Properties

Label 5225.2.a.h.1.4
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(5\)
Coefficient field: 5.5.246832.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) 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 \(1.71250\) 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)
 
\(f(q)\) \(=\) \(q+0.779856 q^{2} +2.98063 q^{3} -1.39182 q^{4} +2.32446 q^{6} -1.06736 q^{7} -2.64513 q^{8} +5.88418 q^{9} +O(q^{10})\) \(q+0.779856 q^{2} +2.98063 q^{3} -1.39182 q^{4} +2.32446 q^{6} -1.06736 q^{7} -2.64513 q^{8} +5.88418 q^{9} +1.00000 q^{11} -4.14852 q^{12} +0.0563258 q^{13} -0.832387 q^{14} +0.720827 q^{16} +4.53628 q^{17} +4.58881 q^{18} -1.00000 q^{19} -3.18141 q^{21} +0.779856 q^{22} +1.07949 q^{23} -7.88418 q^{24} +0.0439260 q^{26} +8.59667 q^{27} +1.48558 q^{28} +0.299905 q^{29} +9.18548 q^{31} +5.85241 q^{32} +2.98063 q^{33} +3.53764 q^{34} -8.18974 q^{36} -4.50448 q^{37} -0.779856 q^{38} +0.167887 q^{39} +12.0009 q^{41} -2.48104 q^{42} -10.7260 q^{43} -1.39182 q^{44} +0.841844 q^{46} -2.89630 q^{47} +2.14852 q^{48} -5.86074 q^{49} +13.5210 q^{51} -0.0783957 q^{52} +12.3213 q^{53} +6.70416 q^{54} +2.82331 q^{56} -2.98063 q^{57} +0.233882 q^{58} -1.14582 q^{59} -8.09599 q^{61} +7.16335 q^{62} -6.28054 q^{63} +3.12238 q^{64} +2.32446 q^{66} -11.2733 q^{67} -6.31370 q^{68} +3.21755 q^{69} +13.4948 q^{71} -15.5644 q^{72} +11.1470 q^{73} -3.51284 q^{74} +1.39182 q^{76} -1.06736 q^{77} +0.130927 q^{78} +11.4250 q^{79} +7.97100 q^{81} +9.35899 q^{82} +13.9802 q^{83} +4.42797 q^{84} -8.36475 q^{86} +0.893906 q^{87} -2.64513 q^{88} -0.183185 q^{89} -0.0601200 q^{91} -1.50246 q^{92} +27.3785 q^{93} -2.25870 q^{94} +17.4439 q^{96} -5.66263 q^{97} -4.57053 q^{98} +5.88418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{2} - q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{2} - q^{3} + 6 q^{4} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} + 5 q^{11} - 6 q^{12} - 4 q^{13} - 14 q^{14} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 5 q^{19} + 10 q^{21} - 2 q^{22} - 3 q^{23} - 14 q^{24} - 6 q^{26} + 11 q^{27} + 10 q^{28} + 10 q^{29} + 11 q^{31} - 14 q^{32} - q^{33} - 4 q^{34} - 26 q^{36} - q^{37} + 2 q^{38} + 2 q^{39} + 2 q^{41} + 16 q^{42} - 20 q^{43} + 6 q^{44} - 4 q^{46} + 20 q^{47} - 4 q^{48} + 3 q^{49} + 24 q^{51} - 6 q^{52} + 14 q^{53} + 16 q^{54} - 38 q^{56} + q^{57} + 6 q^{58} + 3 q^{59} - 10 q^{61} + 6 q^{62} - 24 q^{63} - 2 q^{66} - 9 q^{67} - 24 q^{68} - 5 q^{69} + 23 q^{71} + 12 q^{72} + 8 q^{74} - 6 q^{76} - 6 q^{77} + 22 q^{78} + 44 q^{79} + q^{81} + 30 q^{82} + 14 q^{83} + 14 q^{84} + 52 q^{86} - 28 q^{87} - 6 q^{88} - 27 q^{89} + 24 q^{91} - 58 q^{92} + 27 q^{93} - 8 q^{94} + 50 q^{96} - 15 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.779856 0.551441 0.275721 0.961238i \(-0.411084\pi\)
0.275721 + 0.961238i \(0.411084\pi\)
\(3\) 2.98063 1.72087 0.860435 0.509561i \(-0.170192\pi\)
0.860435 + 0.509561i \(0.170192\pi\)
\(4\) −1.39182 −0.695912
\(5\) 0 0
\(6\) 2.32446 0.948959
\(7\) −1.06736 −0.403424 −0.201712 0.979445i \(-0.564651\pi\)
−0.201712 + 0.979445i \(0.564651\pi\)
\(8\) −2.64513 −0.935196
\(9\) 5.88418 1.96139
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −4.14852 −1.19757
\(13\) 0.0563258 0.0156220 0.00781098 0.999969i \(-0.497514\pi\)
0.00781098 + 0.999969i \(0.497514\pi\)
\(14\) −0.832387 −0.222465
\(15\) 0 0
\(16\) 0.720827 0.180207
\(17\) 4.53628 1.10021 0.550104 0.835096i \(-0.314588\pi\)
0.550104 + 0.835096i \(0.314588\pi\)
\(18\) 4.58881 1.08159
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −3.18141 −0.694241
\(22\) 0.779856 0.166266
\(23\) 1.07949 0.225088 0.112544 0.993647i \(-0.464100\pi\)
0.112544 + 0.993647i \(0.464100\pi\)
\(24\) −7.88418 −1.60935
\(25\) 0 0
\(26\) 0.0439260 0.00861460
\(27\) 8.59667 1.65443
\(28\) 1.48558 0.280748
\(29\) 0.299905 0.0556909 0.0278455 0.999612i \(-0.491135\pi\)
0.0278455 + 0.999612i \(0.491135\pi\)
\(30\) 0 0
\(31\) 9.18548 1.64976 0.824880 0.565307i \(-0.191242\pi\)
0.824880 + 0.565307i \(0.191242\pi\)
\(32\) 5.85241 1.03457
\(33\) 2.98063 0.518862
\(34\) 3.53764 0.606701
\(35\) 0 0
\(36\) −8.18974 −1.36496
\(37\) −4.50448 −0.740531 −0.370266 0.928926i \(-0.620733\pi\)
−0.370266 + 0.928926i \(0.620733\pi\)
\(38\) −0.779856 −0.126509
\(39\) 0.167887 0.0268834
\(40\) 0 0
\(41\) 12.0009 1.87423 0.937115 0.349020i \(-0.113486\pi\)
0.937115 + 0.349020i \(0.113486\pi\)
\(42\) −2.48104 −0.382833
\(43\) −10.7260 −1.63570 −0.817851 0.575430i \(-0.804835\pi\)
−0.817851 + 0.575430i \(0.804835\pi\)
\(44\) −1.39182 −0.209826
\(45\) 0 0
\(46\) 0.841844 0.124123
\(47\) −2.89630 −0.422469 −0.211235 0.977435i \(-0.567748\pi\)
−0.211235 + 0.977435i \(0.567748\pi\)
\(48\) 2.14852 0.310112
\(49\) −5.86074 −0.837249
\(50\) 0 0
\(51\) 13.5210 1.89332
\(52\) −0.0783957 −0.0108715
\(53\) 12.3213 1.69246 0.846230 0.532818i \(-0.178867\pi\)
