Properties

Label 230.4.a.h.1.2
Level $230$
Weight $4$
Character 230.1
Self dual yes
Analytic conductor $13.570$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,4,Mod(1,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, 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("230.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 68x^{2} - 111x + 342 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.74869\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -4.74869 q^{3} +4.00000 q^{4} -5.00000 q^{5} +9.49738 q^{6} +29.3684 q^{7} -8.00000 q^{8} -4.44993 q^{9} +10.0000 q^{10} -38.1645 q^{11} -18.9948 q^{12} -22.5396 q^{13} -58.7368 q^{14} +23.7435 q^{15} +16.0000 q^{16} -104.049 q^{17} +8.89986 q^{18} +142.000 q^{19} -20.0000 q^{20} -139.461 q^{21} +76.3291 q^{22} -23.0000 q^{23} +37.9895 q^{24} +25.0000 q^{25} +45.0792 q^{26} +149.346 q^{27} +117.474 q^{28} +241.429 q^{29} -47.4869 q^{30} +99.2706 q^{31} -32.0000 q^{32} +181.232 q^{33} +208.097 q^{34} -146.842 q^{35} -17.7997 q^{36} +59.9452 q^{37} -284.000 q^{38} +107.034 q^{39} +40.0000 q^{40} +249.248 q^{41} +278.923 q^{42} -163.863 q^{43} -152.658 q^{44} +22.2496 q^{45} +46.0000 q^{46} -205.591 q^{47} -75.9791 q^{48} +519.502 q^{49} -50.0000 q^{50} +494.095 q^{51} -90.1584 q^{52} +491.274 q^{53} -298.692 q^{54} +190.823 q^{55} -234.947 q^{56} -674.313 q^{57} -482.858 q^{58} +433.734 q^{59} +94.9738 q^{60} +660.902 q^{61} -198.541 q^{62} -130.687 q^{63} +64.0000 q^{64} +112.698 q^{65} -362.463 q^{66} -323.564 q^{67} -416.195 q^{68} +109.220 q^{69} +293.684 q^{70} +893.243 q^{71} +35.5994 q^{72} +196.273 q^{73} -119.890 q^{74} -118.717 q^{75} +567.999 q^{76} -1120.83 q^{77} -214.067 q^{78} -500.211 q^{79} -80.0000 q^{80} -589.050 q^{81} -498.496 q^{82} +800.944 q^{83} -557.846 q^{84} +520.243 q^{85} +327.726 q^{86} -1146.47 q^{87} +305.316 q^{88} -729.016 q^{89} -44.4993 q^{90} -661.952 q^{91} -92.0000 q^{92} -471.405 q^{93} +411.181 q^{94} -709.999 q^{95} +151.958 q^{96} +1139.96 q^{97} -1039.00 q^{98} +169.829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9} + 40 q^{10} - 39 q^{11} - 16 q^{12} - 20 q^{13} + 2 q^{14} + 20 q^{15} + 64 q^{16} - 23 q^{17} - 64 q^{18} + 53 q^{19}+ \cdots - 2665 q^{99}+O(q^{100}) \) 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
\(3\) −4.74869 −0.913886 −0.456943 0.889496i \(-0.651056\pi\)
−0.456943 + 0.889496i \(0.651056\pi\)
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) 9.49738 0.646215
\(7\) 29.3684 1.58574 0.792872 0.609388i \(-0.208585\pi\)
0.792872 + 0.609388i \(0.208585\pi\)
\(8\) −8.00000 −0.353553
\(9\) −4.44993 −0.164812
\(10\) 10.0000 0.316228
\(11\) −38.1645 −1.04609 −0.523047 0.852304i \(-0.675205\pi\)
−0.523047 + 0.852304i \(0.675205\pi\)
\(12\) −18.9948 −0.456943
\(13\) −22.5396 −0.480874 −0.240437 0.970665i \(-0.577291\pi\)
−0.240437 + 0.970665i \(0.577291\pi\)
\(14\) −58.7368 −1.12129
\(15\) 23.7435 0.408702
\(16\) 16.0000 0.250000
\(17\) −104.049 −1.48444 −0.742221 0.670155i \(-0.766228\pi\)
−0.742221 + 0.670155i \(0.766228\pi\)
\(18\) 8.89986 0.116540
\(19\) 142.000 1.71458 0.857289 0.514835i \(-0.172147\pi\)
0.857289 + 0.514835i \(0.172147\pi\)
\(20\) −20.0000 −0.223607
\(21\) −139.461 −1.44919
\(22\) 76.3291 0.739701
\(23\) −23.0000 −0.208514
\(24\) 37.9895 0.323108
\(25\) 25.0000 0.200000
\(26\) 45.0792 0.340029
\(27\) 149.346 1.06451
\(28\) 117.474 0.792872
\(29\) 241.429 1.54594 0.772969 0.634444i \(-0.218771\pi\)
0.772969 + 0.634444i \(0.218771\pi\)
\(30\) −47.4869 −0.288996
\(31\) 99.2706 0.575146 0.287573 0.957759i \(-0.407152\pi\)
0.287573 + 0.957759i \(0.407152\pi\)
\(32\) −32.0000 −0.176777
\(33\) 181.232 0.956011
\(34\) 208.097 1.04966
\(35\) −146.842 −0.709166
\(36\) −17.7997 −0.0824061
\(37\) 59.9452 0.266349 0.133175 0.991093i \(-0.457483\pi\)
0.133175 + 0.991093i \(0.457483\pi\)
\(38\) −284.000 −1.21239
\(39\) 107.034 0.439464
\(40\) 40.0000 0.158114
\(41\) 249.248 0.949414 0.474707 0.880144i \(-0.342554\pi\)
0.474707 + 0.880144i \(0.342554\pi\)
\(42\) 278.923 1.02473
\(43\) −163.863 −0.581136 −0.290568 0.956854i \(-0.593844\pi\)
−0.290568 + 0.956854i \(0.593844\pi\)
\(44\) −152.658 −0.523047
\(45\) 22.2496 0.0737062
\(46\) 46.0000 0.147442
\(47\) −205.591 −0.638052 −0.319026 0.947746i \(-0.603356\pi\)
−0.319026 + 0.947746i \(0.603356\pi\)
\(48\) −75.9791 −0.228472
\(49\) 519.502 1.51458
\(50\) −50.0000 −0.141421
\(51\) 494.095 1.35661
\(52\) −90.1584 −0.240437
\(53\) 491.274 1.27324 0.636620 0.771178i \(-0.280332\pi\)
0.636620 + 0.771178i \(0.280332\pi\)
\(54\) −298.692 −0.752719
\(55\) 190.823 0.467828
\(56\) −234.947 −0.560645
\(57\) −674.313 −1.56693
\(58\) −482.858 −1.09314
\(59\) 433.734 0.957074 0.478537 0.878067i \(-0.341167\pi\)
0.478537 + 0.878067i \(0.341167\pi\)
\(60\) 94.9738 0.204351
\(61\) 660.902 1.38721 0.693605 0.720355i \(-0.256021\pi\)
0.693605 + 0.720355i \(0.256021\pi\)
\(62\) −198.541 −0.406690
\(63\) −130.687 −0.261350
\(64\) 64.0000 0.125000
\(65\) 112.698 0.215053
\(66\) −362.463 −0.676002
\(67\) −323.564 −0.589995 −0.294997 0.955498i \(-0.595319\pi\)
−0.294997 + 0.955498i \(0.595319\pi\)
\(68\) −416.195 −0.742221
