Properties

Label 6041.2.a.d.1.14
Level $6041$
Weight $2$
Character 6041.1
Self dual yes
Analytic conductor $48.238$
Analytic rank $1$
Dimension $101$
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] = [6041,2,Mod(1,6041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6041, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.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: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.14147 q^{2} -2.96762 q^{3} +2.58591 q^{4} +4.08817 q^{5} +6.35507 q^{6} -1.00000 q^{7} -1.25470 q^{8} +5.80675 q^{9} +O(q^{10})\) \(q-2.14147 q^{2} -2.96762 q^{3} +2.58591 q^{4} +4.08817 q^{5} +6.35507 q^{6} -1.00000 q^{7} -1.25470 q^{8} +5.80675 q^{9} -8.75470 q^{10} -1.22122 q^{11} -7.67398 q^{12} -1.03810 q^{13} +2.14147 q^{14} -12.1321 q^{15} -2.48490 q^{16} +0.790038 q^{17} -12.4350 q^{18} -6.74173 q^{19} +10.5716 q^{20} +2.96762 q^{21} +2.61520 q^{22} -1.01434 q^{23} +3.72348 q^{24} +11.7131 q^{25} +2.22306 q^{26} -8.32935 q^{27} -2.58591 q^{28} +0.298997 q^{29} +25.9806 q^{30} +4.85515 q^{31} +7.83075 q^{32} +3.62410 q^{33} -1.69185 q^{34} -4.08817 q^{35} +15.0157 q^{36} +5.93905 q^{37} +14.4372 q^{38} +3.08067 q^{39} -5.12944 q^{40} +3.01661 q^{41} -6.35507 q^{42} -2.00668 q^{43} -3.15795 q^{44} +23.7389 q^{45} +2.17218 q^{46} -6.33631 q^{47} +7.37422 q^{48} +1.00000 q^{49} -25.0833 q^{50} -2.34453 q^{51} -2.68442 q^{52} +0.704090 q^{53} +17.8371 q^{54} -4.99253 q^{55} +1.25470 q^{56} +20.0069 q^{57} -0.640294 q^{58} -13.3816 q^{59} -31.3725 q^{60} -5.54301 q^{61} -10.3972 q^{62} -5.80675 q^{63} -11.7995 q^{64} -4.24391 q^{65} -7.76092 q^{66} +8.30586 q^{67} +2.04297 q^{68} +3.01017 q^{69} +8.75470 q^{70} -0.459341 q^{71} -7.28575 q^{72} +2.60874 q^{73} -12.7183 q^{74} -34.7600 q^{75} -17.4335 q^{76} +1.22122 q^{77} -6.59718 q^{78} +6.28955 q^{79} -10.1587 q^{80} +7.29807 q^{81} -6.45999 q^{82} +7.99024 q^{83} +7.67398 q^{84} +3.22981 q^{85} +4.29724 q^{86} -0.887308 q^{87} +1.53227 q^{88} -13.3812 q^{89} -50.8363 q^{90} +1.03810 q^{91} -2.62299 q^{92} -14.4082 q^{93} +13.5690 q^{94} -27.5613 q^{95} -23.2387 q^{96} -2.42010 q^{97} -2.14147 q^{98} -7.09129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14147 −1.51425 −0.757125 0.653270i \(-0.773397\pi\)
−0.757125 + 0.653270i \(0.773397\pi\)
\(3\) −2.96762 −1.71335 −0.856677 0.515853i \(-0.827475\pi\)
−0.856677 + 0.515853i \(0.827475\pi\)
\(4\) 2.58591 1.29295
\(5\) 4.08817 1.82828 0.914142 0.405395i \(-0.132866\pi\)
0.914142 + 0.405395i \(0.132866\pi\)
\(6\) 6.35507 2.59445
\(7\) −1.00000 −0.377964
\(8\) −1.25470 −0.443605
\(9\) 5.80675 1.93558
\(10\) −8.75470 −2.76848
\(11\) −1.22122 −0.368211 −0.184105 0.982907i \(-0.558939\pi\)
−0.184105 + 0.982907i \(0.558939\pi\)
\(12\) −7.67398 −2.21529
\(13\) −1.03810 −0.287916 −0.143958 0.989584i \(-0.545983\pi\)
−0.143958 + 0.989584i \(0.545983\pi\)
\(14\) 2.14147 0.572333
\(15\) −12.1321 −3.13250
\(16\) −2.48490 −0.621224
\(17\) 0.790038 0.191612 0.0958062 0.995400i \(-0.469457\pi\)
0.0958062 + 0.995400i \(0.469457\pi\)
\(18\) −12.4350 −2.93096
\(19\) −6.74173 −1.54666 −0.773330 0.634004i \(-0.781410\pi\)
−0.773330 + 0.634004i \(0.781410\pi\)
\(20\) 10.5716 2.36389
\(21\) 2.96762 0.647587
\(22\) 2.61520 0.557563
\(23\) −1.01434 −0.211504 −0.105752 0.994393i \(-0.533725\pi\)
−0.105752 + 0.994393i \(0.533725\pi\)
\(24\) 3.72348 0.760053
\(25\) 11.7131 2.34262
\(26\) 2.22306 0.435977
\(27\) −8.32935 −1.60298
\(28\) −2.58591 −0.488691
\(29\) 0.298997 0.0555223 0.0277612 0.999615i \(-0.491162\pi\)
0.0277612 + 0.999615i \(0.491162\pi\)
\(30\) 25.9806 4.74338
\(31\) 4.85515 0.872012 0.436006 0.899944i \(-0.356393\pi\)
0.436006 + 0.899944i \(0.356393\pi\)
\(32\) 7.83075 1.38429
\(33\) 3.62410 0.630875
\(34\) −1.69185 −0.290149
\(35\) −4.08817 −0.691026
\(36\) 15.0157 2.50262
\(37\) 5.93905 0.976374 0.488187 0.872739i \(-0.337658\pi\)
0.488187 + 0.872739i \(0.337658\pi\)
\(38\) 14.4372 2.34203
\(39\) 3.08067 0.493303
\(40\) −5.12944 −0.811036
\(41\) 3.01661 0.471115 0.235558 0.971860i \(-0.424308\pi\)
0.235558 + 0.971860i \(0.424308\pi\)
\(42\) −6.35507 −0.980609
\(43\) −2.00668 −0.306015 −0.153008 0.988225i \(-0.548896\pi\)
−0.153008 + 0.988225i \(0.548896\pi\)
\(44\) −3.15795 −0.476079
\(45\) 23.7389 3.53879
\(46\) 2.17218 0.320271
\(47\) −6.33631 −0.924246 −0.462123 0.886816i \(-0.652912\pi\)
−0.462123 + 0.886816i \(0.652912\pi\)
\(48\) 7.37422 1.06438
\(49\) 1.00000 0.142857
\(50\) −25.0833 −3.54731
\(51\) −2.34453 −0.328300
\(52\) −2.68442 −0.372263
\(53\) 0.704090 0.0967141 0.0483571 0.998830i \(-0.484601\pi\)
0.0483571 + 0.998830i \(0.484601\pi\)
\(54\) 17.8371 2.42732
\(55\) −4.99253 −0.673193
\(56\) 1.25470 0.167667
\(57\) 20.0069 2.64997
\(58\) −0.640294 −0.0840747
\(59\) −13.3816 −1.74214 −0.871068 0.491162i \(-0.836572\pi\)
−0.871068 + 0.491162i \(0.836572\pi\)
\(60\) −31.3725 −4.05017
\(61\) −5.54301 −0.709710 −0.354855 0.934921i \(-0.615470\pi\)
−0.354855 + 0.934921i \(0.615470\pi\)
\(62\) −10.3972 −1.32044
\(63\) −5.80675 −0.731581
\(64\) −11.7995 −1.47494
\(65\) −4.24391 −0.526393
\(66\) −7.76092 −0.955303
