Properties

Label 2254.4.a.y.1.2
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
Analytic rank $0$
Dimension $11$
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] = [2254,4,Mod(1,2254)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2254.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2254.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: \(132.990305153\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 4 x^{10} - 212 x^{9} + 487 x^{8} + 16315 x^{7} - 9025 x^{6} - 516068 x^{5} - 504693 x^{4} + \cdots - 11394027 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(9.21174\) of defining polynomial
Character \(\chi\) \(=\) 2254.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -7.21174 q^{3} +4.00000 q^{4} +16.2698 q^{5} -14.4235 q^{6} +8.00000 q^{8} +25.0092 q^{9} +32.5396 q^{10} +47.1866 q^{11} -28.8470 q^{12} +15.5988 q^{13} -117.334 q^{15} +16.0000 q^{16} +124.933 q^{17} +50.0183 q^{18} +27.0949 q^{19} +65.0792 q^{20} +94.3732 q^{22} +23.0000 q^{23} -57.6939 q^{24} +139.706 q^{25} +31.1976 q^{26} +14.3573 q^{27} -75.7411 q^{29} -234.667 q^{30} +101.299 q^{31} +32.0000 q^{32} -340.297 q^{33} +249.866 q^{34} +100.037 q^{36} +158.715 q^{37} +54.1898 q^{38} -112.494 q^{39} +130.158 q^{40} -344.393 q^{41} +236.838 q^{43} +188.746 q^{44} +406.894 q^{45} +46.0000 q^{46} +522.231 q^{47} -115.388 q^{48} +279.413 q^{50} -900.985 q^{51} +62.3951 q^{52} -323.061 q^{53} +28.7147 q^{54} +767.716 q^{55} -195.401 q^{57} -151.482 q^{58} +752.228 q^{59} -469.334 q^{60} -751.789 q^{61} +202.598 q^{62} +64.0000 q^{64} +253.789 q^{65} -680.595 q^{66} -870.373 q^{67} +499.733 q^{68} -165.870 q^{69} -386.315 q^{71} +200.073 q^{72} +972.125 q^{73} +317.431 q^{74} -1007.53 q^{75} +108.380 q^{76} -224.989 q^{78} -1011.48 q^{79} +260.317 q^{80} -778.789 q^{81} -688.785 q^{82} +70.9632 q^{83} +2032.64 q^{85} +473.676 q^{86} +546.225 q^{87} +377.493 q^{88} -208.804 q^{89} +813.788 q^{90} +92.0000 q^{92} -730.544 q^{93} +1044.46 q^{94} +440.828 q^{95} -230.776 q^{96} -290.349 q^{97} +1180.10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 22 q^{2} + 18 q^{3} + 44 q^{4} + 33 q^{5} + 36 q^{6} + 88 q^{8} + 171 q^{9} + 66 q^{10} + 8 q^{11} + 72 q^{12} + 185 q^{13} - 186 q^{15} + 176 q^{16} + 107 q^{17} + 342 q^{18} + 114 q^{19} + 132 q^{20}+ \cdots - 1729 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −7.21174 −1.38790 −0.693950 0.720023i \(-0.744131\pi\)
−0.693950 + 0.720023i \(0.744131\pi\)
\(4\) 4.00000 0.500000
\(5\) 16.2698 1.45521 0.727607 0.685994i \(-0.240632\pi\)
0.727607 + 0.685994i \(0.240632\pi\)
\(6\) −14.4235 −0.981393
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 25.0092 0.926266
\(10\) 32.5396 1.02899
\(11\) 47.1866 1.29339 0.646695 0.762749i \(-0.276151\pi\)
0.646695 + 0.762749i \(0.276151\pi\)
\(12\) −28.8470 −0.693950
\(13\) 15.5988 0.332794 0.166397 0.986059i \(-0.446787\pi\)
0.166397 + 0.986059i \(0.446787\pi\)
\(14\) 0 0
\(15\) −117.334 −2.01969
\(16\) 16.0000 0.250000
\(17\) 124.933 1.78240 0.891198 0.453614i \(-0.149865\pi\)
0.891198 + 0.453614i \(0.149865\pi\)
\(18\) 50.0183 0.654969
\(19\) 27.0949 0.327158 0.163579 0.986530i \(-0.447696\pi\)
0.163579 + 0.986530i \(0.447696\pi\)
\(20\) 65.0792 0.727607
\(21\) 0 0
\(22\) 94.3732 0.914565
\(23\) 23.0000 0.208514
\(24\) −57.6939 −0.490697
\(25\) 139.706 1.11765
\(26\) 31.1976 0.235321
\(27\) 14.3573 0.102336
\(28\) 0 0
\(29\) −75.7411 −0.484992 −0.242496 0.970152i \(-0.577966\pi\)
−0.242496 + 0.970152i \(0.577966\pi\)
\(30\) −234.667 −1.42814
\(31\) 101.299 0.586899 0.293450 0.955975i \(-0.405197\pi\)
0.293450 + 0.955975i \(0.405197\pi\)
\(32\) 32.0000 0.176777
\(33\) −340.297 −1.79510
\(34\) 249.866 1.26034
\(35\) 0 0
\(36\) 100.037 0.463133
\(37\) 158.715 0.705207 0.352603 0.935773i \(-0.385296\pi\)
0.352603 + 0.935773i \(0.385296\pi\)
\(38\) 54.1898 0.231335
\(39\) −112.494 −0.461885
\(40\) 130.158 0.514496
\(41\) −344.393 −1.31183 −0.655916 0.754834i \(-0.727717\pi\)
−0.655916 + 0.754834i \(0.727717\pi\)
\(42\) 0 0
\(43\) 236.838 0.839940 0.419970 0.907538i \(-0.362041\pi\)
0.419970 + 0.907538i \(0.362041\pi\)
\(44\) 188.746 0.646695
\(45\) 406.894 1.34792
\(46\) 46.0000 0.147442
\(47\) 522.231 1.62075 0.810375 0.585912i \(-0.199264\pi\)
0.810375 + 0.585912i \(0.199264\pi\)
\(48\) −115.388 −0.346975
\(49\) 0 0
\(50\) 279.413 0.790298
\(51\) −900.985 −2.47379
\(52\) 62.3951 0.166397
\(53\) −323.061 −0.837280 −0.418640 0.908152i \(-0.637493\pi\)
−0.418640 + 0.908152i \(0.637493\pi\)
\(54\) 28.7147 0.0723625
\(55\) 767.716 1.88216
\(56\) 0 0
\(57\) −195.401 −0.454062
\(58\) −151.482 −0.342941
\(59\) 752.228 1.65986 0.829930 0.557867i \(-0.188380\pi\)
0.829930 + 0.557867i \(0.188380\pi\)
\(60\) −469.334 −1.00985
\(61\) −751.789 −1.57798 −0.788990 0.614406i \(-0.789396\pi\)
−0.788990 + 0.614406i \(0.789396\pi\)
\(62\) 202.598 0.415000