\(69\) 109.220 0.190558
\(70\) 293.684 0.501456
\(71\) 893.243 1.49308 0.746538 0.665342i \(-0.231714\pi\)
0.746538 + 0.665342i \(0.231714\pi\)
\(72\) 35.5994 0.0582699
\(73\) 196.273 0.314685 0.157343 0.987544i \(-0.449707\pi\)
0.157343 + 0.987544i \(0.449707\pi\)
\(74\) −119.890 −0.188337
\(75\) −118.717 −0.182777
\(76\) 567.999 0.857289
\(77\) −1120.83 −1.65884
\(78\) −214.067 −0.310748
\(79\) −500.211 −0.712381 −0.356191 0.934413i \(-0.615925\pi\)
−0.356191 + 0.934413i \(0.615925\pi\)
\(80\) −80.0000 −0.111803
\(81\) −589.050 −0.808025
\(82\) −498.496 −0.671337
\(83\) 800.944 1.05922 0.529609 0.848242i \(-0.322339\pi\)
0.529609 + 0.848242i \(0.322339\pi\)
\(84\) −557.846 −0.724595
\(85\) 520.243 0.663863
\(86\) 327.726 0.410925
\(87\) −1146.47 −1.41281
\(88\) 305.316 0.369850
\(89\) −729.016 −0.868264 −0.434132 0.900849i \(-0.642945\pi\)
−0.434132 + 0.900849i \(0.642945\pi\)
\(90\) −44.4993 −0.0521182
\(91\) −661.952 −0.762543
\(92\) −92.0000 −0.104257
\(93\) −471.405 −0.525618
\(94\) 411.181 0.451171
\(95\) −709.999 −0.766783
\(96\) 151.958 0.161554
\(97\) 1139.96 1.19325 0.596626 0.802520i \(-0.296508\pi\)
0.596626 + 0.802520i \(0.296508\pi\)
\(98\) −1039.00 −1.07097
\(99\) 169.829 0.172409
\(100\) 100.000 0.100000
\(101\) −1669.38 −1.64465 −0.822326 0.569017i \(-0.807324\pi\)
−0.822326 + 0.569017i \(0.807324\pi\)
\(102\) −988.190 −0.959269
\(103\) −1110.63 −1.06246 −0.531229 0.847228i \(-0.678270\pi\)
−0.531229 + 0.847228i \(0.678270\pi\)
\(104\) 180.317 0.170015
\(105\) 697.307 0.648097
\(106\) −982.549 −0.900317
\(107\) 39.1892 0.0354071 0.0177036 0.999843i \(-0.494364\pi\)
0.0177036 + 0.999843i \(0.494364\pi\)
\(108\) 597.384 0.532253
\(109\) 807.545 0.709622 0.354811 0.934938i \(-0.384545\pi\)
0.354811 + 0.934938i \(0.384545\pi\)
\(110\) −381.645 −0.330804
\(111\) −284.661 −0.243413
\(112\) 469.894 0.396436
\(113\) 1066.58 0.887923 0.443961 0.896046i \(-0.353573\pi\)
0.443961 + 0.896046i \(0.353573\pi\)
\(114\) 1348.63 1.10799
\(115\) 115.000 0.0932505
\(116\) 965.715 0.772969
\(117\) 100.300 0.0792539
\(118\) −867.468 −0.676753
\(119\) −3055.74 −2.35395
\(120\) −189.948 −0.144498
\(121\) 125.532 0.0943139
\(122\) −1321.80 −0.980906
\(123\) −1183.60 −0.867657
\(124\) 397.082 0.287573
\(125\) −125.000 −0.0894427
\(126\) 261.374 0.184802
\(127\) −641.707 −0.448364 −0.224182 0.974547i \(-0.571971\pi\)
−0.224182 + 0.974547i \(0.571971\pi\)
\(128\) −128.000 −0.0883883
\(129\) 778.134 0.531092
\(130\) −225.396 −0.152066
\(131\) 2389.92 1.59396 0.796979 0.604007i \(-0.206430\pi\)
0.796979 + 0.604007i \(0.206430\pi\)
\(132\) 724.926 0.478006
\(133\) 4170.31 2.71888
\(134\) 647.128 0.417189
\(135\) −746.730 −0.476061
\(136\) 832.390 0.524830
\(137\) 899.291 0.560814 0.280407 0.959881i \(-0.409530\pi\)
0.280407 + 0.959881i \(0.409530\pi\)
\(138\) −218.440 −0.134745
\(139\) 309.341 0.188762 0.0943811 0.995536i \(-0.469913\pi\)
0.0943811 + 0.995536i \(0.469913\pi\)
\(140\) −587.368 −0.354583
\(141\) 976.286 0.583107
\(142\) −1786.49 −1.05576
\(143\) 860.214 0.503040
\(144\) −71.1989 −0.0412030
\(145\) −1207.14 −0.691364
\(146\) −392.546 −0.222516
\(147\) −2466.96 −1.38416
\(148\) 239.781 0.133175
\(149\) 2560.87 1.40802 0.704010 0.710190i \(-0.251391\pi\)
0.704010 + 0.710190i \(0.251391\pi\)
\(150\) 237.435 0.129243
\(151\) −2463.15 −1.32747 −0.663737 0.747966i \(-0.731031\pi\)
−0.663737 + 0.747966i \(0.731031\pi\)
\(152\) −1136.00 −0.606195
\(153\) 463.009 0.244654
\(154\) 2241.66 1.17298
\(155\) −496.353 −0.257213
\(156\) 428.135 0.219732
\(157\) −566.720 −0.288084 −0.144042 0.989572i \(-0.546010\pi\)
−0.144042 + 0.989572i \(0.546010\pi\)
\(158\) 1000.42 0.503730
\(159\) −2332.91 −1.16360
\(160\) 160.000 0.0790569
\(161\) −675.473 −0.330650
\(162\) 1178.10 0.571360
\(163\) 960.902 0.461740 0.230870 0.972985i \(-0.425843\pi\)
0.230870 + 0.972985i \(0.425843\pi\)
\(164\) 996.992 0.474707
\(165\) −906.158 −0.427541
\(166\) −1601.89 −0.748980
\(167\) −4224.70 −1.95759 −0.978794 0.204847i \(-0.934330\pi\)
−0.978794 + 0.204847i \(0.934330\pi\)
\(168\) 1115.69 0.512366
\(169\) −1688.97 −0.768760
\(170\) −1040.49 −0.469422
\(171\) −631.889 −0.282583
\(172\) −655.451 −0.290568
\(173\) 3448.98 1.51573 0.757865 0.652412i \(-0.226243\pi\)
0.757865 + 0.652412i \(0.226243\pi\)
\(174\) 2292.94 0.999008
\(175\) 734.210 0.317149
\(176\) −610.633 −0.261524
\(177\) −2059.67 −0.874657
\(178\) 1458.03 0.613955
\(179\) 1457.82 0.608728 0.304364 0.952556i \(-0.401556\pi\)
0.304364 + 0.952556i \(0.401556\pi\)
\(180\) 88.9986 0.0368531
\(181\) −3634.97 −1.49274 −0.746368 0.665534i \(-0.768204\pi\)
−0.746368 + 0.665534i \(0.768204\pi\)
\(182\) 1323.90 0.539199
\(183\) −3138.42 −1.26775
\(184\) 184.000 0.0737210
\(185\) −299.726 −0.119115
\(186\) 942.811 0.371668
\(187\) 3970.97 1.55287
\(188\) −822.362 −0.319026
\(189\) 4386.05 1.68803
\(190\) 1420.00 0.542197
\(191\) 448.811 0.170025 0.0850127 0.996380i \(-0.472907\pi\)
0.0850127 + 0.996380i \(0.472907\pi\)
\(192\) −303.916 −0.114236
\(193\) 4259.35 1.58857 0.794286 0.607544i \(-0.207845\pi\)
0.794286 + 0.607544i \(0.207845\pi\)
\(194\) −2279.92 −0.843756
