Properties

Label 1064.2.a.b.1.1
Level $1064$
Weight $2$
Character 1064.1
Self dual yes
Analytic conductor $8.496$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1064,2,Mod(1,1064)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1064, 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("1064.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.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: \(8.49608277506\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 1064.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.30278 q^{3} -1.00000 q^{5} -1.00000 q^{7} +2.30278 q^{9} +O(q^{10})\) \(q-2.30278 q^{3} -1.00000 q^{5} -1.00000 q^{7} +2.30278 q^{9} +1.30278 q^{11} +3.60555 q^{13} +2.30278 q^{15} +5.30278 q^{17} +1.00000 q^{19} +2.30278 q^{21} -7.60555 q^{23} -4.00000 q^{25} +1.60555 q^{27} -0.697224 q^{29} -4.69722 q^{31} -3.00000 q^{33} +1.00000 q^{35} -3.60555 q^{37} -8.30278 q^{39} -3.30278 q^{41} -7.21110 q^{43} -2.30278 q^{45} -0.394449 q^{47} +1.00000 q^{49} -12.2111 q^{51} +6.90833 q^{53} -1.30278 q^{55} -2.30278 q^{57} -1.60555 q^{59} -6.21110 q^{61} -2.30278 q^{63} -3.60555 q^{65} -0.0916731 q^{67} +17.5139 q^{69} -12.8167 q^{71} +4.90833 q^{73} +9.21110 q^{75} -1.30278 q^{77} -14.0000 q^{79} -10.6056 q^{81} +7.51388 q^{83} -5.30278 q^{85} +1.60555 q^{87} -7.81665 q^{89} -3.60555 q^{91} +10.8167 q^{93} -1.00000 q^{95} -4.81665 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - q^{11} + q^{15} + 7 q^{17} + 2 q^{19} + q^{21} - 8 q^{23} - 8 q^{25} - 4 q^{27} - 5 q^{29} - 13 q^{31} - 6 q^{33} + 2 q^{35} - 13 q^{39} - 3 q^{41} - q^{45} - 8 q^{47} + 2 q^{49} - 10 q^{51} + 3 q^{53} + q^{55} - q^{57} + 4 q^{59} + 2 q^{61} - q^{63} - 11 q^{67} + 17 q^{69} - 4 q^{71} - q^{73} + 4 q^{75} + q^{77} - 28 q^{79} - 14 q^{81} - 3 q^{83} - 7 q^{85} - 4 q^{87} + 6 q^{89} - 2 q^{95} + 12 q^{97} + 6 q^{99}+O(q^{100}) \) 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
\(3\) −2.30278 −1.32951 −0.664754 0.747062i \(-0.731464\pi\)
−0.664754 + 0.747062i \(0.731464\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.30278 0.767592
\(10\) 0 0
\(11\) 1.30278 0.392802 0.196401 0.980524i \(-0.437075\pi\)
0.196401 + 0.980524i \(0.437075\pi\)
\(12\) 0 0
\(13\) 3.60555 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0 0
\(15\) 2.30278 0.594574
\(16\) 0 0
\(17\) 5.30278 1.28611 0.643056 0.765819i \(-0.277666\pi\)
0.643056 + 0.765819i \(0.277666\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 2.30278 0.502507
\(22\) 0 0
\(23\) −7.60555 −1.58587 −0.792934 0.609308i \(-0.791447\pi\)
−0.792934 + 0.609308i \(0.791447\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.60555 0.308988
\(28\) 0 0
\(29\) −0.697224 −0.129471 −0.0647357 0.997902i \(-0.520620\pi\)
−0.0647357 + 0.997902i \(0.520620\pi\)
\(30\) 0 0
\(31\) −4.69722 −0.843646 −0.421823 0.906678i \(-0.638610\pi\)
−0.421823 + 0.906678i \(0.638610\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −3.60555 −0.592749 −0.296374 0.955072i \(-0.595778\pi\)
−0.296374 + 0.955072i \(0.595778\pi\)
\(38\) 0 0
\(39\) −8.30278 −1.32951
\(40\) 0 0
\(41\) −3.30278 −0.515807 −0.257903 0.966171i \(-0.583032\pi\)
−0.257903 + 0.966171i \(0.583032\pi\)
\(42\) 0 0
\(43\) −7.21110 −1.09968 −0.549841 0.835269i \(-0.685312\pi\)
−0.549841 + 0.835269i \(0.685312\pi\)
\(44\) 0 0
\(45\) −2.30278 −0.343278
\(46\) 0 0
\(47\) −0.394449 −0.0575363 −0.0287681 0.999586i \(-0.509158\pi\)
−0.0287681 + 0.999586i \(0.509158\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −12.2111 −1.70990
\(52\) 0 0
\(53\) 6.90833 0.948932 0.474466 0.880274i \(-0.342641\pi\)
0.474466 + 0.880274i \(0.342641\pi\)
\(54\) 0 0
\(55\) −1.30278 −0.175666
\(56\) 0 0
\(57\) −2.30278 −0.305010
\(58\) 0 0
\(59\) −1.60555 −0.209025 −0.104512 0.994524i \(-0.533328\pi\)
−0.104512 + 0.994524i \(0.533328\pi\)
\(60\) 0 0
\(61\) −6.21110 −0.795250 −0.397625 0.917548i \(-0.630166\pi\)
−0.397625 + 0.917548i \(0.630166\pi\)
\(62\) 0 0
\(63\) −2.30278 −0.290122
\(64\) 0 0
\(65\) −3.60555 −0.447214
\(66\) 0 0
\(67\) −0.0916731 −0.0111997 −0.00559983 0.999984i \(-0.501782\pi\)
−0.00559983 + 0.999984i \(0.501782\pi\)