\(67\) 8.30586 1.01472 0.507361 0.861733i \(-0.330621\pi\)
0.507361 + 0.861733i \(0.330621\pi\)
\(68\) 2.04297 0.247746
\(69\) 3.01017 0.362382
\(70\) 8.75470 1.04639
\(71\) −0.459341 −0.0545138 −0.0272569 0.999628i \(-0.508677\pi\)
−0.0272569 + 0.999628i \(0.508677\pi\)
\(72\) −7.28575 −0.858634
\(73\) 2.60874 0.305329 0.152665 0.988278i \(-0.451215\pi\)
0.152665 + 0.988278i \(0.451215\pi\)
\(74\) −12.7183 −1.47847
\(75\) −34.7600 −4.01374
\(76\) −17.4335 −1.99976
\(77\) 1.22122 0.139170
\(78\) −6.59718 −0.746984
\(79\) 6.28955 0.707630 0.353815 0.935315i \(-0.384884\pi\)
0.353815 + 0.935315i \(0.384884\pi\)
\(80\) −10.1587 −1.13577
\(81\) 7.29807 0.810897
\(82\) −6.45999 −0.713386
\(83\) 7.99024 0.877043 0.438521 0.898721i \(-0.355502\pi\)
0.438521 + 0.898721i \(0.355502\pi\)
\(84\) 7.67398 0.837300
\(85\) 3.22981 0.350322
\(86\) 4.29724 0.463384
\(87\) −0.887308 −0.0951294
\(88\) 1.53227 0.163340
\(89\) −13.3812 −1.41841 −0.709204 0.705003i \(-0.750945\pi\)
−0.709204 + 0.705003i \(0.750945\pi\)
\(90\) −50.8363 −5.35862
\(91\) 1.03810 0.108822
\(92\) −2.62299 −0.273465
\(93\) −14.4082 −1.49406
\(94\) 13.5690 1.39954
\(95\) −27.5613 −2.82773
\(96\) −23.2387 −2.37179
\(97\) −2.42010 −0.245724 −0.122862 0.992424i \(-0.539207\pi\)
−0.122862 + 0.992424i \(0.539207\pi\)
\(98\) −2.14147 −0.216321
\(99\) −7.09129 −0.712702
\(100\) 30.2890 3.02890
\(101\) 0.782837 0.0778952 0.0389476 0.999241i \(-0.487599\pi\)
0.0389476 + 0.999241i \(0.487599\pi\)
\(102\) 5.02075 0.497128
\(103\) −7.37645 −0.726823 −0.363412 0.931629i \(-0.618388\pi\)
−0.363412 + 0.931629i \(0.618388\pi\)
\(104\) 1.30251 0.127721
\(105\) 12.1321 1.18397
\(106\) −1.50779 −0.146449
\(107\) 5.21716 0.504362 0.252181 0.967680i \(-0.418852\pi\)
0.252181 + 0.967680i \(0.418852\pi\)
\(108\) −21.5389 −2.07258
\(109\) −3.99109 −0.382277 −0.191138 0.981563i \(-0.561218\pi\)
−0.191138 + 0.981563i \(0.561218\pi\)
\(110\) 10.6914 1.01938
\(111\) −17.6248 −1.67287
\(112\) 2.48490 0.234801
\(113\) 2.97109 0.279497 0.139748 0.990187i \(-0.455371\pi\)
0.139748 + 0.990187i \(0.455371\pi\)
\(114\) −42.8442 −4.01272
\(115\) −4.14679 −0.386690
\(116\) 0.773178 0.0717878
\(117\) −6.02797 −0.557286
\(118\) 28.6563 2.63803
\(119\) −0.790038 −0.0724227
\(120\) 15.2222 1.38959
\(121\) −9.50863 −0.864421
\(122\) 11.8702 1.07468
\(123\) −8.95214 −0.807187
\(124\) 12.5550 1.12747
\(125\) 27.4443 2.45469
\(126\) 12.4350 1.10780
\(127\) 11.0275 0.978529 0.489264 0.872135i \(-0.337265\pi\)
0.489264 + 0.872135i \(0.337265\pi\)
\(128\) 9.60691 0.849139
\(129\) 5.95505 0.524313
\(130\) 9.08823 0.797090
\(131\) −3.07149 −0.268357 −0.134179 0.990957i \(-0.542840\pi\)
−0.134179 + 0.990957i \(0.542840\pi\)
\(132\) 9.37159 0.815692
\(133\) 6.74173 0.584582
\(134\) −17.7868 −1.53654
\(135\) −34.0518 −2.93071
\(136\) −0.991265 −0.0850003
\(137\) −15.4926 −1.32363 −0.661813 0.749669i \(-0.730213\pi\)
−0.661813 + 0.749669i \(0.730213\pi\)
\(138\) −6.44620 −0.548737
\(139\) −0.313077 −0.0265549 −0.0132774 0.999912i \(-0.504226\pi\)
−0.0132774 + 0.999912i \(0.504226\pi\)
\(140\) −10.5716 −0.893465
\(141\) 18.8037 1.58356
\(142\) 0.983667 0.0825475
\(143\) 1.26774 0.106014
\(144\) −14.4292 −1.20243
\(145\) 1.22235 0.101511
\(146\) −5.58654 −0.462345
\(147\) −2.96762 −0.244765
\(148\) 15.3578 1.26241
\(149\) 0.793653 0.0650186 0.0325093 0.999471i \(-0.489650\pi\)
0.0325093 + 0.999471i \(0.489650\pi\)
\(150\) 74.4376 6.07780
\(151\) −12.0804 −0.983093 −0.491546 0.870851i \(-0.663568\pi\)
−0.491546 + 0.870851i \(0.663568\pi\)
\(152\) 8.45888 0.686106
\(153\) 4.58755 0.370882
\(154\) −2.61520 −0.210739
\(155\) 19.8487 1.59428
\(156\) 7.96634 0.637818
\(157\) 18.7427 1.49583 0.747917 0.663792i \(-0.231054\pi\)
0.747917 + 0.663792i \(0.231054\pi\)
\(158\) −13.4689 −1.07153
\(159\) −2.08947 −0.165706
\(160\) 32.0134 2.53088
\(161\) 1.01434 0.0799412
\(162\) −15.6286 −1.22790
\(163\) 0.965844 0.0756507 0.0378254 0.999284i \(-0.487957\pi\)
0.0378254 + 0.999284i \(0.487957\pi\)
\(164\) 7.80067 0.609130
\(165\) 14.8159 1.15342
\(166\) −17.1109 −1.32806
\(167\) 24.9963 1.93427 0.967134 0.254266i \(-0.0818340\pi\)
0.967134 + 0.254266i \(0.0818340\pi\)
\(168\) −3.72348 −0.287273
\(169\) −11.9224 −0.917104
\(170\) −6.91655 −0.530475
\(171\) −39.1475 −2.99369
\(172\) −5.18908 −0.395664
\(173\) −21.6920 −1.64921 −0.824606 0.565707i \(-0.808603\pi\)
−0.824606 + 0.565707i \(0.808603\pi\)
\(174\) 1.90015 0.144050
\(175\) −11.7131 −0.885427
\(176\) 3.03460 0.228741
\(177\) 39.7115 2.98490
\(178\) 28.6556 2.14782
\(179\) −9.99625 −0.747155 −0.373577 0.927599i \(-0.621869\pi\)
−0.373577 + 0.927599i \(0.621869\pi\)
\(180\) 61.3867 4.57550
\(181\) −17.9866 −1.33694 −0.668468 0.743741i \(-0.733050\pi\)
−0.668468 + 0.743741i \(0.733050\pi\)
\(182\) −2.22306 −0.164784
\(183\) 16.4495 1.21598
\(184\) 1.27270 0.0938244
\(185\) 24.2798 1.78509
\(186\) 30.8549 2.26239
\(187\) −0.964808 −0.0705537
\(188\) −16.3851 −1.19501
\(189\) 8.32935 0.605871
\(190\) 59.0218 4.28189
\(191\) −7.09796 −0.513590 −0.256795 0.966466i \(-0.582667\pi\)