0.846230 + 0.532818i \(0.178867\pi\)
\(54\) 6.70416 0.912321
\(55\) 0 0
\(56\) 2.82331 0.377281
\(57\) −2.98063 −0.394795
\(58\) 0.233882 0.0307103
\(59\) −1.14582 −0.149173 −0.0745863 0.997215i \(-0.523764\pi\)
−0.0745863 + 0.997215i \(0.523764\pi\)
\(60\) 0 0
\(61\) −8.09599 −1.03659 −0.518293 0.855203i \(-0.673432\pi\)
−0.518293 + 0.855203i \(0.673432\pi\)
\(62\) 7.16335 0.909746
\(63\) −6.28054 −0.791273
\(64\) 3.12238 0.390298
\(65\) 0 0
\(66\) 2.32446 0.286122
\(67\) −11.2733 −1.37726 −0.688628 0.725115i \(-0.741787\pi\)
−0.688628 + 0.725115i \(0.741787\pi\)
\(68\) −6.31370 −0.765649
\(69\) 3.21755 0.387348
\(70\) 0 0
\(71\) 13.4948 1.60154 0.800771 0.598970i \(-0.204423\pi\)
0.800771 + 0.598970i \(0.204423\pi\)
\(72\) −15.5644 −1.83429
\(73\) 11.1470 1.30466 0.652330 0.757935i \(-0.273792\pi\)
0.652330 + 0.757935i \(0.273792\pi\)
\(74\) −3.51284 −0.408360
\(75\) 0 0
\(76\) 1.39182 0.159653
\(77\) −1.06736 −0.121637
\(78\) 0.130927 0.0148246
\(79\) 11.4250 1.28541 0.642706 0.766113i \(-0.277812\pi\)
0.642706 + 0.766113i \(0.277812\pi\)
\(80\) 0 0
\(81\) 7.97100 0.885666
\(82\) 9.35899 1.03353
\(83\) 13.9802 1.53452 0.767261 0.641335i \(-0.221619\pi\)
0.767261 + 0.641335i \(0.221619\pi\)
\(84\) 4.42797 0.483131
\(85\) 0 0
\(86\) −8.36475 −0.901994
\(87\) 0.893906 0.0958368
\(88\) −2.64513 −0.281972
\(89\) −0.183185 −0.0194176 −0.00970878 0.999953i \(-0.503090\pi\)
−0.00970878 + 0.999953i \(0.503090\pi\)
\(90\) 0 0
\(91\) −0.0601200 −0.00630228
\(92\) −1.50246 −0.156642
\(93\) 27.3785 2.83902
\(94\) −2.25870 −0.232967
\(95\) 0 0
\(96\) 17.4439 1.78036
\(97\) −5.66263 −0.574953 −0.287477 0.957788i \(-0.592816\pi\)
−0.287477 + 0.957788i \(0.592816\pi\)
\(98\) −4.57053 −0.461694
\(99\) 5.88418 0.591382
\(100\) 0 0
\(101\) 8.00759 0.796785 0.398392 0.917215i \(-0.369568\pi\)
0.398392 + 0.917215i \(0.369568\pi\)
\(102\) 10.5444 1.04405
\(103\) −6.18725 −0.609648 −0.304824 0.952409i \(-0.598598\pi\)
−0.304824 + 0.952409i \(0.598598\pi\)
\(104\) −0.148989 −0.0146096
\(105\) 0 0
\(106\) 9.60883 0.933292
\(107\) 7.29027 0.704777 0.352388 0.935854i \(-0.385370\pi\)
0.352388 + 0.935854i \(0.385370\pi\)
\(108\) −11.9651 −1.15134
\(109\) 7.79895 0.747004 0.373502 0.927629i \(-0.378157\pi\)
0.373502 + 0.927629i \(0.378157\pi\)
\(110\) 0 0
\(111\) −13.4262 −1.27436
\(112\) −0.769382 −0.0726998
\(113\) 0.430558 0.0405035 0.0202517 0.999795i \(-0.493553\pi\)
0.0202517 + 0.999795i \(0.493553\pi\)
\(114\) −2.32446 −0.217706
\(115\) 0 0
\(116\) −0.417415 −0.0387560
\(117\) 0.331431 0.0306408
\(118\) −0.893572 −0.0822600
\(119\) −4.84184 −0.443851
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −6.31370 −0.571616
\(123\) 35.7704 3.22531
\(124\) −12.7846 −1.14809
\(125\) 0 0
\(126\) −4.89791 −0.436341
\(127\) 3.13888 0.278531 0.139265 0.990255i \(-0.455526\pi\)
0.139265 + 0.990255i \(0.455526\pi\)
\(128\) −9.26981 −0.819343
\(129\) −31.9703 −2.81483
\(130\) 0 0
\(131\) 12.4315 1.08615 0.543075 0.839684i \(-0.317260\pi\)
0.543075 + 0.839684i \(0.317260\pi\)
\(132\) −4.14852 −0.361082
\(133\) 1.06736 0.0925519
\(134\) −8.79157 −0.759476
\(135\) 0 0
\(136\) −11.9991 −1.02891
\(137\) −13.8301 −1.18159 −0.590794 0.806822i \(-0.701186\pi\)
−0.590794 + 0.806822i \(0.701186\pi\)
\(138\) 2.50923 0.213600
\(139\) 15.9968 1.35683 0.678417 0.734677i \(-0.262666\pi\)
0.678417 + 0.734677i \(0.262666\pi\)
\(140\) 0 0
\(141\) −8.63281 −0.727014
\(142\) 10.5240 0.883157
\(143\) 0.0563258 0.00471020
\(144\) 4.24147 0.353456
\(145\) 0 0
\(146\) 8.69307 0.719443
\(147\) −17.4687 −1.44080
\(148\) 6.26944 0.515345
\(149\) 11.3620 0.930812 0.465406 0.885097i \(-0.345908\pi\)
0.465406 + 0.885097i \(0.345908\pi\)
\(150\) 0 0
\(151\) 4.66341 0.379503 0.189751 0.981832i \(-0.439232\pi\)
0.189751 + 0.981832i \(0.439232\pi\)
\(152\) 2.64513 0.214549
\(153\) 26.6923 2.15794
\(154\) −0.832387 −0.0670757
\(155\) 0 0
\(156\) −0.233669 −0.0187085
\(157\) 9.05206 0.722433 0.361217 0.932482i \(-0.382361\pi\)
0.361217 + 0.932482i \(0.382361\pi\)
\(158\) 8.90984 0.708829
\(159\) 36.7253 2.91250
\(160\) 0 0
\(161\) −1.15220 −0.0908062
\(162\) 6.21623 0.488393
\(163\) −2.36761 −0.185446 −0.0927229 0.995692i \(-0.529557\pi\)
−0.0927229 + 0.995692i \(0.529557\pi\)
\(164\) −16.7032 −1.30430
\(165\) 0 0
\(166\) 10.9025 0.846199
\(167\) 9.27361 0.717613 0.358807 0.933412i \(-0.383184\pi\)
0.358807 + 0.933412i \(0.383184\pi\)
\(168\) 8.41526 0.649251
\(169\) −12.9968 −0.999756
\(170\) 0 0
\(171\) −5.88418 −0.449974
\(172\) 14.9287 1.13831
\(173\) −10.7172 −0.814812 −0.407406 0.913247i \(-0.633567\pi\)
−0.407406 + 0.913247i \(0.633567\pi\)
\(174\) 0.697118 0.0528484
\(175\) 0 0
\(176\) 0.720827 0.0543344
\(177\) −3.41526 −0.256707
\(178\) −0.142858 −0.0107076
\(179\) −22.9070 −1.71215 −0.856073 0.516854i \(-0.827103\pi\)
−0.856073 + 0.516854i \(0.827103\pi\)
\(180\) 0 0
