Properties

Label 2013.4.a.b.1.16
Level $2013$
Weight $4$
Character 2013.1
Self dual yes
Analytic conductor $118.771$
Analytic rank $1$
Dimension $36$
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] = [2013,4,Mod(1,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2013.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2013.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: \(118.770844842\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 2013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.691390 q^{2} -3.00000 q^{3} -7.52198 q^{4} -5.77110 q^{5} +2.07417 q^{6} +9.57605 q^{7} +10.7317 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-0.691390 q^{2} -3.00000 q^{3} -7.52198 q^{4} -5.77110 q^{5} +2.07417 q^{6} +9.57605 q^{7} +10.7317 q^{8} +9.00000 q^{9} +3.99008 q^{10} -11.0000 q^{11} +22.5659 q^{12} +4.33531 q^{13} -6.62079 q^{14} +17.3133 q^{15} +52.7560 q^{16} -93.4391 q^{17} -6.22251 q^{18} -19.5165 q^{19} +43.4101 q^{20} -28.7282 q^{21} +7.60529 q^{22} +105.934 q^{23} -32.1952 q^{24} -91.6944 q^{25} -2.99739 q^{26} -27.0000 q^{27} -72.0309 q^{28} -157.498 q^{29} -11.9702 q^{30} +208.500 q^{31} -122.329 q^{32} +33.0000 q^{33} +64.6029 q^{34} -55.2643 q^{35} -67.6978 q^{36} -270.554 q^{37} +13.4935 q^{38} -13.0059 q^{39} -61.9339 q^{40} +401.469 q^{41} +19.8624 q^{42} +125.478 q^{43} +82.7418 q^{44} -51.9399 q^{45} -73.2414 q^{46} +22.5963 q^{47} -158.268 q^{48} -251.299 q^{49} +63.3966 q^{50} +280.317 q^{51} -32.6101 q^{52} +722.523 q^{53} +18.6675 q^{54} +63.4821 q^{55} +102.768 q^{56} +58.5495 q^{57} +108.892 q^{58} -208.134 q^{59} -130.230 q^{60} +61.0000 q^{61} -144.155 q^{62} +86.1845 q^{63} -337.471 q^{64} -25.0195 q^{65} -22.8159 q^{66} +441.709 q^{67} +702.847 q^{68} -317.801 q^{69} +38.2092 q^{70} +1021.30 q^{71} +96.5857 q^{72} -950.129 q^{73} +187.058 q^{74} +275.083 q^{75} +146.803 q^{76} -105.337 q^{77} +8.99217 q^{78} +1068.50 q^{79} -304.460 q^{80} +81.0000 q^{81} -277.571 q^{82} +448.493 q^{83} +216.093 q^{84} +539.246 q^{85} -86.7541 q^{86} +472.493 q^{87} -118.049 q^{88} -1018.27 q^{89} +35.9107 q^{90} +41.5151 q^{91} -796.830 q^{92} -625.501 q^{93} -15.6228 q^{94} +112.632 q^{95} +366.987 q^{96} +1383.13 q^{97} +173.746 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.691390 −0.244443 −0.122222 0.992503i \(-0.539002\pi\)
−0.122222 + 0.992503i \(0.539002\pi\)
\(3\) −3.00000 −0.577350
\(4\) −7.52198 −0.940247
\(5\) −5.77110 −0.516183 −0.258091 0.966121i \(-0.583094\pi\)
−0.258091 + 0.966121i \(0.583094\pi\)
\(6\) 2.07417 0.141129
\(7\) 9.57605 0.517058 0.258529 0.966003i \(-0.416762\pi\)
0.258529 + 0.966003i \(0.416762\pi\)
\(8\) 10.7317 0.474281
\(9\) 9.00000 0.333333
\(10\) 3.99008 0.126177
\(11\) −11.0000 −0.301511
\(12\) 22.5659 0.542852
\(13\) 4.33531 0.0924922 0.0462461 0.998930i \(-0.485274\pi\)
0.0462461 + 0.998930i \(0.485274\pi\)
\(14\) −6.62079 −0.126391
\(15\) 17.3133 0.298018
\(16\) 52.7560 0.824313
\(17\) −93.4391 −1.33308 −0.666539 0.745470i \(-0.732225\pi\)
−0.666539 + 0.745470i \(0.732225\pi\)
\(18\) −6.22251 −0.0814811
\(19\) −19.5165 −0.235652 −0.117826 0.993034i \(-0.537593\pi\)
−0.117826 + 0.993034i \(0.537593\pi\)
\(20\) 43.4101 0.485339
\(21\) −28.7282 −0.298524
\(22\) 7.60529 0.0737024
\(23\) 105.934 0.960377 0.480188 0.877165i \(-0.340568\pi\)
0.480188 + 0.877165i \(0.340568\pi\)
\(24\) −32.1952 −0.273826
\(25\) −91.6944 −0.733555
\(26\) −2.99739 −0.0226091
\(27\) −27.0000 −0.192450
\(28\) −72.0309 −0.486163
\(29\) −157.498 −1.00850 −0.504252 0.863557i \(-0.668232\pi\)
−0.504252 + 0.863557i \(0.668232\pi\)
\(30\) −11.9702 −0.0728485
\(31\) 208.500 1.20799 0.603997 0.796987i \(-0.293574\pi\)
0.603997 + 0.796987i \(0.293574\pi\)
\(32\) −122.329 −0.675778
\(33\) 33.0000 0.174078
\(34\) 64.6029 0.325862
\(35\) −55.2643 −0.266896
\(36\) −67.6978 −0.313416
\(37\) −270.554 −1.20213 −0.601064 0.799201i \(-0.705256\pi\)
−0.601064 + 0.799201i \(0.705256\pi\)
\(38\) 13.4935 0.0576037
\(39\) −13.0059 −0.0534004
\(40\) −61.9339 −0.244815
\(41\) 401.469 1.52924 0.764620 0.644481i \(-0.222927\pi\)
0.764620 + 0.644481i \(0.222927\pi\)
\(42\) 19.8624 0.0729721
\(43\) 125.478 0.445004 0.222502 0.974932i \(-0.428578\pi\)
0.222502 + 0.974932i \(0.428578\pi\)
\(44\) 82.7418 0.283495
\(45\) −51.9399 −0.172061
\(46\) −73.2414 −0.234758
\(47\) 22.5963 0.0701277 0.0350639 0.999385i \(-0.488837\pi\)
0.0350639 + 0.999385i \(0.488837\pi\)
\(48\) −158.268 −0.475917
\(49\) −251.299 −0.732651
\(50\) 63.3966 0.179313
\(51\) 280.317 0.769653
\(52\) −32.6101 −0.0869655
\(53\) 722.523 1.87257 0.936284 0.351244i \(-0.114241\pi\)
0.936284 + 0.351244i \(0.114241\pi\)
\(54\) 18.6675 0.0470431
\(55\) 63.4821 0.155635
\(56\) 102.768 0.245231
\(57\) 58.5495 0.136054
\(58\) 108.892 0.246522
\(59\) −208.134 −0.459266 −0.229633 0.973277i \(-0.573753\pi\)
−0.229633 + 0.973277i \(0.573753\pi\)
\(60\) −130.230 −0.280211
\(61\) 61.0000 0.128037
\(62\) −144.155 −0.295286
\(63\) 86.1845 0.172353
\(64\) −337.471 −0.659123
\(65\) −25.0195 −0.0477429
\(66\) −22.8159 −0.0425521
\(67\) 441.709 0.805423 0.402711 0.915327i \(-0.368068\pi\)
0.402711 + 0.915327i \(0.368068\pi\)
