Properties

Label 4028.2.a.c.1.19
Level $4028$
Weight $2$
Character 4028.1
Self dual yes
Analytic conductor $32.164$
Analytic rank $1$
Dimension $19$
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] = [4028,2,Mod(1,4028)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4028.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4028.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: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{19} - 5 x^{18} - 27 x^{17} + 161 x^{16} + 253 x^{15} - 2103 x^{14} - 683 x^{13} + 14442 x^{12} - 4144 x^{11} - 56325 x^{10} + 37245 x^{9} + 124233 x^{8} - 117486 x^{7} + \cdots - 4088 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Root \(-3.04822\) of defining polynomial
Character \(\chi\) \(=\) 4028.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.04822 q^{3} -1.16277 q^{5} -3.09586 q^{7} +6.29166 q^{9} +O(q^{10})\) \(q+3.04822 q^{3} -1.16277 q^{5} -3.09586 q^{7} +6.29166 q^{9} -0.740609 q^{11} -7.01696 q^{13} -3.54439 q^{15} +5.39632 q^{17} +1.00000 q^{19} -9.43686 q^{21} -1.27050 q^{23} -3.64796 q^{25} +10.0337 q^{27} -5.83714 q^{29} +4.81429 q^{31} -2.25754 q^{33} +3.59979 q^{35} -4.16138 q^{37} -21.3893 q^{39} -7.66017 q^{41} +8.98019 q^{43} -7.31578 q^{45} -7.19701 q^{47} +2.58434 q^{49} +16.4492 q^{51} -1.00000 q^{53} +0.861161 q^{55} +3.04822 q^{57} -4.18347 q^{59} +2.39640 q^{61} -19.4781 q^{63} +8.15915 q^{65} -12.6421 q^{67} -3.87278 q^{69} -15.0821 q^{71} -13.9346 q^{73} -11.1198 q^{75} +2.29282 q^{77} +11.9623 q^{79} +11.7100 q^{81} -2.76424 q^{83} -6.27470 q^{85} -17.7929 q^{87} -0.783312 q^{89} +21.7235 q^{91} +14.6750 q^{93} -1.16277 q^{95} -12.2450 q^{97} -4.65966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19 q - 5 q^{3} - 5 q^{5} - 10 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 19 q - 5 q^{3} - 5 q^{5} - 10 q^{7} + 22 q^{9} - 3 q^{11} - 23 q^{13} - 18 q^{15} - 7 q^{17} + 19 q^{19} - 4 q^{21} - 6 q^{23} + 18 q^{25} - 17 q^{27} - 4 q^{29} - 30 q^{31} - 10 q^{33} - q^{35} - 31 q^{37} + 5 q^{39} - 15 q^{41} - 29 q^{43} + 6 q^{45} - 18 q^{47} + 23 q^{49} - 5 q^{51} - 19 q^{53} - 19 q^{55} - 5 q^{57} + 8 q^{59} - 4 q^{61} - 64 q^{63} - 26 q^{65} - 62 q^{67} + 3 q^{69} - 17 q^{71} + q^{73} - 40 q^{75} - 14 q^{77} - 28 q^{79} + 11 q^{81} + 4 q^{83} - 31 q^{85} - 20 q^{87} + 33 q^{89} - 29 q^{91} - 59 q^{93} - 5 q^{95} + 5 q^{97} - 48 q^{99}+O(q^{100}) \) 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
\(3\) 3.04822 1.75989 0.879946 0.475074i \(-0.157579\pi\)
0.879946 + 0.475074i \(0.157579\pi\)
\(4\) 0 0
\(5\) −1.16277 −0.520009 −0.260004 0.965607i \(-0.583724\pi\)
−0.260004 + 0.965607i \(0.583724\pi\)
\(6\) 0 0
\(7\) −3.09586 −1.17012 −0.585062 0.810988i \(-0.698930\pi\)
−0.585062 + 0.810988i \(0.698930\pi\)
\(8\) 0 0
\(9\) 6.29166 2.09722
\(10\) 0 0
\(11\) −0.740609 −0.223302 −0.111651 0.993747i \(-0.535614\pi\)
−0.111651 + 0.993747i \(0.535614\pi\)
\(12\) 0 0
\(13\) −7.01696 −1.94616 −0.973078 0.230476i \(-0.925972\pi\)
−0.973078 + 0.230476i \(0.925972\pi\)
\(14\) 0 0
\(15\) −3.54439 −0.915159
\(16\) 0 0
\(17\) 5.39632 1.30880 0.654400 0.756149i \(-0.272921\pi\)
0.654400 + 0.756149i \(0.272921\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −9.43686 −2.05929
\(22\) 0 0
\(23\) −1.27050 −0.264918 −0.132459 0.991188i \(-0.542287\pi\)
−0.132459 + 0.991188i \(0.542287\pi\)
\(24\) 0 0
\(25\) −3.64796 −0.729591
\(26\) 0 0
\(27\) 10.0337 1.93099
\(28\) 0 0
\(29\) −5.83714 −1.08393 −0.541965 0.840401i \(-0.682319\pi\)
−0.541965 + 0.840401i \(0.682319\pi\)
\(30\) 0 0
\(31\) 4.81429 0.864672 0.432336 0.901713i \(-0.357690\pi\)
0.432336 + 0.901713i \(0.357690\pi\)
\(32\) 0 0
\(33\) −2.25754 −0.392987
\(34\) 0 0
\(35\) 3.59979 0.608475
\(36\) 0 0
\(37\) −4.16138 −0.684127 −0.342063 0.939677i \(-0.611126\pi\)
−0.342063 + 0.939677i \(0.611126\pi\)
\(38\) 0 0
\(39\) −21.3893 −3.42502
\(40\) 0 0
\(41\) −7.66017 −1.19632 −0.598158 0.801378i \(-0.704101\pi\)
−0.598158 + 0.801378i \(0.704101\pi\)
\(42\) 0 0
\(43\) 8.98019 1.36947 0.684733 0.728794i \(-0.259919\pi\)
0.684733 + 0.728794i \(0.259919\pi\)
\(44\) 0 0
\(45\) −7.31578 −1.09057
\(46\) 0 0
\(47\) −7.19701 −1.04979 −0.524896 0.851167i \(-0.675896\pi\)
−0.524896 + 0.851167i \(0.675896\pi\)