\(181\) 5.90522 0.438931 0.219466 0.975620i \(-0.429569\pi\)
0.219466 + 0.975620i \(0.429569\pi\)
\(182\) −0.0468849 −0.00347534
\(183\) −24.1312 −1.78383
\(184\) −2.85539 −0.210502
\(185\) 0 0
\(186\) 21.3513 1.56555
\(187\) 4.53628 0.331725
\(188\) 4.03114 0.294001
\(189\) −9.17575 −0.667438
\(190\) 0 0
\(191\) 6.44628 0.466437 0.233218 0.972424i \(-0.425074\pi\)
0.233218 + 0.972424i \(0.425074\pi\)
\(192\) 9.30668 0.671652
\(193\) −1.43606 −0.103370 −0.0516849 0.998663i \(-0.516459\pi\)
−0.0516849 + 0.998663i \(0.516459\pi\)
\(194\) −4.41604 −0.317053
\(195\) 0 0
\(196\) 8.15713 0.582652
\(197\) 4.75399 0.338708 0.169354 0.985555i \(-0.445832\pi\)
0.169354 + 0.985555i \(0.445832\pi\)
\(198\) 4.58881 0.326112
\(199\) −2.36002 −0.167298 −0.0836489 0.996495i \(-0.526657\pi\)
−0.0836489 + 0.996495i \(0.526657\pi\)
\(200\) 0 0
\(201\) −33.6017 −2.37008
\(202\) 6.24476 0.439380
\(203\) −0.320107 −0.0224671
\(204\) −18.8188 −1.31758
\(205\) 0 0
\(206\) −4.82517 −0.336185
\(207\) 6.35189 0.441487
\(208\) 0.0406011 0.00281518
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −24.5133 −1.68756 −0.843781 0.536687i \(-0.819676\pi\)
−0.843781 + 0.536687i \(0.819676\pi\)
\(212\) −17.1491 −1.17780
\(213\) 40.2232 2.75605
\(214\) 5.68536 0.388643
\(215\) 0 0
\(216\) −22.7393 −1.54722
\(217\) −9.80422 −0.665554
\(218\) 6.08205 0.411929
\(219\) 33.2252 2.24515
\(220\) 0 0
\(221\) 0.255509 0.0171874
\(222\) −10.4705 −0.702734
\(223\) −8.47427 −0.567479 −0.283740 0.958901i \(-0.591575\pi\)
−0.283740 + 0.958901i \(0.591575\pi\)
\(224\) −6.24663 −0.417371
\(225\) 0 0
\(226\) 0.335773 0.0223353
\(227\) −13.7491 −0.912558 −0.456279 0.889837i \(-0.650818\pi\)
−0.456279 + 0.889837i \(0.650818\pi\)
\(228\) 4.14852 0.274742
\(229\) −1.99640 −0.131926 −0.0659629 0.997822i \(-0.521012\pi\)
−0.0659629 + 0.997822i \(0.521012\pi\)
\(230\) 0 0
\(231\) −3.18141 −0.209321
\(232\) −0.793288 −0.0520819
\(233\) −11.3481 −0.743437 −0.371718 0.928346i \(-0.621231\pi\)
−0.371718 + 0.928346i \(0.621231\pi\)
\(234\) 0.258468 0.0168966
\(235\) 0 0
\(236\) 1.59478 0.103811
\(237\) 34.0537 2.21203
\(238\) −3.77594 −0.244758
\(239\) 5.21045 0.337036 0.168518 0.985699i \(-0.446102\pi\)
0.168518 + 0.985699i \(0.446102\pi\)
\(240\) 0 0
\(241\) 6.60827 0.425676 0.212838 0.977087i \(-0.431729\pi\)
0.212838 + 0.977087i \(0.431729\pi\)
\(242\) 0.779856 0.0501310
\(243\) −2.03139 −0.130314
\(244\) 11.2682 0.721373
\(245\) 0 0
\(246\) 27.8957 1.77857
\(247\) −0.0563258 −0.00358393
\(248\) −24.2968 −1.54285
\(249\) 41.6697 2.64071
\(250\) 0 0
\(251\) 24.0024 1.51502 0.757510 0.652823i \(-0.226415\pi\)
0.757510 + 0.652823i \(0.226415\pi\)
\(252\) 8.74141 0.550657
\(253\) 1.07949 0.0678667
\(254\) 2.44788 0.153593
\(255\) 0 0
\(256\) −13.4739 −0.842117
\(257\) 5.68903 0.354872 0.177436 0.984132i \(-0.443220\pi\)
0.177436 + 0.984132i \(0.443220\pi\)
\(258\) −24.9322 −1.55221
\(259\) 4.80790 0.298748
\(260\) 0 0
\(261\) 1.76469 0.109232
\(262\) 9.69481 0.598948
\(263\) −13.9857 −0.862395 −0.431197 0.902258i \(-0.641909\pi\)
−0.431197 + 0.902258i \(0.641909\pi\)
\(264\) −7.88418 −0.485237
\(265\) 0 0
\(266\) 0.832387 0.0510369
\(267\) −0.546007 −0.0334151
\(268\) 15.6905 0.958450
\(269\) 15.4020 0.939075 0.469538 0.882912i \(-0.344421\pi\)
0.469538 + 0.882912i \(0.344421\pi\)
\(270\) 0 0
\(271\) −25.3911 −1.54240 −0.771199 0.636595i \(-0.780342\pi\)
−0.771199 + 0.636595i \(0.780342\pi\)
\(272\) 3.26987 0.198265
\(273\) −0.179196 −0.0108454
\(274\) −10.7855 −0.651577
\(275\) 0 0
\(276\) −4.47827 −0.269560
\(277\) −19.9798 −1.20047 −0.600235 0.799824i \(-0.704926\pi\)
−0.600235 + 0.799824i \(0.704926\pi\)
\(278\) 12.4752 0.748214
\(279\) 54.0490 3.23583
\(280\) 0 0
\(281\) 6.18130 0.368745 0.184373 0.982856i \(-0.440975\pi\)
0.184373 + 0.982856i \(0.440975\pi\)
\(282\) −6.73235 −0.400906
\(283\) 7.12127 0.423316 0.211658 0.977344i \(-0.432114\pi\)
0.211658 + 0.977344i \(0.432114\pi\)
\(284\) −18.7825 −1.11453
\(285\) 0 0
\(286\) 0.0439260 0.00259740
\(287\) −12.8093 −0.756110
\(288\) 34.4366 2.02920
\(289\) 3.57781 0.210459
\(290\) 0 0
\(291\) −16.8782 −0.989420
\(292\) −15.5147 −0.907929
\(293\) −19.1342 −1.11783 −0.558916 0.829224i \(-0.688783\pi\)
−0.558916 + 0.829224i \(0.688783\pi\)
\(294\) −13.6231 −0.794514
\(295\) 0 0
\(296\) 11.9149 0.692542
\(297\) 8.59667 0.498829
\(298\) 8.86073 0.513288
\(299\) 0.0608030 0.00351633
\(300\) 0 0
\(301\) 11.4485 0.659882
\(302\) 3.63679 0.209274
\(303\) 23.8677 1.37116
\(304\) −0.720827 −0.0413422
\(305\) 0 0
\(306\) 20.8161 1.18998
\(307\) −6.82573 −0.389565 −0.194782 0.980846i \(-0.562400\pi\)
−0.194782 + 0.980846i \(0.562400\pi\)
\(308\) 1.48558 0.0846487
\(309\) −18.4419 −1.04912
\(310\) 0 0
\(311\) −12.8609 −0.729276 −0.364638 0.931149i \(-0.618807\pi\)
−0.364638 + 0.931149i \(0.618807\pi\)
\(312\) −0.444083 −0.0251412
\(313\) 3.01707 0.170535 0.0852673 0.996358i \(-0.472826\pi\)
