Properties

Label 8002.2.a.g.1.16
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $0$
Dimension $95$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(95\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.22303 q^{3} +1.00000 q^{4} -1.84239 q^{5} -2.22303 q^{6} +1.24832 q^{7} +1.00000 q^{8} +1.94184 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.22303 q^{3} +1.00000 q^{4} -1.84239 q^{5} -2.22303 q^{6} +1.24832 q^{7} +1.00000 q^{8} +1.94184 q^{9} -1.84239 q^{10} -1.09381 q^{11} -2.22303 q^{12} -5.48845 q^{13} +1.24832 q^{14} +4.09568 q^{15} +1.00000 q^{16} -3.04073 q^{17} +1.94184 q^{18} +6.62860 q^{19} -1.84239 q^{20} -2.77505 q^{21} -1.09381 q^{22} +1.09612 q^{23} -2.22303 q^{24} -1.60561 q^{25} -5.48845 q^{26} +2.35231 q^{27} +1.24832 q^{28} -9.70507 q^{29} +4.09568 q^{30} -3.13129 q^{31} +1.00000 q^{32} +2.43156 q^{33} -3.04073 q^{34} -2.29989 q^{35} +1.94184 q^{36} +5.21032 q^{37} +6.62860 q^{38} +12.2010 q^{39} -1.84239 q^{40} +3.75054 q^{41} -2.77505 q^{42} -2.33949 q^{43} -1.09381 q^{44} -3.57763 q^{45} +1.09612 q^{46} -3.47861 q^{47} -2.22303 q^{48} -5.44170 q^{49} -1.60561 q^{50} +6.75962 q^{51} -5.48845 q^{52} -5.70073 q^{53} +2.35231 q^{54} +2.01522 q^{55} +1.24832 q^{56} -14.7356 q^{57} -9.70507 q^{58} +6.61961 q^{59} +4.09568 q^{60} -1.94182 q^{61} -3.13129 q^{62} +2.42404 q^{63} +1.00000 q^{64} +10.1119 q^{65} +2.43156 q^{66} +1.81145 q^{67} -3.04073 q^{68} -2.43671 q^{69} -2.29989 q^{70} -1.19425 q^{71} +1.94184 q^{72} +1.38065 q^{73} +5.21032 q^{74} +3.56930 q^{75} +6.62860 q^{76} -1.36542 q^{77} +12.2010 q^{78} -9.55379 q^{79} -1.84239 q^{80} -11.0548 q^{81} +3.75054 q^{82} +12.4170 q^{83} -2.77505 q^{84} +5.60220 q^{85} -2.33949 q^{86} +21.5746 q^{87} -1.09381 q^{88} +12.8515 q^{89} -3.57763 q^{90} -6.85134 q^{91} +1.09612 q^{92} +6.96095 q^{93} -3.47861 q^{94} -12.2125 q^{95} -2.22303 q^{96} -4.57839 q^{97} -5.44170 q^{98} -2.12400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.22303 −1.28346 −0.641732 0.766929i \(-0.721784\pi\)
−0.641732 + 0.766929i \(0.721784\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.84239 −0.823941 −0.411970 0.911197i \(-0.635159\pi\)
−0.411970 + 0.911197i \(0.635159\pi\)
\(6\) −2.22303 −0.907546
\(7\) 1.24832 0.471820 0.235910 0.971775i \(-0.424193\pi\)
0.235910 + 0.971775i \(0.424193\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.94184 0.647281
\(10\) −1.84239 −0.582614
\(11\) −1.09381 −0.329795 −0.164898 0.986311i \(-0.552729\pi\)
−0.164898 + 0.986311i \(0.552729\pi\)
\(12\) −2.22303 −0.641732
\(13\) −5.48845 −1.52222 −0.761112 0.648621i \(-0.775346\pi\)
