Properties

Label 4024.2.a.f.1.17
Level $4024$
Weight $2$
Character 4024.1
Self dual yes
Analytic conductor $32.132$
Analytic rank $0$
Dimension $33$
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] = [4024,2,Mod(1,4024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4024, 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("4024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4024.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: \(32.1318017734\)
Analytic rank: \(0\)
Dimension: \(33\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 4024.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.0147975 q^{3} -2.88853 q^{5} -1.61248 q^{7} -2.99978 q^{9} +O(q^{10})\) \(q+0.0147975 q^{3} -2.88853 q^{5} -1.61248 q^{7} -2.99978 q^{9} -3.67687 q^{11} -5.42310 q^{13} -0.0427431 q^{15} -0.739860 q^{17} -2.07178 q^{19} -0.0238606 q^{21} -2.75750 q^{23} +3.34363 q^{25} -0.0887818 q^{27} +0.0289230 q^{29} +3.10947 q^{31} -0.0544085 q^{33} +4.65769 q^{35} -1.40122 q^{37} -0.0802483 q^{39} -11.0456 q^{41} -4.99763 q^{43} +8.66497 q^{45} -7.39726 q^{47} -4.39992 q^{49} -0.0109481 q^{51} +7.42772 q^{53} +10.6208 q^{55} -0.0306571 q^{57} +13.1711 q^{59} -3.31482 q^{61} +4.83707 q^{63} +15.6648 q^{65} +0.0846196 q^{67} -0.0408041 q^{69} -6.58897 q^{71} -7.88606 q^{73} +0.0494774 q^{75} +5.92887 q^{77} +6.88374 q^{79} +8.99803 q^{81} +4.85024 q^{83} +2.13711 q^{85} +0.000427988 q^{87} +10.6708 q^{89} +8.74462 q^{91} +0.0460123 q^{93} +5.98439 q^{95} -11.7602 q^{97} +11.0298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 33 q - 2 q^{3} + 12 q^{5} + 4 q^{7} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 33 q - 2 q^{3} + 12 q^{5} + 4 q^{7} + 43 q^{9} + 22 q^{11} + 25 q^{13} - 4 q^{15} + 17 q^{17} + 6 q^{19} + 18 q^{21} + 16 q^{23} + 47 q^{25} - 20 q^{27} + 47 q^{29} - 7 q^{31} - 6 q^{33} + 19 q^{35} + 75 q^{37} + 21 q^{39} + 22 q^{41} - 5 q^{43} + 33 q^{45} + 10 q^{47} + 31 q^{49} + 9 q^{51} + 64 q^{53} - 3 q^{55} + 5 q^{57} + 28 q^{59} + 49 q^{61} - 10 q^{63} + 46 q^{65} - 14 q^{67} + 30 q^{69} + 35 q^{71} + 19 q^{73} - 33 q^{75} + 32 q^{77} - 12 q^{79} + 57 q^{81} + 82 q^{85} - 5 q^{87} + 42 q^{89} - 15 q^{91} + 55 q^{93} + 33 q^{95} + 4 q^{97} + 22 q^{99}+O(q^{100}) \) 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
\(3\) 0.0147975 0.00854334 0.00427167 0.999991i \(-0.498640\pi\)
0.00427167 + 0.999991i \(0.498640\pi\)
\(4\) 0 0
\(5\) −2.88853 −1.29179 −0.645896 0.763425i \(-0.723516\pi\)
−0.645896 + 0.763425i \(0.723516\pi\)
\(6\) 0 0
\(7\) −1.61248 −0.609459 −0.304729 0.952439i \(-0.598566\pi\)
−0.304729 + 0.952439i \(0.598566\pi\)
\(8\) 0 0
\(9\) −2.99978 −0.999927
\(10\) 0 0
\(11\) −3.67687 −1.10862 −0.554309 0.832311i \(-0.687018\pi\)
−0.554309 + 0.832311i \(0.687018\pi\)
\(12\) 0 0
\(13\) −5.42310 −1.50410 −0.752049 0.659108i \(-0.770934\pi\)
−0.752049 + 0.659108i \(0.770934\pi\)
\(14\) 0 0
\(15\) −0.0427431 −0.0110362
\(16\) 0 0
\(17\) −0.739860 −0.179442 −0.0897212 0.995967i \(-0.528598\pi\)
−0.0897212 + 0.995967i \(0.528598\pi\)
\(18\) 0 0
\(19\) −2.07178 −0.475298 −0.237649 0.971351i \(-0.576377\pi\)
−0.237649 + 0.971351i \(0.576377\pi\)
\(20\) 0 0
\(21\) −0.0238606 −0.00520681
\(22\) 0 0
\(23\) −2.75750 −0.574978 −0.287489 0.957784i \(-0.592820\pi\)
−0.287489 + 0.957784i \(0.592820\pi\)
\(24\) 0 0
\(25\) 3.34363 0.668727
\(26\) 0 0
\(27\) −0.0887818 −0.0170861
\(28\) 0 0
\(29\) 0.0289230 0.00537086 0.00268543 0.999996i \(-0.499145\pi\)
0.00268543 + 0.999996i \(0.499145\pi\)
\(30\) 0 0
\(31\) 3.10947 0.558477 0.279238 0.960222i \(-0.409918\pi\)
0.279238 + 0.960222i \(0.409918\pi\)
\(32\) 0 0
\(33\) −0.0544085 −0.00947131
\(34\) 0 0
\(35\) 4.65769 0.787294
\(36\) 0 0
\(37\) −1.40122 −0.230359 −0.115180 0.993345i \(-0.536744\pi\)
−0.115180 + 0.993345i \(0.536744\pi\)
\(38\) 0 0
\(39\) −0.0802483 −0.0128500
\(40\) 0 0
\(41\) −11.0456 −1.72503 −0.862513 0.506035i \(-0.831111\pi\)
−0.862513 + 0.506035i \(0.831111\pi\)
\(42\) 0 0
\(43\) −4.99763 −0.762131 −0.381066 0.924548i \(-0.624443\pi\)
−0.381066 + 0.924548i \(0.624443\pi\)
\(44\) 0 0
\(45\) 8.66497 1.29170
\(46\) 0 0
\(47\) −7.39726 −1.07900 −0.539500 0.841985i \(-0.681387\pi\)
−0.539500 + 0.841985i \(0.681387\pi\)
\(48\) 0 0
\(49\) −4.39992 −0.628560
\(50\) 0 0
\(51\) −0.0109481 −0.00153304
\(52\) 0 0
