Properties

Label 8031.2.a.c.1.2
Level $8031$
Weight $2$
Character 8031.1
Self dual yes
Analytic conductor $64.128$
Analytic rank $0$
Dimension $121$
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] = [8031,2,Mod(1,8031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8031, 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("8031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8031.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: \(64.1278578633\)
Analytic rank: \(0\)
Dimension: \(121\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 8031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.74757 q^{2} -1.00000 q^{3} +5.54913 q^{4} +2.21252 q^{5} +2.74757 q^{6} -1.55769 q^{7} -9.75147 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.74757 q^{2} -1.00000 q^{3} +5.54913 q^{4} +2.21252 q^{5} +2.74757 q^{6} -1.55769 q^{7} -9.75147 q^{8} +1.00000 q^{9} -6.07904 q^{10} +6.00610 q^{11} -5.54913 q^{12} +6.05867 q^{13} +4.27986 q^{14} -2.21252 q^{15} +15.6946 q^{16} +4.46030 q^{17} -2.74757 q^{18} -4.53083 q^{19} +12.2775 q^{20} +1.55769 q^{21} -16.5022 q^{22} -3.96954 q^{23} +9.75147 q^{24} -0.104767 q^{25} -16.6466 q^{26} -1.00000 q^{27} -8.64382 q^{28} -6.62434 q^{29} +6.07904 q^{30} +1.30598 q^{31} -23.6190 q^{32} -6.00610 q^{33} -12.2550 q^{34} -3.44642 q^{35} +5.54913 q^{36} +8.30005 q^{37} +12.4488 q^{38} -6.05867 q^{39} -21.5753 q^{40} +8.28247 q^{41} -4.27986 q^{42} -7.55710 q^{43} +33.3286 q^{44} +2.21252 q^{45} +10.9066 q^{46} -6.00883 q^{47} -15.6946 q^{48} -4.57360 q^{49} +0.287855 q^{50} -4.46030 q^{51} +33.6203 q^{52} -5.93758 q^{53} +2.74757 q^{54} +13.2886 q^{55} +15.1898 q^{56} +4.53083 q^{57} +18.2008 q^{58} +10.4522 q^{59} -12.2775 q^{60} +12.7662 q^{61} -3.58826 q^{62} -1.55769 q^{63} +33.5055 q^{64} +13.4049 q^{65} +16.5022 q^{66} -1.73062 q^{67} +24.7508 q^{68} +3.96954 q^{69} +9.46926 q^{70} +8.40701 q^{71} -9.75147 q^{72} -0.502247 q^{73} -22.8050 q^{74} +0.104767 q^{75} -25.1422 q^{76} -9.35564 q^{77} +16.6466 q^{78} -16.1915 q^{79} +34.7245 q^{80} +1.00000 q^{81} -22.7566 q^{82} +3.50690 q^{83} +8.64382 q^{84} +9.86848 q^{85} +20.7636 q^{86} +6.62434 q^{87} -58.5683 q^{88} +3.54616 q^{89} -6.07904 q^{90} -9.43753 q^{91} -22.0275 q^{92} -1.30598 q^{93} +16.5097 q^{94} -10.0245 q^{95} +23.6190 q^{96} +4.69477 q^{97} +12.5663 q^{98} +6.00610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74757 −1.94282 −0.971412 0.237400i \(-0.923705\pi\)
−0.971412 + 0.237400i \(0.923705\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.54913 2.77456
\(5\) 2.21252 0.989468 0.494734 0.869045i \(-0.335266\pi\)
0.494734 + 0.869045i \(0.335266\pi\)
\(6\) 2.74757 1.12169
\(7\) −1.55769 −0.588752 −0.294376 0.955690i \(-0.595112\pi\)
−0.294376 + 0.955690i \(0.595112\pi\)
\(8\) −9.75147 −3.44767
\(9\) 1.00000 0.333333
\(10\) −6.07904 −1.92236
\(11\) 6.00610 1.81091 0.905453 0.424446i \(-0.139531\pi\)
0.905453 + 0.424446i \(0.139531\pi\)
\(12\) −5.54913 −1.60190
\(13\) 6.05867 1.68037 0.840186 0.542299i \(-0.182446\pi\)
0.840186 + 0.542299i \(0.182446\pi\)
\(14\) 4.27986 1.14384
\(15\) −2.21252 −0.571270
\(16\) 15.6946 3.92364
\(17\) 4.46030 1.08178 0.540890 0.841093i \(-0.318087\pi\)
0.540890 + 0.841093i \(0.318087\pi\)
\(18\) −2.74757 −0.647608
\(19\) −4.53083 −1.03944 −0.519722 0.854336i \(-0.673964\pi\)
−0.519722 + 0.854336i \(0.673964\pi\)
\(20\) 12.2775 2.74534
\(21\) 1.55769 0.339916
\(22\) −16.5022 −3.51827
\(23\) −3.96954 −0.827706 −0.413853 0.910344i \(-0.635817\pi\)
−0.413853 + 0.910344i \(0.635817\pi\)
\(24\) 9.75147 1.99051
\(25\) −0.104767 −0.0209535
\(26\) −16.6466 −3.26467
\(27\) −1.00000 −0.192450
\(28\) −8.64382 −1.63353
\(29\) −6.62434 −1.23011 −0.615055 0.788484i \(-0.710866\pi\)
−0.615055 + 0.788484i \(0.710866\pi\)
\(30\) 6.07904 1.10988
\(31\) 1.30598 0.234560 0.117280 0.993099i \(-0.462582\pi\)
0.117280 + 0.993099i \(0.462582\pi\)
\(32\) −23.6190 −4.17528
\(33\) −6.00610 −1.04553
\(34\) −12.2550 −2.10171
\(35\) −3.44642 −0.582551
\(36\) 5.54913 0.924855
\(37\) 8.30005 1.36452 0.682260 0.731110i \(-0.260997\pi\)
0.682260 + 0.731110i \(0.260997\pi\)
\(38\) 12.4488 2.01946
\(39\) −6.05867 −0.970163
\(40\) −21.5753 −3.41135
\(41\) 8.28247 1.29350 0.646752 0.762700i \(-0.276127\pi\)
0.646752 + 0.762700i \(0.276127\pi\)
\(42\) −4.27986 −0.660397
\(43\) −7.55710 −1.15245 −0.576223 0.817292i \(-0.695474\pi\)
−0.576223 + 0.817292i \(0.695474\pi\)
\(44\) 33.3286 5.02448
\(45\) 2.21252 0.329823
\(46\) 10.9066 1.60809
\(47\) −6.00883 −0.876477 −0.438239 0.898859i \(-0.644398\pi\)
−0.438239 + 0.898859i \(0.644398\pi\)
\(48\) −15.6946 −2.26532
\(49\) −4.57360 −0.653371
\(50\) 0.287855 0.0407089
\(51\) −4.46030 −0.624566
\(52\) 33.6203 4.66230
\(53\) −5.93758 −0.815589 −0.407795 0.913074i \(-0.633702\pi\)
−0.407795 + 0.913074i \(0.633702\pi\)
\(54\) 2.74757 0.373897
\(55\) 13.2886 1.79183
\(56\) 15.1898 2.02982
\(57\) 4.53083 0.600123
\(58\) 18.2008 2.38989
\(59\) 10.4522 1.36076 0.680378 0.732861i \(-0.261816\pi\)
0.680378 + 0.732861i \(0.261816\pi\)
\(60\) −12.2775 −1.58502
\(61\) 12.7662 1.63454 0.817271 0.576254i \(-0.195486\pi\)