\(68\) 702.847 1.25342
\(69\) −317.801 −0.554474
\(70\) 38.2092 0.0652410
\(71\) 1021.30 1.70714 0.853568 0.520982i \(-0.174434\pi\)
0.853568 + 0.520982i \(0.174434\pi\)
\(72\) 96.5857 0.158094
\(73\) −950.129 −1.52335 −0.761673 0.647962i \(-0.775622\pi\)
−0.761673 + 0.647962i \(0.775622\pi\)
\(74\) 187.058 0.293852
\(75\) 275.083 0.423518
\(76\) 146.803 0.221572
\(77\) −105.337 −0.155899
\(78\) 8.99217 0.0130534
\(79\) 1068.50 1.52172 0.760858 0.648919i \(-0.224779\pi\)
0.760858 + 0.648919i \(0.224779\pi\)
\(80\) −304.460 −0.425496
\(81\) 81.0000 0.111111
\(82\) −277.571 −0.373813
\(83\) 448.493 0.593115 0.296558 0.955015i \(-0.404161\pi\)
0.296558 + 0.955015i \(0.404161\pi\)
\(84\) 216.093 0.280686
\(85\) 539.246 0.688111
\(86\) −86.7541 −0.108778
\(87\) 472.493 0.582260
\(88\) −118.049 −0.143001
\(89\) −1018.27 −1.21276 −0.606382 0.795173i \(-0.707380\pi\)
−0.606382 + 0.795173i \(0.707380\pi\)
\(90\) 35.9107 0.0420591
\(91\) 41.5151 0.0478238
\(92\) −796.830 −0.902992
\(93\) −625.501 −0.697435
\(94\) −15.6228 −0.0171422
\(95\) 112.632 0.121640
\(96\) 366.987 0.390161
\(97\) 1383.13 1.44779 0.723895 0.689910i \(-0.242350\pi\)
0.723895 + 0.689910i \(0.242350\pi\)
\(98\) 173.746 0.179092
\(99\) −99.0000 −0.100504
\(100\) 689.724 0.689724
\(101\) −1365.97 −1.34573 −0.672866 0.739764i \(-0.734937\pi\)
−0.672866 + 0.739764i \(0.734937\pi\)
\(102\) −193.809 −0.188136
\(103\) −34.9333 −0.0334182 −0.0167091 0.999860i \(-0.505319\pi\)
−0.0167091 + 0.999860i \(0.505319\pi\)
\(104\) 46.5254 0.0438672
\(105\) 165.793 0.154093
\(106\) −499.545 −0.457737
\(107\) 1822.90 1.64698 0.823490 0.567331i \(-0.192024\pi\)
0.823490 + 0.567331i \(0.192024\pi\)
\(108\) 203.093 0.180951
\(109\) 589.626 0.518128 0.259064 0.965860i \(-0.416586\pi\)
0.259064 + 0.965860i \(0.416586\pi\)
\(110\) −43.8909 −0.0380439
\(111\) 811.661 0.694049
\(112\) 505.194 0.426218
\(113\) −782.039 −0.651045 −0.325522 0.945534i \(-0.605540\pi\)
−0.325522 + 0.945534i \(0.605540\pi\)
\(114\) −40.4806 −0.0332575
\(115\) −611.353 −0.495730
\(116\) 1184.69 0.948243
\(117\) 39.0178 0.0308307
\(118\) 143.902 0.112265
\(119\) −894.778 −0.689278
\(120\) 185.802 0.141344
\(121\) 121.000 0.0909091
\(122\) −42.1748 −0.0312978
\(123\) −1204.41 −0.882907
\(124\) −1568.34 −1.13581
\(125\) 1250.56 0.894831
\(126\) −59.5871 −0.0421305
\(127\) 56.0503 0.0391627 0.0195813 0.999808i \(-0.493767\pi\)
0.0195813 + 0.999808i \(0.493767\pi\)
\(128\) 1211.96 0.836897
\(129\) −376.433 −0.256923
\(130\) 17.2982 0.0116704
\(131\) 1040.66 0.694065 0.347032 0.937853i \(-0.387189\pi\)
0.347032 + 0.937853i \(0.387189\pi\)
\(132\) −248.225 −0.163676
\(133\) −186.891 −0.121846
\(134\) −305.393 −0.196880
\(135\) 155.820 0.0993394
\(136\) −1002.76 −0.632253
\(137\) −617.195 −0.384894 −0.192447 0.981307i \(-0.561642\pi\)
−0.192447 + 0.981307i \(0.561642\pi\)
\(138\) 219.724 0.135537
\(139\) 735.445 0.448774 0.224387 0.974500i \(-0.427962\pi\)
0.224387 + 0.974500i \(0.427962\pi\)
\(140\) 415.697 0.250949
\(141\) −67.7888 −0.0404883
\(142\) −706.120 −0.417298
\(143\) −47.6884 −0.0278874
\(144\) 474.804 0.274771
\(145\) 908.935 0.520572
\(146\) 656.910 0.372372
\(147\) 753.898 0.422996
\(148\) 2035.10 1.13030
\(149\) 1817.50 0.999297 0.499649 0.866228i \(-0.333462\pi\)
0.499649 + 0.866228i \(0.333462\pi\)
\(150\) −190.190 −0.103526
\(151\) 42.7845 0.0230579 0.0115290 0.999934i \(-0.496330\pi\)
0.0115290 + 0.999934i \(0.496330\pi\)
\(152\) −209.446 −0.111765
\(153\) −840.952 −0.444359
\(154\) 72.8286 0.0381084
\(155\) −1203.28 −0.623545
\(156\) 97.8303 0.0502096
\(157\) −3035.49 −1.54305 −0.771525 0.636199i \(-0.780506\pi\)
−0.771525 + 0.636199i \(0.780506\pi\)
\(158\) −738.749 −0.371973
\(159\) −2167.57 −1.08113
\(160\) 705.972 0.348825
\(161\) 1014.42 0.496571
\(162\) −56.0026 −0.0271604
\(163\) −1475.93 −0.709225 −0.354613 0.935013i \(-0.615387\pi\)
−0.354613 + 0.935013i \(0.615387\pi\)
\(164\) −3019.84 −1.43786
\(165\) −190.446 −0.0898559
\(166\) −310.084 −0.144983
\(167\) −1020.18 −0.472717 −0.236359 0.971666i \(-0.575954\pi\)
−0.236359 + 0.971666i \(0.575954\pi\)
\(168\) −308.303 −0.141584
\(169\) −2178.21 −0.991445
\(170\) −372.829 −0.168204
\(171\) −175.649 −0.0785508
\(172\) −943.841 −0.418414
\(173\) −3434.79 −1.50949 −0.754747 0.656016i \(-0.772240\pi\)
−0.754747 + 0.656016i \(0.772240\pi\)
\(174\) −326.677 −0.142329
\(175\) −878.071 −0.379291
\(176\) −580.316 −0.248540
\(177\) 624.401 0.265157
\(178\) 704.019 0.296452
\(179\) −17.3569 −0.00724758 −0.00362379 0.999993i \(-0.501153\pi\)
−0.00362379 + 0.999993i \(0.501153\pi\)
\(180\) 390.691 0.161780
\(181\) 3102.71 1.27416 0.637078 0.770799i \(-0.280143\pi\)
0.637078 + 0.770799i \(0.280143\pi\)
\(182\) −28.7032 −0.0116902
\(183\) −183.000 −0.0739221
\(184\) 1136.85 0.455488
\(185\) 1561.39 0.620518
\(186\) 432.465 0.170483
\(187\) 1027.83 0.401938
\(188\) −169.969 −0.0659374
\(189\) −258.553 −0.0995079
\(190\) −77.8724 −0.0297340
\(191\) 49.1965 0.0186373 0.00931867 0.999957i \(-0.497034\pi\)
0.00931867 + 0.999957i \(0.497034\pi\)
\(192\) 1012.41 0.380545
\(193\) −835.282 −0.311528 −0.155764 0.987794i \(-0.549784\pi\)
