Properties

Label 2254.4.a.l.1.3
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
Analytic rank $1$
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] = [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: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 92x^{3} - 28x^{2} + 1593x - 1782 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.26012\) 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)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +0.260120 q^{3} +4.00000 q^{4} -15.2484 q^{5} +0.520240 q^{6} +8.00000 q^{8} -26.9323 q^{9} -30.4969 q^{10} +63.1379 q^{11} +1.04048 q^{12} -40.8864 q^{13} -3.96643 q^{15} +16.0000 q^{16} +57.0717 q^{17} -53.8647 q^{18} -34.4579 q^{19} -60.9938 q^{20} +126.276 q^{22} +23.0000 q^{23} +2.08096 q^{24} +107.515 q^{25} -81.7727 q^{26} -14.0289 q^{27} +180.951 q^{29} -7.93285 q^{30} +5.92805 q^{31} +32.0000 q^{32} +16.4234 q^{33} +114.143 q^{34} -107.729 q^{36} -161.864 q^{37} -68.9158 q^{38} -10.6354 q^{39} -121.988 q^{40} +104.432 q^{41} +16.5725 q^{43} +252.552 q^{44} +410.676 q^{45} +46.0000 q^{46} -333.754 q^{47} +4.16192 q^{48} +215.030 q^{50} +14.8455 q^{51} -163.545 q^{52} +296.103 q^{53} -28.0578 q^{54} -962.756 q^{55} -8.96319 q^{57} +361.902 q^{58} +805.644 q^{59} -15.8657 q^{60} -715.603 q^{61} +11.8561 q^{62} +64.0000 q^{64} +623.454 q^{65} +32.8469 q^{66} +301.232 q^{67} +228.287 q^{68} +5.98276 q^{69} -871.046 q^{71} -215.459 q^{72} -894.771 q^{73} -323.728 q^{74} +27.9668 q^{75} -137.832 q^{76} -21.2707 q^{78} -1246.19 q^{79} -243.975 q^{80} +723.524 q^{81} +208.863 q^{82} +1223.93 q^{83} -870.255 q^{85} +33.1451 q^{86} +47.0690 q^{87} +505.104 q^{88} +86.3579 q^{89} +821.353 q^{90} +92.0000 q^{92} +1.54200 q^{93} -667.507 q^{94} +525.429 q^{95} +8.32384 q^{96} -343.939 q^{97} -1700.45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 10 q^{2} - 5 q^{3} + 20 q^{4} - 22 q^{5} - 10 q^{6} + 40 q^{8} + 54 q^{9} - 44 q^{10} + 42 q^{11} - 20 q^{12} - 107 q^{13} + 122 q^{15} + 80 q^{16} - 218 q^{17} + 108 q^{18} - 194 q^{19} - 88 q^{20}+ \cdots - 2616 q^{99}+O(q^{100}) \) 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
\(3\) 0.260120 0.0500601 0.0250301 0.999687i \(-0.492032\pi\)
0.0250301 + 0.999687i \(0.492032\pi\)
\(4\) 4.00000 0.500000
\(5\) −15.2484 −1.36386 −0.681931 0.731416i \(-0.738860\pi\)
−0.681931 + 0.731416i \(0.738860\pi\)
\(6\) 0.520240 0.0353978
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −26.9323 −0.997494
\(10\) −30.4969 −0.964397
\(11\) 63.1379 1.73062 0.865309 0.501238i \(-0.167122\pi\)
0.865309 + 0.501238i \(0.167122\pi\)
\(12\) 1.04048 0.0250301
\(13\) −40.8864 −0.872295 −0.436148 0.899875i \(-0.643657\pi\)
−0.436148 + 0.899875i \(0.643657\pi\)
\(14\) 0 0
\(15\) −3.96643 −0.0682751
\(16\) 16.0000 0.250000
\(17\) 57.0717 0.814231 0.407115 0.913377i \(-0.366535\pi\)
0.407115 + 0.913377i \(0.366535\pi\)
\(18\) −53.8647 −0.705335
\(19\) −34.4579 −0.416062 −0.208031 0.978122i \(-0.566706\pi\)
−0.208031 + 0.978122i \(0.566706\pi\)
\(20\) −60.9938 −0.681931
\(21\) 0 0
\(22\) 126.276 1.22373
\(23\) 23.0000 0.208514
\(24\) 2.08096 0.0176989
\(25\) 107.515 0.860121
\(26\) −81.7727 −0.616806
\(27\) −14.0289 −0.0999948
\(28\) 0 0
\(29\) 180.951 1.15868 0.579340 0.815086i \(-0.303310\pi\)
0.579340 + 0.815086i \(0.303310\pi\)
\(30\) −7.93285 −0.0482778
\(31\) 5.92805 0.0343455 0.0171727 0.999853i \(-0.494533\pi\)
0.0171727 + 0.999853i \(0.494533\pi\)
\(32\) 32.0000 0.176777
\(33\) 16.4234 0.0866350
\(34\) 114.143 0.575748
\(35\) 0 0
\(36\) −107.729 −0.498747
\(37\) −161.864 −0.719196 −0.359598 0.933107i \(-0.617086\pi\)
−0.359598 + 0.933107i \(0.617086\pi\)
\(38\) −68.9158 −0.294200
\(39\) −10.6354 −0.0436672
\(40\) −121.988 −0.482198
\(41\) 104.432 0.397792 0.198896 0.980021i \(-0.436264\pi\)
0.198896 + 0.980021i \(0.436264\pi\)
\(42\) 0 0
\(43\) 16.5725 0.0587742 0.0293871 0.999568i \(-0.490644\pi\)
0.0293871 + 0.999568i \(0.490644\pi\)
\(44\) 252.552 0.865309
\(45\) 410.676 1.36044
\(46\) 46.0000 0.147442
\(47\) −333.754 −1.03581 −0.517904 0.855439i \(-0.673287\pi\)
−0.517904 + 0.855439i \(0.673287\pi\)
\(48\) 4.16192 0.0125150
\(49\) 0 0
\(50\) 215.030 0.608198
\(51\) 14.8455 0.0407605
\(52\) −163.545 −0.436148
\(53\) 296.103 0.767412 0.383706 0.923455i \(-0.374648\pi\)
0.383706 + 0.923455i \(0.374648\pi\)
\(54\) −28.0578 −0.0707070
\(55\) −962.756 −2.36033
\(56\) 0 0
\(57\) −8.96319 −0.0208281
\(58\) 361.902 0.819311
\(59\) 805.644 1.77773 0.888864 0.458171i \(-0.151495\pi\)
0.888864 + 0.458171i \(0.151495\pi\)
\(60\) −15.8657 −0.0341376
\(61\) −715.603 −1.50202 −0.751012 0.660288i \(-0.770434\pi\)
−0.751012 + 0.660288i \(0.770434\pi\)
\(62\) 11.8561 0.0242859
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 623.454 1.18969
\(66\) 32.8469 0.0612602
\(67\) 301.232 0.549275 0.274637 0.961548i \(-0.411442\pi\)
0.274637 + 0.961548i \(0.411442\pi\)
