Properties

Label 8021.2.a.d.1.1
Level $8021$
Weight $2$
Character 8021.1
Self dual yes
Analytic conductor $64.048$
Analytic rank $0$
Dimension $174$
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] = [8021,2,Mod(1,8021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8021, 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("8021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8021 = 13 \cdot 617 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8021.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: \(64.0480074613\)
Analytic rank: \(0\)
Dimension: \(174\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.81586 q^{2} +1.36738 q^{3} +5.92908 q^{4} -2.81839 q^{5} -3.85036 q^{6} -0.890414 q^{7} -11.0638 q^{8} -1.13027 q^{9} +O(q^{10})\) \(q-2.81586 q^{2} +1.36738 q^{3} +5.92908 q^{4} -2.81839 q^{5} -3.85036 q^{6} -0.890414 q^{7} -11.0638 q^{8} -1.13027 q^{9} +7.93620 q^{10} -5.19095 q^{11} +8.10732 q^{12} +1.00000 q^{13} +2.50728 q^{14} -3.85382 q^{15} +19.2959 q^{16} +6.81972 q^{17} +3.18268 q^{18} +4.77719 q^{19} -16.7105 q^{20} -1.21754 q^{21} +14.6170 q^{22} -3.65966 q^{23} -15.1284 q^{24} +2.94333 q^{25} -2.81586 q^{26} -5.64765 q^{27} -5.27934 q^{28} -3.09025 q^{29} +10.8518 q^{30} -9.56903 q^{31} -32.2070 q^{32} -7.09801 q^{33} -19.2034 q^{34} +2.50953 q^{35} -6.70145 q^{36} +3.83986 q^{37} -13.4519 q^{38} +1.36738 q^{39} +31.1820 q^{40} -1.36139 q^{41} +3.42841 q^{42} -3.24758 q^{43} -30.7776 q^{44} +3.18553 q^{45} +10.3051 q^{46} +2.91161 q^{47} +26.3848 q^{48} -6.20716 q^{49} -8.28801 q^{50} +9.32516 q^{51} +5.92908 q^{52} +9.64024 q^{53} +15.9030 q^{54} +14.6301 q^{55} +9.85133 q^{56} +6.53224 q^{57} +8.70171 q^{58} -5.16660 q^{59} -22.8496 q^{60} -6.62776 q^{61} +26.9451 q^{62} +1.00641 q^{63} +52.0988 q^{64} -2.81839 q^{65} +19.9870 q^{66} -10.0518 q^{67} +40.4347 q^{68} -5.00415 q^{69} -7.06651 q^{70} +7.71839 q^{71} +12.5050 q^{72} +4.11268 q^{73} -10.8125 q^{74} +4.02466 q^{75} +28.3244 q^{76} +4.62209 q^{77} -3.85036 q^{78} -5.30061 q^{79} -54.3833 q^{80} -4.33170 q^{81} +3.83348 q^{82} -10.5174 q^{83} -7.21887 q^{84} -19.2206 q^{85} +9.14474 q^{86} -4.22555 q^{87} +57.4314 q^{88} +1.60169 q^{89} -8.97003 q^{90} -0.890414 q^{91} -21.6984 q^{92} -13.0845 q^{93} -8.19869 q^{94} -13.4640 q^{95} -44.0393 q^{96} -1.11488 q^{97} +17.4785 q^{98} +5.86716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81586 −1.99112 −0.995558 0.0941512i \(-0.969986\pi\)
−0.995558 + 0.0941512i \(0.969986\pi\)
\(3\) 1.36738 0.789458 0.394729 0.918798i \(-0.370838\pi\)
0.394729 + 0.918798i \(0.370838\pi\)
\(4\) 5.92908 2.96454
\(5\) −2.81839 −1.26042 −0.630211 0.776424i \(-0.717032\pi\)
−0.630211 + 0.776424i \(0.717032\pi\)
\(6\) −3.85036 −1.57190
\(7\) −0.890414 −0.336545 −0.168272 0.985741i \(-0.553819\pi\)
−0.168272 + 0.985741i \(0.553819\pi\)
\(8\) −11.0638 −3.91163
\(9\) −1.13027 −0.376756
\(10\) 7.93620 2.50965
\(11\) −5.19095 −1.56513 −0.782565 0.622569i \(-0.786089\pi\)
−0.782565 + 0.622569i \(0.786089\pi\)
\(12\) 8.10732 2.34038
\(13\) 1.00000 0.277350
\(14\) 2.50728 0.670100
\(15\) −3.85382 −0.995051
\(16\) 19.2959 4.82397
\(17\) 6.81972 1.65402 0.827012 0.562184i \(-0.190039\pi\)
0.827012 + 0.562184i \(0.190039\pi\)
\(18\) 3.18268 0.750164
\(19\) 4.77719 1.09596 0.547981 0.836491i \(-0.315397\pi\)
0.547981 + 0.836491i \(0.315397\pi\)
\(20\) −16.7105 −3.73658
\(21\) −1.21754 −0.265688
\(22\) 14.6170 3.11635
\(23\) −3.65966 −0.763092 −0.381546 0.924350i \(-0.624608\pi\)
−0.381546 + 0.924350i \(0.624608\pi\)
\(24\) −15.1284 −3.08807
\(25\) 2.94333 0.588666
\(26\) −2.81586 −0.552236
\(27\) −5.64765 −1.08689
\(28\) −5.27934 −0.997701
\(29\) −3.09025 −0.573845 −0.286922 0.957954i \(-0.592632\pi\)
−0.286922 + 0.957954i \(0.592632\pi\)
\(30\) 10.8518 1.98126
\(31\) −9.56903 −1.71865 −0.859324 0.511431i \(-0.829116\pi\)
−0.859324 + 0.511431i \(0.829116\pi\)
\(32\) −32.2070 −5.69345
\(33\) −7.09801 −1.23560
\(34\) −19.2034 −3.29335
\(35\) 2.50953 0.424189
\(36\) −6.70145 −1.11691
\(37\) 3.83986 0.631269 0.315635 0.948881i \(-0.397783\pi\)
0.315635 + 0.948881i \(0.397783\pi\)
\(38\) −13.4519 −2.18219
\(39\) 1.36738 0.218956
\(40\) 31.1820 4.93031
\(41\) −1.36139 −0.212613 −0.106306 0.994333i \(-0.533902\pi\)
−0.106306 + 0.994333i \(0.533902\pi\)
\(42\) 3.42841 0.529016
\(43\) −3.24758 −0.495251 −0.247626 0.968856i \(-0.579650\pi\)
−0.247626 + 0.968856i \(0.579650\pi\)
\(44\) −30.7776 −4.63989
\(45\) 3.18553 0.474871
\(46\) 10.3051 1.51940
\(47\) 2.91161 0.424702 0.212351 0.977194i \(-0.431888\pi\)
0.212351 + 0.977194i \(0.431888\pi\)
\(48\) 26.3848 3.80832
\(49\) −6.20716 −0.886738
\(50\) −8.28801 −1.17210
\(51\) 9.32516 1.30578
\(52\) 5.92908 0.822216
\(53\) 9.64024 1.32419 0.662095 0.749420i \(-0.269668\pi\)
0.662095 + 0.749420i \(0.269668\pi\)
\(54\) 15.9030 2.16413
\(55\) 14.6301 1.97272
\(56\) 9.85133 1.31644
\(57\) 6.53224 0.865217
\(58\) 8.70171 1.14259
\(59\) −5.16660 −0.672633 −0.336317 0.941749i \(-0.609181\pi\)
−0.336317 + 0.941749i \(0.609181\pi\)
\(60\) −22.8496 −2.94987