\(68\) 0 0
\(69\) 17.5139 2.10842
\(70\) 0 0
\(71\) −12.8167 −1.52106 −0.760528 0.649305i \(-0.775060\pi\)
−0.760528 + 0.649305i \(0.775060\pi\)
\(72\) 0 0
\(73\) 4.90833 0.574476 0.287238 0.957859i \(-0.407263\pi\)
0.287238 + 0.957859i \(0.407263\pi\)
\(74\) 0 0
\(75\) 9.21110 1.06361
\(76\) 0 0
\(77\) −1.30278 −0.148465
\(78\) 0 0
\(79\) −14.0000 −1.57512 −0.787562 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(80\) 0 0
\(81\) −10.6056 −1.17839
\(82\) 0 0
\(83\) 7.51388 0.824755 0.412378 0.911013i \(-0.364698\pi\)
0.412378 + 0.911013i \(0.364698\pi\)
\(84\) 0 0
\(85\) −5.30278 −0.575167
\(86\) 0 0
\(87\) 1.60555 0.172133
\(88\) 0 0
\(89\) −7.81665 −0.828564 −0.414282 0.910149i \(-0.635967\pi\)
−0.414282 + 0.910149i \(0.635967\pi\)
\(90\) 0 0
\(91\) −3.60555 −0.377964
\(92\) 0 0
\(93\) 10.8167 1.12163
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) −4.81665 −0.489057 −0.244529 0.969642i \(-0.578633\pi\)
−0.244529 + 0.969642i \(0.578633\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 9.60555 0.955788 0.477894 0.878417i \(-0.341400\pi\)
0.477894 + 0.878417i \(0.341400\pi\)
\(102\) 0 0
\(103\) −11.6056 −1.14353 −0.571764 0.820418i \(-0.693741\pi\)
−0.571764 + 0.820418i \(0.693741\pi\)
\(104\) 0 0
\(105\) −2.30278 −0.224728
\(106\) 0 0
\(107\) −10.8167 −1.04569 −0.522843 0.852429i \(-0.675128\pi\)
−0.522843 + 0.852429i \(0.675128\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 8.30278 0.788065
\(112\) 0 0
\(113\) −8.11943 −0.763812 −0.381906 0.924201i \(-0.624732\pi\)
−0.381906 + 0.924201i \(0.624732\pi\)
\(114\) 0 0
\(115\) 7.60555 0.709221
\(116\) 0 0
\(117\) 8.30278 0.767592
\(118\) 0 0
\(119\) −5.30278 −0.486105
\(120\) 0 0
\(121\) −9.30278 −0.845707
\(122\) 0 0
\(123\) 7.60555 0.685769
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 21.0278 1.86591 0.932956 0.359991i \(-0.117220\pi\)
0.932956 + 0.359991i \(0.117220\pi\)
\(128\) 0 0
\(129\) 16.6056 1.46204
\(130\) 0 0
\(131\) −10.6972 −0.934621 −0.467310 0.884093i \(-0.654777\pi\)
−0.467310 + 0.884093i \(0.654777\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) −1.60555 −0.138184
\(136\) 0 0
\(137\) 15.2111 1.29957 0.649786 0.760117i \(-0.274858\pi\)
0.649786 + 0.760117i \(0.274858\pi\)
\(138\) 0 0
\(139\) 11.6056 0.984370 0.492185 0.870491i \(-0.336198\pi\)
0.492185 + 0.870491i \(0.336198\pi\)
\(140\) 0 0
\(141\) 0.908327 0.0764949
\(142\) 0 0
\(143\) 4.69722 0.392802
\(144\) 0 0
\(145\) 0.697224 0.0579013
\(146\) 0 0
\(147\) −2.30278 −0.189930
\(148\) 0 0
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) −15.9083 −1.29460 −0.647301 0.762235i \(-0.724102\pi\)
−0.647301 + 0.762235i \(0.724102\pi\)
\(152\) 0 0
\(153\) 12.2111 0.987209
\(154\) 0 0
\(155\) 4.69722 0.377290
\(156\) 0 0
\(157\) −20.5139 −1.63719 −0.818593 0.574374i \(-0.805245\pi\)
−0.818593 + 0.574374i \(0.805245\pi\)
\(158\) 0 0
\(159\) −15.9083 −1.26161
\(160\) 0 0
\(161\) 7.60555 0.599401
\(162\) 0 0
\(163\) 17.5139 1.37179 0.685896 0.727699i \(-0.259410\pi\)
0.685896 + 0.727699i \(0.259410\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) 0 0
\(167\) 7.42221 0.574347 0.287174 0.957879i \(-0.407284\pi\)
0.287174 + 0.957879i \(0.407284\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 2.30278 0.176098
\(172\) 0 0
\(173\) −7.81665 −0.594289 −0.297145 0.954832i \(-0.596034\pi\)
−0.297145 + 0.954832i \(0.596034\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 3.69722 0.277900
\(178\) 0 0
\(179\) −4.69722 −0.351087 −0.175544 0.984472i \(-0.556168\pi\)
−0.175544 + 0.984472i \(0.556168\pi\)
\(180\) 0 0
\(181\) 9.30278 0.691470 0.345735 0.938332i \(-0.387630\pi\)
0.345735 + 0.938332i \(0.387630\pi\)
\(182\) 0 0
\(183\) 14.3028 1.05729
\(184\) 0 0
\(185\) 3.60555 0.265085
\(186\) 0 0
\(187\) 6.90833 0.505187
\(188\) 0 0
\(189\) −1.60555 −0.116787
\(190\) 0 0
\(191\) 22.7250 1.64432 0.822161 0.569255i \(-0.192768\pi\)
0.822161 + 0.569255i \(0.192768\pi\)
\(192\) 0 0
\(193\) −19.3028 −1.38944 −0.694722 0.719278i \(-0.744473\pi\)
−0.694722 + 0.719278i \(0.744473\pi\)
\(194\) 0 0
\(195\) 8.30278 0.594574
\(196\) 0 0
\(197\) −6.90833 −0.492198 −0.246099 0.969245i \(-0.579149\pi\)
