Properties

Label 1849.4.a.k.1.9
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $60$
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] = [1849,4,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1849.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.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: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(60\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.40707 q^{2} -0.148254 q^{3} +11.4223 q^{4} +15.4121 q^{5} +0.653363 q^{6} +27.6883 q^{7} -15.0821 q^{8} -26.9780 q^{9} +O(q^{10})\) \(q-4.40707 q^{2} -0.148254 q^{3} +11.4223 q^{4} +15.4121 q^{5} +0.653363 q^{6} +27.6883 q^{7} -15.0821 q^{8} -26.9780 q^{9} -67.9222 q^{10} -49.2082 q^{11} -1.69339 q^{12} +14.7161 q^{13} -122.024 q^{14} -2.28490 q^{15} -24.9102 q^{16} -20.0795 q^{17} +118.894 q^{18} -125.091 q^{19} +176.041 q^{20} -4.10489 q^{21} +216.864 q^{22} +148.291 q^{23} +2.23597 q^{24} +112.533 q^{25} -64.8548 q^{26} +8.00243 q^{27} +316.263 q^{28} +152.891 q^{29} +10.0697 q^{30} -7.42094 q^{31} +230.438 q^{32} +7.29529 q^{33} +88.4919 q^{34} +426.736 q^{35} -308.150 q^{36} -209.184 q^{37} +551.286 q^{38} -2.18171 q^{39} -232.447 q^{40} -136.945 q^{41} +18.0905 q^{42} -562.069 q^{44} -415.788 q^{45} -653.530 q^{46} -18.4081 q^{47} +3.69302 q^{48} +423.644 q^{49} -495.941 q^{50} +2.97686 q^{51} +168.091 q^{52} -67.1286 q^{53} -35.2673 q^{54} -758.402 q^{55} -417.598 q^{56} +18.5452 q^{57} -673.801 q^{58} +210.432 q^{59} -26.0987 q^{60} +842.655 q^{61} +32.7046 q^{62} -746.977 q^{63} -816.273 q^{64} +226.806 q^{65} -32.1508 q^{66} -698.336 q^{67} -229.353 q^{68} -21.9847 q^{69} -1880.65 q^{70} -1102.14 q^{71} +406.885 q^{72} -602.172 q^{73} +921.888 q^{74} -16.6834 q^{75} -1428.82 q^{76} -1362.49 q^{77} +9.61496 q^{78} +353.014 q^{79} -383.918 q^{80} +727.220 q^{81} +603.525 q^{82} -907.095 q^{83} -46.8871 q^{84} -309.468 q^{85} -22.6666 q^{87} +742.163 q^{88} +389.331 q^{89} +1832.41 q^{90} +407.464 q^{91} +1693.82 q^{92} +1.10018 q^{93} +81.1258 q^{94} -1927.92 q^{95} -34.1632 q^{96} +1796.17 q^{97} -1867.03 q^{98} +1327.54 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.40707 −1.55813 −0.779067 0.626941i \(-0.784307\pi\)
−0.779067 + 0.626941i \(0.784307\pi\)
\(3\) −0.148254 −0.0285314 −0.0142657 0.999898i \(-0.504541\pi\)
−0.0142657 + 0.999898i \(0.504541\pi\)
\(4\) 11.4223 1.42778
\(5\) 15.4121 1.37850 0.689250 0.724523i \(-0.257940\pi\)
0.689250 + 0.724523i \(0.257940\pi\)
\(6\) 0.653363 0.0444558
\(7\) 27.6883 1.49503 0.747515 0.664245i \(-0.231247\pi\)
0.747515 + 0.664245i \(0.231247\pi\)
\(8\) −15.0821 −0.666541
\(9\) −26.9780 −0.999186
\(10\) −67.9222 −2.14789
\(11\) −49.2082 −1.34880 −0.674401 0.738365i \(-0.735598\pi\)
−0.674401 + 0.738365i \(0.735598\pi\)
\(12\) −1.69339 −0.0407366
\(13\) 14.7161 0.313962 0.156981 0.987602i \(-0.449824\pi\)
0.156981 + 0.987602i \(0.449824\pi\)
\(14\) −122.024 −2.32946
\(15\) −2.28490 −0.0393306
\(16\) −24.9102 −0.389222
\(17\) −20.0795 −0.286471 −0.143235 0.989689i \(-0.545751\pi\)
−0.143235 + 0.989689i \(0.545751\pi\)
\(18\) 118.894 1.55687
\(19\) −125.091 −1.51042 −0.755208 0.655485i \(-0.772464\pi\)
−0.755208 + 0.655485i \(0.772464\pi\)
\(20\) 176.041 1.96820
\(21\) −4.10489 −0.0426553
\(22\) 216.864 2.10162
\(23\) 148.291 1.34439 0.672193 0.740376i \(-0.265353\pi\)
0.672193 + 0.740376i \(0.265353\pi\)
\(24\) 2.23597 0.0190173
\(25\) 112.533 0.900264
\(26\) −64.8548 −0.489195
\(27\) 8.00243 0.0570396
\(28\) 316.263 2.13458
\(29\) 152.891 0.979005 0.489503 0.872002i \(-0.337178\pi\)
0.489503 + 0.872002i \(0.337178\pi\)
\(30\) 10.0697 0.0612823
\(31\) −7.42094 −0.0429948 −0.0214974 0.999769i \(-0.506843\pi\)
−0.0214974 + 0.999769i \(0.506843\pi\)
\(32\) 230.438 1.27300
\(33\) 7.29529 0.0384832
\(34\) 88.4919 0.446360
\(35\) 426.736 2.06090
\(36\) −308.150 −1.42662
\(37\) −209.184 −0.929450 −0.464725 0.885455i \(-0.653847\pi\)
−0.464725 + 0.885455i \(0.653847\pi\)
\(38\) 551.286 2.35343
\(39\) −2.18171 −0.00895779
\(40\) −232.447 −0.918827
\(41\) −136.945 −0.521639 −0.260819 0.965388i \(-0.583993\pi\)
−0.260819 + 0.965388i \(0.583993\pi\)
\(42\) 18.0905 0.0664627
\(43\) 0 0
\(44\) −562.069 −1.92580
\(45\) −415.788 −1.37738
\(46\) −653.530 −2.09473
\(47\) −18.4081 −0.0571298 −0.0285649 0.999592i \(-0.509094\pi\)
−0.0285649 + 0.999592i \(0.509094\pi\)
\(48\) 3.69302 0.0111050
\(49\) 423.644 1.23511
\(50\) −495.941 −1.40273
\(51\) 2.97686 0.00817341
\(52\) 168.091 0.448270
\(53\) −67.1286 −0.173978 −0.0869889 0.996209i \(-0.527724\pi\)
−0.0869889 + 0.996209i \(0.527724\pi\)
\(54\) −35.2673 −0.0888753
\(55\) −758.402 −1.85933
\(56\) −417.598 −0.996498
\(57\) 18.5452 0.0430943
\(58\) −673.801 −1.52542
\(59\) 210.432 0.464338 0.232169 0.972675i \(-0.425418\pi\)
0.232169 + 0.972675i \(0.425418\pi\)
\(60\) −26.0987 −0.0561554
\(61\) 842.655 1.76870 0.884352 0.466821i \(-0.154601\pi\)
0.884352 + 0.466821i \(0.154601\pi\)
\(62\) 32.7046 0.0669917
\(63\) −746.977 −1.49381
\(64\) −816.273 −1.59428
\(65\) 226.806 0.432797
\(66\) −32.1508 −0.0599620
\(67\) −698.336 −1.27336 −0.636681 0.771127i \(-0.719693\pi\)