\(61\) −6.62776 −0.848598 −0.424299 0.905522i \(-0.639479\pi\)
−0.424299 + 0.905522i \(0.639479\pi\)
\(62\) 26.9451 3.42203
\(63\) 1.00641 0.126795
\(64\) 52.0988 6.51235
\(65\) −2.81839 −0.349578
\(66\) 19.9870 2.46023
\(67\) −10.0518 −1.22802 −0.614010 0.789298i \(-0.710445\pi\)
−0.614010 + 0.789298i \(0.710445\pi\)
\(68\) 40.4347 4.90342
\(69\) −5.00415 −0.602429
\(70\) −7.06651 −0.844609
\(71\) 7.71839 0.916005 0.458002 0.888951i \(-0.348565\pi\)
0.458002 + 0.888951i \(0.348565\pi\)
\(72\) 12.5050 1.47373
\(73\) 4.11268 0.481353 0.240677 0.970605i \(-0.422631\pi\)
0.240677 + 0.970605i \(0.422631\pi\)
\(74\) −10.8125 −1.25693
\(75\) 4.02466 0.464727
\(76\) 28.3244 3.24903
\(77\) 4.62209 0.526736
\(78\) −3.85036 −0.435967
\(79\) −5.30061 −0.596365 −0.298183 0.954509i \(-0.596380\pi\)
−0.298183 + 0.954509i \(0.596380\pi\)
\(80\) −54.3833 −6.08024
\(81\) −4.33170 −0.481300
\(82\) 3.83348 0.423337
\(83\) −10.5174 −1.15444 −0.577218 0.816590i \(-0.695862\pi\)
−0.577218 + 0.816590i \(0.695862\pi\)
\(84\) −7.21887 −0.787644
\(85\) −19.2206 −2.08477
\(86\) 9.14474 0.986102
\(87\) −4.22555 −0.453026
\(88\) 57.4314 6.12221
\(89\) 1.60169 0.169779 0.0848893 0.996390i \(-0.472946\pi\)
0.0848893 + 0.996390i \(0.472946\pi\)
\(90\) −8.97003 −0.945524
\(91\) −0.890414 −0.0933407
\(92\) −21.6984 −2.26222
\(93\) −13.0845 −1.35680
\(94\) −8.19869 −0.845630
\(95\) −13.4640 −1.38138
\(96\) −44.0393 −4.49474
\(97\) −1.11488 −0.113199 −0.0565996 0.998397i \(-0.518026\pi\)
−0.0565996 + 0.998397i \(0.518026\pi\)
\(98\) 17.4785 1.76560
\(99\) 5.86716 0.589671
\(100\) 17.4512 1.74512
\(101\) −14.3178 −1.42468 −0.712338 0.701836i \(-0.752364\pi\)
−0.712338 + 0.701836i \(0.752364\pi\)
\(102\) −26.2584 −2.59997
\(103\) −0.233744 −0.0230315 −0.0115157 0.999934i \(-0.503666\pi\)
−0.0115157 + 0.999934i \(0.503666\pi\)
\(104\) −11.0638 −1.08489
\(105\) 3.43149 0.334879
\(106\) −27.1456 −2.63661
\(107\) −18.4949 −1.78797 −0.893983 0.448100i \(-0.852101\pi\)
−0.893983 + 0.448100i \(0.852101\pi\)
\(108\) −33.4854 −3.22213
\(109\) 17.7624 1.70133 0.850665 0.525708i \(-0.176200\pi\)
0.850665 + 0.525708i \(0.176200\pi\)
\(110\) −41.1964 −3.92792
\(111\) 5.25055 0.498361
\(112\) −17.1813 −1.62348
\(113\) −14.5875 −1.37228 −0.686140 0.727470i \(-0.740696\pi\)
−0.686140 + 0.727470i \(0.740696\pi\)
\(114\) −18.3939 −1.72275
\(115\) 10.3144 0.961819
\(116\) −18.3223 −1.70119
\(117\) −1.13027 −0.104493
\(118\) 14.5484 1.33929
\(119\) −6.07237 −0.556653
\(120\) 42.6377 3.89227
\(121\) 15.9459 1.44963
\(122\) 18.6629 1.68966
\(123\) −1.86154 −0.167849
\(124\) −56.7356 −5.09501
\(125\) 5.79650 0.518455
\(126\) −2.83390 −0.252464
\(127\) 20.4899 1.81818 0.909091 0.416599i \(-0.136778\pi\)
0.909091 + 0.416599i \(0.136778\pi\)
\(128\) −82.2890 −7.27339
\(129\) −4.44068 −0.390980
\(130\) 7.93620 0.696051
\(131\) 12.5531 1.09677 0.548385 0.836226i \(-0.315243\pi\)
0.548385 + 0.836226i \(0.315243\pi\)
\(132\) −42.0847 −3.66300
\(133\) −4.25368 −0.368840
\(134\) 28.3044 2.44513
\(135\) 15.9173 1.36994
\(136\) −75.4517 −6.46993
\(137\) −20.9783 −1.79230 −0.896150 0.443752i \(-0.853647\pi\)
−0.896150 + 0.443752i \(0.853647\pi\)
\(138\) 14.0910 1.19951
\(139\) 1.09302 0.0927085 0.0463543 0.998925i \(-0.485240\pi\)
0.0463543 + 0.998925i \(0.485240\pi\)
\(140\) 14.8792 1.25753
\(141\) 3.98128 0.335284
\(142\) −21.7339 −1.82387
\(143\) −5.19095 −0.434089
\(144\) −21.8095 −1.81746
\(145\) 8.70953 0.723287
\(146\) −11.5808 −0.958430
\(147\) −8.48756 −0.700042
\(148\) 22.7669 1.87142
\(149\) −5.91776 −0.484801 −0.242401 0.970176i \(-0.577935\pi\)
−0.242401 + 0.970176i \(0.577935\pi\)
\(150\) −11.3329 −0.925326
\(151\) 6.71847 0.546742 0.273371 0.961909i \(-0.411861\pi\)
0.273371 + 0.961909i \(0.411861\pi\)
\(152\) −52.8537 −4.28700
\(153\) −7.70810 −0.623163
\(154\) −13.0152 −1.04879
\(155\) 26.9693 2.16622
\(156\) 8.10732 0.649105
\(157\) −9.07044 −0.723900 −0.361950 0.932197i \(-0.617889\pi\)
−0.361950 + 0.932197i \(0.617889\pi\)
\(158\) 14.9258 1.18743
\(159\) 13.1819 1.04539
\(160\) 90.7719 7.17615
\(161\) 3.25861 0.256815
\(162\) 12.1975 0.958323
\(163\) 2.18550 0.171181 0.0855907 0.996330i \(-0.472722\pi\)
0.0855907 + 0.996330i \(0.472722\pi\)
\(164\) −8.07178 −0.630300
\(165\) 20.0050 1.55738
\(166\) 29.6156 2.29862
\(167\) 7.54304 0.583698 0.291849 0.956464i \(-0.405729\pi\)
0.291849 + 0.956464i \(0.405729\pi\)
\(168\) 13.4705 1.03927
\(169\) 1.00000 0.0769231
\(170\) 54.1227 4.15102
\(171\) −5.39950 −0.412910
\(172\) −19.2552 −1.46819
\(173\) 21.7276 1.65192 0.825959 0.563731i \(-0.190634\pi\)
0.825959 + 0.563731i \(0.190634\pi\)
\(174\) 11.8986 0.902028
\(175\) −2.62078 −0.198112
\(176\) −100.164 −7.55013
\(177\) −7.06471 −0.531016
\(178\) −4.51014 −0.338049
\(179\) −1.68407 −0.125874 −0.0629368 0.998018i \(-0.520047\pi\)
−0.0629368 + 0.998018i \(0.520047\pi\)
\(180\) 18.8873 1.40778
\(181\) −7.49746 −0.557282 −0.278641 0.960395i \(-0.589884\pi\)
−0.278641 + 0.960395i \(0.589884\pi\)
\(182\) 2.50728 0.185852
\(183\) −9.06268 −0.669933
\(184\) 40.4896 2.98493
\(185\) −10.8222 −0.795666
\(186\) 36.8442 2.70155