−0.256795 + 0.966466i \(0.582667\pi\)
\(192\) 35.0165 2.52710
\(193\) 17.5611 1.26408 0.632039 0.774936i \(-0.282218\pi\)
0.632039 + 0.774936i \(0.282218\pi\)
\(194\) 5.18259 0.372088
\(195\) 12.5943 0.901897
\(196\) 2.58591 0.184708
\(197\) 9.60162 0.684087 0.342044 0.939684i \(-0.388881\pi\)
0.342044 + 0.939684i \(0.388881\pi\)
\(198\) 15.1858 1.07921
\(199\) −0.668850 −0.0474135 −0.0237067 0.999719i \(-0.507547\pi\)
−0.0237067 + 0.999719i \(0.507547\pi\)
\(200\) −14.6965 −1.03920
\(201\) −24.6486 −1.73858
\(202\) −1.67642 −0.117953
\(203\) −0.298997 −0.0209855
\(204\) −6.06274 −0.424477
\(205\) 12.3324 0.861332
\(206\) 15.7965 1.10059
\(207\) −5.89001 −0.409384
\(208\) 2.57957 0.178861
\(209\) 8.23311 0.569496
\(210\) −25.9806 −1.79283
\(211\) 19.9415 1.37283 0.686415 0.727210i \(-0.259184\pi\)
0.686415 + 0.727210i \(0.259184\pi\)
\(212\) 1.82071 0.125047
\(213\) 1.36315 0.0934014
\(214\) −11.1724 −0.763730
\(215\) −8.20363 −0.559483
\(216\) 10.4509 0.711092
\(217\) −4.85515 −0.329589
\(218\) 8.54681 0.578863
\(219\) −7.74173 −0.523137
\(220\) −12.9102 −0.870407
\(221\) −0.820137 −0.0551684
\(222\) 37.7431 2.53315
\(223\) −14.9010 −0.997845 −0.498922 0.866647i \(-0.666271\pi\)
−0.498922 + 0.866647i \(0.666271\pi\)
\(224\) −7.83075 −0.523214
\(225\) 68.0150 4.53433
\(226\) −6.36251 −0.423228
\(227\) −25.3656 −1.68358 −0.841789 0.539807i \(-0.818497\pi\)
−0.841789 + 0.539807i \(0.818497\pi\)
\(228\) 51.7359 3.42629
\(229\) 7.44148 0.491747 0.245874 0.969302i \(-0.420925\pi\)
0.245874 + 0.969302i \(0.420925\pi\)
\(230\) 8.88023 0.585545
\(231\) −3.62410 −0.238448
\(232\) −0.375153 −0.0246300
\(233\) −14.6179 −0.957648 −0.478824 0.877911i \(-0.658937\pi\)
−0.478824 + 0.877911i \(0.658937\pi\)
\(234\) 12.9087 0.843870
\(235\) −25.9039 −1.68978
\(236\) −34.6036 −2.25250
\(237\) −18.6650 −1.21242
\(238\) 1.69185 0.109666
\(239\) 9.59754 0.620813 0.310407 0.950604i \(-0.399535\pi\)
0.310407 + 0.950604i \(0.399535\pi\)
\(240\) 30.1470 1.94598
\(241\) 4.66658 0.300601 0.150301 0.988640i \(-0.451976\pi\)
0.150301 + 0.988640i \(0.451976\pi\)
\(242\) 20.3625 1.30895
\(243\) 3.33017 0.213630
\(244\) −14.3337 −0.917622
\(245\) 4.08817 0.261183
\(246\) 19.1708 1.22228
\(247\) 6.99857 0.445308
\(248\) −6.09179 −0.386829
\(249\) −23.7120 −1.50269
\(250\) −58.7711 −3.71701
\(251\) 4.16453 0.262863 0.131431 0.991325i \(-0.458043\pi\)
0.131431 + 0.991325i \(0.458043\pi\)
\(252\) −15.0157 −0.945901
\(253\) 1.23873 0.0778781
\(254\) −23.6150 −1.48174
\(255\) −9.58483 −0.600225
\(256\) 3.02615 0.189134
\(257\) 22.9966 1.43449 0.717246 0.696820i \(-0.245403\pi\)
0.717246 + 0.696820i \(0.245403\pi\)
\(258\) −12.7526 −0.793941
\(259\) −5.93905 −0.369035
\(260\) −10.9744 −0.680601
\(261\) 1.73620 0.107468
\(262\) 6.57751 0.406360
\(263\) −13.6389 −0.841008 −0.420504 0.907291i \(-0.638147\pi\)
−0.420504 + 0.907291i \(0.638147\pi\)
\(264\) −4.54718 −0.279859
\(265\) 2.87843 0.176821
\(266\) −14.4372 −0.885204
\(267\) 39.7104 2.43024
\(268\) 21.4782 1.31199
\(269\) 31.6968 1.93259 0.966294 0.257441i \(-0.0828792\pi\)
0.966294 + 0.257441i \(0.0828792\pi\)
\(270\) 72.9209 4.43783
\(271\) −9.47546 −0.575593 −0.287797 0.957692i \(-0.592923\pi\)
−0.287797 + 0.957692i \(0.592923\pi\)
\(272\) −1.96316 −0.119034
\(273\) −3.08067 −0.186451
\(274\) 33.1771 2.00430
\(275\) −14.3042 −0.862577
\(276\) 7.78402 0.468543
\(277\) 0.716541 0.0430528 0.0215264 0.999768i \(-0.493147\pi\)
0.0215264 + 0.999768i \(0.493147\pi\)
\(278\) 0.670447 0.0402107
\(279\) 28.1927 1.68785
\(280\) 5.12944 0.306543
\(281\) −17.5181 −1.04504 −0.522522 0.852626i \(-0.675009\pi\)
−0.522522 + 0.852626i \(0.675009\pi\)
\(282\) −40.2677 −2.39791
\(283\) 4.58582 0.272599 0.136299 0.990668i \(-0.456479\pi\)
0.136299 + 0.990668i \(0.456479\pi\)
\(284\) −1.18781 −0.0704838
\(285\) 81.7914 4.84490
\(286\) −2.71483 −0.160531
\(287\) −3.01661 −0.178065
\(288\) 45.4712 2.67942
\(289\) −16.3758 −0.963285
\(290\) −2.61763 −0.153712
\(291\) 7.18194 0.421013
\(292\) 6.74595 0.394777
\(293\) 19.8669 1.16063 0.580317 0.814390i \(-0.302929\pi\)
0.580317 + 0.814390i \(0.302929\pi\)
\(294\) 6.35507 0.370635
\(295\) −54.7062 −3.18512
\(296\) −7.45175 −0.433124
\(297\) 10.1719 0.590236
\(298\) −1.69959 −0.0984544
\(299\) 1.05298 0.0608956
\(300\) −89.8861 −5.18958
\(301\) 2.00668 0.115663
\(302\) 25.8700 1.48865
\(303\) −2.32316 −0.133462
\(304\) 16.7525 0.960823
\(305\) −22.6607 −1.29755
\(306\) −9.82412 −0.561608
\(307\) 8.65275 0.493839 0.246919 0.969036i \(-0.420582\pi\)
0.246919 + 0.969036i \(0.420582\pi\)
\(308\) 3.15795 0.179941
\(309\) 21.8905 1.24531
\(310\) −42.5054 −2.41414
\(311\) −14.6622 −0.831416 −0.415708 0.909498i \(-0.636466\pi\)
−0.415708 + 0.909498i \(0.636466\pi\)
\(312\) −3.86534 −0.218832
\(313\) −33.7333 −1.90672 −0.953360 0.301836i \(-0.902400\pi\)
−0.953360 + 0.301836i \(0.902400\pi\)
\(314\) −40.1371 −2.26507
\(315\) −23.7389 −1.33754
\(316\) 16.2642 0.914933
\(317\) −21.5073 −1.20797 −0.603986 0.796995i \(-0.706422\pi\)
−0.603986 + 0.796995i \(0.706422\pi\)
\(318\) 4.47454 0.250920
\(319\) −0.365140 −0.0204439