\(195\) −535.168 −0.196534
\(196\) 2078.01 0.757292
\(197\) −1767.37 −0.639189 −0.319594 0.947554i \(-0.603547\pi\)
−0.319594 + 0.947554i \(0.603547\pi\)
\(198\) −339.659 −0.121912
\(199\) 1004.29 0.357750 0.178875 0.983872i \(-0.442754\pi\)
0.178875 + 0.983872i \(0.442754\pi\)
\(200\) −200.000 −0.0707107
\(201\) 1536.51 0.539188
\(202\) 3338.76 1.16294
\(203\) 7090.37 2.45146
\(204\) 1976.38 0.678305
\(205\) −1246.24 −0.424591
\(206\) 2221.25 0.751272
\(207\) 102.348 0.0343657
\(208\) −360.634 −0.120218
\(209\) −5419.36 −1.79361
\(210\) −1394.61 −0.458274
\(211\) 5395.17 1.76028 0.880140 0.474714i \(-0.157449\pi\)
0.880140 + 0.474714i \(0.157449\pi\)
\(212\) 1965.10 0.636620
\(213\) −4241.74 −1.36450
\(214\) −78.3783 −0.0250366
\(215\) 819.314 0.259892
\(216\) −1194.77 −0.376360
\(217\) 2915.42 0.912034
\(218\) −1615.09 −0.501779
\(219\) −932.041 −0.287587
\(220\) 763.291 0.233914
\(221\) 2345.22 0.713830
\(222\) 569.322 0.172119
\(223\) −1504.79 −0.451876 −0.225938 0.974142i \(-0.572545\pi\)
−0.225938 + 0.974142i \(0.572545\pi\)
\(224\) −939.788 −0.280323
\(225\) −111.248 −0.0329624
\(226\) −2133.16 −0.627856
\(227\) −1779.44 −0.520288 −0.260144 0.965570i \(-0.583770\pi\)
−0.260144 + 0.965570i \(0.583770\pi\)
\(228\) −2697.25 −0.783465
\(229\) 3976.16 1.14739 0.573694 0.819070i \(-0.305510\pi\)
0.573694 + 0.819070i \(0.305510\pi\)
\(230\) −230.000 −0.0659380
\(231\) 5322.48 1.51599
\(232\) −1931.43 −0.546572
\(233\) −2311.12 −0.649815 −0.324907 0.945746i \(-0.605333\pi\)
−0.324907 + 0.945746i \(0.605333\pi\)
\(234\) −200.599 −0.0560410
\(235\) 1027.95 0.285346
\(236\) 1734.94 0.478537
\(237\) 2375.35 0.651035
\(238\) 6111.49 1.66449
\(239\) 824.267 0.223085 0.111543 0.993760i \(-0.464421\pi\)
0.111543 + 0.993760i \(0.464421\pi\)
\(240\) 379.895 0.102176
\(241\) 3641.83 0.973406 0.486703 0.873567i \(-0.338199\pi\)
0.486703 + 0.873567i \(0.338199\pi\)
\(242\) −251.064 −0.0666900
\(243\) −1235.13 −0.326063
\(244\) 2643.61 0.693605
\(245\) −2597.51 −0.677343
\(246\) 2367.20 0.613526
\(247\) −3200.62 −0.824496
\(248\) −794.165 −0.203345
\(249\) −3803.44 −0.968004
\(250\) 250.000 0.0632456
\(251\) −7767.51 −1.95331 −0.976655 0.214813i \(-0.931086\pi\)
−0.976655 + 0.214813i \(0.931086\pi\)
\(252\) −522.749 −0.130675
\(253\) 877.784 0.218126
\(254\) 1283.41 0.317042
\(255\) −2470.48 −0.606695
\(256\) 256.000 0.0625000
\(257\) −1501.17 −0.364359 −0.182179 0.983265i \(-0.558315\pi\)
−0.182179 + 0.983265i \(0.558315\pi\)
\(258\) −1556.27 −0.375539
\(259\) 1760.49 0.422362
\(260\) 450.792 0.107527
\(261\) −1074.34 −0.254789
\(262\) −4779.84 −1.12710
\(263\) −5430.98 −1.27334 −0.636671 0.771136i \(-0.719689\pi\)
−0.636671 + 0.771136i \(0.719689\pi\)
\(264\) −1449.85 −0.338001
\(265\) −2456.37 −0.569410
\(266\) −8340.61 −1.92254
\(267\) 3461.87 0.793494
\(268\) −1294.26 −0.294997
\(269\) −5014.20 −1.13651 −0.568255 0.822852i \(-0.692381\pi\)
−0.568255 + 0.822852i \(0.692381\pi\)
\(270\) 1493.46 0.336626
\(271\) 7215.54 1.61739 0.808695 0.588228i \(-0.200174\pi\)
0.808695 + 0.588228i \(0.200174\pi\)
\(272\) −1664.78 −0.371111
\(273\) 3143.41 0.696877
\(274\) −1798.58 −0.396556
\(275\) −954.113 −0.209219
\(276\) 436.880 0.0952792
\(277\) −7439.60 −1.61373 −0.806863 0.590738i \(-0.798837\pi\)
−0.806863 + 0.590738i \(0.798837\pi\)
\(278\) −618.681 −0.133475
\(279\) −441.747 −0.0947910
\(280\) 1174.74 0.250728
\(281\) −2605.59 −0.553155 −0.276578 0.960992i \(-0.589200\pi\)
−0.276578 + 0.960992i \(0.589200\pi\)
\(282\) −1952.57 −0.412319
\(283\) −7162.57 −1.50449 −0.752245 0.658884i \(-0.771029\pi\)
−0.752245 + 0.658884i \(0.771029\pi\)
\(284\) 3572.97 0.746538
\(285\) 3371.57 0.700752
\(286\) −1720.43 −0.355703
\(287\) 7320.01 1.50553
\(288\) 142.398 0.0291349
\(289\) 5913.13 1.20357
\(290\) 2414.29 0.488868
\(291\) −5413.32 −1.09050
\(292\) 785.093 0.157343
\(293\) 9310.55 1.85641 0.928205 0.372069i \(-0.121351\pi\)
0.928205 + 0.372069i \(0.121351\pi\)
\(294\) 4933.91 0.978747
\(295\) −2168.67 −0.428016
\(296\) −479.562 −0.0941687
\(297\) −5699.72 −1.11357
\(298\) −5121.74 −0.995620
\(299\) 518.411 0.100269
\(300\) −474.869 −0.0913886
\(301\) −4812.39 −0.921533
\(302\) 4926.31 0.938666
\(303\) 7927.38 1.50302
\(304\) 2272.00 0.428645
\(305\) −3304.51 −0.620380
\(306\) −926.018 −0.172997
\(307\) 3359.07 0.624470 0.312235 0.950005i \(-0.398922\pi\)
0.312235 + 0.950005i \(0.398922\pi\)
\(308\) −4483.32 −0.829419
\(309\) 5274.02 0.970966
\(310\) 992.706 0.181877
\(311\) −5509.20 −1.00450 −0.502248 0.864724i \(-0.667493\pi\)
−0.502248 + 0.864724i \(0.667493\pi\)
\(312\) −856.269 −0.155374
\(313\) 2401.42 0.433661 0.216831 0.976209i \(-0.430428\pi\)
0.216831 + 0.976209i \(0.430428\pi\)
\(314\) 1133.44 0.203706
\(315\) 653.436 0.116879
\(316\) −2000.84 −0.356191
\(317\) −1057.36 −0.187341 −0.0936704 0.995603i \(-0.529860\pi\)
−0.0936704 + 0.995603i \(0.529860\pi\)
\(318\) 4665.82 0.822787
\(319\) −9214.02 −1.61720
\(320\) −320.000 −0.0559017
\(321\) −186.097 −0.0323581
\(322\) 1350.95 0.233805
\(323\) −14774.9 −2.54519
\(324\) −2356.20 −0.404012
\(325\) −563.490 −0.0961748
\(326\) −1921.80 −0.326500
\(327\) −3834.78 −0.648514