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 253.789 0.484287
\(66\) −680.595 −1.26932
\(67\) −870.373 −1.58706 −0.793530 0.608532i \(-0.791759\pi\)
−0.793530 + 0.608532i \(0.791759\pi\)
\(68\) 499.733 0.891198
\(69\) −165.870 −0.289397
\(70\) 0 0
\(71\) −386.315 −0.645734 −0.322867 0.946444i \(-0.604647\pi\)
−0.322867 + 0.946444i \(0.604647\pi\)
\(72\) 200.073 0.327484
\(73\) 972.125 1.55861 0.779306 0.626644i \(-0.215572\pi\)
0.779306 + 0.626644i \(0.215572\pi\)
\(74\) 317.431 0.498656
\(75\) −1007.53 −1.55119
\(76\) 108.380 0.163579
\(77\) 0 0
\(78\) −224.989 −0.326602
\(79\) −1011.48 −1.44052 −0.720259 0.693705i \(-0.755977\pi\)
−0.720259 + 0.693705i \(0.755977\pi\)
\(80\) 260.317 0.363804
\(81\) −778.789 −1.06830
\(82\) −688.785 −0.927605
\(83\) 70.9632 0.0938460 0.0469230 0.998899i \(-0.485058\pi\)
0.0469230 + 0.998899i \(0.485058\pi\)
\(84\) 0 0
\(85\) 2032.64 2.59377
\(86\) 473.676 0.593927
\(87\) 546.225 0.673121
\(88\) 377.493 0.457282
\(89\) −208.804 −0.248688 −0.124344 0.992239i \(-0.539683\pi\)
−0.124344 + 0.992239i \(0.539683\pi\)
\(90\) 813.788 0.953120
\(91\) 0 0
\(92\) 92.0000 0.104257
\(93\) −730.544 −0.814557
\(94\) 1044.46 1.14604
\(95\) 440.828 0.476085
\(96\) −230.776 −0.245348
\(97\) −290.349 −0.303922 −0.151961 0.988386i \(-0.548559\pi\)
−0.151961 + 0.988386i \(0.548559\pi\)
\(98\) 0 0
\(99\) 1180.10 1.19802
\(100\) 558.825 0.558825
\(101\) 1242.66 1.22425 0.612124 0.790762i \(-0.290315\pi\)
0.612124 + 0.790762i \(0.290315\pi\)
\(102\) −1801.97 −1.74923
\(103\) −764.386 −0.731235 −0.365617 0.930765i \(-0.619142\pi\)
−0.365617 + 0.930765i \(0.619142\pi\)
\(104\) 124.790 0.117660
\(105\) 0 0
\(106\) −646.122 −0.592047
\(107\) 717.558 0.648308 0.324154 0.946004i \(-0.394920\pi\)
0.324154 + 0.946004i \(0.394920\pi\)
\(108\) 57.4294 0.0511680
\(109\) −526.649 −0.462787 −0.231394 0.972860i \(-0.574328\pi\)
−0.231394 + 0.972860i \(0.574328\pi\)
\(110\) 1535.43 1.33089
\(111\) −1144.61 −0.978756
\(112\) 0 0
\(113\) −561.697 −0.467610 −0.233805 0.972283i \(-0.575118\pi\)
−0.233805 + 0.972283i \(0.575118\pi\)
\(114\) −390.802 −0.321070
\(115\) 374.205 0.303433
\(116\) −302.965 −0.242496
\(117\) 390.113 0.308256
\(118\) 1504.46 1.17370
\(119\) 0 0
\(120\) −938.668 −0.714069
\(121\) 895.573 0.672857
\(122\) −1503.58 −1.11580
\(123\) 2483.67 1.82069
\(124\) 405.197 0.293450
\(125\) 239.269 0.171207
\(126\) 0 0
\(127\) −2396.56 −1.67449 −0.837246 0.546827i \(-0.815836\pi\)
−0.837246 + 0.546827i \(0.815836\pi\)
\(128\) 128.000 0.0883883
\(129\) −1708.01 −1.16575
\(130\) 507.578 0.342443
\(131\) 858.844 0.572806 0.286403 0.958109i \(-0.407540\pi\)
0.286403 + 0.958109i \(0.407540\pi\)
\(132\) −1361.19 −0.897548
\(133\) 0 0
\(134\) −1740.75 −1.12222
\(135\) 233.591 0.148921
\(136\) 999.465 0.630172
\(137\) 151.005 0.0941697 0.0470849 0.998891i \(-0.485007\pi\)
0.0470849 + 0.998891i \(0.485007\pi\)
\(138\) −331.740 −0.204635
\(139\) −1987.82 −1.21298 −0.606492 0.795090i \(-0.707424\pi\)
−0.606492 + 0.795090i \(0.707424\pi\)
\(140\) 0 0
\(141\) −3766.19 −2.24944
\(142\) −772.630 −0.456603
\(143\) 736.053 0.430432
\(144\) 400.147 0.231566
\(145\) −1232.29 −0.705768
\(146\) 1944.25 1.10210
\(147\) 0 0
\(148\) 634.862 0.352603
\(149\) 1160.23 0.637915 0.318958 0.947769i \(-0.396667\pi\)
0.318958 + 0.947769i \(0.396667\pi\)
\(150\) −2015.05 −1.09685
\(151\) 1500.02 0.808411 0.404205 0.914668i \(-0.367548\pi\)
0.404205 + 0.914668i \(0.367548\pi\)
\(152\) 216.759 0.115668
\(153\) 3124.47 1.65097
\(154\) 0 0
\(155\) 1648.12 0.854065
\(156\) −449.977 −0.230942
\(157\) −2825.24 −1.43617 −0.718085 0.695955i \(-0.754981\pi\)
−0.718085 + 0.695955i \(0.754981\pi\)
\(158\) −2022.97 −1.01860
\(159\) 2329.83 1.16206
\(160\) 520.634 0.257248
\(161\) 0 0
\(162\) −1557.58 −0.755401
\(163\) 3629.02 1.74385 0.871923 0.489642i \(-0.162873\pi\)
0.871923 + 0.489642i \(0.162873\pi\)
\(164\) −1377.57 −0.655916
\(165\) −5536.57 −2.61225
\(166\) 141.926 0.0663592
\(167\) 854.192 0.395805 0.197902 0.980222i \(-0.436587\pi\)
0.197902 + 0.980222i \(0.436587\pi\)
\(168\) 0 0
\(169\) −1953.68 −0.889248
\(170\) 4065.27 1.83407
\(171\) 677.621 0.303035
\(172\) 947.351 0.419970
\(173\) −2567.49 −1.12834 −0.564170 0.825659i \(-0.690804\pi\)
−0.564170 + 0.825659i \(0.690804\pi\)
\(174\) 1092.45 0.475968
\(175\) 0 0
\(176\) 754.985 0.323347
\(177\) −5424.87 −2.30372
\(178\) −417.609 −0.175849
\(179\) −3427.63 −1.43125 −0.715623 0.698487i \(-0.753857\pi\)
−0.715623 + 0.698487i \(0.753857\pi\)
\(180\) 1627.58 0.673958
\(181\) 1081.50 0.444130 0.222065 0.975032i \(-0.428720\pi\)
0.222065 + 0.975032i \(0.428720\pi\)
\(182\) 0 0
\(183\) 5421.71 2.19008
\(184\) 184.000 0.0737210
\(185\) 2582.27 1.02623
\(186\) −1461.09 −0.575979
\(187\) 5895.17 2.30533
\(188\) 2088.92 0.810375
\(189\) 0 0
\(190\) 881.657 0.336643
\(191\) −1975.98 −0.748568 −0.374284 0.927314i \(-0.622112\pi\)