\(53\) 7.42772 1.02028 0.510138 0.860093i \(-0.329594\pi\)
0.510138 + 0.860093i \(0.329594\pi\)
\(54\) 0 0
\(55\) 10.6208 1.43210
\(56\) 0 0
\(57\) −0.0306571 −0.00406063
\(58\) 0 0
\(59\) 13.1711 1.71473 0.857365 0.514710i \(-0.172100\pi\)
0.857365 + 0.514710i \(0.172100\pi\)
\(60\) 0 0
\(61\) −3.31482 −0.424419 −0.212210 0.977224i \(-0.568066\pi\)
−0.212210 + 0.977224i \(0.568066\pi\)
\(62\) 0 0
\(63\) 4.83707 0.609414
\(64\) 0 0
\(65\) 15.6648 1.94298
\(66\) 0 0
\(67\) 0.0846196 0.0103379 0.00516897 0.999987i \(-0.498355\pi\)
0.00516897 + 0.999987i \(0.498355\pi\)
\(68\) 0 0
\(69\) −0.0408041 −0.00491223
\(70\) 0 0
\(71\) −6.58897 −0.781967 −0.390983 0.920398i \(-0.627865\pi\)
−0.390983 + 0.920398i \(0.627865\pi\)
\(72\) 0 0
\(73\) −7.88606 −0.922994 −0.461497 0.887142i \(-0.652687\pi\)
−0.461497 + 0.887142i \(0.652687\pi\)
\(74\) 0 0
\(75\) 0.0494774 0.00571316
\(76\) 0 0
\(77\) 5.92887 0.675657
\(78\) 0 0
\(79\) 6.88374 0.774481 0.387241 0.921979i \(-0.373428\pi\)
0.387241 + 0.921979i \(0.373428\pi\)
\(80\) 0 0
\(81\) 8.99803 0.999781
\(82\) 0 0
\(83\) 4.85024 0.532383 0.266192 0.963920i \(-0.414235\pi\)
0.266192 + 0.963920i \(0.414235\pi\)
\(84\) 0 0
\(85\) 2.13711 0.231802
\(86\) 0 0
\(87\) 0.000427988 0 4.58851e−5 0
\(88\) 0 0
\(89\) 10.6708 1.13110 0.565552 0.824713i \(-0.308663\pi\)
0.565552 + 0.824713i \(0.308663\pi\)
\(90\) 0 0
\(91\) 8.74462 0.916685
\(92\) 0 0
\(93\) 0.0460123 0.00477126
\(94\) 0 0
\(95\) 5.98439 0.613986
\(96\) 0 0
\(97\) −11.7602 −1.19407 −0.597034 0.802216i \(-0.703654\pi\)
−0.597034 + 0.802216i \(0.703654\pi\)
\(98\) 0 0
\(99\) 11.0298 1.10854
\(100\) 0 0
\(101\) 11.6147 1.15571 0.577854 0.816140i \(-0.303890\pi\)
0.577854 + 0.816140i \(0.303890\pi\)
\(102\) 0 0
\(103\) 1.99357 0.196432 0.0982162 0.995165i \(-0.468686\pi\)
0.0982162 + 0.995165i \(0.468686\pi\)
\(104\) 0 0
\(105\) 0.0689222 0.00672612
\(106\) 0 0
\(107\) −6.10156 −0.589861 −0.294930 0.955519i \(-0.595296\pi\)
−0.294930 + 0.955519i \(0.595296\pi\)
\(108\) 0 0
\(109\) 11.2132 1.07403 0.537014 0.843573i \(-0.319552\pi\)
0.537014 + 0.843573i \(0.319552\pi\)
\(110\) 0 0
\(111\) −0.0207346 −0.00196804
\(112\) 0 0
\(113\) −5.70315 −0.536507 −0.268254 0.963348i \(-0.586447\pi\)
−0.268254 + 0.963348i \(0.586447\pi\)
\(114\) 0 0
\(115\) 7.96513 0.742752
\(116\) 0 0
\(117\) 16.2681 1.50399
\(118\) 0 0
\(119\) 1.19301 0.109363
\(120\) 0 0
\(121\) 2.51939 0.229035
\(122\) 0 0
\(123\) −0.163447 −0.0147375
\(124\) 0 0
\(125\) 4.78447 0.427936
\(126\) 0 0
\(127\) −15.1852 −1.34747 −0.673735 0.738973i \(-0.735311\pi\)
−0.673735 + 0.738973i \(0.735311\pi\)
\(128\) 0 0
\(129\) −0.0739524 −0.00651115
\(130\) 0 0
\(131\) 6.76214 0.590811 0.295406 0.955372i \(-0.404545\pi\)
0.295406 + 0.955372i \(0.404545\pi\)
\(132\) 0 0
\(133\) 3.34069 0.289674
\(134\) 0 0
\(135\) 0.256449 0.0220716
\(136\) 0 0
\(137\) −15.2609 −1.30383 −0.651914 0.758293i \(-0.726034\pi\)
−0.651914 + 0.758293i \(0.726034\pi\)
\(138\) 0 0
\(139\) −20.8633 −1.76960 −0.884802 0.465966i \(-0.845707\pi\)
−0.884802 + 0.465966i \(0.845707\pi\)
\(140\) 0 0
\(141\) −0.109461 −0.00921827
\(142\) 0 0
\(143\) 19.9400 1.66747
\(144\) 0 0
\(145\) −0.0835450 −0.00693804
\(146\) 0 0
\(147\) −0.0651078 −0.00537000
\(148\) 0 0
\(149\) −8.90707 −0.729696 −0.364848 0.931067i \(-0.618879\pi\)
−0.364848 + 0.931067i \(0.618879\pi\)
\(150\) 0 0
\(151\) −20.1837 −1.64252 −0.821262 0.570552i \(-0.806729\pi\)
−0.821262 + 0.570552i \(0.806729\pi\)
\(152\) 0 0
\(153\) 2.21942 0.179429
\(154\) 0 0
\(155\) −8.98180 −0.721436
\(156\) 0 0
\(157\) 5.58543 0.445766 0.222883 0.974845i \(-0.428453\pi\)
0.222883 + 0.974845i \(0.428453\pi\)
\(158\) 0 0
\(159\) 0.109912 0.00871656
\(160\) 0 0
\(161\) 4.44640 0.350425
\(162\) 0 0
\(163\) 17.9753 1.40793 0.703966 0.710234i \(-0.251411\pi\)
0.703966 + 0.710234i \(0.251411\pi\)
\(164\) 0 0
\(165\) 0.157161 0.0122350
\(166\) 0 0
\(167\) 5.70835 0.441726 0.220863 0.975305i \(-0.429113\pi\)
0.220863 + 0.975305i \(0.429113\pi\)
\(168\) 0 0
\(169\) 16.4100 1.26231
\(170\) 0 0
\(171\) 6.21487 0.475263
\(172\) 0 0
\(173\) −1.02020 −0.0775641 −0.0387821 0.999248i \(-0.512348\pi\)
−0.0387821 + 0.999248i \(0.512348\pi\)
\(174\) 0 0
\(175\) −5.39153 −0.407561
\(176\) 0 0
\(177\) 0.194899 0.0146495
\(178\) 0 0