\(328\) −1993.98 −0.335669
\(329\) −6037.86 −1.01179
\(330\) 1812.32 0.302317
\(331\) −9680.21 −1.60747 −0.803735 0.594987i \(-0.797157\pi\)
−0.803735 + 0.594987i \(0.797157\pi\)
\(332\) 3203.78 0.529609
\(333\) −266.752 −0.0438976
\(334\) 8449.40 1.38422
\(335\) 1617.82 0.263854
\(336\) −2231.38 −0.362297
\(337\) 467.694 0.0755991 0.0377996 0.999285i \(-0.487965\pi\)
0.0377996 + 0.999285i \(0.487965\pi\)
\(338\) 3377.93 0.543596
\(339\) −5064.85 −0.811460
\(340\) 2080.97 0.331931
\(341\) −3788.62 −0.601657
\(342\) 1263.78 0.199817
\(343\) 5183.59 0.815998
\(344\) 1310.90 0.205463
\(345\) −546.100 −0.0852203
\(346\) −6897.96 −1.07178
\(347\) 3371.55 0.521597 0.260798 0.965393i \(-0.416014\pi\)
0.260798 + 0.965393i \(0.416014\pi\)
\(348\) −4585.88 −0.706406
\(349\) 10958.7 1.68082 0.840412 0.541947i \(-0.182313\pi\)
0.840412 + 0.541947i \(0.182313\pi\)
\(350\) −1468.42 −0.224258
\(351\) −3366.20 −0.511893
\(352\) 1221.27 0.184925
\(353\) −1584.76 −0.238947 −0.119474 0.992837i \(-0.538121\pi\)
−0.119474 + 0.992837i \(0.538121\pi\)
\(354\) 4119.34 0.618476
\(355\) −4466.21 −0.667724
\(356\) −2916.06 −0.434132
\(357\) 14510.8 2.15124
\(358\) −2915.63 −0.430436
\(359\) 5130.67 0.754280 0.377140 0.926156i \(-0.376908\pi\)
0.377140 + 0.926156i \(0.376908\pi\)
\(360\) −177.997 −0.0260591
\(361\) 13304.9 1.93978
\(362\) 7269.94 1.05552
\(363\) −596.112 −0.0861922
\(364\) −2647.81 −0.381271
\(365\) −981.366 −0.140732
\(366\) 6276.84 0.896437
\(367\) 2811.27 0.399856 0.199928 0.979811i \(-0.435929\pi\)
0.199928 + 0.979811i \(0.435929\pi\)
\(368\) −368.000 −0.0521286
\(369\) −1109.14 −0.156475
\(370\) 599.452 0.0842271
\(371\) 14427.9 2.01903
\(372\) −1885.62 −0.262809
\(373\) −1952.42 −0.271026 −0.135513 0.990776i \(-0.543268\pi\)
−0.135513 + 0.990776i \(0.543268\pi\)
\(374\) −7941.94 −1.09804
\(375\) 593.586 0.0817405
\(376\) 1644.72 0.225586
\(377\) −5441.71 −0.743401
\(378\) −8772.10 −1.19362
\(379\) 9609.27 1.30236 0.651181 0.758923i \(-0.274274\pi\)
0.651181 + 0.758923i \(0.274274\pi\)
\(380\) −2840.00 −0.383391
\(381\) 3047.27 0.409754
\(382\) −897.623 −0.120226
\(383\) 5027.44 0.670732 0.335366 0.942088i \(-0.391140\pi\)
0.335366 + 0.942088i \(0.391140\pi\)
\(384\) 607.833 0.0807769
\(385\) 5604.15 0.741855
\(386\) −8518.70 −1.12329
\(387\) 729.178 0.0957783
\(388\) 4559.84 0.596626
\(389\) 5892.29 0.767997 0.383999 0.923334i \(-0.374547\pi\)
0.383999 + 0.923334i \(0.374547\pi\)
\(390\) 1070.34 0.138971
\(391\) 2393.12 0.309528
\(392\) −4156.02 −0.535486
\(393\) −11349.0 −1.45670
\(394\) 3534.75 0.451975
\(395\) 2501.05 0.318587
\(396\) 679.318 0.0862046
\(397\) −2454.41 −0.310285 −0.155143 0.987892i \(-0.549584\pi\)
−0.155143 + 0.987892i \(0.549584\pi\)
\(398\) −2008.58 −0.252967
\(399\) −19803.5 −2.48475
\(400\) 400.000 0.0500000
\(401\) 9458.39 1.17788 0.588939 0.808177i \(-0.299546\pi\)
0.588939 + 0.808177i \(0.299546\pi\)
\(402\) −3073.01 −0.381264
\(403\) −2237.52 −0.276573
\(404\) −6677.53 −0.822326
\(405\) 2945.25 0.361360
\(406\) −14180.7 −1.73345
\(407\) −2287.78 −0.278627
\(408\) −3952.76 −0.479634
\(409\) −5857.25 −0.708123 −0.354062 0.935222i \(-0.615200\pi\)
−0.354062 + 0.935222i \(0.615200\pi\)
\(410\) 2492.48 0.300231
\(411\) −4270.45 −0.512521
\(412\) −4442.51 −0.531229
\(413\) 12738.1 1.51767
\(414\) −204.697 −0.0243002
\(415\) −4004.72 −0.473696
\(416\) 721.267 0.0850073
\(417\) −1468.96 −0.172507
\(418\) 10838.7 1.26827
\(419\) −5252.61 −0.612426 −0.306213 0.951963i \(-0.599062\pi\)
−0.306213 + 0.951963i \(0.599062\pi\)
\(420\) 2789.23 0.324049
\(421\) −203.517 −0.0235602 −0.0117801 0.999931i \(-0.503750\pi\)
−0.0117801 + 0.999931i \(0.503750\pi\)
\(422\) −10790.3 −1.24471
\(423\) 914.863 0.105159
\(424\) −3930.20 −0.450158
\(425\) −2601.22 −0.296888
\(426\) 8483.47 0.964849
\(427\) 19409.6 2.19976
\(428\) 156.757 0.0177036
\(429\) −4084.89 −0.459721
\(430\) −1638.63 −0.183771
\(431\) 3107.72 0.347317 0.173659 0.984806i \(-0.444441\pi\)
0.173659 + 0.984806i \(0.444441\pi\)
\(432\) 2389.54 0.266126
\(433\) −5713.46 −0.634114 −0.317057 0.948406i \(-0.602695\pi\)
−0.317057 + 0.948406i \(0.602695\pi\)
\(434\) −5830.83 −0.644905
\(435\) 5732.35 0.631828
\(436\) 3230.18 0.354811
\(437\) −3266.00 −0.357514
\(438\) 1864.08 0.203354
\(439\) −4587.14 −0.498706 −0.249353 0.968413i \(-0.580218\pi\)
−0.249353 + 0.968413i \(0.580218\pi\)
\(440\) −1526.58 −0.165402
\(441\) −2311.75 −0.249622
\(442\) −4690.43 −0.504754
\(443\) 5268.01 0.564990 0.282495 0.959269i \(-0.408838\pi\)
0.282495 + 0.959269i \(0.408838\pi\)
\(444\) −1138.64 −0.121707
\(445\) 3645.08 0.388299
\(446\) 3009.58 0.319525
\(447\) −12160.8 −1.28677
\(448\) 1879.58 0.198218
\(449\) 16866.8 1.77282 0.886409 0.462902i \(-0.153192\pi\)
0.886409 + 0.462902i \(0.153192\pi\)
\(450\) 222.496 0.0233080
\(451\) −9512.43 −0.993177
\(452\) 4266.31 0.443961
\(453\) 11696.8 1.21316
\(454\) 3558.87 0.367899
\(455\) 3309.76 0.341020
\(456\) 5394.51 0.553993
\(457\) 9124.25 0.933948 0.466974 0.884271i \(-0.345344\pi\)
0.466974 + 0.884271i \(0.345344\pi\)
\(458\) −7952.31 −0.811326
\(459\) −15539.3 −1.58020
\(460\) 460.000 0.0466252