−0.246099 + 0.969245i \(0.579149\pi\)
\(198\) 0 0
\(199\) −1.60555 −0.113815 −0.0569073 0.998379i \(-0.518124\pi\)
−0.0569073 + 0.998379i \(0.518124\pi\)
\(200\) 0 0
\(201\) 0.211103 0.0148900
\(202\) 0 0
\(203\) 0.697224 0.0489356
\(204\) 0 0
\(205\) 3.30278 0.230676
\(206\) 0 0
\(207\) −17.5139 −1.21730
\(208\) 0 0
\(209\) 1.30278 0.0901149
\(210\) 0 0
\(211\) 14.3028 0.984644 0.492322 0.870413i \(-0.336148\pi\)
0.492322 + 0.870413i \(0.336148\pi\)
\(212\) 0 0
\(213\) 29.5139 2.02226
\(214\) 0 0
\(215\) 7.21110 0.491793
\(216\) 0 0
\(217\) 4.69722 0.318868
\(218\) 0 0
\(219\) −11.3028 −0.763771
\(220\) 0 0
\(221\) 19.1194 1.28611
\(222\) 0 0
\(223\) −6.21110 −0.415926 −0.207963 0.978137i \(-0.566683\pi\)
−0.207963 + 0.978137i \(0.566683\pi\)
\(224\) 0 0
\(225\) −9.21110 −0.614074
\(226\) 0 0
\(227\) 15.3028 1.01568 0.507840 0.861451i \(-0.330444\pi\)
0.507840 + 0.861451i \(0.330444\pi\)
\(228\) 0 0
\(229\) −11.2111 −0.740851 −0.370425 0.928862i \(-0.620788\pi\)
−0.370425 + 0.928862i \(0.620788\pi\)
\(230\) 0 0
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) 11.4861 0.752481 0.376240 0.926522i \(-0.377217\pi\)
0.376240 + 0.926522i \(0.377217\pi\)
\(234\) 0 0
\(235\) 0.394449 0.0257310
\(236\) 0 0
\(237\) 32.2389 2.09414
\(238\) 0 0
\(239\) 22.0278 1.42486 0.712429 0.701745i \(-0.247595\pi\)
0.712429 + 0.701745i \(0.247595\pi\)
\(240\) 0 0
\(241\) −21.8167 −1.40533 −0.702667 0.711519i \(-0.748008\pi\)
−0.702667 + 0.711519i \(0.748008\pi\)
\(242\) 0 0
\(243\) 19.6056 1.25770
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 3.60555 0.229416
\(248\) 0 0
\(249\) −17.3028 −1.09652
\(250\) 0 0
\(251\) −5.72498 −0.361358 −0.180679 0.983542i \(-0.557829\pi\)
−0.180679 + 0.983542i \(0.557829\pi\)
\(252\) 0 0
\(253\) −9.90833 −0.622931
\(254\) 0 0
\(255\) 12.2111 0.764689
\(256\) 0 0
\(257\) −4.90833 −0.306173 −0.153087 0.988213i \(-0.548921\pi\)
−0.153087 + 0.988213i \(0.548921\pi\)
\(258\) 0 0
\(259\) 3.60555 0.224038
\(260\) 0 0
\(261\) −1.60555 −0.0993811
\(262\) 0 0
\(263\) −8.30278 −0.511971 −0.255986 0.966681i \(-0.582400\pi\)
−0.255986 + 0.966681i \(0.582400\pi\)
\(264\) 0 0
\(265\) −6.90833 −0.424375
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) 0 0
\(269\) 15.5139 0.945898 0.472949 0.881090i \(-0.343190\pi\)
0.472949 + 0.881090i \(0.343190\pi\)
\(270\) 0 0
\(271\) −15.9083 −0.966362 −0.483181 0.875520i \(-0.660519\pi\)
−0.483181 + 0.875520i \(0.660519\pi\)
\(272\) 0 0
\(273\) 8.30278 0.502507
\(274\) 0 0
\(275\) −5.21110 −0.314241
\(276\) 0 0
\(277\) −6.18335 −0.371521 −0.185761 0.982595i \(-0.559475\pi\)
−0.185761 + 0.982595i \(0.559475\pi\)
\(278\) 0 0
\(279\) −10.8167 −0.647576
\(280\) 0 0
\(281\) −9.42221 −0.562082 −0.281041 0.959696i \(-0.590680\pi\)
−0.281041 + 0.959696i \(0.590680\pi\)
\(282\) 0 0
\(283\) 4.48612 0.266672 0.133336 0.991071i \(-0.457431\pi\)
0.133336 + 0.991071i \(0.457431\pi\)
\(284\) 0 0
\(285\) 2.30278 0.136405
\(286\) 0 0
\(287\) 3.30278 0.194957
\(288\) 0 0
\(289\) 11.1194 0.654084
\(290\) 0 0
\(291\) 11.0917 0.650205
\(292\) 0 0
\(293\) −24.6333 −1.43909 −0.719547 0.694444i \(-0.755650\pi\)
−0.719547 + 0.694444i \(0.755650\pi\)
\(294\) 0 0
\(295\) 1.60555 0.0934788
\(296\) 0 0
\(297\) 2.09167 0.121371
\(298\) 0 0
\(299\) −27.4222 −1.58587
\(300\) 0 0
\(301\) 7.21110 0.415641
\(302\) 0 0
\(303\) −22.1194 −1.27073
\(304\) 0 0
\(305\) 6.21110 0.355647
\(306\) 0 0
\(307\) 11.1194 0.634619 0.317310 0.948322i \(-0.397221\pi\)
0.317310 + 0.948322i \(0.397221\pi\)
\(308\) 0 0
\(309\) 26.7250 1.52033
\(310\) 0 0
\(311\) −32.3305 −1.83330 −0.916648 0.399695i \(-0.869116\pi\)
−0.916648 + 0.399695i \(0.869116\pi\)
\(312\) 0 0
\(313\) −6.18335 −0.349503 −0.174752 0.984613i \(-0.555912\pi\)
−0.174752 + 0.984613i \(0.555912\pi\)
\(314\) 0 0
\(315\) 2.30278 0.129747
\(316\) 0 0
\(317\) 3.21110 0.180353 0.0901767 0.995926i \(-0.471257\pi\)
0.0901767 + 0.995926i \(0.471257\pi\)
\(318\) 0 0
\(319\) −0.908327 −0.0508565
\(320\) 0 0
\(321\) 24.9083 1.39025
\(322\) 0 0
\(323\) 5.30278 0.295054
\(324\) 0 0
\(325\) −14.4222 −0.800000
\(326\) 0 0
\(327\) 16.1194 0.891406