\(48\) 0 0
\(49\) 2.58434 0.369191
\(50\) 0 0
\(51\) 16.4492 2.30335
\(52\) 0 0
\(53\) −1.00000 −0.137361
\(54\) 0 0
\(55\) 0.861161 0.116119
\(56\) 0 0
\(57\) 3.04822 0.403747
\(58\) 0 0
\(59\) −4.18347 −0.544642 −0.272321 0.962206i \(-0.587791\pi\)
−0.272321 + 0.962206i \(0.587791\pi\)
\(60\) 0 0
\(61\) 2.39640 0.306828 0.153414 0.988162i \(-0.450973\pi\)
0.153414 + 0.988162i \(0.450973\pi\)
\(62\) 0 0
\(63\) −19.4781 −2.45401
\(64\) 0 0
\(65\) 8.15915 1.01202
\(66\) 0 0
\(67\) −12.6421 −1.54448 −0.772238 0.635334i \(-0.780863\pi\)
−0.772238 + 0.635334i \(0.780863\pi\)
\(68\) 0 0
\(69\) −3.87278 −0.466228
\(70\) 0 0
\(71\) −15.0821 −1.78991 −0.894957 0.446152i \(-0.852794\pi\)
−0.894957 + 0.446152i \(0.852794\pi\)
\(72\) 0 0
\(73\) −13.9346 −1.63093 −0.815463 0.578809i \(-0.803518\pi\)
−0.815463 + 0.578809i \(0.803518\pi\)
\(74\) 0 0
\(75\) −11.1198 −1.28400
\(76\) 0 0
\(77\) 2.29282 0.261291
\(78\) 0 0
\(79\) 11.9623 1.34587 0.672934 0.739703i \(-0.265034\pi\)
0.672934 + 0.739703i \(0.265034\pi\)
\(80\) 0 0
\(81\) 11.7100 1.30111
\(82\) 0 0
\(83\) −2.76424 −0.303415 −0.151708 0.988425i \(-0.548477\pi\)
−0.151708 + 0.988425i \(0.548477\pi\)
\(84\) 0 0
\(85\) −6.27470 −0.680587
\(86\) 0 0
\(87\) −17.7929 −1.90760
\(88\) 0 0
\(89\) −0.783312 −0.0830309 −0.0415155 0.999138i \(-0.513219\pi\)
−0.0415155 + 0.999138i \(0.513219\pi\)
\(90\) 0 0
\(91\) 21.7235 2.27724
\(92\) 0 0
\(93\) 14.6750 1.52173
\(94\) 0 0
\(95\) −1.16277 −0.119298
\(96\) 0 0
\(97\) −12.2450 −1.24329 −0.621647 0.783297i \(-0.713536\pi\)
−0.621647 + 0.783297i \(0.713536\pi\)
\(98\) 0 0
\(99\) −4.65966 −0.468313
\(100\) 0 0
\(101\) 15.0356 1.49609 0.748047 0.663646i \(-0.230992\pi\)
0.748047 + 0.663646i \(0.230992\pi\)
\(102\) 0 0
\(103\) 7.36543 0.725737 0.362869 0.931840i \(-0.381797\pi\)
0.362869 + 0.931840i \(0.381797\pi\)
\(104\) 0 0
\(105\) 10.9729 1.07085
\(106\) 0 0
\(107\) −4.04862 −0.391395 −0.195697 0.980664i \(-0.562697\pi\)
−0.195697 + 0.980664i \(0.562697\pi\)
\(108\) 0 0
\(109\) −7.89989 −0.756673 −0.378336 0.925668i \(-0.623504\pi\)
−0.378336 + 0.925668i \(0.623504\pi\)
\(110\) 0 0
\(111\) −12.6848 −1.20399
\(112\) 0 0
\(113\) 6.64480 0.625090 0.312545 0.949903i \(-0.398819\pi\)
0.312545 + 0.949903i \(0.398819\pi\)
\(114\) 0 0
\(115\) 1.47731 0.137760
\(116\) 0 0
\(117\) −44.1483 −4.08151
\(118\) 0 0
\(119\) −16.7062 −1.53146
\(120\) 0 0
\(121\) −10.4515 −0.950136
\(122\) 0 0
\(123\) −23.3499 −2.10539
\(124\) 0 0
\(125\) 10.0556 0.899402
\(126\) 0 0
\(127\) −1.17268 −0.104058 −0.0520292 0.998646i \(-0.516569\pi\)
−0.0520292 + 0.998646i \(0.516569\pi\)
\(128\) 0 0
\(129\) 27.3736 2.41011
\(130\) 0 0
\(131\) −10.3480 −0.904112 −0.452056 0.891990i \(-0.649309\pi\)
−0.452056 + 0.891990i \(0.649309\pi\)
\(132\) 0 0
\(133\) −3.09586 −0.268445
\(134\) 0 0
\(135\) −11.6669 −1.00413
\(136\) 0 0
\(137\) 7.99811 0.683324 0.341662 0.939823i \(-0.389010\pi\)
0.341662 + 0.939823i \(0.389010\pi\)
\(138\) 0 0
\(139\) 16.5659 1.40510 0.702551 0.711633i \(-0.252044\pi\)
0.702551 + 0.711633i \(0.252044\pi\)
\(140\) 0 0
\(141\) −21.9381 −1.84752
\(142\) 0 0
\(143\) 5.19682 0.434580
\(144\) 0 0
\(145\) 6.78728 0.563653
\(146\) 0 0
\(147\) 7.87764 0.649737
\(148\) 0 0
\(149\) −5.13277 −0.420493 −0.210246 0.977648i \(-0.567427\pi\)
−0.210246 + 0.977648i \(0.567427\pi\)
\(150\) 0 0
\(151\) −11.7033 −0.952398 −0.476199 0.879337i \(-0.657986\pi\)
−0.476199 + 0.879337i \(0.657986\pi\)
\(152\) 0 0
\(153\) 33.9518 2.74484
\(154\) 0 0
\(155\) −5.59793 −0.449637
\(156\) 0 0
\(157\) 20.2992 1.62005 0.810026 0.586393i \(-0.199453\pi\)
0.810026 + 0.586393i \(0.199453\pi\)
\(158\) 0 0
\(159\) −3.04822 −0.241740
\(160\) 0 0
\(161\) 3.93330 0.309987
\(162\) 0 0
\(163\) 14.5405 1.13890 0.569449 0.822027i \(-0.307157\pi\)
0.569449 + 0.822027i \(0.307157\pi\)
\(164\) 0 0
\(165\) 2.62501 0.204357
\(166\) 0 0
\(167\) 2.10737 0.163073 0.0815366 0.996670i \(-0.474017\pi\)
0.0815366 + 0.996670i \(0.474017\pi\)
\(168\) 0 0
\(169\) 36.2378 2.78752
\(170\) 0 0
\(171\) 6.29166 0.481135
\(172\) 0 0
\(173\) −20.9904 −1.59587 −0.797935 0.602743i \(-0.794074\pi\)
−0.797935 + 0.602743i \(0.794074\pi\)
\(174\) 0 0
\(175\) 11.2936 0.853712
\(176\) 0 0
\(177\) −12.7522 −0.958511
\(178\) 0 0