\(187\) −35.4008 −2.58876
\(188\) 17.2632 1.25905
\(189\) 5.02875 0.365788
\(190\) 37.9127 2.75048
\(191\) −22.0653 −1.59659 −0.798295 0.602266i \(-0.794265\pi\)
−0.798295 + 0.602266i \(0.794265\pi\)
\(192\) 71.2389 5.14123
\(193\) 7.27390 0.523587 0.261793 0.965124i \(-0.415686\pi\)
0.261793 + 0.965124i \(0.415686\pi\)
\(194\) 3.13936 0.225393
\(195\) −3.85382 −0.275978
\(196\) −36.8028 −2.62877
\(197\) −15.9931 −1.13946 −0.569731 0.821831i \(-0.692953\pi\)
−0.569731 + 0.821831i \(0.692953\pi\)
\(198\) −16.5211 −1.17410
\(199\) −11.9028 −0.843766 −0.421883 0.906650i \(-0.638631\pi\)
−0.421883 + 0.906650i \(0.638631\pi\)
\(200\) −32.5643 −2.30264
\(201\) −13.7446 −0.969471
\(202\) 40.3170 2.83670
\(203\) 2.75160 0.193124
\(204\) 55.2896 3.87105
\(205\) 3.83692 0.267982
\(206\) 0.658190 0.0458583
\(207\) 4.13639 0.287499
\(208\) 19.2959 1.33793
\(209\) −24.7981 −1.71532
\(210\) −9.66261 −0.666784
\(211\) 19.5185 1.34371 0.671854 0.740683i \(-0.265498\pi\)
0.671854 + 0.740683i \(0.265498\pi\)
\(212\) 57.1578 3.92562
\(213\) 10.5540 0.723148
\(214\) 52.0790 3.56005
\(215\) 9.15295 0.624226
\(216\) 62.4843 4.25152
\(217\) 8.52040 0.578402
\(218\) −50.0165 −3.38755
\(219\) 5.62361 0.380008
\(220\) 86.7432 5.84823
\(221\) 6.81972 0.458744
\(222\) −14.7848 −0.992294
\(223\) 20.0607 1.34337 0.671683 0.740838i \(-0.265572\pi\)
0.671683 + 0.740838i \(0.265572\pi\)
\(224\) 28.6776 1.91610
\(225\) −3.32675 −0.221783
\(226\) 41.0765 2.73237
\(227\) −1.00059 −0.0664113 −0.0332057 0.999449i \(-0.510572\pi\)
−0.0332057 + 0.999449i \(0.510572\pi\)
\(228\) 38.7302 2.56497
\(229\) −1.96655 −0.129953 −0.0649765 0.997887i \(-0.520697\pi\)
−0.0649765 + 0.997887i \(0.520697\pi\)
\(230\) −29.0438 −1.91509
\(231\) 6.32016 0.415836
\(232\) 34.1898 2.24467
\(233\) −11.8398 −0.775649 −0.387825 0.921733i \(-0.626773\pi\)
−0.387825 + 0.921733i \(0.626773\pi\)
\(234\) 3.18268 0.208058
\(235\) −8.20605 −0.535304
\(236\) −30.6332 −1.99405
\(237\) −7.24796 −0.470805
\(238\) 17.0990 1.10836
\(239\) 8.05869 0.521273 0.260637 0.965437i \(-0.416068\pi\)
0.260637 + 0.965437i \(0.416068\pi\)
\(240\) −74.3628 −4.80010
\(241\) −9.81208 −0.632052 −0.316026 0.948751i \(-0.602349\pi\)
−0.316026 + 0.948751i \(0.602349\pi\)
\(242\) −44.9015 −2.88638
\(243\) 11.0199 0.706925
\(244\) −39.2966 −2.51570
\(245\) 17.4942 1.11766
\(246\) 5.24183 0.334207
\(247\) 4.77719 0.303965
\(248\) 105.869 6.72272
\(249\) −14.3813 −0.911379
\(250\) −16.3222 −1.03230
\(251\) 1.01801 0.0642562 0.0321281 0.999484i \(-0.489772\pi\)
0.0321281 + 0.999484i \(0.489772\pi\)
\(252\) 5.96706 0.375890
\(253\) 18.9971 1.19434
\(254\) −57.6966 −3.62021
\(255\) −26.2819 −1.64584
\(256\) 127.517 7.96981
\(257\) −5.00999 −0.312514 −0.156257 0.987716i \(-0.549943\pi\)
−0.156257 + 0.987716i \(0.549943\pi\)
\(258\) 12.5043 0.778487
\(259\) −3.41906 −0.212450
\(260\) −16.7105 −1.03634
\(261\) 3.49280 0.216199
\(262\) −35.3478 −2.18380
\(263\) 15.3038 0.943672 0.471836 0.881686i \(-0.343591\pi\)
0.471836 + 0.881686i \(0.343591\pi\)
\(264\) 78.5307 4.83323
\(265\) −27.1700 −1.66904
\(266\) 11.9778 0.734404
\(267\) 2.19012 0.134033
\(268\) −59.5978 −3.64052
\(269\) −21.9523 −1.33845 −0.669227 0.743058i \(-0.733375\pi\)
−0.669227 + 0.743058i \(0.733375\pi\)
\(270\) −44.8209 −2.72771
\(271\) −30.8855 −1.87616 −0.938079 0.346422i \(-0.887397\pi\)
−0.938079 + 0.346422i \(0.887397\pi\)
\(272\) 131.592 7.97896
\(273\) −1.21754 −0.0736886
\(274\) 59.0721 3.56868
\(275\) −15.2787 −0.921338
\(276\) −29.6700 −1.78593
\(277\) −13.7135 −0.823965 −0.411982 0.911192i \(-0.635163\pi\)
−0.411982 + 0.911192i \(0.635163\pi\)
\(278\) −3.07779 −0.184593
\(279\) 10.8156 0.647511
\(280\) −27.7649 −1.65927
\(281\) −6.15411 −0.367124 −0.183562 0.983008i \(-0.558763\pi\)
−0.183562 + 0.983008i \(0.558763\pi\)
\(282\) −11.2107 −0.667590
\(283\) 16.7963 0.998436 0.499218 0.866477i \(-0.333621\pi\)
0.499218 + 0.866477i \(0.333621\pi\)
\(284\) 45.7630 2.71554
\(285\) −18.4104 −1.09054
\(286\) 14.6170 0.864321
\(287\) 1.21220 0.0715538
\(288\) 36.4025 2.14504
\(289\) 29.5085 1.73580
\(290\) −24.5248 −1.44015
\(291\) −1.52447 −0.0893661
\(292\) 24.3844 1.42699
\(293\) −13.2050 −0.771443 −0.385722 0.922615i \(-0.626047\pi\)
−0.385722 + 0.922615i \(0.626047\pi\)
\(294\) 23.8998 1.39387
\(295\) 14.5615 0.847803
\(296\) −42.4833 −2.46929
\(297\) 29.3167 1.70113
\(298\) 16.6636 0.965296
\(299\) −3.65966 −0.211644
\(300\) 23.8625 1.37770
\(301\) 2.89169 0.166674
\(302\) −18.9183 −1.08863
\(303\) −19.5779 −1.12472
\(304\) 92.1800 5.28689
\(305\) 18.6796 1.06959
\(306\) 21.7050 1.24079
\(307\) 12.6903 0.724275 0.362137 0.932125i \(-0.382047\pi\)
0.362137 + 0.932125i \(0.382047\pi\)
\(308\) 27.4048 1.56153
\(309\) −0.319617 −0.0181824
\(310\) −75.9418 −4.31320
\(311\) 9.47046 0.537021 0.268510 0.963277i \(-0.413469\pi\)
0.268510 + 0.963277i \(0.413469\pi\)
\(312\) −15.1284 −0.856476
\(313\) −29.6412 −1.67542 −0.837711 0.546114i \(-0.816107\pi\)
−0.837711 + 0.546114i \(0.816107\pi\)
\(314\) 25.5411 1.44137
\(315\) −2.83644 −0.159816
\(316\) −31.4278 −1.76795
