Properties

Label 5225.2.a.n.1.4
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $7$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 209)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.456669\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.456669 q^{2} +0.835165 q^{3} -1.79145 q^{4} +0.381394 q^{6} -4.69915 q^{7} -1.73144 q^{8} -2.30250 q^{9} +O(q^{10})\) \(q+0.456669 q^{2} +0.835165 q^{3} -1.79145 q^{4} +0.381394 q^{6} -4.69915 q^{7} -1.73144 q^{8} -2.30250 q^{9} -1.00000 q^{11} -1.49616 q^{12} -5.89016 q^{13} -2.14596 q^{14} +2.79221 q^{16} -7.06513 q^{17} -1.05148 q^{18} +1.00000 q^{19} -3.92457 q^{21} -0.456669 q^{22} -1.06348 q^{23} -1.44604 q^{24} -2.68985 q^{26} -4.42846 q^{27} +8.41832 q^{28} -7.62662 q^{29} +0.901295 q^{31} +4.73799 q^{32} -0.835165 q^{33} -3.22642 q^{34} +4.12482 q^{36} +2.71758 q^{37} +0.456669 q^{38} -4.91925 q^{39} +0.788714 q^{41} -1.79223 q^{42} -0.714571 q^{43} +1.79145 q^{44} -0.485656 q^{46} -3.96368 q^{47} +2.33196 q^{48} +15.0820 q^{49} -5.90055 q^{51} +10.5519 q^{52} +9.69714 q^{53} -2.02234 q^{54} +8.13629 q^{56} +0.835165 q^{57} -3.48284 q^{58} -7.33476 q^{59} +8.15179 q^{61} +0.411593 q^{62} +10.8198 q^{63} -3.42073 q^{64} -0.381394 q^{66} -7.86697 q^{67} +12.6569 q^{68} -0.888178 q^{69} -3.13400 q^{71} +3.98664 q^{72} +6.49076 q^{73} +1.24103 q^{74} -1.79145 q^{76} +4.69915 q^{77} -2.24647 q^{78} +12.0148 q^{79} +3.20900 q^{81} +0.360181 q^{82} -16.3902 q^{83} +7.03068 q^{84} -0.326322 q^{86} -6.36948 q^{87} +1.73144 q^{88} -12.9487 q^{89} +27.6788 q^{91} +1.90517 q^{92} +0.752730 q^{93} -1.81009 q^{94} +3.95701 q^{96} -8.14414 q^{97} +6.88750 q^{98} +2.30250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9} - 7 q^{11} + 16 q^{12} + 4 q^{13} + 6 q^{14} + 27 q^{16} - 2 q^{17} - 9 q^{18} + 7 q^{19} - 14 q^{21} - q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{26} + 4 q^{27} - 26 q^{28} - 18 q^{29} + 24 q^{31} + 49 q^{32} + 2 q^{33} - 6 q^{34} + 29 q^{36} + q^{38} + 24 q^{39} - 12 q^{41} + 44 q^{42} - 2 q^{43} - 15 q^{44} - 4 q^{46} - 8 q^{47} + 72 q^{48} + 17 q^{49} - 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} + 26 q^{56} - 2 q^{57} + 8 q^{58} - 10 q^{59} + 14 q^{61} - 14 q^{62} + 55 q^{64} + 2 q^{66} - 8 q^{67} + 18 q^{68} - 6 q^{69} + 10 q^{71} - 53 q^{72} + 6 q^{73} + 26 q^{74} + 15 q^{76} + 10 q^{77} - 22 q^{78} + 52 q^{79} - q^{81} - 24 q^{82} + 10 q^{83} - 6 q^{84} + 8 q^{86} - 6 q^{87} - 9 q^{88} + 12 q^{91} - 2 q^{93} + 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.456669 0.322914 0.161457 0.986880i \(-0.448381\pi\)
0.161457 + 0.986880i \(0.448381\pi\)
\(3\) 0.835165 0.482183 0.241091 0.970502i \(-0.422495\pi\)
0.241091 + 0.970502i \(0.422495\pi\)
\(4\) −1.79145 −0.895727
\(5\) 0 0
\(6\) 0.381394 0.155703
\(7\) −4.69915 −1.77611 −0.888057 0.459734i \(-0.847945\pi\)
−0.888057 + 0.459734i \(0.847945\pi\)
\(8\) −1.73144 −0.612156
\(9\) −2.30250 −0.767500
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −1.49616 −0.431904
\(13\) −5.89016 −1.63364 −0.816818 0.576895i \(-0.804264\pi\)
−0.816818 + 0.576895i \(0.804264\pi\)
\(14\) −2.14596 −0.573531
\(15\) 0 0
\(16\) 2.79221 0.698053
\(17\) −7.06513 −1.71355 −0.856773 0.515694i \(-0.827534\pi\)
−0.856773 + 0.515694i \(0.827534\pi\)
\(18\) −1.05148 −0.247836
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −3.92457 −0.856411
\(22\) −0.456669 −0.0973621
\(23\) −1.06348 −0.221750 −0.110875 0.993834i \(-0.535365\pi\)
−0.110875 + 0.993834i \(0.535365\pi\)
\(24\) −1.44604 −0.295171
\(25\) 0 0
\(26\) −2.68985 −0.527523
\(27\) −4.42846 −0.852258
\(28\) 8.41832 1.59091
\(29\) −7.62662 −1.41623 −0.708114 0.706098i \(-0.750454\pi\)
−0.708114 + 0.706098i \(0.750454\pi\)
\(30\) 0 0
\(31\) 0.901295 0.161877 0.0809387 0.996719i \(-0.474208\pi\)
0.0809387 + 0.996719i \(0.474208\pi\)
\(32\) 4.73799 0.837567
\(33\) −0.835165 −0.145384
\(34\) −3.22642 −0.553327
\(35\) 0 0
\(36\) 4.12482 0.687470
\(37\) 2.71758 0.446768 0.223384 0.974731i \(-0.428290\pi\)
0.223384 + 0.974731i \(0.428290\pi\)
\(38\) 0.456669 0.0740815
\(39\) −4.91925 −0.787711
\(40\) 0 0
\(41\) 0.788714 0.123176 0.0615882 0.998102i \(-0.480383\pi\)
0.0615882 + 0.998102i \(0.480383\pi\)
\(42\) −1.79223 −0.276547
\(43\) −0.714571 −0.108971 −0.0544855 0.998515i \(-0.517352\pi\)
−0.0544855 + 0.998515i \(0.517352\pi\)
\(44\) 1.79145 0.270072
\(45\) 0 0
\(46\) −0.485656 −0.0716061
\(47\) −3.96368 −0.578163 −0.289081 0.957305i \(-0.593350\pi\)
−0.289081 + 0.957305i \(0.593350\pi\)
\(48\) 2.33196 0.336589
\(49\) 15.0820 2.15458
\(50\) 0 0
\(51\) −5.90055 −0.826242
\(52\) 10.5519 1.46329
\(53\) 9.69714 1.33200 0.666002 0.745950i \(-0.268004\pi\)
0.666002 + 0.745950i \(0.268004\pi\)
\(54\) −2.02234 −0.275206
\(55\) 0 0
\(56\) 8.13629 1.08726
\(57\) 0.835165 0.110620
\(58\) −3.48284 −0.457319