−0.374284 + 0.927314i \(0.622112\pi\)
\(192\) −461.551 −0.173487
\(193\) 1594.03 0.594514 0.297257 0.954798i \(-0.403928\pi\)
0.297257 + 0.954798i \(0.403928\pi\)
\(194\) −580.698 −0.214906
\(195\) −1830.26 −0.672142
\(196\) 0 0
\(197\) −2249.35 −0.813501 −0.406751 0.913539i \(-0.633338\pi\)
−0.406751 + 0.913539i \(0.633338\pi\)
\(198\) 2360.19 0.847130
\(199\) 4968.79 1.76999 0.884995 0.465600i \(-0.154161\pi\)
0.884995 + 0.465600i \(0.154161\pi\)
\(200\) 1117.65 0.395149
\(201\) 6276.90 2.20268
\(202\) 2485.31 0.865674
\(203\) 0 0
\(204\) −3603.94 −1.23689
\(205\) −5603.20 −1.90900
\(206\) −1528.77 −0.517061
\(207\) 575.211 0.193140
\(208\) 249.580 0.0831985
\(209\) 1278.52 0.423142
\(210\) 0 0
\(211\) 2530.95 0.825771 0.412885 0.910783i \(-0.364521\pi\)
0.412885 + 0.910783i \(0.364521\pi\)
\(212\) −1292.24 −0.418640
\(213\) 2786.00 0.896214
\(214\) 1435.12 0.458423
\(215\) 3853.30 1.22229
\(216\) 114.859 0.0361812
\(217\) 0 0
\(218\) −1053.30 −0.327240
\(219\) −7010.71 −2.16320
\(220\) 3070.86 0.941080
\(221\) 1948.80 0.593171
\(222\) −2289.23 −0.692085
\(223\) 5807.13 1.74383 0.871915 0.489658i \(-0.162878\pi\)
0.871915 + 0.489658i \(0.162878\pi\)
\(224\) 0 0
\(225\) 3493.94 1.03524
\(226\) −1123.39 −0.330651
\(227\) 4762.82 1.39260 0.696299 0.717752i \(-0.254829\pi\)
0.696299 + 0.717752i \(0.254829\pi\)
\(228\) −781.605 −0.227031
\(229\) 384.176 0.110861 0.0554303 0.998463i \(-0.482347\pi\)
0.0554303 + 0.998463i \(0.482347\pi\)
\(230\) 748.411 0.214560
\(231\) 0 0
\(232\) −605.929 −0.171471
\(233\) 1398.62 0.393249 0.196624 0.980479i \(-0.437002\pi\)
0.196624 + 0.980479i \(0.437002\pi\)
\(234\) 780.225 0.217970
\(235\) 8496.59 2.35854
\(236\) 3008.91 0.829930
\(237\) 7294.56 1.99929
\(238\) 0 0
\(239\) 1755.23 0.475048 0.237524 0.971382i \(-0.423664\pi\)
0.237524 + 0.971382i \(0.423664\pi\)
\(240\) −1877.34 −0.504923
\(241\) −2783.24 −0.743917 −0.371959 0.928249i \(-0.621314\pi\)
−0.371959 + 0.928249i \(0.621314\pi\)
\(242\) 1791.15 0.475782
\(243\) 5228.77 1.38035
\(244\) −3007.16 −0.788990
\(245\) 0 0
\(246\) 4967.34 1.28742
\(247\) 422.647 0.108876
\(248\) 810.394 0.207500
\(249\) −511.768 −0.130249
\(250\) 478.537 0.121061
\(251\) −5021.71 −1.26282 −0.631410 0.775450i \(-0.717523\pi\)
−0.631410 + 0.775450i \(0.717523\pi\)
\(252\) 0 0
\(253\) 1085.29 0.269690
\(254\) −4793.12 −1.18404
\(255\) −14658.8 −3.59989
\(256\) 256.000 0.0625000
\(257\) −974.857 −0.236614 −0.118307 0.992977i \(-0.537747\pi\)
−0.118307 + 0.992977i \(0.537747\pi\)
\(258\) −3416.02 −0.824312
\(259\) 0 0
\(260\) 1015.16 0.242143
\(261\) −1894.22 −0.449232
\(262\) 1717.69 0.405035
\(263\) −491.619 −0.115264 −0.0576322 0.998338i \(-0.518355\pi\)
−0.0576322 + 0.998338i \(0.518355\pi\)
\(264\) −2722.38 −0.634662
\(265\) −5256.14 −1.21842
\(266\) 0 0
\(267\) 1505.84 0.345154
\(268\) −3481.49 −0.793530
\(269\) −358.977 −0.0813651 −0.0406825 0.999172i \(-0.512953\pi\)
−0.0406825 + 0.999172i \(0.512953\pi\)
\(270\) 467.182 0.105303
\(271\) 4638.86 1.03982 0.519909 0.854222i \(-0.325966\pi\)
0.519909 + 0.854222i \(0.325966\pi\)
\(272\) 1998.93 0.445599
\(273\) 0 0
\(274\) 302.011 0.0665881
\(275\) 6592.26 1.44556
\(276\) −663.480 −0.144699
\(277\) 2524.96 0.547690 0.273845 0.961774i \(-0.411704\pi\)
0.273845 + 0.961774i \(0.411704\pi\)
\(278\) −3975.64 −0.857709
\(279\) 2533.41 0.543625
\(280\) 0 0
\(281\) 3278.39 0.695986 0.347993 0.937497i \(-0.386863\pi\)
0.347993 + 0.937497i \(0.386863\pi\)
\(282\) −7532.39 −1.59059
\(283\) 6720.68 1.41167 0.705836 0.708375i \(-0.250572\pi\)
0.705836 + 0.708375i \(0.250572\pi\)
\(284\) −1545.26 −0.322867
\(285\) −3179.14 −0.660758
\(286\) 1472.11 0.304362
\(287\) 0 0
\(288\) 800.293 0.163742
\(289\) 10695.3 2.17694
\(290\) −2464.59 −0.499053
\(291\) 2093.92 0.421814
\(292\) 3888.50 0.779306
\(293\) −1554.24 −0.309896 −0.154948 0.987923i \(-0.549521\pi\)
−0.154948 + 0.987923i \(0.549521\pi\)
\(294\) 0 0
\(295\) 12238.6 2.41545
\(296\) 1269.72 0.249328
\(297\) 677.474 0.132360
\(298\) 2320.45 0.451074
\(299\) 358.772 0.0693924
\(300\) −4030.10 −0.775593
\(301\) 0 0
\(302\) 3000.04 0.571633
\(303\) −8961.72 −1.69913
\(304\) 433.518 0.0817894
\(305\) −12231.5 −2.29630
\(306\) 6248.95 1.16741
\(307\) 3942.91 0.733010 0.366505 0.930416i \(-0.380554\pi\)
0.366505 + 0.930416i \(0.380554\pi\)
\(308\) 0 0
\(309\) 5512.55 1.01488
\(310\) 3296.24 0.603915
\(311\) −7176.79 −1.30855 −0.654274 0.756258i \(-0.727026\pi\)
−0.654274 + 0.756258i \(0.727026\pi\)
\(312\) −899.954 −0.163301
\(313\) −5888.35 −1.06335 −0.531676 0.846948i \(-0.678438\pi\)
−0.531676 + 0.846948i \(0.678438\pi\)
\(314\) −5650.48 −1.01553
\(315\) 0 0
\(316\) −4045.94 −0.720259
\(317\) −8438.25 −1.49508 −0.747539 0.664218i \(-0.768765\pi\)
−0.747539 + 0.664218i \(0.768765\pi\)
\(318\) 4659.67 0.821701
\(319\) −3573.97 −0.627284
\(320\) 1041.27 0.181902