0.817271 + 0.576254i \(0.195486\pi\)
\(62\) −3.58826 −0.455709
\(63\) −1.55769 −0.196251
\(64\) 33.5055 4.18819
\(65\) 13.4049 1.66267
\(66\) 16.5022 2.03128
\(67\) −1.73062 −0.211429 −0.105715 0.994397i \(-0.533713\pi\)
−0.105715 + 0.994397i \(0.533713\pi\)
\(68\) 24.7508 3.00147
\(69\) 3.96954 0.477876
\(70\) 9.46926 1.13179
\(71\) 8.40701 0.997729 0.498864 0.866680i \(-0.333751\pi\)
0.498864 + 0.866680i \(0.333751\pi\)
\(72\) −9.75147 −1.14922
\(73\) −0.502247 −0.0587836 −0.0293918 0.999568i \(-0.509357\pi\)
−0.0293918 + 0.999568i \(0.509357\pi\)
\(74\) −22.8050 −2.65102
\(75\) 0.104767 0.0120975
\(76\) −25.1422 −2.88400
\(77\) −9.35564 −1.06617
\(78\) 16.6466 1.88486
\(79\) −16.1915 −1.82168 −0.910840 0.412759i \(-0.864565\pi\)
−0.910840 + 0.412759i \(0.864565\pi\)
\(80\) 34.7245 3.88232
\(81\) 1.00000 0.111111
\(82\) −22.7566 −2.51305
\(83\) 3.50690 0.384932 0.192466 0.981304i \(-0.438352\pi\)
0.192466 + 0.981304i \(0.438352\pi\)
\(84\) 8.64382 0.943119
\(85\) 9.86848 1.07039
\(86\) 20.7636 2.23900
\(87\) 6.62434 0.710204
\(88\) −58.5683 −6.24340
\(89\) 3.54616 0.375892 0.187946 0.982179i \(-0.439817\pi\)
0.187946 + 0.982179i \(0.439817\pi\)
\(90\) −6.07904 −0.640787
\(91\) −9.43753 −0.989322
\(92\) −22.0275 −2.29652
\(93\) −1.30598 −0.135423
\(94\) 16.5097 1.70284
\(95\) −10.0245 −1.02850
\(96\) 23.6190 2.41060
\(97\) 4.69477 0.476682 0.238341 0.971182i \(-0.423396\pi\)
0.238341 + 0.971182i \(0.423396\pi\)
\(98\) 12.5663 1.26939
\(99\) 6.00610 0.603636
\(100\) −0.581367 −0.0581367
\(101\) 3.25149 0.323535 0.161767 0.986829i \(-0.448281\pi\)
0.161767 + 0.986829i \(0.448281\pi\)
\(102\) 12.2550 1.21342
\(103\) −15.1892 −1.49664 −0.748319 0.663339i \(-0.769139\pi\)
−0.748319 + 0.663339i \(0.769139\pi\)
\(104\) −59.0809 −5.79336
\(105\) 3.44642 0.336336
\(106\) 16.3139 1.58455
\(107\) 19.3046 1.86624 0.933121 0.359562i \(-0.117074\pi\)
0.933121 + 0.359562i \(0.117074\pi\)
\(108\) −5.54913 −0.533965
\(109\) −2.16302 −0.207179 −0.103590 0.994620i \(-0.533033\pi\)
−0.103590 + 0.994620i \(0.533033\pi\)
\(110\) −36.5113 −3.48122
\(111\) −8.30005 −0.787806
\(112\) −24.4473 −2.31005
\(113\) 17.6074 1.65636 0.828181 0.560461i \(-0.189376\pi\)
0.828181 + 0.560461i \(0.189376\pi\)
\(114\) −12.4488 −1.16593
\(115\) −8.78267 −0.818988
\(116\) −36.7593 −3.41302
\(117\) 6.05867 0.560124
\(118\) −28.7180 −2.64371
\(119\) −6.94776 −0.636900
\(120\) 21.5753 1.96955
\(121\) 25.0732 2.27938
\(122\) −35.0759 −3.17563
\(123\) −8.28247 −0.746805
\(124\) 7.24703 0.650803
\(125\) −11.2944 −1.01020
\(126\) 4.27986 0.381280
\(127\) −15.7505 −1.39763 −0.698816 0.715301i \(-0.746289\pi\)
−0.698816 + 0.715301i \(0.746289\pi\)
\(128\) −44.8208 −3.96164
\(129\) 7.55710 0.665365
\(130\) −36.8309 −3.23028
\(131\) 11.3099 0.988150 0.494075 0.869419i \(-0.335507\pi\)
0.494075 + 0.869419i \(0.335507\pi\)
\(132\) −33.3286 −2.90088
\(133\) 7.05763 0.611974
\(134\) 4.75500 0.410770
\(135\) −2.21252 −0.190423
\(136\) −43.4944 −3.72962
\(137\) 4.38239 0.374413 0.187207 0.982321i \(-0.440057\pi\)
0.187207 + 0.982321i \(0.440057\pi\)
\(138\) −10.9066 −0.928429
\(139\) 23.4390 1.98807 0.994035 0.109063i \(-0.0347850\pi\)
0.994035 + 0.109063i \(0.0347850\pi\)
\(140\) −19.1246 −1.61632
\(141\) 6.00883 0.506034
\(142\) −23.0988 −1.93841
\(143\) 36.3889 3.04300
\(144\) 15.6946 1.30788
\(145\) −14.6565 −1.21715
\(146\) 1.37996 0.114206
\(147\) 4.57360 0.377224
\(148\) 46.0581 3.78595
\(149\) 19.2293 1.57533 0.787663 0.616106i \(-0.211291\pi\)
0.787663 + 0.616106i \(0.211291\pi\)
\(150\) −0.287855 −0.0235033
\(151\) −4.55171 −0.370413 −0.185206 0.982700i \(-0.559295\pi\)
−0.185206 + 0.982700i \(0.559295\pi\)
\(152\) 44.1823 3.58365
\(153\) 4.46030 0.360594
\(154\) 25.7053 2.07139
\(155\) 2.88950 0.232090
\(156\) −33.6203 −2.69178
\(157\) −2.77945 −0.221824 −0.110912 0.993830i \(-0.535377\pi\)
−0.110912 + 0.993830i \(0.535377\pi\)
\(158\) 44.4871 3.53920
\(159\) 5.93758 0.470881
\(160\) −52.2573 −4.13131
\(161\) 6.18331 0.487313
\(162\) −2.74757 −0.215869
\(163\) 1.21163 0.0949018 0.0474509 0.998874i \(-0.484890\pi\)
0.0474509 + 0.998874i \(0.484890\pi\)
\(164\) 45.9605 3.58891
\(165\) −13.2886 −1.03452
\(166\) −9.63543 −0.747855
\(167\) 4.46349 0.345396 0.172698 0.984975i \(-0.444752\pi\)
0.172698 + 0.984975i \(0.444752\pi\)
\(168\) −15.1898 −1.17192
\(169\) 23.7074 1.82365
\(170\) −27.1143 −2.07957
\(171\) −4.53083 −0.346481
\(172\) −41.9353 −3.19754
\(173\) −18.7613 −1.42640 −0.713198 0.700963i \(-0.752754\pi\)
−0.713198 + 0.700963i \(0.752754\pi\)
\(174\) −18.2008 −1.37980
\(175\) 0.163195 0.0123364
\(176\) 94.2631 7.10535
\(177\) −10.4522 −0.785633
\(178\) −9.74331 −0.730292
\(179\) 0.436788 0.0326471 0.0163235 0.999867i \(-0.494804\pi\)
0.0163235 + 0.999867i \(0.494804\pi\)
\(180\) 12.2775 0.915114
\(181\) 4.76246 0.353991 0.176995 0.984212i \(-0.443362\pi\)
0.176995 + 0.984212i \(0.443362\pi\)
\(182\) 25.9302 1.92208
\(183\) −12.7662 −0.943703
\(184\) 38.7088 2.85365
\(185\) 18.3640 1.35015
\(186\) 3.58826 0.263104
\(187\) 26.7890 1.95900
\(188\) −33.3437 −2.43184