\(317\) 4.35475 0.244587 0.122294 0.992494i \(-0.460975\pi\)
0.122294 + 0.992494i \(0.460975\pi\)
\(318\) −37.1184 −2.08150
\(319\) 16.0413 0.898141
\(320\) −146.835 −8.20831
\(321\) −25.2896 −1.41153
\(322\) −9.17581 −0.511348
\(323\) 32.5791 1.81275
\(324\) −25.6830 −1.42683
\(325\) 2.94333 0.163267
\(326\) −6.15406 −0.340842
\(327\) 24.2880 1.34313
\(328\) 15.0621 0.831663
\(329\) −2.59254 −0.142931
\(330\) −56.3312 −3.10093
\(331\) 30.7960 1.69270 0.846351 0.532626i \(-0.178795\pi\)
0.846351 + 0.532626i \(0.178795\pi\)
\(332\) −62.3586 −3.42238
\(333\) −4.34007 −0.237834
\(334\) −21.2402 −1.16221
\(335\) 28.3298 1.54782
\(336\) −23.4934 −1.28167
\(337\) 22.6814 1.23553 0.617766 0.786362i \(-0.288038\pi\)
0.617766 + 0.786362i \(0.288038\pi\)
\(338\) −2.81586 −0.153163
\(339\) −19.9467 −1.08336
\(340\) −113.961 −6.18039
\(341\) 49.6723 2.68991
\(342\) 15.2042 0.822152
\(343\) 11.7598 0.634972
\(344\) 35.9304 1.93724
\(345\) 14.1037 0.759316
\(346\) −61.1819 −3.28916
\(347\) 10.8949 0.584871 0.292435 0.956285i \(-0.405534\pi\)
0.292435 + 0.956285i \(0.405534\pi\)
\(348\) −25.0536 −1.34302
\(349\) 14.5526 0.778985 0.389492 0.921030i \(-0.372650\pi\)
0.389492 + 0.921030i \(0.372650\pi\)
\(350\) 7.37976 0.394465
\(351\) −5.64765 −0.301449
\(352\) 167.185 8.91098
\(353\) 29.5581 1.57322 0.786609 0.617452i \(-0.211835\pi\)
0.786609 + 0.617452i \(0.211835\pi\)
\(354\) 19.8933 1.05731
\(355\) −21.7535 −1.15455
\(356\) 9.49655 0.503316
\(357\) −8.30325 −0.439455
\(358\) 4.74212 0.250629
\(359\) 34.1868 1.80431 0.902154 0.431414i \(-0.141985\pi\)
0.902154 + 0.431414i \(0.141985\pi\)
\(360\) −35.2440 −1.85752
\(361\) 3.82154 0.201133
\(362\) 21.1118 1.10961
\(363\) 21.8042 1.14442
\(364\) −5.27934 −0.276713
\(365\) −11.5911 −0.606709
\(366\) 25.5193 1.33391
\(367\) −19.5711 −1.02160 −0.510802 0.859698i \(-0.670652\pi\)
−0.510802 + 0.859698i \(0.670652\pi\)
\(368\) −70.6163 −3.68113
\(369\) 1.53873 0.0801031
\(370\) 30.4739 1.58426
\(371\) −8.58381 −0.445649
\(372\) −77.5792 −4.02230
\(373\) −0.741225 −0.0383792 −0.0191896 0.999816i \(-0.506109\pi\)
−0.0191896 + 0.999816i \(0.506109\pi\)
\(374\) 99.6838 5.15452
\(375\) 7.92603 0.409299
\(376\) −32.2133 −1.66128
\(377\) −3.09025 −0.159156
\(378\) −14.1603 −0.728325
\(379\) 23.4901 1.20660 0.603302 0.797512i \(-0.293851\pi\)
0.603302 + 0.797512i \(0.293851\pi\)
\(380\) −79.8291 −4.09515
\(381\) 28.0175 1.43538
\(382\) 62.1329 3.17900
\(383\) −7.85307 −0.401273 −0.200637 0.979666i \(-0.564301\pi\)
−0.200637 + 0.979666i \(0.564301\pi\)
\(384\) −112.520 −5.74204
\(385\) −13.0269 −0.663910
\(386\) −20.4823 −1.04252
\(387\) 3.67063 0.186589
\(388\) −6.61024 −0.335584
\(389\) 29.9332 1.51767 0.758837 0.651280i \(-0.225768\pi\)
0.758837 + 0.651280i \(0.225768\pi\)
\(390\) 10.8518 0.549503
\(391\) −24.9578 −1.26217
\(392\) 68.6746 3.46859
\(393\) 17.1649 0.865854
\(394\) 45.0344 2.26880
\(395\) 14.9392 0.751672
\(396\) 34.7869 1.74811
\(397\) −13.4144 −0.673249 −0.336625 0.941639i \(-0.609285\pi\)
−0.336625 + 0.941639i \(0.609285\pi\)
\(398\) 33.5166 1.68004
\(399\) −5.81640 −0.291184
\(400\) 56.7941 2.83971
\(401\) 22.1318 1.10521 0.552605 0.833443i \(-0.313634\pi\)
0.552605 + 0.833443i \(0.313634\pi\)
\(402\) 38.7030 1.93033
\(403\) −9.56903 −0.476667
\(404\) −84.8916 −4.22351
\(405\) 12.2084 0.606641
\(406\) −7.74813 −0.384533
\(407\) −19.9325 −0.988018
\(408\) −103.171 −5.10774
\(409\) −15.9103 −0.786715 −0.393358 0.919386i \(-0.628687\pi\)
−0.393358 + 0.919386i \(0.628687\pi\)
\(410\) −10.8042 −0.533583
\(411\) −28.6854 −1.41495
\(412\) −1.38589 −0.0682777
\(413\) 4.60041 0.226371
\(414\) −11.6475 −0.572444
\(415\) 29.6422 1.45508
\(416\) −32.2070 −1.57908
\(417\) 1.49457 0.0731895
\(418\) 69.8281 3.41541
\(419\) 33.4699 1.63511 0.817555 0.575850i \(-0.195329\pi\)
0.817555 + 0.575850i \(0.195329\pi\)
\(420\) 20.3456 0.992764
\(421\) −29.9163 −1.45803 −0.729016 0.684496i \(-0.760022\pi\)
−0.729016 + 0.684496i \(0.760022\pi\)
\(422\) −54.9614 −2.67548
\(423\) −3.29089 −0.160009
\(424\) −106.657 −5.17974
\(425\) 20.0727 0.973668
\(426\) −29.7186 −1.43987
\(427\) 5.90145 0.285591
\(428\) −109.658 −5.30050
\(429\) −7.09801 −0.342695
\(430\) −25.7734 −1.24291
\(431\) 7.46140 0.359403 0.179702 0.983721i \(-0.442487\pi\)
0.179702 + 0.983721i \(0.442487\pi\)
\(432\) −108.976 −5.24313
\(433\) −17.1887 −0.826037 −0.413019 0.910723i \(-0.635526\pi\)
−0.413019 + 0.910723i \(0.635526\pi\)
\(434\) −23.9923 −1.15167
\(435\) 11.9093 0.571005
\(436\) 105.315 5.04367
\(437\) −17.4829 −0.836320
\(438\) −15.8353 −0.756640
\(439\) −1.75209 −0.0836229 −0.0418114 0.999126i \(-0.513313\pi\)
−0.0418114 + 0.999126i \(0.513313\pi\)
\(440\) −161.864 −7.71657
\(441\) 7.01575 0.334083
\(442\) −19.2034 −0.913412
\(443\) 34.4167 1.63519 0.817593 0.575797i \(-0.195308\pi\)
0.817593 + 0.575797i \(0.195308\pi\)
\(444\) 31.1310 1.47741
\(445\) −4.51419 −0.213993
\(446\) −56.4883 −2.67480
\(447\) −8.09183 −0.382731
\(448\) −46.3895 −2.19170
\(449\) 11.8819 0.560742 0.280371 0.959892i \(-0.409543\pi\)
0.280371 + 0.959892i \(0.409543\pi\)