\(321\) −5174.84 −0.899786
\(322\) 0 0
\(323\) 3385.05 0.583125
\(324\) −3115.16 −0.534149
\(325\) 2179.25 0.371947
\(326\) 7258.05 1.23309
\(327\) 3798.05 0.642302
\(328\) −2755.14 −0.463803
\(329\) 0 0
\(330\) −11073.1 −1.84714
\(331\) 5617.36 0.932803 0.466402 0.884573i \(-0.345550\pi\)
0.466402 + 0.884573i \(0.345550\pi\)
\(332\) 283.853 0.0469230
\(333\) 3969.34 0.653209
\(334\) 1708.38 0.279876
\(335\) −14160.8 −2.30951
\(336\) 0 0
\(337\) 1180.08 0.190750 0.0953752 0.995441i \(-0.469595\pi\)
0.0953752 + 0.995441i \(0.469595\pi\)
\(338\) −3907.36 −0.628793
\(339\) 4050.81 0.648996
\(340\) 8130.55 1.29689
\(341\) 4779.96 0.759090
\(342\) 1355.24 0.214278
\(343\) 0 0
\(344\) 1894.70 0.296964
\(345\) −2698.67 −0.421135
\(346\) −5134.99 −0.797857
\(347\) −583.578 −0.0902827 −0.0451413 0.998981i \(-0.514374\pi\)
−0.0451413 + 0.998981i \(0.514374\pi\)
\(348\) 2184.90 0.336560
\(349\) 10239.5 1.57051 0.785253 0.619175i \(-0.212533\pi\)
0.785253 + 0.619175i \(0.212533\pi\)
\(350\) 0 0
\(351\) 223.957 0.0340568
\(352\) 1509.97 0.228641
\(353\) −2364.68 −0.356542 −0.178271 0.983981i \(-0.557050\pi\)
−0.178271 + 0.983981i \(0.557050\pi\)
\(354\) −10849.7 −1.62898
\(355\) −6285.26 −0.939682
\(356\) −835.217 −0.124344
\(357\) 0 0
\(358\) −6855.26 −1.01204
\(359\) −96.6164 −0.0142040 −0.00710198 0.999975i \(-0.502261\pi\)
−0.00710198 + 0.999975i \(0.502261\pi\)
\(360\) 3255.15 0.476560
\(361\) −6124.87 −0.892968
\(362\) 2163.01 0.314047
\(363\) −6458.64 −0.933859
\(364\) 0 0
\(365\) 15816.3 2.26812
\(366\) 10843.4 1.54862
\(367\) 625.870 0.0890194 0.0445097 0.999009i \(-0.485827\pi\)
0.0445097 + 0.999009i \(0.485827\pi\)
\(368\) 368.000 0.0521286
\(369\) −8612.98 −1.21510
\(370\) 5164.53 0.725652
\(371\) 0 0
\(372\) −2922.17 −0.407279
\(373\) −1947.36 −0.270323 −0.135162 0.990824i \(-0.543155\pi\)
−0.135162 + 0.990824i \(0.543155\pi\)
\(374\) 11790.3 1.63012
\(375\) −1725.54 −0.237618
\(376\) 4177.85 0.573021
\(377\) −1181.47 −0.161403
\(378\) 0 0
\(379\) 6434.94 0.872139 0.436069 0.899913i \(-0.356370\pi\)
0.436069 + 0.899913i \(0.356370\pi\)
\(380\) 1763.31 0.238042
\(381\) 17283.4 2.32403
\(382\) −3951.95 −0.529318
\(383\) 5381.85 0.718014 0.359007 0.933335i \(-0.383115\pi\)
0.359007 + 0.933335i \(0.383115\pi\)
\(384\) −923.103 −0.122674
\(385\) 0 0
\(386\) 3188.07 0.420385
\(387\) 5923.12 0.778008
\(388\) −1161.40 −0.151961
\(389\) 1793.47 0.233760 0.116880 0.993146i \(-0.462711\pi\)
0.116880 + 0.993146i \(0.462711\pi\)
\(390\) −3660.52 −0.475276
\(391\) 2873.46 0.371655
\(392\) 0 0
\(393\) −6193.76 −0.794997
\(394\) −4498.71 −0.575232
\(395\) −16456.6 −2.09626
\(396\) 4720.39 0.599011
\(397\) −4504.05 −0.569399 −0.284700 0.958617i \(-0.591894\pi\)
−0.284700 + 0.958617i \(0.591894\pi\)
\(398\) 9937.58 1.25157
\(399\) 0 0
\(400\) 2235.30 0.279413
\(401\) 6831.76 0.850777 0.425389 0.905011i \(-0.360137\pi\)
0.425389 + 0.905011i \(0.360137\pi\)
\(402\) 12553.8 1.55753
\(403\) 1580.14 0.195317
\(404\) 4970.63 0.612124
\(405\) −12670.7 −1.55460
\(406\) 0 0
\(407\) 7489.24 0.912107
\(408\) −7207.88 −0.874616
\(409\) 7577.51 0.916097 0.458048 0.888927i \(-0.348549\pi\)
0.458048 + 0.888927i \(0.348549\pi\)
\(410\) −11206.4 −1.34986
\(411\) −1089.01 −0.130698
\(412\) −3057.54 −0.365617
\(413\) 0 0
\(414\) 1150.42 0.136570
\(415\) 1154.56 0.136566
\(416\) 499.161 0.0588302
\(417\) 14335.6 1.68350
\(418\) 2557.03 0.299207
\(419\) −15291.7 −1.78293 −0.891463 0.453093i \(-0.850321\pi\)
−0.891463 + 0.453093i \(0.850321\pi\)
\(420\) 0 0
\(421\) −4676.53 −0.541378 −0.270689 0.962667i \(-0.587252\pi\)
−0.270689 + 0.962667i \(0.587252\pi\)
\(422\) 5061.90 0.583908
\(423\) 13060.6 1.50124
\(424\) −2584.49 −0.296023
\(425\) 17454.0 1.99210
\(426\) 5572.00 0.633719
\(427\) 0 0
\(428\) 2870.23 0.324154
\(429\) −5308.22 −0.597397
\(430\) 7706.61 0.864292
\(431\) 1791.88 0.200259 0.100130 0.994974i \(-0.468074\pi\)
0.100130 + 0.994974i \(0.468074\pi\)
\(432\) 229.718 0.0255840
\(433\) −5834.03 −0.647495 −0.323748 0.946143i \(-0.604943\pi\)
−0.323748 + 0.946143i \(0.604943\pi\)
\(434\) 0 0
\(435\) 8886.97 0.979535
\(436\) −2106.59 −0.231394
\(437\) 623.182 0.0682171
\(438\) −14021.4 −1.52961
\(439\) 15116.1 1.64340 0.821700 0.569921i \(-0.193026\pi\)
0.821700 + 0.569921i \(0.193026\pi\)
\(440\) 6141.73 0.665444
\(441\) 0 0
\(442\) 3897.61 0.419435
\(443\) 15050.6 1.61416 0.807082 0.590439i \(-0.201045\pi\)
0.807082 + 0.590439i \(0.201045\pi\)
\(444\) −4578.46 −0.489378
\(445\) −3397.20 −0.361894
\(446\) 11614.3 1.23307
\(447\) −8367.24 −0.885362
\(448\) 0 0
\(449\) 4182.76 0.439636 0.219818 0.975541i \(-0.429454\pi\)
0.219818 + 0.975541i \(0.429454\pi\)
\(450\) 6987.88 0.732026
\(451\) −16250.7 −1.69671
\(452\) −2246.79 −0.233805
\(453\) −10817.8 −1.12199
\(454\) 9525.64 0.984715
\(455\) 0 0
\(456\) −1563.21 −0.160535
\(457\) 63.6901 0.00651925 0.00325962 0.999995i \(-0.498962\pi\)