\(189\) 1.55769 0.113305
\(190\) 27.5431 1.99819
\(191\) 0.772465 0.0558936 0.0279468 0.999609i \(-0.491103\pi\)
0.0279468 + 0.999609i \(0.491103\pi\)
\(192\) −33.5055 −2.41805
\(193\) 10.0741 0.725152 0.362576 0.931954i \(-0.381897\pi\)
0.362576 + 0.931954i \(0.381897\pi\)
\(194\) −12.8992 −0.926109
\(195\) −13.4049 −0.959945
\(196\) −25.3795 −1.81282
\(197\) −16.5714 −1.18066 −0.590331 0.807161i \(-0.701003\pi\)
−0.590331 + 0.807161i \(0.701003\pi\)
\(198\) −16.5022 −1.17276
\(199\) −11.8970 −0.843355 −0.421677 0.906746i \(-0.638559\pi\)
−0.421677 + 0.906746i \(0.638559\pi\)
\(200\) 1.02164 0.0722405
\(201\) 1.73062 0.122069
\(202\) −8.93368 −0.628571
\(203\) 10.3187 0.724229
\(204\) −24.7508 −1.73290
\(205\) 18.3251 1.27988
\(206\) 41.7334 2.90770
\(207\) −3.96954 −0.275902
\(208\) 95.0882 6.59318
\(209\) −27.2126 −1.88234
\(210\) −9.46926 −0.653441
\(211\) −5.38451 −0.370685 −0.185343 0.982674i \(-0.559339\pi\)
−0.185343 + 0.982674i \(0.559339\pi\)
\(212\) −32.9484 −2.26290
\(213\) −8.40701 −0.576039
\(214\) −53.0406 −3.62578
\(215\) −16.7202 −1.14031
\(216\) 9.75147 0.663504
\(217\) −2.03431 −0.138098
\(218\) 5.94303 0.402513
\(219\) 0.502247 0.0339387
\(220\) 73.7401 4.97156
\(221\) 27.0234 1.81779
\(222\) 22.8050 1.53057
\(223\) −18.7497 −1.25557 −0.627786 0.778386i \(-0.716039\pi\)
−0.627786 + 0.778386i \(0.716039\pi\)
\(224\) 36.7910 2.45820
\(225\) −0.104767 −0.00698449
\(226\) −48.3774 −3.21802
\(227\) −0.0521256 −0.00345970 −0.00172985 0.999999i \(-0.500551\pi\)
−0.00172985 + 0.999999i \(0.500551\pi\)
\(228\) 25.1422 1.66508
\(229\) 4.20753 0.278041 0.139021 0.990289i \(-0.455605\pi\)
0.139021 + 0.990289i \(0.455605\pi\)
\(230\) 24.1310 1.59115
\(231\) 9.35564 0.615556
\(232\) 64.5971 4.24101
\(233\) 28.7006 1.88024 0.940119 0.340846i \(-0.110713\pi\)
0.940119 + 0.340846i \(0.110713\pi\)
\(234\) −16.6466 −1.08822
\(235\) −13.2946 −0.867246
\(236\) 58.0004 3.77551
\(237\) 16.1915 1.05175
\(238\) 19.0894 1.23738
\(239\) 25.1940 1.62967 0.814833 0.579696i \(-0.196829\pi\)
0.814833 + 0.579696i \(0.196829\pi\)
\(240\) −34.7245 −2.24146
\(241\) 18.6150 1.19910 0.599549 0.800338i \(-0.295347\pi\)
0.599549 + 0.800338i \(0.295347\pi\)
\(242\) −68.8903 −4.42844
\(243\) −1.00000 −0.0641500
\(244\) 70.8411 4.53514
\(245\) −10.1192 −0.646490
\(246\) 22.7566 1.45091
\(247\) −27.4508 −1.74665
\(248\) −12.7352 −0.808686
\(249\) −3.50690 −0.222240
\(250\) 31.0321 1.96264
\(251\) 23.3464 1.47361 0.736807 0.676103i \(-0.236333\pi\)
0.736807 + 0.676103i \(0.236333\pi\)
\(252\) −8.64382 −0.544510
\(253\) −23.8414 −1.49890
\(254\) 43.2756 2.71535
\(255\) −9.86848 −0.617988
\(256\) 56.1371 3.50857
\(257\) −13.6295 −0.850183 −0.425092 0.905150i \(-0.639758\pi\)
−0.425092 + 0.905150i \(0.639758\pi\)
\(258\) −20.7636 −1.29269
\(259\) −12.9289 −0.803363
\(260\) 74.3855 4.61319
\(261\) −6.62434 −0.410036
\(262\) −31.0747 −1.91980
\(263\) 23.1750 1.42903 0.714515 0.699620i \(-0.246647\pi\)
0.714515 + 0.699620i \(0.246647\pi\)
\(264\) 58.5683 3.60463
\(265\) −13.1370 −0.806999
\(266\) −19.3913 −1.18896
\(267\) −3.54616 −0.217021
\(268\) −9.60345 −0.586624
\(269\) −22.1242 −1.34893 −0.674467 0.738305i \(-0.735627\pi\)
−0.674467 + 0.738305i \(0.735627\pi\)
\(270\) 6.07904 0.369959
\(271\) −28.9996 −1.76160 −0.880799 0.473490i \(-0.842994\pi\)
−0.880799 + 0.473490i \(0.842994\pi\)
\(272\) 70.0024 4.24452
\(273\) 9.43753 0.571185
\(274\) −12.0409 −0.727419
\(275\) −0.629243 −0.0379448
\(276\) 22.0275 1.32590
\(277\) −31.0328 −1.86458 −0.932290 0.361711i \(-0.882193\pi\)
−0.932290 + 0.361711i \(0.882193\pi\)
\(278\) −64.4002 −3.86247
\(279\) 1.30598 0.0781868
\(280\) 33.6076 2.00844
\(281\) 26.9054 1.60504 0.802519 0.596626i \(-0.203492\pi\)
0.802519 + 0.596626i \(0.203492\pi\)
\(282\) −16.5097 −0.983136
\(283\) 6.18102 0.367424 0.183712 0.982980i \(-0.441189\pi\)
0.183712 + 0.982980i \(0.441189\pi\)
\(284\) 46.6516 2.76826
\(285\) 10.0245 0.593802
\(286\) −99.9811 −5.91201
\(287\) −12.9015 −0.761553
\(288\) −23.6190 −1.39176
\(289\) 2.89423 0.170249
\(290\) 40.2696 2.36471
\(291\) −4.69477 −0.275212
\(292\) −2.78703 −0.163099
\(293\) 6.45950 0.377368 0.188684 0.982038i \(-0.439578\pi\)
0.188684 + 0.982038i \(0.439578\pi\)
\(294\) −12.5663 −0.732880
\(295\) 23.1256 1.34642
\(296\) −80.9377 −4.70441
\(297\) −6.00610 −0.348509
\(298\) −52.8338 −3.06058
\(299\) −24.0501 −1.39085
\(300\) 0.581367 0.0335653
\(301\) 11.7716 0.678505
\(302\) 12.5061 0.719647
\(303\) −3.25149 −0.186793
\(304\) −71.1094 −4.07841
\(305\) 28.2454 1.61733
\(306\) −12.2550 −0.700570
\(307\) 31.6904 1.80867 0.904333 0.426829i \(-0.140369\pi\)
0.904333 + 0.426829i \(0.140369\pi\)
\(308\) −51.9157 −2.95817
\(309\) 15.1892 0.864084
\(310\) −7.93909 −0.450910
\(311\) 1.83262 0.103918 0.0519592 0.998649i \(-0.483453\pi\)
0.0519592 + 0.998649i \(0.483453\pi\)
\(312\) 59.0809 3.34480
\(313\) −7.97844 −0.450968 −0.225484 0.974247i \(-0.572396\pi\)
−0.225484 + 0.974247i \(0.572396\pi\)
\(314\) 7.63672 0.430965
\(315\) −3.44642 −0.194184
\(316\) −89.8484 −5.05437
\(317\) −18.8827 −1.06056 −0.530279 0.847823i \(-0.677913\pi\)