\(450\) 9.36767 0.441596
\(451\) 7.06689 0.332767
\(452\) −86.4907 −4.06818
\(453\) 9.18672 0.431630
\(454\) 2.81752 0.132233
\(455\) 2.50953 0.117649
\(456\) −72.2712 −3.38441
\(457\) −29.8747 −1.39748 −0.698740 0.715376i \(-0.746255\pi\)
−0.698740 + 0.715376i \(0.746255\pi\)
\(458\) 5.53753 0.258752
\(459\) −38.5154 −1.79774
\(460\) 61.1547 2.85135
\(461\) 3.65956 0.170443 0.0852215 0.996362i \(-0.472840\pi\)
0.0852215 + 0.996362i \(0.472840\pi\)
\(462\) −17.7967 −0.827978
\(463\) −19.6029 −0.911026 −0.455513 0.890229i \(-0.650544\pi\)
−0.455513 + 0.890229i \(0.650544\pi\)
\(464\) −59.6290 −2.76821
\(465\) 36.8773 1.71014
\(466\) 33.3392 1.54441
\(467\) 20.8779 0.966114 0.483057 0.875589i \(-0.339526\pi\)
0.483057 + 0.875589i \(0.339526\pi\)
\(468\) −6.70145 −0.309775
\(469\) 8.95024 0.413284
\(470\) 23.1071 1.06585
\(471\) −12.4028 −0.571489
\(472\) 57.1620 2.63109
\(473\) 16.8580 0.775132
\(474\) 20.4092 0.937428
\(475\) 14.0608 0.645156
\(476\) −36.0036 −1.65022
\(477\) −10.8960 −0.498896
\(478\) −22.6922 −1.03792
\(479\) 43.1723 1.97259 0.986296 0.164985i \(-0.0527574\pi\)
0.986296 + 0.164985i \(0.0527574\pi\)
\(480\) 124.120 5.66527
\(481\) 3.83986 0.175083
\(482\) 27.6295 1.25849
\(483\) 4.45577 0.202744
\(484\) 94.5447 4.29749
\(485\) 3.14218 0.142679
\(486\) −31.0305 −1.40757
\(487\) −7.06716 −0.320243 −0.160122 0.987097i \(-0.551189\pi\)
−0.160122 + 0.987097i \(0.551189\pi\)
\(488\) 73.3280 3.31940
\(489\) 2.98841 0.135141
\(490\) −49.2613 −2.22540
\(491\) 9.51917 0.429594 0.214797 0.976659i \(-0.431091\pi\)
0.214797 + 0.976659i \(0.431091\pi\)
\(492\) −11.0372 −0.497595
\(493\) −21.0746 −0.949153
\(494\) −13.4519 −0.605230
\(495\) −16.5359 −0.743235
\(496\) −184.643 −8.29071
\(497\) −6.87257 −0.308277
\(498\) 40.4958 1.81466
\(499\) 41.5433 1.85974 0.929868 0.367895i \(-0.119921\pi\)
0.929868 + 0.367895i \(0.119921\pi\)
\(500\) 34.3680 1.53698
\(501\) 10.3142 0.460805
\(502\) −2.86658 −0.127942
\(503\) −30.5253 −1.36106 −0.680528 0.732722i \(-0.738249\pi\)
−0.680528 + 0.732722i \(0.738249\pi\)
\(504\) −11.1346 −0.495976
\(505\) 40.3532 1.79569
\(506\) −53.4932 −2.37806
\(507\) 1.36738 0.0607276
\(508\) 121.486 5.39007
\(509\) −33.2341 −1.47308 −0.736538 0.676396i \(-0.763541\pi\)
−0.736538 + 0.676396i \(0.763541\pi\)
\(510\) 74.0063 3.27706
\(511\) −3.66199 −0.161997
\(512\) −194.492 −8.59543
\(513\) −26.9799 −1.19119
\(514\) 14.1074 0.622252
\(515\) 0.658781 0.0290294
\(516\) −26.3292 −1.15908
\(517\) −15.1140 −0.664713
\(518\) 9.62762 0.423013
\(519\) 29.7099 1.30412
\(520\) 31.1820 1.36742
\(521\) 32.4373 1.42110 0.710552 0.703644i \(-0.248445\pi\)
0.710552 + 0.703644i \(0.248445\pi\)
\(522\) −9.83526 −0.430478
\(523\) 3.01659 0.131906 0.0659532 0.997823i \(-0.478991\pi\)
0.0659532 + 0.997823i \(0.478991\pi\)
\(524\) 74.4285 3.25142
\(525\) −3.58361 −0.156402
\(526\) −43.0934 −1.87896
\(527\) −65.2581 −2.84269
\(528\) −136.962 −5.96052
\(529\) −9.60689 −0.417691
\(530\) 76.5069 3.32325
\(531\) 5.83963 0.253418
\(532\) −25.2204 −1.09344
\(533\) −1.36139 −0.0589682
\(534\) −6.16708 −0.266876
\(535\) 52.1258 2.25359
\(536\) 111.211 4.80356
\(537\) −2.30277 −0.0993720
\(538\) 61.8146 2.66502
\(539\) 32.2211 1.38786
\(540\) 94.3750 4.06125
\(541\) −4.34782 −0.186927 −0.0934637 0.995623i \(-0.529794\pi\)
−0.0934637 + 0.995623i \(0.529794\pi\)
\(542\) 86.9692 3.73565
\(543\) −10.2519 −0.439951
\(544\) −219.643 −9.41710
\(545\) −50.0614 −2.14440
\(546\) 3.42841 0.146723
\(547\) 25.2797 1.08088 0.540440 0.841382i \(-0.318258\pi\)
0.540440 + 0.841382i \(0.318258\pi\)
\(548\) −124.382 −5.31335
\(549\) 7.49114 0.319714
\(550\) 43.0226 1.83449
\(551\) −14.7627 −0.628912
\(552\) 55.3648 2.35648
\(553\) 4.71974 0.200704
\(554\) 38.6154 1.64061
\(555\) −14.7981 −0.628145
\(556\) 6.48059 0.274838
\(557\) −6.68514 −0.283258 −0.141629 0.989920i \(-0.545234\pi\)
−0.141629 + 0.989920i \(0.545234\pi\)
\(558\) −30.4551 −1.28927
\(559\) −3.24758 −0.137358
\(560\) 48.4237 2.04627
\(561\) −48.4064 −2.04372
\(562\) 17.3291 0.730986
\(563\) 9.24535 0.389645 0.194822 0.980839i \(-0.437587\pi\)
0.194822 + 0.980839i \(0.437587\pi\)
\(564\) 23.6053 0.993964
\(565\) 41.1134 1.72965
\(566\) −47.2960 −1.98800
\(567\) 3.85700 0.161979
\(568\) −85.3945 −3.58307
\(569\) 6.54291 0.274293 0.137146 0.990551i \(-0.456207\pi\)
0.137146 + 0.990551i \(0.456207\pi\)
\(570\) 51.8412 2.17139
\(571\) 1.91545 0.0801590 0.0400795 0.999196i \(-0.487239\pi\)
0.0400795 + 0.999196i \(0.487239\pi\)
\(572\) −30.7776 −1.28687
\(573\) −30.1717 −1.26044
\(574\) −3.41338 −0.142472
\(575\) −10.7716 −0.449206
\(576\) −58.8855 −2.45356
\(577\) 8.03199 0.334376 0.167188 0.985925i \(-0.446531\pi\)
0.167188 + 0.985925i \(0.446531\pi\)
\(578\) −83.0920 −3.45617
\(579\) 9.94619 0.413350
\(580\) 51.6395 2.14421
\(581\) 9.36485 0.388520
\(582\) 4.29270 0.177938
\(583\) −50.0420 −2.07253
\(584\) −45.5018 −1.88288
\(585\) 3.18553 0.131706
\(586\) 37.1834 1.53603
\(587\) 34.9900 1.44419 0.722097 0.691792i \(-0.243178\pi\)
0.722097 + 0.691792i \(0.243178\pi\)
\(588\) −50.3235 −2.07530