\(59\) −7.33476 −0.954904 −0.477452 0.878658i \(-0.658440\pi\)
−0.477452 + 0.878658i \(0.658440\pi\)
\(60\) 0 0
\(61\) 8.15179 1.04373 0.521865 0.853028i \(-0.325236\pi\)
0.521865 + 0.853028i \(0.325236\pi\)
\(62\) 0.411593 0.0522724
\(63\) 10.8198 1.36317
\(64\) −3.42073 −0.427592
\(65\) 0 0
\(66\) −0.381394 −0.0469463
\(67\) −7.86697 −0.961104 −0.480552 0.876966i \(-0.659564\pi\)
−0.480552 + 0.876966i \(0.659564\pi\)
\(68\) 12.6569 1.53487
\(69\) −0.888178 −0.106924
\(70\) 0 0
\(71\) −3.13400 −0.371937 −0.185969 0.982556i \(-0.559542\pi\)
−0.185969 + 0.982556i \(0.559542\pi\)
\(72\) 3.98664 0.469830
\(73\) 6.49076 0.759687 0.379843 0.925051i \(-0.375978\pi\)
0.379843 + 0.925051i \(0.375978\pi\)
\(74\) 1.24103 0.144267
\(75\) 0 0
\(76\) −1.79145 −0.205494
\(77\) 4.69915 0.535518
\(78\) −2.24647 −0.254363
\(79\) 12.0148 1.35177 0.675884 0.737008i \(-0.263762\pi\)
0.675884 + 0.737008i \(0.263762\pi\)
\(80\) 0 0
\(81\) 3.20900 0.356556
\(82\) 0.360181 0.0397753
\(83\) −16.3902 −1.79906 −0.899528 0.436863i \(-0.856089\pi\)
−0.899528 + 0.436863i \(0.856089\pi\)
\(84\) 7.03068 0.767110
\(85\) 0 0
\(86\) −0.326322 −0.0351882
\(87\) −6.36948 −0.682880
\(88\) 1.73144 0.184572
\(89\) −12.9487 −1.37256 −0.686281 0.727336i \(-0.740758\pi\)
−0.686281 + 0.727336i \(0.740758\pi\)
\(90\) 0 0
\(91\) 27.6788 2.90152
\(92\) 1.90517 0.198628
\(93\) 0.752730 0.0780545
\(94\) −1.81009 −0.186697
\(95\) 0 0
\(96\) 3.95701 0.403860
\(97\) −8.14414 −0.826912 −0.413456 0.910524i \(-0.635679\pi\)
−0.413456 + 0.910524i \(0.635679\pi\)
\(98\) 6.88750 0.695742
\(99\) 2.30250 0.231410
\(100\) 0 0
\(101\) −15.3713 −1.52950 −0.764750 0.644327i \(-0.777138\pi\)
−0.764750 + 0.644327i \(0.777138\pi\)
\(102\) −2.69460 −0.266805
\(103\) 8.83682 0.870718 0.435359 0.900257i \(-0.356622\pi\)
0.435359 + 0.900257i \(0.356622\pi\)
\(104\) 10.1984 1.00004
\(105\) 0 0
\(106\) 4.42838 0.430122
\(107\) 9.04360 0.874277 0.437139 0.899394i \(-0.355992\pi\)
0.437139 + 0.899394i \(0.355992\pi\)
\(108\) 7.93338 0.763390
\(109\) −18.5950 −1.78107 −0.890537 0.454911i \(-0.849671\pi\)
−0.890537 + 0.454911i \(0.849671\pi\)
\(110\) 0 0
\(111\) 2.26963 0.215424
\(112\) −13.1210 −1.23982
\(113\) 4.42423 0.416196 0.208098 0.978108i \(-0.433273\pi\)
0.208098 + 0.978108i \(0.433273\pi\)
\(114\) 0.381394 0.0357208
\(115\) 0 0
\(116\) 13.6627 1.26855
\(117\) 13.5621 1.25382
\(118\) −3.34955 −0.308352
\(119\) 33.2001 3.04345
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 3.72267 0.337035
\(123\) 0.658706 0.0593935
\(124\) −1.61463 −0.144998
\(125\) 0 0
\(126\) 4.94106 0.440185
\(127\) 0.338657 0.0300510 0.0150255 0.999887i \(-0.495217\pi\)
0.0150255 + 0.999887i \(0.495217\pi\)
\(128\) −11.0381 −0.975642
\(129\) −0.596784 −0.0525439
\(130\) 0 0
\(131\) −4.55211 −0.397720 −0.198860 0.980028i \(-0.563724\pi\)
−0.198860 + 0.980028i \(0.563724\pi\)
\(132\) 1.49616 0.130224
\(133\) −4.69915 −0.407468
\(134\) −3.59260 −0.310353
\(135\) 0 0
\(136\) 12.2328 1.04896
\(137\) 0.654263 0.0558974 0.0279487 0.999609i \(-0.491102\pi\)
0.0279487 + 0.999609i \(0.491102\pi\)
\(138\) −0.405603 −0.0345272
\(139\) 11.0479 0.937072 0.468536 0.883444i \(-0.344782\pi\)
0.468536 + 0.883444i \(0.344782\pi\)
\(140\) 0 0
\(141\) −3.31033 −0.278780
\(142\) −1.43120 −0.120104
\(143\) 5.89016 0.492560
\(144\) −6.42907 −0.535756
\(145\) 0 0
\(146\) 2.96413 0.245313
\(147\) 12.5960 1.03890
\(148\) −4.86842 −0.400182
\(149\) −7.57743 −0.620767 −0.310384 0.950611i \(-0.600457\pi\)
−0.310384 + 0.950611i \(0.600457\pi\)
\(150\) 0 0
\(151\) −6.95296 −0.565824 −0.282912 0.959146i \(-0.591300\pi\)
−0.282912 + 0.959146i \(0.591300\pi\)
\(152\) −1.73144 −0.140438
\(153\) 16.2675 1.31515
\(154\) 2.14596 0.172926
\(155\) 0 0
\(156\) 8.81261 0.705574
\(157\) 14.7427 1.17659 0.588297 0.808645i \(-0.299799\pi\)
0.588297 + 0.808645i \(0.299799\pi\)
\(158\) 5.48678 0.436504
\(159\) 8.09871 0.642270
\(160\) 0 0
\(161\) 4.99744 0.393853
\(162\) 1.46545 0.115137
\(163\) 4.94015 0.386942 0.193471 0.981106i \(-0.438025\pi\)
0.193471 + 0.981106i \(0.438025\pi\)
\(164\) −1.41294 −0.110332
\(165\) 0 0
\(166\) −7.48488 −0.580940
\(167\) −22.6032 −1.74909 −0.874544 0.484946i \(-0.838839\pi\)
−0.874544 + 0.484946i \(0.838839\pi\)
\(168\) 6.79515 0.524257
\(169\) 21.6940 1.66877
\(170\) 0 0
\(171\) −2.30250 −0.176077
\(172\) 1.28012 0.0976083
\(173\) 8.18620 0.622385 0.311193 0.950347i \(-0.399272\pi\)
0.311193 + 0.950347i \(0.399272\pi\)
\(174\) −2.90874 −0.220511
\(175\) 0 0
\(176\) −2.79221 −0.210471
\(177\) −6.12573 −0.460438
\(178\) −5.91328 −0.443219
\(179\) −14.0830 −1.05261 −0.526305 0.850296i \(-0.676423\pi\)
−0.526305 + 0.850296i \(0.676423\pi\)
\(180\) 0 0
\(181\) −14.3260 −1.06484 −0.532422 0.846479i \(-0.678718\pi\)
−0.532422 + 0.846479i \(0.678718\pi\)
\(182\) 12.6400 0.936941
\(183\) 6.80809 0.503268
\(184\) 1.84134 0.135746