−0.530279 + 0.847823i \(0.677913\pi\)
\(318\) −16.3139 −0.914838
\(319\) −39.7864 −2.22761
\(320\) 74.1316 4.14408
\(321\) −19.3046 −1.07748
\(322\) −16.9891 −0.946763
\(323\) −20.2088 −1.12445
\(324\) 5.54913 0.308285
\(325\) −0.634750 −0.0352096
\(326\) −3.32902 −0.184378
\(327\) 2.16302 0.119615
\(328\) −80.7662 −4.45957
\(329\) 9.35989 0.516027
\(330\) 36.5113 2.00988
\(331\) −3.82207 −0.210080 −0.105040 0.994468i \(-0.533497\pi\)
−0.105040 + 0.994468i \(0.533497\pi\)
\(332\) 19.4602 1.06802
\(333\) 8.30005 0.454840
\(334\) −12.2638 −0.671043
\(335\) −3.82903 −0.209202
\(336\) 24.4473 1.33371
\(337\) 11.2743 0.614150 0.307075 0.951685i \(-0.400650\pi\)
0.307075 + 0.951685i \(0.400650\pi\)
\(338\) −65.1378 −3.54303
\(339\) −17.6074 −0.956301
\(340\) 54.7615 2.96986
\(341\) 7.84383 0.424767
\(342\) 12.4488 0.673152
\(343\) 18.0281 0.973425
\(344\) 73.6928 3.97325
\(345\) 8.78267 0.472843
\(346\) 51.5479 2.77123
\(347\) 20.0963 1.07883 0.539413 0.842041i \(-0.318646\pi\)
0.539413 + 0.842041i \(0.318646\pi\)
\(348\) 36.7593 1.97051
\(349\) 4.54278 0.243169 0.121585 0.992581i \(-0.461202\pi\)
0.121585 + 0.992581i \(0.461202\pi\)
\(350\) −0.448389 −0.0239674
\(351\) −6.05867 −0.323388
\(352\) −141.858 −7.56104
\(353\) 15.6005 0.830329 0.415164 0.909746i \(-0.363724\pi\)
0.415164 + 0.909746i \(0.363724\pi\)
\(354\) 28.7180 1.52635
\(355\) 18.6007 0.987220
\(356\) 19.6781 1.04294
\(357\) 6.94776 0.367714
\(358\) −1.20011 −0.0634276
\(359\) 0.108663 0.00573500 0.00286750 0.999996i \(-0.499087\pi\)
0.00286750 + 0.999996i \(0.499087\pi\)
\(360\) −21.5753 −1.13712
\(361\) 1.52842 0.0804432
\(362\) −13.0852 −0.687741
\(363\) −25.0732 −1.31600
\(364\) −52.3700 −2.74494
\(365\) −1.11123 −0.0581644
\(366\) 35.0759 1.83345
\(367\) −2.93528 −0.153221 −0.0766103 0.997061i \(-0.524410\pi\)
−0.0766103 + 0.997061i \(0.524410\pi\)
\(368\) −62.3002 −3.24762
\(369\) 8.28247 0.431168
\(370\) −50.4564 −2.62310
\(371\) 9.24891 0.480179
\(372\) −7.24703 −0.375741
\(373\) −11.3967 −0.590099 −0.295050 0.955482i \(-0.595336\pi\)
−0.295050 + 0.955482i \(0.595336\pi\)
\(374\) −73.6045 −3.80600
\(375\) 11.2944 0.583240
\(376\) 58.5949 3.02180
\(377\) −40.1347 −2.06704
\(378\) −4.27986 −0.220132
\(379\) 2.70586 0.138991 0.0694953 0.997582i \(-0.477861\pi\)
0.0694953 + 0.997582i \(0.477861\pi\)
\(380\) −55.6275 −2.85363
\(381\) 15.7505 0.806923
\(382\) −2.12240 −0.108591
\(383\) −10.6807 −0.545758 −0.272879 0.962048i \(-0.587976\pi\)
−0.272879 + 0.962048i \(0.587976\pi\)
\(384\) 44.8208 2.28725
\(385\) −20.6995 −1.05495
\(386\) −27.6794 −1.40884
\(387\) −7.55710 −0.384149
\(388\) 26.0519 1.32258
\(389\) −12.6876 −0.643288 −0.321644 0.946861i \(-0.604235\pi\)
−0.321644 + 0.946861i \(0.604235\pi\)
\(390\) 36.8309 1.86500
\(391\) −17.7053 −0.895396
\(392\) 44.5993 2.25261
\(393\) −11.3099 −0.570508
\(394\) 45.5310 2.29382
\(395\) −35.8239 −1.80249
\(396\) 33.3286 1.67483
\(397\) 25.4445 1.27702 0.638512 0.769612i \(-0.279550\pi\)
0.638512 + 0.769612i \(0.279550\pi\)
\(398\) 32.6878 1.63849
\(399\) −7.05763 −0.353323
\(400\) −1.64428 −0.0822139
\(401\) −18.5924 −0.928458 −0.464229 0.885715i \(-0.653669\pi\)
−0.464229 + 0.885715i \(0.653669\pi\)
\(402\) −4.75500 −0.237158
\(403\) 7.91248 0.394149
\(404\) 18.0429 0.897668
\(405\) 2.21252 0.109941
\(406\) −28.3513 −1.40705
\(407\) 49.8509 2.47102
\(408\) 43.4944 2.15330
\(409\) −17.5494 −0.867763 −0.433882 0.900970i \(-0.642856\pi\)
−0.433882 + 0.900970i \(0.642856\pi\)
\(410\) −50.3495 −2.48658
\(411\) −4.38239 −0.216168
\(412\) −84.2869 −4.15252
\(413\) −16.2812 −0.801148
\(414\) 10.9066 0.536029
\(415\) 7.75907 0.380878
\(416\) −143.099 −7.01602
\(417\) −23.4390 −1.14781
\(418\) 74.7685 3.65705
\(419\) 1.68013 0.0820798 0.0410399 0.999158i \(-0.486933\pi\)
0.0410399 + 0.999158i \(0.486933\pi\)
\(420\) 19.1246 0.933185
\(421\) 1.72155 0.0839033 0.0419517 0.999120i \(-0.486642\pi\)
0.0419517 + 0.999120i \(0.486642\pi\)
\(422\) 14.7943 0.720176
\(423\) −6.00883 −0.292159
\(424\) 57.9001 2.81188
\(425\) −0.467293 −0.0226670
\(426\) 23.0988 1.11914
\(427\) −19.8857 −0.962339
\(428\) 107.124 5.17801
\(429\) −36.3889 −1.75687
\(430\) 45.9399 2.21542
\(431\) −34.5959 −1.66643 −0.833214 0.552951i \(-0.813502\pi\)
−0.833214 + 0.552951i \(0.813502\pi\)
\(432\) −15.6946 −0.755105
\(433\) 38.3222 1.84165 0.920825 0.389977i \(-0.127517\pi\)
0.920825 + 0.389977i \(0.127517\pi\)
\(434\) 5.58940 0.268300
\(435\) 14.6565 0.702724
\(436\) −12.0029 −0.574832
\(437\) 17.9853 0.860353
\(438\) −1.37996 −0.0659369
\(439\) −11.1961 −0.534359 −0.267180 0.963647i \(-0.586092\pi\)
−0.267180 + 0.963647i \(0.586092\pi\)
\(440\) −129.583 −6.17764
\(441\) −4.57360 −0.217790
\(442\) −74.2487 −3.53165
\(443\) −19.8137 −0.941378 −0.470689 0.882299i \(-0.655995\pi\)
−0.470689 + 0.882299i \(0.655995\pi\)
\(444\) −46.0581 −2.18582
\(445\) 7.84594 0.371933
\(446\) 51.5161 2.43936
\(447\) −19.2293 −0.909515
\(448\) −52.1912 −2.46580
\(449\) −37.6608 −1.77732 −0.888662 0.458563i \(-0.848364\pi\)
−0.888662 + 0.458563i \(0.848364\pi\)
\(450\) 0.287855 0.0135696
\(451\) 49.7453 2.34241