\(589\) −45.7131 −1.88357
\(590\) −41.0032 −1.68807
\(591\) −21.8687 −0.899558
\(592\) 74.0934 3.04522
\(593\) 28.0531 1.15200 0.576001 0.817449i \(-0.304612\pi\)
0.576001 + 0.817449i \(0.304612\pi\)
\(594\) −82.5517 −3.38714
\(595\) 17.1143 0.701619
\(596\) −35.0869 −1.43721
\(597\) −16.2756 −0.666118
\(598\) 10.3051 0.421407
\(599\) 27.0572 1.10553 0.552765 0.833337i \(-0.313573\pi\)
0.552765 + 0.833337i \(0.313573\pi\)
\(600\) −44.5278 −1.81784
\(601\) 32.5369 1.32721 0.663603 0.748085i \(-0.269026\pi\)
0.663603 + 0.748085i \(0.269026\pi\)
\(602\) −8.14260 −0.331868
\(603\) 11.3612 0.462664
\(604\) 39.8344 1.62084
\(605\) −44.9419 −1.82715
\(606\) 55.1288 2.23945
\(607\) −36.4986 −1.48143 −0.740716 0.671818i \(-0.765514\pi\)
−0.740716 + 0.671818i \(0.765514\pi\)
\(608\) −153.859 −6.23980
\(609\) 3.76249 0.152464
\(610\) −52.5993 −2.12968
\(611\) 2.91161 0.117791
\(612\) −45.7020 −1.84739
\(613\) −29.3119 −1.18390 −0.591949 0.805975i \(-0.701641\pi\)
−0.591949 + 0.805975i \(0.701641\pi\)
\(614\) −35.7342 −1.44212
\(615\) 5.24654 0.211561
\(616\) −51.1377 −2.06040
\(617\) −1.00000 −0.0402585
\(618\) 0.899998 0.0362032
\(619\) 13.3805 0.537807 0.268904 0.963167i \(-0.413339\pi\)
0.268904 + 0.963167i \(0.413339\pi\)
\(620\) 159.903 6.42186
\(621\) 20.6685 0.829398
\(622\) −26.6675 −1.06927
\(623\) −1.42617 −0.0571381
\(624\) 26.3848 1.05624
\(625\) −31.0535 −1.24214
\(626\) 83.4657 3.33596
\(627\) −33.9085 −1.35418
\(628\) −53.7794 −2.14603
\(629\) 26.1868 1.04413
\(630\) 7.98704 0.318211
\(631\) 10.9849 0.437301 0.218650 0.975803i \(-0.429835\pi\)
0.218650 + 0.975803i \(0.429835\pi\)
\(632\) 58.6447 2.33276
\(633\) 26.6892 1.06080
\(634\) −12.2624 −0.487002
\(635\) −57.7484 −2.29168
\(636\) 78.1566 3.09911
\(637\) −6.20716 −0.245937
\(638\) −45.1701 −1.78830
\(639\) −8.72385 −0.345110
\(640\) 231.923 9.16755
\(641\) 31.8229 1.25693 0.628465 0.777838i \(-0.283683\pi\)
0.628465 + 0.777838i \(0.283683\pi\)
\(642\) 71.2119 2.81051
\(643\) 21.7351 0.857149 0.428575 0.903506i \(-0.359016\pi\)
0.428575 + 0.903506i \(0.359016\pi\)
\(644\) 19.3206 0.761338
\(645\) 12.5156 0.492800
\(646\) −91.7382 −3.60939
\(647\) −4.24628 −0.166938 −0.0834692 0.996510i \(-0.526600\pi\)
−0.0834692 + 0.996510i \(0.526600\pi\)
\(648\) 47.9249 1.88267
\(649\) 26.8195 1.05276
\(650\) −8.28801 −0.325083
\(651\) 11.6506 0.456625
\(652\) 12.9580 0.507475
\(653\) 23.4940 0.919392 0.459696 0.888076i \(-0.347958\pi\)
0.459696 + 0.888076i \(0.347958\pi\)
\(654\) −68.3917 −2.67433
\(655\) −35.3796 −1.38239
\(656\) −26.2691 −1.02564
\(657\) −4.64843 −0.181353
\(658\) 7.30022 0.284592
\(659\) −34.7736 −1.35459 −0.677294 0.735713i \(-0.736847\pi\)
−0.677294 + 0.735713i \(0.736847\pi\)
\(660\) 118.611 4.61693
\(661\) 4.53835 0.176521 0.0882606 0.996097i \(-0.471869\pi\)
0.0882606 + 0.996097i \(0.471869\pi\)
\(662\) −86.7173 −3.37037
\(663\) 9.32516 0.362159
\(664\) 116.362 4.51573
\(665\) 11.9885 0.464895
\(666\) 12.2210 0.473555
\(667\) 11.3093 0.437896
\(668\) 44.7233 1.73040
\(669\) 27.4307 1.06053
\(670\) −79.7730 −3.08190
\(671\) 34.4044 1.32817
\(672\) 39.2132 1.51268
\(673\) −41.7173 −1.60808 −0.804042 0.594573i \(-0.797321\pi\)
−0.804042 + 0.594573i \(0.797321\pi\)
\(674\) −63.8676 −2.46009
\(675\) −16.6229 −0.639816
\(676\) 5.92908 0.228042
\(677\) 2.37370 0.0912287 0.0456144 0.998959i \(-0.485475\pi\)
0.0456144 + 0.998959i \(0.485475\pi\)
\(678\) 56.1673 2.15709
\(679\) 0.992708 0.0380966
\(680\) 212.652 8.15485
\(681\) −1.36819 −0.0524290
\(682\) −139.870 −5.35592
\(683\) 31.6335 1.21042 0.605212 0.796065i \(-0.293088\pi\)
0.605212 + 0.796065i \(0.293088\pi\)
\(684\) −32.0141 −1.22409
\(685\) 59.1251 2.25905
\(686\) −33.1141 −1.26430
\(687\) −2.68902 −0.102593
\(688\) −62.6649 −2.38908
\(689\) 9.64024 0.367264
\(690\) −39.7140 −1.51189
\(691\) −1.46610 −0.0557732 −0.0278866 0.999611i \(-0.508878\pi\)
−0.0278866 + 0.999611i \(0.508878\pi\)
\(692\) 128.825 4.89718
\(693\) −5.22420 −0.198451
\(694\) −30.6786 −1.16455
\(695\) −3.08055 −0.116852
\(696\) 46.7505 1.77207
\(697\) −9.28427 −0.351667
\(698\) −40.9782 −1.55105
\(699\) −16.1895 −0.612343
\(700\) −15.5388 −0.587313
\(701\) −11.5812 −0.437415 −0.218708 0.975790i \(-0.570184\pi\)
−0.218708 + 0.975790i \(0.570184\pi\)
\(702\) 15.9030 0.600221
\(703\) 18.3437 0.691847
\(704\) −270.442 −10.1927
\(705\) −11.2208 −0.422600
\(706\) −83.2315 −3.13246
\(707\) 12.7488 0.479467
\(708\) −41.8873 −1.57422
\(709\) 22.5602 0.847267 0.423634 0.905834i \(-0.360754\pi\)
0.423634 + 0.905834i \(0.360754\pi\)
\(710\) 61.2547 2.29885
\(711\) 5.99110 0.224684
\(712\) −17.7207 −0.664111
\(713\) 35.0194 1.31149
\(714\) 23.3808 0.875005
\(715\) 14.6301 0.547135
\(716\) −9.98502 −0.373158
\(717\) 11.0193 0.411524
\(718\) −96.2652 −3.59259
\(719\) 14.4724 0.539728 0.269864 0.962898i \(-0.413021\pi\)
0.269864 + 0.962898i \(0.413021\pi\)
\(720\) 61.4677 2.29076
\(721\) 0.208129 0.00775112
\(722\) −10.7609 −0.400480
\(723\) −13.4169 −0.498979
\(724\) −44.4531 −1.65209
\(725\) −9.09562 −0.337803
\(726\) −61.3976 −2.27868