\(179\) −21.3043 −1.59236 −0.796179 0.605062i \(-0.793148\pi\)
−0.796179 + 0.605062i \(0.793148\pi\)
\(180\) 0 0
\(181\) −13.2130 −0.982111 −0.491055 0.871128i \(-0.663389\pi\)
−0.491055 + 0.871128i \(0.663389\pi\)
\(182\) 0 0
\(183\) 7.30476 0.539983
\(184\) 0 0
\(185\) 4.83875 0.355752
\(186\) 0 0
\(187\) −3.99656 −0.292257
\(188\) 0 0
\(189\) −31.0629 −2.25949
\(190\) 0 0
\(191\) −16.2450 −1.17544 −0.587722 0.809063i \(-0.699975\pi\)
−0.587722 + 0.809063i \(0.699975\pi\)
\(192\) 0 0
\(193\) 16.3832 1.17929 0.589644 0.807663i \(-0.299268\pi\)
0.589644 + 0.807663i \(0.299268\pi\)
\(194\) 0 0
\(195\) 24.8709 1.78104
\(196\) 0 0
\(197\) 10.0911 0.718960 0.359480 0.933153i \(-0.382954\pi\)
0.359480 + 0.933153i \(0.382954\pi\)
\(198\) 0 0
\(199\) −11.3050 −0.801391 −0.400695 0.916211i \(-0.631231\pi\)
−0.400695 + 0.916211i \(0.631231\pi\)
\(200\) 0 0
\(201\) −38.5359 −2.71811
\(202\) 0 0
\(203\) 18.0710 1.26833
\(204\) 0 0
\(205\) 8.90705 0.622095
\(206\) 0 0
\(207\) −7.99357 −0.555592
\(208\) 0 0
\(209\) −0.740609 −0.0512290
\(210\) 0 0
\(211\) 9.97727 0.686864 0.343432 0.939178i \(-0.388411\pi\)
0.343432 + 0.939178i \(0.388411\pi\)
\(212\) 0 0
\(213\) −45.9735 −3.15006
\(214\) 0 0
\(215\) −10.4419 −0.712134
\(216\) 0 0
\(217\) −14.9044 −1.01177
\(218\) 0 0
\(219\) −42.4759 −2.87025
\(220\) 0 0
\(221\) −37.8658 −2.54713
\(222\) 0 0
\(223\) −7.63982 −0.511600 −0.255800 0.966730i \(-0.582339\pi\)
−0.255800 + 0.966730i \(0.582339\pi\)
\(224\) 0 0
\(225\) −22.9517 −1.53011
\(226\) 0 0
\(227\) 25.9854 1.72471 0.862356 0.506303i \(-0.168988\pi\)
0.862356 + 0.506303i \(0.168988\pi\)
\(228\) 0 0
\(229\) −10.1641 −0.671664 −0.335832 0.941922i \(-0.609017\pi\)
−0.335832 + 0.941922i \(0.609017\pi\)
\(230\) 0 0
\(231\) 6.98902 0.459844
\(232\) 0 0
\(233\) −10.3490 −0.677984 −0.338992 0.940789i \(-0.610086\pi\)
−0.338992 + 0.940789i \(0.610086\pi\)
\(234\) 0 0
\(235\) 8.36849 0.545900
\(236\) 0 0
\(237\) 36.4639 2.36858
\(238\) 0 0
\(239\) 20.8350 1.34770 0.673850 0.738868i \(-0.264639\pi\)
0.673850 + 0.738868i \(0.264639\pi\)
\(240\) 0 0
\(241\) 19.5401 1.25869 0.629345 0.777126i \(-0.283323\pi\)
0.629345 + 0.777126i \(0.283323\pi\)
\(242\) 0 0
\(243\) 5.59350 0.358823
\(244\) 0 0
\(245\) −3.00500 −0.191983
\(246\) 0 0
\(247\) −7.01696 −0.446479
\(248\) 0 0
\(249\) −8.42602 −0.533978
\(250\) 0 0
\(251\) 22.4084 1.41441 0.707204 0.707010i \(-0.249956\pi\)
0.707204 + 0.707010i \(0.249956\pi\)
\(252\) 0 0
\(253\) 0.940946 0.0591568
\(254\) 0 0
\(255\) −19.1267 −1.19776
\(256\) 0 0
\(257\) −4.89503 −0.305344 −0.152672 0.988277i \(-0.548788\pi\)
−0.152672 + 0.988277i \(0.548788\pi\)
\(258\) 0 0
\(259\) 12.8830 0.800514
\(260\) 0 0
\(261\) −36.7253 −2.27324
\(262\) 0 0
\(263\) 19.6614 1.21237 0.606186 0.795323i \(-0.292699\pi\)
0.606186 + 0.795323i \(0.292699\pi\)
\(264\) 0 0
\(265\) 1.16277 0.0714287
\(266\) 0 0
\(267\) −2.38771 −0.146125
\(268\) 0 0
\(269\) −12.7626 −0.778146 −0.389073 0.921207i \(-0.627205\pi\)
−0.389073 + 0.921207i \(0.627205\pi\)
\(270\) 0 0
\(271\) 20.5820 1.25027 0.625134 0.780517i \(-0.285044\pi\)
0.625134 + 0.780517i \(0.285044\pi\)
\(272\) 0 0
\(273\) 66.2181 4.00770
\(274\) 0 0
\(275\) 2.70171 0.162919
\(276\) 0 0
\(277\) −1.81797 −0.109231 −0.0546155 0.998507i \(-0.517393\pi\)
−0.0546155 + 0.998507i \(0.517393\pi\)
\(278\) 0 0
\(279\) 30.2898 1.81341
\(280\) 0 0
\(281\) 18.1060 1.08011 0.540057 0.841628i \(-0.318403\pi\)
0.540057 + 0.841628i \(0.318403\pi\)
\(282\) 0 0
\(283\) −17.1952 −1.02215 −0.511075 0.859536i \(-0.670752\pi\)
−0.511075 + 0.859536i \(0.670752\pi\)
\(284\) 0 0
\(285\) −3.54439 −0.209952
\(286\) 0 0
\(287\) 23.7148 1.39984
\(288\) 0 0
\(289\) 12.1203 0.712956
\(290\) 0 0
\(291\) −37.3256 −2.18806
\(292\) 0 0
\(293\) −26.7819 −1.56461 −0.782307 0.622893i \(-0.785957\pi\)
−0.782307 + 0.622893i \(0.785957\pi\)
\(294\) 0 0
\(295\) 4.86444 0.283218
\(296\) 0 0
\(297\) −7.43104 −0.431193
\(298\) 0 0
\(299\) 8.91508 0.515572
\(300\) 0 0
\(301\) −27.8014 −1.60245
\(302\) 0 0
\(303\) 45.8317 2.63296
\(304\) 0 0
\(305\) −2.78647 −0.159553
\(306\) 0 0
\(307\) −25.6481 −1.46382 −0.731909 0.681403i \(-0.761370\pi\)
−0.731909 + 0.681403i \(0.761370\pi\)
\(308\) 0 0
\(309\) 22.4515 1.27722
\(310\) 0 0