\(320\) −48.2385 −2.69661
\(321\) −15.4825 −0.864151
\(322\) −2.17218 −0.121051
\(323\) −5.32623 −0.296359
\(324\) 18.8721 1.04845
\(325\) −12.1593 −0.674478
\(326\) −2.06833 −0.114554
\(327\) 11.8440 0.654976
\(328\) −3.78495 −0.208989
\(329\) 6.33631 0.349332
\(330\) −31.7279 −1.74656
\(331\) 9.33855 0.513293 0.256647 0.966505i \(-0.417382\pi\)
0.256647 + 0.966505i \(0.417382\pi\)
\(332\) 20.6620 1.13398
\(333\) 34.4866 1.88985
\(334\) −53.5288 −2.92897
\(335\) 33.9557 1.85520
\(336\) −7.37422 −0.402297
\(337\) 1.58249 0.0862039 0.0431019 0.999071i \(-0.486276\pi\)
0.0431019 + 0.999071i \(0.486276\pi\)
\(338\) 25.5314 1.38873
\(339\) −8.81706 −0.478877
\(340\) 8.35198 0.452950
\(341\) −5.92919 −0.321084
\(342\) 83.8334 4.53319
\(343\) −1.00000 −0.0539949
\(344\) 2.51779 0.135750
\(345\) 12.3061 0.662537
\(346\) 46.4528 2.49732
\(347\) 0.0859145 0.00461213 0.00230607 0.999997i \(-0.499266\pi\)
0.00230607 + 0.999997i \(0.499266\pi\)
\(348\) −2.29450 −0.122998
\(349\) −22.4504 −1.20174 −0.600872 0.799345i \(-0.705180\pi\)
−0.600872 + 0.799345i \(0.705180\pi\)
\(350\) 25.0833 1.34076
\(351\) 8.64667 0.461525
\(352\) −9.56304 −0.509712
\(353\) 17.5258 0.932805 0.466402 0.884573i \(-0.345550\pi\)
0.466402 + 0.884573i \(0.345550\pi\)
\(354\) −85.0410 −4.51988
\(355\) −1.87786 −0.0996667
\(356\) −34.6026 −1.83394
\(357\) 2.34453 0.124086
\(358\) 21.4067 1.13138
\(359\) 24.2749 1.28118 0.640589 0.767884i \(-0.278690\pi\)
0.640589 + 0.767884i \(0.278690\pi\)
\(360\) −29.7854 −1.56983
\(361\) 26.4509 1.39215
\(362\) 38.5179 2.02446
\(363\) 28.2180 1.48106
\(364\) 2.68442 0.140702
\(365\) 10.6649 0.558229
\(366\) −35.2262 −1.84130
\(367\) −13.1637 −0.687140 −0.343570 0.939127i \(-0.611636\pi\)
−0.343570 + 0.939127i \(0.611636\pi\)
\(368\) 2.52053 0.131392
\(369\) 17.5167 0.911882
\(370\) −51.9946 −2.70307
\(371\) −0.704090 −0.0365545
\(372\) −37.2584 −1.93176
\(373\) −5.30068 −0.274459 −0.137230 0.990539i \(-0.543820\pi\)
−0.137230 + 0.990539i \(0.543820\pi\)
\(374\) 2.06611 0.106836
\(375\) −81.4440 −4.20575
\(376\) 7.95020 0.410000
\(377\) −0.310388 −0.0159858
\(378\) −17.8371 −0.917440
\(379\) −11.6288 −0.597333 −0.298666 0.954358i \(-0.596542\pi\)
−0.298666 + 0.954358i \(0.596542\pi\)
\(380\) −71.2710 −3.65612
\(381\) −32.7253 −1.67657
\(382\) 15.2001 0.777704
\(383\) −19.7281 −1.00806 −0.504029 0.863687i \(-0.668150\pi\)
−0.504029 + 0.863687i \(0.668150\pi\)
\(384\) −28.5096 −1.45488
\(385\) 4.99253 0.254443
\(386\) −37.6067 −1.91413
\(387\) −11.6523 −0.592318
\(388\) −6.25817 −0.317710
\(389\) −3.77387 −0.191343 −0.0956714 0.995413i \(-0.530500\pi\)
−0.0956714 + 0.995413i \(0.530500\pi\)
\(390\) −26.9704 −1.36570
\(391\) −0.801367 −0.0405269
\(392\) −1.25470 −0.0633722
\(393\) 9.11500 0.459791
\(394\) −20.5616 −1.03588
\(395\) 25.7127 1.29375
\(396\) −18.3374 −0.921490
\(397\) 4.81283 0.241549 0.120774 0.992680i \(-0.461462\pi\)
0.120774 + 0.992680i \(0.461462\pi\)
\(398\) 1.43232 0.0717959
\(399\) −20.0069 −1.00160
\(400\) −29.1059 −1.45529
\(401\) −25.8242 −1.28960 −0.644800 0.764351i \(-0.723059\pi\)
−0.644800 + 0.764351i \(0.723059\pi\)
\(402\) 52.7843 2.63264
\(403\) −5.04012 −0.251066
\(404\) 2.02434 0.100715
\(405\) 29.8357 1.48255
\(406\) 0.640294 0.0317772
\(407\) −7.25286 −0.359511
\(408\) 2.94169 0.145636
\(409\) −31.2218 −1.54382 −0.771909 0.635733i \(-0.780698\pi\)
−0.771909 + 0.635733i \(0.780698\pi\)
\(410\) −26.4095 −1.30427
\(411\) 45.9762 2.26784
\(412\) −19.0748 −0.939749
\(413\) 13.3816 0.658466
\(414\) 12.6133 0.619910
\(415\) 32.6654 1.60348
\(416\) −8.12908 −0.398561
\(417\) 0.929094 0.0454979
\(418\) −17.6310 −0.862360
\(419\) −18.6478 −0.911003 −0.455502 0.890235i \(-0.650540\pi\)
−0.455502 + 0.890235i \(0.650540\pi\)
\(420\) 31.3725 1.53082
\(421\) 16.7591 0.816786 0.408393 0.912806i \(-0.366089\pi\)
0.408393 + 0.912806i \(0.366089\pi\)
\(422\) −42.7042 −2.07881
\(423\) −36.7933 −1.78895
\(424\) −0.883425 −0.0429029
\(425\) 9.25380 0.448875
\(426\) −2.91915 −0.141433
\(427\) 5.54301 0.268245
\(428\) 13.4911 0.652117
\(429\) −3.76217 −0.181639
\(430\) 17.5678 0.847197
\(431\) 15.6708 0.754838 0.377419 0.926043i \(-0.376812\pi\)
0.377419 + 0.926043i \(0.376812\pi\)
\(432\) 20.6976 0.995813
\(433\) 5.98440 0.287592 0.143796 0.989607i \(-0.454069\pi\)
0.143796 + 0.989607i \(0.454069\pi\)
\(434\) 10.3972 0.499081
\(435\) −3.62746 −0.173923
\(436\) −10.3206 −0.494266
\(437\) 6.83840 0.327125
\(438\) 16.5787 0.792161
\(439\) −0.831232 −0.0396725 −0.0198363 0.999803i \(-0.506314\pi\)
−0.0198363 + 0.999803i \(0.506314\pi\)
\(440\) 6.26416 0.298632
\(441\) 5.80675 0.276512
\(442\) 1.75630 0.0835387
\(443\) 41.1819 1.95661 0.978306 0.207167i \(-0.0664244\pi\)
0.978306 + 0.207167i \(0.0664244\pi\)
\(444\) −45.5762 −2.16295
\(445\) −54.7047 −2.59325
\(446\) 31.9101 1.51099
\(447\) −2.35526 −0.111400
\(448\) 11.7995 0.557476
\(449\) 12.4920 0.589536 0.294768 0.955569i \(-0.404758\pi\)
0.294768 + 0.955569i \(0.404758\pi\)
\(450\) −145.652 −6.86611
\(451\) −3.68393 −0.173470
\(452\) 7.68297 0.361376
\(453\) 35.8501 1.68439
\(454\) 54.3199 2.54936