−0.155764 + 0.987794i \(0.549784\pi\)
\(194\) −956.283 −0.353903
\(195\) 75.0585 0.0275644
\(196\) 1890.27 0.688873
\(197\) 1664.85 0.602111 0.301056 0.953607i \(-0.402661\pi\)
0.301056 + 0.953607i \(0.402661\pi\)
\(198\) 68.4476 0.0245675
\(199\) −4475.48 −1.59426 −0.797131 0.603807i \(-0.793650\pi\)
−0.797131 + 0.603807i \(0.793650\pi\)
\(200\) −984.041 −0.347911
\(201\) −1325.13 −0.465011
\(202\) 944.417 0.328955
\(203\) −1508.21 −0.521455
\(204\) −2108.54 −0.723664
\(205\) −2316.91 −0.789367
\(206\) 24.1525 0.00816887
\(207\) 953.402 0.320126
\(208\) 228.714 0.0762425
\(209\) 214.682 0.0710519
\(210\) −114.628 −0.0376669
\(211\) −235.867 −0.0769562 −0.0384781 0.999259i \(-0.512251\pi\)
−0.0384781 + 0.999259i \(0.512251\pi\)
\(212\) −5434.80 −1.76068
\(213\) −3063.91 −0.985615
\(214\) −1260.34 −0.402593
\(215\) −724.144 −0.229703
\(216\) −289.757 −0.0912753
\(217\) 1996.61 0.624603
\(218\) −407.661 −0.126653
\(219\) 2850.39 0.879504
\(220\) −477.511 −0.146335
\(221\) −405.087 −0.123299
\(222\) −561.175 −0.169656
\(223\) −3441.70 −1.03351 −0.516756 0.856133i \(-0.672860\pi\)
−0.516756 + 0.856133i \(0.672860\pi\)
\(224\) −1171.43 −0.349417
\(225\) −825.250 −0.244518
\(226\) 540.694 0.159144
\(227\) −2413.10 −0.705563 −0.352782 0.935706i \(-0.614764\pi\)
−0.352782 + 0.935706i \(0.614764\pi\)
\(228\) −440.409 −0.127924
\(229\) −4545.17 −1.31159 −0.655793 0.754941i \(-0.727665\pi\)
−0.655793 + 0.754941i \(0.727665\pi\)
\(230\) 422.683 0.121178
\(231\) 316.010 0.0900083
\(232\) −1690.23 −0.478313
\(233\) −3810.75 −1.07146 −0.535731 0.844389i \(-0.679964\pi\)
−0.535731 + 0.844389i \(0.679964\pi\)
\(234\) −26.9765 −0.00753637
\(235\) −130.405 −0.0361987
\(236\) 1565.58 0.431824
\(237\) −3205.50 −0.878563
\(238\) 618.640 0.168489
\(239\) −18.7088 −0.00506347 −0.00253173 0.999997i \(-0.500806\pi\)
−0.00253173 + 0.999997i \(0.500806\pi\)
\(240\) 913.380 0.245660
\(241\) 3310.23 0.884775 0.442388 0.896824i \(-0.354132\pi\)
0.442388 + 0.896824i \(0.354132\pi\)
\(242\) −83.6582 −0.0222221
\(243\) −243.000 −0.0641500
\(244\) −458.841 −0.120386
\(245\) 1450.27 0.378182
\(246\) 832.714 0.215821
\(247\) −84.6101 −0.0217960
\(248\) 2237.57 0.572928
\(249\) −1345.48 −0.342435
\(250\) −864.628 −0.218736
\(251\) 3873.30 0.974025 0.487012 0.873395i \(-0.338087\pi\)
0.487012 + 0.873395i \(0.338087\pi\)
\(252\) −648.278 −0.162054
\(253\) −1165.27 −0.289565
\(254\) −38.7526 −0.00957306
\(255\) −1617.74 −0.397281
\(256\) 1861.84 0.454550
\(257\) −1747.26 −0.424089 −0.212044 0.977260i \(-0.568012\pi\)
−0.212044 + 0.977260i \(0.568012\pi\)
\(258\) 260.262 0.0628032
\(259\) −2590.84 −0.621570
\(260\) 188.196 0.0448901
\(261\) −1417.48 −0.336168
\(262\) −719.499 −0.169660
\(263\) 1521.15 0.356648 0.178324 0.983972i \(-0.442932\pi\)
0.178324 + 0.983972i \(0.442932\pi\)
\(264\) 354.148 0.0825616
\(265\) −4169.75 −0.966587
\(266\) 129.215 0.0297844
\(267\) 3054.80 0.700190
\(268\) −3322.52 −0.757297
\(269\) −4991.11 −1.13128 −0.565638 0.824653i \(-0.691370\pi\)
−0.565638 + 0.824653i \(0.691370\pi\)
\(270\) −107.732 −0.0242828
\(271\) 1377.97 0.308877 0.154438 0.988002i \(-0.450643\pi\)
0.154438 + 0.988002i \(0.450643\pi\)
\(272\) −4929.48 −1.09887
\(273\) −124.545 −0.0276111
\(274\) 426.723 0.0940849
\(275\) 1008.64 0.221175
\(276\) 2390.49 0.521343
\(277\) 1232.77 0.267400 0.133700 0.991022i \(-0.457314\pi\)
0.133700 + 0.991022i \(0.457314\pi\)
\(278\) −508.480 −0.109700
\(279\) 1876.50 0.402664
\(280\) −593.082 −0.126584
\(281\) −2368.83 −0.502892 −0.251446 0.967871i \(-0.580906\pi\)
−0.251446 + 0.967871i \(0.580906\pi\)
\(282\) 46.8685 0.00989708
\(283\) −983.445 −0.206572 −0.103286 0.994652i \(-0.532936\pi\)
−0.103286 + 0.994652i \(0.532936\pi\)
\(284\) −7682.23 −1.60513
\(285\) −337.895 −0.0702287
\(286\) 32.9713 0.00681690
\(287\) 3844.48 0.790706
\(288\) −1100.96 −0.225259
\(289\) 3817.87 0.777095
\(290\) −628.429 −0.127250
\(291\) −4149.39 −0.835882
\(292\) 7146.85 1.43232
\(293\) −6326.87 −1.26150 −0.630750 0.775986i \(-0.717253\pi\)
−0.630750 + 0.775986i \(0.717253\pi\)
\(294\) −521.237 −0.103399
\(295\) 1201.16 0.237065
\(296\) −2903.51 −0.570146
\(297\) 297.000 0.0580259
\(298\) −1256.60 −0.244272
\(299\) 459.255 0.0888274
\(300\) −2069.17 −0.398212
\(301\) 1201.58 0.230093
\(302\) −29.5807 −0.00563636
\(303\) 4097.90 0.776959
\(304\) −1029.61 −0.194251
\(305\) −352.037 −0.0660904
\(306\) 581.426 0.108621
\(307\) −167.480 −0.0311354 −0.0155677 0.999879i \(-0.504956\pi\)
−0.0155677 + 0.999879i \(0.504956\pi\)
\(308\) 792.339 0.146584
\(309\) 104.800 0.0192940
\(310\) 831.933 0.152421
\(311\) 4838.40 0.882189 0.441094 0.897461i \(-0.354590\pi\)
0.441094 + 0.897461i \(0.354590\pi\)
\(312\) −139.576 −0.0253268
\(313\) −7205.76 −1.30126 −0.650629 0.759396i \(-0.725495\pi\)
−0.650629 + 0.759396i \(0.725495\pi\)
\(314\) 2098.71 0.377188
\(315\) −497.379 −0.0889655
\(316\) −8037.23 −1.43079
\(317\) −6064.61 −1.07452 −0.537259 0.843417i \(-0.680540\pi\)
−0.537259 + 0.843417i \(0.680540\pi\)
\(318\) 1498.63 0.264274
\(319\) 1732.48 0.304075
\(320\) 1947.58 0.340228
\(321\) −5468.71 −0.950884
\(322\) −701.363 −0.121383