\(185\) 0 0
\(186\) 0.343748 0.0252049
\(187\) 7.06513 0.516653
\(188\) 7.10076 0.517876
\(189\) 20.8100 1.51371
\(190\) 0 0
\(191\) 0.394967 0.0285788 0.0142894 0.999898i \(-0.495451\pi\)
0.0142894 + 0.999898i \(0.495451\pi\)
\(192\) −2.85688 −0.206177
\(193\) −9.03423 −0.650298 −0.325149 0.945663i \(-0.605414\pi\)
−0.325149 + 0.945663i \(0.605414\pi\)
\(194\) −3.71918 −0.267021
\(195\) 0 0
\(196\) −27.0188 −1.92991
\(197\) −7.85313 −0.559512 −0.279756 0.960071i \(-0.590254\pi\)
−0.279756 + 0.960071i \(0.590254\pi\)
\(198\) 1.05148 0.0747254
\(199\) 7.81540 0.554019 0.277009 0.960867i \(-0.410657\pi\)
0.277009 + 0.960867i \(0.410657\pi\)
\(200\) 0 0
\(201\) −6.57022 −0.463427
\(202\) −7.01959 −0.493897
\(203\) 35.8386 2.51538
\(204\) 10.5706 0.740087
\(205\) 0 0
\(206\) 4.03550 0.281167
\(207\) 2.44865 0.170193
\(208\) −16.4466 −1.14037
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −21.5955 −1.48670 −0.743348 0.668905i \(-0.766763\pi\)
−0.743348 + 0.668905i \(0.766763\pi\)
\(212\) −17.3720 −1.19311
\(213\) −2.61741 −0.179342
\(214\) 4.12993 0.282316
\(215\) 0 0
\(216\) 7.66761 0.521715
\(217\) −4.23533 −0.287513
\(218\) −8.49174 −0.575133
\(219\) 5.42086 0.366308
\(220\) 0 0
\(221\) 41.6147 2.79931
\(222\) 1.03647 0.0695632
\(223\) 6.95854 0.465979 0.232989 0.972479i \(-0.425149\pi\)
0.232989 + 0.972479i \(0.425149\pi\)
\(224\) −22.2646 −1.48761
\(225\) 0 0
\(226\) 2.02041 0.134395
\(227\) −7.67819 −0.509619 −0.254810 0.966991i \(-0.582013\pi\)
−0.254810 + 0.966991i \(0.582013\pi\)
\(228\) −1.49616 −0.0990855
\(229\) 5.83925 0.385869 0.192934 0.981212i \(-0.438200\pi\)
0.192934 + 0.981212i \(0.438200\pi\)
\(230\) 0 0
\(231\) 3.92457 0.258218
\(232\) 13.2050 0.866952
\(233\) 21.8431 1.43099 0.715494 0.698619i \(-0.246202\pi\)
0.715494 + 0.698619i \(0.246202\pi\)
\(234\) 6.19338 0.404874
\(235\) 0 0
\(236\) 13.1399 0.855333
\(237\) 10.0343 0.651799
\(238\) 15.1615 0.982772
\(239\) 4.21004 0.272325 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(240\) 0 0
\(241\) −17.4276 −1.12261 −0.561304 0.827610i \(-0.689700\pi\)
−0.561304 + 0.827610i \(0.689700\pi\)
\(242\) 0.456669 0.0293558
\(243\) 15.9654 1.02418
\(244\) −14.6036 −0.934897
\(245\) 0 0
\(246\) 0.300810 0.0191790
\(247\) −5.89016 −0.374782
\(248\) −1.56054 −0.0990942
\(249\) −13.6885 −0.867474
\(250\) 0 0
\(251\) 2.14594 0.135451 0.0677254 0.997704i \(-0.478426\pi\)
0.0677254 + 0.997704i \(0.478426\pi\)
\(252\) −19.3832 −1.22102
\(253\) 1.06348 0.0668602
\(254\) 0.154654 0.00970387
\(255\) 0 0
\(256\) 1.80070 0.112544
\(257\) 5.23899 0.326799 0.163399 0.986560i \(-0.447754\pi\)
0.163399 + 0.986560i \(0.447754\pi\)
\(258\) −0.272533 −0.0169672
\(259\) −12.7703 −0.793510
\(260\) 0 0
\(261\) 17.5603 1.08695
\(262\) −2.07881 −0.128429
\(263\) −12.2597 −0.755967 −0.377983 0.925812i \(-0.623382\pi\)
−0.377983 + 0.925812i \(0.623382\pi\)
\(264\) 1.44604 0.0889974
\(265\) 0 0
\(266\) −2.14596 −0.131577
\(267\) −10.8143 −0.661826
\(268\) 14.0933 0.860886
\(269\) −9.37273 −0.571465 −0.285733 0.958309i \(-0.592237\pi\)
−0.285733 + 0.958309i \(0.592237\pi\)
\(270\) 0 0
\(271\) −13.3131 −0.808716 −0.404358 0.914601i \(-0.632505\pi\)
−0.404358 + 0.914601i \(0.632505\pi\)
\(272\) −19.7273 −1.19615
\(273\) 23.1163 1.39906
\(274\) 0.298781 0.0180500
\(275\) 0 0
\(276\) 1.59113 0.0957748
\(277\) 14.5641 0.875073 0.437537 0.899201i \(-0.355851\pi\)
0.437537 + 0.899201i \(0.355851\pi\)
\(278\) 5.04524 0.302593
\(279\) −2.07523 −0.124241
\(280\) 0 0
\(281\) 20.2411 1.20748 0.603741 0.797180i \(-0.293676\pi\)
0.603741 + 0.797180i \(0.293676\pi\)
\(282\) −1.51172 −0.0900219
\(283\) −14.6230 −0.869248 −0.434624 0.900612i \(-0.643119\pi\)
−0.434624 + 0.900612i \(0.643119\pi\)
\(284\) 5.61442 0.333154
\(285\) 0 0
\(286\) 2.68985 0.159054
\(287\) −3.70629 −0.218775
\(288\) −10.9092 −0.642833
\(289\) 32.9161 1.93624
\(290\) 0 0
\(291\) −6.80170 −0.398723
\(292\) −11.6279 −0.680472
\(293\) −27.6524 −1.61547 −0.807737 0.589543i \(-0.799308\pi\)
−0.807737 + 0.589543i \(0.799308\pi\)
\(294\) 5.75220 0.335475
\(295\) 0 0
\(296\) −4.70533 −0.273491
\(297\) 4.42846 0.256965
\(298\) −3.46037 −0.200454
\(299\) 6.26404 0.362259
\(300\) 0 0
\(301\) 3.35788 0.193545
\(302\) −3.17520 −0.182712
\(303\) −12.8376 −0.737499
\(304\) 2.79221 0.160144
\(305\) 0 0
\(306\) 7.42884 0.424679
\(307\) 0.756065 0.0431509 0.0215755 0.999767i \(-0.493132\pi\)
0.0215755 + 0.999767i \(0.493132\pi\)
\(308\) −8.41832 −0.479678
\(309\) 7.38020 0.419845
\(310\) 0 0
\(311\) 1.13352 0.0642761 0.0321381 0.999483i \(-0.489768\pi\)
0.0321381 + 0.999483i \(0.489768\pi\)
\(312\) 8.51738 0.482202
\(313\) 10.9012 0.616172 0.308086 0.951359i \(-0.400312\pi\)
0.308086 + 0.951359i \(0.400312\pi\)
\(314\) 6.73252 0.379938
\(315\) 0 0
\(316\) −21.5239 −1.21082
\(317\) −8.32326 −0.467481 −0.233741 0.972299i \(-0.575097\pi\)