\(68\) 228.287 0.407115
\(69\) 5.98276 0.0104383
\(70\) 0 0
\(71\) −871.046 −1.45597 −0.727987 0.685591i \(-0.759544\pi\)
−0.727987 + 0.685591i \(0.759544\pi\)
\(72\) −215.459 −0.352667
\(73\) −894.771 −1.43459 −0.717295 0.696770i \(-0.754620\pi\)
−0.717295 + 0.696770i \(0.754620\pi\)
\(74\) −323.728 −0.508548
\(75\) 27.9668 0.0430578
\(76\) −137.832 −0.208031
\(77\) 0 0
\(78\) −21.2707 −0.0308774
\(79\) −1246.19 −1.77477 −0.887386 0.461028i \(-0.847481\pi\)
−0.887386 + 0.461028i \(0.847481\pi\)
\(80\) −243.975 −0.340966
\(81\) 723.524 0.992488
\(82\) 208.863 0.281281
\(83\) 1223.93 1.61860 0.809300 0.587395i \(-0.199846\pi\)
0.809300 + 0.587395i \(0.199846\pi\)
\(84\) 0 0
\(85\) −870.255 −1.11050
\(86\) 33.1451 0.0415596
\(87\) 47.0690 0.0580037
\(88\) 505.104 0.611866
\(89\) 86.3579 0.102853 0.0514265 0.998677i \(-0.483623\pi\)
0.0514265 + 0.998677i \(0.483623\pi\)
\(90\) 821.353 0.961980
\(91\) 0 0
\(92\) 92.0000 0.104257
\(93\) 1.54200 0.00171934
\(94\) −667.507 −0.732426
\(95\) 525.429 0.567452
\(96\) 8.32384 0.00884946
\(97\) −343.939 −0.360018 −0.180009 0.983665i \(-0.557613\pi\)
−0.180009 + 0.983665i \(0.557613\pi\)
\(98\) 0 0
\(99\) −1700.45 −1.72628
\(100\) 430.061 0.430061
\(101\) −458.505 −0.451713 −0.225856 0.974161i \(-0.572518\pi\)
−0.225856 + 0.974161i \(0.572518\pi\)
\(102\) 29.6910 0.0288220
\(103\) 574.886 0.549954 0.274977 0.961451i \(-0.411330\pi\)
0.274977 + 0.961451i \(0.411330\pi\)
\(104\) −327.091 −0.308403
\(105\) 0 0
\(106\) 592.205 0.542642
\(107\) −1451.76 −1.31165 −0.655825 0.754913i \(-0.727679\pi\)
−0.655825 + 0.754913i \(0.727679\pi\)
\(108\) −56.1155 −0.0499974
\(109\) −1812.89 −1.59306 −0.796530 0.604598i \(-0.793334\pi\)
−0.796530 + 0.604598i \(0.793334\pi\)
\(110\) −1925.51 −1.66900
\(111\) −42.1040 −0.0360030
\(112\) 0 0
\(113\) −1693.79 −1.41007 −0.705035 0.709173i \(-0.749069\pi\)
−0.705035 + 0.709173i \(0.749069\pi\)
\(114\) −17.9264 −0.0147277
\(115\) −350.714 −0.284385
\(116\) 723.804 0.579340
\(117\) 1101.17 0.870109
\(118\) 1611.29 1.25704
\(119\) 0 0
\(120\) −31.7314 −0.0241389
\(121\) 2655.40 1.99504
\(122\) −1431.21 −1.06209
\(123\) 27.1647 0.0199135
\(124\) 23.7122 0.0171727
\(125\) 266.616 0.190775
\(126\) 0 0
\(127\) 251.950 0.176039 0.0880194 0.996119i \(-0.471946\pi\)
0.0880194 + 0.996119i \(0.471946\pi\)
\(128\) 128.000 0.0883883
\(129\) 4.31085 0.00294224
\(130\) 1246.91 0.841238
\(131\) 1844.44 1.23015 0.615074 0.788469i \(-0.289126\pi\)
0.615074 + 0.788469i \(0.289126\pi\)
\(132\) 65.6938 0.0433175
\(133\) 0 0
\(134\) 602.465 0.388396
\(135\) 213.919 0.136379
\(136\) 456.574 0.287874
\(137\) −1169.93 −0.729592 −0.364796 0.931087i \(-0.618861\pi\)
−0.364796 + 0.931087i \(0.618861\pi\)
\(138\) 11.9655 0.00738096
\(139\) 1618.44 0.987585 0.493792 0.869580i \(-0.335610\pi\)
0.493792 + 0.869580i \(0.335610\pi\)
\(140\) 0 0
\(141\) −86.8160 −0.0518526
\(142\) −1742.09 −1.02953
\(143\) −2581.48 −1.50961
\(144\) −430.917 −0.249373
\(145\) −2759.22 −1.58028
\(146\) −1789.54 −1.01441
\(147\) 0 0
\(148\) −647.455 −0.359598
\(149\) −1745.63 −0.959785 −0.479892 0.877327i \(-0.659324\pi\)
−0.479892 + 0.877327i \(0.659324\pi\)
\(150\) 55.9337 0.0304464
\(151\) −2520.41 −1.35833 −0.679167 0.733984i \(-0.737659\pi\)
−0.679167 + 0.733984i \(0.737659\pi\)
\(152\) −275.663 −0.147100
\(153\) −1537.07 −0.812190
\(154\) 0 0
\(155\) −90.3936 −0.0468425
\(156\) −42.5414 −0.0218336
\(157\) −1122.56 −0.570635 −0.285318 0.958433i \(-0.592099\pi\)
−0.285318 + 0.958433i \(0.592099\pi\)
\(158\) −2492.37 −1.25495
\(159\) 77.0222 0.0384167
\(160\) −487.950 −0.241099
\(161\) 0 0
\(162\) 1447.05 0.701795
\(163\) 149.438 0.0718091 0.0359045 0.999355i \(-0.488569\pi\)
0.0359045 + 0.999355i \(0.488569\pi\)
\(164\) 417.726 0.198896
\(165\) −250.432 −0.118158
\(166\) 2447.86 1.14452
\(167\) −1950.78 −0.903927 −0.451963 0.892037i \(-0.649276\pi\)
−0.451963 + 0.892037i \(0.649276\pi\)
\(168\) 0 0
\(169\) −525.306 −0.239101
\(170\) −1740.51 −0.785241
\(171\) 928.032 0.415020
\(172\) 66.2902 0.0293871
\(173\) −2850.79 −1.25284 −0.626420 0.779486i \(-0.715480\pi\)
−0.626420 + 0.779486i \(0.715480\pi\)
\(174\) 94.1379 0.0410148
\(175\) 0 0
\(176\) 1010.21 0.432655
\(177\) 209.564 0.0889933
\(178\) 172.716 0.0727280
\(179\) 1847.62 0.771493 0.385747 0.922605i \(-0.373944\pi\)
0.385747 + 0.922605i \(0.373944\pi\)
\(180\) 1642.71 0.680222
\(181\) −3260.42 −1.33892 −0.669461 0.742847i \(-0.733475\pi\)
−0.669461 + 0.742847i \(0.733475\pi\)
\(182\) 0 0
\(183\) −186.143 −0.0751915
\(184\) 184.000 0.0737210
\(185\) 2468.17 0.980884
\(186\) 3.08401 0.00121576
\(187\) 3603.39 1.40912
\(188\) −1335.01 −0.517904
\(189\) 0 0
\(190\) 1050.86 0.401249
\(191\) 1616.13 0.612247 0.306123 0.951992i \(-0.400968\pi\)
0.306123 + 0.951992i \(0.400968\pi\)
\(192\) 16.6477 0.00625751
\(193\) −4746.87 −1.77040 −0.885200 0.465211i \(-0.845979\pi\)