−0.636681 + 0.771127i \(0.719693\pi\)
\(68\) −229.353 −0.409018
\(69\) −21.9847 −0.0383572
\(70\) −1880.65 −3.21116
\(71\) −1102.14 −1.84225 −0.921125 0.389266i \(-0.872729\pi\)
−0.921125 + 0.389266i \(0.872729\pi\)
\(72\) 406.885 0.665998
\(73\) −602.172 −0.965465 −0.482732 0.875768i \(-0.660356\pi\)
−0.482732 + 0.875768i \(0.660356\pi\)
\(74\) 921.888 1.44821
\(75\) −16.6834 −0.0256858
\(76\) −1428.82 −2.15654
\(77\) −1362.49 −2.01650
\(78\) 9.61496 0.0139574
\(79\) 353.014 0.502748 0.251374 0.967890i \(-0.419118\pi\)
0.251374 + 0.967890i \(0.419118\pi\)
\(80\) −383.918 −0.536542
\(81\) 727.220 0.997559
\(82\) 603.525 0.812783
\(83\) −907.095 −1.19960 −0.599799 0.800151i \(-0.704753\pi\)
−0.599799 + 0.800151i \(0.704753\pi\)
\(84\) −46.8871 −0.0609024
\(85\) −309.468 −0.394900
\(86\) 0 0
\(87\) −22.6666 −0.0279324
\(88\) 742.163 0.899032
\(89\) 389.331 0.463697 0.231848 0.972752i \(-0.425523\pi\)
0.231848 + 0.972752i \(0.425523\pi\)
\(90\) 1832.41 2.14614
\(91\) 407.464 0.469383
\(92\) 1693.82 1.91949
\(93\) 1.10018 0.00122670
\(94\) 81.1258 0.0890158
\(95\) −1927.92 −2.08211
\(96\) −34.1632 −0.0363205
\(97\) 1796.17 1.88014 0.940069 0.340984i \(-0.110760\pi\)
0.940069 + 0.340984i \(0.110760\pi\)
\(98\) −1867.03 −1.92447
\(99\) 1327.54 1.34770
\(100\) 1285.38 1.28538
\(101\) 95.9143 0.0944934 0.0472467 0.998883i \(-0.484955\pi\)
0.0472467 + 0.998883i \(0.484955\pi\)
\(102\) −13.1192 −0.0127353
\(103\) −982.689 −0.940070 −0.470035 0.882648i \(-0.655759\pi\)
−0.470035 + 0.882648i \(0.655759\pi\)
\(104\) −221.950 −0.209269
\(105\) −63.2651 −0.0588004
\(106\) 295.840 0.271081
\(107\) −415.959 −0.375816 −0.187908 0.982187i \(-0.560171\pi\)
−0.187908 + 0.982187i \(0.560171\pi\)
\(108\) 91.4058 0.0814401
\(109\) −47.6757 −0.0418946 −0.0209473 0.999781i \(-0.506668\pi\)
−0.0209473 + 0.999781i \(0.506668\pi\)
\(110\) 3342.33 2.89708
\(111\) 31.0123 0.0265185
\(112\) −689.721 −0.581898
\(113\) −1385.15 −1.15313 −0.576566 0.817051i \(-0.695608\pi\)
−0.576566 + 0.817051i \(0.695608\pi\)
\(114\) −81.7300 −0.0671467
\(115\) 2285.48 1.85324
\(116\) 1746.36 1.39781
\(117\) −397.011 −0.313707
\(118\) −927.389 −0.723501
\(119\) −555.969 −0.428282
\(120\) 34.4611 0.0262154
\(121\) 1090.45 0.819269
\(122\) −3713.64 −2.75588
\(123\) 20.3026 0.0148831
\(124\) −84.7638 −0.0613872
\(125\) −192.143 −0.137486
\(126\) 3291.98 2.32756
\(127\) 57.3111 0.0400436 0.0200218 0.999800i \(-0.493626\pi\)
0.0200218 + 0.999800i \(0.493626\pi\)
\(128\) 1753.87 1.21111
\(129\) 0 0
\(130\) −999.550 −0.674356
\(131\) 1651.64 1.10156 0.550782 0.834649i \(-0.314330\pi\)
0.550782 + 0.834649i \(0.314330\pi\)
\(132\) 83.3286 0.0549457
\(133\) −3463.57 −2.25812
\(134\) 3077.61 1.98407
\(135\) 123.334 0.0786291
\(136\) 302.841 0.190944
\(137\) −1757.57 −1.09605 −0.548027 0.836461i \(-0.684621\pi\)
−0.548027 + 0.836461i \(0.684621\pi\)
\(138\) 96.8881 0.0597657
\(139\) −1440.14 −0.878785 −0.439393 0.898295i \(-0.644806\pi\)
−0.439393 + 0.898295i \(0.644806\pi\)
\(140\) 4874.28 2.94251
\(141\) 2.72907 0.00162999
\(142\) 4857.20 2.87047
\(143\) −724.153 −0.423473
\(144\) 672.027 0.388905
\(145\) 2356.37 1.34956
\(146\) 2653.81 1.50432
\(147\) −62.8067 −0.0352395
\(148\) −2389.35 −1.32705
\(149\) −3154.30 −1.73430 −0.867148 0.498051i \(-0.834049\pi\)
−0.867148 + 0.498051i \(0.834049\pi\)
\(150\) 73.5249 0.0400219
\(151\) 494.931 0.266735 0.133367 0.991067i \(-0.457421\pi\)
0.133367 + 0.991067i \(0.457421\pi\)
\(152\) 1886.64 1.00675
\(153\) 541.706 0.286237
\(154\) 6004.60 3.14198
\(155\) −114.372 −0.0592684
\(156\) −24.9201 −0.0127898
\(157\) 483.013 0.245533 0.122766 0.992436i \(-0.460823\pi\)
0.122766 + 0.992436i \(0.460823\pi\)
\(158\) −1555.75 −0.783349
\(159\) 9.95205 0.00496383
\(160\) 3551.53 1.75483
\(161\) 4105.94 2.00990
\(162\) −3204.91 −1.55433
\(163\) 3585.81 1.72308 0.861540 0.507690i \(-0.169500\pi\)
0.861540 + 0.507690i \(0.169500\pi\)
\(164\) −1564.22 −0.744786
\(165\) 112.436 0.0530492
\(166\) 3997.63 1.86913
\(167\) −286.311 −0.132667 −0.0663336 0.997797i \(-0.521130\pi\)
−0.0663336 + 0.997797i \(0.521130\pi\)
\(168\) 61.9104 0.0284315
\(169\) −1980.44 −0.901428
\(170\) 1363.85 0.615307
\(171\) 3374.71 1.50919
\(172\) 0 0
\(173\) −2073.21 −0.911118 −0.455559 0.890206i \(-0.650561\pi\)
−0.455559 + 0.890206i \(0.650561\pi\)
\(174\) 99.8934 0.0435224
\(175\) 3115.85 1.34592
\(176\) 1225.79 0.524983
\(177\) −31.1973 −0.0132482
\(178\) −1715.81 −0.722501
\(179\) −662.622 −0.276685 −0.138343 0.990384i \(-0.544178\pi\)
−0.138343 + 0.990384i \(0.544178\pi\)
\(180\) −4749.24 −1.96660
\(181\) −3001.11 −1.23243 −0.616217 0.787576i \(-0.711336\pi\)
−0.616217 + 0.787576i \(0.711336\pi\)
\(182\) −1795.72 −0.731362
\(183\) −124.927 −0.0504636
\(184\) −2236.54 −0.896088
\(185\) −3223.97 −1.28125
\(186\) −4.84857 −0.00191137
\(187\) 988.078 0.386392
\(188\) −210.262 −0.0815688
\(189\) 221.574 0.0852759
\(190\) 8496.47 3.24420
\(191\) −3214.18 −1.21764 −0.608822 0.793307i \(-0.708357\pi\)
−0.608822 + 0.793307i \(0.708357\pi\)
\(192\) 121.015 0.0454871
\(193\) 2252.15 0.839966 0.419983 0.907532i \(-0.362036\pi\)