\(461\) 6011.92 0.607382 0.303691 0.952771i \(-0.401781\pi\)
0.303691 + 0.952771i \(0.401781\pi\)
\(462\) −10645.0 −1.07197
\(463\) −8584.09 −0.861634 −0.430817 0.902439i \(-0.641775\pi\)
−0.430817 + 0.902439i \(0.641775\pi\)
\(464\) 3862.86 0.386484
\(465\) 2357.03 0.235063
\(466\) 4622.25 0.459488
\(467\) 3954.09 0.391806 0.195903 0.980623i \(-0.437236\pi\)
0.195903 + 0.980623i \(0.437236\pi\)
\(468\) 401.198 0.0396269
\(469\) −9502.56 −0.935581
\(470\) −2055.91 −0.201770
\(471\) 2691.18 0.263276
\(472\) −3469.87 −0.338377
\(473\) 6253.75 0.607923
\(474\) −4750.69 −0.460351
\(475\) 3549.99 0.342916
\(476\) −12223.0 −1.17697
\(477\) −2186.14 −0.209845
\(478\) −1648.53 −0.157745
\(479\) −95.3377 −0.00909413 −0.00454707 0.999990i \(-0.501447\pi\)
−0.00454707 + 0.999990i \(0.501447\pi\)
\(480\) −759.791 −0.0722490
\(481\) −1351.14 −0.128080
\(482\) −7283.66 −0.688302
\(483\) 3207.61 0.302177
\(484\) 502.127 0.0471570
\(485\) −5699.80 −0.533638
\(486\) 2470.25 0.230561
\(487\) 13915.2 1.29478 0.647391 0.762158i \(-0.275860\pi\)
0.647391 + 0.762158i \(0.275860\pi\)
\(488\) −5287.22 −0.490453
\(489\) −4563.03 −0.421978
\(490\) 5195.02 0.478954
\(491\) 6291.33 0.578256 0.289128 0.957290i \(-0.406635\pi\)
0.289128 + 0.957290i \(0.406635\pi\)
\(492\) −4734.41 −0.433828
\(493\) −25120.3 −2.29486
\(494\) 6401.24 0.583007
\(495\) −849.147 −0.0771037
\(496\) 1588.33 0.143786
\(497\) 26233.1 2.36764
\(498\) 7606.87 0.684482
\(499\) −638.332 −0.0572658 −0.0286329 0.999590i \(-0.509115\pi\)
−0.0286329 + 0.999590i \(0.509115\pi\)
\(500\) −500.000 −0.0447214
\(501\) 20061.8 1.78901
\(502\) 15535.0 1.38120
\(503\) 15063.4 1.33527 0.667637 0.744487i \(-0.267306\pi\)
0.667637 + 0.744487i \(0.267306\pi\)
\(504\) 1045.50 0.0924011
\(505\) 8346.91 0.735510
\(506\) −1755.57 −0.154238
\(507\) 8020.38 0.702559
\(508\) −2566.83 −0.224182
\(509\) −13623.1 −1.18631 −0.593157 0.805087i \(-0.702119\pi\)
−0.593157 + 0.805087i \(0.702119\pi\)
\(510\) 4940.95 0.428998
\(511\) 5764.23 0.499010
\(512\) −512.000 −0.0441942
\(513\) 21207.1 1.82518
\(514\) 3002.33 0.257640
\(515\) 5553.13 0.475146
\(516\) 3112.54 0.265546
\(517\) 7846.27 0.667463
\(518\) −3520.99 −0.298655
\(519\) −16378.2 −1.38520
\(520\) −901.584 −0.0760328
\(521\) −21659.4 −1.82133 −0.910666 0.413143i \(-0.864431\pi\)
−0.910666 + 0.413143i \(0.864431\pi\)
\(522\) 2148.68 0.180163
\(523\) −3813.85 −0.318868 −0.159434 0.987209i \(-0.550967\pi\)
−0.159434 + 0.987209i \(0.550967\pi\)
\(524\) 9559.69 0.796979
\(525\) −3486.54 −0.289838
\(526\) 10862.0 0.900388
\(527\) −10329.0 −0.853771
\(528\) 2899.71 0.239003
\(529\) 529.000 0.0434783
\(530\) 4912.74 0.402634
\(531\) −1930.09 −0.157737
\(532\) 16681.2 1.35944
\(533\) −5617.95 −0.456549
\(534\) −6923.74 −0.561085
\(535\) −195.946 −0.0158345
\(536\) 2588.51 0.208595
\(537\) −6922.72 −0.556308
\(538\) 10028.4 0.803634
\(539\) −19826.6 −1.58440
\(540\) −2986.92 −0.238031
\(541\) 9727.32 0.773031 0.386516 0.922283i \(-0.373679\pi\)
0.386516 + 0.922283i \(0.373679\pi\)
\(542\) −14431.1 −1.14367
\(543\) 17261.3 1.36419
\(544\) 3329.56 0.262415
\(545\) −4037.73 −0.317353
\(546\) −6286.81 −0.492767
\(547\) 782.647 0.0611766 0.0305883 0.999532i \(-0.490262\pi\)
0.0305883 + 0.999532i \(0.490262\pi\)
\(548\) 3597.16 0.280407
\(549\) −2940.97 −0.228629
\(550\) 1908.23 0.147940
\(551\) 34282.8 2.65063
\(552\) −873.759 −0.0673726
\(553\) −14690.4 −1.12965
\(554\) 14879.2 1.14108
\(555\) 1423.31 0.108858
\(556\) 1237.36 0.0943811
\(557\) 3472.87 0.264184 0.132092 0.991237i \(-0.457831\pi\)
0.132092 + 0.991237i \(0.457831\pi\)
\(558\) 883.494 0.0670274
\(559\) 3693.40 0.279453
\(560\) −2349.47 −0.177292
\(561\) −18856.9 −1.41914
\(562\) 5211.18 0.391140
\(563\) 7544.75 0.564784 0.282392 0.959299i \(-0.408872\pi\)
0.282392 + 0.959299i \(0.408872\pi\)
\(564\) 3905.14 0.291554
\(565\) −5332.89 −0.397091
\(566\) 14325.1 1.06383
\(567\) −17299.5 −1.28132
\(568\) −7145.94 −0.527882
\(569\) 13222.5 0.974193 0.487096 0.873348i \(-0.338056\pi\)
0.487096 + 0.873348i \(0.338056\pi\)
\(570\) −6743.13 −0.495507
\(571\) 4069.49 0.298254 0.149127 0.988818i \(-0.452354\pi\)
0.149127 + 0.988818i \(0.452354\pi\)
\(572\) 3440.85 0.251520
\(573\) −2131.27 −0.155384
\(574\) −14640.0 −1.06457
\(575\) −575.000 −0.0417029
\(576\) −284.795 −0.0206015
\(577\) 846.627 0.0610841 0.0305421 0.999533i \(-0.490277\pi\)
0.0305421 + 0.999533i \(0.490277\pi\)
\(578\) −11826.3 −0.851051
\(579\) −20226.3 −1.45177
\(580\) −4828.58 −0.345682
\(581\) 23522.4 1.67965
\(582\) 10826.6 0.771097
\(583\) −18749.3 −1.33193
\(584\) −1570.19 −0.111258
\(585\) −501.498 −0.0354434
\(586\) −18621.1 −1.31268
\(587\) 4702.77 0.330672 0.165336 0.986237i \(-0.447129\pi\)
0.165336 + 0.986237i \(0.447129\pi\)
\(588\) −9867.82 −0.692079
\(589\) 14096.4 0.986133
\(590\) 4337.34 0.302653
\(591\) 8392.71 0.584146
\(592\) 959.123 0.0665874
\(593\) −14016.5 −0.970640 −0.485320 0.874337i \(-0.661297\pi\)
−0.485320 + 0.874337i \(0.661297\pi\)
\(594\) 11399.4 0.787415
\(595\) 15278.7 1.05272
\(596\) 10243.5 0.704010
\(597\) −4769.07 −0.326943
\(598\) −1036.82 −0.0709010
