 2 21.20 even 2
8512.2.a.e.1.1 2 24.5 odd 2
8512.2.a.ba.1.2 2 24.11 even 2
9576.2.a.bc.1.1 2 1.1 even 1 trivial