0.419983 + 0.907532i \(0.362036\pi\)
\(194\) −7915.84 −2.92951
\(195\) −33.6248 −0.0123483
\(196\) 4838.97 1.76347
\(197\) −1231.52 −0.445393 −0.222696 0.974888i \(-0.571486\pi\)
−0.222696 + 0.974888i \(0.571486\pi\)
\(198\) −5850.56 −2.09990
\(199\) 1251.30 0.445740 0.222870 0.974848i \(-0.428457\pi\)
0.222870 + 0.974848i \(0.428457\pi\)
\(200\) −1697.23 −0.600063
\(201\) 103.531 0.0363308
\(202\) −422.701 −0.147233
\(203\) 4233.30 1.46364
\(204\) 34.0025 0.0116698
\(205\) −2110.61 −0.719079
\(206\) 4330.78 1.46476
\(207\) −4000.61 −1.34329
\(208\) −366.581 −0.122201
\(209\) 6155.52 2.03725
\(210\) 278.813 0.0916188
\(211\) −2574.37 −0.839938 −0.419969 0.907538i \(-0.637959\pi\)
−0.419969 + 0.907538i \(0.637959\pi\)
\(212\) −766.759 −0.248402
\(213\) 163.396 0.0525620
\(214\) 1833.16 0.585572
\(215\) 0 0
\(216\) −120.693 −0.0380192
\(217\) −205.473 −0.0642785
\(218\) 210.110 0.0652773
\(219\) 89.2742 0.0275461
\(220\) −8662.66 −2.65471
\(221\) −295.492 −0.0899410
\(222\) −136.673 −0.0413194
\(223\) −324.499 −0.0974443 −0.0487221 0.998812i \(-0.515515\pi\)
−0.0487221 + 0.998812i \(0.515515\pi\)
\(224\) 6380.44 1.90317
\(225\) −3035.92 −0.899531
\(226\) 6104.45 1.79673
\(227\) −2741.93 −0.801710 −0.400855 0.916142i \(-0.631287\pi\)
−0.400855 + 0.916142i \(0.631287\pi\)
\(228\) 211.828 0.0615292
\(229\) 995.241 0.287194 0.143597 0.989636i \(-0.454133\pi\)
0.143597 + 0.989636i \(0.454133\pi\)
\(230\) −10072.3 −2.88759
\(231\) 201.994 0.0575336
\(232\) −2305.92 −0.652547
\(233\) −2034.51 −0.572041 −0.286020 0.958224i \(-0.592332\pi\)
−0.286020 + 0.958224i \(0.592332\pi\)
\(234\) 1749.66 0.488797
\(235\) −283.708 −0.0787534
\(236\) 2403.61 0.662973
\(237\) −52.3355 −0.0143441
\(238\) 2450.19 0.667321
\(239\) 2343.82 0.634348 0.317174 0.948367i \(-0.397266\pi\)
0.317174 + 0.948367i \(0.397266\pi\)
\(240\) 56.9172 0.0153083
\(241\) 2300.34 0.614847 0.307423 0.951573i \(-0.400533\pi\)
0.307423 + 0.951573i \(0.400533\pi\)
\(242\) −4805.68 −1.27653
\(243\) −323.879 −0.0855013
\(244\) 9625.02 2.52532
\(245\) 6529.25 1.70261
\(246\) −89.4747 −0.0231898
\(247\) −1840.85 −0.474214
\(248\) 111.923 0.0286578
\(249\) 134.480 0.0342262
\(250\) 846.786 0.214222
\(251\) 2168.50 0.545316 0.272658 0.962111i \(-0.412097\pi\)
0.272658 + 0.962111i \(0.412097\pi\)
\(252\) −8532.15 −2.13284
\(253\) −7297.15 −1.81331
\(254\) −252.574 −0.0623933
\(255\) 45.8797 0.0112671
\(256\) −1199.24 −0.292783
\(257\) −7909.72 −1.91982 −0.959912 0.280302i \(-0.909565\pi\)
−0.959912 + 0.280302i \(0.909565\pi\)
\(258\) 0 0
\(259\) −5791.96 −1.38956
\(260\) 2590.64 0.617940
\(261\) −4124.70 −0.978208
\(262\) −7278.91 −1.71638
\(263\) −96.5256 −0.0226313 −0.0113156 0.999936i \(-0.503602\pi\)
−0.0113156 + 0.999936i \(0.503602\pi\)
\(264\) −110.028 −0.0256507
\(265\) −1034.59 −0.239828
\(266\) 15264.2 3.51845
\(267\) −57.7197 −0.0132299
\(268\) −7976.56 −1.81808
\(269\) 4568.99 1.03560 0.517800 0.855502i \(-0.326751\pi\)
0.517800 + 0.855502i \(0.326751\pi\)
\(270\) −543.543 −0.122515
\(271\) −4983.94 −1.11717 −0.558584 0.829448i \(-0.688655\pi\)
−0.558584 + 0.829448i \(0.688655\pi\)
\(272\) 500.185 0.111501
\(273\) −60.4080 −0.0133922
\(274\) 7745.74 1.70780
\(275\) −5537.55 −1.21428
\(276\) −251.115 −0.0547657
\(277\) 4752.99 1.03097 0.515487 0.856898i \(-0.327611\pi\)
0.515487 + 0.856898i \(0.327611\pi\)
\(278\) 6346.80 1.36927
\(279\) 200.202 0.0429598
\(280\) −6436.07 −1.37367
\(281\) 736.557 0.156368 0.0781838 0.996939i \(-0.475088\pi\)
0.0781838 + 0.996939i \(0.475088\pi\)
\(282\) −12.0272 −0.00253975
\(283\) −2987.95 −0.627616 −0.313808 0.949486i \(-0.601605\pi\)
−0.313808 + 0.949486i \(0.601605\pi\)
\(284\) −12588.9 −2.63033
\(285\) 285.821 0.0594055
\(286\) 3191.39 0.659828
\(287\) −3791.77 −0.779865
\(288\) −6216.75 −1.27196
\(289\) −4509.81 −0.917935
\(290\) −10384.7 −2.10279
\(291\) −266.289 −0.0536430
\(292\) −6878.16 −1.37847
\(293\) −4201.98 −0.837823 −0.418912 0.908027i \(-0.637588\pi\)
−0.418912 + 0.908027i \(0.637588\pi\)
\(294\) 276.794 0.0549079
\(295\) 3243.20 0.640090
\(296\) 3154.93 0.619516
\(297\) −393.785 −0.0769352
\(298\) 13901.2 2.70226
\(299\) 2182.27 0.422087
\(300\) −190.562 −0.0366737
\(301\) 0 0
\(302\) −2181.19 −0.415608
\(303\) −14.2196 −0.00269603
\(304\) 3116.04 0.587886
\(305\) 12987.1 2.43816
\(306\) −2387.34 −0.445996
\(307\) 9337.54 1.73590 0.867950 0.496651i \(-0.165437\pi\)
0.867950 + 0.496651i \(0.165437\pi\)
\(308\) −15562.7 −2.87912
\(309\) 145.687 0.0268215
\(310\) 504.046 0.0923481
\(311\) 592.021 0.107943 0.0539717 0.998542i \(-0.482812\pi\)
0.0539717 + 0.998542i \(0.482812\pi\)
\(312\) 32.9048 0.00597073
\(313\) −1752.01 −0.316388 −0.158194 0.987408i \(-0.550567\pi\)
−0.158194 + 0.987408i \(0.550567\pi\)
\(314\) −2128.67 −0.382573
\(315\) −11512.5 −2.05922
\(316\) 4032.21 0.717815
\(317\) −7339.63 −1.30043 −0.650213 0.759752i \(-0.725320\pi\)
−0.650213 + 0.759752i \(0.725320\pi\)
\(318\) −43.8594 −0.00773431
\(319\) −7523.49 −1.32049
\(320\) −12580.5 −2.19772
\(321\) 61.6674 0.0107226
\(322\) −18095.2 −3.13169
\(323\) 2511.77 0.432690
\(324\) 8306.49 1.42430