−0.233741 + 0.972299i \(0.575097\pi\)
\(318\) 3.69843 0.207398
\(319\) 7.62662 0.427009
\(320\) 0 0
\(321\) 7.55289 0.421561
\(322\) 2.28217 0.127181
\(323\) −7.06513 −0.393114
\(324\) −5.74878 −0.319377
\(325\) 0 0
\(326\) 2.25601 0.124949
\(327\) −15.5299 −0.858803
\(328\) −1.36561 −0.0754031
\(329\) 18.6260 1.02688
\(330\) 0 0
\(331\) −2.47466 −0.136020 −0.0680098 0.997685i \(-0.521665\pi\)
−0.0680098 + 0.997685i \(0.521665\pi\)
\(332\) 29.3622 1.61146
\(333\) −6.25723 −0.342894
\(334\) −10.3222 −0.564804
\(335\) 0 0
\(336\) −10.9582 −0.597820
\(337\) 30.3242 1.65187 0.825933 0.563768i \(-0.190649\pi\)
0.825933 + 0.563768i \(0.190649\pi\)
\(338\) 9.90696 0.538867
\(339\) 3.69496 0.200683
\(340\) 0 0
\(341\) −0.901295 −0.0488079
\(342\) −1.05148 −0.0568575
\(343\) −37.9788 −2.05066
\(344\) 1.23724 0.0667073
\(345\) 0 0
\(346\) 3.73838 0.200977
\(347\) 10.4332 0.560081 0.280041 0.959988i \(-0.409652\pi\)
0.280041 + 0.959988i \(0.409652\pi\)
\(348\) 11.4106 0.611674
\(349\) 4.89049 0.261782 0.130891 0.991397i \(-0.458216\pi\)
0.130891 + 0.991397i \(0.458216\pi\)
\(350\) 0 0
\(351\) 26.0843 1.39228
\(352\) −4.73799 −0.252536
\(353\) −34.1254 −1.81631 −0.908155 0.418634i \(-0.862509\pi\)
−0.908155 + 0.418634i \(0.862509\pi\)
\(354\) −2.79743 −0.148682
\(355\) 0 0
\(356\) 23.1970 1.22944
\(357\) 27.7276 1.46750
\(358\) −6.43125 −0.339902
\(359\) 10.5366 0.556103 0.278051 0.960566i \(-0.410311\pi\)
0.278051 + 0.960566i \(0.410311\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −6.54224 −0.343853
\(363\) 0.835165 0.0438348
\(364\) −49.5852 −2.59897
\(365\) 0 0
\(366\) 3.10904 0.162512
\(367\) −31.1277 −1.62485 −0.812427 0.583062i \(-0.801854\pi\)
−0.812427 + 0.583062i \(0.801854\pi\)
\(368\) −2.96945 −0.154793
\(369\) −1.81601 −0.0945378
\(370\) 0 0
\(371\) −45.5684 −2.36579
\(372\) −1.34848 −0.0699155
\(373\) −28.9881 −1.50095 −0.750473 0.660901i \(-0.770174\pi\)
−0.750473 + 0.660901i \(0.770174\pi\)
\(374\) 3.22642 0.166834
\(375\) 0 0
\(376\) 6.86288 0.353926
\(377\) 44.9220 2.31360
\(378\) 9.50329 0.488796
\(379\) −26.4204 −1.35712 −0.678561 0.734544i \(-0.737396\pi\)
−0.678561 + 0.734544i \(0.737396\pi\)
\(380\) 0 0
\(381\) 0.282835 0.0144901
\(382\) 0.180369 0.00922849
\(383\) 13.6280 0.696360 0.348180 0.937428i \(-0.386800\pi\)
0.348180 + 0.937428i \(0.386800\pi\)
\(384\) −9.21866 −0.470438
\(385\) 0 0
\(386\) −4.12565 −0.209990
\(387\) 1.64530 0.0836353
\(388\) 14.5899 0.740688
\(389\) −15.7277 −0.797428 −0.398714 0.917075i \(-0.630543\pi\)
−0.398714 + 0.917075i \(0.630543\pi\)
\(390\) 0 0
\(391\) 7.51360 0.379979
\(392\) −26.1136 −1.31894
\(393\) −3.80176 −0.191774
\(394\) −3.58628 −0.180674
\(395\) 0 0
\(396\) −4.12482 −0.207280
\(397\) −16.8523 −0.845790 −0.422895 0.906179i \(-0.638986\pi\)
−0.422895 + 0.906179i \(0.638986\pi\)
\(398\) 3.56905 0.178900
\(399\) −3.92457 −0.196474
\(400\) 0 0
\(401\) 30.3744 1.51682 0.758412 0.651775i \(-0.225975\pi\)
0.758412 + 0.651775i \(0.225975\pi\)
\(402\) −3.00041 −0.149647
\(403\) −5.30877 −0.264449
\(404\) 27.5370 1.37001
\(405\) 0 0
\(406\) 16.3664 0.812250
\(407\) −2.71758 −0.134706
\(408\) 10.2164 0.505789
\(409\) −1.31844 −0.0651925 −0.0325962 0.999469i \(-0.510378\pi\)
−0.0325962 + 0.999469i \(0.510378\pi\)
\(410\) 0 0
\(411\) 0.546417 0.0269528
\(412\) −15.8307 −0.779925
\(413\) 34.4672 1.69602
\(414\) 1.11822 0.0549577
\(415\) 0 0
\(416\) −27.9075 −1.36828
\(417\) 9.22683 0.451840
\(418\) −0.456669 −0.0223364
\(419\) −30.3257 −1.48151 −0.740753 0.671778i \(-0.765531\pi\)
−0.740753 + 0.671778i \(0.765531\pi\)
\(420\) 0 0
\(421\) 8.27204 0.403154 0.201577 0.979473i \(-0.435393\pi\)
0.201577 + 0.979473i \(0.435393\pi\)
\(422\) −9.86200 −0.480075
\(423\) 9.12638 0.443740
\(424\) −16.7900 −0.815395
\(425\) 0 0
\(426\) −1.19529 −0.0579119
\(427\) −38.3065 −1.85378
\(428\) −16.2012 −0.783114
\(429\) 4.91925 0.237504
\(430\) 0 0
\(431\) 22.9574 1.10582 0.552909 0.833241i \(-0.313518\pi\)
0.552909 + 0.833241i \(0.313518\pi\)
\(432\) −12.3652 −0.594921
\(433\) −11.4207 −0.548846 −0.274423 0.961609i \(-0.588487\pi\)
−0.274423 + 0.961609i \(0.588487\pi\)
\(434\) −1.93414 −0.0928417
\(435\) 0 0
\(436\) 33.3120 1.59536
\(437\) −1.06348 −0.0508730
\(438\) 2.47554 0.118286
\(439\) 5.43642 0.259466 0.129733 0.991549i \(-0.458588\pi\)
0.129733 + 0.991549i \(0.458588\pi\)
\(440\) 0 0
\(441\) −34.7264 −1.65364
\(442\) 19.0041 0.903935
\(443\) 34.7494 1.65100 0.825498 0.564405i \(-0.190894\pi\)
0.825498 + 0.564405i \(0.190894\pi\)
\(444\) −4.06593 −0.192961
\(445\) 0 0
\(446\) 3.17775 0.150471
\(447\) −6.32840 −0.299323
\(448\) 16.0745 0.759451
\(449\) −11.3505 −0.535662 −0.267831 0.963466i \(-0.586307\pi\)
−0.267831 + 0.963466i \(0.586307\pi\)
\(450\) 0 0
\(451\) −0.788714 −0.0371391
\(452\) −7.92580 −0.372798
\(453\) −5.80687 −0.272830