\(179\) −26.3011 −1.96584 −0.982920 0.184033i \(-0.941085\pi\)
−0.982920 + 0.184033i \(0.941085\pi\)
\(180\) 0 0
\(181\) 6.91194 0.513760 0.256880 0.966443i \(-0.417305\pi\)
0.256880 + 0.966443i \(0.417305\pi\)
\(182\) 0 0
\(183\) −0.0490510 −0.00362596
\(184\) 0 0
\(185\) 4.04748 0.297576
\(186\) 0 0
\(187\) 2.72037 0.198933
\(188\) 0 0
\(189\) 0.143158 0.0104132
\(190\) 0 0
\(191\) 24.6600 1.78434 0.892168 0.451704i \(-0.149184\pi\)
0.892168 + 0.451704i \(0.149184\pi\)
\(192\) 0 0
\(193\) 1.62448 0.116933 0.0584664 0.998289i \(-0.481379\pi\)
0.0584664 + 0.998289i \(0.481379\pi\)
\(194\) 0 0
\(195\) 0.231800 0.0165996
\(196\) 0 0
\(197\) 21.8372 1.55584 0.777919 0.628365i \(-0.216275\pi\)
0.777919 + 0.628365i \(0.216275\pi\)
\(198\) 0 0
\(199\) −20.0279 −1.41974 −0.709869 0.704334i \(-0.751246\pi\)
−0.709869 + 0.704334i \(0.751246\pi\)
\(200\) 0 0
\(201\) 0.00125216 8.83205e−5 0
\(202\) 0 0
\(203\) −0.0466376 −0.00327332
\(204\) 0 0
\(205\) 31.9055 2.22837
\(206\) 0 0
\(207\) 8.27189 0.574936
\(208\) 0 0
\(209\) 7.61765 0.526924
\(210\) 0 0
\(211\) −9.88027 −0.680186 −0.340093 0.940392i \(-0.610459\pi\)
−0.340093 + 0.940392i \(0.610459\pi\)
\(212\) 0 0
\(213\) −0.0975003 −0.00668061
\(214\) 0 0
\(215\) 14.4358 0.984515
\(216\) 0 0
\(217\) −5.01394 −0.340368
\(218\) 0 0
\(219\) −0.116694 −0.00788545
\(220\) 0 0
\(221\) 4.01234 0.269899
\(222\) 0 0
\(223\) −14.7872 −0.990227 −0.495113 0.868828i \(-0.664874\pi\)
−0.495113 + 0.868828i \(0.664874\pi\)
\(224\) 0 0
\(225\) −10.0302 −0.668678
\(226\) 0 0
\(227\) 3.51449 0.233265 0.116632 0.993175i \(-0.462790\pi\)
0.116632 + 0.993175i \(0.462790\pi\)
\(228\) 0 0
\(229\) 0.697824 0.0461135 0.0230568 0.999734i \(-0.492660\pi\)
0.0230568 + 0.999734i \(0.492660\pi\)
\(230\) 0 0
\(231\) 0.0877324 0.00577237
\(232\) 0 0
\(233\) −0.532456 −0.0348824 −0.0174412 0.999848i \(-0.505552\pi\)
−0.0174412 + 0.999848i \(0.505552\pi\)
\(234\) 0 0
\(235\) 21.3672 1.39384
\(236\) 0 0
\(237\) 0.101862 0.00661666
\(238\) 0 0
\(239\) −20.7798 −1.34414 −0.672068 0.740490i \(-0.734594\pi\)
−0.672068 + 0.740490i \(0.734594\pi\)
\(240\) 0 0
\(241\) 10.9898 0.707917 0.353959 0.935261i \(-0.384835\pi\)
0.353959 + 0.935261i \(0.384835\pi\)
\(242\) 0 0
\(243\) 0.399494 0.0256275
\(244\) 0 0
\(245\) 12.7093 0.811969
\(246\) 0 0
\(247\) 11.2354 0.714894
\(248\) 0 0
\(249\) 0.0717715 0.00454833
\(250\) 0 0
\(251\) −10.5002 −0.662765 −0.331383 0.943496i \(-0.607515\pi\)
−0.331383 + 0.943496i \(0.607515\pi\)
\(252\) 0 0
\(253\) 10.1390 0.637431
\(254\) 0 0
\(255\) 0.0316239 0.00198037
\(256\) 0 0
\(257\) −17.3616 −1.08299 −0.541495 0.840704i \(-0.682141\pi\)
−0.541495 + 0.840704i \(0.682141\pi\)
\(258\) 0 0
\(259\) 2.25944 0.140394
\(260\) 0 0
\(261\) −0.0867626 −0.00537047
\(262\) 0 0
\(263\) −2.78239 −0.171569 −0.0857847 0.996314i \(-0.527340\pi\)
−0.0857847 + 0.996314i \(0.527340\pi\)
\(264\) 0 0
\(265\) −21.4552 −1.31798
\(266\) 0 0
\(267\) 0.157901 0.00966341
\(268\) 0 0
\(269\) −22.9762 −1.40089 −0.700443 0.713708i \(-0.747014\pi\)
−0.700443 + 0.713708i \(0.747014\pi\)
\(270\) 0 0
\(271\) −3.22861 −0.196124 −0.0980621 0.995180i \(-0.531264\pi\)
−0.0980621 + 0.995180i \(0.531264\pi\)
\(272\) 0 0
\(273\) 0.129399 0.00783155
\(274\) 0 0
\(275\) −12.2941 −0.741363
\(276\) 0 0
\(277\) 31.8434 1.91328 0.956641 0.291270i \(-0.0940776\pi\)
0.956641 + 0.291270i \(0.0940776\pi\)
\(278\) 0 0
\(279\) −9.32772 −0.558436
\(280\) 0 0
\(281\) 10.0084 0.597050 0.298525 0.954402i \(-0.403505\pi\)
0.298525 + 0.954402i \(0.403505\pi\)
\(282\) 0 0
\(283\) −19.0070 −1.12985 −0.564925 0.825142i \(-0.691095\pi\)
−0.564925 + 0.825142i \(0.691095\pi\)
\(284\) 0 0
\(285\) 0.0885541 0.00524549
\(286\) 0 0
\(287\) 17.8107 1.05133
\(288\) 0 0
\(289\) −16.4526 −0.967800
\(290\) 0 0
\(291\) −0.174022 −0.0102013
\(292\) 0 0
\(293\) −10.7160 −0.626033 −0.313017 0.949748i \(-0.601340\pi\)
−0.313017 + 0.949748i \(0.601340\pi\)
\(294\) 0 0
\(295\) −38.0451 −2.21507
\(296\) 0 0
\(297\) 0.326439 0.0189419
\(298\) 0 0
\(299\) 14.9542 0.864823
\(300\) 0 0
\(301\) 8.05856 0.464488
\(302\) 0 0
\(303\) 0.171869 0.00987360
\(304\) 0 0
\(305\) 9.57497 0.548261
\(306\) 0 0
\(307\) −0.596611 −0.0340504 −0.0170252 0.999855i \(-0.505420\pi\)
−0.0170252 + 0.999855i \(0.505420\pi\)
\(308\) 0 0
\(309\) 0.0294999 0.00167819
\(310\) 0 0