\(455\) 4.24391 0.198958
\(456\) −25.1027 −1.17554
\(457\) −36.4861 −1.70675 −0.853373 0.521301i \(-0.825447\pi\)
−0.853373 + 0.521301i \(0.825447\pi\)
\(458\) −15.9357 −0.744628
\(459\) −6.58051 −0.307152
\(460\) −10.7232 −0.499972
\(461\) 24.9288 1.16105 0.580526 0.814242i \(-0.302847\pi\)
0.580526 + 0.814242i \(0.302847\pi\)
\(462\) 7.76092 0.361070
\(463\) −20.1236 −0.935224 −0.467612 0.883934i \(-0.654886\pi\)
−0.467612 + 0.883934i \(0.654886\pi\)
\(464\) −0.742976 −0.0344918
\(465\) −58.9033 −2.73157
\(466\) 31.3038 1.45012
\(467\) −5.98664 −0.277029 −0.138514 0.990360i \(-0.544233\pi\)
−0.138514 + 0.990360i \(0.544233\pi\)
\(468\) −15.5878 −0.720545
\(469\) −8.30586 −0.383529
\(470\) 55.4725 2.55875
\(471\) −55.6213 −2.56289
\(472\) 16.7900 0.772821
\(473\) 2.45059 0.112678
\(474\) 39.9705 1.83591
\(475\) −78.9665 −3.62323
\(476\) −2.04297 −0.0936392
\(477\) 4.08847 0.187198
\(478\) −20.5529 −0.940066
\(479\) 3.18045 0.145319 0.0726593 0.997357i \(-0.476851\pi\)
0.0726593 + 0.997357i \(0.476851\pi\)
\(480\) −95.0035 −4.33630
\(481\) −6.16531 −0.281114
\(482\) −9.99336 −0.455185
\(483\) −3.01017 −0.136968
\(484\) −24.5884 −1.11766
\(485\) −9.89379 −0.449254
\(486\) −7.13146 −0.323490
\(487\) −13.2634 −0.601023 −0.300511 0.953778i \(-0.597157\pi\)
−0.300511 + 0.953778i \(0.597157\pi\)
\(488\) 6.95484 0.314831
\(489\) −2.86625 −0.129617
\(490\) −8.75470 −0.395497
\(491\) 4.46870 0.201670 0.100835 0.994903i \(-0.467849\pi\)
0.100835 + 0.994903i \(0.467849\pi\)
\(492\) −23.1494 −1.04366
\(493\) 0.236219 0.0106388
\(494\) −14.9873 −0.674308
\(495\) −28.9904 −1.30302
\(496\) −12.0646 −0.541715
\(497\) 0.459341 0.0206043
\(498\) 50.7785 2.27544
\(499\) 10.8611 0.486209 0.243105 0.970000i \(-0.421834\pi\)
0.243105 + 0.970000i \(0.421834\pi\)
\(500\) 70.9683 3.17380
\(501\) −74.1793 −3.31409
\(502\) −8.91822 −0.398040
\(503\) 2.05559 0.0916540 0.0458270 0.998949i \(-0.485408\pi\)
0.0458270 + 0.998949i \(0.485408\pi\)
\(504\) 7.28575 0.324533
\(505\) 3.20037 0.142414
\(506\) −2.65270 −0.117927
\(507\) 35.3810 1.57132
\(508\) 28.5160 1.26519
\(509\) 16.8368 0.746278 0.373139 0.927776i \(-0.378282\pi\)
0.373139 + 0.927776i \(0.378282\pi\)
\(510\) 20.5257 0.908891
\(511\) −2.60874 −0.115404
\(512\) −25.6942 −1.13554
\(513\) 56.1542 2.47927
\(514\) −49.2467 −2.17218
\(515\) −30.1561 −1.32884
\(516\) 15.3992 0.677912
\(517\) 7.73800 0.340317
\(518\) 12.7183 0.558811
\(519\) 64.3735 2.82568
\(520\) 5.32486 0.233510
\(521\) 21.0599 0.922653 0.461327 0.887230i \(-0.347374\pi\)
0.461327 + 0.887230i \(0.347374\pi\)
\(522\) −3.71802 −0.162733
\(523\) −22.5602 −0.986488 −0.493244 0.869891i \(-0.664189\pi\)
−0.493244 + 0.869891i \(0.664189\pi\)
\(524\) −7.94259 −0.346974
\(525\) 34.7600 1.51705
\(526\) 29.2072 1.27350
\(527\) 3.83576 0.167088
\(528\) −9.00552 −0.391915
\(529\) −21.9711 −0.955266
\(530\) −6.16409 −0.267751
\(531\) −77.7036 −3.37205
\(532\) 17.4335 0.755838
\(533\) −3.13153 −0.135642
\(534\) −85.0387 −3.67998
\(535\) 21.3286 0.922116
\(536\) −10.4214 −0.450136
\(537\) 29.6650 1.28014
\(538\) −67.8779 −2.92642
\(539\) −1.22122 −0.0526015
\(540\) −88.0547 −3.78927
\(541\) 38.5252 1.65633 0.828164 0.560486i \(-0.189386\pi\)
0.828164 + 0.560486i \(0.189386\pi\)
\(542\) 20.2914 0.871592
\(543\) 53.3775 2.29065
\(544\) 6.18659 0.265248
\(545\) −16.3162 −0.698911
\(546\) 6.59718 0.282333
\(547\) 25.6941 1.09860 0.549301 0.835624i \(-0.314894\pi\)
0.549301 + 0.835624i \(0.314894\pi\)
\(548\) −40.0625 −1.71139
\(549\) −32.1869 −1.37370
\(550\) 30.6321 1.30616
\(551\) −2.01576 −0.0858741
\(552\) −3.77688 −0.160754
\(553\) −6.28955 −0.267459
\(554\) −1.53445 −0.0651927
\(555\) −72.0532 −3.05849
\(556\) −0.809589 −0.0343342
\(557\) −38.1445 −1.61623 −0.808117 0.589022i \(-0.799513\pi\)
−0.808117 + 0.589022i \(0.799513\pi\)
\(558\) −60.3738 −2.55583
\(559\) 2.08313 0.0881068
\(560\) 10.1587 0.429282
\(561\) 2.86318 0.120884
\(562\) 37.5146 1.58246
\(563\) −2.27122 −0.0957207 −0.0478604 0.998854i \(-0.515240\pi\)
−0.0478604 + 0.998854i \(0.515240\pi\)
\(564\) 48.6247 2.04747
\(565\) 12.1463 0.510999
\(566\) −9.82042 −0.412783
\(567\) −7.29807 −0.306490
\(568\) 0.576338 0.0241826
\(569\) 6.49595 0.272324 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(570\) −175.154 −7.33640
\(571\) 45.6161 1.90898 0.954488 0.298249i \(-0.0964027\pi\)
0.954488 + 0.298249i \(0.0964027\pi\)
\(572\) 3.27826 0.137071
\(573\) 21.0640 0.879962
\(574\) 6.45999 0.269635
\(575\) −11.8811 −0.495474
\(576\) −68.5170 −2.85488
\(577\) −40.0053 −1.66544 −0.832721 0.553693i \(-0.813218\pi\)
−0.832721 + 0.553693i \(0.813218\pi\)
\(578\) 35.0684 1.45865
\(579\) −52.1147 −2.16581
\(580\) 3.16088 0.131248
\(581\) −7.99024 −0.331491
\(582\) −15.3799 −0.637519
\(583\) −0.859846 −0.0356112
\(584\) −3.27319 −0.135446
\(585\) −24.6433 −1.01888
\(586\) −42.5444 −1.75749
\(587\) 12.0349 0.496734 0.248367 0.968666i \(-0.420106\pi\)
0.248367 + 0.968666i \(0.420106\pi\)
\(588\) −7.67398 −0.316470
\(589\) −32.7321 −1.34870
\(590\) 117.152 4.82307
\(591\) −28.4939 −1.17208
\(592\) −14.7579 −0.606547