\(311\) 21.6832 1.22954 0.614771 0.788706i \(-0.289248\pi\)
0.614771 + 0.788706i \(0.289248\pi\)
\(312\) 0 0
\(313\) 19.9277 1.12638 0.563189 0.826328i \(-0.309574\pi\)
0.563189 + 0.826328i \(0.309574\pi\)
\(314\) 0 0
\(315\) 22.6486 1.27610
\(316\) 0 0
\(317\) 17.9589 1.00867 0.504335 0.863508i \(-0.331738\pi\)
0.504335 + 0.863508i \(0.331738\pi\)
\(318\) 0 0
\(319\) 4.32303 0.242043
\(320\) 0 0
\(321\) −12.3411 −0.688813
\(322\) 0 0
\(323\) 5.39632 0.300259
\(324\) 0 0
\(325\) 25.5976 1.41990
\(326\) 0 0
\(327\) −24.0806 −1.33166
\(328\) 0 0
\(329\) 22.2809 1.22839
\(330\) 0 0
\(331\) −24.0397 −1.32134 −0.660671 0.750676i \(-0.729728\pi\)
−0.660671 + 0.750676i \(0.729728\pi\)
\(332\) 0 0
\(333\) −26.1820 −1.43476
\(334\) 0 0
\(335\) 14.6999 0.803141
\(336\) 0 0
\(337\) 4.89808 0.266815 0.133408 0.991061i \(-0.457408\pi\)
0.133408 + 0.991061i \(0.457408\pi\)
\(338\) 0 0
\(339\) 20.2548 1.10009
\(340\) 0 0
\(341\) −3.56550 −0.193083
\(342\) 0 0
\(343\) 13.6703 0.738125
\(344\) 0 0
\(345\) 4.50317 0.242442
\(346\) 0 0
\(347\) 18.3665 0.985968 0.492984 0.870038i \(-0.335906\pi\)
0.492984 + 0.870038i \(0.335906\pi\)
\(348\) 0 0
\(349\) 26.6377 1.42589 0.712943 0.701222i \(-0.247362\pi\)
0.712943 + 0.701222i \(0.247362\pi\)
\(350\) 0 0
\(351\) −70.4061 −3.75800
\(352\) 0 0
\(353\) −4.76409 −0.253567 −0.126783 0.991930i \(-0.540465\pi\)
−0.126783 + 0.991930i \(0.540465\pi\)
\(354\) 0 0
\(355\) 17.5371 0.930771
\(356\) 0 0
\(357\) −50.9243 −2.69520
\(358\) 0 0
\(359\) 11.0425 0.582800 0.291400 0.956601i \(-0.405879\pi\)
0.291400 + 0.956601i \(0.405879\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −31.8585 −1.67214
\(364\) 0 0
\(365\) 16.2028 0.848096
\(366\) 0 0
\(367\) −0.880221 −0.0459472 −0.0229736 0.999736i \(-0.507313\pi\)
−0.0229736 + 0.999736i \(0.507313\pi\)
\(368\) 0 0
\(369\) −48.1951 −2.50894
\(370\) 0 0
\(371\) 3.09586 0.160729
\(372\) 0 0
\(373\) −2.50328 −0.129615 −0.0648075 0.997898i \(-0.520643\pi\)
−0.0648075 + 0.997898i \(0.520643\pi\)
\(374\) 0 0
\(375\) 30.6518 1.58285
\(376\) 0 0
\(377\) 40.9590 2.10950
\(378\) 0 0
\(379\) −24.5729 −1.26222 −0.631112 0.775692i \(-0.717401\pi\)
−0.631112 + 0.775692i \(0.717401\pi\)
\(380\) 0 0
\(381\) −3.57459 −0.183132
\(382\) 0 0
\(383\) 7.34290 0.375204 0.187602 0.982245i \(-0.439928\pi\)
0.187602 + 0.982245i \(0.439928\pi\)
\(384\) 0 0
\(385\) −2.66603 −0.135874
\(386\) 0 0
\(387\) 56.5003 2.87207
\(388\) 0 0
\(389\) 36.1517 1.83296 0.916482 0.400075i \(-0.131016\pi\)
0.916482 + 0.400075i \(0.131016\pi\)
\(390\) 0 0
\(391\) −6.85604 −0.346725
\(392\) 0 0
\(393\) −31.5431 −1.59114
\(394\) 0 0
\(395\) −13.9095 −0.699863
\(396\) 0 0
\(397\) −11.4015 −0.572224 −0.286112 0.958196i \(-0.592363\pi\)
−0.286112 + 0.958196i \(0.592363\pi\)
\(398\) 0 0
\(399\) −9.43686 −0.472434
\(400\) 0 0
\(401\) −28.8683 −1.44161 −0.720806 0.693137i \(-0.756228\pi\)
−0.720806 + 0.693137i \(0.756228\pi\)
\(402\) 0 0
\(403\) −33.7817 −1.68279
\(404\) 0 0
\(405\) −13.6161 −0.676587
\(406\) 0 0
\(407\) 3.08195 0.152767
\(408\) 0 0
\(409\) −25.2528 −1.24867 −0.624336 0.781156i \(-0.714630\pi\)
−0.624336 + 0.781156i \(0.714630\pi\)
\(410\) 0 0
\(411\) 24.3800 1.20258
\(412\) 0 0
\(413\) 12.9514 0.637299
\(414\) 0 0
\(415\) 3.21419 0.157778
\(416\) 0 0
\(417\) 50.4966 2.47283
\(418\) 0 0
\(419\) 19.5676 0.955942 0.477971 0.878376i \(-0.341372\pi\)
0.477971 + 0.878376i \(0.341372\pi\)
\(420\) 0 0
\(421\) 35.8639 1.74790 0.873950 0.486015i \(-0.161550\pi\)
0.873950 + 0.486015i \(0.161550\pi\)
\(422\) 0 0
\(423\) −45.2811 −2.20164
\(424\) 0 0
\(425\) −19.6855 −0.954888
\(426\) 0 0
\(427\) −7.41892 −0.359027
\(428\) 0 0
\(429\) 15.8411 0.764814
\(430\) 0 0
\(431\) 37.6114 1.81168 0.905839 0.423621i \(-0.139241\pi\)
0.905839 + 0.423621i \(0.139241\pi\)
\(432\) 0 0
\(433\) −28.6407 −1.37638 −0.688191 0.725530i \(-0.741595\pi\)
−0.688191 + 0.725530i \(0.741595\pi\)
\(434\) 0 0
\(435\) 20.6891 0.991967
\(436\) 0 0
\(437\) −1.27050 −0.0607764
\(438\) 0 0
\(439\) 26.9827 1.28781 0.643907 0.765103i \(-0.277312\pi\)
0.643907 + 0.765103i \(0.277312\pi\)
\(440\) 0 0
\(441\) 16.2598 0.774275
\(442\) 0 0
\(443\) 8.11043 0.385338 0.192669 0.981264i \(-0.438286\pi\)
0.192669 + 0.981264i \(0.438286\pi\)