\(325\) 1656.05 0.282649
\(326\) −15802.9 −2.68479
\(327\) 7.06809 0.00119531
\(328\) 2065.42 0.347694
\(329\) −509.690 −0.0854107
\(330\) −495.512 −0.0826577
\(331\) −5741.22 −0.953372 −0.476686 0.879074i \(-0.658162\pi\)
−0.476686 + 0.879074i \(0.658162\pi\)
\(332\) −10361.1 −1.71276
\(333\) 5643.37 0.928693
\(334\) 1261.79 0.206713
\(335\) −10762.8 −1.75533
\(336\) 102.254 0.0166024
\(337\) 4523.93 0.731259 0.365629 0.930761i \(-0.380854\pi\)
0.365629 + 0.930761i \(0.380854\pi\)
\(338\) 8727.92 1.40455
\(339\) 205.353 0.0329005
\(340\) −3534.82 −0.563831
\(341\) 365.171 0.0579915
\(342\) −14872.6 −2.35151
\(343\) 2232.90 0.351502
\(344\) 0 0
\(345\) −338.831 −0.0528754
\(346\) 9136.78 1.41964
\(347\) 1795.05 0.277704 0.138852 0.990313i \(-0.455659\pi\)
0.138852 + 0.990313i \(0.455659\pi\)
\(348\) −258.904 −0.0398814
\(349\) 5427.46 0.832451 0.416225 0.909261i \(-0.363353\pi\)
0.416225 + 0.909261i \(0.363353\pi\)
\(350\) −13731.8 −2.09713
\(351\) 117.765 0.0179083
\(352\) −11339.4 −1.71703
\(353\) 6592.90 0.994064 0.497032 0.867732i \(-0.334423\pi\)
0.497032 + 0.867732i \(0.334423\pi\)
\(354\) 137.489 0.0206425
\(355\) −16986.3 −2.53954
\(356\) 4447.04 0.662057
\(357\) 82.4243 0.0122195
\(358\) 2920.22 0.431113
\(359\) −915.664 −0.134615 −0.0673077 0.997732i \(-0.521441\pi\)
−0.0673077 + 0.997732i \(0.521441\pi\)
\(360\) 6270.96 0.918079
\(361\) 8788.82 1.28136
\(362\) 13226.1 1.92030
\(363\) −161.663 −0.0233749
\(364\) 4654.16 0.670176
\(365\) −9280.74 −1.33089
\(366\) 550.560 0.0786291
\(367\) 5689.49 0.809235 0.404617 0.914486i \(-0.367405\pi\)
0.404617 + 0.914486i \(0.367405\pi\)
\(368\) −3693.96 −0.523264
\(369\) 3694.50 0.521214
\(370\) 14208.2 1.99635
\(371\) −1858.68 −0.260102
\(372\) 12.5665 0.00175146
\(373\) −5695.13 −0.790570 −0.395285 0.918558i \(-0.629354\pi\)
−0.395285 + 0.918558i \(0.629354\pi\)
\(374\) −4354.53 −0.602051
\(375\) 28.4858 0.00392267
\(376\) 277.633 0.0380793
\(377\) 2249.96 0.307371
\(378\) −976.492 −0.132871
\(379\) −9058.43 −1.22771 −0.613853 0.789420i \(-0.710381\pi\)
−0.613853 + 0.789420i \(0.710381\pi\)
\(380\) −22021.2 −2.97280
\(381\) −8.49657 −0.00114250
\(382\) 14165.1 1.89725
\(383\) −837.542 −0.111740 −0.0558700 0.998438i \(-0.517793\pi\)
−0.0558700 + 0.998438i \(0.517793\pi\)
\(384\) −260.017 −0.0345546
\(385\) −20998.9 −2.77975
\(386\) −9925.39 −1.30878
\(387\) 0 0
\(388\) 20516.3 2.68443
\(389\) −5940.26 −0.774250 −0.387125 0.922027i \(-0.626532\pi\)
−0.387125 + 0.922027i \(0.626532\pi\)
\(390\) 148.187 0.0192403
\(391\) −2977.62 −0.385127
\(392\) −6389.44 −0.823254
\(393\) −244.862 −0.0314292
\(394\) 5427.41 0.693982
\(395\) 5440.68 0.693039
\(396\) 15163.5 1.92423
\(397\) 13073.7 1.65277 0.826387 0.563103i \(-0.190393\pi\)
0.826387 + 0.563103i \(0.190393\pi\)
\(398\) −5514.56 −0.694522
\(399\) 513.486 0.0644272
\(400\) −2803.22 −0.350402
\(401\) −2500.54 −0.311400 −0.155700 0.987804i \(-0.549763\pi\)
−0.155700 + 0.987804i \(0.549763\pi\)
\(402\) −456.267 −0.0566083
\(403\) −109.207 −0.0134988
\(404\) 1095.56 0.134916
\(405\) 11208.0 1.37514
\(406\) −18656.4 −2.28055
\(407\) 10293.6 1.25364
\(408\) −44.8973 −0.00544791
\(409\) −3771.59 −0.455974 −0.227987 0.973664i \(-0.573214\pi\)
−0.227987 + 0.973664i \(0.573214\pi\)
\(410\) 9301.59 1.12042
\(411\) 260.566 0.0312720
\(412\) −11224.5 −1.34221
\(413\) 5826.52 0.694199
\(414\) 17630.9 2.09303
\(415\) −13980.2 −1.65365
\(416\) 3391.14 0.399674
\(417\) 213.506 0.0250730
\(418\) −27127.8 −3.17431
\(419\) −8733.46 −1.01828 −0.509138 0.860685i \(-0.670036\pi\)
−0.509138 + 0.860685i \(0.670036\pi\)
\(420\) −722.629 −0.0839541
\(421\) −1186.37 −0.137340 −0.0686698 0.997639i \(-0.521875\pi\)
−0.0686698 + 0.997639i \(0.521875\pi\)
\(422\) 11345.4 1.30874
\(423\) 496.614 0.0570833
\(424\) 1012.44 0.115963
\(425\) −2259.61 −0.257899
\(426\) −720.097 −0.0818986
\(427\) 23331.7 2.64426
\(428\) −4751.19 −0.536583
\(429\) 107.358 0.0120823
\(430\) 0 0
\(431\) −5136.09 −0.574007 −0.287003 0.957930i \(-0.592659\pi\)
−0.287003 + 0.957930i \(0.592659\pi\)
\(432\) −199.342 −0.0222010
\(433\) 1680.47 0.186509 0.0932544 0.995642i \(-0.470273\pi\)
0.0932544 + 0.995642i \(0.470273\pi\)
\(434\) 905.535 0.100155
\(435\) −349.341 −0.0385048
\(436\) −544.564 −0.0598163
\(437\) −18549.9 −2.03058
\(438\) −393.437 −0.0429205
\(439\) −9868.00 −1.07283 −0.536417 0.843953i \(-0.680222\pi\)
−0.536417 + 0.843953i \(0.680222\pi\)
\(440\) 11438.3 1.23932
\(441\) −11429.1 −1.23411
\(442\) 1302.25 0.140140
\(443\) −6533.37 −0.700699 −0.350350 0.936619i \(-0.613937\pi\)
−0.350350 + 0.936619i \(0.613937\pi\)
\(444\) 354.230 0.0378626
\(445\) 6000.41 0.639206
\(446\) 1430.09 0.151831
\(447\) 467.635 0.0494819
\(448\) −22601.2 −2.38350
\(449\) 12041.4 1.26564 0.632818 0.774301i \(-0.281898\pi\)
0.632818 + 0.774301i \(0.281898\pi\)
\(450\) 13379.5 1.40159
\(451\) 6738.81 0.703588
\(452\) −15821.5 −1.64642
\(453\) −73.3753 −0.00761031
\(454\) 12083.9 1.24917
\(455\) 6279.88 0.647045
\(456\) −279.701 −0.0287241
\(457\) −13506.5 −1.38251 −0.691257 0.722609i \(-0.742943\pi\)
−0.691257 + 0.722609i \(0.742943\pi\)