\(328\) 0 0
\(329\) 0.394449 0.0217467
\(330\) 0 0
\(331\) −27.5139 −1.51230 −0.756150 0.654399i \(-0.772922\pi\)
−0.756150 + 0.654399i \(0.772922\pi\)
\(332\) 0 0
\(333\) −8.30278 −0.454989
\(334\) 0 0
\(335\) 0.0916731 0.00500864
\(336\) 0 0
\(337\) −33.3028 −1.81412 −0.907059 0.421004i \(-0.861678\pi\)
−0.907059 + 0.421004i \(0.861678\pi\)
\(338\) 0 0
\(339\) 18.6972 1.01549
\(340\) 0 0
\(341\) −6.11943 −0.331386
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −17.5139 −0.942916
\(346\) 0 0
\(347\) −14.3028 −0.767813 −0.383907 0.923372i \(-0.625422\pi\)
−0.383907 + 0.923372i \(0.625422\pi\)
\(348\) 0 0
\(349\) −11.5139 −0.616324 −0.308162 0.951334i \(-0.599714\pi\)
−0.308162 + 0.951334i \(0.599714\pi\)
\(350\) 0 0
\(351\) 5.78890 0.308988
\(352\) 0 0
\(353\) 33.7250 1.79500 0.897500 0.441015i \(-0.145381\pi\)
0.897500 + 0.441015i \(0.145381\pi\)
\(354\) 0 0
\(355\) 12.8167 0.680237
\(356\) 0 0
\(357\) 12.2111 0.646280
\(358\) 0 0
\(359\) −6.69722 −0.353466 −0.176733 0.984259i \(-0.556553\pi\)
−0.176733 + 0.984259i \(0.556553\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 21.4222 1.12437
\(364\) 0 0
\(365\) −4.90833 −0.256914
\(366\) 0 0
\(367\) 3.78890 0.197779 0.0988894 0.995098i \(-0.468471\pi\)
0.0988894 + 0.995098i \(0.468471\pi\)
\(368\) 0 0
\(369\) −7.60555 −0.395929
\(370\) 0 0
\(371\) −6.90833 −0.358662
\(372\) 0 0
\(373\) 9.09167 0.470749 0.235374 0.971905i \(-0.424368\pi\)
0.235374 + 0.971905i \(0.424368\pi\)
\(374\) 0 0
\(375\) −20.7250 −1.07023
\(376\) 0 0
\(377\) −2.51388 −0.129471
\(378\) 0 0
\(379\) −7.42221 −0.381253 −0.190627 0.981663i \(-0.561052\pi\)
−0.190627 + 0.981663i \(0.561052\pi\)
\(380\) 0 0
\(381\) −48.4222 −2.48074
\(382\) 0 0
\(383\) 32.4500 1.65812 0.829058 0.559163i \(-0.188877\pi\)
0.829058 + 0.559163i \(0.188877\pi\)
\(384\) 0 0
\(385\) 1.30278 0.0663956
\(386\) 0 0
\(387\) −16.6056 −0.844108
\(388\) 0 0
\(389\) −7.30278 −0.370265 −0.185133 0.982714i \(-0.559271\pi\)
−0.185133 + 0.982714i \(0.559271\pi\)
\(390\) 0 0
\(391\) −40.3305 −2.03960
\(392\) 0 0
\(393\) 24.6333 1.24259
\(394\) 0 0
\(395\) 14.0000 0.704416
\(396\) 0 0
\(397\) 2.60555 0.130769 0.0653844 0.997860i \(-0.479173\pi\)
0.0653844 + 0.997860i \(0.479173\pi\)
\(398\) 0 0
\(399\) 2.30278 0.115283
\(400\) 0 0
\(401\) −2.09167 −0.104453 −0.0522266 0.998635i \(-0.516632\pi\)
−0.0522266 + 0.998635i \(0.516632\pi\)
\(402\) 0 0
\(403\) −16.9361 −0.843646
\(404\) 0 0
\(405\) 10.6056 0.526994
\(406\) 0 0
\(407\) −4.69722 −0.232833
\(408\) 0 0
\(409\) 29.7527 1.47118 0.735589 0.677428i \(-0.236905\pi\)
0.735589 + 0.677428i \(0.236905\pi\)
\(410\) 0 0
\(411\) −35.0278 −1.72779
\(412\) 0 0
\(413\) 1.60555 0.0790040
\(414\) 0 0
\(415\) −7.51388 −0.368842
\(416\) 0 0
\(417\) −26.7250 −1.30873
\(418\) 0 0
\(419\) 18.8167 0.919254 0.459627 0.888112i \(-0.347983\pi\)
0.459627 + 0.888112i \(0.347983\pi\)
\(420\) 0 0
\(421\) −36.8167 −1.79433 −0.897167 0.441692i \(-0.854379\pi\)
−0.897167 + 0.441692i \(0.854379\pi\)
\(422\) 0 0
\(423\) −0.908327 −0.0441644
\(424\) 0 0
\(425\) −21.2111 −1.02889
\(426\) 0 0
\(427\) 6.21110 0.300576
\(428\) 0 0
\(429\) −10.8167 −0.522233
\(430\) 0 0
\(431\) −7.57779 −0.365010 −0.182505 0.983205i \(-0.558420\pi\)
−0.182505 + 0.983205i \(0.558420\pi\)
\(432\) 0 0
\(433\) 22.2111 1.06740 0.533699 0.845675i \(-0.320802\pi\)
0.533699 + 0.845675i \(0.320802\pi\)
\(434\) 0 0
\(435\) −1.60555 −0.0769803
\(436\) 0 0
\(437\) −7.60555 −0.363823
\(438\) 0 0
\(439\) −9.21110 −0.439622 −0.219811 0.975542i \(-0.570544\pi\)
−0.219811 + 0.975542i \(0.570544\pi\)
\(440\) 0 0
\(441\) 2.30278 0.109656
\(442\) 0 0
\(443\) 24.9083 1.18343 0.591715 0.806147i \(-0.298451\pi\)
0.591715 + 0.806147i \(0.298451\pi\)
\(444\) 0 0
\(445\) 7.81665 0.370545
\(446\) 0 0
\(447\) −6.90833 −0.326753
\(448\) 0 0
\(449\) 8.11943 0.383180 0.191590 0.981475i \(-0.438636\pi\)
0.191590 + 0.981475i \(0.438636\pi\)
\(450\) 0 0
\(451\) −4.30278 −0.202610
\(452\) 0 0
\(453\) 36.6333 1.72118
\(454\) 0 0
\(455\) 3.60555 0.169031
\(456\) 0 0
\(457\) 21.9361 1.02613 0.513063 0.858351i \(-0.328511\pi\)
0.513063 + 0.858351i \(0.328511\pi\)