\(452\) 97.7055 4.59568
\(453\) 4.55171 0.213858
\(454\) 0.143219 0.00672158
\(455\) −20.8807 −0.978902
\(456\) −44.1823 −2.06902
\(457\) −23.2165 −1.08602 −0.543012 0.839725i \(-0.682716\pi\)
−0.543012 + 0.839725i \(0.682716\pi\)
\(458\) −11.5605 −0.540185
\(459\) −4.46030 −0.208189
\(460\) −48.7362 −2.27234
\(461\) 37.7809 1.75963 0.879816 0.475314i \(-0.157666\pi\)
0.879816 + 0.475314i \(0.157666\pi\)
\(462\) −25.7053 −1.19592
\(463\) 42.0857 1.95589 0.977945 0.208863i \(-0.0669762\pi\)
0.977945 + 0.208863i \(0.0669762\pi\)
\(464\) −103.966 −4.82651
\(465\) −2.88950 −0.133997
\(466\) −78.8568 −3.65297
\(467\) −36.7484 −1.70052 −0.850258 0.526367i \(-0.823554\pi\)
−0.850258 + 0.526367i \(0.823554\pi\)
\(468\) 33.6203 1.55410
\(469\) 2.69577 0.124479
\(470\) 36.5279 1.68491
\(471\) 2.77945 0.128070
\(472\) −101.924 −4.69143
\(473\) −45.3887 −2.08697
\(474\) −44.4871 −2.04336
\(475\) 0.474683 0.0217799
\(476\) −38.5540 −1.76712
\(477\) −5.93758 −0.271863
\(478\) −69.2223 −3.16615
\(479\) 9.37331 0.428277 0.214139 0.976803i \(-0.431306\pi\)
0.214139 + 0.976803i \(0.431306\pi\)
\(480\) 52.2573 2.38521
\(481\) 50.2872 2.29290
\(482\) −51.1460 −2.32963
\(483\) −6.18331 −0.281350
\(484\) 139.134 6.32429
\(485\) 10.3873 0.471661
\(486\) 2.74757 0.124632
\(487\) −13.3452 −0.604727 −0.302363 0.953193i \(-0.597776\pi\)
−0.302363 + 0.953193i \(0.597776\pi\)
\(488\) −124.489 −5.63535
\(489\) −1.21163 −0.0547916
\(490\) 27.8031 1.25602
\(491\) 7.91585 0.357238 0.178619 0.983918i \(-0.442837\pi\)
0.178619 + 0.983918i \(0.442837\pi\)
\(492\) −45.9605 −2.07206
\(493\) −29.5465 −1.33071
\(494\) 75.4229 3.39344
\(495\) 13.2886 0.597278
\(496\) 20.4967 0.920331
\(497\) −13.0955 −0.587414
\(498\) 9.63543 0.431774
\(499\) 31.8490 1.42576 0.712879 0.701287i \(-0.247391\pi\)
0.712879 + 0.701287i \(0.247391\pi\)
\(500\) −62.6740 −2.80287
\(501\) −4.46349 −0.199414
\(502\) −64.1459 −2.86297
\(503\) −9.28352 −0.413932 −0.206966 0.978348i \(-0.566359\pi\)
−0.206966 + 0.978348i \(0.566359\pi\)
\(504\) 15.1898 0.676606
\(505\) 7.19397 0.320127
\(506\) 65.5059 2.91209
\(507\) −23.7074 −1.05288
\(508\) −87.4016 −3.87782
\(509\) −13.2090 −0.585478 −0.292739 0.956192i \(-0.594567\pi\)
−0.292739 + 0.956192i \(0.594567\pi\)
\(510\) 27.1143 1.20064
\(511\) 0.782345 0.0346089
\(512\) −64.5990 −2.85490
\(513\) 4.53083 0.200041
\(514\) 37.4479 1.65176
\(515\) −33.6064 −1.48087
\(516\) 41.9353 1.84610
\(517\) −36.0896 −1.58722
\(518\) 35.5231 1.56079
\(519\) 18.7613 0.823530
\(520\) −130.718 −5.73234
\(521\) −16.7692 −0.734670 −0.367335 0.930089i \(-0.619730\pi\)
−0.367335 + 0.930089i \(0.619730\pi\)
\(522\) 18.2008 0.796629
\(523\) 4.20465 0.183856 0.0919282 0.995766i \(-0.470697\pi\)
0.0919282 + 0.995766i \(0.470697\pi\)
\(524\) 62.7600 2.74168
\(525\) −0.163195 −0.00712242
\(526\) −63.6748 −2.77635
\(527\) 5.82504 0.253743
\(528\) −94.2631 −4.10228
\(529\) −7.24278 −0.314903
\(530\) 36.0948 1.56786
\(531\) 10.4522 0.453585
\(532\) 39.1637 1.69796
\(533\) 50.1807 2.17357
\(534\) 9.74331 0.421634
\(535\) 42.7117 1.84659
\(536\) 16.8761 0.728937
\(537\) −0.436788 −0.0188488
\(538\) 60.7877 2.62074
\(539\) −27.4695 −1.18319
\(540\) −12.2775 −0.528341
\(541\) 7.46536 0.320961 0.160480 0.987039i \(-0.448696\pi\)
0.160480 + 0.987039i \(0.448696\pi\)
\(542\) 79.6783 3.42248
\(543\) −4.76246 −0.204377
\(544\) −105.347 −4.51674
\(545\) −4.78571 −0.204997
\(546\) −25.9302 −1.10971
\(547\) 2.12491 0.0908548 0.0454274 0.998968i \(-0.485535\pi\)
0.0454274 + 0.998968i \(0.485535\pi\)
\(548\) 24.3185 1.03883
\(549\) 12.7662 0.544847
\(550\) 1.72889 0.0737200
\(551\) 30.0138 1.27863
\(552\) −38.7088 −1.64756
\(553\) 25.2213 1.07252
\(554\) 85.2647 3.62255
\(555\) −18.3640 −0.779509
\(556\) 130.066 5.51603
\(557\) 28.6682 1.21471 0.607355 0.794430i \(-0.292230\pi\)
0.607355 + 0.794430i \(0.292230\pi\)
\(558\) −3.58826 −0.151903
\(559\) −45.7859 −1.93654
\(560\) −54.0900 −2.28572
\(561\) −26.7890 −1.13103
\(562\) −73.9243 −3.11831
\(563\) −11.0213 −0.464493 −0.232247 0.972657i \(-0.574608\pi\)
−0.232247 + 0.972657i \(0.574608\pi\)
\(564\) 33.3437 1.40402
\(565\) 38.9566 1.63892
\(566\) −16.9828 −0.713840
\(567\) −1.55769 −0.0654169
\(568\) −81.9807 −3.43983
\(569\) 22.1356 0.927974 0.463987 0.885842i \(-0.346418\pi\)
0.463987 + 0.885842i \(0.346418\pi\)
\(570\) −27.5431 −1.15365
\(571\) −17.1742 −0.718718 −0.359359 0.933199i \(-0.617005\pi\)
−0.359359 + 0.933199i \(0.617005\pi\)
\(572\) 201.927 8.44299
\(573\) −0.772465 −0.0322702
\(574\) 35.4478 1.47956
\(575\) 0.415878 0.0173433
\(576\) 33.5055 1.39606
\(577\) −36.2145 −1.50763 −0.753816 0.657086i \(-0.771789\pi\)
−0.753816 + 0.657086i \(0.771789\pi\)
\(578\) −7.95210 −0.330764
\(579\) −10.0741 −0.418667
\(580\) −81.3306 −3.37707
\(581\) −5.46266 −0.226629
\(582\) 12.8992 0.534689
\(583\) −35.6617 −1.47696
\(584\) 4.89765 0.202666
\(585\) 13.4049 0.554225
\(586\) −17.7479 −0.733159
\(587\) −9.70486 −0.400562 −0.200281 0.979738i \(-0.564186\pi\)
−0.200281 + 0.979738i \(0.564186\pi\)
\(588\) 25.3795 1.04663
\(589\) −5.91716 −0.243812
\(590\) −63.5392 −2.61587