\(323\) 1823.61 0.314143
\(324\) −609.280 −0.104472
\(325\) −397.524 −0.0678482
\(326\) 1020.44 0.173365
\(327\) −1768.88 −0.299141
\(328\) 4308.46 0.725289
\(329\) 216.383 0.0362601
\(330\) 131.673 0.0219647
\(331\) −9237.23 −1.53391 −0.766955 0.641701i \(-0.778229\pi\)
−0.766955 + 0.641701i \(0.778229\pi\)
\(332\) −3373.56 −0.557675
\(333\) −2434.98 −0.400710
\(334\) 705.341 0.115553
\(335\) −2549.14 −0.415745
\(336\) −1515.58 −0.246077
\(337\) 5647.02 0.912798 0.456399 0.889775i \(-0.349139\pi\)
0.456399 + 0.889775i \(0.349139\pi\)
\(338\) 1505.99 0.242352
\(339\) 2346.12 0.375881
\(340\) −4056.20 −0.646995
\(341\) −2293.51 −0.364224
\(342\) 121.442 0.0192012
\(343\) −5691.04 −0.895881
\(344\) 1346.60 0.211057
\(345\) 1834.06 0.286210
\(346\) 2374.78 0.368986
\(347\) −2697.74 −0.417356 −0.208678 0.977984i \(-0.566916\pi\)
−0.208678 + 0.977984i \(0.566916\pi\)
\(348\) −3554.08 −0.547468
\(349\) −1031.77 −0.158251 −0.0791254 0.996865i \(-0.525213\pi\)
−0.0791254 + 0.996865i \(0.525213\pi\)
\(350\) 607.089 0.0927151
\(351\) −117.053 −0.0178001
\(352\) 1345.62 0.203755
\(353\) 10049.0 1.51516 0.757580 0.652742i \(-0.226381\pi\)
0.757580 + 0.652742i \(0.226381\pi\)
\(354\) −431.705 −0.0648160
\(355\) −5894.05 −0.881193
\(356\) 7659.38 1.14030
\(357\) 2684.33 0.397955
\(358\) 12.0004 0.00177162
\(359\) −7448.59 −1.09505 −0.547523 0.836791i \(-0.684429\pi\)
−0.547523 + 0.836791i \(0.684429\pi\)
\(360\) −557.405 −0.0816051
\(361\) −6478.11 −0.944468
\(362\) −2145.18 −0.311459
\(363\) −363.000 −0.0524864
\(364\) −312.276 −0.0449662
\(365\) 5483.29 0.786325
\(366\) 126.524 0.0180698
\(367\) 6837.94 0.972582 0.486291 0.873797i \(-0.338350\pi\)
0.486291 + 0.873797i \(0.338350\pi\)
\(368\) 5588.63 0.791651
\(369\) 3613.22 0.509747
\(370\) −1079.53 −0.151681
\(371\) 6918.91 0.968227
\(372\) 4705.01 0.655762
\(373\) −6477.65 −0.899195 −0.449598 0.893231i \(-0.648433\pi\)
−0.449598 + 0.893231i \(0.648433\pi\)
\(374\) −710.632 −0.0982510
\(375\) −3751.69 −0.516631
\(376\) 242.497 0.0332602
\(377\) −682.801 −0.0932787
\(378\) 178.761 0.0243240
\(379\) 6982.26 0.946318 0.473159 0.880977i \(-0.343114\pi\)
0.473159 + 0.880977i \(0.343114\pi\)
\(380\) −847.213 −0.114371
\(381\) −168.151 −0.0226106
\(382\) −34.0140 −0.00455577
\(383\) 8827.37 1.17770 0.588848 0.808244i \(-0.299582\pi\)
0.588848 + 0.808244i \(0.299582\pi\)
\(384\) −3635.87 −0.483182
\(385\) 607.907 0.0804723
\(386\) 577.506 0.0761510
\(387\) 1129.30 0.148335
\(388\) −10403.9 −1.36128
\(389\) −7531.99 −0.981714 −0.490857 0.871240i \(-0.663316\pi\)
−0.490857 + 0.871240i \(0.663316\pi\)
\(390\) −51.8947 −0.00673792
\(391\) −9898.34 −1.28026
\(392\) −2696.88 −0.347482
\(393\) −3121.97 −0.400719
\(394\) −1151.06 −0.147182
\(395\) −6166.41 −0.785483
\(396\) 744.676 0.0944984
\(397\) −2514.47 −0.317879 −0.158939 0.987288i \(-0.550807\pi\)
−0.158939 + 0.987288i \(0.550807\pi\)
\(398\) 3094.30 0.389707
\(399\) 560.673 0.0703478
\(400\) −4837.43 −0.604679
\(401\) 13254.8 1.65066 0.825330 0.564651i \(-0.190989\pi\)
0.825330 + 0.564651i \(0.190989\pi\)
\(402\) 916.179 0.113669
\(403\) 903.914 0.111730
\(404\) 10274.8 1.26532
\(405\) −467.459 −0.0573536
\(406\) 1042.76 0.127466
\(407\) 2976.09 0.362455
\(408\) 3008.29 0.365031
\(409\) −3996.59 −0.483176 −0.241588 0.970379i \(-0.577668\pi\)
−0.241588 + 0.970379i \(0.577668\pi\)
\(410\) 1601.89 0.192956
\(411\) 1851.59 0.222219
\(412\) 262.767 0.0314214
\(413\) −1993.10 −0.237467
\(414\) −659.173 −0.0782526
\(415\) −2588.30 −0.306156
\(416\) −530.334 −0.0625042
\(417\) −2206.34 −0.259100
\(418\) −148.429 −0.0173682
\(419\) 16323.6 1.90324 0.951621 0.307273i \(-0.0994165\pi\)
0.951621 + 0.307273i \(0.0994165\pi\)
\(420\) −1247.09 −0.144885
\(421\) −6285.98 −0.727696 −0.363848 0.931458i \(-0.618537\pi\)
−0.363848 + 0.931458i \(0.618537\pi\)
\(422\) 163.076 0.0188114
\(423\) 203.366 0.0233759
\(424\) 7753.93 0.888123
\(425\) 8567.85 0.977886
\(426\) 2118.36 0.240927
\(427\) 584.139 0.0662025
\(428\) −13711.8 −1.54857
\(429\) 143.065 0.0161008
\(430\) 500.666 0.0561495
\(431\) 12368.1 1.38225 0.691124 0.722736i \(-0.257116\pi\)
0.691124 + 0.722736i \(0.257116\pi\)
\(432\) −1424.41 −0.158639
\(433\) 12508.6 1.38828 0.694139 0.719841i \(-0.255785\pi\)
0.694139 + 0.719841i \(0.255785\pi\)
\(434\) −1380.44 −0.152680
\(435\) −2726.80 −0.300552
\(436\) −4435.15 −0.487168
\(437\) −2067.45 −0.226315
\(438\) −1970.73 −0.214989
\(439\) −9708.25 −1.05547 −0.527733 0.849410i \(-0.676958\pi\)
−0.527733 + 0.849410i \(0.676958\pi\)
\(440\) 681.273 0.0738146
\(441\) −2261.69 −0.244217
\(442\) 280.073 0.0301397
\(443\) 12399.9 1.32988 0.664941 0.746896i \(-0.268457\pi\)
0.664941 + 0.746896i \(0.268457\pi\)
\(444\) −6105.30 −0.652578
\(445\) 5876.51 0.626008
\(446\) 2379.56 0.252635
\(447\) −5452.50 −0.576945
\(448\) −3231.64 −0.340805
\(449\) −6452.34 −0.678185 −0.339092 0.940753i \(-0.610120\pi\)
−0.339092 + 0.940753i \(0.610120\pi\)
\(450\) 570.570 0.0597709
\(451\) −4416.15 −0.461083
\(452\) 5882.49 0.612143
\(453\) −128.353 −0.0133125
\(454\) 1668.39 0.172470
\(455\) −239.588 −0.0246858
\(456\) 628.339 0.0645277