\(458\) −4386.10 −0.447486
\(459\) −160.685 −0.0163402
\(460\) 26105.3 2.64602
\(461\) 17597.0 1.77781 0.888907 0.458089i \(-0.151466\pi\)
0.888907 + 0.458089i \(0.151466\pi\)
\(462\) −890.203 −0.0896450
\(463\) 10200.5 1.02388 0.511940 0.859021i \(-0.328927\pi\)
0.511940 + 0.859021i \(0.328927\pi\)
\(464\) −3808.54 −0.381050
\(465\) 16.9561 0.00169101
\(466\) 8966.24 0.891316
\(467\) −9581.35 −0.949405 −0.474702 0.880146i \(-0.657444\pi\)
−0.474702 + 0.880146i \(0.657444\pi\)
\(468\) −4534.76 −0.447905
\(469\) −19335.8 −1.90371
\(470\) 1250.32 0.122708
\(471\) −71.6084 −0.00700539
\(472\) −3173.76 −0.309500
\(473\) 0 0
\(474\) 230.646 0.0223501
\(475\) −14076.9 −1.35977
\(476\) −6350.42 −0.611493
\(477\) 1811.00 0.173836
\(478\) −10329.4 −0.988398
\(479\) 6024.59 0.574677 0.287339 0.957829i \(-0.407230\pi\)
0.287339 + 0.957829i \(0.407230\pi\)
\(480\) −526.527 −0.0500678
\(481\) −3078.37 −0.291812
\(482\) −10137.8 −0.958014
\(483\) −608.720 −0.0573452
\(484\) 12455.4 1.16974
\(485\) 27682.8 2.59177
\(486\) 1427.36 0.133223
\(487\) −10790.9 −1.00407 −0.502037 0.864846i \(-0.667416\pi\)
−0.502037 + 0.864846i \(0.667416\pi\)
\(488\) −12709.0 −1.17891
\(489\) −531.608 −0.0491619
\(490\) −28774.8 −2.65289
\(491\) −2808.02 −0.258094 −0.129047 0.991638i \(-0.541192\pi\)
−0.129047 + 0.991638i \(0.541192\pi\)
\(492\) 231.901 0.0212498
\(493\) −3069.98 −0.280456
\(494\) 8112.77 0.738888
\(495\) 20460.2 1.85781
\(496\) 184.857 0.0167345
\(497\) −30516.4 −2.75422
\(498\) −592.663 −0.0533290
\(499\) −11448.8 −1.02709 −0.513546 0.858062i \(-0.671668\pi\)
−0.513546 + 0.858062i \(0.671668\pi\)
\(500\) −2194.70 −0.196300
\(501\) 42.4467 0.00378518
\(502\) −9556.72 −0.849676
\(503\) −17619.7 −1.56188 −0.780940 0.624606i \(-0.785260\pi\)
−0.780940 + 0.624606i \(0.785260\pi\)
\(504\) 11266.0 0.995687
\(505\) 1478.24 0.130259
\(506\) 32159.0 2.82538
\(507\) 293.607 0.0257190
\(508\) 654.622 0.0571735
\(509\) 19675.8 1.71339 0.856696 0.515822i \(-0.172513\pi\)
0.856696 + 0.515822i \(0.172513\pi\)
\(510\) −202.195 −0.0175556
\(511\) −16673.2 −1.44340
\(512\) −8745.82 −0.754911
\(513\) −1001.03 −0.0861535
\(514\) 34858.7 2.99134
\(515\) −15145.3 −1.29589
\(516\) 0 0
\(517\) 905.830 0.0770568
\(518\) 25525.6 2.16511
\(519\) 307.361 0.0259955
\(520\) −3420.71 −0.288477
\(521\) −9437.66 −0.793611 −0.396805 0.917903i \(-0.629881\pi\)
−0.396805 + 0.917903i \(0.629881\pi\)
\(522\) 18177.8 1.52418
\(523\) 9442.26 0.789448 0.394724 0.918800i \(-0.370840\pi\)
0.394724 + 0.918800i \(0.370840\pi\)
\(524\) 18865.5 1.57279
\(525\) −461.936 −0.0384010
\(526\) 425.395 0.0352626
\(527\) 149.009 0.0123168
\(528\) −181.727 −0.0149785
\(529\) 9823.31 0.807373
\(530\) 4559.52 0.373685
\(531\) −5677.05 −0.463960
\(532\) −39561.8 −3.22410
\(533\) −2015.29 −0.163775
\(534\) 254.375 0.0206140
\(535\) −6410.81 −0.518062
\(536\) 10532.4 0.848748
\(537\) 98.2360 0.00789422
\(538\) −20135.9 −1.61360
\(539\) −20846.8 −1.66593
\(540\) 1408.76 0.112265
\(541\) −15227.6 −1.21014 −0.605069 0.796173i \(-0.706854\pi\)
−0.605069 + 0.796173i \(0.706854\pi\)
\(542\) 21964.6 1.74070
\(543\) 444.925 0.0351631
\(544\) −4627.08 −0.364677
\(545\) −734.783 −0.0577517
\(546\) 266.222 0.0208668
\(547\) 16610.6 1.29839 0.649196 0.760622i \(-0.275106\pi\)
0.649196 + 0.760622i \(0.275106\pi\)
\(548\) −20075.4 −1.56493
\(549\) −22733.2 −1.76726
\(550\) 24404.3 1.89201
\(551\) −19125.3 −1.47870
\(552\) 331.576 0.0255667
\(553\) 9774.36 0.751624
\(554\) −20946.8 −1.60639
\(555\) 477.964 0.0365558
\(556\) −16449.7 −1.25471
\(557\) 299.887 0.0228126 0.0114063 0.999935i \(-0.496369\pi\)
0.0114063 + 0.999935i \(0.496369\pi\)
\(558\) −882.305 −0.0669372
\(559\) 0 0
\(560\) −10630.1 −0.802146
\(561\) −146.486 −0.0110243
\(562\) −3246.06 −0.243642
\(563\) 2044.50 0.153047 0.0765234 0.997068i \(-0.475618\pi\)
0.0765234 + 0.997068i \(0.475618\pi\)
\(564\) 31.1721 0.00232727
\(565\) −21348.1 −1.58959
\(566\) 13168.1 0.977910
\(567\) 20135.5 1.49138
\(568\) 16622.6 1.22794
\(569\) −23154.9 −1.70598 −0.852990 0.521927i \(-0.825213\pi\)
−0.852990 + 0.521927i \(0.825213\pi\)
\(570\) −1259.63 −0.0925617
\(571\) −9709.83 −0.711635 −0.355818 0.934555i \(-0.615798\pi\)
−0.355818 + 0.934555i \(0.615798\pi\)
\(572\) −8271.45 −0.604627
\(573\) 476.513 0.0347411
\(574\) 16710.6 1.21513
\(575\) 16687.7 1.21030
\(576\) 22021.4 1.59299
\(577\) 11397.7 0.822342 0.411171 0.911558i \(-0.365120\pi\)
0.411171 + 0.911558i \(0.365120\pi\)
\(578\) 19875.1 1.43027
\(579\) −333.889 −0.0239654
\(580\) 26915.1 1.92688
\(581\) −25116.0 −1.79343
\(582\) 1173.55 0.0835830
\(583\) 3303.28 0.234662
\(584\) 9082.02 0.643522
\(585\) −6118.78 −0.432445
\(586\) 18518.4 1.30544
\(587\) −14700.5 −1.03366 −0.516828 0.856089i \(-0.672887\pi\)
−0.516828 + 0.856089i \(0.672887\pi\)
\(588\) −717.394 −0.0503144
\(589\) 928.294 0.0649401
\(590\) −14293.0 −0.997347
\(591\) 182.578 0.0127077
\(592\) 5210.81 0.361762
\(593\) −7917.91 −0.548313 −0.274157 0.961685i \(-0.588399\pi\)
−0.274157 + 0.961685i \(0.588399\pi\)
\(594\) 1735.44 0.119875
\(595\) −8568.65 −0.590387
\(596\) −36029.2 −2.47619