−0.885200 + 0.465211i \(0.845979\pi\)
\(194\) −687.878 −0.254571
\(195\) 162.173 0.0595560
\(196\) 0 0
\(197\) −1471.77 −0.532280 −0.266140 0.963934i \(-0.585748\pi\)
−0.266140 + 0.963934i \(0.585748\pi\)
\(198\) −3400.90 −1.22067
\(199\) −3296.74 −1.17437 −0.587184 0.809453i \(-0.699764\pi\)
−0.587184 + 0.809453i \(0.699764\pi\)
\(200\) 860.121 0.304099
\(201\) 78.3566 0.0274967
\(202\) −917.011 −0.319409
\(203\) 0 0
\(204\) 59.3820 0.0203802
\(205\) −1592.42 −0.542533
\(206\) 1149.77 0.388876
\(207\) −619.444 −0.207992
\(208\) −654.182 −0.218074
\(209\) −2175.60 −0.720045
\(210\) 0 0
\(211\) −2436.09 −0.794821 −0.397410 0.917641i \(-0.630091\pi\)
−0.397410 + 0.917641i \(0.630091\pi\)
\(212\) 1184.41 0.383706
\(213\) −226.577 −0.0728862
\(214\) −2903.51 −0.927477
\(215\) −252.706 −0.0801599
\(216\) −112.231 −0.0353535
\(217\) 0 0
\(218\) −3625.79 −1.12646
\(219\) −232.748 −0.0718157
\(220\) −3851.02 −1.18016
\(221\) −2333.45 −0.710250
\(222\) −84.2080 −0.0254580
\(223\) −1464.12 −0.439662 −0.219831 0.975538i \(-0.570551\pi\)
−0.219831 + 0.975538i \(0.570551\pi\)
\(224\) 0 0
\(225\) −2895.64 −0.857966
\(226\) −3387.57 −0.997070
\(227\) 3419.39 0.999794 0.499897 0.866085i \(-0.333371\pi\)
0.499897 + 0.866085i \(0.333371\pi\)
\(228\) −35.8527 −0.0104141
\(229\) 3437.40 0.991922 0.495961 0.868345i \(-0.334816\pi\)
0.495961 + 0.868345i \(0.334816\pi\)
\(230\) −701.429 −0.201091
\(231\) 0 0
\(232\) 1447.61 0.409656
\(233\) 3049.48 0.857415 0.428708 0.903443i \(-0.358969\pi\)
0.428708 + 0.903443i \(0.358969\pi\)
\(234\) 2202.33 0.615260
\(235\) 5089.22 1.41270
\(236\) 3222.58 0.888864
\(237\) −324.158 −0.0888453
\(238\) 0 0
\(239\) 1961.10 0.530767 0.265383 0.964143i \(-0.414501\pi\)
0.265383 + 0.964143i \(0.414501\pi\)
\(240\) −63.4628 −0.0170688
\(241\) −6121.70 −1.63624 −0.818119 0.575049i \(-0.804983\pi\)
−0.818119 + 0.575049i \(0.804983\pi\)
\(242\) 5310.80 1.41071
\(243\) 566.983 0.149679
\(244\) −2862.41 −0.751012
\(245\) 0 0
\(246\) 54.3295 0.0140810
\(247\) 1408.86 0.362929
\(248\) 47.4244 0.0121430
\(249\) 318.369 0.0810273
\(250\) 533.233 0.134898
\(251\) −4112.95 −1.03429 −0.517145 0.855898i \(-0.673005\pi\)
−0.517145 + 0.855898i \(0.673005\pi\)
\(252\) 0 0
\(253\) 1452.17 0.360859
\(254\) 503.899 0.124478
\(255\) −226.371 −0.0555917
\(256\) 256.000 0.0625000
\(257\) 2135.52 0.518328 0.259164 0.965833i \(-0.416553\pi\)
0.259164 + 0.965833i \(0.416553\pi\)
\(258\) 8.62170 0.00208048
\(259\) 0 0
\(260\) 2493.81 0.594845
\(261\) −4873.43 −1.15578
\(262\) 3688.88 0.869846
\(263\) 7005.80 1.64257 0.821286 0.570517i \(-0.193257\pi\)
0.821286 + 0.570517i \(0.193257\pi\)
\(264\) 131.388 0.0306301
\(265\) −4515.10 −1.04664
\(266\) 0 0
\(267\) 22.4634 0.00514883
\(268\) 1204.93 0.274637
\(269\) −6566.34 −1.48831 −0.744157 0.668004i \(-0.767149\pi\)
−0.744157 + 0.668004i \(0.767149\pi\)
\(270\) 427.837 0.0964346
\(271\) 5759.43 1.29100 0.645499 0.763761i \(-0.276649\pi\)
0.645499 + 0.763761i \(0.276649\pi\)
\(272\) 913.147 0.203558
\(273\) 0 0
\(274\) −2339.87 −0.515900
\(275\) 6788.29 1.48854
\(276\) 23.9310 0.00521913
\(277\) 356.886 0.0774123 0.0387061 0.999251i \(-0.487676\pi\)
0.0387061 + 0.999251i \(0.487676\pi\)
\(278\) 3236.88 0.698328
\(279\) −159.656 −0.0342594
\(280\) 0 0
\(281\) −925.745 −0.196531 −0.0982657 0.995160i \(-0.531329\pi\)
−0.0982657 + 0.995160i \(0.531329\pi\)
\(282\) −173.632 −0.0366654
\(283\) −6928.18 −1.45526 −0.727629 0.685971i \(-0.759378\pi\)
−0.727629 + 0.685971i \(0.759378\pi\)
\(284\) −3484.19 −0.727987
\(285\) 136.675 0.0284067
\(286\) −5162.96 −1.06746
\(287\) 0 0
\(288\) −861.835 −0.176334
\(289\) −1655.82 −0.337028
\(290\) −5518.44 −1.11743
\(291\) −89.4655 −0.0180225
\(292\) −3579.08 −0.717295
\(293\) −148.190 −0.0295472 −0.0147736 0.999891i \(-0.504703\pi\)
−0.0147736 + 0.999891i \(0.504703\pi\)
\(294\) 0 0
\(295\) −12284.8 −2.42458
\(296\) −1294.91 −0.254274
\(297\) −885.755 −0.173053
\(298\) −3491.27 −0.678670
\(299\) −940.386 −0.181886
\(300\) 111.867 0.0215289
\(301\) 0 0
\(302\) −5040.83 −0.960487
\(303\) −119.266 −0.0226128
\(304\) −551.326 −0.104016
\(305\) 10911.8 2.04856
\(306\) −3074.15 −0.574305
\(307\) 10096.8 1.87705 0.938527 0.345207i \(-0.112191\pi\)
0.938527 + 0.345207i \(0.112191\pi\)
\(308\) 0 0
\(309\) 149.539 0.0275308
\(310\) −180.787 −0.0331227
\(311\) 1063.81 0.193965 0.0969826 0.995286i \(-0.469081\pi\)
0.0969826 + 0.995286i \(0.469081\pi\)
\(312\) −85.0829 −0.0154387
\(313\) −1953.88 −0.352844 −0.176422 0.984315i \(-0.556452\pi\)
−0.176422 + 0.984315i \(0.556452\pi\)
\(314\) −2245.11 −0.403500
\(315\) 0 0
\(316\) −4984.75 −0.887386
\(317\) −2939.51 −0.520819 −0.260409 0.965498i \(-0.583858\pi\)
−0.260409 + 0.965498i \(0.583858\pi\)
\(318\) 154.044 0.0271647
\(319\) 11424.9 2.00523
\(320\) −975.901 −0.170483
\(321\) −377.631 −0.0656614
\(322\) 0 0
\(323\) −1966.57 −0.338771