\(457\) 753.511 0.0771286 0.0385643 0.999256i \(-0.487722\pi\)
0.0385643 + 0.999256i \(0.487722\pi\)
\(458\) 3142.48 0.320608
\(459\) 2522.86 0.256551
\(460\) 4598.58 0.466109
\(461\) −16347.1 −1.65154 −0.825771 0.564006i \(-0.809260\pi\)
−0.825771 + 0.564006i \(0.809260\pi\)
\(462\) −218.486 −0.0220019
\(463\) 4770.36 0.478828 0.239414 0.970918i \(-0.423045\pi\)
0.239414 + 0.970918i \(0.423045\pi\)
\(464\) −8308.95 −0.831322
\(465\) 3609.83 0.360004
\(466\) 2634.71 0.261912
\(467\) −11452.5 −1.13481 −0.567406 0.823438i \(-0.692053\pi\)
−0.567406 + 0.823438i \(0.692053\pi\)
\(468\) −293.491 −0.0289885
\(469\) 4229.83 0.416450
\(470\) 90.1608 0.00884853
\(471\) 9106.48 0.890880
\(472\) −2233.64 −0.217821
\(473\) −1380.26 −0.134174
\(474\) 2216.25 0.214759
\(475\) 1789.56 0.172864
\(476\) 6730.50 0.648092
\(477\) 6502.70 0.624189
\(478\) 12.9350 0.00123773
\(479\) 2864.72 0.273261 0.136631 0.990622i \(-0.456373\pi\)
0.136631 + 0.990622i \(0.456373\pi\)
\(480\) −2117.92 −0.201394
\(481\) −1172.93 −0.111188
\(482\) −2288.66 −0.216277
\(483\) −3043.27 −0.286695
\(484\) −910.160 −0.0854770
\(485\) −7982.18 −0.747324
\(486\) 168.008 0.0156810
\(487\) −11482.6 −1.06843 −0.534215 0.845348i \(-0.679393\pi\)
−0.534215 + 0.845348i \(0.679393\pi\)
\(488\) 654.636 0.0607254
\(489\) 4427.79 0.409471
\(490\) −1002.70 −0.0924440
\(491\) −16656.7 −1.53097 −0.765485 0.643454i \(-0.777501\pi\)
−0.765485 + 0.643454i \(0.777501\pi\)
\(492\) 9059.51 0.830151
\(493\) 14716.5 1.34441
\(494\) 58.4986 0.00532789
\(495\) 571.339 0.0518783
\(496\) 10999.7 0.995764
\(497\) 9780.07 0.882688
\(498\) 930.252 0.0837060
\(499\) 133.927 0.0120148 0.00600740 0.999982i \(-0.498088\pi\)
0.00600740 + 0.999982i \(0.498088\pi\)
\(500\) −9406.72 −0.841363
\(501\) 3060.53 0.272923
\(502\) −2677.96 −0.238094
\(503\) 13578.4 1.20364 0.601818 0.798633i \(-0.294443\pi\)
0.601818 + 0.798633i \(0.294443\pi\)
\(504\) 924.909 0.0817435
\(505\) 7883.14 0.694643
\(506\) 805.655 0.0707821
\(507\) 6534.62 0.572411
\(508\) −421.609 −0.0368226
\(509\) 5715.38 0.497701 0.248851 0.968542i \(-0.419947\pi\)
0.248851 + 0.968542i \(0.419947\pi\)
\(510\) 1118.49 0.0971127
\(511\) −9098.49 −0.787658
\(512\) −10982.9 −0.948008
\(513\) 526.946 0.0453513
\(514\) 1208.04 0.103666
\(515\) 201.603 0.0172499
\(516\) 2831.52 0.241571
\(517\) −248.559 −0.0211443
\(518\) 1791.28 0.151939
\(519\) 10304.4 0.871507
\(520\) −268.503 −0.0226435
\(521\) −4008.33 −0.337060 −0.168530 0.985697i \(-0.553902\pi\)
−0.168530 + 0.985697i \(0.553902\pi\)
\(522\) 980.031 0.0821740
\(523\) −9654.48 −0.807191 −0.403596 0.914938i \(-0.632240\pi\)
−0.403596 + 0.914938i \(0.632240\pi\)
\(524\) −7827.79 −0.652593
\(525\) 2634.21 0.218984
\(526\) −1051.71 −0.0871802
\(527\) −19482.1 −1.61035
\(528\) 1740.95 0.143494
\(529\) −945.086 −0.0776761
\(530\) 2882.92 0.236276
\(531\) −1873.20 −0.153089
\(532\) 1405.79 0.114565
\(533\) 1740.49 0.141443
\(534\) −2112.06 −0.171157
\(535\) −10520.2 −0.850142
\(536\) 4740.31 0.381996
\(537\) 52.0708 0.00418439
\(538\) 3450.80 0.276533
\(539\) 2764.29 0.220903
\(540\) −1172.07 −0.0934036
\(541\) −9846.84 −0.782530 −0.391265 0.920278i \(-0.627962\pi\)
−0.391265 + 0.920278i \(0.627962\pi\)
\(542\) −952.714 −0.0755029
\(543\) −9308.12 −0.735635
\(544\) 11430.3 0.900865
\(545\) −3402.79 −0.267449
\(546\) 86.1095 0.00674935
\(547\) −4488.13 −0.350820 −0.175410 0.984495i \(-0.556125\pi\)
−0.175410 + 0.984495i \(0.556125\pi\)
\(548\) 4642.53 0.361896
\(549\) 549.000 0.0426790
\(550\) −697.363 −0.0540648
\(551\) 3073.81 0.237656
\(552\) −3410.55 −0.262976
\(553\) 10232.0 0.786815
\(554\) −852.322 −0.0653641
\(555\) −4684.18 −0.358256
\(556\) −5532.00 −0.421959
\(557\) 2353.34 0.179020 0.0895101 0.995986i \(-0.471470\pi\)
0.0895101 + 0.995986i \(0.471470\pi\)
\(558\) −1297.40 −0.0984286
\(559\) 543.985 0.0411594
\(560\) −2915.53 −0.220006
\(561\) −3083.49 −0.232059
\(562\) 1637.79 0.122929
\(563\) −20402.6 −1.52729 −0.763646 0.645635i \(-0.776593\pi\)
−0.763646 + 0.645635i \(0.776593\pi\)
\(564\) 509.906 0.0380690
\(565\) 4513.23 0.336058
\(566\) 679.944 0.0504950
\(567\) 775.660 0.0574509
\(568\) 10960.4 0.809661
\(569\) −15098.8 −1.11243 −0.556215 0.831038i \(-0.687747\pi\)
−0.556215 + 0.831038i \(0.687747\pi\)
\(570\) 233.617 0.0171669
\(571\) −24889.9 −1.82418 −0.912091 0.409987i \(-0.865533\pi\)
−0.912091 + 0.409987i \(0.865533\pi\)
\(572\) 358.711 0.0262211
\(573\) −147.589 −0.0107603
\(574\) −2658.04 −0.193283
\(575\) −9713.52 −0.704490
\(576\) −3037.24 −0.219708
\(577\) −2787.82 −0.201142 −0.100571 0.994930i \(-0.532067\pi\)
−0.100571 + 0.994930i \(0.532067\pi\)
\(578\) −2639.64 −0.189956
\(579\) 2505.85 0.179861
\(580\) −6836.99 −0.489466
\(581\) 4294.80 0.306675
\(582\) 2868.85 0.204326
\(583\) −7947.75 −0.564601
\(584\) −10196.5 −0.722493
\(585\) −225.175 −0.0159143
\(586\) 4374.33 0.308365
\(587\) −7595.35 −0.534061 −0.267030 0.963688i \(-0.586042\pi\)
−0.267030 + 0.963688i \(0.586042\pi\)
\(588\) −5670.80 −0.397721
\(589\) −4069.20 −0.284666
\(590\) −830.470 −0.0579490
\(591\) −4994.56 −0.347629
\(592\) −14273.3 −0.990930
\(593\) 4203.35 0.291081 0.145540 0.989352i \(-0.453508\pi\)