−0.761112 + 0.648621i \(0.775346\pi\)
\(14\) 1.24832 0.333627
\(15\) 4.09568 1.05750
\(16\) 1.00000 0.250000
\(17\) −3.04073 −0.737485 −0.368742 0.929532i \(-0.620212\pi\)
−0.368742 + 0.929532i \(0.620212\pi\)
\(18\) 1.94184 0.457697
\(19\) 6.62860 1.52071 0.760353 0.649510i \(-0.225026\pi\)
0.760353 + 0.649510i \(0.225026\pi\)
\(20\) −1.84239 −0.411970
\(21\) −2.77505 −0.605565
\(22\) −1.09381 −0.233200
\(23\) 1.09612 0.228557 0.114279 0.993449i \(-0.463544\pi\)
0.114279 + 0.993449i \(0.463544\pi\)
\(24\) −2.22303 −0.453773
\(25\) −1.60561 −0.321121
\(26\) −5.48845 −1.07637
\(27\) 2.35231 0.452702
\(28\) 1.24832 0.235910
\(29\) −9.70507 −1.80219 −0.901093 0.433626i \(-0.857234\pi\)
−0.901093 + 0.433626i \(0.857234\pi\)
\(30\) 4.09568 0.747765
\(31\) −3.13129 −0.562397 −0.281198 0.959650i \(-0.590732\pi\)
−0.281198 + 0.959650i \(0.590732\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.43156 0.423280
\(34\) −3.04073 −0.521481
\(35\) −2.29989 −0.388752
\(36\) 1.94184 0.323640
\(37\) 5.21032 0.856572 0.428286 0.903643i \(-0.359118\pi\)
0.428286 + 0.903643i \(0.359118\pi\)
\(38\) 6.62860 1.07530
\(39\) 12.2010 1.95372
\(40\) −1.84239 −0.291307
\(41\) 3.75054 0.585736 0.292868 0.956153i \(-0.405390\pi\)
0.292868 + 0.956153i \(0.405390\pi\)
\(42\) −2.77505 −0.428199
\(43\) −2.33949 −0.356769 −0.178385 0.983961i \(-0.557087\pi\)
−0.178385 + 0.983961i \(0.557087\pi\)
\(44\) −1.09381 −0.164898
\(45\) −3.57763 −0.533321
\(46\) 1.09612 0.161614
\(47\) −3.47861 −0.507407 −0.253703 0.967282i \(-0.581649\pi\)
−0.253703 + 0.967282i \(0.581649\pi\)
\(48\) −2.22303 −0.320866
\(49\) −5.44170 −0.777385
\(50\) −1.60561 −0.227067
\(51\) 6.75962 0.946536
\(52\) −5.48845 −0.761112
\(53\) −5.70073 −0.783056 −0.391528 0.920166i \(-0.628053\pi\)
−0.391528 + 0.920166i \(0.628053\pi\)
\(54\) 2.35231 0.320109
\(55\) 2.01522 0.271732
\(56\) 1.24832 0.166814
\(57\) −14.7356 −1.95177
\(58\) −9.70507 −1.27434
\(59\) 6.61961 0.861799 0.430900 0.902400i \(-0.358196\pi\)
0.430900 + 0.902400i \(0.358196\pi\)
\(60\) 4.09568 0.528749
\(61\) −1.94182 −0.248625 −0.124312 0.992243i \(-0.539673\pi\)
−0.124312 + 0.992243i \(0.539673\pi\)
\(62\) −3.13129 −0.397675
\(63\) 2.42404 0.305400
\(64\) 1.00000 0.125000
\(65\) 10.1119 1.25422
\(66\) 2.43156 0.299304
\(67\) 1.81145 0.221304 0.110652 0.993859i \(-0.464706\pi\)
0.110652 + 0.993859i \(0.464706\pi\)
\(68\) −3.04073 −0.368742
\(69\) −2.43671 −0.293345
\(70\) −2.29989 −0.274889
\(71\) −1.19425 −0.141732 −0.0708659 0.997486i \(-0.522576\pi\)
−0.0708659 + 0.997486i \(0.522576\pi\)
\(72\) 1.94184 0.228848