\(597\) −185.509 −0.0127176
\(598\) −9617.41 −0.657667
\(599\) −8348.80 −0.569487 −0.284743 0.958604i \(-0.591908\pi\)
−0.284743 + 0.958604i \(0.591908\pi\)
\(600\) 251.621 0.0171206
\(601\) −9292.38 −0.630689 −0.315345 0.948977i \(-0.602120\pi\)
−0.315345 + 0.948977i \(0.602120\pi\)
\(602\) 0 0
\(603\) 18839.7 1.27233
\(604\) 5653.23 0.380839
\(605\) 16806.1 1.12936
\(606\) 62.6669 0.00420078
\(607\) 7326.80 0.489927 0.244964 0.969532i \(-0.421224\pi\)
0.244964 + 0.969532i \(0.421224\pi\)
\(608\) −28825.7 −1.92276
\(609\) −627.601 −0.0417598
\(610\) −57235.0 −3.79898
\(611\) −270.896 −0.0179366
\(612\) 6187.50 0.408685
\(613\) 3020.41 0.199010 0.0995050 0.995037i \(-0.468274\pi\)
0.0995050 + 0.995037i \(0.468274\pi\)
\(614\) −41151.2 −2.70477
\(615\) 312.905 0.0205163
\(616\) 20549.3 1.34408
\(617\) −10714.8 −0.699130 −0.349565 0.936912i \(-0.613671\pi\)
−0.349565 + 0.936912i \(0.613671\pi\)
\(618\) −642.053 −0.0417915
\(619\) 233.807 0.0151818 0.00759088 0.999971i \(-0.497584\pi\)
0.00759088 + 0.999971i \(0.497584\pi\)
\(620\) −1306.39 −0.0846223
\(621\) 1186.69 0.0766832
\(622\) −2609.08 −0.168190
\(623\) 10779.9 0.693240
\(624\) 54.3469 0.00348656
\(625\) −17027.9 −1.08979
\(626\) 7721.22 0.492975
\(627\) −912.577 −0.0581257
\(628\) 5517.09 0.350567
\(629\) 4200.32 0.266260
\(630\) 50736.3 3.20854
\(631\) 223.889 0.0141250 0.00706250 0.999975i \(-0.497752\pi\)
0.00706250 + 0.999975i \(0.497752\pi\)
\(632\) −5324.18 −0.335102
\(633\) 381.660 0.0239646
\(634\) 32346.3 2.02624
\(635\) 883.285 0.0552001
\(636\) 113.675 0.00708726
\(637\) 6234.39 0.387779
\(638\) 33156.5 2.05749
\(639\) 29733.5 1.84075
\(640\) 27030.8 1.66951
\(641\) 30800.3 1.89788 0.948938 0.315463i \(-0.102160\pi\)
0.948938 + 0.315463i \(0.102160\pi\)
\(642\) −271.773 −0.0167072
\(643\) 16963.7 1.04041 0.520204 0.854042i \(-0.325856\pi\)
0.520204 + 0.854042i \(0.325856\pi\)
\(644\) 46899.1 2.86969
\(645\) 0 0
\(646\) −11069.6 −0.674189
\(647\) −22076.7 −1.34146 −0.670730 0.741701i \(-0.734019\pi\)
−0.670730 + 0.741701i \(0.734019\pi\)
\(648\) −10968.0 −0.664914
\(649\) −10355.0 −0.626301
\(650\) −7298.31 −0.440405
\(651\) 30.4622 0.00183396
\(652\) 40958.0 2.46018
\(653\) 629.038 0.0376970 0.0188485 0.999822i \(-0.494000\pi\)
0.0188485 + 0.999822i \(0.494000\pi\)
\(654\) −31.1496 −0.00186245
\(655\) 25455.3 1.51851
\(656\) 3411.32 0.203033
\(657\) 16245.4 0.964679
\(658\) 2246.24 0.133081
\(659\) 22663.0 1.33964 0.669821 0.742523i \(-0.266371\pi\)
0.669821 + 0.742523i \(0.266371\pi\)
\(660\) 1284.27 0.0757426
\(661\) −8652.12 −0.509120 −0.254560 0.967057i \(-0.581931\pi\)
−0.254560 + 0.967057i \(0.581931\pi\)
\(662\) 25302.0 1.48548
\(663\) 43.8078 0.00256614
\(664\) 13680.9 0.799581
\(665\) −53380.9 −3.11281
\(666\) −24870.7 −1.44703
\(667\) 22672.4 1.31616
\(668\) −3270.32 −0.189420
\(669\) 48.1081 0.00278022
\(670\) 47432.5 2.73504
\(671\) −41465.5 −2.38563
\(672\) −945.922 −0.0543002
\(673\) 27477.3 1.57381 0.786904 0.617076i \(-0.211683\pi\)
0.786904 + 0.617076i \(0.211683\pi\)
\(674\) −19937.3 −1.13940
\(675\) 900.538 0.0513507
\(676\) −22621.0 −1.28704
\(677\) 12923.5 0.733663 0.366831 0.930287i \(-0.380443\pi\)
0.366831 + 0.930287i \(0.380443\pi\)
\(678\) −905.006 −0.0512633
\(679\) 49733.0 2.81086
\(680\) 4667.42 0.263217
\(681\) 406.501 0.0228739
\(682\) −1609.33 −0.0903586
\(683\) −9451.83 −0.529523 −0.264762 0.964314i \(-0.585293\pi\)
−0.264762 + 0.964314i \(0.585293\pi\)
\(684\) 38546.8 2.15479
\(685\) −27087.9 −1.51091
\(686\) −9840.55 −0.547688
\(687\) −147.548 −0.00819404
\(688\) 0 0
\(689\) −987.870 −0.0546224
\(690\) 1493.25 0.0823870
\(691\) 30813.4 1.69638 0.848188 0.529696i \(-0.177694\pi\)
0.848188 + 0.529696i \(0.177694\pi\)
\(692\) −23680.7 −1.30088
\(693\) 36757.4 2.01486
\(694\) −7910.91 −0.432701
\(695\) −22195.6 −1.21141
\(696\) 341.860 0.0186181
\(697\) 2749.79 0.149434
\(698\) −23919.2 −1.29707
\(699\) 301.624 0.0163211
\(700\) 35590.0 1.92168
\(701\) 8156.30 0.439457 0.219728 0.975561i \(-0.429483\pi\)
0.219728 + 0.975561i \(0.429483\pi\)
\(702\) −518.996 −0.0279035
\(703\) 26167.1 1.40386
\(704\) 40167.3 2.15037
\(705\) 42.0607 0.00224695
\(706\) −29055.4 −1.54889
\(707\) 2655.71 0.141270
\(708\) −356.344 −0.0189156
\(709\) 185.334 0.00981717 0.00490859 0.999988i \(-0.498438\pi\)
0.00490859 + 0.999988i \(0.498438\pi\)
\(710\) 74859.7 3.95695
\(711\) −9523.61 −0.502339
\(712\) −5871.93 −0.309073
\(713\) −1100.46 −0.0578016
\(714\) −363.250 −0.0190396
\(715\) −11160.7 −0.583758
\(716\) −7568.64 −0.395046
\(717\) −347.479 −0.0180988
\(718\) 4035.40 0.209749
\(719\) 7215.59 0.374264 0.187132 0.982335i \(-0.440081\pi\)
0.187132 + 0.982335i \(0.440081\pi\)
\(720\) 10357.4 0.536105
\(721\) −27209.0 −1.40543
\(722\) −38732.9 −1.99652
\(723\) −341.034 −0.0175424
\(724\) −34279.4 −1.75965
\(725\) 17205.3 0.881363
\(726\) 712.458 0.0364212
\(727\) −32590.1 −1.66259 −0.831293 0.555835i \(-0.812399\pi\)
−0.831293 + 0.555835i \(0.812399\pi\)
\(728\) −6145.42 −0.312863
\(729\) −19586.9 −0.995119
\(730\) 40900.9 2.07371
\(731\) 0 0
\(732\) −1426.94 −0.0720510