\(593\) −22.4965 −0.923821 −0.461910 0.886927i \(-0.652836\pi\)
−0.461910 + 0.886927i \(0.652836\pi\)
\(594\) −21.7829 −0.893764
\(595\) −3.22981 −0.132409
\(596\) 2.05231 0.0840660
\(597\) 1.98489 0.0812361
\(598\) −2.25493 −0.0922111
\(599\) −11.5702 −0.472747 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(600\) 43.6135 1.78051
\(601\) −10.5903 −0.431985 −0.215993 0.976395i \(-0.569299\pi\)
−0.215993 + 0.976395i \(0.569299\pi\)
\(602\) −4.29724 −0.175143
\(603\) 48.2300 1.96408
\(604\) −31.2389 −1.27109
\(605\) −38.8729 −1.58041
\(606\) 4.97498 0.202095
\(607\) 30.5891 1.24157 0.620787 0.783980i \(-0.286813\pi\)
0.620787 + 0.783980i \(0.286813\pi\)
\(608\) −52.7928 −2.14103
\(609\) 0.887308 0.0359555
\(610\) 48.5274 1.96482
\(611\) 6.57770 0.266105
\(612\) 11.8630 0.479533
\(613\) −8.50547 −0.343533 −0.171766 0.985138i \(-0.554947\pi\)
−0.171766 + 0.985138i \(0.554947\pi\)
\(614\) −18.5296 −0.747795
\(615\) −36.5978 −1.47577
\(616\) −1.53227 −0.0617367
\(617\) 6.18369 0.248946 0.124473 0.992223i \(-0.460276\pi\)
0.124473 + 0.992223i \(0.460276\pi\)
\(618\) −46.8779 −1.88570
\(619\) −24.6957 −0.992605 −0.496303 0.868150i \(-0.665309\pi\)
−0.496303 + 0.868150i \(0.665309\pi\)
\(620\) 51.3268 2.06134
\(621\) 8.44879 0.339038
\(622\) 31.3987 1.25897
\(623\) 13.3812 0.536108
\(624\) −7.65516 −0.306452
\(625\) 53.6312 2.14525
\(626\) 72.2390 2.88725
\(627\) −24.4327 −0.975749
\(628\) 48.4670 1.93404
\(629\) 4.69208 0.187085
\(630\) 50.8363 2.02537
\(631\) 7.87080 0.313331 0.156666 0.987652i \(-0.449925\pi\)
0.156666 + 0.987652i \(0.449925\pi\)
\(632\) −7.89153 −0.313908
\(633\) −59.1787 −2.35214
\(634\) 46.0573 1.82917
\(635\) 45.0821 1.78903
\(636\) −5.40317 −0.214250
\(637\) −1.03810 −0.0411309
\(638\) 0.781937 0.0309572
\(639\) −2.66728 −0.105516
\(640\) 39.2747 1.55247
\(641\) −2.10803 −0.0832620 −0.0416310 0.999133i \(-0.513255\pi\)
−0.0416310 + 0.999133i \(0.513255\pi\)
\(642\) 33.1554 1.30854
\(643\) −31.3600 −1.23672 −0.618358 0.785896i \(-0.712202\pi\)
−0.618358 + 0.785896i \(0.712202\pi\)
\(644\) 2.62299 0.103360
\(645\) 24.3452 0.958592
\(646\) 11.4060 0.448762
\(647\) −43.6695 −1.71682 −0.858412 0.512961i \(-0.828549\pi\)
−0.858412 + 0.512961i \(0.828549\pi\)
\(648\) −9.15693 −0.359718
\(649\) 16.3418 0.641473
\(650\) 26.0389 1.02133
\(651\) 14.4082 0.564703
\(652\) 2.49758 0.0978129
\(653\) 30.0767 1.17699 0.588496 0.808500i \(-0.299720\pi\)
0.588496 + 0.808500i \(0.299720\pi\)
\(654\) −25.3637 −0.991797
\(655\) −12.5568 −0.490633
\(656\) −7.49596 −0.292668
\(657\) 15.1483 0.590990
\(658\) −13.5690 −0.528976
\(659\) −36.8704 −1.43627 −0.718133 0.695906i \(-0.755003\pi\)
−0.718133 + 0.695906i \(0.755003\pi\)
\(660\) 38.3126 1.49132
\(661\) 20.1476 0.783651 0.391826 0.920039i \(-0.371844\pi\)
0.391826 + 0.920039i \(0.371844\pi\)
\(662\) −19.9983 −0.777255
\(663\) 2.43385 0.0945229
\(664\) −10.0254 −0.389061
\(665\) 27.5613 1.06878
\(666\) −73.8521 −2.86171
\(667\) −0.303284 −0.0117432
\(668\) 64.6380 2.50092
\(669\) 44.2204 1.70966
\(670\) −72.7153 −2.80924
\(671\) 6.76922 0.261323
\(672\) 23.2387 0.896451
\(673\) −33.4916 −1.29101 −0.645504 0.763757i \(-0.723352\pi\)
−0.645504 + 0.763757i \(0.723352\pi\)
\(674\) −3.38887 −0.130534
\(675\) −97.5625 −3.75518
\(676\) −30.8301 −1.18577
\(677\) −3.32961 −0.127967 −0.0639836 0.997951i \(-0.520381\pi\)
−0.0639836 + 0.997951i \(0.520381\pi\)
\(678\) 18.8815 0.725139
\(679\) 2.42010 0.0928751
\(680\) −4.05246 −0.155405
\(681\) 75.2755 2.88456
\(682\) 12.6972 0.486201
\(683\) 42.7127 1.63436 0.817178 0.576385i \(-0.195537\pi\)
0.817178 + 0.576385i \(0.195537\pi\)
\(684\) −101.232 −3.87070
\(685\) −63.3365 −2.41996
\(686\) 2.14147 0.0817618
\(687\) −22.0835 −0.842537
\(688\) 4.98639 0.190104
\(689\) −0.730913 −0.0278456
\(690\) −26.3531 −1.00325
\(691\) −39.4462 −1.50060 −0.750301 0.661096i \(-0.770092\pi\)
−0.750301 + 0.661096i \(0.770092\pi\)
\(692\) −56.0935 −2.13236
\(693\) 7.09129 0.269376
\(694\) −0.183984 −0.00698392
\(695\) −1.27991 −0.0485499
\(696\) 1.11331 0.0421999
\(697\) 2.38324 0.0902715
\(698\) 48.0770 1.81974
\(699\) 43.3802 1.64079
\(700\) −30.2890 −1.14482
\(701\) −17.6782 −0.667697 −0.333848 0.942627i \(-0.608347\pi\)
−0.333848 + 0.942627i \(0.608347\pi\)
\(702\) −18.5166 −0.698865
\(703\) −40.0395 −1.51012
\(704\) 14.4098 0.543090
\(705\) 76.8728 2.89520
\(706\) −37.5311 −1.41250
\(707\) −0.782837 −0.0294416
\(708\) 102.690 3.85933
\(709\) −48.6822 −1.82830 −0.914150 0.405376i \(-0.867141\pi\)
−0.914150 + 0.405376i \(0.867141\pi\)
\(710\) 4.02139 0.150920
\(711\) 36.5218 1.36968
\(712\) 16.7895 0.629213
\(713\) −4.92478 −0.184434
\(714\) −5.02075 −0.187897
\(715\) 5.18274 0.193823
\(716\) −25.8494 −0.966036
\(717\) −28.4818 −1.06367
\(718\) −51.9840 −1.94002
\(719\) 22.8359 0.851635 0.425818 0.904809i \(-0.359987\pi\)
0.425818 + 0.904809i \(0.359987\pi\)
\(720\) −58.9889 −2.19838
\(721\) 7.37645 0.274713
\(722\) −56.6440 −2.10807
\(723\) −13.8486 −0.515036
\(724\) −46.5118 −1.72860
\(725\) 3.50218 0.130068
\(726\) −60.4280 −2.24269
\(727\) −23.5966 −0.875151 −0.437575 0.899182i \(-0.644163\pi\)