0.00325962 + 0.999995i \(0.498962\pi\)
\(458\) 768.353 0.0783903
\(459\) 1793.71 0.182403
\(460\) 1496.82 0.151717
\(461\) 13051.3 1.31856 0.659281 0.751896i \(-0.270861\pi\)
0.659281 + 0.751896i \(0.270861\pi\)
\(462\) 0 0
\(463\) 5158.36 0.517774 0.258887 0.965908i \(-0.416644\pi\)
0.258887 + 0.965908i \(0.416644\pi\)
\(464\) −1211.86 −0.121248
\(465\) −11885.8 −1.18536
\(466\) 2797.25 0.278069
\(467\) −4486.79 −0.444591 −0.222296 0.974979i \(-0.571355\pi\)
−0.222296 + 0.974979i \(0.571355\pi\)
\(468\) 1560.45 0.154128
\(469\) 0 0
\(470\) 16993.2 1.66774
\(471\) 20374.9 1.99326
\(472\) 6017.83 0.586849
\(473\) 11175.6 1.08637
\(474\) 14589.1 1.41371
\(475\) 3785.33 0.365648
\(476\) 0 0
\(477\) −8079.49 −0.775544
\(478\) 3510.46 0.335910
\(479\) −7266.52 −0.693144 −0.346572 0.938023i \(-0.612654\pi\)
−0.346572 + 0.938023i \(0.612654\pi\)
\(480\) −3754.67 −0.357035
\(481\) 2475.77 0.234689
\(482\) −5566.47 −0.526029
\(483\) 0 0
\(484\) 3582.29 0.336429
\(485\) −4723.92 −0.442272
\(486\) 10457.5 0.976058
\(487\) 8606.70 0.800835 0.400418 0.916333i \(-0.368865\pi\)
0.400418 + 0.916333i \(0.368865\pi\)
\(488\) −6014.31 −0.557900
\(489\) −26171.6 −2.42028
\(490\) 0 0
\(491\) −10692.5 −0.982779 −0.491389 0.870940i \(-0.663511\pi\)
−0.491389 + 0.870940i \(0.663511\pi\)
\(492\) 9934.68 0.910346
\(493\) −9462.58 −0.864449
\(494\) 845.294 0.0769870
\(495\) 19199.9 1.74338
\(496\) 1620.79 0.146725
\(497\) 0 0
\(498\) −1023.54 −0.0920998
\(499\) −1940.11 −0.174050 −0.0870252 0.996206i \(-0.527736\pi\)
−0.0870252 + 0.996206i \(0.527736\pi\)
\(500\) 957.074 0.0856033
\(501\) −6160.21 −0.549337
\(502\) −10043.4 −0.892948
\(503\) 15043.4 1.33350 0.666751 0.745280i \(-0.267684\pi\)
0.666751 + 0.745280i \(0.267684\pi\)
\(504\) 0 0
\(505\) 20217.8 1.78154
\(506\) 2170.58 0.190700
\(507\) 14089.4 1.23419
\(508\) −9586.25 −0.837246
\(509\) 2212.59 0.192675 0.0963374 0.995349i \(-0.469287\pi\)
0.0963374 + 0.995349i \(0.469287\pi\)
\(510\) −29317.7 −2.54551
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 389.011 0.0334800
\(514\) −1949.71 −0.167312
\(515\) −12436.4 −1.06410
\(516\) −6832.05 −0.582876
\(517\) 24642.3 2.09626
\(518\) 0 0
\(519\) 18516.1 1.56602
\(520\) 2030.31 0.171221
\(521\) −237.881 −0.0200034 −0.0100017 0.999950i \(-0.503184\pi\)
−0.0100017 + 0.999950i \(0.503184\pi\)
\(522\) −3788.45 −0.317655
\(523\) −16907.0 −1.41356 −0.706778 0.707435i \(-0.749852\pi\)
−0.706778 + 0.707435i \(0.749852\pi\)
\(524\) 3435.38 0.286403
\(525\) 0 0
\(526\) −983.238 −0.0815042
\(527\) 12655.6 1.04609
\(528\) −5444.76 −0.448774
\(529\) 529.000 0.0434783
\(530\) −10512.3 −0.861555
\(531\) 18812.6 1.53747
\(532\) 0 0
\(533\) −5372.11 −0.436570
\(534\) 3011.68 0.244060
\(535\) 11674.5 0.943427
\(536\) −6962.98 −0.561110
\(537\) 24719.2 1.98643
\(538\) −717.954 −0.0575338
\(539\) 0 0
\(540\) 934.364 0.0744604
\(541\) −1410.42 −0.112086 −0.0560431 0.998428i \(-0.517848\pi\)
−0.0560431 + 0.998428i \(0.517848\pi\)
\(542\) 9277.71 0.735262
\(543\) −7799.52 −0.616408
\(544\) 3997.86 0.315086
\(545\) −8568.47 −0.673455
\(546\) 0 0
\(547\) −23165.7 −1.81078 −0.905388 0.424585i \(-0.860420\pi\)
−0.905388 + 0.424585i \(0.860420\pi\)
\(548\) 604.021 0.0470849
\(549\) −18801.6 −1.46163
\(550\) 13184.5 1.02216
\(551\) −2052.20 −0.158669
\(552\) −1326.96 −0.102317
\(553\) 0 0
\(554\) 5049.92 0.387275
\(555\) −18622.6 −1.42430
\(556\) −7951.29 −0.606492
\(557\) −9563.65 −0.727513 −0.363757 0.931494i \(-0.618506\pi\)
−0.363757 + 0.931494i \(0.618506\pi\)
\(558\) 5066.82 0.384401
\(559\) 3694.38 0.279527
\(560\) 0 0
\(561\) −42514.4 −3.19957
\(562\) 6556.77 0.492136
\(563\) −1124.59 −0.0841841 −0.0420920 0.999114i \(-0.513402\pi\)
−0.0420920 + 0.999114i \(0.513402\pi\)
\(564\) −15064.8 −1.12472
\(565\) −9138.69 −0.680474
\(566\) 13441.4 0.998203
\(567\) 0 0
\(568\) −3090.52 −0.228302
\(569\) −15300.7 −1.12731 −0.563653 0.826012i \(-0.690604\pi\)
−0.563653 + 0.826012i \(0.690604\pi\)
\(570\) −6358.28 −0.467226
\(571\) 15344.6 1.12461 0.562303 0.826931i \(-0.309915\pi\)
0.562303 + 0.826931i \(0.309915\pi\)
\(572\) 2944.21 0.215216
\(573\) 14250.2 1.03894
\(574\) 0 0
\(575\) 3213.24 0.233046
\(576\) 1600.59 0.115783
\(577\) −17787.8 −1.28339 −0.641693 0.766961i \(-0.721768\pi\)
−0.641693 + 0.766961i \(0.721768\pi\)
\(578\) 21390.6 1.53933
\(579\) −11495.8 −0.825125
\(580\) −4929.17 −0.352884
\(581\) 0 0
\(582\) 4187.84 0.298267
\(583\) −15244.2 −1.08293
\(584\) 7777.00 0.551052
\(585\) 6347.05 0.448578
\(586\) −3108.47 −0.219129
\(587\) −28030.3 −1.97093 −0.985464 0.169884i \(-0.945661\pi\)
−0.985464 + 0.169884i \(0.945661\pi\)
\(588\) 0 0
\(589\) 2744.69 0.192009
\(590\) 24477.2 1.70798
\(591\) 16221.7 1.12906
\(592\) 2539.45 0.176302
\(593\) −16069.1 −1.11278 −0.556389 0.830922i \(-0.687813\pi\)
−0.556389 + 0.830922i \(0.687813\pi\)
\(594\) 1354.95 0.0935929