\(454\) −3.50639 −0.164563
\(455\) 0 0
\(456\) −1.44604 −0.0677169
\(457\) −6.89453 −0.322513 −0.161256 0.986913i \(-0.551555\pi\)
−0.161256 + 0.986913i \(0.551555\pi\)
\(458\) 2.66660 0.124602
\(459\) 31.2877 1.46038
\(460\) 0 0
\(461\) 13.5620 0.631643 0.315822 0.948819i \(-0.397720\pi\)
0.315822 + 0.948819i \(0.397720\pi\)
\(462\) 1.79223 0.0833820
\(463\) 18.6923 0.868704 0.434352 0.900743i \(-0.356977\pi\)
0.434352 + 0.900743i \(0.356977\pi\)
\(464\) −21.2951 −0.988602
\(465\) 0 0
\(466\) 9.97505 0.462085
\(467\) 14.7156 0.680957 0.340479 0.940252i \(-0.389411\pi\)
0.340479 + 0.940252i \(0.389411\pi\)
\(468\) −24.2959 −1.12308
\(469\) 36.9681 1.70703
\(470\) 0 0
\(471\) 12.3126 0.567333
\(472\) 12.6997 0.584550
\(473\) 0.714571 0.0328560
\(474\) 4.58236 0.210475
\(475\) 0 0
\(476\) −59.4765 −2.72610
\(477\) −22.3277 −1.02231
\(478\) 1.92259 0.0879374
\(479\) −16.3467 −0.746901 −0.373450 0.927650i \(-0.621825\pi\)
−0.373450 + 0.927650i \(0.621825\pi\)
\(480\) 0 0
\(481\) −16.0070 −0.729856
\(482\) −7.95863 −0.362505
\(483\) 4.17368 0.189909
\(484\) −1.79145 −0.0814297
\(485\) 0 0
\(486\) 7.29091 0.330723
\(487\) 24.8625 1.12663 0.563314 0.826243i \(-0.309526\pi\)
0.563314 + 0.826243i \(0.309526\pi\)
\(488\) −14.1143 −0.638926
\(489\) 4.12584 0.186577
\(490\) 0 0
\(491\) 17.5025 0.789878 0.394939 0.918707i \(-0.370766\pi\)
0.394939 + 0.918707i \(0.370766\pi\)
\(492\) −1.18004 −0.0532003
\(493\) 53.8830 2.42677
\(494\) −2.68985 −0.121022
\(495\) 0 0
\(496\) 2.51661 0.112999
\(497\) 14.7271 0.660603
\(498\) −6.25111 −0.280119
\(499\) −3.13006 −0.140121 −0.0700603 0.997543i \(-0.522319\pi\)
−0.0700603 + 0.997543i \(0.522319\pi\)
\(500\) 0 0
\(501\) −18.8774 −0.843380
\(502\) 0.979986 0.0437389
\(503\) 8.98965 0.400829 0.200414 0.979711i \(-0.435771\pi\)
0.200414 + 0.979711i \(0.435771\pi\)
\(504\) −18.7338 −0.834471
\(505\) 0 0
\(506\) 0.485656 0.0215901
\(507\) 18.1180 0.804650
\(508\) −0.606689 −0.0269175
\(509\) 23.6416 1.04790 0.523949 0.851750i \(-0.324458\pi\)
0.523949 + 0.851750i \(0.324458\pi\)
\(510\) 0 0
\(511\) −30.5011 −1.34929
\(512\) 22.8986 1.01198
\(513\) −4.42846 −0.195521
\(514\) 2.39248 0.105528
\(515\) 0 0
\(516\) 1.06911 0.0470650
\(517\) 3.96368 0.174323
\(518\) −5.83181 −0.256235
\(519\) 6.83683 0.300103
\(520\) 0 0
\(521\) 36.0036 1.57735 0.788673 0.614813i \(-0.210768\pi\)
0.788673 + 0.614813i \(0.210768\pi\)
\(522\) 8.01923 0.350992
\(523\) −7.08081 −0.309622 −0.154811 0.987944i \(-0.549477\pi\)
−0.154811 + 0.987944i \(0.549477\pi\)
\(524\) 8.15489 0.356248
\(525\) 0 0
\(526\) −5.59863 −0.244112
\(527\) −6.36777 −0.277384
\(528\) −2.33196 −0.101485
\(529\) −21.8690 −0.950827
\(530\) 0 0
\(531\) 16.8883 0.732889
\(532\) 8.41832 0.364980
\(533\) −4.64565 −0.201225
\(534\) −4.93856 −0.213712
\(535\) 0 0
\(536\) 13.6212 0.588345
\(537\) −11.7616 −0.507550
\(538\) −4.28023 −0.184534
\(539\) −15.0820 −0.649630
\(540\) 0 0
\(541\) −4.23609 −0.182124 −0.0910619 0.995845i \(-0.529026\pi\)
−0.0910619 + 0.995845i \(0.529026\pi\)
\(542\) −6.07970 −0.261145
\(543\) −11.9646 −0.513449
\(544\) −33.4745 −1.43521
\(545\) 0 0
\(546\) 10.5565 0.451777
\(547\) −9.53317 −0.407609 −0.203805 0.979012i \(-0.565331\pi\)
−0.203805 + 0.979012i \(0.565331\pi\)
\(548\) −1.17208 −0.0500688
\(549\) −18.7695 −0.801063
\(550\) 0 0
\(551\) −7.62662 −0.324905
\(552\) 1.53783 0.0654542
\(553\) −56.4593 −2.40089
\(554\) 6.65098 0.282573
\(555\) 0 0
\(556\) −19.7918 −0.839361
\(557\) −2.85948 −0.121160 −0.0605800 0.998163i \(-0.519295\pi\)
−0.0605800 + 0.998163i \(0.519295\pi\)
\(558\) −0.947694 −0.0401191
\(559\) 4.20894 0.178019
\(560\) 0 0
\(561\) 5.90055 0.249121
\(562\) 9.24347 0.389912
\(563\) −12.8091 −0.539841 −0.269920 0.962883i \(-0.586997\pi\)
−0.269920 + 0.962883i \(0.586997\pi\)
\(564\) 5.93030 0.249711
\(565\) 0 0
\(566\) −6.67787 −0.280692
\(567\) −15.0796 −0.633284
\(568\) 5.42633 0.227684
\(569\) −10.5273 −0.441327 −0.220664 0.975350i \(-0.570822\pi\)
−0.220664 + 0.975350i \(0.570822\pi\)
\(570\) 0 0
\(571\) −24.9055 −1.04226 −0.521132 0.853476i \(-0.674490\pi\)
−0.521132 + 0.853476i \(0.674490\pi\)
\(572\) −10.5519 −0.441199
\(573\) 0.329863 0.0137802
\(574\) −1.69255 −0.0706455
\(575\) 0 0
\(576\) 7.87624 0.328177
\(577\) 26.7799 1.11486 0.557430 0.830224i \(-0.311787\pi\)
0.557430 + 0.830224i \(0.311787\pi\)
\(578\) 15.0317 0.625238
\(579\) −7.54507 −0.313562
\(580\) 0 0
\(581\) 77.0200 3.19533
\(582\) −3.10612 −0.128753
\(583\) −9.69714 −0.401615
\(584\) −11.2384 −0.465047
\(585\) 0 0
\(586\) −12.6280 −0.521658
\(587\) −18.7991 −0.775920 −0.387960 0.921676i \(-0.626820\pi\)
−0.387960 + 0.921676i \(0.626820\pi\)
\(588\) −22.5651 −0.930570
\(589\) 0.901295 0.0371372
\(590\) 0 0
\(591\) −6.55866 −0.269787
\(592\) 7.58807 0.311868
\(593\) 3.68216 0.151208 0.0756041 0.997138i \(-0.475911\pi\)