\(444\) 0 0
\(445\) 0.910815 0.0431768
\(446\) 0 0
\(447\) −15.6458 −0.740022
\(448\) 0 0
\(449\) 25.7519 1.21531 0.607654 0.794202i \(-0.292111\pi\)
0.607654 + 0.794202i \(0.292111\pi\)
\(450\) 0 0
\(451\) 5.67319 0.267140
\(452\) 0 0
\(453\) −35.6741 −1.67612
\(454\) 0 0
\(455\) −25.2596 −1.18419
\(456\) 0 0
\(457\) 20.4909 0.958524 0.479262 0.877672i \(-0.340904\pi\)
0.479262 + 0.877672i \(0.340904\pi\)
\(458\) 0 0
\(459\) 54.1450 2.52727
\(460\) 0 0
\(461\) 1.41508 0.0659068 0.0329534 0.999457i \(-0.489509\pi\)
0.0329534 + 0.999457i \(0.489509\pi\)
\(462\) 0 0
\(463\) −13.8270 −0.642594 −0.321297 0.946978i \(-0.604119\pi\)
−0.321297 + 0.946978i \(0.604119\pi\)
\(464\) 0 0
\(465\) −17.0637 −0.791312
\(466\) 0 0
\(467\) −33.2695 −1.53953 −0.769764 0.638329i \(-0.779626\pi\)
−0.769764 + 0.638329i \(0.779626\pi\)
\(468\) 0 0
\(469\) 39.1381 1.80723
\(470\) 0 0
\(471\) 61.8765 2.85112
\(472\) 0 0
\(473\) −6.65081 −0.305805
\(474\) 0 0
\(475\) −3.64796 −0.167380
\(476\) 0 0
\(477\) −6.29166 −0.288075
\(478\) 0 0
\(479\) −6.22234 −0.284306 −0.142153 0.989845i \(-0.545402\pi\)
−0.142153 + 0.989845i \(0.545402\pi\)
\(480\) 0 0
\(481\) 29.2003 1.33142
\(482\) 0 0
\(483\) 11.9896 0.545544
\(484\) 0 0
\(485\) 14.2382 0.646524
\(486\) 0 0
\(487\) −13.4589 −0.609881 −0.304941 0.952371i \(-0.598637\pi\)
−0.304941 + 0.952371i \(0.598637\pi\)
\(488\) 0 0
\(489\) 44.3226 2.00434
\(490\) 0 0
\(491\) −23.0456 −1.04003 −0.520016 0.854156i \(-0.674074\pi\)
−0.520016 + 0.854156i \(0.674074\pi\)
\(492\) 0 0
\(493\) −31.4991 −1.41865
\(494\) 0 0
\(495\) 5.41813 0.243527
\(496\) 0 0
\(497\) 46.6920 2.09442
\(498\) 0 0
\(499\) 19.9850 0.894650 0.447325 0.894372i \(-0.352377\pi\)
0.447325 + 0.894372i \(0.352377\pi\)
\(500\) 0 0
\(501\) 6.42373 0.286991
\(502\) 0 0
\(503\) −7.04829 −0.314268 −0.157134 0.987577i \(-0.550225\pi\)
−0.157134 + 0.987577i \(0.550225\pi\)
\(504\) 0 0
\(505\) −17.4830 −0.777982
\(506\) 0 0
\(507\) 110.461 4.90574
\(508\) 0 0
\(509\) 18.2695 0.809780 0.404890 0.914365i \(-0.367310\pi\)
0.404890 + 0.914365i \(0.367310\pi\)
\(510\) 0 0
\(511\) 43.1397 1.90839
\(512\) 0 0
\(513\) 10.0337 0.442999
\(514\) 0 0
\(515\) −8.56433 −0.377390
\(516\) 0 0
\(517\) 5.33016 0.234420
\(518\) 0 0
\(519\) −63.9834 −2.80856
\(520\) 0 0
\(521\) −35.5708 −1.55839 −0.779193 0.626784i \(-0.784371\pi\)
−0.779193 + 0.626784i \(0.784371\pi\)
\(522\) 0 0
\(523\) −17.0717 −0.746495 −0.373248 0.927732i \(-0.621756\pi\)
−0.373248 + 0.927732i \(0.621756\pi\)
\(524\) 0 0
\(525\) 34.4253 1.50244
\(526\) 0 0
\(527\) 25.9794 1.13168
\(528\) 0 0
\(529\) −21.3858 −0.929818
\(530\) 0 0
\(531\) −26.3210 −1.14223
\(532\) 0 0
\(533\) 53.7511 2.32822
\(534\) 0 0
\(535\) 4.70763 0.203529
\(536\) 0 0
\(537\) −64.9402 −2.80238
\(538\) 0 0
\(539\) −1.91398 −0.0824411
\(540\) 0 0
\(541\) −43.1129 −1.85357 −0.926785 0.375592i \(-0.877439\pi\)
−0.926785 + 0.375592i \(0.877439\pi\)
\(542\) 0 0
\(543\) −40.2760 −1.72841
\(544\) 0 0
\(545\) 9.18580 0.393476
\(546\) 0 0
\(547\) −21.0629 −0.900586 −0.450293 0.892881i \(-0.648680\pi\)
−0.450293 + 0.892881i \(0.648680\pi\)
\(548\) 0 0
\(549\) 15.0773 0.643485
\(550\) 0 0
\(551\) −5.83714 −0.248670
\(552\) 0 0
\(553\) −37.0337 −1.57483
\(554\) 0 0
\(555\) 14.7496 0.626085
\(556\) 0 0
\(557\) −7.64874 −0.324088 −0.162044 0.986784i \(-0.551809\pi\)
−0.162044 + 0.986784i \(0.551809\pi\)
\(558\) 0 0
\(559\) −63.0137 −2.66520
\(560\) 0 0
\(561\) −12.1824 −0.514341
\(562\) 0 0
\(563\) −36.5312 −1.53961 −0.769803 0.638282i \(-0.779645\pi\)
−0.769803 + 0.638282i \(0.779645\pi\)
\(564\) 0 0
\(565\) −7.72640 −0.325052
\(566\) 0 0
\(567\) −36.2524 −1.52246
\(568\) 0 0
\(569\) −17.1777 −0.720125 −0.360063 0.932928i \(-0.617245\pi\)
−0.360063 + 0.932928i \(0.617245\pi\)
\(570\) 0 0
\(571\) −31.0730 −1.30037 −0.650183 0.759777i \(-0.725308\pi\)
−0.650183 + 0.759777i \(0.725308\pi\)
\(572\) 0 0
\(573\) −49.5182 −2.06865
\(574\) 0 0
\(575\) 4.63474 0.193282
\(576\) 0 0
\(577\) −12.0608 −0.502096 −0.251048 0.967975i \(-0.580775\pi\)
−0.251048 + 0.967975i \(0.580775\pi\)
\(578\) 0 0
\(579\) 49.9396 2.07542
\(580\) 0 0
\(581\) 8.55770 0.355033
\(582\) 0 0
\(583\) 0.740609 0.0306729
\(584\) 0 0
\(585\) 51.3346 2.12242
\(586\) 0 0