\(311\) 6.82381 0.386943 0.193471 0.981106i \(-0.438025\pi\)
0.193471 + 0.981106i \(0.438025\pi\)
\(312\) 0 0
\(313\) 11.1226 0.628684 0.314342 0.949310i \(-0.398216\pi\)
0.314342 + 0.949310i \(0.398216\pi\)
\(314\) 0 0
\(315\) −13.9721 −0.787236
\(316\) 0 0
\(317\) 9.76165 0.548269 0.274134 0.961691i \(-0.411609\pi\)
0.274134 + 0.961691i \(0.411609\pi\)
\(318\) 0 0
\(319\) −0.106346 −0.00595424
\(320\) 0 0
\(321\) −0.0902879 −0.00503938
\(322\) 0 0
\(323\) 1.53282 0.0852886
\(324\) 0 0
\(325\) −18.1329 −1.00583
\(326\) 0 0
\(327\) 0.165927 0.00917580
\(328\) 0 0
\(329\) 11.9279 0.657606
\(330\) 0 0
\(331\) 6.83632 0.375758 0.187879 0.982192i \(-0.439839\pi\)
0.187879 + 0.982192i \(0.439839\pi\)
\(332\) 0 0
\(333\) 4.20336 0.230343
\(334\) 0 0
\(335\) −0.244427 −0.0133545
\(336\) 0 0
\(337\) 30.1341 1.64151 0.820754 0.571282i \(-0.193554\pi\)
0.820754 + 0.571282i \(0.193554\pi\)
\(338\) 0 0
\(339\) −0.0843924 −0.00458357
\(340\) 0 0
\(341\) −11.4331 −0.619137
\(342\) 0 0
\(343\) 18.3821 0.992540
\(344\) 0 0
\(345\) 0.117864 0.00634558
\(346\) 0 0
\(347\) 9.89878 0.531394 0.265697 0.964057i \(-0.414398\pi\)
0.265697 + 0.964057i \(0.414398\pi\)
\(348\) 0 0
\(349\) 34.2313 1.83236 0.916179 0.400769i \(-0.131257\pi\)
0.916179 + 0.400769i \(0.131257\pi\)
\(350\) 0 0
\(351\) 0.481472 0.0256991
\(352\) 0 0
\(353\) −22.0633 −1.17431 −0.587156 0.809474i \(-0.699753\pi\)
−0.587156 + 0.809474i \(0.699753\pi\)
\(354\) 0 0
\(355\) 19.0325 1.01014
\(356\) 0 0
\(357\) 0.0176535 0.000934323 0
\(358\) 0 0
\(359\) 32.2127 1.70012 0.850061 0.526684i \(-0.176565\pi\)
0.850061 + 0.526684i \(0.176565\pi\)
\(360\) 0 0
\(361\) −14.7077 −0.774092
\(362\) 0 0
\(363\) 0.0372806 0.00195672
\(364\) 0 0
\(365\) 22.7792 1.19232
\(366\) 0 0
\(367\) −6.17329 −0.322243 −0.161121 0.986935i \(-0.551511\pi\)
−0.161121 + 0.986935i \(0.551511\pi\)
\(368\) 0 0
\(369\) 33.1343 1.72490
\(370\) 0 0
\(371\) −11.9770 −0.621816
\(372\) 0 0
\(373\) −8.28364 −0.428911 −0.214455 0.976734i \(-0.568798\pi\)
−0.214455 + 0.976734i \(0.568798\pi\)
\(374\) 0 0
\(375\) 0.0707983 0.00365601
\(376\) 0 0
\(377\) −0.156852 −0.00807830
\(378\) 0 0
\(379\) −20.7329 −1.06498 −0.532489 0.846437i \(-0.678743\pi\)
−0.532489 + 0.846437i \(0.678743\pi\)
\(380\) 0 0
\(381\) −0.224703 −0.0115119
\(382\) 0 0
\(383\) −9.29514 −0.474959 −0.237480 0.971393i \(-0.576321\pi\)
−0.237480 + 0.971393i \(0.576321\pi\)
\(384\) 0 0
\(385\) −17.1257 −0.872808
\(386\) 0 0
\(387\) 14.9918 0.762076
\(388\) 0 0
\(389\) 0.814216 0.0412824 0.0206412 0.999787i \(-0.493429\pi\)
0.0206412 + 0.999787i \(0.493429\pi\)
\(390\) 0 0
\(391\) 2.04016 0.103175
\(392\) 0 0
\(393\) 0.100063 0.00504750
\(394\) 0 0
\(395\) −19.8839 −1.00047
\(396\) 0 0
\(397\) −26.9942 −1.35480 −0.677401 0.735614i \(-0.736894\pi\)
−0.677401 + 0.735614i \(0.736894\pi\)
\(398\) 0 0
\(399\) 0.0494338 0.00247479
\(400\) 0 0
\(401\) 34.4537 1.72054 0.860269 0.509841i \(-0.170296\pi\)
0.860269 + 0.509841i \(0.170296\pi\)
\(402\) 0 0
\(403\) −16.8629 −0.840003
\(404\) 0 0
\(405\) −25.9911 −1.29151
\(406\) 0 0
\(407\) 5.15211 0.255381
\(408\) 0 0
\(409\) −32.3626 −1.60023 −0.800115 0.599847i \(-0.795228\pi\)
−0.800115 + 0.599847i \(0.795228\pi\)
\(410\) 0 0
\(411\) −0.225824 −0.0111391
\(412\) 0 0
\(413\) −21.2381 −1.04506
\(414\) 0 0
\(415\) −14.0101 −0.687729
\(416\) 0 0
\(417\) −0.308725 −0.0151183
\(418\) 0 0
\(419\) −15.2742 −0.746193 −0.373096 0.927793i \(-0.621704\pi\)
−0.373096 + 0.927793i \(0.621704\pi\)
\(420\) 0 0
\(421\) −6.04350 −0.294542 −0.147271 0.989096i \(-0.547049\pi\)
−0.147271 + 0.989096i \(0.547049\pi\)
\(422\) 0 0
\(423\) 22.1901 1.07892
\(424\) 0 0
\(425\) −2.47382 −0.119998
\(426\) 0 0
\(427\) 5.34507 0.258666
\(428\) 0 0
\(429\) 0.295063 0.0142458
\(430\) 0 0
\(431\) 11.6695 0.562101 0.281050 0.959693i \(-0.409317\pi\)
0.281050 + 0.959693i \(0.409317\pi\)
\(432\) 0 0
\(433\) 17.6689 0.849113 0.424556 0.905402i \(-0.360430\pi\)
0.424556 + 0.905402i \(0.360430\pi\)
\(434\) 0 0
\(435\) −0.00123626 −5.92740e−5 0
\(436\) 0 0
\(437\) 5.71291 0.273286
\(438\) 0 0
\(439\) −32.5165 −1.55193 −0.775965 0.630777i \(-0.782736\pi\)
−0.775965 + 0.630777i \(0.782736\pi\)
\(440\) 0 0
\(441\) 13.1988 0.628514
\(442\) 0 0
\(443\) −22.6653 −1.07686 −0.538431 0.842669i \(-0.680983\pi\)
−0.538431 + 0.842669i \(0.680983\pi\)