\(727\) 18.2250 0.675927 0.337964 0.941159i \(-0.390262\pi\)
0.337964 + 0.941159i \(0.390262\pi\)
\(728\) 9.85133 0.365115
\(729\) 28.0635 1.03939
\(730\) 32.6391 1.20803
\(731\) −22.1476 −0.819157
\(732\) −53.7334 −1.98604
\(733\) 1.12995 0.0417358 0.0208679 0.999782i \(-0.493357\pi\)
0.0208679 + 0.999782i \(0.493357\pi\)
\(734\) 55.1096 2.03413
\(735\) 23.9213 0.882349
\(736\) 117.867 4.34462
\(737\) 52.1782 1.92201
\(738\) −4.33285 −0.159495
\(739\) −16.6853 −0.613780 −0.306890 0.951745i \(-0.599288\pi\)
−0.306890 + 0.951745i \(0.599288\pi\)
\(740\) −64.1659 −2.35879
\(741\) 6.53224 0.239968
\(742\) 24.1708 0.887339
\(743\) 41.3991 1.51879 0.759394 0.650632i \(-0.225496\pi\)
0.759394 + 0.650632i \(0.225496\pi\)
\(744\) 144.764 5.30731
\(745\) 16.6786 0.611055
\(746\) 2.08719 0.0764173
\(747\) 11.8875 0.434940
\(748\) −209.894 −7.67449
\(749\) 16.4681 0.601731
\(750\) −22.3186 −0.814961
\(751\) −42.0670 −1.53505 −0.767524 0.641020i \(-0.778511\pi\)
−0.767524 + 0.641020i \(0.778511\pi\)
\(752\) 56.1820 2.04875
\(753\) 1.39201 0.0507276
\(754\) 8.70171 0.316898
\(755\) −18.9353 −0.689126
\(756\) 29.8159 1.08439
\(757\) −44.7513 −1.62651 −0.813257 0.581904i \(-0.802308\pi\)
−0.813257 + 0.581904i \(0.802308\pi\)
\(758\) −66.1449 −2.40249
\(759\) 25.9763 0.942880
\(760\) 148.962 5.40343
\(761\) 13.8708 0.502817 0.251409 0.967881i \(-0.419106\pi\)
0.251409 + 0.967881i \(0.419106\pi\)
\(762\) −78.8933 −2.85800
\(763\) −15.8159 −0.572574
\(764\) −130.827 −4.73316
\(765\) 21.7244 0.785449
\(766\) 22.1132 0.798981
\(767\) −5.16660 −0.186555
\(768\) 174.364 6.29183
\(769\) 46.7759 1.68678 0.843391 0.537300i \(-0.180556\pi\)
0.843391 + 0.537300i \(0.180556\pi\)
\(770\) 36.6819 1.32192
\(771\) −6.85057 −0.246717
\(772\) 43.1275 1.55219
\(773\) −6.50928 −0.234123 −0.117061 0.993125i \(-0.537347\pi\)
−0.117061 + 0.993125i \(0.537347\pi\)
\(774\) −10.3360 −0.371520
\(775\) −28.1648 −1.01171
\(776\) 12.3348 0.442794
\(777\) −4.67517 −0.167721
\(778\) −84.2879 −3.02187
\(779\) −6.50360 −0.233016
\(780\) −22.8496 −0.818147
\(781\) −40.0658 −1.43367
\(782\) 70.2779 2.51313
\(783\) 17.4526 0.623707
\(784\) −119.773 −4.27759
\(785\) 25.5641 0.912420
\(786\) −48.3340 −1.72402
\(787\) −8.41698 −0.300033 −0.150016 0.988684i \(-0.547933\pi\)
−0.150016 + 0.988684i \(0.547933\pi\)
\(788\) −94.8246 −3.37799
\(789\) 20.9261 0.744990
\(790\) −42.0667 −1.49667
\(791\) 12.9889 0.461834
\(792\) −64.9128 −2.30658
\(793\) −6.62776 −0.235359
\(794\) 37.7731 1.34052
\(795\) −37.1517 −1.31764
\(796\) −70.5726 −2.50138
\(797\) −7.38839 −0.261710 −0.130855 0.991402i \(-0.541772\pi\)
−0.130855 + 0.991402i \(0.541772\pi\)
\(798\) 16.3782 0.579781
\(799\) 19.8563 0.702467
\(800\) −94.7958 −3.35154
\(801\) −1.81034 −0.0639651
\(802\) −62.3201 −2.20060
\(803\) −21.3487 −0.753380
\(804\) −81.4930 −2.87404
\(805\) −9.18405 −0.323695
\(806\) 26.9451 0.949100
\(807\) −30.0171 −1.05665
\(808\) 158.409 5.57281
\(809\) 29.7531 1.04606 0.523031 0.852314i \(-0.324801\pi\)
0.523031 + 0.852314i \(0.324801\pi\)
\(810\) −34.3772 −1.20789
\(811\) 52.6864 1.85007 0.925034 0.379884i \(-0.124036\pi\)
0.925034 + 0.379884i \(0.124036\pi\)
\(812\) 16.3145 0.572526
\(813\) −42.2322 −1.48115
\(814\) 56.1272 1.96726
\(815\) −6.15959 −0.215761
\(816\) 179.937 6.29906
\(817\) −15.5143 −0.542777
\(818\) 44.8013 1.56644
\(819\) 1.00641 0.0351667
\(820\) 22.7494 0.794444
\(821\) −29.4862 −1.02908 −0.514538 0.857467i \(-0.672037\pi\)
−0.514538 + 0.857467i \(0.672037\pi\)
\(822\) 80.7741 2.81732
\(823\) 26.9336 0.938845 0.469422 0.882974i \(-0.344462\pi\)
0.469422 + 0.882974i \(0.344462\pi\)
\(824\) 2.58609 0.0900906
\(825\) −20.8918 −0.727358
\(826\) −12.9541 −0.450732
\(827\) 15.1888 0.528166 0.264083 0.964500i \(-0.414931\pi\)
0.264083 + 0.964500i \(0.414931\pi\)
\(828\) 24.5250 0.852303
\(829\) 20.2181 0.702205 0.351103 0.936337i \(-0.385807\pi\)
0.351103 + 0.936337i \(0.385807\pi\)
\(830\) −83.4684 −2.89723
\(831\) −18.7516 −0.650486
\(832\) 52.0988 1.80620
\(833\) −42.3311 −1.46669
\(834\) −4.20851 −0.145729
\(835\) −21.2592 −0.735707
\(836\) −147.030 −5.08515
\(837\) 54.0426 1.86798
\(838\) −94.2466 −3.25569
\(839\) 20.2834 0.700260 0.350130 0.936701i \(-0.386137\pi\)
0.350130 + 0.936701i \(0.386137\pi\)
\(840\) −37.9652 −1.30992
\(841\) −19.4504 −0.670702
\(842\) 84.2403 2.90311
\(843\) −8.41502 −0.289829
\(844\) 115.727 3.98348
\(845\) −2.81839 −0.0969556
\(846\) 9.26670 0.318596
\(847\) −14.1985 −0.487865
\(848\) 186.017 6.38785
\(849\) 22.9669 0.788223
\(850\) −56.5219 −1.93868
\(851\) −14.0526 −0.481716
\(852\) 62.5755 2.14380
\(853\) −52.2858 −1.79023 −0.895117 0.445832i \(-0.852908\pi\)
−0.895117 + 0.445832i \(0.852908\pi\)
\(854\) −16.6177 −0.568645
\(855\) 15.2179 0.520441
\(856\) 204.623 6.99387
\(857\) −39.6212 −1.35344 −0.676718 0.736242i \(-0.736598\pi\)
−0.676718 + 0.736242i \(0.736598\pi\)
\(858\) 19.9870 0.682345
\(859\) 23.9547 0.817325 0.408663 0.912685i \(-0.365995\pi\)
0.408663 + 0.912685i \(0.365995\pi\)
\(860\) 54.2686 1.85054
\(861\) 1.65754 0.0564887
\(862\) −21.0103 −0.715613