\(599\) 12885.0 0.878910 0.439455 0.898265i \(-0.355172\pi\)
0.439455 + 0.898265i \(0.355172\pi\)
\(600\) 949.738 0.0646215
\(601\) −4753.41 −0.322622 −0.161311 0.986904i \(-0.551572\pi\)
−0.161311 + 0.986904i \(0.551572\pi\)
\(602\) 9624.77 0.651622
\(603\) 1439.84 0.0972383
\(604\) −9852.61 −0.663737
\(605\) −627.659 −0.0421785
\(606\) −15854.8 −1.06280
\(607\) −6800.06 −0.454705 −0.227352 0.973813i \(-0.573007\pi\)
−0.227352 + 0.973813i \(0.573007\pi\)
\(608\) −4543.99 −0.303097
\(609\) −33670.0 −2.24036
\(610\) 6609.02 0.438675
\(611\) 4633.93 0.306823
\(612\) 1852.04 0.122327
\(613\) 20842.3 1.37327 0.686634 0.727003i \(-0.259087\pi\)
0.686634 + 0.727003i \(0.259087\pi\)
\(614\) −6718.14 −0.441567
\(615\) 5918.01 0.388028
\(616\) 8966.65 0.586488
\(617\) 18917.7 1.23436 0.617179 0.786823i \(-0.288276\pi\)
0.617179 + 0.786823i \(0.288276\pi\)
\(618\) −10548.0 −0.686577
\(619\) −28044.8 −1.82103 −0.910513 0.413480i \(-0.864313\pi\)
−0.910513 + 0.413480i \(0.864313\pi\)
\(620\) −1985.41 −0.128607
\(621\) −3434.96 −0.221965
\(622\) 11018.4 0.710285
\(623\) −21410.0 −1.37684
\(624\) 1712.54 0.109866
\(625\) 625.000 0.0400000
\(626\) −4802.83 −0.306645
\(627\) 25734.9 1.63916
\(628\) −2266.88 −0.144042
\(629\) −6237.22 −0.395380
\(630\) −1306.87 −0.0826461
\(631\) −25796.2 −1.62746 −0.813732 0.581241i \(-0.802567\pi\)
−0.813732 + 0.581241i \(0.802567\pi\)
\(632\) 4001.69 0.251865
\(633\) −25620.0 −1.60870
\(634\) 2114.71 0.132470
\(635\) 3208.54 0.200515
\(636\) −9331.64 −0.581798
\(637\) −11709.4 −0.728324
\(638\) 18428.0 1.14353
\(639\) −3974.87 −0.246077
\(640\) 640.000 0.0395285
\(641\) −26482.3 −1.63181 −0.815903 0.578188i \(-0.803760\pi\)
−0.815903 + 0.578188i \(0.803760\pi\)
\(642\) 372.195 0.0228806
\(643\) 30458.1 1.86804 0.934020 0.357219i \(-0.116275\pi\)
0.934020 + 0.357219i \(0.116275\pi\)
\(644\) −2701.89 −0.165325
\(645\) −3890.67 −0.237512
\(646\) 29549.8 1.79972
\(647\) −6746.24 −0.409926 −0.204963 0.978770i \(-0.565707\pi\)
−0.204963 + 0.978770i \(0.565707\pi\)
\(648\) 4712.40 0.285680
\(649\) −16553.3 −1.00119
\(650\) 1126.98 0.0680058
\(651\) −13844.4 −0.833495
\(652\) 3843.61 0.230870
\(653\) 12976.2 0.777640 0.388820 0.921314i \(-0.372883\pi\)
0.388820 + 0.921314i \(0.372883\pi\)
\(654\) 7669.57 0.458569
\(655\) −11949.6 −0.712840
\(656\) 3987.97 0.237354
\(657\) −873.401 −0.0518640
\(658\) 12075.7 0.715442
\(659\) −6538.56 −0.386504 −0.193252 0.981149i \(-0.561903\pi\)
−0.193252 + 0.981149i \(0.561903\pi\)
\(660\) −3624.63 −0.213771
\(661\) −25177.1 −1.48151 −0.740753 0.671777i \(-0.765531\pi\)
−0.740753 + 0.671777i \(0.765531\pi\)
\(662\) 19360.4 1.13665
\(663\) −11136.7 −0.652359
\(664\) −6407.55 −0.374490
\(665\) −20851.5 −1.21592
\(666\) 533.504 0.0310403
\(667\) −5552.86 −0.322350
\(668\) −16898.8 −0.978794
\(669\) 7145.79 0.412963
\(670\) −3235.64 −0.186573
\(671\) −25223.0 −1.45115
\(672\) 4462.77 0.256183
\(673\) 18339.3 1.05041 0.525207 0.850975i \(-0.323988\pi\)
0.525207 + 0.850975i \(0.323988\pi\)
\(674\) −935.388 −0.0534567
\(675\) 3733.65 0.212901
\(676\) −6755.86 −0.384380
\(677\) 31876.9 1.80965 0.904823 0.425789i \(-0.140003\pi\)
0.904823 + 0.425789i \(0.140003\pi\)
\(678\) 10129.7 0.573789
\(679\) 33478.8 1.89219
\(680\) −4161.95 −0.234711
\(681\) 8450.00 0.475484
\(682\) 7577.23 0.425436
\(683\) −28843.7 −1.61592 −0.807959 0.589239i \(-0.799428\pi\)
−0.807959 + 0.589239i \(0.799428\pi\)
\(684\) −2527.56 −0.141292
\(685\) −4496.45 −0.250804
\(686\) −10367.2 −0.576998
\(687\) −18881.5 −1.04858
\(688\) −2621.80 −0.145284
\(689\) −11073.1 −0.612268
\(690\) 1092.20 0.0602599
\(691\) −18327.7 −1.00900 −0.504499 0.863413i \(-0.668323\pi\)
−0.504499 + 0.863413i \(0.668323\pi\)
\(692\) 13795.9 0.757865
\(693\) 4987.62 0.273397
\(694\) −6743.09 −0.368825
\(695\) −1546.70 −0.0844170
\(696\) 9171.77 0.499504
\(697\) −25933.9 −1.40935
\(698\) −21917.5 −1.18852
\(699\) 10974.8 0.593857
\(700\) 2936.84 0.158574
\(701\) −8329.48 −0.448788 −0.224394 0.974499i \(-0.572040\pi\)
−0.224394 + 0.974499i \(0.572040\pi\)
\(702\) 6732.40 0.361963
\(703\) 8512.20 0.456677
\(704\) −2442.53 −0.130762
\(705\) −4881.43 −0.260773
\(706\) 3169.52 0.168961
\(707\) −49027.1 −2.60800
\(708\) −8238.68 −0.437328
\(709\) −6169.85 −0.326818 −0.163409 0.986558i \(-0.552249\pi\)
−0.163409 + 0.986558i \(0.552249\pi\)
\(710\) 8932.43 0.472152
\(711\) 2225.90 0.117409
\(712\) 5832.12 0.306978
\(713\) −2283.22 −0.119926
\(714\) −29021.6 −1.52115
\(715\) −4301.07 −0.224966
\(716\) 5831.27 0.304364
\(717\) −3914.19 −0.203875
\(718\) −10261.3 −0.533356
\(719\) 28740.8 1.49075 0.745377 0.666644i \(-0.232270\pi\)
0.745377 + 0.666644i \(0.232270\pi\)
\(720\) 355.994 0.0184266
\(721\) −32617.3 −1.68479
\(722\) −26609.9 −1.37163
\(723\) −17293.9 −0.889583
\(724\) −14539.9 −0.746368
\(725\) 6035.72 0.309188
\(726\) 1192.22 0.0609471
\(727\) 11174.0 0.570041 0.285021 0.958521i \(-0.408000\pi\)
0.285021 + 0.958521i \(0.408000\pi\)
\(728\) 5295.62 0.269600
\(729\) 21769.6 1.10601
\(730\) 1962.73 0.0995123
\(731\) 17049.7 0.862663
\(732\) −12553.7 −0.633876
\(733\) −23560.7 −1.18722 −0.593612 0.804751i \(-0.702299\pi\)