\(444\) 0 0
\(445\) −30.8230 −1.46115
\(446\) 0 0
\(447\) −0.131802 −0.00623404
\(448\) 0 0
\(449\) 30.5743 1.44289 0.721446 0.692470i \(-0.243478\pi\)
0.721446 + 0.692470i \(0.243478\pi\)
\(450\) 0 0
\(451\) 40.6131 1.91240
\(452\) 0 0
\(453\) −0.298668 −0.0140326
\(454\) 0 0
\(455\) −25.2591 −1.18417
\(456\) 0 0
\(457\) −3.74447 −0.175159 −0.0875794 0.996158i \(-0.527913\pi\)
−0.0875794 + 0.996158i \(0.527913\pi\)
\(458\) 0 0
\(459\) 0.0656861 0.00306596
\(460\) 0 0
\(461\) 8.56887 0.399092 0.199546 0.979888i \(-0.436053\pi\)
0.199546 + 0.979888i \(0.436053\pi\)
\(462\) 0 0
\(463\) −11.7295 −0.545116 −0.272558 0.962139i \(-0.587870\pi\)
−0.272558 + 0.962139i \(0.587870\pi\)
\(464\) 0 0
\(465\) −0.132908 −0.00616347
\(466\) 0 0
\(467\) −36.8900 −1.70707 −0.853533 0.521038i \(-0.825545\pi\)
−0.853533 + 0.521038i \(0.825545\pi\)
\(468\) 0 0
\(469\) −0.136447 −0.00630054
\(470\) 0 0
\(471\) 0.0826504 0.00380833
\(472\) 0 0
\(473\) 18.3756 0.844913
\(474\) 0 0
\(475\) −6.92726 −0.317844
\(476\) 0 0
\(477\) −22.2815 −1.02020
\(478\) 0 0
\(479\) 11.7603 0.537342 0.268671 0.963232i \(-0.413416\pi\)
0.268671 + 0.963232i \(0.413416\pi\)
\(480\) 0 0
\(481\) 7.59896 0.346483
\(482\) 0 0
\(483\) 0.0657956 0.00299380
\(484\) 0 0
\(485\) 33.9698 1.54249
\(486\) 0 0
\(487\) −32.5200 −1.47362 −0.736810 0.676100i \(-0.763669\pi\)
−0.736810 + 0.676100i \(0.763669\pi\)
\(488\) 0 0
\(489\) 0.265989 0.0120284
\(490\) 0 0
\(491\) −3.68312 −0.166217 −0.0831085 0.996541i \(-0.526485\pi\)
−0.0831085 + 0.996541i \(0.526485\pi\)
\(492\) 0 0
\(493\) −0.0213990 −0.000963760 0
\(494\) 0 0
\(495\) −31.8600 −1.43200
\(496\) 0 0
\(497\) 10.6246 0.476576
\(498\) 0 0
\(499\) −20.7311 −0.928052 −0.464026 0.885822i \(-0.653596\pi\)
−0.464026 + 0.885822i \(0.653596\pi\)
\(500\) 0 0
\(501\) 0.0844694 0.00377381
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −33.5495 −1.49293
\(506\) 0 0
\(507\) 0.242827 0.0107843
\(508\) 0 0
\(509\) 21.0782 0.934273 0.467137 0.884185i \(-0.345286\pi\)
0.467137 + 0.884185i \(0.345286\pi\)
\(510\) 0 0
\(511\) 12.7161 0.562526
\(512\) 0 0
\(513\) 0.183936 0.00812097
\(514\) 0 0
\(515\) −5.75850 −0.253750
\(516\) 0 0
\(517\) 27.1988 1.19620
\(518\) 0 0
\(519\) −0.0150964 −0.000662657 0
\(520\) 0 0
\(521\) −11.2059 −0.490939 −0.245470 0.969404i \(-0.578942\pi\)
−0.245470 + 0.969404i \(0.578942\pi\)
\(522\) 0 0
\(523\) −10.2726 −0.449191 −0.224596 0.974452i \(-0.572106\pi\)
−0.224596 + 0.974452i \(0.572106\pi\)
\(524\) 0 0
\(525\) −0.0797811 −0.00348193
\(526\) 0 0
\(527\) −2.30057 −0.100214
\(528\) 0 0
\(529\) −15.3962 −0.669400
\(530\) 0 0
\(531\) −39.5104 −1.71460
\(532\) 0 0
\(533\) 59.9012 2.59461
\(534\) 0 0
\(535\) 17.6246 0.761977
\(536\) 0 0
\(537\) −0.389191 −0.0167948
\(538\) 0 0
\(539\) 16.1779 0.696834
\(540\) 0 0
\(541\) 18.6431 0.801532 0.400766 0.916181i \(-0.368744\pi\)
0.400766 + 0.916181i \(0.368744\pi\)
\(542\) 0 0
\(543\) 0.102279 0.00438923
\(544\) 0 0
\(545\) −32.3897 −1.38742
\(546\) 0 0
\(547\) −28.8545 −1.23373 −0.616865 0.787069i \(-0.711598\pi\)
−0.616865 + 0.787069i \(0.711598\pi\)
\(548\) 0 0
\(549\) 9.94373 0.424388
\(550\) 0 0
\(551\) −0.0599219 −0.00255276
\(552\) 0 0
\(553\) −11.0999 −0.472014
\(554\) 0 0
\(555\) 0.0598925 0.00254230
\(556\) 0 0
\(557\) 6.96301 0.295032 0.147516 0.989060i \(-0.452872\pi\)
0.147516 + 0.989060i \(0.452872\pi\)
\(558\) 0 0
\(559\) 27.1026 1.14632
\(560\) 0 0
\(561\) 0.0402547 0.00169955
\(562\) 0 0
\(563\) −20.8136 −0.877190 −0.438595 0.898685i \(-0.644524\pi\)
−0.438595 + 0.898685i \(0.644524\pi\)
\(564\) 0 0
\(565\) 16.4738 0.693056
\(566\) 0 0
\(567\) −14.5091 −0.609325
\(568\) 0 0
\(569\) 14.0034 0.587055 0.293528 0.955951i \(-0.405171\pi\)
0.293528 + 0.955951i \(0.405171\pi\)
\(570\) 0 0
\(571\) −20.7234 −0.867247 −0.433623 0.901094i \(-0.642765\pi\)
−0.433623 + 0.901094i \(0.642765\pi\)
\(572\) 0 0
\(573\) 0.364907 0.0152442
\(574\) 0 0
\(575\) −9.22006 −0.384503
\(576\) 0 0
\(577\) 17.6902 0.736455 0.368227 0.929736i \(-0.379965\pi\)
0.368227 + 0.929736i \(0.379965\pi\)
\(578\) 0 0
\(579\) 0.0240383 0.000998997 0
\(580\) 0 0
\(581\) −7.82090 −0.324466
\(582\) 0 0
\(583\) −27.3108 −1.13110
\(584\) 0 0
\(585\) −46.9910 −1.94284
\(586\) 0 0
\(587\) 14.7140 0.607312 0.303656 0.952782i \(-0.401793\pi\)