0.0852673 + 0.996358i \(0.472826\pi\)
\(314\) 7.05930 0.398380
\(315\) 0 0
\(316\) −15.9016 −0.894534
\(317\) −17.7857 −0.998943 −0.499471 0.866330i \(-0.666472\pi\)
−0.499471 + 0.866330i \(0.666472\pi\)
\(318\) 28.6404 1.60607
\(319\) 0.299905 0.0167914
\(320\) 0 0
\(321\) 21.7296 1.21283
\(322\) −0.898551 −0.0500743
\(323\) −4.53628 −0.252405
\(324\) −11.0942 −0.616346
\(325\) 0 0
\(326\) −1.84640 −0.102262
\(327\) 23.2458 1.28550
\(328\) −31.7441 −1.75277
\(329\) 3.09140 0.170434
\(330\) 0 0
\(331\) −26.3860 −1.45030 −0.725152 0.688589i \(-0.758230\pi\)
−0.725152 + 0.688589i \(0.758230\pi\)
\(332\) −19.4579 −1.06789
\(333\) −26.5051 −1.45247
\(334\) 7.23207 0.395722
\(335\) 0 0
\(336\) −2.29325 −0.125107
\(337\) 13.2024 0.719181 0.359590 0.933110i \(-0.382916\pi\)
0.359590 + 0.933110i \(0.382916\pi\)
\(338\) −10.1357 −0.551307
\(339\) 1.28334 0.0697012
\(340\) 0 0
\(341\) 9.18548 0.497422
\(342\) −4.58881 −0.248134
\(343\) 13.7271 0.741191
\(344\) 28.3718 1.52970
\(345\) 0 0
\(346\) −8.35786 −0.449321
\(347\) −16.4809 −0.884740 −0.442370 0.896833i \(-0.645862\pi\)
−0.442370 + 0.896833i \(0.645862\pi\)
\(348\) −1.24416 −0.0666940
\(349\) −19.0165 −1.01793 −0.508966 0.860787i \(-0.669972\pi\)
−0.508966 + 0.860787i \(0.669972\pi\)
\(350\) 0 0
\(351\) 0.484214 0.0258455
\(352\) 5.85241 0.311934
\(353\) −13.1955 −0.702325 −0.351162 0.936315i \(-0.614213\pi\)
−0.351162 + 0.936315i \(0.614213\pi\)
\(354\) −2.66341 −0.141559
\(355\) 0 0
\(356\) 0.254961 0.0135129
\(357\) −14.4318 −0.763810
\(358\) −17.8641 −0.944148
\(359\) −2.88756 −0.152400 −0.0761998 0.997093i \(-0.524279\pi\)
−0.0761998 + 0.997093i \(0.524279\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 4.60522 0.242045
\(363\) 2.98063 0.156443
\(364\) 0.0836765 0.00438584
\(365\) 0 0
\(366\) −18.8188 −0.983676
\(367\) 2.10833 0.110054 0.0550269 0.998485i \(-0.482476\pi\)
0.0550269 + 0.998485i \(0.482476\pi\)
\(368\) 0.778123 0.0405624
\(369\) 70.6156 3.67610
\(370\) 0 0
\(371\) −13.1513 −0.682780
\(372\) −38.1061 −1.97571
\(373\) −8.07305 −0.418007 −0.209003 0.977915i \(-0.567022\pi\)
−0.209003 + 0.977915i \(0.567022\pi\)
\(374\) 3.53764 0.182927
\(375\) 0 0
\(376\) 7.66111 0.395091
\(377\) 0.0168924 0.000870002 0
\(378\) −7.15576 −0.368053
\(379\) 14.3355 0.736365 0.368183 0.929754i \(-0.379980\pi\)
0.368183 + 0.929754i \(0.379980\pi\)
\(380\) 0 0
\(381\) 9.35586 0.479315
\(382\) 5.02717 0.257212
\(383\) 9.79867 0.500689 0.250344 0.968157i \(-0.419456\pi\)
0.250344 + 0.968157i \(0.419456\pi\)
\(384\) −27.6299 −1.40998
\(385\) 0 0
\(386\) −1.11992 −0.0570024
\(387\) −63.1138 −3.20825
\(388\) 7.88139 0.400117
\(389\) −19.9236 −1.01016 −0.505082 0.863071i \(-0.668538\pi\)
−0.505082 + 0.863071i \(0.668538\pi\)
\(390\) 0 0
\(391\) 4.89685 0.247644
\(392\) 15.5024 0.782992
\(393\) 37.0539 1.86912
\(394\) 3.70743 0.186778
\(395\) 0 0
\(396\) −8.18974 −0.411550
\(397\) −13.9941 −0.702342 −0.351171 0.936311i \(-0.614216\pi\)
−0.351171 + 0.936311i \(0.614216\pi\)
\(398\) −1.84048 −0.0922549
\(399\) 3.18141 0.159270
\(400\) 0 0
\(401\) −18.6293 −0.930301 −0.465151 0.885232i \(-0.654000\pi\)
−0.465151 + 0.885232i \(0.654000\pi\)
\(402\) −26.2045 −1.30696
\(403\) 0.517380 0.0257725
\(404\) −11.1452 −0.554492
\(405\) 0 0
\(406\) −0.249637 −0.0123893
\(407\) −4.50448 −0.223279
\(408\) −35.7648 −1.77062
\(409\) −30.8428 −1.52508 −0.762540 0.646941i \(-0.776048\pi\)
−0.762540 + 0.646941i \(0.776048\pi\)
\(410\) 0 0
\(411\) −41.2226 −2.03336
\(412\) 8.61157 0.424262
\(413\) 1.22300 0.0601799
\(414\) 4.95356 0.243454
\(415\) 0 0
\(416\) 0.329642 0.0161620
\(417\) 47.6807 2.33493
\(418\) −0.779856 −0.0381440
\(419\) 37.9347 1.85323 0.926616 0.376009i \(-0.122704\pi\)
0.926616 + 0.376009i \(0.122704\pi\)
\(420\) 0 0
\(421\) −18.4642 −0.899891 −0.449945 0.893056i \(-0.648557\pi\)
−0.449945 + 0.893056i \(0.648557\pi\)
\(422\) −19.1168 −0.930592
\(423\) −17.0423 −0.828627
\(424\) −32.5915 −1.58278
\(425\) 0 0
\(426\) 31.3683 1.51980
\(427\) 8.64134 0.418184
\(428\) −10.1468 −0.490463
\(429\) 0.167887 0.00810564
\(430\) 0 0
\(431\) 33.6742 1.62203 0.811013 0.585027i \(-0.198916\pi\)
0.811013 + 0.585027i \(0.198916\pi\)
\(432\) 6.19671 0.298139
\(433\) −11.4041 −0.548047 −0.274024 0.961723i \(-0.588355\pi\)
−0.274024 + 0.961723i \(0.588355\pi\)
\(434\) −7.64588 −0.367014
\(435\) 0 0
\(436\) −10.8548 −0.519849
\(437\) −1.07949 −0.0516388
\(438\) 25.9108 1.23807
\(439\) −3.76890 −0.179880 −0.0899399 0.995947i \(-0.528667\pi\)
−0.0899399 + 0.995947i \(0.528667\pi\)
\(440\) 0 0
\(441\) −34.4856 −1.64217
\(442\) 0.199261 0.00947786
\(443\) −4.51841 −0.214676 −0.107338 0.994223i \(-0.534233\pi\)
−0.107338 + 0.994223i \(0.534233\pi\)
\(444\) 18.6869 0.886842
\(445\) 0 0
\(446\) −6.60871 −0.312931
\(447\) 33.8660 1.60181
\(448\) −3.33271 −0.157456
\(449\) −37.3611 −1.76318 −0.881590 0.472016i \(-0.843526\pi\)