0.0756041 + 0.997138i \(0.475911\pi\)
\(594\) 2.02234 0.0829776
\(595\) 0 0
\(596\) 13.5746 0.556038
\(597\) 6.52715 0.267138
\(598\) 2.86059 0.116978
\(599\) 43.2659 1.76780 0.883899 0.467677i \(-0.154909\pi\)
0.883899 + 0.467677i \(0.154909\pi\)
\(600\) 0 0
\(601\) −14.4072 −0.587683 −0.293842 0.955854i \(-0.594934\pi\)
−0.293842 + 0.955854i \(0.594934\pi\)
\(602\) 1.53344 0.0624983
\(603\) 18.1137 0.737647
\(604\) 12.4559 0.506824
\(605\) 0 0
\(606\) −5.86251 −0.238148
\(607\) 6.06496 0.246169 0.123084 0.992396i \(-0.460721\pi\)
0.123084 + 0.992396i \(0.460721\pi\)
\(608\) 4.73799 0.192151
\(609\) 29.9312 1.21287
\(610\) 0 0
\(611\) 23.3467 0.944508
\(612\) −29.1424 −1.17801
\(613\) 3.51855 0.142113 0.0710565 0.997472i \(-0.477363\pi\)
0.0710565 + 0.997472i \(0.477363\pi\)
\(614\) 0.345271 0.0139340
\(615\) 0 0
\(616\) −8.13629 −0.327821
\(617\) −7.17642 −0.288912 −0.144456 0.989511i \(-0.546143\pi\)
−0.144456 + 0.989511i \(0.546143\pi\)
\(618\) 3.37031 0.135574
\(619\) −8.27421 −0.332568 −0.166284 0.986078i \(-0.553177\pi\)
−0.166284 + 0.986078i \(0.553177\pi\)
\(620\) 0 0
\(621\) 4.70956 0.188988
\(622\) 0.517644 0.0207556
\(623\) 60.8480 2.43783
\(624\) −13.7356 −0.549864
\(625\) 0 0
\(626\) 4.97824 0.198970
\(627\) −0.835165 −0.0333533
\(628\) −26.4108 −1.05391
\(629\) −19.2001 −0.765557
\(630\) 0 0
\(631\) −9.09560 −0.362090 −0.181045 0.983475i \(-0.557948\pi\)
−0.181045 + 0.983475i \(0.557948\pi\)
\(632\) −20.8029 −0.827493
\(633\) −18.0358 −0.716859
\(634\) −3.80097 −0.150956
\(635\) 0 0
\(636\) −14.5085 −0.575298
\(637\) −88.8356 −3.51980
\(638\) 3.48284 0.137887
\(639\) 7.21604 0.285462
\(640\) 0 0
\(641\) 16.4386 0.649285 0.324642 0.945837i \(-0.394756\pi\)
0.324642 + 0.945837i \(0.394756\pi\)
\(642\) 3.44917 0.136128
\(643\) −7.04594 −0.277865 −0.138932 0.990302i \(-0.544367\pi\)
−0.138932 + 0.990302i \(0.544367\pi\)
\(644\) −8.95268 −0.352785
\(645\) 0 0
\(646\) −3.22642 −0.126942
\(647\) −18.1024 −0.711679 −0.355840 0.934547i \(-0.615805\pi\)
−0.355840 + 0.934547i \(0.615805\pi\)
\(648\) −5.55619 −0.218268
\(649\) 7.33476 0.287914
\(650\) 0 0
\(651\) −3.53719 −0.138634
\(652\) −8.85005 −0.346595
\(653\) −37.2985 −1.45960 −0.729802 0.683659i \(-0.760388\pi\)
−0.729802 + 0.683659i \(0.760388\pi\)
\(654\) −7.09200 −0.277319
\(655\) 0 0
\(656\) 2.20226 0.0859837
\(657\) −14.9450 −0.583059
\(658\) 8.50590 0.331594
\(659\) 13.2223 0.515068 0.257534 0.966269i \(-0.417090\pi\)
0.257534 + 0.966269i \(0.417090\pi\)
\(660\) 0 0
\(661\) −17.6212 −0.685385 −0.342692 0.939448i \(-0.611339\pi\)
−0.342692 + 0.939448i \(0.611339\pi\)
\(662\) −1.13010 −0.0439226
\(663\) 34.7552 1.34978
\(664\) 28.3786 1.10130
\(665\) 0 0
\(666\) −2.85748 −0.110725
\(667\) 8.11073 0.314049
\(668\) 40.4926 1.56671
\(669\) 5.81153 0.224687
\(670\) 0 0
\(671\) −8.15179 −0.314696
\(672\) −18.5946 −0.717301
\(673\) −32.2335 −1.24251 −0.621255 0.783609i \(-0.713377\pi\)
−0.621255 + 0.783609i \(0.713377\pi\)
\(674\) 13.8481 0.533410
\(675\) 0 0
\(676\) −38.8637 −1.49476
\(677\) 10.2788 0.395045 0.197523 0.980298i \(-0.436710\pi\)
0.197523 + 0.980298i \(0.436710\pi\)
\(678\) 1.68737 0.0648031
\(679\) 38.2706 1.46869
\(680\) 0 0
\(681\) −6.41255 −0.245730
\(682\) −0.411593 −0.0157607
\(683\) −25.4018 −0.971973 −0.485986 0.873966i \(-0.661540\pi\)
−0.485986 + 0.873966i \(0.661540\pi\)
\(684\) 4.12482 0.157716
\(685\) 0 0
\(686\) −17.3437 −0.662186
\(687\) 4.87674 0.186059
\(688\) −1.99523 −0.0760676
\(689\) −57.1177 −2.17601
\(690\) 0 0
\(691\) −2.58092 −0.0981828 −0.0490914 0.998794i \(-0.515633\pi\)
−0.0490914 + 0.998794i \(0.515633\pi\)
\(692\) −14.6652 −0.557487
\(693\) −10.8198 −0.411010
\(694\) 4.76450 0.180858
\(695\) 0 0
\(696\) 11.0284 0.418029
\(697\) −5.57236 −0.211068
\(698\) 2.23334 0.0845330
\(699\) 18.2426 0.689998
\(700\) 0 0
\(701\) −30.0612 −1.13540 −0.567698 0.823237i \(-0.692166\pi\)
−0.567698 + 0.823237i \(0.692166\pi\)
\(702\) 11.9119 0.449586
\(703\) 2.71758 0.102496
\(704\) 3.42073 0.128924
\(705\) 0 0
\(706\) −15.5840 −0.586511
\(707\) 72.2321 2.71657
\(708\) 10.9740 0.412427
\(709\) −6.90683 −0.259391 −0.129696 0.991554i \(-0.541400\pi\)
−0.129696 + 0.991554i \(0.541400\pi\)
\(710\) 0 0
\(711\) −27.6640 −1.03748
\(712\) 22.4199 0.840222
\(713\) −0.958506 −0.0358963
\(714\) 12.6623 0.473875
\(715\) 0 0
\(716\) 25.2290 0.942851
\(717\) 3.51608 0.131310
\(718\) 4.81175 0.179573
\(719\) 13.1525 0.490506 0.245253 0.969459i \(-0.421129\pi\)
0.245253 + 0.969459i \(0.421129\pi\)
\(720\) 0 0
\(721\) −41.5256 −1.54649
\(722\) 0.456669 0.0169955
\(723\) −14.5549 −0.541302
\(724\) 25.6644 0.953810
\(725\) 0 0
\(726\) 0.381394 0.0141548
\(727\) 46.8434 1.73733 0.868663 0.495404i \(-0.164980\pi\)
0.868663 + 0.495404i \(0.164980\pi\)
\(728\) −47.9241 −1.77618
\(729\) 3.70675 0.137287
\(730\) 0 0
\(731\) 5.04854 0.186727