\(458\) 0 0
\(459\) 8.51388 0.397394
\(460\) 0 0
\(461\) −10.1194 −0.471309 −0.235654 0.971837i \(-0.575723\pi\)
−0.235654 + 0.971837i \(0.575723\pi\)
\(462\) 0 0
\(463\) 2.21110 0.102759 0.0513793 0.998679i \(-0.483638\pi\)
0.0513793 + 0.998679i \(0.483638\pi\)
\(464\) 0 0
\(465\) −10.8167 −0.501610
\(466\) 0 0
\(467\) −3.88057 −0.179571 −0.0897857 0.995961i \(-0.528618\pi\)
−0.0897857 + 0.995961i \(0.528618\pi\)
\(468\) 0 0
\(469\) 0.0916731 0.00423307
\(470\) 0 0
\(471\) 47.2389 2.17665
\(472\) 0 0
\(473\) −9.39445 −0.431957
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 15.9083 0.728392
\(478\) 0 0
\(479\) 6.69722 0.306004 0.153002 0.988226i \(-0.451106\pi\)
0.153002 + 0.988226i \(0.451106\pi\)
\(480\) 0 0
\(481\) −13.0000 −0.592749
\(482\) 0 0
\(483\) −17.5139 −0.796909
\(484\) 0 0
\(485\) 4.81665 0.218713
\(486\) 0 0
\(487\) 13.2389 0.599910 0.299955 0.953953i \(-0.403028\pi\)
0.299955 + 0.953953i \(0.403028\pi\)
\(488\) 0 0
\(489\) −40.3305 −1.82381
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) −3.69722 −0.166515
\(494\) 0 0
\(495\) −3.00000 −0.134840
\(496\) 0 0
\(497\) 12.8167 0.574905
\(498\) 0 0
\(499\) 21.3305 0.954886 0.477443 0.878663i \(-0.341564\pi\)
0.477443 + 0.878663i \(0.341564\pi\)
\(500\) 0 0
\(501\) −17.0917 −0.763600
\(502\) 0 0
\(503\) −32.8444 −1.46446 −0.732230 0.681058i \(-0.761520\pi\)
−0.732230 + 0.681058i \(0.761520\pi\)
\(504\) 0 0
\(505\) −9.60555 −0.427441
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −23.2111 −1.02881 −0.514407 0.857546i \(-0.671988\pi\)
−0.514407 + 0.857546i \(0.671988\pi\)
\(510\) 0 0
\(511\) −4.90833 −0.217132
\(512\) 0 0
\(513\) 1.60555 0.0708868
\(514\) 0 0
\(515\) 11.6056 0.511402
\(516\) 0 0
\(517\) −0.513878 −0.0226003
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 15.4222 0.675659 0.337830 0.941207i \(-0.390307\pi\)
0.337830 + 0.941207i \(0.390307\pi\)
\(522\) 0 0
\(523\) −23.4222 −1.02418 −0.512091 0.858931i \(-0.671129\pi\)
−0.512091 + 0.858931i \(0.671129\pi\)
\(524\) 0 0
\(525\) −9.21110 −0.402005
\(526\) 0 0
\(527\) −24.9083 −1.08502
\(528\) 0 0
\(529\) 34.8444 1.51497
\(530\) 0 0
\(531\) −3.69722 −0.160446
\(532\) 0 0
\(533\) −11.9083 −0.515807
\(534\) 0 0
\(535\) 10.8167 0.467645
\(536\) 0 0
\(537\) 10.8167 0.466773
\(538\) 0 0
\(539\) 1.30278 0.0561145
\(540\) 0 0
\(541\) −24.7889 −1.06576 −0.532879 0.846191i \(-0.678890\pi\)
−0.532879 + 0.846191i \(0.678890\pi\)
\(542\) 0 0
\(543\) −21.4222 −0.919315
\(544\) 0 0
\(545\) 7.00000 0.299847
\(546\) 0 0
\(547\) 11.5139 0.492298 0.246149 0.969232i \(-0.420835\pi\)
0.246149 + 0.969232i \(0.420835\pi\)
\(548\) 0 0
\(549\) −14.3028 −0.610428
\(550\) 0 0
\(551\) −0.697224 −0.0297028
\(552\) 0 0
\(553\) 14.0000 0.595341
\(554\) 0 0
\(555\) −8.30278 −0.352433
\(556\) 0 0
\(557\) −32.7527 −1.38778 −0.693889 0.720082i \(-0.744104\pi\)
−0.693889 + 0.720082i \(0.744104\pi\)
\(558\) 0 0
\(559\) −26.0000 −1.09968
\(560\) 0 0
\(561\) −15.9083 −0.671650
\(562\) 0 0
\(563\) 16.0278 0.675489 0.337745 0.941238i \(-0.390336\pi\)
0.337745 + 0.941238i \(0.390336\pi\)
\(564\) 0 0
\(565\) 8.11943 0.341587
\(566\) 0 0
\(567\) 10.6056 0.445391
\(568\) 0 0
\(569\) 22.0278 0.923452 0.461726 0.887023i \(-0.347230\pi\)
0.461726 + 0.887023i \(0.347230\pi\)
\(570\) 0 0
\(571\) −32.2111 −1.34799 −0.673996 0.738735i \(-0.735424\pi\)
−0.673996 + 0.738735i \(0.735424\pi\)
\(572\) 0 0
\(573\) −52.3305 −2.18614
\(574\) 0 0
\(575\) 30.4222 1.26869
\(576\) 0 0
\(577\) −28.7250 −1.19584 −0.597918 0.801557i \(-0.704005\pi\)
−0.597918 + 0.801557i \(0.704005\pi\)
\(578\) 0 0
\(579\) 44.4500 1.84728
\(580\) 0 0
\(581\) −7.51388 −0.311728
\(582\) 0 0
\(583\) 9.00000 0.372742
\(584\) 0 0
\(585\) −8.30278 −0.343278
\(586\) 0 0
\(587\) 33.6333 1.38820 0.694098 0.719881i \(-0.255804\pi\)
0.694098 + 0.719881i \(0.255804\pi\)
\(588\) 0 0
\(589\) −4.69722 −0.193546
\(590\) 0 0
\(591\) 15.9083 0.654381
\(592\) 0 0
\(593\) 44.8167 1.84040 0.920200 0.391449i \(-0.128026\pi\)
0.920200 + 0.391449i \(0.128026\pi\)
\(594\) 0 0
\(595\) 5.30278 0.217393
\(596\) 0 0
\(597\) 3.69722 0.151317
\(598\) 0 0