−0.881590 + 0.472016i \(0.843526\pi\)
\(450\) 0 0
\(451\) 12.0009 0.565102
\(452\) −0.599261 −0.0281869
\(453\) 13.8999 0.653075
\(454\) −10.7223 −0.503222
\(455\) 0 0
\(456\) 7.88418 0.369210
\(457\) −9.37773 −0.438672 −0.219336 0.975649i \(-0.570389\pi\)
−0.219336 + 0.975649i \(0.570389\pi\)
\(458\) −1.55690 −0.0727494
\(459\) 38.9969 1.82022
\(460\) 0 0
\(461\) 31.6785 1.47542 0.737708 0.675120i \(-0.235908\pi\)
0.737708 + 0.675120i \(0.235908\pi\)
\(462\) −2.48104 −0.115429
\(463\) 37.1284 1.72550 0.862752 0.505628i \(-0.168739\pi\)
0.862752 + 0.505628i \(0.168739\pi\)
\(464\) 0.216179 0.0100359
\(465\) 0 0
\(466\) −8.84986 −0.409962
\(467\) 15.9678 0.738902 0.369451 0.929250i \(-0.379546\pi\)
0.369451 + 0.929250i \(0.379546\pi\)
\(468\) −0.461294 −0.0213233
\(469\) 12.0327 0.555619
\(470\) 0 0
\(471\) 26.9809 1.24321
\(472\) 3.03084 0.139506
\(473\) −10.7260 −0.493183
\(474\) 26.5570 1.21980
\(475\) 0 0
\(476\) 6.73900 0.308882
\(477\) 72.5006 3.31958
\(478\) 4.06340 0.185855
\(479\) 28.1729 1.28725 0.643627 0.765340i \(-0.277429\pi\)
0.643627 + 0.765340i \(0.277429\pi\)
\(480\) 0 0
\(481\) −0.253718 −0.0115686
\(482\) 5.15350 0.234735
\(483\) −3.43429 −0.156266
\(484\) −1.39182 −0.0632648
\(485\) 0 0
\(486\) −1.58419 −0.0718604
\(487\) −24.0613 −1.09032 −0.545161 0.838331i \(-0.683532\pi\)
−0.545161 + 0.838331i \(0.683532\pi\)
\(488\) 21.4150 0.969410
\(489\) −7.05699 −0.319128
\(490\) 0 0
\(491\) −29.0197 −1.30964 −0.654821 0.755784i \(-0.727256\pi\)
−0.654821 + 0.755784i \(0.727256\pi\)
\(492\) −49.7861 −2.24453
\(493\) 1.36045 0.0612716
\(494\) −0.0439260 −0.00197632
\(495\) 0 0
\(496\) 6.62114 0.297298
\(497\) −14.4039 −0.646102
\(498\) 32.4964 1.45620
\(499\) −15.0257 −0.672642 −0.336321 0.941747i \(-0.609183\pi\)
−0.336321 + 0.941747i \(0.609183\pi\)
\(500\) 0 0
\(501\) 27.6412 1.23492
\(502\) 18.7184 0.835445
\(503\) 28.7785 1.28317 0.641585 0.767052i \(-0.278277\pi\)
0.641585 + 0.767052i \(0.278277\pi\)
\(504\) 16.6129 0.739996
\(505\) 0 0
\(506\) 0.841844 0.0374245
\(507\) −38.7388 −1.72045
\(508\) −4.36878 −0.193833
\(509\) −10.4772 −0.464395 −0.232197 0.972669i \(-0.574592\pi\)
−0.232197 + 0.972669i \(0.574592\pi\)
\(510\) 0 0
\(511\) −11.8979 −0.526332
\(512\) 8.03194 0.354965
\(513\) −8.59667 −0.379552
\(514\) 4.43662 0.195691
\(515\) 0 0
\(516\) 44.4971 1.95888
\(517\) −2.89630 −0.127379
\(518\) 3.74947 0.164742
\(519\) −31.9440 −1.40219
\(520\) 0 0
\(521\) −24.7590 −1.08471 −0.542357 0.840148i \(-0.682468\pi\)
−0.542357 + 0.840148i \(0.682468\pi\)
\(522\) 1.37621 0.0602349
\(523\) −14.8566 −0.649635 −0.324818 0.945777i \(-0.605303\pi\)
−0.324818 + 0.945777i \(0.605303\pi\)
\(524\) −17.3025 −0.755865
\(525\) 0 0
\(526\) −10.9068 −0.475560
\(527\) 41.6679 1.81508
\(528\) 2.14852 0.0935023
\(529\) −21.8347 −0.949335
\(530\) 0 0
\(531\) −6.74219 −0.292586
\(532\) −1.48558 −0.0644080
\(533\) 0.675962 0.0292792
\(534\) −0.425807 −0.0184265
\(535\) 0 0
\(536\) 29.8195 1.28801
\(537\) −68.2773 −2.94638
\(538\) 12.0113 0.517845
\(539\) −5.86074 −0.252440
\(540\) 0 0
\(541\) 3.88960 0.167227 0.0836134 0.996498i \(-0.473354\pi\)
0.0836134 + 0.996498i \(0.473354\pi\)
\(542\) −19.8014 −0.850541
\(543\) 17.6013 0.755343
\(544\) 26.5481 1.13824
\(545\) 0 0
\(546\) −0.139747 −0.00598061
\(547\) −17.5180 −0.749015 −0.374507 0.927224i \(-0.622188\pi\)
−0.374507 + 0.927224i \(0.622188\pi\)
\(548\) 19.2491 0.822283
\(549\) −47.6382 −2.03315
\(550\) 0 0
\(551\) −0.299905 −0.0127764
\(552\) −8.51086 −0.362246
\(553\) −12.1946 −0.518567
\(554\) −15.5814 −0.661988
\(555\) 0 0
\(556\) −22.2648 −0.944237
\(557\) −28.9860 −1.22818 −0.614088 0.789237i \(-0.710476\pi\)
−0.614088 + 0.789237i \(0.710476\pi\)
\(558\) 42.1504 1.78437
\(559\) −0.604152 −0.0255529
\(560\) 0 0
\(561\) 13.5210 0.570856
\(562\) 4.82052 0.203341
\(563\) −29.6112 −1.24796 −0.623982 0.781438i \(-0.714486\pi\)
−0.623982 + 0.781438i \(0.714486\pi\)
\(564\) 12.0154 0.505938
\(565\) 0 0
\(566\) 5.55356 0.233434
\(567\) −8.50793 −0.357299
\(568\) −35.6957 −1.49776
\(569\) −4.05818 −0.170128 −0.0850640 0.996375i \(-0.527109\pi\)
−0.0850640 + 0.996375i \(0.527109\pi\)
\(570\) 0 0
\(571\) 20.3380 0.851117 0.425559 0.904931i \(-0.360078\pi\)
0.425559 + 0.904931i \(0.360078\pi\)
\(572\) −0.0783957 −0.00327789
\(573\) 19.2140 0.802677
\(574\) −9.98942 −0.416950
\(575\) 0 0
\(576\) 18.3726 0.765527
\(577\) −24.4768 −1.01898 −0.509492 0.860476i \(-0.670167\pi\)
−0.509492 + 0.860476i \(0.670167\pi\)
\(578\) 2.79017 0.116056
\(579\) −4.28037 −0.177886
\(580\) 0 0
\(581\) −14.9219 −0.619064
\(582\) −13.1626 −0.545607
\(583\) 12.3213 0.510296
\(584\) −29.4854 −1.22011
\(585\) 0 0
\(586\) −14.9219 −0.616419
\(587\) 3.34628 0.138116 0.0690579 0.997613i \(-0.478001\pi\)
0.0690579 + 0.997613i \(0.478001\pi\)
\(588\) 24.3134 1.00267
\(589\) −9.18548 −0.378481
\(590\) 0 0
\(591\) 14.1699 0.582872