\(73\) 1.38065 0.161592 0.0807962 0.996731i \(-0.474254\pi\)
0.0807962 + 0.996731i \(0.474254\pi\)
\(74\) 5.21032 0.605688
\(75\) 3.56930 0.412148
\(76\) 6.62860 0.760353
\(77\) −1.36542 −0.155604
\(78\) 12.2010 1.38149
\(79\) −9.55379 −1.07488 −0.537442 0.843300i \(-0.680609\pi\)
−0.537442 + 0.843300i \(0.680609\pi\)
\(80\) −1.84239 −0.205985
\(81\) −11.0548 −1.22831
\(82\) 3.75054 0.414178
\(83\) 12.4170 1.36295 0.681473 0.731843i \(-0.261340\pi\)
0.681473 + 0.731843i \(0.261340\pi\)
\(84\) −2.77505 −0.302782
\(85\) 5.60220 0.607644
\(86\) −2.33949 −0.252274
\(87\) 21.5746 2.31304
\(88\) −1.09381 −0.116600
\(89\) 12.8515 1.36226 0.681128 0.732165i \(-0.261490\pi\)
0.681128 + 0.732165i \(0.261490\pi\)
\(90\) −3.57763 −0.377115
\(91\) −6.85134 −0.718216
\(92\) 1.09612 0.114279
\(93\) 6.96095 0.721816
\(94\) −3.47861 −0.358791
\(95\) −12.2125 −1.25297
\(96\) −2.22303 −0.226887
\(97\) −4.57839 −0.464865 −0.232433 0.972612i \(-0.574669\pi\)
−0.232433 + 0.972612i \(0.574669\pi\)
\(98\) −5.44170 −0.549695
\(99\) −2.12400 −0.213470
\(100\) −1.60561 −0.160561
\(101\) −11.0170 −1.09623 −0.548116 0.836403i \(-0.684655\pi\)
−0.548116 + 0.836403i \(0.684655\pi\)
\(102\) 6.75962 0.669302
\(103\) −11.5103 −1.13415 −0.567073 0.823667i \(-0.691924\pi\)
−0.567073 + 0.823667i \(0.691924\pi\)
\(104\) −5.48845 −0.538187
\(105\) 5.11271 0.498950
\(106\) −5.70073 −0.553704
\(107\) 10.6131 1.02601 0.513005 0.858386i \(-0.328532\pi\)
0.513005 + 0.858386i \(0.328532\pi\)
\(108\) 2.35231 0.226351
\(109\) 10.3963 0.995782 0.497891 0.867240i \(-0.334108\pi\)
0.497891 + 0.867240i \(0.334108\pi\)
\(110\) 2.01522 0.192143
\(111\) −11.5827 −1.09938
\(112\) 1.24832 0.117955
\(113\) −5.68217 −0.534533 −0.267267 0.963623i \(-0.586120\pi\)
−0.267267 + 0.963623i \(0.586120\pi\)
\(114\) −14.7356 −1.38011
\(115\) −2.01948 −0.188318
\(116\) −9.70507 −0.901093
\(117\) −10.6577 −0.985306
\(118\) 6.61961 0.609384
\(119\) −3.79580 −0.347960
\(120\) 4.09568 0.373882
\(121\) −9.80359 −0.891235
\(122\) −1.94182 −0.175804
\(123\) −8.33754 −0.751771
\(124\) −3.13129 −0.281198
\(125\) 12.1701 1.08853
\(126\) 2.42404 0.215951
\(127\) 14.0797 1.24937 0.624686 0.780876i \(-0.285227\pi\)
0.624686 + 0.780876i \(0.285227\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.20075 0.457901
\(130\) 10.1119 0.886869
\(131\) 19.4452 1.69893 0.849466 0.527643i \(-0.176924\pi\)
0.849466 + 0.527643i \(0.176924\pi\)
\(132\) 2.43156 0.211640
\(133\) 8.27462 0.717500
\(134\) 1.81145 0.156485
\(135\) −4.33387 −0.373000
\(136\) −3.04073 −0.260740
\(137\) 3.66236 0.312896 0.156448 0.987686i \(-0.449996\pi\)