\(591\) 16.5714 0.681655
\(592\) 130.266 5.35389
\(593\) 6.66096 0.273533 0.136767 0.990603i \(-0.456329\pi\)
0.136767 + 0.990603i \(0.456329\pi\)
\(594\) 16.5022 0.677092
\(595\) −15.3720 −0.630192
\(596\) 106.706 4.37084
\(597\) 11.8970 0.486911
\(598\) 66.0793 2.70218
\(599\) −3.19469 −0.130532 −0.0652658 0.997868i \(-0.520790\pi\)
−0.0652658 + 0.997868i \(0.520790\pi\)
\(600\) −1.02164 −0.0417081
\(601\) −15.9699 −0.651426 −0.325713 0.945469i \(-0.605604\pi\)
−0.325713 + 0.945469i \(0.605604\pi\)
\(602\) −32.3433 −1.31822
\(603\) −1.73062 −0.0704764
\(604\) −25.2580 −1.02773
\(605\) 55.4749 2.25538
\(606\) 8.93368 0.362906
\(607\) −27.1464 −1.10184 −0.550919 0.834559i \(-0.685723\pi\)
−0.550919 + 0.834559i \(0.685723\pi\)
\(608\) 107.013 4.33997
\(609\) −10.3187 −0.418134
\(610\) −77.6061 −3.14218
\(611\) −36.4055 −1.47281
\(612\) 24.7508 1.00049
\(613\) 37.5344 1.51600 0.757999 0.652256i \(-0.226177\pi\)
0.757999 + 0.652256i \(0.226177\pi\)
\(614\) −87.0714 −3.51392
\(615\) −18.3251 −0.738939
\(616\) 91.2313 3.67581
\(617\) −16.3640 −0.658788 −0.329394 0.944193i \(-0.606844\pi\)
−0.329394 + 0.944193i \(0.606844\pi\)
\(618\) −41.7334 −1.67876
\(619\) −7.16607 −0.288029 −0.144014 0.989576i \(-0.546001\pi\)
−0.144014 + 0.989576i \(0.546001\pi\)
\(620\) 16.0342 0.643948
\(621\) 3.96954 0.159292
\(622\) −5.03525 −0.201895
\(623\) −5.52382 −0.221307
\(624\) −95.0882 −3.80657
\(625\) −24.4652 −0.978607
\(626\) 21.9213 0.876152
\(627\) 27.2126 1.08677
\(628\) −15.4235 −0.615465
\(629\) 37.0207 1.47611
\(630\) 9.46926 0.377265
\(631\) −5.30805 −0.211310 −0.105655 0.994403i \(-0.533694\pi\)
−0.105655 + 0.994403i \(0.533694\pi\)
\(632\) 157.890 6.28055
\(633\) 5.38451 0.214015
\(634\) 51.8815 2.06048
\(635\) −34.8483 −1.38291
\(636\) 32.9484 1.30649
\(637\) −27.7099 −1.09791
\(638\) 109.316 4.32786
\(639\) 8.40701 0.332576
\(640\) −99.1668 −3.91991
\(641\) 22.5211 0.889530 0.444765 0.895647i \(-0.353287\pi\)
0.444765 + 0.895647i \(0.353287\pi\)
\(642\) 53.0406 2.09335
\(643\) 6.32161 0.249300 0.124650 0.992201i \(-0.460219\pi\)
0.124650 + 0.992201i \(0.460219\pi\)
\(644\) 34.3120 1.35208
\(645\) 16.7202 0.658358
\(646\) 55.5252 2.18461
\(647\) −35.8582 −1.40973 −0.704865 0.709341i \(-0.748993\pi\)
−0.704865 + 0.709341i \(0.748993\pi\)
\(648\) −9.75147 −0.383074
\(649\) 62.7767 2.46420
\(650\) 1.74402 0.0684061
\(651\) 2.03431 0.0797308
\(652\) 6.72346 0.263311
\(653\) 26.1548 1.02351 0.511757 0.859130i \(-0.328995\pi\)
0.511757 + 0.859130i \(0.328995\pi\)
\(654\) −5.94303 −0.232391
\(655\) 25.0233 0.977742
\(656\) 129.990 5.07525
\(657\) −0.502247 −0.0195945
\(658\) −25.7169 −1.00255
\(659\) 27.4431 1.06903 0.534516 0.845158i \(-0.320494\pi\)
0.534516 + 0.845158i \(0.320494\pi\)
\(660\) −73.7401 −2.87033
\(661\) 34.9362 1.35886 0.679430 0.733741i \(-0.262227\pi\)
0.679430 + 0.733741i \(0.262227\pi\)
\(662\) 10.5014 0.408148
\(663\) −27.0234 −1.04950
\(664\) −34.1974 −1.32712
\(665\) 15.6151 0.605529
\(666\) −22.8050 −0.883674
\(667\) 26.2956 1.01817
\(668\) 24.7685 0.958322
\(669\) 18.7497 0.724905
\(670\) 10.5205 0.406443
\(671\) 76.6749 2.96000
\(672\) −36.7910 −1.41924
\(673\) −13.8123 −0.532426 −0.266213 0.963914i \(-0.585772\pi\)
−0.266213 + 0.963914i \(0.585772\pi\)
\(674\) −30.9769 −1.19318
\(675\) 0.104767 0.00403250
\(676\) 131.556 5.05983
\(677\) −45.5712 −1.75144 −0.875722 0.482815i \(-0.839614\pi\)
−0.875722 + 0.482815i \(0.839614\pi\)
\(678\) 48.3774 1.85792
\(679\) −7.31300 −0.280647
\(680\) −96.2322 −3.69034
\(681\) 0.0521256 0.00199746
\(682\) −21.5514 −0.825247
\(683\) 47.1810 1.80533 0.902666 0.430342i \(-0.141607\pi\)
0.902666 + 0.430342i \(0.141607\pi\)
\(684\) −25.1422 −0.961334
\(685\) 9.69612 0.370470
\(686\) −49.5334 −1.89119
\(687\) −4.20753 −0.160527
\(688\) −118.605 −4.52179
\(689\) −35.9738 −1.37049
\(690\) −24.1310 −0.918651
\(691\) 16.2660 0.618788 0.309394 0.950934i \(-0.399874\pi\)
0.309394 + 0.950934i \(0.399874\pi\)
\(692\) −104.109 −3.95763
\(693\) −9.35564 −0.355391
\(694\) −55.2160 −2.09597
\(695\) 51.8592 1.96713
\(696\) −64.5971 −2.44855
\(697\) 36.9422 1.39929
\(698\) −12.4816 −0.472435
\(699\) −28.7006 −1.08556
\(700\) 0.905590 0.0342281
\(701\) 5.78202 0.218384 0.109192 0.994021i \(-0.465174\pi\)
0.109192 + 0.994021i \(0.465174\pi\)
\(702\) 16.6466 0.628285
\(703\) −37.6061 −1.41834
\(704\) 201.237 7.58442
\(705\) 13.2946 0.500705
\(706\) −42.8633 −1.61318
\(707\) −5.06481 −0.190482
\(708\) −58.0004 −2.17979
\(709\) 39.1600 1.47069 0.735343 0.677695i \(-0.237021\pi\)
0.735343 + 0.677695i \(0.237021\pi\)
\(710\) −51.1066 −1.91800
\(711\) −16.1915 −0.607227
\(712\) −34.5803 −1.29595
\(713\) −5.18412 −0.194147
\(714\) −19.0894 −0.714404
\(715\) 80.5112 3.01095
\(716\) 2.42379 0.0905815
\(717\) −25.1940 −0.940888
\(718\) −0.298558 −0.0111421
\(719\) −22.9261 −0.854997 −0.427499 0.904016i \(-0.640605\pi\)
−0.427499 + 0.904016i \(0.640605\pi\)
\(720\) 34.7245 1.29411
\(721\) 23.6601 0.881148
\(722\) −4.19944 −0.156287
\(723\) −18.6150 −0.692299
\(724\) 26.4275 0.982170
\(725\) 0.694014 0.0257751
\(726\) 68.8903 2.55676