\(592\) −3.24695 −0.133449
\(593\) 39.2063 1.61001 0.805006 0.593267i \(-0.202162\pi\)
0.805006 + 0.593267i \(0.202162\pi\)
\(594\) 6.70416 0.275075
\(595\) 0 0
\(596\) −15.8139 −0.647764
\(597\) −7.03437 −0.287898
\(598\) 0.0474175 0.00193905
\(599\) 5.72987 0.234116 0.117058 0.993125i \(-0.462654\pi\)
0.117058 + 0.993125i \(0.462654\pi\)
\(600\) 0 0
\(601\) 13.9163 0.567656 0.283828 0.958875i \(-0.408395\pi\)
0.283828 + 0.958875i \(0.408395\pi\)
\(602\) 8.92820 0.363886
\(603\) −66.3343 −2.70134
\(604\) −6.49065 −0.264101
\(605\) 0 0
\(606\) 18.6134 0.756116
\(607\) −0.156175 −0.00633897 −0.00316948 0.999995i \(-0.501009\pi\)
−0.00316948 + 0.999995i \(0.501009\pi\)
\(608\) −5.85241 −0.237347
\(609\) −0.954120 −0.0386629
\(610\) 0 0
\(611\) −0.163137 −0.00659980
\(612\) −37.1509 −1.50174
\(613\) −40.1902 −1.62327 −0.811634 0.584166i \(-0.801422\pi\)
−0.811634 + 0.584166i \(0.801422\pi\)
\(614\) −5.32308 −0.214822
\(615\) 0 0
\(616\) 2.82331 0.113755
\(617\) −12.8606 −0.517747 −0.258874 0.965911i \(-0.583351\pi\)
−0.258874 + 0.965911i \(0.583351\pi\)
\(618\) −14.3820 −0.578531
\(619\) −2.03398 −0.0817526 −0.0408763 0.999164i \(-0.513015\pi\)
−0.0408763 + 0.999164i \(0.513015\pi\)
\(620\) 0 0
\(621\) 9.27999 0.372393
\(622\) −10.0297 −0.402153
\(623\) 0.195524 0.00783352
\(624\) 0.121017 0.00484456
\(625\) 0 0
\(626\) 2.35288 0.0940398
\(627\) −2.98063 −0.119035
\(628\) −12.5989 −0.502750
\(629\) −20.4336 −0.814739
\(630\) 0 0
\(631\) 37.6984 1.50075 0.750375 0.661012i \(-0.229873\pi\)
0.750375 + 0.661012i \(0.229873\pi\)
\(632\) −30.2206 −1.20211
\(633\) −73.0651 −2.90408
\(634\) −13.8703 −0.550858
\(635\) 0 0
\(636\) −51.1151 −2.02685
\(637\) −0.330111 −0.0130795
\(638\) 0.233882 0.00925950
\(639\) 79.4060 3.14125
\(640\) 0 0
\(641\) 2.84360 0.112315 0.0561576 0.998422i \(-0.482115\pi\)
0.0561576 + 0.998422i \(0.482115\pi\)
\(642\) 16.9460 0.668804
\(643\) −30.6389 −1.20828 −0.604140 0.796878i \(-0.706483\pi\)
−0.604140 + 0.796878i \(0.706483\pi\)
\(644\) 1.60366 0.0631932
\(645\) 0 0
\(646\) −3.53764 −0.139187
\(647\) 6.76617 0.266006 0.133003 0.991116i \(-0.457538\pi\)
0.133003 + 0.991116i \(0.457538\pi\)
\(648\) −21.0844 −0.828272
\(649\) −1.14582 −0.0449772
\(650\) 0 0
\(651\) −29.2228 −1.14533
\(652\) 3.29530 0.129054
\(653\) −11.9015 −0.465743 −0.232872 0.972508i \(-0.574812\pi\)
−0.232872 + 0.972508i \(0.574812\pi\)
\(654\) 18.1284 0.708876
\(655\) 0 0
\(656\) 8.65059 0.337749
\(657\) 65.5910 2.55895
\(658\) 2.41085 0.0939845
\(659\) −11.2353 −0.437664 −0.218832 0.975763i \(-0.570225\pi\)
−0.218832 + 0.975763i \(0.570225\pi\)
\(660\) 0 0
\(661\) −22.9273 −0.891768 −0.445884 0.895091i \(-0.647111\pi\)
−0.445884 + 0.895091i \(0.647111\pi\)
\(662\) −20.5772 −0.799757
\(663\) 0.761580 0.0295773
\(664\) −36.9794 −1.43508
\(665\) 0 0
\(666\) −20.6702 −0.800953
\(667\) 0.323743 0.0125354
\(668\) −12.9072 −0.499396
\(669\) −25.2587 −0.976558
\(670\) 0 0
\(671\) −8.09599 −0.312542
\(672\) −18.6189 −0.718240
\(673\) 3.09828 0.119430 0.0597150 0.998215i \(-0.480981\pi\)
0.0597150 + 0.998215i \(0.480981\pi\)
\(674\) 10.2960 0.396586
\(675\) 0 0
\(676\) 18.0893 0.695743
\(677\) −33.3985 −1.28361 −0.641804 0.766868i \(-0.721814\pi\)
−0.641804 + 0.766868i \(0.721814\pi\)
\(678\) 1.00082 0.0384361
\(679\) 6.04407 0.231950
\(680\) 0 0
\(681\) −40.9810 −1.57039
\(682\) 7.16335 0.274299
\(683\) −6.01634 −0.230209 −0.115104 0.993353i \(-0.536720\pi\)
−0.115104 + 0.993353i \(0.536720\pi\)
\(684\) 8.18974 0.313143
\(685\) 0 0
\(686\) 10.7051 0.408723
\(687\) −5.95054 −0.227027
\(688\) −7.73160 −0.294765
\(689\) 0.694007 0.0264396
\(690\) 0 0
\(691\) −15.6730 −0.596227 −0.298114 0.954530i \(-0.596357\pi\)
−0.298114 + 0.954530i \(0.596357\pi\)
\(692\) 14.9164 0.567038
\(693\) −6.28054 −0.238578
\(694\) −12.8527 −0.487882
\(695\) 0 0
\(696\) −2.36450 −0.0896262
\(697\) 54.4395 2.06204
\(698\) −14.8302 −0.561330
\(699\) −33.8244 −1.27936
\(700\) 0 0
\(701\) 18.0567 0.681992 0.340996 0.940065i \(-0.389236\pi\)
0.340996 + 0.940065i \(0.389236\pi\)
\(702\) 0.377617 0.0142523
\(703\) 4.50448 0.169890
\(704\) 3.12238 0.117679
\(705\) 0 0
\(706\) −10.2906 −0.387291
\(707\) −8.54699 −0.321442
\(708\) 4.75344 0.178645
\(709\) 16.2048 0.608586 0.304293 0.952579i \(-0.401580\pi\)
0.304293 + 0.952579i \(0.401580\pi\)
\(710\) 0 0
\(711\) 67.2266 2.52120
\(712\) 0.484549 0.0181592
\(713\) 9.91560 0.371342
\(714\) −11.2547 −0.421196
\(715\) 0 0
\(716\) 31.8825 1.19150
\(717\) 15.5304 0.579995
\(718\) −2.25188 −0.0840395
\(719\) −27.9403 −1.04200 −0.520998 0.853558i \(-0.674440\pi\)
−0.520998 + 0.853558i \(0.674440\pi\)
\(720\) 0 0
\(721\) 6.60403 0.245947
\(722\) 0.779856 0.0290232
\(723\) 19.6968 0.732533
\(724\) −8.21903 −0.305458
\(725\) 0 0
\(726\) 2.32446 0.0862690
\(727\) 30.7020 1.13867 0.569337 0.822104i \(-0.307200\pi\)
0.569337 + 0.822104i \(0.307200\pi\)