\(732\) −12.1964 −0.450791
\(733\) 31.9162 1.17885 0.589426 0.807822i \(-0.299354\pi\)
0.589426 + 0.807822i \(0.299354\pi\)
\(734\) −14.2151 −0.524688
\(735\) 0 0
\(736\) −5.03874 −0.185731
\(737\) 7.86697 0.289784
\(738\) −0.829316 −0.0305276
\(739\) 30.0302 1.10468 0.552339 0.833620i \(-0.313736\pi\)
0.552339 + 0.833620i \(0.313736\pi\)
\(740\) 0 0
\(741\) −4.91925 −0.180713
\(742\) −20.8096 −0.763946
\(743\) 42.6871 1.56604 0.783019 0.621998i \(-0.213679\pi\)
0.783019 + 0.621998i \(0.213679\pi\)
\(744\) −1.30331 −0.0477815
\(745\) 0 0
\(746\) −13.2380 −0.484676
\(747\) 37.7384 1.38078
\(748\) −12.6569 −0.462780
\(749\) −42.4972 −1.55282
\(750\) 0 0
\(751\) 30.7211 1.12103 0.560514 0.828145i \(-0.310604\pi\)
0.560514 + 0.828145i \(0.310604\pi\)
\(752\) −11.0675 −0.403589
\(753\) 1.79222 0.0653120
\(754\) 20.5145 0.747093
\(755\) 0 0
\(756\) −37.2802 −1.35587
\(757\) 49.0714 1.78353 0.891765 0.452498i \(-0.149467\pi\)
0.891765 + 0.452498i \(0.149467\pi\)
\(758\) −12.0654 −0.438233
\(759\) 0.888178 0.0322388
\(760\) 0 0
\(761\) −24.8178 −0.899645 −0.449822 0.893118i \(-0.648513\pi\)
−0.449822 + 0.893118i \(0.648513\pi\)
\(762\) 0.129162 0.00467904
\(763\) 87.3806 3.16339
\(764\) −0.707565 −0.0255988
\(765\) 0 0
\(766\) 6.22350 0.224864
\(767\) 43.2029 1.55997
\(768\) 1.50388 0.0542666
\(769\) −38.9862 −1.40588 −0.702940 0.711250i \(-0.748130\pi\)
−0.702940 + 0.711250i \(0.748130\pi\)
\(770\) 0 0
\(771\) 4.37542 0.157577
\(772\) 16.1844 0.582489
\(773\) −0.998099 −0.0358991 −0.0179496 0.999839i \(-0.505714\pi\)
−0.0179496 + 0.999839i \(0.505714\pi\)
\(774\) 0.751357 0.0270070
\(775\) 0 0
\(776\) 14.1011 0.506199
\(777\) −10.6653 −0.382617
\(778\) −7.18237 −0.257500
\(779\) 0.788714 0.0282586
\(780\) 0 0
\(781\) 3.13400 0.112143
\(782\) 3.43123 0.122700
\(783\) 33.7742 1.20699
\(784\) 42.1123 1.50401
\(785\) 0 0
\(786\) −1.73615 −0.0619263
\(787\) −18.7420 −0.668082 −0.334041 0.942559i \(-0.608412\pi\)
−0.334041 + 0.942559i \(0.608412\pi\)
\(788\) 14.0685 0.501170
\(789\) −10.2389 −0.364514
\(790\) 0 0
\(791\) −20.7901 −0.739211
\(792\) −3.98664 −0.141659
\(793\) −48.0153 −1.70507
\(794\) −7.69590 −0.273117
\(795\) 0 0
\(796\) −14.0009 −0.496250
\(797\) −5.05128 −0.178925 −0.0894627 0.995990i \(-0.528515\pi\)
−0.0894627 + 0.995990i \(0.528515\pi\)
\(798\) −1.79223 −0.0634442
\(799\) 28.0039 0.990708
\(800\) 0 0
\(801\) 29.8144 1.05344
\(802\) 13.8710 0.489803
\(803\) −6.49076 −0.229054
\(804\) 11.7702 0.415104
\(805\) 0 0
\(806\) −2.42435 −0.0853941
\(807\) −7.82777 −0.275551
\(808\) 26.6144 0.936293
\(809\) −4.98214 −0.175163 −0.0875813 0.996157i \(-0.527914\pi\)
−0.0875813 + 0.996157i \(0.527914\pi\)
\(810\) 0 0
\(811\) 25.3145 0.888913 0.444456 0.895800i \(-0.353397\pi\)
0.444456 + 0.895800i \(0.353397\pi\)
\(812\) −64.2033 −2.25309
\(813\) −11.1187 −0.389949
\(814\) −1.24103 −0.0434982
\(815\) 0 0
\(816\) −16.4756 −0.576761
\(817\) −0.714571 −0.0249997
\(818\) −0.602089 −0.0210515
\(819\) −63.7303 −2.22692
\(820\) 0 0
\(821\) 5.81543 0.202960 0.101480 0.994838i \(-0.467642\pi\)
0.101480 + 0.994838i \(0.467642\pi\)
\(822\) 0.249532 0.00870342
\(823\) −47.7881 −1.66579 −0.832895 0.553431i \(-0.813318\pi\)
−0.832895 + 0.553431i \(0.813318\pi\)
\(824\) −15.3004 −0.533015
\(825\) 0 0
\(826\) 15.7401 0.547667
\(827\) 39.0692 1.35857 0.679284 0.733875i \(-0.262290\pi\)
0.679284 + 0.733875i \(0.262290\pi\)
\(828\) −4.38665 −0.152447
\(829\) −7.57440 −0.263070 −0.131535 0.991312i \(-0.541991\pi\)
−0.131535 + 0.991312i \(0.541991\pi\)
\(830\) 0 0
\(831\) 12.1634 0.421945
\(832\) 20.1487 0.698529
\(833\) −106.557 −3.69197
\(834\) 4.21361 0.145905
\(835\) 0 0
\(836\) 1.79145 0.0619587
\(837\) −3.99135 −0.137961
\(838\) −13.8488 −0.478398
\(839\) −28.0343 −0.967850 −0.483925 0.875110i \(-0.660789\pi\)
−0.483925 + 0.875110i \(0.660789\pi\)
\(840\) 0 0
\(841\) 29.1653 1.00570
\(842\) 3.77758 0.130184
\(843\) 16.9046 0.582227
\(844\) 38.6874 1.33167
\(845\) 0 0
\(846\) 4.16773 0.143290
\(847\) −4.69915 −0.161465
\(848\) 27.0765 0.929811
\(849\) −12.2126 −0.419136
\(850\) 0 0
\(851\) −2.89008 −0.0990708
\(852\) 4.68896 0.160641
\(853\) 27.9605 0.957349 0.478674 0.877992i \(-0.341117\pi\)
0.478674 + 0.877992i \(0.341117\pi\)
\(854\) −17.4934 −0.598612
\(855\) 0 0
\(856\) −15.6584 −0.535194
\(857\) −17.8805 −0.610787 −0.305393 0.952226i \(-0.598788\pi\)
−0.305393 + 0.952226i \(0.598788\pi\)
\(858\) 2.24647 0.0766932
\(859\) 7.76017 0.264774 0.132387 0.991198i \(-0.457736\pi\)
0.132387 + 0.991198i \(0.457736\pi\)
\(860\) 0 0
\(861\) −3.09536 −0.105490
\(862\) 10.4839 0.357084
\(863\) −31.9699 −1.08827 −0.544135 0.838998i \(-0.683142\pi\)
−0.544135 + 0.838998i \(0.683142\pi\)
\(864\) −20.9820 −0.713823
\(865\) 0 0
\(866\) −5.21549 −0.177230
\(867\) 27.4903 0.933621
\(868\) 7.58739 0.257533
\(869\) −12.0148 −0.407574
\(870\) 0 0