\(587\) 35.7852 1.47701 0.738507 0.674245i \(-0.235531\pi\)
0.738507 + 0.674245i \(0.235531\pi\)
\(588\) 0 0
\(589\) 4.81429 0.198369
\(590\) 0 0
\(591\) 30.7599 1.26529
\(592\) 0 0
\(593\) 40.8186 1.67622 0.838110 0.545501i \(-0.183661\pi\)
0.838110 + 0.545501i \(0.183661\pi\)
\(594\) 0 0
\(595\) 19.4256 0.796372
\(596\) 0 0
\(597\) −34.4602 −1.41036
\(598\) 0 0
\(599\) 7.09856 0.290039 0.145020 0.989429i \(-0.453675\pi\)
0.145020 + 0.989429i \(0.453675\pi\)
\(600\) 0 0
\(601\) 16.6077 0.677443 0.338722 0.940887i \(-0.390006\pi\)
0.338722 + 0.940887i \(0.390006\pi\)
\(602\) 0 0
\(603\) −79.5396 −3.23910
\(604\) 0 0
\(605\) 12.1527 0.494079
\(606\) 0 0
\(607\) −36.8221 −1.49456 −0.747281 0.664508i \(-0.768641\pi\)
−0.747281 + 0.664508i \(0.768641\pi\)
\(608\) 0 0
\(609\) 55.0843 2.23213
\(610\) 0 0
\(611\) 50.5011 2.04306
\(612\) 0 0
\(613\) −12.0996 −0.488699 −0.244350 0.969687i \(-0.578574\pi\)
−0.244350 + 0.969687i \(0.578574\pi\)
\(614\) 0 0
\(615\) 27.1507 1.09482
\(616\) 0 0
\(617\) −0.604854 −0.0243505 −0.0121752 0.999926i \(-0.503876\pi\)
−0.0121752 + 0.999926i \(0.503876\pi\)
\(618\) 0 0
\(619\) −16.5794 −0.666383 −0.333191 0.942859i \(-0.608126\pi\)
−0.333191 + 0.942859i \(0.608126\pi\)
\(620\) 0 0
\(621\) −12.7479 −0.511554
\(622\) 0 0
\(623\) 2.42502 0.0971565
\(624\) 0 0
\(625\) 6.54735 0.261894
\(626\) 0 0
\(627\) −2.25754 −0.0901574
\(628\) 0 0
\(629\) −22.4561 −0.895385
\(630\) 0 0
\(631\) 21.7550 0.866052 0.433026 0.901381i \(-0.357446\pi\)
0.433026 + 0.901381i \(0.357446\pi\)
\(632\) 0 0
\(633\) 30.4129 1.20881
\(634\) 0 0
\(635\) 1.36356 0.0541113
\(636\) 0 0
\(637\) −18.1342 −0.718504
\(638\) 0 0
\(639\) −94.8913 −3.75384
\(640\) 0 0
\(641\) −0.517139 −0.0204257 −0.0102129 0.999948i \(-0.503251\pi\)
−0.0102129 + 0.999948i \(0.503251\pi\)
\(642\) 0 0
\(643\) −33.9671 −1.33953 −0.669766 0.742572i \(-0.733606\pi\)
−0.669766 + 0.742572i \(0.733606\pi\)
\(644\) 0 0
\(645\) −31.8294 −1.25328
\(646\) 0 0
\(647\) −32.8904 −1.29305 −0.646527 0.762891i \(-0.723779\pi\)
−0.646527 + 0.762891i \(0.723779\pi\)
\(648\) 0 0
\(649\) 3.09832 0.121620
\(650\) 0 0
\(651\) −45.4318 −1.78061
\(652\) 0 0
\(653\) −1.17030 −0.0457975 −0.0228988 0.999738i \(-0.507290\pi\)
−0.0228988 + 0.999738i \(0.507290\pi\)
\(654\) 0 0
\(655\) 12.0324 0.470146
\(656\) 0 0
\(657\) −87.6720 −3.42041
\(658\) 0 0
\(659\) −3.49037 −0.135966 −0.0679828 0.997686i \(-0.521656\pi\)
−0.0679828 + 0.997686i \(0.521656\pi\)
\(660\) 0 0
\(661\) 12.2910 0.478064 0.239032 0.971012i \(-0.423170\pi\)
0.239032 + 0.971012i \(0.423170\pi\)
\(662\) 0 0
\(663\) −115.423 −4.48267
\(664\) 0 0
\(665\) 3.59979 0.139594
\(666\) 0 0
\(667\) 7.41611 0.287153
\(668\) 0 0
\(669\) −23.2879 −0.900361
\(670\) 0 0
\(671\) −1.77479 −0.0685152
\(672\) 0 0
\(673\) −2.72180 −0.104918 −0.0524588 0.998623i \(-0.516706\pi\)
−0.0524588 + 0.998623i \(0.516706\pi\)
\(674\) 0 0
\(675\) −36.6025 −1.40883
\(676\) 0 0
\(677\) −32.6667 −1.25548 −0.627742 0.778421i \(-0.716021\pi\)
−0.627742 + 0.778421i \(0.716021\pi\)
\(678\) 0 0
\(679\) 37.9089 1.45481
\(680\) 0 0
\(681\) 79.2093 3.03531
\(682\) 0 0
\(683\) −41.0703 −1.57151 −0.785757 0.618536i \(-0.787726\pi\)
−0.785757 + 0.618536i \(0.787726\pi\)
\(684\) 0 0
\(685\) −9.29999 −0.355334
\(686\) 0 0
\(687\) −30.9825 −1.18206
\(688\) 0 0
\(689\) 7.01696 0.267325
\(690\) 0 0
\(691\) −27.3355 −1.03989 −0.519946 0.854199i \(-0.674048\pi\)
−0.519946 + 0.854199i \(0.674048\pi\)
\(692\) 0 0
\(693\) 14.4256 0.547984
\(694\) 0 0
\(695\) −19.2624 −0.730665
\(696\) 0 0
\(697\) −41.3367 −1.56574
\(698\) 0 0
\(699\) −31.5460 −1.19318
\(700\) 0 0
\(701\) 12.7553 0.481760 0.240880 0.970555i \(-0.422564\pi\)
0.240880 + 0.970555i \(0.422564\pi\)
\(702\) 0 0
\(703\) −4.16138 −0.156949
\(704\) 0 0
\(705\) 25.5090 0.960726
\(706\) 0 0
\(707\) −46.5480 −1.75062
\(708\) 0 0
\(709\) 3.78797 0.142260 0.0711302 0.997467i \(-0.477339\pi\)
0.0711302 + 0.997467i \(0.477339\pi\)
\(710\) 0 0
\(711\) 75.2629 2.82258
\(712\) 0 0
\(713\) −6.11657 −0.229067
\(714\) 0 0
\(715\) −6.04274 −0.225985
\(716\) 0 0
\(717\) 63.5096 2.37181
\(718\) 0 0
\(719\) −35.4850 −1.32337 −0.661685 0.749782i \(-0.730158\pi\)
−0.661685 + 0.749782i \(0.730158\pi\)
\(720\) 0 0
\(721\) −22.8023 −0.849203