\(324\) 2894.10 0.496244
\(325\) −4395.90 −0.750280
\(326\) 298.876 0.0507767
\(327\) −471.570 −0.0797488
\(328\) 835.452 0.140641
\(329\) 0 0
\(330\) −500.864 −0.0835505
\(331\) −8808.46 −1.46271 −0.731354 0.681998i \(-0.761111\pi\)
−0.731354 + 0.681998i \(0.761111\pi\)
\(332\) 4895.72 0.809300
\(333\) 4359.37 0.717393
\(334\) −3901.56 −0.639173
\(335\) −4593.33 −0.749135
\(336\) 0 0
\(337\) 3966.73 0.641191 0.320596 0.947216i \(-0.396117\pi\)
0.320596 + 0.947216i \(0.396117\pi\)
\(338\) −1050.61 −0.169070
\(339\) −440.587 −0.0705883
\(340\) −3481.02 −0.555250
\(341\) 374.285 0.0594389
\(342\) 1856.06 0.293463
\(343\) 0 0
\(344\) 132.580 0.0207798
\(345\) −91.2278 −0.0142363
\(346\) −5701.57 −0.885891
\(347\) 5747.24 0.889129 0.444565 0.895747i \(-0.353358\pi\)
0.444565 + 0.895747i \(0.353358\pi\)
\(348\) 188.276 0.0290018
\(349\) −8367.21 −1.28334 −0.641671 0.766980i \(-0.721759\pi\)
−0.641671 + 0.766980i \(0.721759\pi\)
\(350\) 0 0
\(351\) 573.590 0.0872249
\(352\) 2020.41 0.305933
\(353\) −4056.10 −0.611571 −0.305785 0.952100i \(-0.598919\pi\)
−0.305785 + 0.952100i \(0.598919\pi\)
\(354\) 419.128 0.0629278
\(355\) 13282.1 1.98575
\(356\) 345.431 0.0514265
\(357\) 0 0
\(358\) 3695.23 0.545528
\(359\) −2580.13 −0.379315 −0.189658 0.981850i \(-0.560738\pi\)
−0.189658 + 0.981850i \(0.560738\pi\)
\(360\) 3285.41 0.480990
\(361\) −5671.65 −0.826892
\(362\) −6520.83 −0.946761
\(363\) 690.722 0.0998720
\(364\) 0 0
\(365\) 13643.9 1.95658
\(366\) −372.285 −0.0531684
\(367\) −938.253 −0.133451 −0.0667254 0.997771i \(-0.521255\pi\)
−0.0667254 + 0.997771i \(0.521255\pi\)
\(368\) 368.000 0.0521286
\(369\) −2812.59 −0.396795
\(370\) 4936.34 0.693590
\(371\) 0 0
\(372\) 6.16802 0.000859669 0
\(373\) 10951.6 1.52025 0.760125 0.649777i \(-0.225138\pi\)
0.760125 + 0.649777i \(0.225138\pi\)
\(374\) 7206.78 0.996401
\(375\) 69.3522 0.00955023
\(376\) −2670.03 −0.366213
\(377\) −7398.42 −1.01071
\(378\) 0 0
\(379\) 9520.76 1.29037 0.645183 0.764028i \(-0.276781\pi\)
0.645183 + 0.764028i \(0.276781\pi\)
\(380\) 2101.72 0.283726
\(381\) 65.5371 0.00881252
\(382\) 3232.26 0.432924
\(383\) 3099.25 0.413484 0.206742 0.978396i \(-0.433714\pi\)
0.206742 + 0.978396i \(0.433714\pi\)
\(384\) 33.2954 0.00442473
\(385\) 0 0
\(386\) −9493.74 −1.25186
\(387\) −446.337 −0.0586269
\(388\) −1375.76 −0.180009
\(389\) 4368.35 0.569368 0.284684 0.958621i \(-0.408111\pi\)
0.284684 + 0.958621i \(0.408111\pi\)
\(390\) 324.345 0.0421125
\(391\) 1312.65 0.169779
\(392\) 0 0
\(393\) 479.775 0.0615813
\(394\) −2943.54 −0.376379
\(395\) 19002.4 2.42054
\(396\) −6801.81 −0.863141
\(397\) −6306.06 −0.797210 −0.398605 0.917123i \(-0.630505\pi\)
−0.398605 + 0.917123i \(0.630505\pi\)
\(398\) −6593.47 −0.830404
\(399\) 0 0
\(400\) 1720.24 0.215030
\(401\) −83.0874 −0.0103471 −0.00517355 0.999987i \(-0.501647\pi\)
−0.00517355 + 0.999987i \(0.501647\pi\)
\(402\) 156.713 0.0194431
\(403\) −242.376 −0.0299594
\(404\) −1834.02 −0.225856
\(405\) −11032.6 −1.35362
\(406\) 0 0
\(407\) −10219.7 −1.24465
\(408\) 118.764 0.0144110
\(409\) −1594.33 −0.192750 −0.0963749 0.995345i \(-0.530725\pi\)
−0.0963749 + 0.995345i \(0.530725\pi\)
\(410\) −3184.84 −0.383629
\(411\) −304.323 −0.0365235
\(412\) 2299.55 0.274977
\(413\) 0 0
\(414\) −1238.89 −0.147072
\(415\) −18663.0 −2.20755
\(416\) −1308.36 −0.154201
\(417\) 420.988 0.0494386
\(418\) −4351.20 −0.509149
\(419\) 3260.67 0.380177 0.190089 0.981767i \(-0.439122\pi\)
0.190089 + 0.981767i \(0.439122\pi\)
\(420\) 0 0
\(421\) −7104.66 −0.822471 −0.411235 0.911529i \(-0.634903\pi\)
−0.411235 + 0.911529i \(0.634903\pi\)
\(422\) −4872.18 −0.562023
\(423\) 8988.76 1.03321
\(424\) 2368.82 0.271321
\(425\) 6136.08 0.700337
\(426\) −453.153 −0.0515384
\(427\) 0 0
\(428\) −5807.02 −0.655825
\(429\) −671.495 −0.0755712
\(430\) −505.411 −0.0566816
\(431\) 10760.4 1.20258 0.601290 0.799031i \(-0.294654\pi\)
0.601290 + 0.799031i \(0.294654\pi\)
\(432\) −224.462 −0.0249987
\(433\) 11537.4 1.28049 0.640245 0.768171i \(-0.278833\pi\)
0.640245 + 0.768171i \(0.278833\pi\)
\(434\) 0 0
\(435\) −717.729 −0.0791091
\(436\) −7251.57 −0.796530
\(437\) −792.532 −0.0867550
\(438\) −465.496 −0.0507814
\(439\) 10785.2 1.17255 0.586277 0.810111i \(-0.300593\pi\)
0.586277 + 0.810111i \(0.300593\pi\)
\(440\) −7702.05 −0.834501
\(441\) 0 0
\(442\) −4666.91 −0.502222
\(443\) 2483.46 0.266349 0.133175 0.991093i \(-0.457483\pi\)
0.133175 + 0.991093i \(0.457483\pi\)
\(444\) −168.416 −0.0180015
\(445\) −1316.82 −0.140277
\(446\) −2928.24 −0.310888
\(447\) −454.074 −0.0480469
\(448\) 0 0
\(449\) −3010.79 −0.316454 −0.158227 0.987403i \(-0.550578\pi\)
−0.158227 + 0.987403i \(0.550578\pi\)
\(450\) −5791.27 −0.606674
\(451\) 6593.59 0.688426
\(452\) −6775.14 −0.705035
\(453\) −655.610 −0.0679983
\(454\) 6838.79 0.706961
\(455\) 0 0
\(456\) −71.7055 −0.00736385
\(457\) −12906.5 −1.32110 −0.660549 0.750783i \(-0.729677\pi\)