0.145540 + 0.989352i \(0.453508\pi\)
\(594\) −205.343 −0.0141840
\(595\) 5163.85 0.355794
\(596\) −13671.2 −0.939587
\(597\) 13426.4 0.920447
\(598\) −317.524 −0.0217133
\(599\) −9560.25 −0.652122 −0.326061 0.945349i \(-0.605722\pi\)
−0.326061 + 0.945349i \(0.605722\pi\)
\(600\) 2952.12 0.200867
\(601\) −4567.57 −0.310008 −0.155004 0.987914i \(-0.549539\pi\)
−0.155004 + 0.987914i \(0.549539\pi\)
\(602\) −830.761 −0.0562447
\(603\) 3975.38 0.268474
\(604\) −321.824 −0.0216802
\(605\) −698.303 −0.0469257
\(606\) −2833.25 −0.189922
\(607\) 7570.91 0.506250 0.253125 0.967434i \(-0.418542\pi\)
0.253125 + 0.967434i \(0.418542\pi\)
\(608\) 2387.43 0.159249
\(609\) 4524.62 0.301062
\(610\) 243.395 0.0161554
\(611\) 97.9618 0.00648627
\(612\) 6325.62 0.417808
\(613\) −6472.22 −0.426445 −0.213222 0.977004i \(-0.568396\pi\)
−0.213222 + 0.977004i \(0.568396\pi\)
\(614\) 115.794 0.00761083
\(615\) 6950.74 0.455741
\(616\) −1130.44 −0.0739398
\(617\) 17863.6 1.16558 0.582788 0.812624i \(-0.301962\pi\)
0.582788 + 0.812624i \(0.301962\pi\)
\(618\) −72.4576 −0.00471630
\(619\) −24730.9 −1.60585 −0.802924 0.596081i \(-0.796724\pi\)
−0.802924 + 0.596081i \(0.796724\pi\)
\(620\) 9051.02 0.586287
\(621\) −2860.21 −0.184825
\(622\) −3345.22 −0.215645
\(623\) −9750.97 −0.627070
\(624\) −686.141 −0.0440186
\(625\) 4244.67 0.271659
\(626\) 4981.99 0.318084
\(627\) −644.045 −0.0410218
\(628\) 22832.9 1.45085
\(629\) 25280.3 1.60253
\(630\) 343.883 0.0217470
\(631\) 1133.99 0.0715425 0.0357713 0.999360i \(-0.488611\pi\)
0.0357713 + 0.999360i \(0.488611\pi\)
\(632\) 11466.9 0.721720
\(633\) 707.601 0.0444307
\(634\) 4193.01 0.262659
\(635\) −323.472 −0.0202151
\(636\) 16304.4 1.01653
\(637\) −1089.46 −0.0677645
\(638\) −1197.82 −0.0743291
\(639\) 9191.74 0.569045
\(640\) −6994.31 −0.431991
\(641\) 8252.20 0.508490 0.254245 0.967140i \(-0.418173\pi\)
0.254245 + 0.967140i \(0.418173\pi\)
\(642\) 3781.01 0.232437
\(643\) −10318.2 −0.632831 −0.316416 0.948621i \(-0.602479\pi\)
−0.316416 + 0.948621i \(0.602479\pi\)
\(644\) −7630.48 −0.466899
\(645\) 2172.43 0.132619
\(646\) −1260.82 −0.0767901
\(647\) 22922.7 1.39286 0.696432 0.717623i \(-0.254770\pi\)
0.696432 + 0.717623i \(0.254770\pi\)
\(648\) 869.271 0.0526978
\(649\) 2289.47 0.138474
\(650\) 274.844 0.0165850
\(651\) −5989.83 −0.360615
\(652\) 11101.9 0.666847
\(653\) 3186.91 0.190985 0.0954927 0.995430i \(-0.469557\pi\)
0.0954927 + 0.995430i \(0.469557\pi\)
\(654\) 1222.98 0.0731231
\(655\) −6005.73 −0.358264
\(656\) 21179.9 1.26057
\(657\) −8551.17 −0.507782
\(658\) −149.605 −0.00886354
\(659\) 7696.64 0.454960 0.227480 0.973783i \(-0.426951\pi\)
0.227480 + 0.973783i \(0.426951\pi\)
\(660\) 1432.53 0.0844867
\(661\) −17859.0 −1.05088 −0.525441 0.850830i \(-0.676100\pi\)
−0.525441 + 0.850830i \(0.676100\pi\)
\(662\) 6386.53 0.374954
\(663\) 1215.26 0.0711868
\(664\) 4813.12 0.281303
\(665\) 1078.57 0.0628948
\(666\) 1683.52 0.0979508
\(667\) −16684.3 −0.968543
\(668\) 7673.76 0.444471
\(669\) 10325.1 0.596698
\(670\) 1762.45 0.101626
\(671\) −671.000 −0.0386046
\(672\) 3514.28 0.201736
\(673\) 2562.62 0.146778 0.0733890 0.997303i \(-0.476619\pi\)
0.0733890 + 0.997303i \(0.476619\pi\)
\(674\) −3904.29 −0.223127
\(675\) 2475.75 0.141173
\(676\) 16384.4 0.932204
\(677\) 2836.43 0.161024 0.0805118 0.996754i \(-0.474345\pi\)
0.0805118 + 0.996754i \(0.474345\pi\)
\(678\) −1622.08 −0.0918816
\(679\) 13244.9 0.748591
\(680\) 5787.05 0.326358
\(681\) 7239.29 0.407357
\(682\) 1585.71 0.0890320
\(683\) 7120.78 0.398930 0.199465 0.979905i \(-0.436080\pi\)
0.199465 + 0.979905i \(0.436080\pi\)
\(684\) 1321.23 0.0738572
\(685\) 3561.89 0.198676
\(686\) 3934.73 0.218992
\(687\) 13635.5 0.757244
\(688\) 6619.71 0.366823
\(689\) 3132.36 0.173198
\(690\) −1268.05 −0.0699621
\(691\) 20058.2 1.10427 0.552136 0.833754i \(-0.313813\pi\)
0.552136 + 0.833754i \(0.313813\pi\)
\(692\) 25836.4 1.41930
\(693\) −948.029 −0.0519663
\(694\) 1865.19 0.102020
\(695\) −4244.33 −0.231650
\(696\) 5070.68 0.276154
\(697\) −37512.9 −2.03860
\(698\) 713.357 0.0386833
\(699\) 11432.2 0.618608
\(700\) 6604.83 0.356627
\(701\) 1876.96 0.101130 0.0505649 0.998721i \(-0.483898\pi\)
0.0505649 + 0.998721i \(0.483898\pi\)
\(702\) 80.9295 0.00435112
\(703\) 5280.27 0.283285
\(704\) 3712.18 0.198733
\(705\) 391.216 0.0208993
\(706\) −6947.75 −0.370371
\(707\) −13080.6 −0.695822
\(708\) −4696.73 −0.249314
\(709\) −18659.3 −0.988384 −0.494192 0.869353i \(-0.664536\pi\)
−0.494192 + 0.869353i \(0.664536\pi\)
\(710\) 4075.09 0.215402
\(711\) 9616.49 0.507238
\(712\) −10927.8 −0.575190
\(713\) 22087.2 1.16013
\(714\) −1855.92 −0.0972775
\(715\) 275.214 0.0143950
\(716\) 130.558 0.00681452
\(717\) 56.1263 0.00292339
\(718\) 5149.88 0.267677
\(719\) −26207.5 −1.35935 −0.679676 0.733512i \(-0.737880\pi\)
−0.679676 + 0.733512i \(0.737880\pi\)
\(720\) −2740.14 −0.141832
\(721\) −334.523 −0.0172792
\(722\) 4478.90 0.230869
\(723\) −9930.70 −0.510825
\(724\) −23338.5 −1.19802
\(725\) 14441.7 0.739793
\(726\) 250.975 0.0128299
\(727\) 2640.28 0.134694 0.0673469 0.997730i \(-0.478547\pi\)
0.0673469 + 0.997730i \(0.478547\pi\)