\(722\) 0 0
\(723\) 59.5627 2.21516
\(724\) 0 0
\(725\) 21.2936 0.790825
\(726\) 0 0
\(727\) −19.8987 −0.738002 −0.369001 0.929429i \(-0.620300\pi\)
−0.369001 + 0.929429i \(0.620300\pi\)
\(728\) 0 0
\(729\) −18.0797 −0.669619
\(730\) 0 0
\(731\) 48.4600 1.79236
\(732\) 0 0
\(733\) −26.2945 −0.971210 −0.485605 0.874178i \(-0.661401\pi\)
−0.485605 + 0.874178i \(0.661401\pi\)
\(734\) 0 0
\(735\) −9.15992 −0.337869
\(736\) 0 0
\(737\) 9.36283 0.344884
\(738\) 0 0
\(739\) −16.4215 −0.604076 −0.302038 0.953296i \(-0.597667\pi\)
−0.302038 + 0.953296i \(0.597667\pi\)
\(740\) 0 0
\(741\) −21.3893 −0.785754
\(742\) 0 0
\(743\) 4.23096 0.155219 0.0776094 0.996984i \(-0.475271\pi\)
0.0776094 + 0.996984i \(0.475271\pi\)
\(744\) 0 0
\(745\) 5.96825 0.218660
\(746\) 0 0
\(747\) −17.3917 −0.636328
\(748\) 0 0
\(749\) 12.5340 0.457981
\(750\) 0 0
\(751\) −32.4440 −1.18390 −0.591948 0.805976i \(-0.701641\pi\)
−0.591948 + 0.805976i \(0.701641\pi\)
\(752\) 0 0
\(753\) 68.3059 2.48920
\(754\) 0 0
\(755\) 13.6083 0.495255
\(756\) 0 0
\(757\) −28.9795 −1.05328 −0.526640 0.850089i \(-0.676548\pi\)
−0.526640 + 0.850089i \(0.676548\pi\)
\(758\) 0 0
\(759\) 2.86821 0.104110
\(760\) 0 0
\(761\) −8.20808 −0.297543 −0.148771 0.988872i \(-0.547532\pi\)
−0.148771 + 0.988872i \(0.547532\pi\)
\(762\) 0 0
\(763\) 24.4570 0.885401
\(764\) 0 0
\(765\) −39.4783 −1.42734
\(766\) 0 0
\(767\) 29.3553 1.05996
\(768\) 0 0
\(769\) 17.0560 0.615056 0.307528 0.951539i \(-0.400498\pi\)
0.307528 + 0.951539i \(0.400498\pi\)
\(770\) 0 0
\(771\) −14.9212 −0.537372
\(772\) 0 0
\(773\) 2.48355 0.0893271 0.0446636 0.999002i \(-0.485778\pi\)
0.0446636 + 0.999002i \(0.485778\pi\)
\(774\) 0 0
\(775\) −17.5623 −0.630857
\(776\) 0 0
\(777\) 39.2704 1.40882
\(778\) 0 0
\(779\) −7.66017 −0.274454
\(780\) 0 0
\(781\) 11.1699 0.399691
\(782\) 0 0
\(783\) −58.5681 −2.09305
\(784\) 0 0
\(785\) −23.6034 −0.842441
\(786\) 0 0
\(787\) 19.2381 0.685764 0.342882 0.939378i \(-0.388597\pi\)
0.342882 + 0.939378i \(0.388597\pi\)
\(788\) 0 0
\(789\) 59.9322 2.13364
\(790\) 0 0
\(791\) −20.5713 −0.731433
\(792\) 0 0
\(793\) −16.8155 −0.597134
\(794\) 0 0
\(795\) 3.54439 0.125707
\(796\) 0 0
\(797\) 24.9359 0.883275 0.441637 0.897194i \(-0.354398\pi\)
0.441637 + 0.897194i \(0.354398\pi\)
\(798\) 0 0
\(799\) −38.8373 −1.37397
\(800\) 0 0
\(801\) −4.92833 −0.174134
\(802\) 0 0
\(803\) 10.3201 0.364189
\(804\) 0 0
\(805\) −4.57354 −0.161196
\(806\) 0 0
\(807\) −38.9031 −1.36945
\(808\) 0 0
\(809\) 12.2484 0.430631 0.215316 0.976545i \(-0.430922\pi\)
0.215316 + 0.976545i \(0.430922\pi\)
\(810\) 0 0
\(811\) 24.1065 0.846494 0.423247 0.906014i \(-0.360890\pi\)
0.423247 + 0.906014i \(0.360890\pi\)
\(812\) 0 0
\(813\) 62.7386 2.20034
\(814\) 0 0
\(815\) −16.9073 −0.592236
\(816\) 0 0
\(817\) 8.98019 0.314177
\(818\) 0 0
\(819\) 136.677 4.77588
\(820\) 0 0
\(821\) −4.27035 −0.149036 −0.0745181 0.997220i \(-0.523742\pi\)
−0.0745181 + 0.997220i \(0.523742\pi\)
\(822\) 0 0
\(823\) 1.20527 0.0420129 0.0210065 0.999779i \(-0.493313\pi\)
0.0210065 + 0.999779i \(0.493313\pi\)
\(824\) 0 0
\(825\) 8.23540 0.286720
\(826\) 0 0
\(827\) −0.801213 −0.0278609 −0.0139305 0.999903i \(-0.504434\pi\)
−0.0139305 + 0.999903i \(0.504434\pi\)
\(828\) 0 0
\(829\) 30.5026 1.05940 0.529699 0.848186i \(-0.322305\pi\)
0.529699 + 0.848186i \(0.322305\pi\)
\(830\) 0 0
\(831\) −5.54157 −0.192235
\(832\) 0 0
\(833\) 13.9459 0.483197
\(834\) 0 0
\(835\) −2.45040 −0.0847995
\(836\) 0 0
\(837\) 48.3051 1.66967
\(838\) 0 0
\(839\) 8.03688 0.277464 0.138732 0.990330i \(-0.455697\pi\)
0.138732 + 0.990330i \(0.455697\pi\)
\(840\) 0 0
\(841\) 5.07218 0.174903
\(842\) 0 0
\(843\) 55.1911 1.90088
\(844\) 0 0
\(845\) −42.1364 −1.44954
\(846\) 0 0
\(847\) 32.3564 1.11178
\(848\) 0 0
\(849\) −52.4148 −1.79887
\(850\) 0 0
\(851\) 5.28705 0.181238
\(852\) 0 0
\(853\) −10.3377 −0.353956 −0.176978 0.984215i \(-0.556632\pi\)
−0.176978 + 0.984215i \(0.556632\pi\)
\(854\) 0 0
\(855\) −7.31578 −0.250194
\(856\) 0 0
\(857\) −7.72909 −0.264021 −0.132010 0.991248i \(-0.542143\pi\)
−0.132010 + 0.991248i \(0.542143\pi\)
\(858\) 0 0
\(859\) −12.0954 −0.412689 −0.206345 0.978479i \(-0.566157\pi\)
−0.206345 + 0.978479i \(0.566157\pi\)
\(860\) 0 0
\(861\) 72.2879 2.46357