\(728\) 0.159025 0.00589387
\(729\) −29.9678 −1.10992
\(730\) 0 0
\(731\) −48.6562 −1.79961
\(732\) 33.5864 1.24139
\(733\) −44.9333 −1.65965 −0.829826 0.558023i \(-0.811560\pi\)
−0.829826 + 0.558023i \(0.811560\pi\)
\(734\) 1.64419 0.0606882
\(735\) 0 0
\(736\) 6.31760 0.232870
\(737\) −11.2733 −0.415258
\(738\) 55.0700 2.02715
\(739\) −3.19172 −0.117409 −0.0587047 0.998275i \(-0.518697\pi\)
−0.0587047 + 0.998275i \(0.518697\pi\)
\(740\) 0 0
\(741\) −0.167887 −0.00616747
\(742\) −10.2561 −0.376513
\(743\) −17.4348 −0.639619 −0.319810 0.947482i \(-0.603619\pi\)
−0.319810 + 0.947482i \(0.603619\pi\)
\(744\) −72.4199 −2.65504
\(745\) 0 0
\(746\) −6.29581 −0.230506
\(747\) 82.2617 3.00980
\(748\) −6.31370 −0.230852
\(749\) −7.78135 −0.284324
\(750\) 0 0
\(751\) 9.55633 0.348715 0.174358 0.984682i \(-0.444215\pi\)
0.174358 + 0.984682i \(0.444215\pi\)
\(752\) −2.08773 −0.0761317
\(753\) 71.5425 2.60715
\(754\) 0.0131736 0.000479755 0
\(755\) 0 0
\(756\) 12.7710 0.464478
\(757\) 48.5259 1.76370 0.881852 0.471527i \(-0.156297\pi\)
0.881852 + 0.471527i \(0.156297\pi\)
\(758\) 11.1796 0.406062
\(759\) 3.21755 0.116790
\(760\) 0 0
\(761\) 38.6035 1.39937 0.699687 0.714449i \(-0.253323\pi\)
0.699687 + 0.714449i \(0.253323\pi\)
\(762\) 7.29622 0.264314
\(763\) −8.32429 −0.301360
\(764\) −8.97210 −0.324599
\(765\) 0 0
\(766\) 7.64155 0.276101
\(767\) −0.0645391 −0.00233037
\(768\) −40.1607 −1.44917
\(769\) 53.2658 1.92081 0.960406 0.278603i \(-0.0898712\pi\)
0.960406 + 0.278603i \(0.0898712\pi\)
\(770\) 0 0
\(771\) 16.9569 0.610688
\(772\) 1.99874 0.0719363
\(773\) −9.31748 −0.335126 −0.167563 0.985861i \(-0.553590\pi\)
−0.167563 + 0.985861i \(0.553590\pi\)
\(774\) −49.2196 −1.76916
\(775\) 0 0
\(776\) 14.9784 0.537694
\(777\) 14.3306 0.514107
\(778\) −15.5375 −0.557047
\(779\) −12.0009 −0.429978
\(780\) 0 0
\(781\) 13.4948 0.482883
\(782\) 3.81884 0.136561
\(783\) 2.57818 0.0921367
\(784\) −4.22458 −0.150878
\(785\) 0 0
\(786\) 28.8967 1.03071
\(787\) 15.0616 0.536889 0.268444 0.963295i \(-0.413490\pi\)
0.268444 + 0.963295i \(0.413490\pi\)
\(788\) −6.61672 −0.235711
\(789\) −41.6862 −1.48407
\(790\) 0 0
\(791\) −0.459561 −0.0163401
\(792\) −15.5644 −0.553058
\(793\) −0.456013 −0.0161935
\(794\) −10.9133 −0.387300
\(795\) 0 0
\(796\) 3.28474 0.116425
\(797\) 19.0593 0.675114 0.337557 0.941305i \(-0.390399\pi\)
0.337557 + 0.941305i \(0.390399\pi\)
\(798\) 2.48104 0.0878279
\(799\) −13.1384 −0.464804
\(800\) 0 0
\(801\) −1.07789 −0.0380855
\(802\) −14.5281 −0.513006
\(803\) 11.1470 0.393370
\(804\) 46.7676 1.64937
\(805\) 0 0
\(806\) 0.403481 0.0142120
\(807\) 45.9077 1.61603
\(808\) −21.1811 −0.745150
\(809\) −15.2273 −0.535363 −0.267681 0.963507i \(-0.586257\pi\)
−0.267681 + 0.963507i \(0.586257\pi\)
\(810\) 0 0
\(811\) −43.3354 −1.52171 −0.760857 0.648920i \(-0.775221\pi\)
−0.760857 + 0.648920i \(0.775221\pi\)
\(812\) 0.445532 0.0156351
\(813\) −75.6814 −2.65426
\(814\) −3.51284 −0.123125
\(815\) 0 0
\(816\) 9.74628 0.341188
\(817\) 10.7260 0.375256
\(818\) −24.0530 −0.840992
\(819\) −0.353756 −0.0123612
\(820\) 0 0
\(821\) 19.4279 0.678040 0.339020 0.940779i \(-0.389905\pi\)
0.339020 + 0.940779i \(0.389905\pi\)
\(822\) −32.1477 −1.12128
\(823\) −2.35683 −0.0821539 −0.0410769 0.999156i \(-0.513079\pi\)
−0.0410769 + 0.999156i \(0.513079\pi\)
\(824\) 16.3661 0.570141
\(825\) 0 0
\(826\) 0.953763 0.0331857
\(827\) 29.8127 1.03669 0.518344 0.855172i \(-0.326549\pi\)
0.518344 + 0.855172i \(0.326549\pi\)
\(828\) −8.84072 −0.307236
\(829\) 52.6510 1.82864 0.914322 0.404988i \(-0.132724\pi\)
0.914322 + 0.404988i \(0.132724\pi\)
\(830\) 0 0
\(831\) −59.5524 −2.06585
\(832\) 0.175871 0.00609722
\(833\) −26.5859 −0.921148
\(834\) 37.1841 1.28758
\(835\) 0 0
\(836\) 1.39182 0.0481373
\(837\) 78.9645 2.72941
\(838\) 29.5836 1.02195
\(839\) 29.7892 1.02844 0.514218 0.857660i \(-0.328082\pi\)
0.514218 + 0.857660i \(0.328082\pi\)
\(840\) 0 0
\(841\) −28.9101 −0.996899
\(842\) −14.3994 −0.496237
\(843\) 18.4242 0.634563
\(844\) 34.1182 1.17440
\(845\) 0 0
\(846\) −13.2906 −0.456939
\(847\) −1.06736 −0.0366749
\(848\) 8.88152 0.304992
\(849\) 21.2259 0.728471
\(850\) 0 0
\(851\) −4.86252 −0.166685
\(852\) −55.9836 −1.91797
\(853\) 35.2393 1.20657 0.603285 0.797526i \(-0.293858\pi\)
0.603285 + 0.797526i \(0.293858\pi\)
\(854\) 6.73900 0.230604
\(855\) 0 0
\(856\) −19.2837 −0.659105
\(857\) 21.5877 0.737421 0.368711 0.929544i \(-0.379799\pi\)
0.368711 + 0.929544i \(0.379799\pi\)
\(858\) 0.130927 0.00446979
\(859\) 27.7669 0.947396 0.473698 0.880687i \(-0.342919\pi\)
0.473698 + 0.880687i \(0.342919\pi\)
\(860\) 0 0
\(861\) −38.1799 −1.30117
\(862\) 26.2610 0.894453
\(863\) −7.11774 −0.242291 −0.121145 0.992635i \(-0.538657\pi\)
−0.121145 + 0.992635i \(0.538657\pi\)
\(864\) 50.3112 1.71162
\(865\) 0 0
\(866\) −8.89357 −0.302216
\(867\) 10.6641 0.362173
\(868\) 13.6458 0.463167