0.156448 + 0.987686i \(0.449996\pi\)
\(138\) −2.43671 −0.207426
\(139\) −8.43371 −0.715338 −0.357669 0.933848i \(-0.616428\pi\)
−0.357669 + 0.933848i \(0.616428\pi\)
\(140\) −2.29989 −0.194376
\(141\) 7.73303 0.651239
\(142\) −1.19425 −0.100220
\(143\) 6.00331 0.502022
\(144\) 1.94184 0.161820
\(145\) 17.8805 1.48490
\(146\) 1.38065 0.114263
\(147\) 12.0970 0.997747
\(148\) 5.21032 0.428286
\(149\) −23.6461 −1.93717 −0.968583 0.248689i \(-0.920000\pi\)
−0.968583 + 0.248689i \(0.920000\pi\)
\(150\) 3.56930 0.291433
\(151\) 13.2692 1.07983 0.539914 0.841720i \(-0.318457\pi\)
0.539914 + 0.841720i \(0.318457\pi\)
\(152\) 6.62860 0.537651
\(153\) −5.90462 −0.477360
\(154\) −1.36542 −0.110029
\(155\) 5.76906 0.463382
\(156\) 12.2010 0.976860
\(157\) −3.20259 −0.255595 −0.127797 0.991800i \(-0.540791\pi\)
−0.127797 + 0.991800i \(0.540791\pi\)
\(158\) −9.55379 −0.760058
\(159\) 12.6729 1.00502
\(160\) −1.84239 −0.145654
\(161\) 1.36831 0.107838
\(162\) −11.0548 −0.868545
\(163\) 8.37302 0.655825 0.327913 0.944708i \(-0.393655\pi\)
0.327913 + 0.944708i \(0.393655\pi\)
\(164\) 3.75054 0.292868
\(165\) −4.47988 −0.348758
\(166\) 12.4170 0.963749
\(167\) 3.94105 0.304968 0.152484 0.988306i \(-0.451273\pi\)
0.152484 + 0.988306i \(0.451273\pi\)
\(168\) −2.77505 −0.214099
\(169\) 17.1231 1.31716
\(170\) 5.60220 0.429669
\(171\) 12.8717 0.984324
\(172\) −2.33949 −0.178385
\(173\) −17.8769 −1.35916 −0.679580 0.733602i \(-0.737838\pi\)
−0.679580 + 0.733602i \(0.737838\pi\)
\(174\) 21.5746 1.63557
\(175\) −2.00431 −0.151512
\(176\) −1.09381 −0.0824488
\(177\) −14.7156 −1.10609
\(178\) 12.8515 0.963260
\(179\) 25.2144 1.88461 0.942306 0.334753i \(-0.108653\pi\)
0.942306 + 0.334753i \(0.108653\pi\)
\(180\) −3.57763 −0.266661
\(181\) −24.1061 −1.79179 −0.895896 0.444263i \(-0.853466\pi\)
−0.895896 + 0.444263i \(0.853466\pi\)
\(182\) −6.85134 −0.507855
\(183\) 4.31672 0.319101
\(184\) 1.09612 0.0808072
\(185\) −9.59944 −0.705765
\(186\) 6.96095 0.510401
\(187\) 3.32597 0.243219
\(188\) −3.47861 −0.253703
\(189\) 2.93644 0.213594
\(190\) −12.2125 −0.885985
\(191\) −2.26690 −0.164027 −0.0820135 0.996631i \(-0.526135\pi\)
−0.0820135 + 0.996631i \(0.526135\pi\)
\(192\) −2.22303 −0.160433
\(193\) −19.5256 −1.40548 −0.702741 0.711446i \(-0.748041\pi\)
−0.702741 + 0.711446i \(0.748041\pi\)
\(194\) −4.57839 −0.328709
\(195\) −22.4789 −1.60975
\(196\) −5.44170 −0.388693
\(197\) 22.9860 1.63768 0.818842 0.574018i \(-0.194616\pi\)
0.818842 + 0.574018i \(0.194616\pi\)
\(198\) −2.12400 −0.150946
\(199\) 12.1639 0.862276 0.431138 0.902286i \(-0.358112\pi\)