\(595\) 0 0
\(596\) 4640.90 0.318958
\(597\) −35833.6 −2.45657
\(598\) 717.544 0.0490678
\(599\) −2013.96 −0.137376 −0.0686879 0.997638i \(-0.521881\pi\)
−0.0686879 + 0.997638i \(0.521881\pi\)
\(600\) −8060.20 −0.548427
\(601\) −11300.5 −0.766984 −0.383492 0.923544i \(-0.625279\pi\)
−0.383492 + 0.923544i \(0.625279\pi\)
\(602\) 0 0
\(603\) −21767.3 −1.47004
\(604\) 6000.09 0.404205
\(605\) 14570.8 0.979152
\(606\) −17923.4 −1.20147
\(607\) 4451.15 0.297639 0.148819 0.988864i \(-0.452453\pi\)
0.148819 + 0.988864i \(0.452453\pi\)
\(608\) 867.036 0.0578338
\(609\) 0 0
\(610\) −24462.9 −1.62373
\(611\) 8146.17 0.539376
\(612\) 12497.9 0.825486
\(613\) 17338.0 1.14237 0.571187 0.820820i \(-0.306483\pi\)
0.571187 + 0.820820i \(0.306483\pi\)
\(614\) 7885.83 0.518316
\(615\) 40408.8 2.64950
\(616\) 0 0
\(617\) 5994.66 0.391144 0.195572 0.980689i \(-0.437344\pi\)
0.195572 + 0.980689i \(0.437344\pi\)
\(618\) 11025.1 0.717629
\(619\) −17923.7 −1.16383 −0.581917 0.813248i \(-0.697697\pi\)
−0.581917 + 0.813248i \(0.697697\pi\)
\(620\) 6592.47 0.427032
\(621\) 330.219 0.0213385
\(622\) −14353.6 −0.925283
\(623\) 0 0
\(624\) −1799.91 −0.115471
\(625\) −13570.4 −0.868508
\(626\) −11776.7 −0.751903
\(627\) −9220.32 −0.587279
\(628\) −11301.0 −0.718085
\(629\) 19828.8 1.25696
\(630\) 0 0
\(631\) −9861.28 −0.622141 −0.311071 0.950387i \(-0.600688\pi\)
−0.311071 + 0.950387i \(0.600688\pi\)
\(632\) −8091.88 −0.509300
\(633\) −18252.5 −1.14609
\(634\) −16876.5 −1.05718
\(635\) −38991.6 −2.43675
\(636\) 9319.33 0.581031
\(637\) 0 0
\(638\) −7147.93 −0.443557
\(639\) −9661.41 −0.598121
\(640\) 2082.53 0.128624
\(641\) −12525.2 −0.771788 −0.385894 0.922543i \(-0.626107\pi\)
−0.385894 + 0.922543i \(0.626107\pi\)
\(642\) −10349.7 −0.636245
\(643\) −25700.9 −1.57628 −0.788139 0.615498i \(-0.788955\pi\)
−0.788139 + 0.615498i \(0.788955\pi\)
\(644\) 0 0
\(645\) −27789.0 −1.69642
\(646\) 6770.10 0.412331
\(647\) −3951.92 −0.240133 −0.120066 0.992766i \(-0.538311\pi\)
−0.120066 + 0.992766i \(0.538311\pi\)
\(648\) −6230.31 −0.377700
\(649\) 35495.1 2.14685
\(650\) 4358.50 0.263007
\(651\) 0 0
\(652\) 14516.1 0.871923
\(653\) −18402.1 −1.10280 −0.551402 0.834240i \(-0.685907\pi\)
−0.551402 + 0.834240i \(0.685907\pi\)
\(654\) 7596.10 0.454176
\(655\) 13973.2 0.833556
\(656\) −5510.28 −0.327958
\(657\) 24312.0 1.44369
\(658\) 0 0
\(659\) −12627.9 −0.746455 −0.373228 0.927740i \(-0.621749\pi\)
−0.373228 + 0.927740i \(0.621749\pi\)
\(660\) −22146.3 −1.30612
\(661\) −4711.79 −0.277258 −0.138629 0.990344i \(-0.544270\pi\)
−0.138629 + 0.990344i \(0.544270\pi\)
\(662\) 11234.7 0.659592
\(663\) −14054.3 −0.823262
\(664\) 567.705 0.0331796
\(665\) 0 0
\(666\) 7938.68 0.461888
\(667\) −1742.05 −0.101128
\(668\) 3416.77 0.197902
\(669\) −41879.5 −2.42026
\(670\) −28321.6 −1.63307
\(671\) −35474.4 −2.04094
\(672\) 0 0
\(673\) 28702.7 1.64399 0.821995 0.569494i \(-0.192861\pi\)
0.821995 + 0.569494i \(0.192861\pi\)
\(674\) 2360.15 0.134881
\(675\) 2005.81 0.114376
\(676\) −7814.71 −0.444624
\(677\) −31186.5 −1.77045 −0.885226 0.465162i \(-0.845996\pi\)
−0.885226 + 0.465162i \(0.845996\pi\)
\(678\) 8101.62 0.458910
\(679\) 0 0
\(680\) 16261.1 0.917036
\(681\) −34348.2 −1.93279
\(682\) 9559.93 0.536757
\(683\) −9293.06 −0.520628 −0.260314 0.965524i \(-0.583826\pi\)
−0.260314 + 0.965524i \(0.583826\pi\)
\(684\) 2710.48 0.151517
\(685\) 2456.83 0.137037
\(686\) 0 0
\(687\) −2770.58 −0.153863
\(688\) 3789.41 0.209985
\(689\) −5039.36 −0.278642
\(690\) −5397.34 −0.297787
\(691\) −14601.0 −0.803834 −0.401917 0.915676i \(-0.631656\pi\)
−0.401917 + 0.915676i \(0.631656\pi\)
\(692\) −10270.0 −0.564170
\(693\) 0 0
\(694\) −1167.16 −0.0638395
\(695\) −32341.4 −1.76515
\(696\) 4369.80 0.237984
\(697\) −43026.1 −2.33820
\(698\) 20479.0 1.11052
\(699\) −10086.5 −0.545789
\(700\) 0 0
\(701\) 8708.03 0.469184 0.234592 0.972094i \(-0.424625\pi\)
0.234592 + 0.972094i \(0.424625\pi\)
\(702\) 447.914 0.0240818
\(703\) 4300.38 0.230714
\(704\) 3019.94 0.161674
\(705\) −61275.2 −3.27341
\(706\) −4729.36 −0.252113
\(707\) 0 0
\(708\) −21699.5 −1.15186
\(709\) 33500.9 1.77455 0.887273 0.461245i \(-0.152597\pi\)
0.887273 + 0.461245i \(0.152597\pi\)
\(710\) −12570.5 −0.664456
\(711\) −25296.4 −1.33430
\(712\) −1670.43 −0.0879244
\(713\) 2329.88 0.122377
\(714\) 0 0
\(715\) 11975.4 0.626372
\(716\) −13710.5 −0.715623
\(717\) −12658.3 −0.659319
\(718\) −193.233 −0.0100437
\(719\) 32105.0 1.66525 0.832625 0.553837i \(-0.186837\pi\)
0.832625 + 0.553837i \(0.186837\pi\)
\(720\) 6510.31 0.336979
\(721\) 0 0
\(722\) −12249.7 −0.631424
\(723\) 20072.0 1.03248
\(724\) 4326.01 0.222065
\(725\) −10581.5 −0.542052
\(726\) −12917.3 −0.660338
\(727\) −15233.0 −0.777113 −0.388557 0.921425i \(-0.627026\pi\)
−0.388557 + 0.921425i \(0.627026\pi\)
\(728\) 0 0
\(729\) −16681.2 −0.847495
\(730\) 31632.6 1.60380