\(727\) 30.4660 1.12992 0.564961 0.825118i \(-0.308891\pi\)
0.564961 + 0.825118i \(0.308891\pi\)
\(728\) 92.0298 3.41085
\(729\) 1.00000 0.0370370
\(730\) 3.05318 0.113003
\(731\) −33.7069 −1.24669
\(732\) −70.8411 −2.61836
\(733\) −3.38895 −0.125174 −0.0625868 0.998040i \(-0.519935\pi\)
−0.0625868 + 0.998040i \(0.519935\pi\)
\(734\) 8.06489 0.297681
\(735\) 10.1192 0.373251
\(736\) 93.7563 3.45590
\(737\) −10.3943 −0.382879
\(738\) −22.7566 −0.837683
\(739\) 4.48104 0.164838 0.0824189 0.996598i \(-0.473735\pi\)
0.0824189 + 0.996598i \(0.473735\pi\)
\(740\) 101.904 3.74607
\(741\) 27.4508 1.00843
\(742\) −25.4120 −0.932904
\(743\) −19.8126 −0.726852 −0.363426 0.931623i \(-0.618393\pi\)
−0.363426 + 0.931623i \(0.618393\pi\)
\(744\) 12.7352 0.466895
\(745\) 42.5452 1.55873
\(746\) 31.3132 1.14646
\(747\) 3.50690 0.128311
\(748\) 148.655 5.43538
\(749\) −30.0705 −1.09875
\(750\) −31.0321 −1.13313
\(751\) 36.9001 1.34650 0.673252 0.739414i \(-0.264897\pi\)
0.673252 + 0.739414i \(0.264897\pi\)
\(752\) −94.3059 −3.43898
\(753\) −23.3464 −0.850792
\(754\) 110.273 4.01590
\(755\) −10.0707 −0.366512
\(756\) 8.64382 0.314373
\(757\) 10.5912 0.384943 0.192472 0.981303i \(-0.438350\pi\)
0.192472 + 0.981303i \(0.438350\pi\)
\(758\) −7.43453 −0.270034
\(759\) 23.8414 0.865389
\(760\) 97.7540 3.54591
\(761\) 7.96614 0.288773 0.144386 0.989521i \(-0.453879\pi\)
0.144386 + 0.989521i \(0.453879\pi\)
\(762\) −43.2756 −1.56771
\(763\) 3.36931 0.121977
\(764\) 4.28651 0.155080
\(765\) 9.86848 0.356796
\(766\) 29.3460 1.06031
\(767\) 63.3262 2.28658
\(768\) −56.1371 −2.02567
\(769\) −1.77309 −0.0639394 −0.0319697 0.999489i \(-0.510178\pi\)
−0.0319697 + 0.999489i \(0.510178\pi\)
\(770\) 56.8733 2.04957
\(771\) 13.6295 0.490854
\(772\) 55.9026 2.01198
\(773\) −30.4558 −1.09542 −0.547710 0.836668i \(-0.684500\pi\)
−0.547710 + 0.836668i \(0.684500\pi\)
\(774\) 20.7636 0.746334
\(775\) −0.136824 −0.00491485
\(776\) −45.7809 −1.64344
\(777\) 12.9289 0.463822
\(778\) 34.8601 1.24980
\(779\) −37.5264 −1.34452
\(780\) −74.3855 −2.66343
\(781\) 50.4933 1.80679
\(782\) 48.6465 1.73960
\(783\) 6.62434 0.236735
\(784\) −71.7807 −2.56360
\(785\) −6.14957 −0.219488
\(786\) 31.0747 1.10840
\(787\) −29.2173 −1.04148 −0.520741 0.853715i \(-0.674344\pi\)
−0.520741 + 0.853715i \(0.674344\pi\)
\(788\) −91.9567 −3.27582
\(789\) −23.1750 −0.825051
\(790\) 98.4285 3.50193
\(791\) −27.4268 −0.975186
\(792\) −58.5683 −2.08113
\(793\) 77.3460 2.74664
\(794\) −69.9105 −2.48103
\(795\) 13.1370 0.465921
\(796\) −66.0179 −2.33994
\(797\) −14.1708 −0.501955 −0.250978 0.967993i \(-0.580752\pi\)
−0.250978 + 0.967993i \(0.580752\pi\)
\(798\) 19.3913 0.686445
\(799\) −26.8011 −0.948156
\(800\) 2.47449 0.0874866
\(801\) 3.54616 0.125297
\(802\) 51.0838 1.80383
\(803\) −3.01654 −0.106452
\(804\) 9.60345 0.338688
\(805\) 13.6807 0.482181
\(806\) −21.7401 −0.765761
\(807\) 22.1242 0.778808
\(808\) −31.7068 −1.11544
\(809\) 46.7791 1.64467 0.822333 0.569006i \(-0.192672\pi\)
0.822333 + 0.569006i \(0.192672\pi\)
\(810\) −6.07904 −0.213596
\(811\) 27.3604 0.960755 0.480378 0.877062i \(-0.340500\pi\)
0.480378 + 0.877062i \(0.340500\pi\)
\(812\) 57.2596 2.00942
\(813\) 28.9996 1.01706
\(814\) −136.969 −4.80075
\(815\) 2.68074 0.0939023
\(816\) −70.0024 −2.45057
\(817\) 34.2399 1.19790
\(818\) 48.2182 1.68591
\(819\) −9.43753 −0.329774
\(820\) 101.688 3.55111
\(821\) 48.9465 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(822\) 12.0409 0.419975
\(823\) 28.3115 0.986877 0.493439 0.869781i \(-0.335740\pi\)
0.493439 + 0.869781i \(0.335740\pi\)
\(824\) 148.117 5.15990
\(825\) 0.629243 0.0219074
\(826\) 44.7338 1.55649
\(827\) 53.5224 1.86116 0.930579 0.366092i \(-0.119305\pi\)
0.930579 + 0.366092i \(0.119305\pi\)
\(828\) −22.0275 −0.765508
\(829\) −32.0943 −1.11468 −0.557340 0.830284i \(-0.688178\pi\)
−0.557340 + 0.830284i \(0.688178\pi\)
\(830\) −21.3186 −0.739978
\(831\) 31.0328 1.07652
\(832\) 202.999 7.03772
\(833\) −20.3996 −0.706805
\(834\) 64.4002 2.23000
\(835\) 9.87556 0.341758
\(836\) −151.006 −5.22266
\(837\) −1.30598 −0.0451412
\(838\) −4.61627 −0.159467
\(839\) −2.16030 −0.0745819 −0.0372909 0.999304i \(-0.511873\pi\)
−0.0372909 + 0.999304i \(0.511873\pi\)
\(840\) −33.6076 −1.15957
\(841\) 14.8819 0.513169
\(842\) −4.73008 −0.163009
\(843\) −26.9054 −0.926670
\(844\) −29.8793 −1.02849
\(845\) 52.4531 1.80444
\(846\) 16.5097 0.567614
\(847\) −39.0563 −1.34199
\(848\) −93.1877 −3.20008
\(849\) −6.18102 −0.212132
\(850\) 1.28392 0.0440381
\(851\) −32.9474 −1.12942
\(852\) −46.6516 −1.59826
\(853\) −29.1123 −0.996785 −0.498392 0.866952i \(-0.666076\pi\)
−0.498392 + 0.866952i \(0.666076\pi\)
\(854\) 54.6374 1.86965
\(855\) −10.0245 −0.342832
\(856\) −188.248 −6.43418
\(857\) −41.9008 −1.43130 −0.715652 0.698457i \(-0.753870\pi\)
−0.715652 + 0.698457i \(0.753870\pi\)
\(858\) 99.9811 3.41330
\(859\) 14.8808 0.507727 0.253863 0.967240i \(-0.418299\pi\)
0.253863 + 0.967240i \(0.418299\pi\)
\(860\) −92.7826 −3.16386
\(861\) 12.9015 0.439683
\(862\) 95.0547 3.23758
\(863\) −5.73504 −0.195223 −0.0976115 0.995225i \(-0.531120\pi\)