\(863\) 23.8100 0.810503 0.405251 0.914205i \(-0.367184\pi\)
0.405251 + 0.914205i \(0.367184\pi\)
\(864\) 181.894 6.18816
\(865\) −61.2368 −2.08211
\(866\) 48.4011 1.64474
\(867\) 40.3494 1.37034
\(868\) 50.5182 1.71470
\(869\) 27.5152 0.933388
\(870\) −33.5348 −1.13694
\(871\) −10.0518 −0.340592
\(872\) −196.519 −6.65498
\(873\) 1.26012 0.0426485
\(874\) 49.2294 1.66521
\(875\) −5.16129 −0.174483
\(876\) 33.3428 1.12655
\(877\) −16.7727 −0.566374 −0.283187 0.959065i \(-0.591392\pi\)
−0.283187 + 0.959065i \(0.591392\pi\)
\(878\) 4.93366 0.166503
\(879\) −18.0562 −0.609022
\(880\) 282.301 9.51636
\(881\) 6.73851 0.227026 0.113513 0.993536i \(-0.463790\pi\)
0.113513 + 0.993536i \(0.463790\pi\)
\(882\) −19.7554 −0.665199
\(883\) −1.05387 −0.0354655 −0.0177327 0.999843i \(-0.505645\pi\)
−0.0177327 + 0.999843i \(0.505645\pi\)
\(884\) 40.4347 1.35997
\(885\) 19.9111 0.669305
\(886\) −96.9126 −3.25584
\(887\) −28.5380 −0.958212 −0.479106 0.877757i \(-0.659039\pi\)
−0.479106 + 0.877757i \(0.659039\pi\)
\(888\) −58.0909 −1.94940
\(889\) −18.2445 −0.611899
\(890\) 12.7113 0.426085
\(891\) 22.4856 0.753296
\(892\) 118.942 3.98247
\(893\) 13.9093 0.465457
\(894\) 22.7855 0.762061
\(895\) 4.74638 0.158654
\(896\) 73.2713 2.44782
\(897\) −5.00415 −0.167084
\(898\) −33.4578 −1.11650
\(899\) 29.5707 0.986237
\(900\) −19.7246 −0.657486
\(901\) 65.7437 2.19024
\(902\) −19.8994 −0.662577
\(903\) 3.95404 0.131582
\(904\) 161.393 5.36785
\(905\) 21.1308 0.702411
\(906\) −25.8685 −0.859425
\(907\) 23.2176 0.770928 0.385464 0.922723i \(-0.374041\pi\)
0.385464 + 0.922723i \(0.374041\pi\)
\(908\) −5.93257 −0.196879
\(909\) 16.1830 0.536755
\(910\) −7.06651 −0.234252
\(911\) 32.3101 1.07048 0.535240 0.844700i \(-0.320221\pi\)
0.535240 + 0.844700i \(0.320221\pi\)
\(912\) 126.045 4.17378
\(913\) 54.5953 1.80684
\(914\) 84.1231 2.78254
\(915\) 25.5422 0.844399
\(916\) −11.6598 −0.385251
\(917\) −11.1775 −0.369112
\(918\) 108.454 3.57952
\(919\) −35.9112 −1.18460 −0.592300 0.805717i \(-0.701780\pi\)
−0.592300 + 0.805717i \(0.701780\pi\)
\(920\) −114.116 −3.76228
\(921\) 17.3525 0.571785
\(922\) −10.3048 −0.339372
\(923\) 7.71839 0.254054
\(924\) 37.4728 1.23276
\(925\) 11.3020 0.371607
\(926\) 55.1992 1.81396
\(927\) 0.264193 0.00867723
\(928\) 99.5276 3.26715
\(929\) −58.9536 −1.93420 −0.967102 0.254389i \(-0.918126\pi\)
−0.967102 + 0.254389i \(0.918126\pi\)
\(930\) −103.841 −3.40509
\(931\) −29.6528 −0.971831
\(932\) −70.1990 −2.29944
\(933\) 12.9497 0.423955
\(934\) −58.7893 −1.92365
\(935\) 99.7733 3.26293
\(936\) 12.5050 0.408739
\(937\) 18.6653 0.609770 0.304885 0.952389i \(-0.401382\pi\)
0.304885 + 0.952389i \(0.401382\pi\)
\(938\) −25.2027 −0.822896
\(939\) −40.5309 −1.32268
\(940\) −48.6544 −1.58693
\(941\) 12.6138 0.411198 0.205599 0.978636i \(-0.434086\pi\)
0.205599 + 0.978636i \(0.434086\pi\)
\(942\) 34.9245 1.13790
\(943\) 4.98221 0.162243
\(944\) −99.6940 −3.24476
\(945\) −14.1730 −0.461047
\(946\) −47.4698 −1.54338
\(947\) 15.0056 0.487615 0.243808 0.969824i \(-0.421603\pi\)
0.243808 + 0.969824i \(0.421603\pi\)
\(948\) −42.9737 −1.39572
\(949\) 4.11268 0.133503
\(950\) −39.5934 −1.28458
\(951\) 5.95461 0.193091
\(952\) 67.1833 2.17742
\(953\) −52.0022 −1.68452 −0.842258 0.539074i \(-0.818774\pi\)
−0.842258 + 0.539074i \(0.818774\pi\)
\(954\) 30.6818 0.993359
\(955\) 62.1887 2.01238
\(956\) 47.7807 1.54534
\(957\) 21.9346 0.709045
\(958\) −121.567 −3.92766
\(959\) 18.6794 0.603189
\(960\) −200.779 −6.48012
\(961\) 60.5664 1.95375
\(962\) −10.8125 −0.348610
\(963\) 20.9041 0.673627
\(964\) −58.1767 −1.87374
\(965\) −20.5007 −0.659940
\(966\) −12.5468 −0.403688
\(967\) −45.7973 −1.47274 −0.736371 0.676578i \(-0.763462\pi\)
−0.736371 + 0.676578i \(0.763462\pi\)
\(968\) −176.422 −5.67042
\(969\) 44.5480 1.43109
\(970\) −8.84794 −0.284090
\(971\) 46.7361 1.49983 0.749916 0.661533i \(-0.230094\pi\)
0.749916 + 0.661533i \(0.230094\pi\)
\(972\) 65.3378 2.09571
\(973\) −0.973238 −0.0312006
\(974\) 19.9001 0.637642
\(975\) 4.02466 0.128892
\(976\) −127.888 −4.09361
\(977\) 31.4383 1.00580 0.502901 0.864344i \(-0.332266\pi\)
0.502901 + 0.864344i \(0.332266\pi\)
\(978\) −8.41495 −0.269081
\(979\) −8.31428 −0.265726
\(980\) 103.725 3.31336
\(981\) −20.0763 −0.640986
\(982\) −26.8047 −0.855372
\(983\) 14.8186 0.472641 0.236320 0.971675i \(-0.424058\pi\)
0.236320 + 0.971675i \(0.424058\pi\)
\(984\) 20.5956 0.656563
\(985\) 45.0749 1.43620
\(986\) 59.3432 1.88987
\(987\) −3.54499 −0.112838
\(988\) 28.3244 0.901118
\(989\) 11.8850 0.377922
\(990\) 46.5629 1.47987
\(991\) −21.8530 −0.694184 −0.347092 0.937831i \(-0.612831\pi\)
−0.347092 + 0.937831i \(0.612831\pi\)
\(992\) 308.190 9.78504
\(993\) 42.1099 1.33632
\(994\) 19.3522 0.613815
\(995\) 33.5467 1.06350
\(996\) −85.2681 −2.70182
\(997\) 48.0583 1.52202 0.761011 0.648739i \(-0.224703\pi\)
0.761011 + 0.648739i \(0.224703\pi\)
\(998\) −116.980 −3.70295
\(999\) −21.6862 −0.686121
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 8021.2.a.d.1.1 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8021.2.a.d.1.1 174 1.1 even 1 trivial