−0.593612 + 0.804751i \(0.702299\pi\)
\(734\) −5622.54 −0.282741
\(735\) 12334.8 0.619014
\(736\) 736.000 0.0368605
\(737\) 12348.7 0.617191
\(738\) 2218.27 0.110645
\(739\) 22713.6 1.13063 0.565313 0.824877i \(-0.308755\pi\)
0.565313 + 0.824877i \(0.308755\pi\)
\(740\) −1198.90 −0.0595575
\(741\) 15198.8 0.753495
\(742\) −28855.9 −1.42767
\(743\) −15882.7 −0.784224 −0.392112 0.919917i \(-0.628255\pi\)
−0.392112 + 0.919917i \(0.628255\pi\)
\(744\) 3771.24 0.185834
\(745\) −12804.4 −0.629685
\(746\) 3904.84 0.191644
\(747\) −3564.14 −0.174572
\(748\) 15883.9 0.776433
\(749\) 1150.92 0.0561466
\(750\) −1187.17 −0.0577992
\(751\) −30250.6 −1.46985 −0.734927 0.678146i \(-0.762784\pi\)
−0.734927 + 0.678146i \(0.762784\pi\)
\(752\) −3289.45 −0.159513
\(753\) 36885.5 1.78510
\(754\) 10883.4 0.525664
\(755\) 12315.8 0.593664
\(756\) 17544.2 0.844017
\(757\) −9611.05 −0.461453 −0.230726 0.973019i \(-0.574110\pi\)
−0.230726 + 0.973019i \(0.574110\pi\)
\(758\) −19218.5 −0.920908
\(759\) −4168.33 −0.199342
\(760\) 5679.99 0.271099
\(761\) 5892.64 0.280694 0.140347 0.990102i \(-0.455178\pi\)
0.140347 + 0.990102i \(0.455178\pi\)
\(762\) −6094.54 −0.289740
\(763\) 23716.3 1.12528
\(764\) 1795.25 0.0850127
\(765\) −2315.05 −0.109413
\(766\) −10054.9 −0.474279
\(767\) −9776.19 −0.460232
\(768\) −1215.67 −0.0571179
\(769\) 1683.72 0.0789553 0.0394777 0.999220i \(-0.487431\pi\)
0.0394777 + 0.999220i \(0.487431\pi\)
\(770\) −11208.3 −0.524571
\(771\) 7128.57 0.332982
\(772\) 17037.4 0.794286
\(773\) 19880.8 0.925048 0.462524 0.886607i \(-0.346944\pi\)
0.462524 + 0.886607i \(0.346944\pi\)
\(774\) −1458.36 −0.0677255
\(775\) 2481.76 0.115029
\(776\) −9119.68 −0.421878
\(777\) −8360.04 −0.385991
\(778\) −11784.6 −0.543056
\(779\) 35393.2 1.62785
\(780\) −2140.67 −0.0982671
\(781\) −34090.2 −1.56190
\(782\) −4786.24 −0.218869
\(783\) 36056.4 1.64566
\(784\) 8312.04 0.378646
\(785\) 2833.60 0.128835
\(786\) 22698.0 1.03004
\(787\) −7622.64 −0.345258 −0.172629 0.984987i \(-0.555226\pi\)
−0.172629 + 0.984987i \(0.555226\pi\)
\(788\) −7069.50 −0.319594
\(789\) 25790.1 1.16369
\(790\) −5002.11 −0.225275
\(791\) 31323.7 1.40802
\(792\) −1358.64 −0.0609558
\(793\) −14896.5 −0.667074
\(794\) 4908.82 0.219405
\(795\) 11664.6 0.520376
\(796\) 4017.16 0.178875
\(797\) −22380.9 −0.994693 −0.497347 0.867552i \(-0.665692\pi\)
−0.497347 + 0.867552i \(0.665692\pi\)
\(798\) 39607.0 1.75698
\(799\) 21391.4 0.947152
\(800\) −800.000 −0.0353553
\(801\) 3244.07 0.143100
\(802\) −18916.8 −0.832886
\(803\) −7490.67 −0.329191
\(804\) 6146.03 0.269594
\(805\) 3377.36 0.147871
\(806\) 4475.04 0.195566
\(807\) 23810.9 1.03864
\(808\) 13355.1 0.581472
\(809\) 8117.18 0.352762 0.176381 0.984322i \(-0.443561\pi\)
0.176381 + 0.984322i \(0.443561\pi\)
\(810\) −5890.50 −0.255520
\(811\) 7221.05 0.312658 0.156329 0.987705i \(-0.450034\pi\)
0.156329 + 0.987705i \(0.450034\pi\)
\(812\) 28361.5 1.22573
\(813\) −34264.4 −1.47811
\(814\) 4575.56 0.197019
\(815\) −4804.51 −0.206497
\(816\) 7905.52 0.339153
\(817\) −23268.5 −0.996403
\(818\) 11714.5 0.500719
\(819\) 2945.64 0.125676
\(820\) −4984.96 −0.212296
\(821\) 34803.3 1.47947 0.739735 0.672899i \(-0.234951\pi\)
0.739735 + 0.672899i \(0.234951\pi\)
\(822\) 8540.91 0.362407
\(823\) 490.883 0.0207911 0.0103956 0.999946i \(-0.496691\pi\)
0.0103956 + 0.999946i \(0.496691\pi\)
\(824\) 8885.01 0.375636
\(825\) 4530.79 0.191202
\(826\) −25476.1 −1.07316
\(827\) 30952.0 1.30146 0.650729 0.759310i \(-0.274463\pi\)
0.650729 + 0.759310i \(0.274463\pi\)
\(828\) 409.393 0.0171829
\(829\) 8587.63 0.359784 0.179892 0.983686i \(-0.442425\pi\)
0.179892 + 0.983686i \(0.442425\pi\)
\(830\) 8009.44 0.334954
\(831\) 35328.4 1.47476
\(832\) −1442.53 −0.0601092
\(833\) −54053.5 −2.24831
\(834\) 2937.93 0.121981
\(835\) 21123.5 0.875460
\(836\) −21677.4 −0.896806
\(837\) 14825.7 0.612246
\(838\) 10505.2 0.433051
\(839\) 3077.94 0.126653 0.0633267 0.997993i \(-0.479829\pi\)
0.0633267 + 0.997993i \(0.479829\pi\)
\(840\) −5578.46 −0.229137
\(841\) 33898.9 1.38992
\(842\) 407.035 0.0166596
\(843\) 12373.2 0.505521
\(844\) 21580.7 0.880140
\(845\) 8444.83 0.343800
\(846\) −1829.73 −0.0743585
\(847\) 3686.67 0.149558
\(848\) 7860.39 0.318310
\(849\) 34012.8 1.37493
\(850\) 5202.43 0.209932
\(851\) −1378.74 −0.0555377
\(852\) −16966.9 −0.682251
\(853\) −9193.14 −0.369012 −0.184506 0.982831i \(-0.559068\pi\)
−0.184506 + 0.982831i \(0.559068\pi\)
\(854\) −38819.3 −1.55547
\(855\) 3159.44 0.126375
\(856\) −313.513 −0.0125183
\(857\) 21445.8 0.854813 0.427407 0.904059i \(-0.359427\pi\)
0.427407 + 0.904059i \(0.359427\pi\)
\(858\) 8169.78 0.325072
\(859\) −40276.7 −1.59979 −0.799897 0.600137i \(-0.795113\pi\)
−0.799897 + 0.600137i \(0.795113\pi\)
\(860\) 3277.26 0.129946
\(861\) −34760.5 −1.37588
\(862\) −6215.44 −0.245590
\(863\) 43713.4 1.72424 0.862120 0.506703i \(-0.169136\pi\)
0.862120 + 0.506703i \(0.169136\pi\)
\(864\) −4779.07 −0.188180
\(865\) −17244.9 −0.677855
\(866\) 11426.9 0.448386
\(867\) −28079.6 −1.09992
\(868\) 11661.7 0.456017
\(869\) 19090.3 0.745218
\(870\) −11464.7 −0.446770
\(871\) 7293.01 0.283713
\(872\) −6460.36 −0.250889