−0.437575 + 0.899182i \(0.644163\pi\)
\(728\) −1.30251 −0.0482741
\(729\) −31.7769 −1.17692
\(730\) −22.8387 −0.845298
\(731\) −1.58535 −0.0586363
\(732\) 42.5370 1.57221
\(733\) 4.27307 0.157829 0.0789147 0.996881i \(-0.474855\pi\)
0.0789147 + 0.996881i \(0.474855\pi\)
\(734\) 28.1897 1.04050
\(735\) −12.1321 −0.447500
\(736\) −7.94304 −0.292784
\(737\) −10.1433 −0.373632
\(738\) −37.5115 −1.38082
\(739\) 7.51649 0.276499 0.138249 0.990397i \(-0.455852\pi\)
0.138249 + 0.990397i \(0.455852\pi\)
\(740\) 62.7854 2.30804
\(741\) −20.7691 −0.762971
\(742\) 1.50779 0.0553527
\(743\) 11.1447 0.408859 0.204430 0.978881i \(-0.434466\pi\)
0.204430 + 0.978881i \(0.434466\pi\)
\(744\) 18.0781 0.662775
\(745\) 3.24458 0.118872
\(746\) 11.3513 0.415600
\(747\) 46.3973 1.69759
\(748\) −2.49490 −0.0912227
\(749\) −5.21716 −0.190631
\(750\) 174.410 6.36856
\(751\) 14.3356 0.523115 0.261557 0.965188i \(-0.415764\pi\)
0.261557 + 0.965188i \(0.415764\pi\)
\(752\) 15.7451 0.574164
\(753\) −12.3587 −0.450377
\(754\) 0.664687 0.0242065
\(755\) −49.3869 −1.79737
\(756\) 21.5389 0.783363
\(757\) −11.2079 −0.407358 −0.203679 0.979038i \(-0.565290\pi\)
−0.203679 + 0.979038i \(0.565290\pi\)
\(758\) 24.9028 0.904511
\(759\) −3.67607 −0.133433
\(760\) 34.5813 1.25440
\(761\) −26.3959 −0.956852 −0.478426 0.878128i \(-0.658792\pi\)
−0.478426 + 0.878128i \(0.658792\pi\)
\(762\) 70.0803 2.53874
\(763\) 3.99109 0.144487
\(764\) −18.3547 −0.664049
\(765\) 18.7547 0.678077
\(766\) 42.2472 1.52645
\(767\) 13.8914 0.501590
\(768\) −8.98045 −0.324054
\(769\) −37.9918 −1.37002 −0.685009 0.728535i \(-0.740202\pi\)
−0.685009 + 0.728535i \(0.740202\pi\)
\(770\) −10.6914 −0.385290
\(771\) −68.2452 −2.45779
\(772\) 45.4115 1.63440
\(773\) −35.3793 −1.27251 −0.636253 0.771481i \(-0.719517\pi\)
−0.636253 + 0.771481i \(0.719517\pi\)
\(774\) 24.9530 0.896918
\(775\) 56.8689 2.04279
\(776\) 3.03652 0.109005
\(777\) 17.6248 0.632287
\(778\) 8.08164 0.289741
\(779\) −20.3372 −0.728654
\(780\) 32.5677 1.16611
\(781\) 0.560955 0.0200726
\(782\) 1.71611 0.0613678
\(783\) −2.49045 −0.0890014
\(784\) −2.48490 −0.0887464
\(785\) 76.6234 2.73481
\(786\) −19.5195 −0.696239
\(787\) −34.7939 −1.24027 −0.620134 0.784496i \(-0.712922\pi\)
−0.620134 + 0.784496i \(0.712922\pi\)
\(788\) 24.8289 0.884493
\(789\) 40.4749 1.44094
\(790\) −55.0631 −1.95906
\(791\) −2.97109 −0.105640
\(792\) 8.89748 0.316158
\(793\) 5.75418 0.204337
\(794\) −10.3065 −0.365766
\(795\) −8.54209 −0.302957
\(796\) −1.72958 −0.0613035
\(797\) 19.6978 0.697731 0.348866 0.937173i \(-0.386567\pi\)
0.348866 + 0.937173i \(0.386567\pi\)
\(798\) 42.8442 1.51667
\(799\) −5.00593 −0.177097
\(800\) 91.7224 3.24288
\(801\) −77.7014 −2.74545
\(802\) 55.3019 1.95278
\(803\) −3.18583 −0.112426
\(804\) −63.7390 −2.24790
\(805\) 4.14679 0.146155
\(806\) 10.7933 0.380177
\(807\) −94.0640 −3.31121
\(808\) −0.982229 −0.0345547
\(809\) −52.0896 −1.83137 −0.915686 0.401893i \(-0.868352\pi\)
−0.915686 + 0.401893i \(0.868352\pi\)
\(810\) −63.8924 −2.24495
\(811\) 11.5070 0.404067 0.202033 0.979379i \(-0.435245\pi\)
0.202033 + 0.979379i \(0.435245\pi\)
\(812\) −0.773178 −0.0271332
\(813\) 28.1195 0.986195
\(814\) 15.5318 0.544390
\(815\) 3.94853 0.138311
\(816\) 5.82592 0.203948
\(817\) 13.5285 0.473301
\(818\) 66.8606 2.33773
\(819\) 6.02797 0.210634
\(820\) 31.8904 1.11366
\(821\) −7.50487 −0.261922 −0.130961 0.991388i \(-0.541806\pi\)
−0.130961 + 0.991388i \(0.541806\pi\)
\(822\) −98.4569 −3.43408
\(823\) 6.46912 0.225499 0.112750 0.993623i \(-0.464034\pi\)
0.112750 + 0.993623i \(0.464034\pi\)
\(824\) 9.25527 0.322422
\(825\) 42.4494 1.47790
\(826\) −28.6563 −0.997082
\(827\) −1.33834 −0.0465387 −0.0232694 0.999729i \(-0.507408\pi\)
−0.0232694 + 0.999729i \(0.507408\pi\)
\(828\) −15.2310 −0.529315
\(829\) 0.343233 0.0119210 0.00596049 0.999982i \(-0.498103\pi\)
0.00596049 + 0.999982i \(0.498103\pi\)
\(830\) −69.9521 −2.42807
\(831\) −2.12642 −0.0737647
\(832\) 12.2491 0.424660
\(833\) 0.790038 0.0273732
\(834\) −1.98963 −0.0688952
\(835\) 102.189 3.53639
\(836\) 21.2901 0.736332
\(837\) −40.4403 −1.39782
\(838\) 39.9337 1.37949
\(839\) −19.0683 −0.658309 −0.329155 0.944276i \(-0.606764\pi\)
−0.329155 + 0.944276i \(0.606764\pi\)
\(840\) −15.2222 −0.525216
\(841\) −28.9106 −0.996917
\(842\) −35.8891 −1.23682
\(843\) 51.9871 1.79053
\(844\) 51.5669 1.77500
\(845\) −48.7406 −1.67673
\(846\) 78.7920 2.70892
\(847\) 9.50863 0.326720
\(848\) −1.74959 −0.0600812
\(849\) −13.6090 −0.467059
\(850\) −19.8168 −0.679709
\(851\) −6.02421 −0.206507
\(852\) 3.52498 0.120764
\(853\) −0.684623 −0.0234410 −0.0117205 0.999931i \(-0.503731\pi\)
−0.0117205 + 0.999931i \(0.503731\pi\)
\(854\) −11.8702 −0.406190
\(855\) −160.042 −5.47331
\(856\) −6.54600 −0.223738
\(857\) 43.7317 1.49385 0.746923 0.664911i \(-0.231531\pi\)
0.746923 + 0.664911i \(0.231531\pi\)
\(858\) 8.05658 0.275047
\(859\) −24.3350 −0.830300 −0.415150 0.909753i \(-0.636271\pi\)
−0.415150 + 0.909753i \(0.636271\pi\)
\(860\) −21.2138 −0.723385
\(861\) 8.95214 0.305088
\(862\) −33.5587 −1.14301