\(871\) 46.3377 1.57009
\(872\) 32.1960 1.09029
\(873\) 18.7519 0.634655
\(874\) −0.485656 −0.0164276
\(875\) 0 0
\(876\) −9.71122 −0.328112
\(877\) 2.12224 0.0716630 0.0358315 0.999358i \(-0.488592\pi\)
0.0358315 + 0.999358i \(0.488592\pi\)
\(878\) 2.48264 0.0837852
\(879\) −23.0944 −0.778953
\(880\) 0 0
\(881\) −15.1859 −0.511627 −0.255814 0.966726i \(-0.582343\pi\)
−0.255814 + 0.966726i \(0.582343\pi\)
\(882\) −15.8585 −0.533982
\(883\) −29.5964 −0.995999 −0.498000 0.867177i \(-0.665932\pi\)
−0.498000 + 0.867177i \(0.665932\pi\)
\(884\) −74.5509 −2.50742
\(885\) 0 0
\(886\) 15.8690 0.533129
\(887\) −23.2340 −0.780121 −0.390061 0.920789i \(-0.627546\pi\)
−0.390061 + 0.920789i \(0.627546\pi\)
\(888\) −3.92972 −0.131873
\(889\) −1.59140 −0.0533740
\(890\) 0 0
\(891\) −3.20900 −0.107506
\(892\) −12.4659 −0.417389
\(893\) −3.96368 −0.132640
\(894\) −2.88998 −0.0966555
\(895\) 0 0
\(896\) 51.8699 1.73285
\(897\) 5.23151 0.174675
\(898\) −5.18340 −0.172972
\(899\) −6.87384 −0.229255
\(900\) 0 0
\(901\) −68.5116 −2.28245
\(902\) −0.360181 −0.0119927
\(903\) 2.80438 0.0933240
\(904\) −7.66028 −0.254777
\(905\) 0 0
\(906\) −2.65181 −0.0881006
\(907\) 35.4985 1.17871 0.589354 0.807875i \(-0.299382\pi\)
0.589354 + 0.807875i \(0.299382\pi\)
\(908\) 13.7551 0.456480
\(909\) 35.3924 1.17389
\(910\) 0 0
\(911\) −38.5075 −1.27581 −0.637905 0.770115i \(-0.720199\pi\)
−0.637905 + 0.770115i \(0.720199\pi\)
\(912\) 2.33196 0.0772189
\(913\) 16.3902 0.542436
\(914\) −3.14852 −0.104144
\(915\) 0 0
\(916\) −10.4608 −0.345633
\(917\) 21.3911 0.706395
\(918\) 14.2881 0.471577
\(919\) 20.9347 0.690572 0.345286 0.938497i \(-0.387782\pi\)
0.345286 + 0.938497i \(0.387782\pi\)
\(920\) 0 0
\(921\) 0.631439 0.0208066
\(922\) 6.19332 0.203966
\(923\) 18.4598 0.607610
\(924\) −7.03068 −0.231292
\(925\) 0 0
\(926\) 8.53618 0.280516
\(927\) −20.3468 −0.668276
\(928\) −36.1349 −1.18619
\(929\) −0.536958 −0.0176170 −0.00880851 0.999961i \(-0.502804\pi\)
−0.00880851 + 0.999961i \(0.502804\pi\)
\(930\) 0 0
\(931\) 15.0820 0.494294
\(932\) −39.1309 −1.28177
\(933\) 0.946677 0.0309928
\(934\) 6.72016 0.219890
\(935\) 0 0
\(936\) −23.4819 −0.767531
\(937\) −34.4984 −1.12701 −0.563507 0.826112i \(-0.690548\pi\)
−0.563507 + 0.826112i \(0.690548\pi\)
\(938\) 16.8822 0.551223
\(939\) 9.10430 0.297107
\(940\) 0 0
\(941\) 17.8959 0.583391 0.291695 0.956511i \(-0.405781\pi\)
0.291695 + 0.956511i \(0.405781\pi\)
\(942\) 5.62276 0.183200
\(943\) −0.838778 −0.0273144
\(944\) −20.4802 −0.666574
\(945\) 0 0
\(946\) 0.326322 0.0106097
\(947\) −16.0979 −0.523111 −0.261556 0.965188i \(-0.584235\pi\)
−0.261556 + 0.965188i \(0.584235\pi\)
\(948\) −17.9760 −0.583834
\(949\) −38.2316 −1.24105
\(950\) 0 0
\(951\) −6.95130 −0.225411
\(952\) −57.4840 −1.86307
\(953\) −29.2828 −0.948562 −0.474281 0.880374i \(-0.657292\pi\)
−0.474281 + 0.880374i \(0.657292\pi\)
\(954\) −10.1963 −0.330119
\(955\) 0 0
\(956\) −7.54210 −0.243929
\(957\) 6.36948 0.205896
\(958\) −7.46504 −0.241184
\(959\) −3.07448 −0.0992802
\(960\) 0 0
\(961\) −30.1877 −0.973796
\(962\) −7.30989 −0.235680
\(963\) −20.8229 −0.671008
\(964\) 31.2207 1.00555
\(965\) 0 0
\(966\) 1.90599 0.0613243
\(967\) 39.4644 1.26909 0.634544 0.772887i \(-0.281188\pi\)
0.634544 + 0.772887i \(0.281188\pi\)
\(968\) −1.73144 −0.0556505
\(969\) −5.90055 −0.189553
\(970\) 0 0
\(971\) 27.0245 0.867257 0.433628 0.901092i \(-0.357233\pi\)
0.433628 + 0.901092i \(0.357233\pi\)
\(972\) −28.6013 −0.917388
\(973\) −51.9159 −1.66435
\(974\) 11.3539 0.363804
\(975\) 0 0
\(976\) 22.7615 0.728579
\(977\) 55.2922 1.76895 0.884477 0.466584i \(-0.154516\pi\)
0.884477 + 0.466584i \(0.154516\pi\)
\(978\) 1.88414 0.0602482
\(979\) 12.9487 0.413843
\(980\) 0 0
\(981\) 42.8149 1.36697
\(982\) 7.99286 0.255062
\(983\) −36.0221 −1.14893 −0.574463 0.818531i \(-0.694789\pi\)
−0.574463 + 0.818531i \(0.694789\pi\)
\(984\) −1.14051 −0.0363581
\(985\) 0 0
\(986\) 24.6067 0.783637
\(987\) 15.5557 0.495145
\(988\) 10.5519 0.335702
\(989\) 0.759929 0.0241643
\(990\) 0 0
\(991\) 50.7944 1.61354 0.806768 0.590868i \(-0.201215\pi\)
0.806768 + 0.590868i \(0.201215\pi\)
\(992\) 4.27033 0.135583
\(993\) −2.06675 −0.0655863
\(994\) 6.72543 0.213318
\(995\) 0 0
\(996\) 24.5223 0.777019
\(997\) 41.8525 1.32548 0.662741 0.748849i \(-0.269393\pi\)
0.662741 + 0.748849i \(0.269393\pi\)
\(998\) −1.42940 −0.0452469
\(999\) −12.0347 −0.380761
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 5225.2.a.n.1.4 7
5.4 even 2 209.2.a.d.1.4 7
15.14 odd 2 1881.2.a.p.1.4 7
20.19 odd 2 3344.2.a.ba.1.5 7
55.54 odd 2 2299.2.a.q.1.4 7
95.94 odd 2 3971.2.a.i.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.d.1.4 7 5.4 even 2
1881.2.a.p.1.4 7 15.14 odd 2
2299.2.a.q.1.4 7 55.54 odd 2
3344.2.a.ba.1.5 7 20.19 odd 2
3971.2.a.i.1.4 7 95.94 odd 2
5225.2.a.n.1.4 7 1.1 even 1 trivial