\(873\) −5072.74 −0.196662
\(874\) 6531.99 0.252801
\(875\) −3671.05 −0.141833
\(876\) −3728.16 −0.143793
\(877\) 24740.5 0.952596 0.476298 0.879284i \(-0.341978\pi\)
0.476298 + 0.879284i \(0.341978\pi\)
\(878\) 9174.27 0.352639
\(879\) −44212.9 −1.69655
\(880\) 3053.16 0.116957
\(881\) −44027.2 −1.68367 −0.841835 0.539735i \(-0.818524\pi\)
−0.841835 + 0.539735i \(0.818524\pi\)
\(882\) 4623.50 0.176509
\(883\) 30245.0 1.15269 0.576344 0.817207i \(-0.304479\pi\)
0.576344 + 0.817207i \(0.304479\pi\)
\(884\) 9380.87 0.356915
\(885\) 10298.3 0.391158
\(886\) −10536.0 −0.399509
\(887\) −7317.82 −0.277010 −0.138505 0.990362i \(-0.544230\pi\)
−0.138505 + 0.990362i \(0.544230\pi\)
\(888\) 2277.29 0.0860595
\(889\) −18845.9 −0.710991
\(890\) −7290.16 −0.274569
\(891\) 22480.8 0.845270
\(892\) −6019.17 −0.225938
\(893\) −29193.8 −1.09399
\(894\) 24321.6 0.909883
\(895\) −7289.08 −0.272232
\(896\) −3759.15 −0.140161
\(897\) −2461.77 −0.0916346
\(898\) −33733.7 −1.25357
\(899\) 23966.8 0.889140
\(900\) −444.993 −0.0164812
\(901\) −51116.5 −1.89005
\(902\) 19024.9 0.702282
\(903\) 22852.5 0.842176
\(904\) −8532.63 −0.313928
\(905\) 18174.8 0.667572
\(906\) −23393.5 −0.857834
\(907\) −35436.0 −1.29728 −0.648640 0.761096i \(-0.724662\pi\)
−0.648640 + 0.761096i \(0.724662\pi\)
\(908\) −7117.75 −0.260144
\(909\) 7428.63 0.271058
\(910\) −6619.52 −0.241137
\(911\) −11359.1 −0.413112 −0.206556 0.978435i \(-0.566225\pi\)
−0.206556 + 0.978435i \(0.566225\pi\)
\(912\) −10789.0 −0.391732
\(913\) −30567.7 −1.10804
\(914\) −18248.5 −0.660401
\(915\) 15692.1 0.566956
\(916\) 15904.6 0.573694
\(917\) 70188.2 2.52761
\(918\) 31078.5 1.11737
\(919\) 40517.5 1.45435 0.727175 0.686452i \(-0.240833\pi\)
0.727175 + 0.686452i \(0.240833\pi\)
\(920\) −920.000 −0.0329690
\(921\) −15951.2 −0.570695
\(922\) −12023.8 −0.429484
\(923\) −20133.3 −0.717982
\(924\) 21289.9 0.757995
\(925\) 1498.63 0.0532699
\(926\) 17168.2 0.609267
\(927\) 4942.21 0.175106
\(928\) −7725.72 −0.273286
\(929\) 16242.2 0.573614 0.286807 0.957988i \(-0.407406\pi\)
0.286807 + 0.957988i \(0.407406\pi\)
\(930\) −4714.05 −0.166215
\(931\) 73769.2 2.59687
\(932\) −9244.50 −0.324907
\(933\) 26161.5 0.917994
\(934\) −7908.19 −0.277049
\(935\) −19854.9 −0.694463
\(936\) −802.397 −0.0280205
\(937\) −47445.0 −1.65417 −0.827087 0.562074i \(-0.810004\pi\)
−0.827087 + 0.562074i \(0.810004\pi\)
\(938\) 19005.1 0.661556
\(939\) −11403.6 −0.396317
\(940\) 4111.81 0.142673
\(941\) −48063.5 −1.66506 −0.832532 0.553976i \(-0.813110\pi\)
−0.832532 + 0.553976i \(0.813110\pi\)
\(942\) −5382.36 −0.186164
\(943\) −5732.70 −0.197967
\(944\) 6939.74 0.239268
\(945\) −21930.3 −0.754912
\(946\) −12507.5 −0.429867
\(947\) 13745.4 0.471663 0.235831 0.971794i \(-0.424219\pi\)
0.235831 + 0.971794i \(0.424219\pi\)
\(948\) 9501.39 0.325518
\(949\) −4423.92 −0.151324
\(950\) −7099.99 −0.242478
\(951\) 5021.06 0.171208
\(952\) 24445.9 0.832245
\(953\) −13999.1 −0.475839 −0.237920 0.971285i \(-0.576465\pi\)
−0.237920 + 0.971285i \(0.576465\pi\)
\(954\) 4372.27 0.148383
\(955\) −2244.06 −0.0760377
\(956\) 3297.07 0.111543
\(957\) 43754.5 1.47793
\(958\) 190.675 0.00643052
\(959\) 26410.7 0.889308
\(960\) 1519.58 0.0510878
\(961\) −19936.4 −0.669207
\(962\) 2702.28 0.0905666
\(963\) −174.389 −0.00583552
\(964\) 14567.3 0.486703
\(965\) −21296.7 −0.710431
\(966\) −6415.23 −0.213671
\(967\) −800.187 −0.0266104 −0.0133052 0.999911i \(-0.504235\pi\)
−0.0133052 + 0.999911i \(0.504235\pi\)
\(968\) −1004.25 −0.0333450
\(969\) 70161.4 2.32602
\(970\) 11399.6 0.377339
\(971\) −11363.5 −0.375563 −0.187782 0.982211i \(-0.560130\pi\)
−0.187782 + 0.982211i \(0.560130\pi\)
\(972\) −4940.50 −0.163032
\(973\) 9084.84 0.299328
\(974\) −27830.4 −0.915549
\(975\) 2675.84 0.0878928
\(976\) 10574.4 0.346803
\(977\) −17444.0 −0.571220 −0.285610 0.958346i \(-0.592196\pi\)
−0.285610 + 0.958346i \(0.592196\pi\)
\(978\) 9126.06 0.298384
\(979\) 27822.5 0.908286
\(980\) −10390.0 −0.338671
\(981\) −3593.52 −0.116954
\(982\) −12582.7 −0.408889
\(983\) −54032.7 −1.75318 −0.876590 0.481237i \(-0.840188\pi\)
−0.876590 + 0.481237i \(0.840188\pi\)
\(984\) 9468.81 0.306763
\(985\) 8836.87 0.285854
\(986\) 50240.7 1.62271
\(987\) 28671.9 0.924659
\(988\) −12802.5 −0.412248
\(989\) 3768.84 0.121175
\(990\) 1698.29 0.0545205
\(991\) 28869.3 0.925392 0.462696 0.886517i \(-0.346882\pi\)
0.462696 + 0.886517i \(0.346882\pi\)
\(992\) −3176.66 −0.101672
\(993\) 45968.3 1.46904
\(994\) −52466.2 −1.67417
\(995\) −5021.45 −0.159991
\(996\) −15213.7 −0.484002
\(997\) 3358.78 0.106694 0.0533469 0.998576i \(-0.483011\pi\)
0.0533469 + 0.998576i \(0.483011\pi\)
\(998\) 1276.66 0.0404931
\(999\) 8952.57 0.283530
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 230.4.a.h.1.2 4
3.2 odd 2 2070.4.a.bj.1.4 4
4.3 odd 2 1840.4.a.m.1.3 4
5.2 odd 4 1150.4.b.n.599.3 8
5.3 odd 4 1150.4.b.n.599.6 8
5.4 even 2 1150.4.a.p.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.h.1.2 4 1.1 even 1 trivial
1150.4.a.p.1.3 4 5.4 even 2
1150.4.b.n.599.3 8 5.2 odd 4
1150.4.b.n.599.6 8 5.3 odd 4
1840.4.a.m.1.3 4 4.3 odd 2
2070.4.a.bj.1.4 4 3.2 odd 2