\(599\) −25.3305 −1.03498 −0.517489 0.855690i \(-0.673133\pi\)
−0.517489 + 0.855690i \(0.673133\pi\)
\(600\) 0 0
\(601\) −31.1472 −1.27052 −0.635260 0.772298i \(-0.719107\pi\)
−0.635260 + 0.772298i \(0.719107\pi\)
\(602\) 0 0
\(603\) −0.211103 −0.00859676
\(604\) 0 0
\(605\) 9.30278 0.378212
\(606\) 0 0
\(607\) 12.8167 0.520212 0.260106 0.965580i \(-0.416243\pi\)
0.260106 + 0.965580i \(0.416243\pi\)
\(608\) 0 0
\(609\) −1.60555 −0.0650602
\(610\) 0 0
\(611\) −1.42221 −0.0575363
\(612\) 0 0
\(613\) −36.3583 −1.46850 −0.734249 0.678881i \(-0.762465\pi\)
−0.734249 + 0.678881i \(0.762465\pi\)
\(614\) 0 0
\(615\) −7.60555 −0.306685
\(616\) 0 0
\(617\) 11.5416 0.464649 0.232324 0.972638i \(-0.425367\pi\)
0.232324 + 0.972638i \(0.425367\pi\)
\(618\) 0 0
\(619\) 43.5694 1.75120 0.875601 0.483035i \(-0.160466\pi\)
0.875601 + 0.483035i \(0.160466\pi\)
\(620\) 0 0
\(621\) −12.2111 −0.490015
\(622\) 0 0
\(623\) 7.81665 0.313168
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) −3.00000 −0.119808
\(628\) 0 0
\(629\) −19.1194 −0.762342
\(630\) 0 0
\(631\) 6.21110 0.247260 0.123630 0.992328i \(-0.460546\pi\)
0.123630 + 0.992328i \(0.460546\pi\)
\(632\) 0 0
\(633\) −32.9361 −1.30909
\(634\) 0 0
\(635\) −21.0278 −0.834461
\(636\) 0 0
\(637\) 3.60555 0.142857
\(638\) 0 0
\(639\) −29.5139 −1.16755
\(640\) 0 0
\(641\) −36.6972 −1.44945 −0.724727 0.689037i \(-0.758034\pi\)
−0.724727 + 0.689037i \(0.758034\pi\)
\(642\) 0 0
\(643\) 43.4222 1.71240 0.856202 0.516641i \(-0.172818\pi\)
0.856202 + 0.516641i \(0.172818\pi\)
\(644\) 0 0
\(645\) −16.6056 −0.653843
\(646\) 0 0
\(647\) 20.8167 0.818387 0.409194 0.912448i \(-0.365810\pi\)
0.409194 + 0.912448i \(0.365810\pi\)
\(648\) 0 0
\(649\) −2.09167 −0.0821054
\(650\) 0 0
\(651\) −10.8167 −0.423938
\(652\) 0 0
\(653\) 12.0278 0.470682 0.235341 0.971913i \(-0.424379\pi\)
0.235341 + 0.971913i \(0.424379\pi\)
\(654\) 0 0
\(655\) 10.6972 0.417975
\(656\) 0 0
\(657\) 11.3028 0.440963
\(658\) 0 0
\(659\) −3.90833 −0.152247 −0.0761234 0.997098i \(-0.524254\pi\)
−0.0761234 + 0.997098i \(0.524254\pi\)
\(660\) 0 0
\(661\) −31.2111 −1.21397 −0.606986 0.794713i \(-0.707621\pi\)
−0.606986 + 0.794713i \(0.707621\pi\)
\(662\) 0 0
\(663\) −44.0278 −1.70990
\(664\) 0 0
\(665\) 1.00000 0.0387783
\(666\) 0 0
\(667\) 5.30278 0.205324
\(668\) 0 0
\(669\) 14.3028 0.552977
\(670\) 0 0
\(671\) −8.09167 −0.312376
\(672\) 0 0
\(673\) 0.724981 0.0279460 0.0139730 0.999902i \(-0.495552\pi\)
0.0139730 + 0.999902i \(0.495552\pi\)
\(674\) 0 0
\(675\) −6.42221 −0.247191
\(676\) 0 0
\(677\) 35.5139 1.36491 0.682455 0.730928i \(-0.260912\pi\)
0.682455 + 0.730928i \(0.260912\pi\)
\(678\) 0 0
\(679\) 4.81665 0.184846
\(680\) 0 0
\(681\) −35.2389 −1.35036
\(682\) 0 0
\(683\) 29.2389 1.11879 0.559397 0.828900i \(-0.311033\pi\)
0.559397 + 0.828900i \(0.311033\pi\)
\(684\) 0 0
\(685\) −15.2111 −0.581186
\(686\) 0 0
\(687\) 25.8167 0.984967
\(688\) 0 0
\(689\) 24.9083 0.948932
\(690\) 0 0
\(691\) −12.6056 −0.479538 −0.239769 0.970830i \(-0.577072\pi\)
−0.239769 + 0.970830i \(0.577072\pi\)
\(692\) 0 0
\(693\) −3.00000 −0.113961
\(694\) 0 0
\(695\) −11.6056 −0.440224
\(696\) 0 0
\(697\) −17.5139 −0.663385
\(698\) 0 0
\(699\) −26.4500 −1.00043
\(700\) 0 0
\(701\) 15.6333 0.590462 0.295231 0.955426i \(-0.404603\pi\)
0.295231 + 0.955426i \(0.404603\pi\)
\(702\) 0 0
\(703\) −3.60555 −0.135986
\(704\) 0 0
\(705\) −0.908327 −0.0342096
\(706\) 0 0
\(707\) −9.60555 −0.361254
\(708\) 0 0
\(709\) 29.2389 1.09809 0.549044 0.835793i \(-0.314992\pi\)
0.549044 + 0.835793i \(0.314992\pi\)
\(710\) 0 0
\(711\) −32.2389 −1.20905
\(712\) 0 0
\(713\) 35.7250 1.33791
\(714\) 0 0
\(715\) −4.69722 −0.175666
\(716\) 0 0
\(717\) −50.7250 −1.89436
\(718\) 0 0
\(719\) −19.6333 −0.732199 −0.366099 0.930576i \(-0.619307\pi\)
−0.366099 + 0.930576i \(0.619307\pi\)
\(720\) 0 0
\(721\) 11.6056 0.432213
\(722\) 0 0
\(723\) 50.2389 1.86840
\(724\) 0 0
\(725\) 2.78890 0.103577
\(726\) 0 0
\(727\) −29.4222 −1.09121 −0.545605 0.838043i \(-0.683700\pi\)
−0.545605 + 0.838043i \(0.683700\pi\)
\(728\) 0 0
\(729\) −13.3305 −0.493723
\(730\) 0 0
\(731\) −38.2389 −1.41432
\(732\) 0 0