−0.660549 + 0.750783i \(0.729677\pi\)
\(458\) 6874.81 0.701395
\(459\) −800.652 −0.0814188
\(460\) −1402.86 −0.142193
\(461\) −1928.01 −0.194786 −0.0973931 0.995246i \(-0.531050\pi\)
−0.0973931 + 0.995246i \(0.531050\pi\)
\(462\) 0 0
\(463\) 2880.38 0.289121 0.144560 0.989496i \(-0.453823\pi\)
0.144560 + 0.989496i \(0.453823\pi\)
\(464\) 2895.22 0.289670
\(465\) −23.5132 −0.00234494
\(466\) 6098.95 0.606284
\(467\) −6861.47 −0.679895 −0.339947 0.940444i \(-0.610409\pi\)
−0.339947 + 0.940444i \(0.610409\pi\)
\(468\) 4404.66 0.435055
\(469\) 0 0
\(470\) 10178.4 0.998929
\(471\) −291.999 −0.0285661
\(472\) 6445.16 0.628522
\(473\) 1046.36 0.101716
\(474\) −648.316 −0.0628231
\(475\) −3704.75 −0.357864
\(476\) 0 0
\(477\) −7974.73 −0.765488
\(478\) 3922.21 0.375309
\(479\) 4580.05 0.436885 0.218443 0.975850i \(-0.429902\pi\)
0.218443 + 0.975850i \(0.429902\pi\)
\(480\) −126.926 −0.0120695
\(481\) 6618.02 0.627351
\(482\) −12243.4 −1.15700
\(483\) 0 0
\(484\) 10621.6 0.997521
\(485\) 5244.54 0.491015
\(486\) 1133.97 0.105839
\(487\) 8844.29 0.822943 0.411471 0.911423i \(-0.365015\pi\)
0.411471 + 0.911423i \(0.365015\pi\)
\(488\) −5724.82 −0.531046
\(489\) 38.8718 0.00359477
\(490\) 0 0
\(491\) −4687.22 −0.430817 −0.215408 0.976524i \(-0.569108\pi\)
−0.215408 + 0.976524i \(0.569108\pi\)
\(492\) 108.659 0.00995675
\(493\) 10327.2 0.943434
\(494\) 2817.72 0.256630
\(495\) 25929.3 2.35441
\(496\) 94.8488 0.00858637
\(497\) 0 0
\(498\) 636.738 0.0572950
\(499\) −10245.1 −0.919107 −0.459553 0.888150i \(-0.651991\pi\)
−0.459553 + 0.888150i \(0.651991\pi\)
\(500\) 1066.47 0.0953876
\(501\) −507.436 −0.0452507
\(502\) −8225.89 −0.731354
\(503\) 10020.9 0.888286 0.444143 0.895956i \(-0.353508\pi\)
0.444143 + 0.895956i \(0.353508\pi\)
\(504\) 0 0
\(505\) 6991.50 0.616074
\(506\) 2904.35 0.255166
\(507\) −136.643 −0.0119694
\(508\) 1007.80 0.0880194
\(509\) 15666.6 1.36427 0.682133 0.731228i \(-0.261053\pi\)
0.682133 + 0.731228i \(0.261053\pi\)
\(510\) −452.741 −0.0393093
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 483.406 0.0416041
\(514\) 4271.05 0.366513
\(515\) −8766.13 −0.750062
\(516\) 17.2434 0.00147112
\(517\) −21072.5 −1.79259
\(518\) 0 0
\(519\) −741.546 −0.0627173
\(520\) 4987.63 0.420619
\(521\) −12571.8 −1.05716 −0.528581 0.848883i \(-0.677276\pi\)
−0.528581 + 0.848883i \(0.677276\pi\)
\(522\) −9746.86 −0.817258
\(523\) −12266.4 −1.02557 −0.512785 0.858517i \(-0.671386\pi\)
−0.512785 + 0.858517i \(0.671386\pi\)
\(524\) 7377.76 0.615074
\(525\) 0 0
\(526\) 14011.6 1.16147
\(527\) 338.324 0.0279651
\(528\) 262.775 0.0216587
\(529\) 529.000 0.0434783
\(530\) −9030.21 −0.740089
\(531\) −21697.9 −1.77327
\(532\) 0 0
\(533\) −4269.83 −0.346992
\(534\) 44.9268 0.00364077
\(535\) 22137.0 1.78891
\(536\) 2409.86 0.194198
\(537\) 480.602 0.0386210
\(538\) −13132.7 −1.05240
\(539\) 0 0
\(540\) 855.675 0.0681896
\(541\) −17141.8 −1.36226 −0.681131 0.732161i \(-0.738512\pi\)
−0.681131 + 0.732161i \(0.738512\pi\)
\(542\) 11518.9 0.912874
\(543\) −848.100 −0.0670266
\(544\) 1826.29 0.143937
\(545\) 27643.8 2.17272
\(546\) 0 0
\(547\) −13619.5 −1.06459 −0.532294 0.846560i \(-0.678670\pi\)
−0.532294 + 0.846560i \(0.678670\pi\)
\(548\) −4679.73 −0.364796
\(549\) 19272.8 1.49826
\(550\) 13576.6 1.05256
\(551\) −6235.19 −0.482083
\(552\) 47.8621 0.00369048
\(553\) 0 0
\(554\) 713.772 0.0547387
\(555\) 642.021 0.0491032
\(556\) 6473.76 0.493792
\(557\) −14755.1 −1.12243 −0.561214 0.827671i \(-0.689666\pi\)
−0.561214 + 0.827671i \(0.689666\pi\)
\(558\) −319.313 −0.0242251
\(559\) −677.591 −0.0512684
\(560\) 0 0
\(561\) 937.314 0.0705409
\(562\) −1851.49 −0.138969
\(563\) −21018.7 −1.57341 −0.786706 0.617327i \(-0.788215\pi\)
−0.786706 + 0.617327i \(0.788215\pi\)
\(564\) −347.264 −0.0259263
\(565\) 25827.6 1.92314
\(566\) −13856.4 −1.02902
\(567\) 0 0
\(568\) −6968.37 −0.514765
\(569\) 13750.9 1.01313 0.506563 0.862203i \(-0.330916\pi\)
0.506563 + 0.862203i \(0.330916\pi\)
\(570\) 273.349 0.0200866
\(571\) 10636.3 0.779535 0.389768 0.920913i \(-0.372555\pi\)
0.389768 + 0.920913i \(0.372555\pi\)
\(572\) −10325.9 −0.754805
\(573\) 420.388 0.0306491
\(574\) 0 0
\(575\) 2472.85 0.179348
\(576\) −1723.67 −0.124687
\(577\) −7290.64 −0.526019 −0.263010 0.964793i \(-0.584715\pi\)
−0.263010 + 0.964793i \(0.584715\pi\)
\(578\) −3311.64 −0.238315
\(579\) −1234.76 −0.0886264
\(580\) −11036.9 −0.790141
\(581\) 0 0
\(582\) −178.931 −0.0127439
\(583\) 18695.3 1.32810
\(584\) −7158.17 −0.507204
\(585\) −16791.1 −1.18671
\(586\) −296.379 −0.0208930
\(587\) 6315.96 0.444102 0.222051 0.975035i \(-0.428725\pi\)
0.222051 + 0.975035i \(0.428725\pi\)
\(588\) 0 0
\(589\) −204.268 −0.0142899
\(590\) −24569.7 −1.71444
\(591\) −382.836 −0.0266460
\(592\) −2589.82 −0.179799
\(593\) −19795.1 −1.37081 −0.685403 0.728164i \(-0.740374\pi\)
−0.685403 + 0.728164i \(0.740374\pi\)