0.303656 + 0.952782i \(0.401793\pi\)
\(588\) 0 0
\(589\) −6.44211 −0.265443
\(590\) 0 0
\(591\) 0.323136 0.0132921
\(592\) 0 0
\(593\) −4.57943 −0.188054 −0.0940272 0.995570i \(-0.529974\pi\)
−0.0940272 + 0.995570i \(0.529974\pi\)
\(594\) 0 0
\(595\) −3.44604 −0.141274
\(596\) 0 0
\(597\) −0.296362 −0.0121293
\(598\) 0 0
\(599\) −11.3967 −0.465658 −0.232829 0.972518i \(-0.574798\pi\)
−0.232829 + 0.972518i \(0.574798\pi\)
\(600\) 0 0
\(601\) −8.43329 −0.344001 −0.172001 0.985097i \(-0.555023\pi\)
−0.172001 + 0.985097i \(0.555023\pi\)
\(602\) 0 0
\(603\) −0.253840 −0.0103372
\(604\) 0 0
\(605\) −7.27733 −0.295866
\(606\) 0 0
\(607\) 3.34250 0.135668 0.0678340 0.997697i \(-0.478391\pi\)
0.0678340 + 0.997697i \(0.478391\pi\)
\(608\) 0 0
\(609\) −0.000690120 0 −2.79651e−5 0
\(610\) 0 0
\(611\) 40.1161 1.62292
\(612\) 0 0
\(613\) −7.11500 −0.287372 −0.143686 0.989623i \(-0.545896\pi\)
−0.143686 + 0.989623i \(0.545896\pi\)
\(614\) 0 0
\(615\) 0.472121 0.0190378
\(616\) 0 0
\(617\) −18.5827 −0.748113 −0.374056 0.927406i \(-0.622033\pi\)
−0.374056 + 0.927406i \(0.622033\pi\)
\(618\) 0 0
\(619\) −6.89042 −0.276949 −0.138475 0.990366i \(-0.544220\pi\)
−0.138475 + 0.990366i \(0.544220\pi\)
\(620\) 0 0
\(621\) 0.244815 0.00982411
\(622\) 0 0
\(623\) −17.2064 −0.689361
\(624\) 0 0
\(625\) −30.5383 −1.22153
\(626\) 0 0
\(627\) 0.112722 0.00450169
\(628\) 0 0
\(629\) 1.03671 0.0413362
\(630\) 0 0
\(631\) −3.84998 −0.153265 −0.0766326 0.997059i \(-0.524417\pi\)
−0.0766326 + 0.997059i \(0.524417\pi\)
\(632\) 0 0
\(633\) −0.146203 −0.00581106
\(634\) 0 0
\(635\) 43.8630 1.74065
\(636\) 0 0
\(637\) 23.8612 0.945416
\(638\) 0 0
\(639\) 19.7655 0.781910
\(640\) 0 0
\(641\) 14.4694 0.571507 0.285753 0.958303i \(-0.407756\pi\)
0.285753 + 0.958303i \(0.407756\pi\)
\(642\) 0 0
\(643\) 11.7064 0.461654 0.230827 0.972995i \(-0.425857\pi\)
0.230827 + 0.972995i \(0.425857\pi\)
\(644\) 0 0
\(645\) 0.213614 0.00841105
\(646\) 0 0
\(647\) 15.0476 0.591583 0.295791 0.955253i \(-0.404417\pi\)
0.295791 + 0.955253i \(0.404417\pi\)
\(648\) 0 0
\(649\) −48.4284 −1.90098
\(650\) 0 0
\(651\) −0.0741938 −0.00290788
\(652\) 0 0
\(653\) 2.61956 0.102511 0.0512557 0.998686i \(-0.483678\pi\)
0.0512557 + 0.998686i \(0.483678\pi\)
\(654\) 0 0
\(655\) −19.5327 −0.763205
\(656\) 0 0
\(657\) 23.6565 0.922926
\(658\) 0 0
\(659\) 27.8485 1.08482 0.542411 0.840113i \(-0.317512\pi\)
0.542411 + 0.840113i \(0.317512\pi\)
\(660\) 0 0
\(661\) 27.7901 1.08091 0.540456 0.841373i \(-0.318252\pi\)
0.540456 + 0.841373i \(0.318252\pi\)
\(662\) 0 0
\(663\) 0.0593725 0.00230584
\(664\) 0 0
\(665\) −9.64969 −0.374199
\(666\) 0 0
\(667\) −0.0797550 −0.00308813
\(668\) 0 0
\(669\) −0.218814 −0.00845985
\(670\) 0 0
\(671\) 12.1882 0.470519
\(672\) 0 0
\(673\) −12.9820 −0.500420 −0.250210 0.968192i \(-0.580500\pi\)
−0.250210 + 0.968192i \(0.580500\pi\)
\(674\) 0 0
\(675\) −0.296854 −0.0114259
\(676\) 0 0
\(677\) −39.6855 −1.52524 −0.762619 0.646848i \(-0.776087\pi\)
−0.762619 + 0.646848i \(0.776087\pi\)
\(678\) 0 0
\(679\) 18.9631 0.727735
\(680\) 0 0
\(681\) 0.0520056 0.00199286
\(682\) 0 0
\(683\) −24.7927 −0.948665 −0.474332 0.880346i \(-0.657310\pi\)
−0.474332 + 0.880346i \(0.657310\pi\)
\(684\) 0 0
\(685\) 44.0817 1.68428
\(686\) 0 0
\(687\) 0.0103261 0.000393964 0
\(688\) 0 0
\(689\) −40.2813 −1.53459
\(690\) 0 0
\(691\) 2.29980 0.0874883 0.0437442 0.999043i \(-0.486071\pi\)
0.0437442 + 0.999043i \(0.486071\pi\)
\(692\) 0 0
\(693\) −17.7853 −0.675608
\(694\) 0 0
\(695\) 60.2645 2.28596
\(696\) 0 0
\(697\) 8.17217 0.309543
\(698\) 0 0
\(699\) −0.00787902 −0.000298012 0
\(700\) 0 0
\(701\) 40.7107 1.53762 0.768811 0.639476i \(-0.220849\pi\)
0.768811 + 0.639476i \(0.220849\pi\)
\(702\) 0 0
\(703\) 2.90302 0.109489
\(704\) 0 0
\(705\) 0.316182 0.0119081
\(706\) 0 0
\(707\) −18.7284 −0.704356
\(708\) 0 0
\(709\) −19.3053 −0.725027 −0.362513 0.931979i \(-0.618081\pi\)
−0.362513 + 0.931979i \(0.618081\pi\)
\(710\) 0 0
\(711\) −20.6497 −0.774425
\(712\) 0 0
\(713\) −8.57434 −0.321112
\(714\) 0 0
\(715\) −57.5975 −2.15402
\(716\) 0 0
\(717\) −0.307490 −0.0114834
\(718\) 0 0
\(719\) 33.1852 1.23760 0.618800 0.785549i \(-0.287619\pi\)
0.618800 + 0.785549i \(0.287619\pi\)
\(720\) 0 0
\(721\) −3.21459 −0.119717
\(722\) 0 0
\(723\) 0.162622 0.00604798
\(724\) 0 0