\(733\) −4.84441 −0.178932 −0.0894662 0.995990i \(-0.528516\pi\)
−0.0894662 + 0.995990i \(0.528516\pi\)
\(734\) 0 0
\(735\) 2.30278 0.0849392
\(736\) 0 0
\(737\) −0.119429 −0.00439924
\(738\) 0 0
\(739\) −3.18335 −0.117101 −0.0585506 0.998284i \(-0.518648\pi\)
−0.0585506 + 0.998284i \(0.518648\pi\)
\(740\) 0 0
\(741\) −8.30278 −0.305010
\(742\) 0 0
\(743\) −27.2389 −0.999297 −0.499648 0.866228i \(-0.666537\pi\)
−0.499648 + 0.866228i \(0.666537\pi\)
\(744\) 0 0
\(745\) −3.00000 −0.109911
\(746\) 0 0
\(747\) 17.3028 0.633075
\(748\) 0 0
\(749\) 10.8167 0.395232
\(750\) 0 0
\(751\) 19.1472 0.698691 0.349345 0.936994i \(-0.386404\pi\)
0.349345 + 0.936994i \(0.386404\pi\)
\(752\) 0 0
\(753\) 13.1833 0.480428
\(754\) 0 0
\(755\) 15.9083 0.578963
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0 0
\(759\) 22.8167 0.828192
\(760\) 0 0
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) 0 0
\(763\) 7.00000 0.253417
\(764\) 0 0
\(765\) −12.2111 −0.441493
\(766\) 0 0
\(767\) −5.78890 −0.209025
\(768\) 0 0
\(769\) 41.2111 1.48611 0.743055 0.669230i \(-0.233376\pi\)
0.743055 + 0.669230i \(0.233376\pi\)
\(770\) 0 0
\(771\) 11.3028 0.407060
\(772\) 0 0
\(773\) 6.18335 0.222400 0.111200 0.993798i \(-0.464531\pi\)
0.111200 + 0.993798i \(0.464531\pi\)
\(774\) 0 0
\(775\) 18.7889 0.674917
\(776\) 0 0
\(777\) −8.30278 −0.297860
\(778\) 0 0
\(779\) −3.30278 −0.118334
\(780\) 0 0
\(781\) −16.6972 −0.597474
\(782\) 0 0
\(783\) −1.11943 −0.0400051
\(784\) 0 0
\(785\) 20.5139 0.732172
\(786\) 0 0
\(787\) −31.6333 −1.12761 −0.563803 0.825909i \(-0.690662\pi\)
−0.563803 + 0.825909i \(0.690662\pi\)
\(788\) 0 0
\(789\) 19.1194 0.680670
\(790\) 0 0
\(791\) 8.11943 0.288694
\(792\) 0 0
\(793\) −22.3944 −0.795250
\(794\) 0 0
\(795\) 15.9083 0.564210
\(796\) 0 0
\(797\) −6.27502 −0.222273 −0.111136 0.993805i \(-0.535449\pi\)
−0.111136 + 0.993805i \(0.535449\pi\)
\(798\) 0 0
\(799\) −2.09167 −0.0739981
\(800\) 0 0
\(801\) −18.0000 −0.635999
\(802\) 0 0
\(803\) 6.39445 0.225655
\(804\) 0 0
\(805\) −7.60555 −0.268060
\(806\) 0 0
\(807\) −35.7250 −1.25758
\(808\) 0 0
\(809\) −32.8167 −1.15377 −0.576886 0.816825i \(-0.695732\pi\)
−0.576886 + 0.816825i \(0.695732\pi\)
\(810\) 0 0
\(811\) 4.42221 0.155285 0.0776423 0.996981i \(-0.475261\pi\)
0.0776423 + 0.996981i \(0.475261\pi\)
\(812\) 0 0
\(813\) 36.6333 1.28479
\(814\) 0 0
\(815\) −17.5139 −0.613484
\(816\) 0 0
\(817\) −7.21110 −0.252285
\(818\) 0 0
\(819\) −8.30278 −0.290122
\(820\) 0 0
\(821\) 4.36669 0.152399 0.0761993 0.997093i \(-0.475721\pi\)
0.0761993 + 0.997093i \(0.475721\pi\)
\(822\) 0 0
\(823\) 44.2389 1.54207 0.771035 0.636793i \(-0.219739\pi\)
0.771035 + 0.636793i \(0.219739\pi\)
\(824\) 0 0
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) −2.39445 −0.0832631 −0.0416316 0.999133i \(-0.513256\pi\)
−0.0416316 + 0.999133i \(0.513256\pi\)
\(828\) 0 0
\(829\) 30.0555 1.04387 0.521936 0.852985i \(-0.325210\pi\)
0.521936 + 0.852985i \(0.325210\pi\)
\(830\) 0 0
\(831\) 14.2389 0.493941
\(832\) 0 0
\(833\) 5.30278 0.183730
\(834\) 0 0
\(835\) −7.42221 −0.256856
\(836\) 0 0
\(837\) −7.54163 −0.260677
\(838\) 0 0
\(839\) −51.6333 −1.78258 −0.891290 0.453434i \(-0.850199\pi\)
−0.891290 + 0.453434i \(0.850199\pi\)
\(840\) 0 0
\(841\) −28.5139 −0.983237
\(842\) 0 0
\(843\) 21.6972 0.747292
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 9.30278 0.319647
\(848\) 0 0
\(849\) −10.3305 −0.354543
\(850\) 0 0
\(851\) 27.4222 0.940021
\(852\) 0 0
\(853\) 25.5139 0.873579 0.436789 0.899564i \(-0.356116\pi\)
0.436789 + 0.899564i \(0.356116\pi\)
\(854\) 0 0
\(855\) −2.30278 −0.0787533
\(856\) 0 0
\(857\) −28.7527 −0.982175 −0.491087 0.871110i \(-0.663400\pi\)
−0.491087 + 0.871110i \(0.663400\pi\)
\(858\) 0 0
\(859\) −32.7527 −1.11751 −0.558754 0.829333i \(-0.688721\pi\)
−0.558754 + 0.829333i \(0.688721\pi\)
\(860\) 0 0
\(861\) −7.60555 −0.259196
\(862\) 0 0
\(863\) −32.4861 −1.10584 −0.552920 0.833234i \(-0.686487\pi\)
−0.552920 + 0.833234i \(0.686487\pi\)
\(864\) 0 0
\(865\) 7.81665 0.265774
\(866\) 0 0
\(867\) −25.6056 −0.869610
\(868\) 0 0
\(869\) −18.2389 −0.618711
\(870\) 0 0
\(871\) −0.330532 −0.0111997