\(869\) 11.4250 0.387566
\(870\) 0 0
\(871\) −0.634980 −0.0215155
\(872\) −20.6293 −0.698595
\(873\) −33.3199 −1.12771
\(874\) −0.841844 −0.0284758
\(875\) 0 0
\(876\) −46.2436 −1.56243
\(877\) 44.1031 1.48925 0.744627 0.667481i \(-0.232627\pi\)
0.744627 + 0.667481i \(0.232627\pi\)
\(878\) −2.93920 −0.0991931
\(879\) −57.0321 −1.92364
\(880\) 0 0
\(881\) −37.9204 −1.27757 −0.638785 0.769385i \(-0.720563\pi\)
−0.638785 + 0.769385i \(0.720563\pi\)
\(882\) −26.8938 −0.905562
\(883\) −4.85252 −0.163300 −0.0816502 0.996661i \(-0.526019\pi\)
−0.0816502 + 0.996661i \(0.526019\pi\)
\(884\) −0.355624 −0.0119609
\(885\) 0 0
\(886\) −3.52371 −0.118381
\(887\) −11.2754 −0.378591 −0.189295 0.981920i \(-0.560620\pi\)
−0.189295 + 0.981920i \(0.560620\pi\)
\(888\) 35.5141 1.19177
\(889\) −3.35032 −0.112366
\(890\) 0 0
\(891\) 7.97100 0.267038
\(892\) 11.7947 0.394916
\(893\) 2.89630 0.0969210
\(894\) 26.4106 0.883302
\(895\) 0 0
\(896\) 9.89423 0.330543
\(897\) 0.181231 0.00605114
\(898\) −29.1363 −0.972290
\(899\) 2.75477 0.0918767
\(900\) 0 0
\(901\) 55.8928 1.86206
\(902\) 9.35899 0.311620
\(903\) 34.1239 1.13557
\(904\) −1.13888 −0.0378787
\(905\) 0 0
\(906\) 10.8399 0.360133
\(907\) −24.0191 −0.797540 −0.398770 0.917051i \(-0.630563\pi\)
−0.398770 + 0.917051i \(0.630563\pi\)
\(908\) 19.1363 0.635061
\(909\) 47.1181 1.56281
\(910\) 0 0
\(911\) 7.48540 0.248002 0.124001 0.992282i \(-0.460427\pi\)
0.124001 + 0.992282i \(0.460427\pi\)
\(912\) −2.14852 −0.0711446
\(913\) 13.9802 0.462676
\(914\) −7.31328 −0.241902
\(915\) 0 0
\(916\) 2.77864 0.0918089
\(917\) −13.2689 −0.438179
\(918\) 30.4119 1.00374
\(919\) 40.0187 1.32009 0.660047 0.751224i \(-0.270536\pi\)
0.660047 + 0.751224i \(0.270536\pi\)
\(920\) 0 0
\(921\) −20.3450 −0.670390
\(922\) 24.7047 0.813605
\(923\) 0.760108 0.0250193
\(924\) 4.42797 0.145669
\(925\) 0 0
\(926\) 28.9548 0.951514
\(927\) −36.4069 −1.19576
\(928\) 1.75517 0.0576161
\(929\) −32.3099 −1.06005 −0.530027 0.847981i \(-0.677818\pi\)
−0.530027 + 0.847981i \(0.677818\pi\)
\(930\) 0 0
\(931\) 5.86074 0.192078
\(932\) 15.7945 0.517367
\(933\) −38.3337 −1.25499
\(934\) 12.4526 0.407461
\(935\) 0 0
\(936\) −0.876679 −0.0286552
\(937\) 54.1000 1.76737 0.883684 0.468083i \(-0.155055\pi\)
0.883684 + 0.468083i \(0.155055\pi\)
\(938\) 9.38378 0.306391
\(939\) 8.99277 0.293468
\(940\) 0 0
\(941\) 26.6955 0.870248 0.435124 0.900371i \(-0.356705\pi\)
0.435124 + 0.900371i \(0.356705\pi\)
\(942\) 21.0412 0.685559
\(943\) 12.9548 0.421868
\(944\) −0.825935 −0.0268819
\(945\) 0 0
\(946\) −8.36475 −0.271961
\(947\) 39.4463 1.28183 0.640916 0.767611i \(-0.278555\pi\)
0.640916 + 0.767611i \(0.278555\pi\)
\(948\) −47.3968 −1.53938
\(949\) 0.627865 0.0203814
\(950\) 0 0
\(951\) −53.0126 −1.71905
\(952\) 12.8073 0.415088
\(953\) 48.7523 1.57924 0.789621 0.613595i \(-0.210277\pi\)
0.789621 + 0.613595i \(0.210277\pi\)
\(954\) 56.5400 1.83055
\(955\) 0 0
\(956\) −7.25203 −0.234547
\(957\) 0.893906 0.0288959
\(958\) 21.9708 0.709845
\(959\) 14.7618 0.476682
\(960\) 0 0
\(961\) 53.3730 1.72171
\(962\) −0.197864 −0.00637938
\(963\) 42.8972 1.38234
\(964\) −9.19755 −0.296233
\(965\) 0 0
\(966\) −2.67825 −0.0861713
\(967\) 1.39478 0.0448532 0.0224266 0.999748i \(-0.492861\pi\)
0.0224266 + 0.999748i \(0.492861\pi\)
\(968\) −2.64513 −0.0850178
\(969\) −13.5210 −0.434356
\(970\) 0 0
\(971\) −3.11733 −0.100040 −0.0500200 0.998748i \(-0.515929\pi\)
−0.0500200 + 0.998748i \(0.515929\pi\)
\(972\) 2.82734 0.0906870
\(973\) −17.0744 −0.547380
\(974\) −18.7644 −0.601249
\(975\) 0 0
\(976\) −5.83580 −0.186800
\(977\) 22.3690 0.715647 0.357823 0.933789i \(-0.383519\pi\)
0.357823 + 0.933789i \(0.383519\pi\)
\(978\) −5.50343 −0.175980
\(979\) −0.183185 −0.00585462
\(980\) 0 0
\(981\) 45.8904 1.46517
\(982\) −22.6312 −0.722191
\(983\) −42.2421 −1.34731 −0.673657 0.739044i \(-0.735277\pi\)
−0.673657 + 0.739044i \(0.735277\pi\)
\(984\) −94.6174 −3.01629
\(985\) 0 0
\(986\) 1.06096 0.0337877
\(987\) 9.21433 0.293295
\(988\) 0.0783957 0.00249410
\(989\) −11.5786 −0.368178
\(990\) 0 0
\(991\) −1.69828 −0.0539477 −0.0269738 0.999636i \(-0.508587\pi\)
−0.0269738 + 0.999636i \(0.508587\pi\)
\(992\) 53.7572 1.70679
\(993\) −78.6469 −2.49578
\(994\) −11.2329 −0.356287
\(995\) 0 0
\(996\) −57.9970 −1.83770
\(997\) −18.9376 −0.599759 −0.299879 0.953977i \(-0.596946\pi\)
−0.299879 + 0.953977i \(0.596946\pi\)
\(998\) −11.7179 −0.370923
\(999\) −38.7235 −1.22516
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.h.1.4 5
5.4 even 2 209.2.a.c.1.2 5
15.14 odd 2 1881.2.a.k.1.4 5
20.19 odd 2 3344.2.a.t.1.5 5
55.54 odd 2 2299.2.a.n.1.4 5
95.94 odd 2 3971.2.a.h.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.c.1.2 5 5.4 even 2
1881.2.a.k.1.4 5 15.14 odd 2
2299.2.a.n.1.4 5 55.54 odd 2
3344.2.a.t.1.5 5 20.19 odd 2
3971.2.a.h.1.4 5 95.94 odd 2
5225.2.a.h.1.4 5 1.1 even 1 trivial