\(594\) −1771.51 −0.122367
\(595\) 0 0
\(596\) −6982.54 −0.479892
\(597\) −857.547 −0.0587890
\(598\) −1880.77 −0.128613
\(599\) 27201.1 1.85544 0.927720 0.373277i \(-0.121766\pi\)
0.927720 + 0.373277i \(0.121766\pi\)
\(600\) 223.735 0.0152232
\(601\) −11695.1 −0.793763 −0.396882 0.917870i \(-0.629908\pi\)
−0.396882 + 0.917870i \(0.629908\pi\)
\(602\) 0 0
\(603\) −8112.89 −0.547898
\(604\) −10081.7 −0.679167
\(605\) −40490.7 −2.72096
\(606\) −238.533 −0.0159897
\(607\) 4523.78 0.302495 0.151247 0.988496i \(-0.451671\pi\)
0.151247 + 0.988496i \(0.451671\pi\)
\(608\) −1102.65 −0.0735501
\(609\) 0 0
\(610\) 21823.7 1.44855
\(611\) 13646.0 0.903530
\(612\) −6148.30 −0.406095
\(613\) 27979.4 1.84352 0.921758 0.387765i \(-0.126753\pi\)
0.921758 + 0.387765i \(0.126753\pi\)
\(614\) 20193.6 1.32728
\(615\) −414.220 −0.0271593
\(616\) 0 0
\(617\) 27419.8 1.78911 0.894553 0.446961i \(-0.147494\pi\)
0.894553 + 0.446961i \(0.147494\pi\)
\(618\) 299.079 0.0194672
\(619\) −4941.83 −0.320887 −0.160443 0.987045i \(-0.551292\pi\)
−0.160443 + 0.987045i \(0.551292\pi\)
\(620\) −361.574 −0.0234213
\(621\) −322.664 −0.0208504
\(622\) 2127.62 0.137154
\(623\) 0 0
\(624\) −170.166 −0.0109168
\(625\) −17504.9 −1.12031
\(626\) −3907.77 −0.249498
\(627\) −565.917 −0.0360455
\(628\) −4490.22 −0.285318
\(629\) −9237.84 −0.585591
\(630\) 0 0
\(631\) −13077.3 −0.825037 −0.412519 0.910949i \(-0.635351\pi\)
−0.412519 + 0.910949i \(0.635351\pi\)
\(632\) −9969.49 −0.627477
\(633\) −633.675 −0.0397888
\(634\) −5879.03 −0.368274
\(635\) −3841.84 −0.240093
\(636\) 308.089 0.0192084
\(637\) 0 0
\(638\) 22849.7 1.41792
\(639\) 23459.3 1.45233
\(640\) −1951.80 −0.120550
\(641\) −1272.72 −0.0784235 −0.0392117 0.999231i \(-0.512485\pi\)
−0.0392117 + 0.999231i \(0.512485\pi\)
\(642\) −755.262 −0.0464296
\(643\) −113.036 −0.00693269 −0.00346634 0.999994i \(-0.501103\pi\)
−0.00346634 + 0.999994i \(0.501103\pi\)
\(644\) 0 0
\(645\) −65.7338 −0.00401281
\(646\) −3933.14 −0.239547
\(647\) 1829.78 0.111184 0.0555919 0.998454i \(-0.482295\pi\)
0.0555919 + 0.998454i \(0.482295\pi\)
\(648\) 5788.19 0.350898
\(649\) 50866.7 3.07657
\(650\) −8791.81 −0.530528
\(651\) 0 0
\(652\) 597.751 0.0359045
\(653\) 1936.86 0.116072 0.0580361 0.998314i \(-0.481516\pi\)
0.0580361 + 0.998314i \(0.481516\pi\)
\(654\) −943.139 −0.0563909
\(655\) −28124.8 −1.67775
\(656\) 1670.90 0.0994480
\(657\) 24098.3 1.43099
\(658\) 0 0
\(659\) −22889.3 −1.35302 −0.676509 0.736434i \(-0.736508\pi\)
−0.676509 + 0.736434i \(0.736508\pi\)
\(660\) −1001.73 −0.0590791
\(661\) −17818.0 −1.04847 −0.524237 0.851573i \(-0.675649\pi\)
−0.524237 + 0.851573i \(0.675649\pi\)
\(662\) −17616.9 −1.03429
\(663\) −606.978 −0.0355552
\(664\) 9791.45 0.572262
\(665\) 0 0
\(666\) 8718.74 0.507274
\(667\) 4161.87 0.241602
\(668\) −7803.11 −0.451963
\(669\) −380.847 −0.0220095
\(670\) −9186.65 −0.529718
\(671\) −45181.7 −2.59943
\(672\) 0 0
\(673\) 20993.6 1.20244 0.601222 0.799082i \(-0.294681\pi\)
0.601222 + 0.799082i \(0.294681\pi\)
\(674\) 7933.46 0.453391
\(675\) −1508.32 −0.0860076
\(676\) −2101.22 −0.119551
\(677\) −5364.75 −0.304555 −0.152278 0.988338i \(-0.548661\pi\)
−0.152278 + 0.988338i \(0.548661\pi\)
\(678\) −881.175 −0.0499134
\(679\) 0 0
\(680\) −6962.04 −0.392621
\(681\) 889.453 0.0500498
\(682\) 748.570 0.0420297
\(683\) −31720.5 −1.77709 −0.888543 0.458793i \(-0.848282\pi\)
−0.888543 + 0.458793i \(0.848282\pi\)
\(684\) 3712.13 0.207510
\(685\) 17839.7 0.995063
\(686\) 0 0
\(687\) 894.138 0.0496557
\(688\) 265.161 0.0146935
\(689\) −12106.6 −0.669409
\(690\) −182.456 −0.0100666
\(691\) 12501.1 0.688228 0.344114 0.938928i \(-0.388179\pi\)
0.344114 + 0.938928i \(0.388179\pi\)
\(692\) −11403.1 −0.626420
\(693\) 0 0
\(694\) 11494.5 0.628709
\(695\) −24678.7 −1.34693
\(696\) 376.552 0.0205074
\(697\) 5960.09 0.323894
\(698\) −16734.4 −0.907460
\(699\) 793.230 0.0429223
\(700\) 0 0
\(701\) −4917.13 −0.264932 −0.132466 0.991188i \(-0.542290\pi\)
−0.132466 + 0.991188i \(0.542290\pi\)
\(702\) 1147.18 0.0616773
\(703\) 5577.48 0.299230
\(704\) 4040.83 0.216327
\(705\) 1323.81 0.0707199
\(706\) −8112.20 −0.432446
\(707\) 0 0
\(708\) 838.257 0.0444966
\(709\) 2043.21 0.108229 0.0541145 0.998535i \(-0.482766\pi\)
0.0541145 + 0.998535i \(0.482766\pi\)
\(710\) 26564.2 1.40414
\(711\) 33562.7 1.77032
\(712\) 690.863 0.0363640
\(713\) 136.345 0.00716153
\(714\) 0 0
\(715\) 39363.6 2.05890
\(716\) 7390.46 0.385747
\(717\) 510.122 0.0265703
\(718\) −5160.27 −0.268216
\(719\) −24690.8 −1.28069 −0.640343 0.768089i \(-0.721208\pi\)
−0.640343 + 0.768089i \(0.721208\pi\)
\(720\) 6570.82 0.340111
\(721\) 0 0
\(722\) −11343.3 −0.584701
\(723\) −1592.38 −0.0819103
\(724\) −13041.7 −0.669461
\(725\) 19455.0 0.996606
\(726\) 1381.44 0.0706202
\(727\) 23243.0 1.18574 0.592872 0.805297i \(-0.297994\pi\)
0.592872 + 0.805297i \(0.297994\pi\)
\(728\) 0 0