\(725\) 0.0967078 0.00359164
\(726\) 0 0
\(727\) −11.9838 −0.444453 −0.222227 0.974995i \(-0.571332\pi\)
−0.222227 + 0.974995i \(0.571332\pi\)
\(728\) 0 0
\(729\) −26.9882 −0.999562
\(730\) 0 0
\(731\) 3.69755 0.136759
\(732\) 0 0
\(733\) −25.1288 −0.928154 −0.464077 0.885795i \(-0.653614\pi\)
−0.464077 + 0.885795i \(0.653614\pi\)
\(734\) 0 0
\(735\) 0.188066 0.00693693
\(736\) 0 0
\(737\) −0.311136 −0.0114608
\(738\) 0 0
\(739\) −10.3059 −0.379109 −0.189554 0.981870i \(-0.560704\pi\)
−0.189554 + 0.981870i \(0.560704\pi\)
\(740\) 0 0
\(741\) 0.166257 0.00610759
\(742\) 0 0
\(743\) 40.0598 1.46965 0.734825 0.678256i \(-0.237264\pi\)
0.734825 + 0.678256i \(0.237264\pi\)
\(744\) 0 0
\(745\) 25.7284 0.942615
\(746\) 0 0
\(747\) −14.5497 −0.532345
\(748\) 0 0
\(749\) 9.83863 0.359496
\(750\) 0 0
\(751\) 16.0804 0.586784 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(752\) 0 0
\(753\) −0.155376 −0.00566223
\(754\) 0 0
\(755\) 58.3012 2.12180
\(756\) 0 0
\(757\) 48.0819 1.74757 0.873783 0.486316i \(-0.161659\pi\)
0.873783 + 0.486316i \(0.161659\pi\)
\(758\) 0 0
\(759\) 0.150031 0.00544579
\(760\) 0 0
\(761\) −50.8538 −1.84345 −0.921724 0.387846i \(-0.873219\pi\)
−0.921724 + 0.387846i \(0.873219\pi\)
\(762\) 0 0
\(763\) −18.0810 −0.654576
\(764\) 0 0
\(765\) −6.41087 −0.231785
\(766\) 0 0
\(767\) −71.4281 −2.57912
\(768\) 0 0
\(769\) −24.8297 −0.895382 −0.447691 0.894188i \(-0.647753\pi\)
−0.447691 + 0.894188i \(0.647753\pi\)
\(770\) 0 0
\(771\) −0.256909 −0.00925235
\(772\) 0 0
\(773\) −9.62167 −0.346067 −0.173034 0.984916i \(-0.555357\pi\)
−0.173034 + 0.984916i \(0.555357\pi\)
\(774\) 0 0
\(775\) 10.3969 0.373468
\(776\) 0 0
\(777\) 0.0334340 0.00119944
\(778\) 0 0
\(779\) 22.8839 0.819901
\(780\) 0 0
\(781\) 24.2268 0.866903
\(782\) 0 0
\(783\) −0.00256783 −9.17669e−5 0
\(784\) 0 0
\(785\) −16.1337 −0.575837
\(786\) 0 0
\(787\) 20.9875 0.748124 0.374062 0.927404i \(-0.377965\pi\)
0.374062 + 0.927404i \(0.377965\pi\)
\(788\) 0 0
\(789\) −0.0411724 −0.00146578
\(790\) 0 0
\(791\) 9.19620 0.326979
\(792\) 0 0
\(793\) 17.9766 0.638368
\(794\) 0 0
\(795\) −0.317484 −0.0112600
\(796\) 0 0
\(797\) −0.0687051 −0.00243366 −0.00121683 0.999999i \(-0.500387\pi\)
−0.00121683 + 0.999999i \(0.500387\pi\)
\(798\) 0 0
\(799\) 5.47293 0.193619
\(800\) 0 0
\(801\) −32.0101 −1.13102
\(802\) 0 0
\(803\) 28.9960 1.02325
\(804\) 0 0
\(805\) −12.8436 −0.452676
\(806\) 0 0
\(807\) −0.339991 −0.0119683
\(808\) 0 0
\(809\) 42.3414 1.48864 0.744322 0.667821i \(-0.232773\pi\)
0.744322 + 0.667821i \(0.232773\pi\)
\(810\) 0 0
\(811\) 29.6941 1.04270 0.521350 0.853343i \(-0.325429\pi\)
0.521350 + 0.853343i \(0.325429\pi\)
\(812\) 0 0
\(813\) −0.0477754 −0.00167556
\(814\) 0 0
\(815\) −51.9222 −1.81875
\(816\) 0 0
\(817\) 10.3540 0.362239
\(818\) 0 0
\(819\) −26.2319 −0.916618
\(820\) 0 0
\(821\) −30.5816 −1.06731 −0.533653 0.845704i \(-0.679181\pi\)
−0.533653 + 0.845704i \(0.679181\pi\)
\(822\) 0 0
\(823\) −40.7249 −1.41958 −0.709791 0.704413i \(-0.751210\pi\)
−0.709791 + 0.704413i \(0.751210\pi\)
\(824\) 0 0
\(825\) −0.181922 −0.00633371
\(826\) 0 0
\(827\) 27.2206 0.946552 0.473276 0.880914i \(-0.343071\pi\)
0.473276 + 0.880914i \(0.343071\pi\)
\(828\) 0 0
\(829\) 13.7317 0.476922 0.238461 0.971152i \(-0.423357\pi\)
0.238461 + 0.971152i \(0.423357\pi\)
\(830\) 0 0
\(831\) 0.471202 0.0163458
\(832\) 0 0
\(833\) 3.25533 0.112790
\(834\) 0 0
\(835\) −16.4888 −0.570618
\(836\) 0 0
\(837\) −0.276064 −0.00954216
\(838\) 0 0
\(839\) −0.483965 −0.0167083 −0.00835416 0.999965i \(-0.502659\pi\)
−0.00835416 + 0.999965i \(0.502659\pi\)
\(840\) 0 0
\(841\) −28.9992 −0.999971
\(842\) 0 0
\(843\) 0.148099 0.00510080
\(844\) 0 0
\(845\) −47.4009 −1.63064
\(846\) 0 0
\(847\) −4.06245 −0.139587
\(848\) 0 0
\(849\) −0.281256 −0.00965269
\(850\) 0 0
\(851\) 3.86386 0.132452
\(852\) 0 0
\(853\) 20.1760 0.690813 0.345406 0.938453i \(-0.387741\pi\)
0.345406 + 0.938453i \(0.387741\pi\)
\(854\) 0 0
\(855\) −17.9519 −0.613941
\(856\) 0 0
\(857\) 36.4272 1.24433 0.622164 0.782887i \(-0.286254\pi\)
0.622164 + 0.782887i \(0.286254\pi\)
\(858\) 0 0
\(859\) −2.32321 −0.0792671 −0.0396335 0.999214i \(-0.512619\pi\)
−0.0396335 + 0.999214i \(0.512619\pi\)
\(860\) 0 0
\(861\) 0.263554 0.00898189
\(862\) 0 0
\(863\) 54.1351 1.84278 0.921391 0.388637i \(-0.127054\pi\)