0.431138 + 0.902286i \(0.358112\pi\)
\(200\) −1.60561 −0.113534
\(201\) −4.02690 −0.284035
\(202\) −11.0170 −0.775152
\(203\) −12.1150 −0.850308
\(204\) 6.75962 0.473268
\(205\) −6.90995 −0.482612
\(206\) −11.5103 −0.801963
\(207\) 2.12850 0.147941
\(208\) −5.48845 −0.380556
\(209\) −7.25041 −0.501521
\(210\) 5.11271 0.352811
\(211\) −11.0249 −0.758988 −0.379494 0.925194i \(-0.623902\pi\)
−0.379494 + 0.925194i \(0.623902\pi\)
\(212\) −5.70073 −0.391528
\(213\) 2.65486 0.181908
\(214\) 10.6131 0.725499
\(215\) 4.31025 0.293957
\(216\) 2.35231 0.160054
\(217\) −3.90885 −0.265350
\(218\) 10.3963 0.704124
\(219\) −3.06921 −0.207398
\(220\) 2.01522 0.135866
\(221\) 16.6889 1.12262
\(222\) −11.5827 −0.777379
\(223\) −21.8149 −1.46083 −0.730416 0.683003i \(-0.760674\pi\)
−0.730416 + 0.683003i \(0.760674\pi\)
\(224\) 1.24832 0.0834069
\(225\) −3.11784 −0.207856
\(226\) −5.68217 −0.377972
\(227\) 23.4640 1.55736 0.778682 0.627419i \(-0.215889\pi\)
0.778682 + 0.627419i \(0.215889\pi\)
\(228\) −14.7356 −0.975886
\(229\) −8.00993 −0.529311 −0.264655 0.964343i \(-0.585258\pi\)
−0.264655 + 0.964343i \(0.585258\pi\)
\(230\) −2.01948 −0.133161
\(231\) 3.03536 0.199712
\(232\) −9.70507 −0.637169
\(233\) 14.4560 0.947041 0.473521 0.880783i \(-0.342983\pi\)
0.473521 + 0.880783i \(0.342983\pi\)
\(234\) −10.6577 −0.696717
\(235\) 6.40894 0.418073
\(236\) 6.61961 0.430900
\(237\) 21.2383 1.37958
\(238\) −3.79580 −0.246045
\(239\) 5.47930 0.354426 0.177213 0.984173i \(-0.443292\pi\)
0.177213 + 0.984173i \(0.443292\pi\)
\(240\) 4.09568 0.264375
\(241\) 22.0387 1.41964 0.709820 0.704383i \(-0.248776\pi\)
0.709820 + 0.704383i \(0.248776\pi\)
\(242\) −9.80359 −0.630198
\(243\) 17.5181 1.12379
\(244\) −1.94182 −0.124312
\(245\) 10.0257 0.640520
\(246\) −8.33754 −0.531582
\(247\) −36.3808 −2.31485
\(248\) −3.13129 −0.198837
\(249\) −27.6034 −1.74929
\(250\) 12.1701 0.769704
\(251\) 18.3170 1.15616 0.578080 0.815980i \(-0.303802\pi\)
0.578080 + 0.815980i \(0.303802\pi\)
\(252\) 2.42404 0.152700
\(253\) −1.19895 −0.0753771
\(254\) 14.0797 0.883439
\(255\) −12.4538 −0.779889
\(256\) 1.00000 0.0625000
\(257\) 23.3720 1.45791 0.728953 0.684564i \(-0.240007\pi\)
0.728953 + 0.684564i \(0.240007\pi\)
\(258\) 5.20075 0.323785
\(259\) 6.50415 0.404148
\(260\) 10.1119 0.627111
\(261\) −18.8457 −1.16652
\(262\) 19.4452 1.20133
\(263\) 15.2298 0.939110 0.469555 0.882903i \(-0.344414\pi\)
0.469555 + 0.882903i \(0.344414\pi\)
\(264\) 2.43156 0.149652
\(265\) 10.5030 0.645192
\(266\) 8.27462 0.507349
\(267\) −28.5692 −1.74841
\(268\) 1.81145 0.110652