\(729\) −19387.7 −0.984995
\(730\) 27287.7 1.38351
\(731\) 945.823 0.0478557
\(732\) −744.570 −0.0375958
\(733\) 35315.4 1.77954 0.889772 0.456406i \(-0.150863\pi\)
0.889772 + 0.456406i \(0.150863\pi\)
\(734\) −1876.51 −0.0943639
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) 19019.2 0.950585
\(738\) −5625.17 −0.280576
\(739\) 10783.2 0.536763 0.268382 0.963313i \(-0.413511\pi\)
0.268382 + 0.963313i \(0.413511\pi\)
\(740\) 9872.69 0.490442
\(741\) 366.472 0.0181683
\(742\) 0 0
\(743\) −4972.73 −0.245534 −0.122767 0.992436i \(-0.539177\pi\)
−0.122767 + 0.992436i \(0.539177\pi\)
\(744\) 12.3360 0.000607878 0
\(745\) 26618.2 1.30901
\(746\) 21903.2 1.07498
\(747\) −32963.3 −1.61454
\(748\) 14413.6 0.704562
\(749\) 0 0
\(750\) 138.704 0.00675303
\(751\) −29604.7 −1.43847 −0.719234 0.694768i \(-0.755507\pi\)
−0.719234 + 0.694768i \(0.755507\pi\)
\(752\) −5340.06 −0.258952
\(753\) −1069.86 −0.0517767
\(754\) −14796.8 −0.714681
\(755\) 38432.4 1.85258
\(756\) 0 0
\(757\) −9958.05 −0.478113 −0.239056 0.971006i \(-0.576838\pi\)
−0.239056 + 0.971006i \(0.576838\pi\)
\(758\) 19041.5 0.912426
\(759\) 377.739 0.0180646
\(760\) 4203.44 0.200625
\(761\) −28654.4 −1.36494 −0.682472 0.730911i \(-0.739095\pi\)
−0.682472 + 0.730911i \(0.739095\pi\)
\(762\) 131.074 0.00623139
\(763\) 0 0
\(764\) 6464.52 0.306123
\(765\) 23438.0 1.10772
\(766\) 6198.50 0.292377
\(767\) −32939.9 −1.55070
\(768\) 66.5907 0.00312876
\(769\) −1580.21 −0.0741011 −0.0370506 0.999313i \(-0.511796\pi\)
−0.0370506 + 0.999313i \(0.511796\pi\)
\(770\) 0 0
\(771\) 555.493 0.0259476
\(772\) −18987.5 −0.885200
\(773\) −36297.7 −1.68892 −0.844461 0.535617i \(-0.820079\pi\)
−0.844461 + 0.535617i \(0.820079\pi\)
\(774\) −892.675 −0.0414555
\(775\) 637.356 0.0295413
\(776\) −2751.51 −0.127286
\(777\) 0 0
\(778\) 8736.69 0.402604
\(779\) −3598.49 −0.165506
\(780\) 648.691 0.0297780
\(781\) −54996.1 −2.51974
\(782\) 2625.30 0.120052
\(783\) −2538.54 −0.115862
\(784\) 0 0
\(785\) 17117.2 0.778268
\(786\) 959.551 0.0435446
\(787\) −3840.61 −0.173956 −0.0869778 0.996210i \(-0.527721\pi\)
−0.0869778 + 0.996210i \(0.527721\pi\)
\(788\) −5887.07 −0.266140
\(789\) 1822.35 0.0822273
\(790\) 38004.8 1.71158
\(791\) 0 0
\(792\) −13603.6 −0.610333
\(793\) 29258.4 1.31021
\(794\) −12612.1 −0.563712
\(795\) −1174.47 −0.0523951
\(796\) −13186.9 −0.587184
\(797\) 24193.7 1.07526 0.537632 0.843179i \(-0.319319\pi\)
0.537632 + 0.843179i \(0.319319\pi\)
\(798\) 0 0
\(799\) −19047.9 −0.843386
\(800\) 3440.49 0.152049
\(801\) −2325.82 −0.102595
\(802\) −166.175 −0.00731650
\(803\) −56494.0 −2.48273
\(804\) 313.426 0.0137484
\(805\) 0 0
\(806\) −484.753 −0.0211845
\(807\) −1708.04 −0.0745052
\(808\) −3668.04 −0.159705
\(809\) −16476.8 −0.716063 −0.358031 0.933710i \(-0.616552\pi\)
−0.358031 + 0.933710i \(0.616552\pi\)
\(810\) −22065.2 −0.957152
\(811\) −2891.58 −0.125200 −0.0625999 0.998039i \(-0.519939\pi\)
−0.0625999 + 0.998039i \(0.519939\pi\)
\(812\) 0 0
\(813\) 1498.14 0.0646275
\(814\) −20439.5 −0.880103
\(815\) −2278.70 −0.0979377
\(816\) 237.528 0.0101901
\(817\) −571.055 −0.0244537
\(818\) −3188.66 −0.136295
\(819\) 0 0
\(820\) −6369.68 −0.271267
\(821\) 36315.1 1.54373 0.771867 0.635785i \(-0.219323\pi\)
0.771867 + 0.635785i \(0.219323\pi\)
\(822\) −608.646 −0.0258260
\(823\) −18744.4 −0.793913 −0.396956 0.917838i \(-0.629934\pi\)
−0.396956 + 0.917838i \(0.629934\pi\)
\(824\) 4599.09 0.194438
\(825\) 1765.77 0.0745166
\(826\) 0 0
\(827\) 25294.4 1.06357 0.531784 0.846880i \(-0.321522\pi\)
0.531784 + 0.846880i \(0.321522\pi\)
\(828\) −2477.78 −0.103996
\(829\) 39438.4 1.65230 0.826148 0.563453i \(-0.190527\pi\)
0.826148 + 0.563453i \(0.190527\pi\)
\(830\) −37326.1 −1.56097
\(831\) 92.8332 0.00387527
\(832\) −2616.73 −0.109037
\(833\) 0 0
\(834\) 841.977 0.0349584
\(835\) 29746.3 1.23283
\(836\) −8702.40 −0.360023
\(837\) −83.1639 −0.00343437
\(838\) 6521.34 0.268826
\(839\) 30165.0 1.24125 0.620627 0.784106i \(-0.286878\pi\)
0.620627 + 0.784106i \(0.286878\pi\)
\(840\) 0 0
\(841\) 8354.24 0.342541
\(842\) −14209.3 −0.581574
\(843\) −240.805 −0.00983838
\(844\) −9744.35 −0.397410
\(845\) 8010.10 0.326101
\(846\) 17977.5 0.730591
\(847\) 0 0
\(848\) 4737.64 0.191853
\(849\) −1802.16 −0.0728503
\(850\) 12272.2 0.495213
\(851\) −3722.87 −0.149963
\(852\) −906.306 −0.0364431
\(853\) −8977.27 −0.360347 −0.180173 0.983635i \(-0.557666\pi\)
−0.180173 + 0.983635i \(0.557666\pi\)
\(854\) 0 0
\(855\) −14151.0 −0.566030
\(856\) −11614.0 −0.463738
\(857\) 40593.6 1.61803 0.809015 0.587789i \(-0.200001\pi\)
0.809015 + 0.587789i \(0.200001\pi\)
\(858\) −1342.99 −0.0534369
\(859\) 14117.7 0.560755 0.280377 0.959890i \(-0.409540\pi\)
0.280377 + 0.959890i \(0.409540\pi\)
\(860\) −1010.82 −0.0400799
\(861\) 0 0
\(862\) 21520.9 0.850352
\(863\) −7080.02 −0.279266 −0.139633 0.990203i \(-0.544592\pi\)
−0.139633 + 0.990203i \(0.544592\pi\)