\(731\) 29588.9 1.49711
\(732\) 21686.8 1.09504
\(733\) 1809.92 0.0912019 0.0456009 0.998960i \(-0.485480\pi\)
0.0456009 + 0.998960i \(0.485480\pi\)
\(734\) 1251.74 0.0629462
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) −41069.9 −2.05269
\(738\) −17226.0 −0.859209
\(739\) −8238.73 −0.410104 −0.205052 0.978751i \(-0.565736\pi\)
−0.205052 + 0.978751i \(0.565736\pi\)
\(740\) 10329.1 0.513114
\(741\) −3048.02 −0.151109
\(742\) 0 0
\(743\) −23854.1 −1.17782 −0.588910 0.808198i \(-0.700443\pi\)
−0.588910 + 0.808198i \(0.700443\pi\)
\(744\) −5844.35 −0.287990
\(745\) 18876.6 0.928304
\(746\) −3894.72 −0.191147
\(747\) 1774.73 0.0869263
\(748\) 23580.7 1.15267
\(749\) 0 0
\(750\) −3451.08 −0.168021
\(751\) −6437.83 −0.312809 −0.156405 0.987693i \(-0.549990\pi\)
−0.156405 + 0.987693i \(0.549990\pi\)
\(752\) 8355.70 0.405187
\(753\) 36215.3 1.75267
\(754\) −2362.94 −0.114129
\(755\) 24405.0 1.17641
\(756\) 0 0
\(757\) 22816.8 1.09550 0.547749 0.836643i \(-0.315485\pi\)
0.547749 + 0.836643i \(0.315485\pi\)
\(758\) 12869.9 0.616695
\(759\) −7826.84 −0.374303
\(760\) 3526.63 0.168321
\(761\) 29454.4 1.40305 0.701525 0.712645i \(-0.252503\pi\)
0.701525 + 0.712645i \(0.252503\pi\)
\(762\) 34566.8 1.64334
\(763\) 0 0
\(764\) −7903.90 −0.374284
\(765\) 50834.6 2.40252
\(766\) 10763.7 0.507713
\(767\) 11733.8 0.552392
\(768\) −1846.21 −0.0867437
\(769\) 20044.0 0.939930 0.469965 0.882685i \(-0.344267\pi\)
0.469965 + 0.882685i \(0.344267\pi\)
\(770\) 0 0
\(771\) 7030.41 0.328397
\(772\) 6376.14 0.297257
\(773\) −13982.7 −0.650611 −0.325305 0.945609i \(-0.605467\pi\)
−0.325305 + 0.945609i \(0.605467\pi\)
\(774\) 11846.2 0.550135
\(775\) 14152.1 0.655948
\(776\) −2322.79 −0.107453
\(777\) 0 0
\(778\) 3586.94 0.165293
\(779\) −9331.28 −0.429176
\(780\) −7321.04 −0.336071
\(781\) −18228.9 −0.835186
\(782\) 5746.93 0.262800
\(783\) −1087.44 −0.0496322
\(784\) 0 0
\(785\) −45966.1 −2.08994
\(786\) −12387.5 −0.562148
\(787\) −35277.3 −1.59784 −0.798919 0.601438i \(-0.794595\pi\)
−0.798919 + 0.601438i \(0.794595\pi\)
\(788\) −8997.41 −0.406751
\(789\) 3545.43 0.159975
\(790\) −32913.3 −1.48228
\(791\) 0 0
\(792\) 9440.78 0.423565
\(793\) −11727.0 −0.525142
\(794\) −9008.09 −0.402626
\(795\) 37905.9 1.69105
\(796\) 19875.2 0.884995
\(797\) 3314.35 0.147303 0.0736513 0.997284i \(-0.476535\pi\)
0.0736513 + 0.997284i \(0.476535\pi\)
\(798\) 0 0
\(799\) 65244.0 2.88882
\(800\) 4470.60 0.197575
\(801\) −5222.02 −0.230351
\(802\) 13663.5 0.601590
\(803\) 45871.3 2.01589
\(804\) 25107.6 1.10134
\(805\) 0 0
\(806\) 3160.29 0.138110
\(807\) 2588.85 0.112927
\(808\) 9941.25 0.432837
\(809\) −11588.9 −0.503640 −0.251820 0.967774i \(-0.581029\pi\)
−0.251820 + 0.967774i \(0.581029\pi\)
\(810\) −25341.5 −1.09927
\(811\) −14907.0 −0.645446 −0.322723 0.946494i \(-0.604598\pi\)
−0.322723 + 0.946494i \(0.604598\pi\)
\(812\) 0 0
\(813\) −33454.2 −1.44316
\(814\) 14978.5 0.644957
\(815\) 59043.5 2.53767
\(816\) −14415.8 −0.618447
\(817\) 6417.09 0.274793
\(818\) 15155.0 0.647778
\(819\) 0 0
\(820\) −22412.8 −0.954499
\(821\) −18754.7 −0.797252 −0.398626 0.917114i \(-0.630513\pi\)
−0.398626 + 0.917114i \(0.630513\pi\)
\(822\) −2178.02 −0.0924176
\(823\) 19230.6 0.814505 0.407252 0.913316i \(-0.366487\pi\)
0.407252 + 0.913316i \(0.366487\pi\)
\(824\) −6115.09 −0.258531
\(825\) −47541.7 −2.00629
\(826\) 0 0
\(827\) −3749.90 −0.157675 −0.0788373 0.996887i \(-0.525121\pi\)
−0.0788373 + 0.996887i \(0.525121\pi\)
\(828\) 2300.84 0.0965699
\(829\) −22579.0 −0.945959 −0.472979 0.881074i \(-0.656821\pi\)
−0.472979 + 0.881074i \(0.656821\pi\)
\(830\) 2309.11 0.0965668
\(831\) −18209.4 −0.760139
\(832\) 998.322 0.0415993
\(833\) 0 0
\(834\) 28671.3 1.19041
\(835\) 13897.5 0.575981
\(836\) 5114.06 0.211571
\(837\) 1454.39 0.0600609
\(838\) −30583.3 −1.26072
\(839\) 9740.05 0.400791 0.200396 0.979715i \(-0.435777\pi\)
0.200396 + 0.979715i \(0.435777\pi\)
\(840\) 0 0
\(841\) −18652.3 −0.764782
\(842\) −9353.07 −0.382812
\(843\) −23642.9 −0.965959
\(844\) 10123.8 0.412885
\(845\) −31785.9 −1.29405
\(846\) 26121.1 1.06154
\(847\) 0 0
\(848\) −5168.98 −0.209320
\(849\) −48467.8 −1.95926
\(850\) 34907.9 1.40862
\(851\) 3650.45 0.147046
\(852\) 11144.0 0.448107
\(853\) −34826.5 −1.39793 −0.698967 0.715154i \(-0.746357\pi\)
−0.698967 + 0.715154i \(0.746357\pi\)
\(854\) 0 0
\(855\) 11024.8 0.440981
\(856\) 5740.46 0.229211
\(857\) −29060.4 −1.15832 −0.579162 0.815212i \(-0.696620\pi\)
−0.579162 + 0.815212i \(0.696620\pi\)
\(858\) −10616.4 −0.422424
\(859\) 36275.1 1.44085 0.720426 0.693532i \(-0.243946\pi\)
0.720426 + 0.693532i \(0.243946\pi\)
\(860\) 15413.2 0.611147
\(861\) 0 0
\(862\) 3583.76 0.141605
\(863\) 25442.3 1.00355 0.501776 0.864997i \(-0.332680\pi\)
0.501776 + 0.864997i \(0.332680\pi\)
\(864\) 459.435 0.0180906
\(865\) −41772.6 −1.64198
\(866\) −11668.1 −0.457848