\(872\) 0 0
\(873\) −11.0917 −0.375396
\(874\) 0 0
\(875\) −9.00000 −0.304256
\(876\) 0 0
\(877\) −41.8722 −1.41392 −0.706961 0.707252i \(-0.749935\pi\)
−0.706961 + 0.707252i \(0.749935\pi\)
\(878\) 0 0
\(879\) 56.7250 1.91329
\(880\) 0 0
\(881\) 52.9638 1.78440 0.892199 0.451643i \(-0.149162\pi\)
0.892199 + 0.451643i \(0.149162\pi\)
\(882\) 0 0
\(883\) −43.6611 −1.46931 −0.734656 0.678440i \(-0.762656\pi\)
−0.734656 + 0.678440i \(0.762656\pi\)
\(884\) 0 0
\(885\) −3.69722 −0.124281
\(886\) 0 0
\(887\) −52.2111 −1.75308 −0.876539 0.481332i \(-0.840153\pi\)
−0.876539 + 0.481332i \(0.840153\pi\)
\(888\) 0 0
\(889\) −21.0278 −0.705248
\(890\) 0 0
\(891\) −13.8167 −0.462875
\(892\) 0 0
\(893\) −0.394449 −0.0131997
\(894\) 0 0
\(895\) 4.69722 0.157011
\(896\) 0 0
\(897\) 63.1472 2.10842
\(898\) 0 0
\(899\) 3.27502 0.109228
\(900\) 0 0
\(901\) 36.6333 1.22043
\(902\) 0 0
\(903\) −16.6056 −0.552598
\(904\) 0 0
\(905\) −9.30278 −0.309235
\(906\) 0 0
\(907\) 29.4222 0.976948 0.488474 0.872578i \(-0.337554\pi\)
0.488474 + 0.872578i \(0.337554\pi\)
\(908\) 0 0
\(909\) 22.1194 0.733655
\(910\) 0 0
\(911\) 27.2111 0.901544 0.450772 0.892639i \(-0.351149\pi\)
0.450772 + 0.892639i \(0.351149\pi\)
\(912\) 0 0
\(913\) 9.78890 0.323965
\(914\) 0 0
\(915\) −14.3028 −0.472835
\(916\) 0 0
\(917\) 10.6972 0.353253
\(918\) 0 0
\(919\) 53.8444 1.77616 0.888082 0.459686i \(-0.152038\pi\)
0.888082 + 0.459686i \(0.152038\pi\)
\(920\) 0 0
\(921\) −25.6056 −0.843732
\(922\) 0 0
\(923\) −46.2111 −1.52106
\(924\) 0 0
\(925\) 14.4222 0.474199
\(926\) 0 0
\(927\) −26.7250 −0.877764
\(928\) 0 0
\(929\) 13.6972 0.449391 0.224696 0.974429i \(-0.427861\pi\)
0.224696 + 0.974429i \(0.427861\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 74.4500 2.43738
\(934\) 0 0
\(935\) −6.90833 −0.225926
\(936\) 0 0
\(937\) 36.9361 1.20665 0.603325 0.797496i \(-0.293842\pi\)
0.603325 + 0.797496i \(0.293842\pi\)
\(938\) 0 0
\(939\) 14.2389 0.464668
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 0 0
\(943\) 25.1194 0.818001
\(944\) 0 0
\(945\) 1.60555 0.0522286
\(946\) 0 0
\(947\) 3.51388 0.114186 0.0570928 0.998369i \(-0.481817\pi\)
0.0570928 + 0.998369i \(0.481817\pi\)
\(948\) 0 0
\(949\) 17.6972 0.574476
\(950\) 0 0
\(951\) −7.39445 −0.239781
\(952\) 0 0
\(953\) 16.8806 0.546815 0.273408 0.961898i \(-0.411849\pi\)
0.273408 + 0.961898i \(0.411849\pi\)
\(954\) 0 0
\(955\) −22.7250 −0.735363
\(956\) 0 0
\(957\) 2.09167 0.0676142
\(958\) 0 0
\(959\) −15.2111 −0.491192
\(960\) 0 0
\(961\) −8.93608 −0.288261
\(962\) 0 0
\(963\) −24.9083 −0.802660
\(964\) 0 0
\(965\) 19.3028 0.621378
\(966\) 0 0
\(967\) −24.5139 −0.788313 −0.394157 0.919043i \(-0.628963\pi\)
−0.394157 + 0.919043i \(0.628963\pi\)
\(968\) 0 0
\(969\) −12.2111 −0.392277
\(970\) 0 0
\(971\) −16.8167 −0.539672 −0.269836 0.962906i \(-0.586970\pi\)
−0.269836 + 0.962906i \(0.586970\pi\)
\(972\) 0 0
\(973\) −11.6056 −0.372057
\(974\) 0 0
\(975\) 33.2111 1.06361
\(976\) 0 0
\(977\) 27.3944 0.876426 0.438213 0.898871i \(-0.355612\pi\)
0.438213 + 0.898871i \(0.355612\pi\)
\(978\) 0 0
\(979\) −10.1833 −0.325461
\(980\) 0 0
\(981\) −16.1194 −0.514654
\(982\) 0 0
\(983\) 35.6611 1.13741 0.568706 0.822541i \(-0.307444\pi\)
0.568706 + 0.822541i \(0.307444\pi\)
\(984\) 0 0
\(985\) 6.90833 0.220118
\(986\) 0 0
\(987\) −0.908327 −0.0289124
\(988\) 0 0
\(989\) 54.8444 1.74395
\(990\) 0 0
\(991\) 28.2389 0.897037 0.448518 0.893774i \(-0.351952\pi\)
0.448518 + 0.893774i \(0.351952\pi\)
\(992\) 0 0
\(993\) 63.3583 2.01061
\(994\) 0 0
\(995\) 1.60555 0.0508994
\(996\) 0 0
\(997\) 18.7250 0.593026 0.296513 0.955029i \(-0.404176\pi\)
0.296513 + 0.955029i \(0.404176\pi\)
\(998\) 0 0
\(999\) −5.78890 −0.183153
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 1064.2.a.b.1.1 2
3.2 odd 2 9576.2.a.bs.1.1 2
4.3 odd 2 2128.2.a.i.1.2 2
7.6 odd 2 7448.2.a.bb.1.2 2
8.3 odd 2 8512.2.a.r.1.1 2
8.5 even 2 8512.2.a.x.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.a.b.1.1 2 1.1 even 1 trivial
2128.2.a.i.1.2 2 4.3 odd 2
7448.2.a.bb.1.2 2 7.6 odd 2
8512.2.a.r.1.1 2 8.3 odd 2
8512.2.a.x.1.2 2 8.5 even 2
9576.2.a.bs.1.1 2 3.2 odd 2