\(733\) −12464.9 −0.628105 −0.314052 0.949406i \(-0.601687\pi\)
−0.314052 + 0.949406i \(0.601687\pi\)
\(734\) −25074.0 −1.26090
\(735\) −967.984 −0.0485777
\(736\) 34171.9 1.71140
\(737\) 34363.8 1.71751
\(738\) −16281.9 −0.812121
\(739\) 15442.3 0.768681 0.384340 0.923191i \(-0.374429\pi\)
0.384340 + 0.923191i \(0.374429\pi\)
\(740\) −36825.0 −1.82934
\(741\) 272.913 0.0135300
\(742\) 8191.32 0.405274
\(743\) −3389.16 −0.167343 −0.0836717 0.996493i \(-0.526665\pi\)
−0.0836717 + 0.996493i \(0.526665\pi\)
\(744\) −16.5930 −0.000817648 0
\(745\) −48614.3 −2.39073
\(746\) 25098.8 1.23181
\(747\) 24471.6 1.19862
\(748\) 11286.1 0.551684
\(749\) −11517.2 −0.561856
\(750\) −125.539 −0.00611205
\(751\) −12106.9 −0.588266 −0.294133 0.955765i \(-0.595031\pi\)
−0.294133 + 0.955765i \(0.595031\pi\)
\(752\) 458.549 0.0222361
\(753\) −321.487 −0.0155586
\(754\) −9915.72 −0.478925
\(755\) 7627.93 0.367694
\(756\) 2530.87 0.121755
\(757\) 13089.0 0.628441 0.314220 0.949350i \(-0.398257\pi\)
0.314220 + 0.949350i \(0.398257\pi\)
\(758\) 39921.1 1.91293
\(759\) 1081.83 0.0517363
\(760\) 29077.1 1.38781
\(761\) −5492.31 −0.261624 −0.130812 0.991407i \(-0.541758\pi\)
−0.130812 + 0.991407i \(0.541758\pi\)
\(762\) 37.4450 0.00178017
\(763\) −1320.06 −0.0626336
\(764\) −36713.2 −1.73853
\(765\) 8348.83 0.394579
\(766\) 3691.10 0.174106
\(767\) 3096.74 0.145785
\(768\) 177.792 0.00835352
\(769\) −689.866 −0.0323501 −0.0161750 0.999869i \(-0.505149\pi\)
−0.0161750 + 0.999869i \(0.505149\pi\)
\(770\) 92543.6 4.33122
\(771\) 1172.64 0.0547753
\(772\) 25724.6 1.19929
\(773\) −24050.5 −1.11906 −0.559532 0.828809i \(-0.689019\pi\)
−0.559532 + 0.828809i \(0.689019\pi\)
\(774\) 0 0
\(775\) −835.100 −0.0387067
\(776\) −27090.0 −1.25319
\(777\) 858.678 0.0396460
\(778\) 26179.2 1.20639
\(779\) 17130.6 0.787891
\(780\) −384.071 −0.0176307
\(781\) 54234.3 2.48483
\(782\) 13122.6 0.600080
\(783\) 1223.50 0.0558420
\(784\) −10553.0 −0.480733
\(785\) 7444.25 0.338467
\(786\) 1079.12 0.0489709
\(787\) 2373.63 0.107511 0.0537553 0.998554i \(-0.482881\pi\)
0.0537553 + 0.998554i \(0.482881\pi\)
\(788\) −14066.8 −0.635924
\(789\) 14.3103 0.000645702 0
\(790\) −23977.5 −1.07985
\(791\) −38352.5 −1.72397
\(792\) −20022.1 −0.898300
\(793\) 12400.6 0.555306
\(794\) −57616.8 −2.57524
\(795\) 153.382 0.00684264
\(796\) 14292.6 0.636419
\(797\) 19870.8 0.883138 0.441569 0.897227i \(-0.354422\pi\)
0.441569 + 0.897227i \(0.354422\pi\)
\(798\) −2262.97 −0.100386
\(799\) 369.626 0.0163660
\(800\) 25931.8 1.14604
\(801\) −10503.4 −0.463319
\(802\) 11020.1 0.485202
\(803\) 29631.8 1.30222
\(804\) 1182.55 0.0518725
\(805\) 63281.2 2.77064
\(806\) 481.284 0.0210329
\(807\) −677.369 −0.0295471
\(808\) −1446.59 −0.0629837
\(809\) 43547.9 1.89254 0.946269 0.323380i \(-0.104819\pi\)
0.946269 + 0.323380i \(0.104819\pi\)
\(810\) −49394.4 −2.14264
\(811\) 16180.7 0.700592 0.350296 0.936639i \(-0.386081\pi\)
0.350296 + 0.936639i \(0.386081\pi\)
\(812\) 48353.8 2.08976
\(813\) 738.887 0.0318744
\(814\) −45364.5 −1.95335
\(815\) 55264.8 2.37527
\(816\) −74.1541 −0.00318127
\(817\) 0 0
\(818\) 16621.7 0.710468
\(819\) −10992.6 −0.469001
\(820\) −24107.9 −1.02669
\(821\) 22531.5 0.957803 0.478901 0.877869i \(-0.341035\pi\)
0.478901 + 0.877869i \(0.341035\pi\)
\(822\) −1148.33 −0.0487259
\(823\) 39498.4 1.67294 0.836468 0.548015i \(-0.184616\pi\)
0.836468 + 0.548015i \(0.184616\pi\)
\(824\) 14821.0 0.626595
\(825\) 820.961 0.0346451
\(826\) −25677.9 −1.08166
\(827\) −13678.9 −0.575165 −0.287583 0.957756i \(-0.592852\pi\)
−0.287583 + 0.957756i \(0.592852\pi\)
\(828\) −45695.9 −1.91793
\(829\) −20316.7 −0.851178 −0.425589 0.904917i \(-0.639933\pi\)
−0.425589 + 0.904917i \(0.639933\pi\)
\(830\) 61611.9 2.57660
\(831\) −704.648 −0.0294151
\(832\) −12012.4 −0.500545
\(833\) −8506.57 −0.353824
\(834\) −940.935 −0.0390671
\(835\) −4412.66 −0.182882
\(836\) 70309.8 2.90875
\(837\) −59.3855 −0.00245241
\(838\) 38489.0 1.58661
\(839\) 32447.8 1.33519 0.667593 0.744526i \(-0.267325\pi\)
0.667593 + 0.744526i \(0.267325\pi\)
\(840\) 954.170 0.0391928
\(841\) −1013.33 −0.0415488
\(842\) 5228.40 0.213994
\(843\) −109.197 −0.00446139
\(844\) −29405.1 −1.19925
\(845\) −30522.7 −1.24262
\(846\) −2188.61 −0.0889434
\(847\) 30192.7 1.22483
\(848\) 1672.18 0.0677159
\(849\) 442.975 0.0179068
\(850\) 9958.26 0.401842
\(851\) −31020.2 −1.24954
\(852\) 1866.35 0.0750471
\(853\) 11503.9 0.461765 0.230883 0.972982i \(-0.425839\pi\)
0.230883 + 0.972982i \(0.425839\pi\)
\(854\) −102824. −4.12012
\(855\) 52011.4 2.08041
\(856\) 6273.54 0.250497
\(857\) −3256.25 −0.129792 −0.0648958 0.997892i \(-0.520672\pi\)
−0.0648958 + 0.997892i \(0.520672\pi\)
\(858\) −473.135 −0.0188258
\(859\) 35756.2 1.42024 0.710119 0.704082i \(-0.248641\pi\)
0.710119 + 0.704082i \(0.248641\pi\)
\(860\) 0 0
\(861\) 562.144 0.0222507
\(862\) 22635.1 0.894379
\(863\) −17388.1 −0.685861 −0.342930 0.939361i \(-0.611420\pi\)
−0.342930 + 0.939361i \(0.611420\pi\)
\(864\) 1844.06 0.0726114
\(865\) −31952.6 −1.25598
\(866\) −7405.96 −0.290606
\(867\) 668.596 0.0261900
\(868\) −2346.97 −0.0917757
\(869\) −17371.2 −0.678108