\(864\) −448.924 −0.0176767
\(865\) 43470.1 1.70870
\(866\) 23074.8 0.905443
\(867\) −430.712 −0.0168717
\(868\) 0 0
\(869\) −78681.7 −3.07145
\(870\) −1435.46 −0.0559386
\(871\) −12316.3 −0.479129
\(872\) −14503.1 −0.563232
\(873\) 9263.09 0.359116
\(874\) −1585.06 −0.0613450
\(875\) 0 0
\(876\) −930.991 −0.0359079
\(877\) −29775.4 −1.14646 −0.573229 0.819395i \(-0.694309\pi\)
−0.573229 + 0.819395i \(0.694309\pi\)
\(878\) 21570.5 0.829120
\(879\) −38.5471 −0.00147914
\(880\) −15404.1 −0.590082
\(881\) −32974.9 −1.26101 −0.630506 0.776184i \(-0.717153\pi\)
−0.630506 + 0.776184i \(0.717153\pi\)
\(882\) 0 0
\(883\) −8286.80 −0.315825 −0.157912 0.987453i \(-0.550476\pi\)
−0.157912 + 0.987453i \(0.550476\pi\)
\(884\) −9333.82 −0.355125
\(885\) −3195.53 −0.121375
\(886\) 4966.91 0.188337
\(887\) 13354.7 0.505533 0.252767 0.967527i \(-0.418659\pi\)
0.252767 + 0.967527i \(0.418659\pi\)
\(888\) −336.832 −0.0127290
\(889\) 0 0
\(890\) −2633.65 −0.0991911
\(891\) 45681.8 1.71762
\(892\) −5856.48 −0.219831
\(893\) 11500.4 0.430960
\(894\) −908.149 −0.0339743
\(895\) −28173.3 −1.05221
\(896\) 0 0
\(897\) −244.613 −0.00910524
\(898\) −6021.57 −0.223767
\(899\) 1072.69 0.0397954
\(900\) −11582.5 −0.428983
\(901\) 16899.1 0.624850
\(902\) 13187.2 0.486791
\(903\) 0 0
\(904\) −13550.3 −0.498535
\(905\) 49716.3 1.82611
\(906\) −1311.22 −0.0480821
\(907\) 53901.6 1.97329 0.986645 0.162885i \(-0.0520801\pi\)
0.986645 + 0.162885i \(0.0520801\pi\)
\(908\) 13677.6 0.499897
\(909\) 12348.6 0.450581
\(910\) 0 0
\(911\) −14861.5 −0.540488 −0.270244 0.962792i \(-0.587104\pi\)
−0.270244 + 0.962792i \(0.587104\pi\)
\(912\) −143.411 −0.00520703
\(913\) 77276.5 2.80118
\(914\) −25813.1 −0.934158
\(915\) 2838.38 0.102551
\(916\) 13749.6 0.495961
\(917\) 0 0
\(918\) −1601.30 −0.0575718
\(919\) 39976.2 1.43492 0.717460 0.696599i \(-0.245304\pi\)
0.717460 + 0.696599i \(0.245304\pi\)
\(920\) −2805.71 −0.100545
\(921\) 2626.38 0.0939655
\(922\) −3856.02 −0.137735
\(923\) 35613.9 1.27004
\(924\) 0 0
\(925\) −17402.8 −0.618596
\(926\) 5760.77 0.204439
\(927\) −15483.0 −0.548576
\(928\) 5790.43 0.204828
\(929\) 7480.52 0.264185 0.132093 0.991237i \(-0.457830\pi\)
0.132093 + 0.991237i \(0.457830\pi\)
\(930\) −47.0264 −0.00165812
\(931\) 0 0
\(932\) 12197.9 0.428708
\(933\) 276.718 0.00970992
\(934\) −13722.9 −0.480758
\(935\) −54946.1 −1.92185
\(936\) 8809.32 0.307630
\(937\) 18057.0 0.629558 0.314779 0.949165i \(-0.398070\pi\)
0.314779 + 0.949165i \(0.398070\pi\)
\(938\) 0 0
\(939\) −508.244 −0.0176634
\(940\) 20356.9 0.706350
\(941\) 18921.5 0.655496 0.327748 0.944765i \(-0.393710\pi\)
0.327748 + 0.944765i \(0.393710\pi\)
\(942\) −583.999 −0.0201993
\(943\) 2401.93 0.0829453
\(944\) 12890.3 0.444432
\(945\) 0 0
\(946\) 2092.71 0.0719238
\(947\) −10147.2 −0.348193 −0.174097 0.984729i \(-0.555701\pi\)
−0.174097 + 0.984729i \(0.555701\pi\)
\(948\) −1296.63 −0.0444226
\(949\) 36583.9 1.25139
\(950\) −7409.49 −0.253048
\(951\) −764.626 −0.0260722
\(952\) 0 0
\(953\) 6284.28 0.213607 0.106804 0.994280i \(-0.465938\pi\)
0.106804 + 0.994280i \(0.465938\pi\)
\(954\) −15949.5 −0.541282
\(955\) −24643.5 −0.835020
\(956\) 7844.42 0.265383
\(957\) 2971.84 0.100382
\(958\) 9160.11 0.308925
\(959\) 0 0
\(960\) −253.851 −0.00853439
\(961\) −29755.9 −0.998820
\(962\) 13236.0 0.443604
\(963\) 39099.2 1.30836
\(964\) −24486.8 −0.818119
\(965\) 72382.4 2.41458
\(966\) 0 0
\(967\) −10750.9 −0.357524 −0.178762 0.983892i \(-0.557209\pi\)
−0.178762 + 0.983892i \(0.557209\pi\)
\(968\) 21243.2 0.705354
\(969\) −511.544 −0.0169589
\(970\) 10489.1 0.347200
\(971\) −21337.3 −0.705198 −0.352599 0.935774i \(-0.614702\pi\)
−0.352599 + 0.935774i \(0.614702\pi\)
\(972\) 2267.93 0.0748394
\(973\) 0 0
\(974\) 17688.6 0.581908
\(975\) −1143.46 −0.0375591
\(976\) −11449.6 −0.375506
\(977\) −713.051 −0.0233496 −0.0116748 0.999932i \(-0.503716\pi\)
−0.0116748 + 0.999932i \(0.503716\pi\)
\(978\) 77.7435 0.00254189
\(979\) 5452.46 0.177999
\(980\) 0 0
\(981\) 48825.4 1.58907
\(982\) −9374.43 −0.304634
\(983\) −31306.7 −1.01580 −0.507898 0.861417i \(-0.669577\pi\)
−0.507898 + 0.861417i \(0.669577\pi\)
\(984\) 217.318 0.00704049
\(985\) 22442.2 0.725956
\(986\) 20654.4 0.667108
\(987\) 0 0
\(988\) 5635.43 0.181465
\(989\) 381.168 0.0122553
\(990\) 51858.5 1.66482
\(991\) 13538.1 0.433956 0.216978 0.976176i \(-0.430380\pi\)
0.216978 + 0.976176i \(0.430380\pi\)
\(992\) 189.698 0.00607148
\(993\) −2291.26 −0.0732234
\(994\) 0 0
\(995\) 50270.1 1.60168
\(996\) 1273.48 0.0405137
\(997\) −44983.5 −1.42893 −0.714464 0.699672i \(-0.753329\pi\)
−0.714464 + 0.699672i \(0.753329\pi\)
\(998\) −20490.2 −0.649907
\(999\) 2270.77 0.0719158
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.l.1.3 5
7.6 odd 2 322.4.a.h.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.a.h.1.3 5 7.6 odd 2
2254.4.a.l.1.3 5 1.1 even 1 trivial