−0.0976115 + 0.995225i \(0.531120\pi\)
\(864\) 23.6190 0.803533
\(865\) −41.5097 −1.41137
\(866\) −105.293 −3.57800
\(867\) −2.89423 −0.0982933
\(868\) −11.2886 −0.383161
\(869\) −97.2474 −3.29889
\(870\) −40.2696 −1.36527
\(871\) −10.4853 −0.355280
\(872\) 21.0926 0.714285
\(873\) 4.69477 0.158894
\(874\) −49.4158 −1.67152
\(875\) 17.5932 0.594757
\(876\) 2.78703 0.0941651
\(877\) 16.4626 0.555902 0.277951 0.960595i \(-0.410345\pi\)
0.277951 + 0.960595i \(0.410345\pi\)
\(878\) 30.7619 1.03817
\(879\) −6.45950 −0.217873
\(880\) 208.559 7.03052
\(881\) 18.1854 0.612683 0.306341 0.951922i \(-0.400895\pi\)
0.306341 + 0.951922i \(0.400895\pi\)
\(882\) 12.5663 0.423129
\(883\) −18.0335 −0.606876 −0.303438 0.952851i \(-0.598135\pi\)
−0.303438 + 0.952851i \(0.598135\pi\)
\(884\) 149.957 5.04358
\(885\) −23.1256 −0.777359
\(886\) 54.4395 1.82893
\(887\) 0.865135 0.0290484 0.0145242 0.999895i \(-0.495377\pi\)
0.0145242 + 0.999895i \(0.495377\pi\)
\(888\) 80.9377 2.71609
\(889\) 24.5344 0.822858
\(890\) −21.5572 −0.722600
\(891\) 6.00610 0.201212
\(892\) −104.044 −3.48367
\(893\) 27.2250 0.911049
\(894\) 52.8338 1.76703
\(895\) 0.966402 0.0323033
\(896\) 69.8169 2.33242
\(897\) 24.0501 0.803009
\(898\) 103.476 3.45303
\(899\) −8.65124 −0.288535
\(900\) −0.581367 −0.0193789
\(901\) −26.4833 −0.882288
\(902\) −136.679 −4.55090
\(903\) −11.7716 −0.391735
\(904\) −171.698 −5.71058
\(905\) 10.5370 0.350262
\(906\) −12.5061 −0.415488
\(907\) 59.5470 1.97723 0.988614 0.150476i \(-0.0480806\pi\)
0.988614 + 0.150476i \(0.0480806\pi\)
\(908\) −0.289252 −0.00959915
\(909\) 3.25149 0.107845
\(910\) 57.3711 1.90183
\(911\) −21.0274 −0.696669 −0.348335 0.937370i \(-0.613253\pi\)
−0.348335 + 0.937370i \(0.613253\pi\)
\(912\) 71.1094 2.35467
\(913\) 21.0628 0.697076
\(914\) 63.7890 2.10995
\(915\) −28.2454 −0.933764
\(916\) 23.3481 0.771444
\(917\) −17.6173 −0.581775
\(918\) 12.2550 0.404474
\(919\) −22.4420 −0.740292 −0.370146 0.928974i \(-0.620692\pi\)
−0.370146 + 0.928974i \(0.620692\pi\)
\(920\) 85.6439 2.82360
\(921\) −31.6904 −1.04423
\(922\) −103.806 −3.41866
\(923\) 50.9353 1.67655
\(924\) 51.9157 1.70790
\(925\) −0.869574 −0.0285914
\(926\) −115.633 −3.79995
\(927\) −15.1892 −0.498879
\(928\) 156.460 5.13605
\(929\) 22.2913 0.731355 0.365678 0.930742i \(-0.380837\pi\)
0.365678 + 0.930742i \(0.380837\pi\)
\(930\) 7.93909 0.260333
\(931\) 20.7222 0.679143
\(932\) 159.263 5.21684
\(933\) −1.83262 −0.0599973
\(934\) 100.969 3.30380
\(935\) 59.2711 1.93837
\(936\) −59.0809 −1.93112
\(937\) −49.6565 −1.62221 −0.811103 0.584903i \(-0.801133\pi\)
−0.811103 + 0.584903i \(0.801133\pi\)
\(938\) −7.40682 −0.241841
\(939\) 7.97844 0.260367
\(940\) −73.7736 −2.40623
\(941\) 19.5649 0.637798 0.318899 0.947789i \(-0.396687\pi\)
0.318899 + 0.947789i \(0.396687\pi\)
\(942\) −7.63672 −0.248818
\(943\) −32.8776 −1.07064
\(944\) 164.042 5.33912
\(945\) 3.44642 0.112112
\(946\) 124.708 4.05462
\(947\) −1.24093 −0.0403248 −0.0201624 0.999797i \(-0.506418\pi\)
−0.0201624 + 0.999797i \(0.506418\pi\)
\(948\) 89.8484 2.91814
\(949\) −3.04295 −0.0987782
\(950\) −1.30422 −0.0423146
\(951\) 18.8827 0.612313
\(952\) 67.7509 2.19582
\(953\) −13.7099 −0.444108 −0.222054 0.975034i \(-0.571276\pi\)
−0.222054 + 0.975034i \(0.571276\pi\)
\(954\) 16.3139 0.528182
\(955\) 1.70909 0.0553049
\(956\) 139.805 4.52161
\(957\) 39.7864 1.28611
\(958\) −25.7538 −0.832067
\(959\) −6.82641 −0.220436
\(960\) −74.1316 −2.39259
\(961\) −29.2944 −0.944981
\(962\) −138.168 −4.45470
\(963\) 19.3046 0.622081
\(964\) 103.297 3.32697
\(965\) 22.2892 0.717514
\(966\) 16.9891 0.546614
\(967\) 25.0489 0.805517 0.402759 0.915306i \(-0.368051\pi\)
0.402759 + 0.915306i \(0.368051\pi\)
\(968\) −244.501 −7.85855
\(969\) 20.2088 0.649201
\(970\) −28.5397 −0.916355
\(971\) −18.0040 −0.577776 −0.288888 0.957363i \(-0.593286\pi\)
−0.288888 + 0.957363i \(0.593286\pi\)
\(972\) −5.54913 −0.177988
\(973\) −36.5107 −1.17048
\(974\) 36.6667 1.17488
\(975\) 0.634750 0.0203283
\(976\) 200.360 6.41336
\(977\) −23.3256 −0.746252 −0.373126 0.927781i \(-0.621714\pi\)
−0.373126 + 0.927781i \(0.621714\pi\)
\(978\) 3.32902 0.106450
\(979\) 21.2986 0.680705
\(980\) −56.1526 −1.79373
\(981\) −2.16302 −0.0690598
\(982\) −21.7493 −0.694050
\(983\) 3.95871 0.126263 0.0631316 0.998005i \(-0.479891\pi\)
0.0631316 + 0.998005i \(0.479891\pi\)
\(984\) 80.7662 2.57473
\(985\) −36.6645 −1.16823
\(986\) 81.1811 2.58533
\(987\) −9.35989 −0.297929
\(988\) −152.328 −4.84620
\(989\) 29.9982 0.953887
\(990\) −36.5113 −1.16041
\(991\) −4.88474 −0.155169 −0.0775845 0.996986i \(-0.524721\pi\)
−0.0775845 + 0.996986i \(0.524721\pi\)
\(992\) −30.8458 −0.979355
\(993\) 3.82207 0.121290
\(994\) 35.9808 1.14124
\(995\) −26.3223 −0.834473
\(996\) −19.4602 −0.616620
\(997\) 56.5284 1.79027 0.895136 0.445793i \(-0.147078\pi\)
0.895136 + 0.445793i \(0.147078\pi\)
\(998\) −87.5073 −2.77000
\(999\) −8.30005 −0.262602
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 8031.2.a.c.1.2 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8031.2.a.c.1.2 121 1.1 even 1 trivial