\(728\) 445.530 0.0226819
\(729\) 729.000 0.0370370
\(730\) −3791.09 −0.192212
\(731\) −11724.5 −0.593225
\(732\) 1376.52 0.0695051
\(733\) 11603.6 0.584706 0.292353 0.956310i \(-0.405562\pi\)
0.292353 + 0.956310i \(0.405562\pi\)
\(734\) −4727.68 −0.237741
\(735\) −4350.82 −0.218343
\(736\) −12958.7 −0.649002
\(737\) −4858.80 −0.242844
\(738\) −2498.14 −0.124604
\(739\) 1984.17 0.0987669 0.0493835 0.998780i \(-0.484274\pi\)
0.0493835 + 0.998780i \(0.484274\pi\)
\(740\) −11744.8 −0.583441
\(741\) 253.830 0.0125839
\(742\) −4783.67 −0.236676
\(743\) −2107.31 −0.104051 −0.0520253 0.998646i \(-0.516568\pi\)
−0.0520253 + 0.998646i \(0.516568\pi\)
\(744\) −6712.72 −0.330780
\(745\) −10489.0 −0.515820
\(746\) 4478.58 0.219802
\(747\) 4036.44 0.197705
\(748\) −7731.32 −0.377921
\(749\) 17456.2 0.851584
\(750\) 2593.88 0.126287
\(751\) −31313.5 −1.52150 −0.760750 0.649044i \(-0.775169\pi\)
−0.760750 + 0.649044i \(0.775169\pi\)
\(752\) 1192.09 0.0578072
\(753\) −11619.9 −0.562353
\(754\) 472.082 0.0228014
\(755\) −246.913 −0.0119021
\(756\) 1944.83 0.0935620
\(757\) −29093.4 −1.39686 −0.698428 0.715681i \(-0.746117\pi\)
−0.698428 + 0.715681i \(0.746117\pi\)
\(758\) −4827.46 −0.231321
\(759\) 3495.81 0.167180
\(760\) 1208.73 0.0576913
\(761\) 12126.2 0.577627 0.288814 0.957385i \(-0.406739\pi\)
0.288814 + 0.957385i \(0.406739\pi\)
\(762\) 116.258 0.00552701
\(763\) 5646.29 0.267902
\(764\) −370.055 −0.0175237
\(765\) 4853.22 0.229370
\(766\) −6103.15 −0.287880
\(767\) −902.324 −0.0424785
\(768\) −5585.51 −0.262434
\(769\) −33071.4 −1.55083 −0.775414 0.631454i \(-0.782459\pi\)
−0.775414 + 0.631454i \(0.782459\pi\)
\(770\) −420.301 −0.0196709
\(771\) 5241.77 0.244848
\(772\) 6282.98 0.292914
\(773\) −8450.24 −0.393188 −0.196594 0.980485i \(-0.562988\pi\)
−0.196594 + 0.980485i \(0.562988\pi\)
\(774\) −780.787 −0.0362594
\(775\) −19118.3 −0.886130
\(776\) 14843.4 0.686658
\(777\) 7772.51 0.358864
\(778\) 5207.54 0.239973
\(779\) −7835.27 −0.360369
\(780\) −564.588 −0.0259173
\(781\) −11234.4 −0.514721
\(782\) 6843.61 0.312950
\(783\) 4252.44 0.194087
\(784\) −13257.5 −0.603934
\(785\) 17518.1 0.796495
\(786\) 2158.50 0.0979530
\(787\) 16384.4 0.742109 0.371054 0.928611i \(-0.378996\pi\)
0.371054 + 0.928611i \(0.378996\pi\)
\(788\) −12523.0 −0.566134
\(789\) −4563.46 −0.205911
\(790\) 4263.39 0.192006
\(791\) −7488.85 −0.336628
\(792\) −1062.44 −0.0476670
\(793\) 264.454 0.0118424
\(794\) 1738.48 0.0777033
\(795\) 12509.2 0.558059
\(796\) 33664.4 1.49900
\(797\) 17380.6 0.772463 0.386232 0.922402i \(-0.373776\pi\)
0.386232 + 0.922402i \(0.373776\pi\)
\(798\) −387.644 −0.0171961
\(799\) −2111.37 −0.0934857
\(800\) 11216.9 0.495721
\(801\) −9164.40 −0.404255
\(802\) −9164.26 −0.403493
\(803\) 10451.4 0.459306
\(804\) 9967.57 0.437225
\(805\) −5854.34 −0.256321
\(806\) −624.957 −0.0273116
\(807\) 14973.3 0.653143
\(808\) −14659.2 −0.638254
\(809\) 29376.8 1.27668 0.638339 0.769755i \(-0.279622\pi\)
0.638339 + 0.769755i \(0.279622\pi\)
\(810\) 323.196 0.0140197
\(811\) 21916.4 0.948936 0.474468 0.880273i \(-0.342640\pi\)
0.474468 + 0.880273i \(0.342640\pi\)
\(812\) 11344.7 0.490297
\(813\) −4133.91 −0.178330
\(814\) −2057.64 −0.0885998
\(815\) 8517.73 0.366090
\(816\) 14788.4 0.634434
\(817\) −2448.89 −0.104866
\(818\) 2763.20 0.118109
\(819\) 373.636 0.0159413
\(820\) 17427.8 0.742201
\(821\) 26037.6 1.10685 0.553423 0.832901i \(-0.313321\pi\)
0.553423 + 0.832901i \(0.313321\pi\)
\(822\) −1280.17 −0.0543199
\(823\) 18719.8 0.792869 0.396435 0.918063i \(-0.370247\pi\)
0.396435 + 0.918063i \(0.370247\pi\)
\(824\) −374.895 −0.0158496
\(825\) −3025.92 −0.127696
\(826\) 1378.01 0.0580473
\(827\) 3873.31 0.162864 0.0814319 0.996679i \(-0.474051\pi\)
0.0814319 + 0.996679i \(0.474051\pi\)
\(828\) −7171.47 −0.300997
\(829\) −29488.0 −1.23542 −0.617708 0.786407i \(-0.711939\pi\)
−0.617708 + 0.786407i \(0.711939\pi\)
\(830\) 1789.52 0.0748377
\(831\) −3698.30 −0.154383
\(832\) −1463.04 −0.0609638
\(833\) 23481.2 0.976680
\(834\) 1525.44 0.0633353
\(835\) 5887.55 0.244008
\(836\) −1614.83 −0.0668063
\(837\) −5629.51 −0.232478
\(838\) −11286.0 −0.465235
\(839\) 18869.6 0.776460 0.388230 0.921562i \(-0.373087\pi\)
0.388230 + 0.921562i \(0.373087\pi\)
\(840\) 1779.25 0.0730832
\(841\) 416.542 0.0170791
\(842\) 4346.07 0.177880
\(843\) 7106.50 0.290345
\(844\) 1774.19 0.0723579
\(845\) 12570.6 0.511767
\(846\) −140.605 −0.00571408
\(847\) 1158.70 0.0470053
\(848\) 38117.4 1.54358
\(849\) 2950.34 0.119264
\(850\) −5923.72 −0.239038
\(851\) −28660.7 −1.15450
\(852\) 23046.7 0.926722
\(853\) −27104.8 −1.08799 −0.543993 0.839090i \(-0.683088\pi\)
−0.543993 + 0.839090i \(0.683088\pi\)
\(854\) −403.868 −0.0161828
\(855\) 1013.69 0.0405466
\(856\) 19562.9 0.781130
\(857\) 4563.91 0.181914 0.0909569 0.995855i \(-0.471007\pi\)
0.0909569 + 0.995855i \(0.471007\pi\)
\(858\) −98.9139 −0.00393574
\(859\) −6440.88 −0.255833 −0.127916 0.991785i \(-0.540829\pi\)
−0.127916 + 0.991785i \(0.540829\pi\)
\(860\) 5447.00 0.215978
\(861\) −11533.4 −0.456514
\(862\) −8551.16 −0.337881
\(863\) 8935.24 0.352444 0.176222 0.984350i \(-0.443612\pi\)