\(870\) 1539.57 0.0599957
\(871\) −10276.8 −0.399788
\(872\) 719.050 0.0279244
\(873\) −48457.1 −1.87861
\(874\) 81750.9 3.16392
\(875\) −5320.11 −0.205546
\(876\) 1019.71 0.0393298
\(877\) 25399.9 0.977986 0.488993 0.872288i \(-0.337364\pi\)
0.488993 + 0.872288i \(0.337364\pi\)
\(878\) 43488.9 1.67162
\(879\) 622.958 0.0239043
\(880\) 18891.9 0.723690
\(881\) −35948.0 −1.37471 −0.687354 0.726323i \(-0.741228\pi\)
−0.687354 + 0.726323i \(0.741228\pi\)
\(882\) 50368.7 1.92291
\(883\) −19959.4 −0.760689 −0.380345 0.924845i \(-0.624195\pi\)
−0.380345 + 0.924845i \(0.624195\pi\)
\(884\) −3375.19 −0.128416
\(885\) −480.816 −0.0182627
\(886\) 28793.0 1.09178
\(887\) −46824.5 −1.77251 −0.886254 0.463200i \(-0.846701\pi\)
−0.886254 + 0.463200i \(0.846701\pi\)
\(888\) −467.730 −0.0176757
\(889\) 1586.85 0.0598664
\(890\) −26444.2 −0.995969
\(891\) −35785.2 −1.34551
\(892\) −3706.51 −0.139129
\(893\) 2302.69 0.0862897
\(894\) −2060.90 −0.0770994
\(895\) −10212.4 −0.381411
\(896\) 48561.7 1.81064
\(897\) −323.529 −0.0120427
\(898\) −53067.4 −1.97203
\(899\) −1134.59 −0.0420922
\(900\) −34677.0 −1.28433
\(901\) 1347.91 0.0498395
\(902\) −29698.4 −1.09628
\(903\) 0 0
\(904\) 20891.0 0.768609
\(905\) −46253.4 −1.69891
\(906\) 323.370 0.0118579
\(907\) −26158.1 −0.957625 −0.478813 0.877917i \(-0.658933\pi\)
−0.478813 + 0.877917i \(0.658933\pi\)
\(908\) −31319.0 −1.14467
\(909\) −2587.58 −0.0944165
\(910\) −27675.9 −1.00818
\(911\) −4449.15 −0.161808 −0.0809038 0.996722i \(-0.525781\pi\)
−0.0809038 + 0.996722i \(0.525781\pi\)
\(912\) −461.965 −0.0167732
\(913\) 44636.5 1.61802
\(914\) 59524.2 2.15414
\(915\) −1925.38 −0.0695641
\(916\) 11367.9 0.410050
\(917\) 45731.3 1.64687
\(918\) 708.150 0.0254602
\(919\) −37998.1 −1.36392 −0.681959 0.731391i \(-0.738872\pi\)
−0.681959 + 0.731391i \(0.738872\pi\)
\(920\) −34469.9 −1.23526
\(921\) −1384.32 −0.0495277
\(922\) −77551.0 −2.77007
\(923\) −16219.2 −0.578397
\(924\) 2307.23 0.0821454
\(925\) −23540.1 −0.836750
\(926\) −44954.2 −1.59534
\(927\) 26511.0 0.939305
\(928\) 35231.8 1.24627
\(929\) −858.473 −0.0303182 −0.0151591 0.999885i \(-0.504825\pi\)
−0.0151591 + 0.999885i \(0.504825\pi\)
\(930\) −74.7267 −0.00263482
\(931\) −52994.2 −1.86554
\(932\) −23238.7 −0.816749
\(933\) −87.7692 −0.00307978
\(934\) 42225.7 1.47930
\(935\) 15228.4 0.532642
\(936\) 5987.76 0.209098
\(937\) −34170.2 −1.19135 −0.595674 0.803226i \(-0.703115\pi\)
−0.595674 + 0.803226i \(0.703115\pi\)
\(938\) 85214.0 2.96624
\(939\) 259.741 0.00902699
\(940\) −3240.58 −0.112443
\(941\) 1570.56 0.0544088 0.0272044 0.999630i \(-0.491340\pi\)
0.0272044 + 0.999630i \(0.491340\pi\)
\(942\) 315.583 0.0109153
\(943\) −20307.7 −0.701284
\(944\) −5241.90 −0.180730
\(945\) 3414.92 0.117553
\(946\) 0 0
\(947\) −20920.3 −0.717866 −0.358933 0.933363i \(-0.616859\pi\)
−0.358933 + 0.933363i \(0.616859\pi\)
\(948\) −597.789 −0.0204803
\(949\) −8861.62 −0.303120
\(950\) 62037.8 2.11871
\(951\) 1088.13 0.0371030
\(952\) 8385.18 0.285468
\(953\) 10346.8 0.351696 0.175848 0.984417i \(-0.443733\pi\)
0.175848 + 0.984417i \(0.443733\pi\)
\(954\) −7981.18 −0.270860
\(955\) −49537.3 −1.67852
\(956\) 26771.7 0.905710
\(957\) 1115.38 0.0376753
\(958\) −26550.8 −0.895424
\(959\) −48664.2 −1.63863
\(960\) 1865.10 0.0627041
\(961\) −29735.9 −0.998151
\(962\) 13566.6 0.454683
\(963\) 11221.8 0.375510
\(964\) 26275.1 0.877867
\(965\) 34710.4 1.15789
\(966\) 2682.67 0.0893515
\(967\) 17292.1 0.575052 0.287526 0.957773i \(-0.407167\pi\)
0.287526 + 0.957773i \(0.407167\pi\)
\(968\) −16446.2 −0.546076
\(969\) −372.379 −0.0123452
\(970\) −122000. −4.03833
\(971\) 7077.25 0.233903 0.116951 0.993138i \(-0.462688\pi\)
0.116951 + 0.993138i \(0.462688\pi\)
\(972\) −3699.42 −0.122077
\(973\) −39875.1 −1.31381
\(974\) 47556.4 1.56448
\(975\) −245.515 −0.00806437
\(976\) −20990.7 −0.688418
\(977\) 369.048 0.0120849 0.00604243 0.999982i \(-0.498077\pi\)
0.00604243 + 0.999982i \(0.498077\pi\)
\(978\) 2342.83 0.0766008
\(979\) −19158.3 −0.625435
\(980\) 74578.7 2.43095
\(981\) 1286.20 0.0418604
\(982\) 12375.1 0.402145
\(983\) −38678.1 −1.25497 −0.627487 0.778627i \(-0.715916\pi\)
−0.627487 + 0.778627i \(0.715916\pi\)
\(984\) −306.205 −0.00992019
\(985\) −18980.4 −0.613974
\(986\) 13529.6 0.436988
\(987\) 75.5633 0.00243689
\(988\) −21026.7 −0.677073
\(989\) 0 0
\(990\) −90169.4 −2.89472
\(991\) 33297.9 1.06735 0.533674 0.845690i \(-0.320811\pi\)
0.533674 + 0.845690i \(0.320811\pi\)
\(992\) −1710.06 −0.0547324
\(993\) 851.156 0.0272010
\(994\) 134488. 4.29144
\(995\) 19285.1 0.614453
\(996\) 1536.06 0.0488676
\(997\) −42935.5 −1.36387 −0.681936 0.731412i \(-0.738862\pi\)
−0.681936 + 0.731412i \(0.738862\pi\)
\(998\) 50455.6 1.60035
\(999\) −1673.98 −0.0530154
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 1849.4.a.k.1.9 60
43.30 odd 42 43.4.g.a.40.2 yes 120
43.33 odd 42 43.4.g.a.14.2 120
43.42 odd 2 1849.4.a.l.1.52 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.g.a.14.2 120 43.33 odd 42
43.4.g.a.40.2 yes 120 43.30 odd 42
1849.4.a.k.1.9 60 1.1 even 1 trivial
1849.4.a.l.1.52 60 43.42 odd 2