\(863\) −1.00000 −0.0340404
\(864\) −65.2251 −2.21900
\(865\) −88.6805 −3.01523
\(866\) −12.8154 −0.435486
\(867\) 48.5972 1.65045
\(868\) −12.5550 −0.426144
\(869\) −7.68090 −0.260557
\(870\) 7.76811 0.263364
\(871\) −8.62229 −0.292155
\(872\) 5.00764 0.169580
\(873\) −14.0529 −0.475620
\(874\) −14.6443 −0.495349
\(875\) −27.4443 −0.927785
\(876\) −20.0194 −0.676392
\(877\) 13.7917 0.465713 0.232857 0.972511i \(-0.425193\pi\)
0.232857 + 0.972511i \(0.425193\pi\)
\(878\) 1.78006 0.0600741
\(879\) −58.9572 −1.98858
\(880\) 12.4059 0.418204
\(881\) −53.9962 −1.81918 −0.909589 0.415509i \(-0.863604\pi\)
−0.909589 + 0.415509i \(0.863604\pi\)
\(882\) −12.4350 −0.418708
\(883\) 17.8108 0.599383 0.299691 0.954036i \(-0.403116\pi\)
0.299691 + 0.954036i \(0.403116\pi\)
\(884\) −2.12080 −0.0713301
\(885\) 162.347 5.45724
\(886\) −88.1899 −2.96280
\(887\) 43.4881 1.46019 0.730094 0.683347i \(-0.239476\pi\)
0.730094 + 0.683347i \(0.239476\pi\)
\(888\) 22.1140 0.742096
\(889\) −11.0275 −0.369849
\(890\) 117.149 3.92683
\(891\) −8.91252 −0.298581
\(892\) −38.5326 −1.29017
\(893\) 42.7177 1.42949
\(894\) 5.04372 0.168687
\(895\) −40.8663 −1.36601
\(896\) −9.60691 −0.320944
\(897\) −3.12485 −0.104336
\(898\) −26.7514 −0.892705
\(899\) 1.45168 0.0484161
\(900\) 175.880 5.86268
\(901\) 0.556258 0.0185316
\(902\) 7.88904 0.262676
\(903\) −5.95505 −0.198172
\(904\) −3.72784 −0.123986
\(905\) −73.5324 −2.44430
\(906\) −76.7721 −2.55058
\(907\) −34.3622 −1.14098 −0.570488 0.821306i \(-0.693246\pi\)
−0.570488 + 0.821306i \(0.693246\pi\)
\(908\) −65.5932 −2.17679
\(909\) 4.54573 0.150773
\(910\) −9.08823 −0.301272
\(911\) −39.4883 −1.30831 −0.654153 0.756362i \(-0.726975\pi\)
−0.654153 + 0.756362i \(0.726975\pi\)
\(912\) −49.7150 −1.64623
\(913\) −9.75781 −0.322936
\(914\) 78.1339 2.58444
\(915\) 67.2484 2.22316
\(916\) 19.2430 0.635806
\(917\) 3.07149 0.101430
\(918\) 14.0920 0.465105
\(919\) −49.0413 −1.61772 −0.808861 0.588000i \(-0.799916\pi\)
−0.808861 + 0.588000i \(0.799916\pi\)
\(920\) 5.20299 0.171538
\(921\) −25.6781 −0.846121
\(922\) −53.3845 −1.75812
\(923\) 0.476841 0.0156954
\(924\) −9.37159 −0.308303
\(925\) 69.5647 2.28727
\(926\) 43.0942 1.41616
\(927\) −42.8332 −1.40683
\(928\) 2.34137 0.0768592
\(929\) −16.7417 −0.549278 −0.274639 0.961547i \(-0.588558\pi\)
−0.274639 + 0.961547i \(0.588558\pi\)
\(930\) 126.140 4.13629
\(931\) −6.74173 −0.220951
\(932\) −37.8004 −1.23819
\(933\) 43.5117 1.42451
\(934\) 12.8202 0.419491
\(935\) −3.94429 −0.128992
\(936\) 7.56332 0.247215
\(937\) 49.0794 1.60335 0.801677 0.597758i \(-0.203942\pi\)
0.801677 + 0.597758i \(0.203942\pi\)
\(938\) 17.7868 0.580759
\(939\) 100.108 3.26689
\(940\) −66.9850 −2.18481
\(941\) 6.28288 0.204816 0.102408 0.994742i \(-0.467345\pi\)
0.102408 + 0.994742i \(0.467345\pi\)
\(942\) 119.111 3.88086
\(943\) −3.05987 −0.0996429
\(944\) 33.2519 1.08226
\(945\) 34.0518 1.10770
\(946\) −5.24786 −0.170623
\(947\) −5.61569 −0.182485 −0.0912427 0.995829i \(-0.529084\pi\)
−0.0912427 + 0.995829i \(0.529084\pi\)
\(948\) −48.2659 −1.56760
\(949\) −2.70812 −0.0879093
\(950\) 169.105 5.48648
\(951\) 63.8255 2.06968
\(952\) 0.991265 0.0321271
\(953\) 36.0636 1.16821 0.584107 0.811677i \(-0.301445\pi\)
0.584107 + 0.811677i \(0.301445\pi\)
\(954\) −8.75535 −0.283465
\(955\) −29.0176 −0.938989
\(956\) 24.8183 0.802683
\(957\) 1.08359 0.0350276
\(958\) −6.81085 −0.220049
\(959\) 15.4926 0.500284
\(960\) 143.153 4.62026
\(961\) −7.42747 −0.239596
\(962\) 13.2028 0.425677
\(963\) 30.2947 0.976234
\(964\) 12.0674 0.388663
\(965\) 71.7929 2.31109
\(966\) 6.44620 0.207403
\(967\) 27.0752 0.870679 0.435340 0.900266i \(-0.356628\pi\)
0.435340 + 0.900266i \(0.356628\pi\)
\(968\) 11.9305 0.383462
\(969\) 15.8062 0.507768
\(970\) 21.1873 0.680283
\(971\) −5.80383 −0.186254 −0.0931268 0.995654i \(-0.529686\pi\)
−0.0931268 + 0.995654i \(0.529686\pi\)
\(972\) 8.61150 0.276214
\(973\) 0.313077 0.0100368
\(974\) 28.4033 0.910099
\(975\) 36.0842 1.15562
\(976\) 13.7738 0.440889
\(977\) −41.1394 −1.31616 −0.658082 0.752946i \(-0.728632\pi\)
−0.658082 + 0.752946i \(0.728632\pi\)
\(978\) 6.13801 0.196272
\(979\) 16.3414 0.522273
\(980\) 10.5716 0.337698
\(981\) −23.1752 −0.739929
\(982\) −9.56961 −0.305379
\(983\) 59.5754 1.90016 0.950081 0.312005i \(-0.101001\pi\)
0.950081 + 0.312005i \(0.101001\pi\)
\(984\) 11.2323 0.358072
\(985\) 39.2530 1.25071
\(986\) −0.505856 −0.0161098
\(987\) −18.8037 −0.598529
\(988\) 18.0977 0.575763
\(989\) 2.03545 0.0647236
\(990\) 62.0821 1.97310
\(991\) −50.3745 −1.60020 −0.800100 0.599867i \(-0.795220\pi\)
−0.800100 + 0.599867i \(0.795220\pi\)
\(992\) 38.0195 1.20712
\(993\) −27.7132 −0.879453
\(994\) −0.983667 −0.0312000
\(995\) −2.73437 −0.0866853
\(996\) −61.3170 −1.94290
\(997\) −1.14652 −0.0363108 −0.0181554 0.999835i \(-0.505779\pi\)
−0.0181554 + 0.999835i \(0.505779\pi\)
\(998\) −23.2587 −0.736242
\(999\) −49.4684 −1.56511
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 6041.2.a.d.1.14 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6041.2.a.d.1.14 101 1.1 even 1 trivial