0.176222 + 0.984350i \(0.443612\pi\)
\(864\) 3302.88 0.130054
\(865\) 19822.5 0.779175
\(866\) −8648.32 −0.339355
\(867\) −11453.6 −0.448656
\(868\) −15018.5 −0.587281
\(869\) −11753.5 −0.458814
\(870\) 1885.29 0.0734680
\(871\) 1914.94 0.0744953
\(872\) 6327.71 0.245738
\(873\) 12448.2 0.482597
\(874\) 1429.42 0.0553212
\(875\) 11975.5 0.462680
\(876\) −21440.6 −0.826952
\(877\) −22372.5 −0.861419 −0.430710 0.902491i \(-0.641737\pi\)
−0.430710 + 0.902491i \(0.641737\pi\)
\(878\) 6712.19 0.258002
\(879\) 18980.6 0.728327
\(880\) 3349.06 0.128292
\(881\) 30759.5 1.17629 0.588147 0.808754i \(-0.299858\pi\)
0.588147 + 0.808754i \(0.299858\pi\)
\(882\) 1563.71 0.0596972
\(883\) −15736.3 −0.599740 −0.299870 0.953980i \(-0.596943\pi\)
−0.299870 + 0.953980i \(0.596943\pi\)
\(884\) 3047.06 0.115932
\(885\) −3603.48 −0.136870
\(886\) −8573.17 −0.325081
\(887\) −24637.2 −0.932621 −0.466310 0.884621i \(-0.654417\pi\)
−0.466310 + 0.884621i \(0.654417\pi\)
\(888\) 8710.54 0.329174
\(889\) 536.741 0.0202494
\(890\) −4062.96 −0.153023
\(891\) −891.000 −0.0335013
\(892\) 25888.4 0.971757
\(893\) −441.000 −0.0165258
\(894\) 3769.80 0.141030
\(895\) 100.168 0.00374108
\(896\) 11605.7 0.432724
\(897\) −1377.76 −0.0512845
\(898\) 4461.09 0.165778
\(899\) −32838.4 −1.21827
\(900\) 6207.51 0.229908
\(901\) −67511.9 −2.49628
\(902\) 3053.28 0.112709
\(903\) −3604.74 −0.132844
\(904\) −8392.65 −0.308778
\(905\) −17906.0 −0.657698
\(906\) 88.7422 0.00325415
\(907\) −1540.61 −0.0564003 −0.0282001 0.999602i \(-0.508978\pi\)
−0.0282001 + 0.999602i \(0.508978\pi\)
\(908\) 18151.3 0.663404
\(909\) −12293.7 −0.448577
\(910\) 165.649 0.00603429
\(911\) 14440.4 0.525174 0.262587 0.964908i \(-0.415424\pi\)
0.262587 + 0.964908i \(0.415424\pi\)
\(912\) 3088.84 0.112151
\(913\) −4933.43 −0.178831
\(914\) −520.970 −0.0188536
\(915\) 1056.11 0.0381573
\(916\) 34188.6 1.23321
\(917\) 9965.37 0.358872
\(918\) −1744.28 −0.0627121
\(919\) 51492.4 1.84829 0.924145 0.382041i \(-0.124779\pi\)
0.924145 + 0.382041i \(0.124779\pi\)
\(920\) −6560.88 −0.235115
\(921\) 502.439 0.0179760
\(922\) 11302.2 0.403708
\(923\) 4427.67 0.157897
\(924\) −2377.02 −0.0846300
\(925\) 24808.3 0.881828
\(926\) −3298.18 −0.117046
\(927\) −314.400 −0.0111394
\(928\) 19266.5 0.681525
\(929\) 14890.5 0.525878 0.262939 0.964813i \(-0.415308\pi\)
0.262939 + 0.964813i \(0.415308\pi\)
\(930\) −2495.80 −0.0880006
\(931\) 4904.49 0.172651
\(932\) 28664.4 1.00744
\(933\) −14515.2 −0.509332
\(934\) 7918.13 0.277397
\(935\) −5931.71 −0.207473
\(936\) 418.729 0.0146224
\(937\) 14349.8 0.500305 0.250153 0.968206i \(-0.419519\pi\)
0.250153 + 0.968206i \(0.419519\pi\)
\(938\) −2924.46 −0.101798
\(939\) 21617.3 0.751282
\(940\) 980.905 0.0340357
\(941\) −47139.8 −1.63307 −0.816533 0.577299i \(-0.804107\pi\)
−0.816533 + 0.577299i \(0.804107\pi\)
\(942\) −6296.13 −0.217770
\(943\) 42529.0 1.46865
\(944\) −10980.3 −0.378579
\(945\) 1492.14 0.0513642
\(946\) 954.295 0.0327979
\(947\) 10424.6 0.357714 0.178857 0.983875i \(-0.442760\pi\)
0.178857 + 0.983875i \(0.442760\pi\)
\(948\) 24111.7 0.826066
\(949\) −4119.11 −0.140898
\(950\) −1237.28 −0.0422555
\(951\) 18193.8 0.620374
\(952\) −9602.52 −0.326911
\(953\) −18189.2 −0.618264 −0.309132 0.951019i \(-0.600038\pi\)
−0.309132 + 0.951019i \(0.600038\pi\)
\(954\) −4495.90 −0.152579
\(955\) −283.918 −0.00962027
\(956\) 140.727 0.00476091
\(957\) −5197.43 −0.175558
\(958\) −1980.64 −0.0667969
\(959\) −5910.29 −0.199013
\(960\) −5842.74 −0.196431
\(961\) 13681.4 0.459248
\(962\) 810.955 0.0271790
\(963\) 16406.1 0.548993
\(964\) −24899.5 −0.831908
\(965\) 4820.50 0.160805
\(966\) 2104.09 0.0700807
\(967\) −8458.98 −0.281305 −0.140653 0.990059i \(-0.544920\pi\)
−0.140653 + 0.990059i \(0.544920\pi\)
\(968\) 1298.54 0.0431164
\(969\) −5470.82 −0.181370
\(970\) 5518.80 0.182678
\(971\) −11544.2 −0.381535 −0.190767 0.981635i \(-0.561098\pi\)
−0.190767 + 0.981635i \(0.561098\pi\)
\(972\) 1827.84 0.0603169
\(973\) 7042.66 0.232042
\(974\) 7938.95 0.261171
\(975\) 1192.57 0.0391721
\(976\) 3218.12 0.105542
\(977\) −30832.8 −1.00965 −0.504825 0.863222i \(-0.668443\pi\)
−0.504825 + 0.863222i \(0.668443\pi\)
\(978\) −3061.33 −0.100093
\(979\) 11200.9 0.365662
\(980\) −10908.9 −0.355584
\(981\) 5306.63 0.172709
\(982\) 11516.3 0.374235
\(983\) −17920.8 −0.581471 −0.290736 0.956803i \(-0.593900\pi\)
−0.290736 + 0.956803i \(0.593900\pi\)
\(984\) −12925.4 −0.418746
\(985\) −9608.03 −0.310799
\(986\) −10174.8 −0.328633
\(987\) −649.149 −0.0209348
\(988\) 636.436 0.0204936
\(989\) 13292.3 0.427372
\(990\) −395.018 −0.0126813
\(991\) −58693.2 −1.88138 −0.940691 0.339265i \(-0.889822\pi\)
−0.940691 + 0.339265i \(0.889822\pi\)
\(992\) −25505.6 −0.816336
\(993\) 27711.7 0.885603
\(994\) −6761.84 −0.215767
\(995\) 25828.4 0.822930
\(996\) 10120.7 0.321974
\(997\) 1278.85 0.0406236 0.0203118 0.999794i \(-0.493534\pi\)
0.0203118 + 0.999794i \(0.493534\pi\)
\(998\) −92.5956 −0.00293694
\(999\) 7304.95 0.231350
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 2013.4.a.b.1.16 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.4.a.b.1.16 36 1.1 even 1 trivial