\(862\) 0 0
\(863\) −19.6215 −0.667925 −0.333963 0.942586i \(-0.608386\pi\)
−0.333963 + 0.942586i \(0.608386\pi\)
\(864\) 0 0
\(865\) 24.4071 0.829866
\(866\) 0 0
\(867\) 36.9452 1.25473
\(868\) 0 0
\(869\) −8.85941 −0.300535
\(870\) 0 0
\(871\) 88.7090 3.00579
\(872\) 0 0
\(873\) −77.0415 −2.60746
\(874\) 0 0
\(875\) −31.1308 −1.05241
\(876\) 0 0
\(877\) −0.158867 −0.00536456 −0.00268228 0.999996i \(-0.500854\pi\)
−0.00268228 + 0.999996i \(0.500854\pi\)
\(878\) 0 0
\(879\) −81.6371 −2.75355
\(880\) 0 0
\(881\) 0.142683 0.00480710 0.00240355 0.999997i \(-0.499235\pi\)
0.00240355 + 0.999997i \(0.499235\pi\)
\(882\) 0 0
\(883\) −12.5685 −0.422964 −0.211482 0.977382i \(-0.567829\pi\)
−0.211482 + 0.977382i \(0.567829\pi\)
\(884\) 0 0
\(885\) 14.8279 0.498434
\(886\) 0 0
\(887\) 9.10854 0.305835 0.152917 0.988239i \(-0.451133\pi\)
0.152917 + 0.988239i \(0.451133\pi\)
\(888\) 0 0
\(889\) 3.63045 0.121761
\(890\) 0 0
\(891\) −8.67251 −0.290540
\(892\) 0 0
\(893\) −7.19701 −0.240839
\(894\) 0 0
\(895\) 24.7721 0.828040
\(896\) 0 0
\(897\) 27.1751 0.907352
\(898\) 0 0
\(899\) −28.1017 −0.937243
\(900\) 0 0
\(901\) −5.39632 −0.179777
\(902\) 0 0
\(903\) −84.7449 −2.82013
\(904\) 0 0
\(905\) 15.3637 0.510706
\(906\) 0 0
\(907\) 48.1536 1.59891 0.799457 0.600723i \(-0.205121\pi\)
0.799457 + 0.600723i \(0.205121\pi\)
\(908\) 0 0
\(909\) 94.5986 3.13764
\(910\) 0 0
\(911\) 26.1851 0.867552 0.433776 0.901021i \(-0.357181\pi\)
0.433776 + 0.901021i \(0.357181\pi\)
\(912\) 0 0
\(913\) 2.04722 0.0677531
\(914\) 0 0
\(915\) −8.49379 −0.280796
\(916\) 0 0
\(917\) 32.0360 1.05792
\(918\) 0 0
\(919\) −27.3973 −0.903755 −0.451878 0.892080i \(-0.649246\pi\)
−0.451878 + 0.892080i \(0.649246\pi\)
\(920\) 0 0
\(921\) −78.1812 −2.57616
\(922\) 0 0
\(923\) 105.830 3.48345
\(924\) 0 0
\(925\) 15.1805 0.499133
\(926\) 0 0
\(927\) 46.3408 1.52203
\(928\) 0 0
\(929\) 0.708375 0.0232410 0.0116205 0.999932i \(-0.496301\pi\)
0.0116205 + 0.999932i \(0.496301\pi\)
\(930\) 0 0
\(931\) 2.58434 0.0846983
\(932\) 0 0
\(933\) 66.0952 2.16386
\(934\) 0 0
\(935\) 4.64710 0.151976
\(936\) 0 0
\(937\) −0.0101807 −0.000332587 0 −0.000166294 1.00000i \(-0.500053\pi\)
−0.000166294 1.00000i \(0.500053\pi\)
\(938\) 0 0
\(939\) 60.7439 1.98230
\(940\) 0 0
\(941\) 19.8896 0.648381 0.324191 0.945992i \(-0.394908\pi\)
0.324191 + 0.945992i \(0.394908\pi\)
\(942\) 0 0
\(943\) 9.73227 0.316926
\(944\) 0 0
\(945\) 36.1192 1.17496
\(946\) 0 0
\(947\) −6.65944 −0.216403 −0.108201 0.994129i \(-0.534509\pi\)
−0.108201 + 0.994129i \(0.534509\pi\)
\(948\) 0 0
\(949\) 97.7789 3.17404
\(950\) 0 0
\(951\) 54.7426 1.77515
\(952\) 0 0
\(953\) 27.1133 0.878286 0.439143 0.898417i \(-0.355282\pi\)
0.439143 + 0.898417i \(0.355282\pi\)
\(954\) 0 0
\(955\) 18.8892 0.611241
\(956\) 0 0
\(957\) 13.1776 0.425970
\(958\) 0 0
\(959\) −24.7610 −0.799574
\(960\) 0 0
\(961\) −7.82263 −0.252343
\(962\) 0 0
\(963\) −25.4725 −0.820841
\(964\) 0 0
\(965\) −19.0500 −0.613240
\(966\) 0 0
\(967\) 12.9830 0.417504 0.208752 0.977969i \(-0.433060\pi\)
0.208752 + 0.977969i \(0.433060\pi\)
\(968\) 0 0
\(969\) 16.4492 0.528424
\(970\) 0 0
\(971\) 3.01652 0.0968047 0.0484024 0.998828i \(-0.484587\pi\)
0.0484024 + 0.998828i \(0.484587\pi\)
\(972\) 0 0
\(973\) −51.2857 −1.64414
\(974\) 0 0
\(975\) 78.0271 2.49887
\(976\) 0 0
\(977\) 52.7315 1.68703 0.843515 0.537105i \(-0.180482\pi\)
0.843515 + 0.537105i \(0.180482\pi\)
\(978\) 0 0
\(979\) 0.580128 0.0185410
\(980\) 0 0
\(981\) −49.7034 −1.58691
\(982\) 0 0
\(983\) 2.56594 0.0818409 0.0409204 0.999162i \(-0.486971\pi\)
0.0409204 + 0.999162i \(0.486971\pi\)
\(984\) 0 0
\(985\) −11.7337 −0.373866
\(986\) 0 0
\(987\) 67.9172 2.16183
\(988\) 0 0
\(989\) −11.4094 −0.362797
\(990\) 0 0
\(991\) −27.2810 −0.866608 −0.433304 0.901248i \(-0.642652\pi\)
−0.433304 + 0.901248i \(0.642652\pi\)
\(992\) 0 0
\(993\) −73.2784 −2.32542
\(994\) 0 0
\(995\) 13.1452 0.416730
\(996\) 0 0
\(997\) 54.1487 1.71491 0.857453 0.514562i \(-0.172046\pi\)
0.857453 + 0.514562i \(0.172046\pi\)
\(998\) 0 0
\(999\) −41.7540 −1.32104
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 4028.2.a.c.1.19 19
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4028.2.a.c.1.19 19 1.1 even 1 trivial