0.921391 + 0.388637i \(0.127054\pi\)
\(864\) 0 0
\(865\) 2.94687 0.100197
\(866\) 0 0
\(867\) −0.243457 −0.00826825
\(868\) 0 0
\(869\) −25.3106 −0.858604
\(870\) 0 0
\(871\) −0.458901 −0.0155493
\(872\) 0 0
\(873\) 35.2781 1.19398
\(874\) 0 0
\(875\) −7.71485 −0.260809
\(876\) 0 0
\(877\) 17.3820 0.586948 0.293474 0.955967i \(-0.405189\pi\)
0.293474 + 0.955967i \(0.405189\pi\)
\(878\) 0 0
\(879\) −0.158569 −0.00534842
\(880\) 0 0
\(881\) −30.7985 −1.03763 −0.518814 0.854887i \(-0.673626\pi\)
−0.518814 + 0.854887i \(0.673626\pi\)
\(882\) 0 0
\(883\) 9.53905 0.321015 0.160507 0.987035i \(-0.448687\pi\)
0.160507 + 0.987035i \(0.448687\pi\)
\(884\) 0 0
\(885\) −0.562973 −0.0189241
\(886\) 0 0
\(887\) −32.0798 −1.07714 −0.538568 0.842582i \(-0.681034\pi\)
−0.538568 + 0.842582i \(0.681034\pi\)
\(888\) 0 0
\(889\) 24.4858 0.821227
\(890\) 0 0
\(891\) −33.0846 −1.10838
\(892\) 0 0
\(893\) 15.3255 0.512847
\(894\) 0 0
\(895\) 75.9718 2.53946
\(896\) 0 0
\(897\) 0.221285 0.00738848
\(898\) 0 0
\(899\) 0.0899350 0.00299950
\(900\) 0 0
\(901\) −5.49547 −0.183081
\(902\) 0 0
\(903\) 0.119247 0.00396828
\(904\) 0 0
\(905\) −19.9654 −0.663671
\(906\) 0 0
\(907\) −32.9792 −1.09506 −0.547529 0.836787i \(-0.684431\pi\)
−0.547529 + 0.836787i \(0.684431\pi\)
\(908\) 0 0
\(909\) −34.8416 −1.15562
\(910\) 0 0
\(911\) −25.7684 −0.853744 −0.426872 0.904312i \(-0.640385\pi\)
−0.426872 + 0.904312i \(0.640385\pi\)
\(912\) 0 0
\(913\) −17.8337 −0.590210
\(914\) 0 0
\(915\) 0.141686 0.00468398
\(916\) 0 0
\(917\) −10.9038 −0.360075
\(918\) 0 0
\(919\) −41.3018 −1.36242 −0.681211 0.732088i \(-0.738546\pi\)
−0.681211 + 0.732088i \(0.738546\pi\)
\(920\) 0 0
\(921\) −0.00882836 −0.000290904 0
\(922\) 0 0
\(923\) 35.7326 1.17615
\(924\) 0 0
\(925\) −4.68517 −0.154047
\(926\) 0 0
\(927\) −5.98028 −0.196418
\(928\) 0 0
\(929\) 27.0830 0.888565 0.444283 0.895887i \(-0.353459\pi\)
0.444283 + 0.895887i \(0.353459\pi\)
\(930\) 0 0
\(931\) 9.11565 0.298753
\(932\) 0 0
\(933\) 0.100975 0.00330578
\(934\) 0 0
\(935\) −7.85789 −0.256980
\(936\) 0 0
\(937\) 47.5951 1.55486 0.777432 0.628967i \(-0.216522\pi\)
0.777432 + 0.628967i \(0.216522\pi\)
\(938\) 0 0
\(939\) 0.164586 0.00537106
\(940\) 0 0
\(941\) −24.5267 −0.799547 −0.399773 0.916614i \(-0.630911\pi\)
−0.399773 + 0.916614i \(0.630911\pi\)
\(942\) 0 0
\(943\) 30.4581 0.991852
\(944\) 0 0
\(945\) −0.413518 −0.0134517
\(946\) 0 0
\(947\) 6.57604 0.213693 0.106846 0.994276i \(-0.465925\pi\)
0.106846 + 0.994276i \(0.465925\pi\)
\(948\) 0 0
\(949\) 42.7669 1.38827
\(950\) 0 0
\(951\) 0.144448 0.00468405
\(952\) 0 0
\(953\) −53.7339 −1.74061 −0.870306 0.492512i \(-0.836079\pi\)
−0.870306 + 0.492512i \(0.836079\pi\)
\(954\) 0 0
\(955\) −71.2313 −2.30499
\(956\) 0 0
\(957\) −0.00157366 −5.08691e−5 0
\(958\) 0 0
\(959\) 24.6079 0.794630
\(960\) 0 0
\(961\) −21.3312 −0.688104
\(962\) 0 0
\(963\) 18.3034 0.589817
\(964\) 0 0
\(965\) −4.69237 −0.151053
\(966\) 0 0
\(967\) −15.8475 −0.509622 −0.254811 0.966991i \(-0.582013\pi\)
−0.254811 + 0.966991i \(0.582013\pi\)
\(968\) 0 0
\(969\) 0.0226820 0.000728650 0
\(970\) 0 0
\(971\) −12.6150 −0.404833 −0.202417 0.979299i \(-0.564880\pi\)
−0.202417 + 0.979299i \(0.564880\pi\)
\(972\) 0 0
\(973\) 33.6416 1.07850
\(974\) 0 0
\(975\) −0.268321 −0.00859315
\(976\) 0 0
\(977\) 9.18447 0.293837 0.146919 0.989149i \(-0.453064\pi\)
0.146919 + 0.989149i \(0.453064\pi\)
\(978\) 0 0
\(979\) −39.2352 −1.25396
\(980\) 0 0
\(981\) −33.6371 −1.07395
\(982\) 0 0
\(983\) −32.1655 −1.02592 −0.512960 0.858413i \(-0.671451\pi\)
−0.512960 + 0.858413i \(0.671451\pi\)
\(984\) 0 0
\(985\) −63.0776 −2.00982
\(986\) 0 0
\(987\) 0.176503 0.00561815
\(988\) 0 0
\(989\) 13.7809 0.438209
\(990\) 0 0
\(991\) 48.8856 1.55290 0.776451 0.630177i \(-0.217018\pi\)
0.776451 + 0.630177i \(0.217018\pi\)
\(992\) 0 0
\(993\) 0.101160 0.00321023
\(994\) 0 0
\(995\) 57.8512 1.83401
\(996\) 0 0
\(997\) −8.95639 −0.283652 −0.141826 0.989892i \(-0.545297\pi\)
−0.141826 + 0.989892i \(0.545297\pi\)
\(998\) 0 0
\(999\) 0.124403 0.00393593
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 4024.2.a.f.1.17 33
4.3 odd 2 8048.2.a.y.1.17 33
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4024.2.a.f.1.17 33 1.1 even 1 trivial
8048.2.a.y.1.17 33 4.3 odd 2