\(867\) −77131.7 −3.02137
\(868\) 0 0
\(869\) −47728.5 −1.86315
\(870\) 17773.9 0.692636
\(871\) −13576.8 −0.528164
\(872\) −4213.19 −0.163620
\(873\) −7261.39 −0.281513
\(874\) 1246.36 0.0482368
\(875\) 0 0
\(876\) −28042.9 −1.08160
\(877\) 37592.9 1.44746 0.723729 0.690084i \(-0.242427\pi\)
0.723729 + 0.690084i \(0.242427\pi\)
\(878\) 30232.2 1.16206
\(879\) 11208.7 0.430104
\(880\) 12283.5 0.470540
\(881\) 17562.2 0.671608 0.335804 0.941932i \(-0.390992\pi\)
0.335804 + 0.941932i \(0.390992\pi\)
\(882\) 0 0
\(883\) 28211.0 1.07517 0.537586 0.843209i \(-0.319337\pi\)
0.537586 + 0.843209i \(0.319337\pi\)
\(884\) 7795.22 0.296586
\(885\) −88261.6 −3.35241
\(886\) 30101.2 1.14139
\(887\) −39743.9 −1.50448 −0.752238 0.658892i \(-0.771025\pi\)
−0.752238 + 0.658892i \(0.771025\pi\)
\(888\) −9156.91 −0.346043
\(889\) 0 0
\(890\) −6794.41 −0.255898
\(891\) −36748.4 −1.38173
\(892\) 23228.5 0.871915
\(893\) 14149.8 0.530240
\(894\) −16734.5 −0.626046
\(895\) −55766.8 −2.08277
\(896\) 0 0
\(897\) −2587.37 −0.0963096
\(898\) 8365.53 0.310870
\(899\) −7672.52 −0.284642
\(900\) 13975.8 0.517621
\(901\) −40361.1 −1.49237
\(902\) −32501.4 −1.19976
\(903\) 0 0
\(904\) −4493.57 −0.165325
\(905\) 17595.8 0.646304
\(906\) −21635.5 −0.793369
\(907\) 10980.3 0.401978 0.200989 0.979594i \(-0.435585\pi\)
0.200989 + 0.979594i \(0.435585\pi\)
\(908\) 19051.3 0.696299
\(909\) 31077.8 1.13398
\(910\) 0 0
\(911\) −1972.75 −0.0717453 −0.0358727 0.999356i \(-0.511421\pi\)
−0.0358727 + 0.999356i \(0.511421\pi\)
\(912\) −3126.42 −0.113515
\(913\) 3348.51 0.121379
\(914\) 127.380 0.00460980
\(915\) 88210.1 3.18703
\(916\) 1536.71 0.0554303
\(917\) 0 0
\(918\) 3587.42 0.128979
\(919\) −45431.0 −1.63072 −0.815359 0.578955i \(-0.803461\pi\)
−0.815359 + 0.578955i \(0.803461\pi\)
\(920\) 2993.64 0.107280
\(921\) −28435.3 −1.01734
\(922\) 26102.5 0.932365
\(923\) −6026.04 −0.214897
\(924\) 0 0
\(925\) 22173.5 0.788175
\(926\) 10316.7 0.366122
\(927\) −19116.7 −0.677318
\(928\) −2423.72 −0.0857353
\(929\) −44731.4 −1.57975 −0.789875 0.613268i \(-0.789855\pi\)
−0.789875 + 0.613268i \(0.789855\pi\)
\(930\) −23771.6 −0.838173
\(931\) 0 0
\(932\) 5594.50 0.196624
\(933\) 51757.1 1.81613
\(934\) −8973.59 −0.314373
\(935\) 95913.2 3.35476
\(936\) 3120.90 0.108985
\(937\) −30506.2 −1.06360 −0.531801 0.846869i \(-0.678484\pi\)
−0.531801 + 0.846869i \(0.678484\pi\)
\(938\) 0 0
\(939\) 42465.2 1.47583
\(940\) 33986.4 1.17927
\(941\) 47720.6 1.65318 0.826592 0.562802i \(-0.190277\pi\)
0.826592 + 0.562802i \(0.190277\pi\)
\(942\) 40749.8 1.40945
\(943\) −7921.03 −0.273536
\(944\) 12035.7 0.414965
\(945\) 0 0
\(946\) 22351.1 0.768180
\(947\) −15551.0 −0.533621 −0.266810 0.963749i \(-0.585970\pi\)
−0.266810 + 0.963749i \(0.585970\pi\)
\(948\) 29178.2 0.999647
\(949\) 15164.0 0.518697
\(950\) 7570.65 0.258552
\(951\) 60854.5 2.07502
\(952\) 0 0
\(953\) −48105.0 −1.63512 −0.817562 0.575840i \(-0.804675\pi\)
−0.817562 + 0.575840i \(0.804675\pi\)
\(954\) −16159.0 −0.548392
\(955\) −32148.7 −1.08933
\(956\) 7020.93 0.237524
\(957\) 25774.5 0.870607
\(958\) −14533.0 −0.490127
\(959\) 0 0
\(960\) −7509.35 −0.252462
\(961\) −19529.5 −0.655549
\(962\) 4951.53 0.165950
\(963\) 17945.5 0.600505
\(964\) −11132.9 −0.371959
\(965\) 25934.6 0.865145
\(966\) 0 0
\(967\) 12889.0 0.428627 0.214313 0.976765i \(-0.431249\pi\)
0.214313 + 0.976765i \(0.431249\pi\)
\(968\) 7164.59 0.237891
\(969\) −24412.1 −0.809318
\(970\) −9447.84 −0.312734
\(971\) −44069.6 −1.45650 −0.728250 0.685312i \(-0.759666\pi\)
−0.728250 + 0.685312i \(0.759666\pi\)
\(972\) 20915.1 0.690177
\(973\) 0 0
\(974\) 17213.4 0.566276
\(975\) −15716.2 −0.516226
\(976\) −12028.6 −0.394495
\(977\) 25964.2 0.850224 0.425112 0.905141i \(-0.360235\pi\)
0.425112 + 0.905141i \(0.360235\pi\)
\(978\) −52343.1 −1.71140
\(979\) −9852.76 −0.321650
\(980\) 0 0
\(981\) −13171.0 −0.428664
\(982\) −21384.9 −0.694929
\(983\) 18666.0 0.605650 0.302825 0.953046i \(-0.402070\pi\)
0.302825 + 0.953046i \(0.402070\pi\)
\(984\) 19869.4 0.643712
\(985\) −36596.5 −1.18382
\(986\) −18925.2 −0.611258
\(987\) 0 0
\(988\) 1690.59 0.0544380
\(989\) 5447.27 0.175140
\(990\) 38399.9 1.23276
\(991\) 49850.9 1.59795 0.798974 0.601365i \(-0.205376\pi\)
0.798974 + 0.601365i \(0.205376\pi\)
\(992\) 3241.58 0.103750
\(993\) −40510.9 −1.29464
\(994\) 0 0
\(995\) 80841.2 2.57572
\(996\) −2047.07 −0.0651244
\(997\) 37492.5 1.19097 0.595486 0.803366i \(-0.296960\pi\)
0.595486 + 0.803366i \(0.296960\pi\)
\(998\) −3880.21 −0.123072
\(999\) 2278.73 0.0721680
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 2254.4.a.y.1.2 11
7.2 even 3 322.4.e.a.277.10 yes 22
7.4 even 3 322.4.e.a.93.10 22
7.6 odd 2 2254.4.a.v.1.10 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.e.a.93.10 22 7.4 even 3
322.4.e.a.277.10 yes 22 7.2 even 3
2254.4.a.v.1.10 11 7.6 odd 2
2254.4.a.y.1.2 11 1.1 even 1 trivial