\(269\) 24.5727 1.49822 0.749111 0.662445i \(-0.230481\pi\)
0.749111 + 0.662445i \(0.230481\pi\)
\(270\) −4.33387 −0.263751
\(271\) 0.531606 0.0322928 0.0161464 0.999870i \(-0.494860\pi\)
0.0161464 + 0.999870i \(0.494860\pi\)
\(272\) −3.04073 −0.184371
\(273\) 15.2307 0.921805
\(274\) 3.66236 0.221251
\(275\) 1.75622 0.105904
\(276\) −2.43671 −0.146673
\(277\) 7.11143 0.427284 0.213642 0.976912i \(-0.431467\pi\)
0.213642 + 0.976912i \(0.431467\pi\)
\(278\) −8.43371 −0.505820
\(279\) −6.08048 −0.364029
\(280\) −2.29989 −0.137445
\(281\) 4.33769 0.258765 0.129383 0.991595i \(-0.458700\pi\)
0.129383 + 0.991595i \(0.458700\pi\)
\(282\) 7.73303 0.460495
\(283\) −2.76378 −0.164289 −0.0821447 0.996620i \(-0.526177\pi\)
−0.0821447 + 0.996620i \(0.526177\pi\)
\(284\) −1.19425 −0.0708659
\(285\) 27.1486 1.60814
\(286\) 6.00331 0.354983
\(287\) 4.68187 0.276362
\(288\) 1.94184 0.114424
\(289\) −7.75397 −0.456116
\(290\) 17.8805 1.04998
\(291\) 10.1779 0.596638
\(292\) 1.38065 0.0807962
\(293\) 21.5468 1.25878 0.629390 0.777090i \(-0.283305\pi\)
0.629390 + 0.777090i \(0.283305\pi\)
\(294\) 12.0970 0.705513
\(295\) −12.1959 −0.710072
\(296\) 5.21032 0.302844
\(297\) −2.57297 −0.149299
\(298\) −23.6461 −1.36978
\(299\) −6.01602 −0.347915
\(300\) 3.56930 0.206074
\(301\) −2.92043 −0.168331
\(302\) 13.2692 0.763554
\(303\) 24.4910 1.40697
\(304\) 6.62860 0.380176
\(305\) 3.57759 0.204852
\(306\) −5.90462 −0.337544
\(307\) 26.9463 1.53791 0.768953 0.639306i \(-0.220778\pi\)
0.768953 + 0.639306i \(0.220778\pi\)
\(308\) −1.36542 −0.0778020
\(309\) 25.5878 1.45564
\(310\) 5.76906 0.327660
\(311\) 14.0062 0.794218 0.397109 0.917771i \(-0.370013\pi\)
0.397109 + 0.917771i \(0.370013\pi\)
\(312\) 12.2010 0.690744
\(313\) 4.91789 0.277976 0.138988 0.990294i \(-0.455615\pi\)
0.138988 + 0.990294i \(0.455615\pi\)
\(314\) −3.20259 −0.180733
\(315\) −4.46602 −0.251632
\(316\) −9.55379 −0.537442
\(317\) −17.5254 −0.984326 −0.492163 0.870503i \(-0.663794\pi\)
−0.492163 + 0.870503i \(0.663794\pi\)
\(318\) 12.6729 0.710659
\(319\) 10.6155 0.594352
\(320\) −1.84239 −0.102993
\(321\) −23.5933 −1.31685
\(322\) 1.36831 0.0762530
\(323\) −20.1558 −1.12150
\(324\) −11.0548 −0.614154
\(325\) 8.81230 0.488818
\(326\) 8.37302 0.463739
\(327\) −23.1112 −1.27805
\(328\) 3.75054 0.207089
\(329\) −4.34241 −0.239405
\(330\) −4.47988 −0.246609
\(331\) 22.9977 1.26407 0.632035 0.774940i \(-0.282220\pi\)
0.632035 + 0.774940i \(0.282220\pi\)
\(332\) 12.4170 0.681473
\(333\) 10.1176 0.554443
\(334\) 3.94105 0.215645
\(335\) −3.33739 −0.182341
\(336\) −2.77505 −0.151391
\(337\) −6.95431 −0.378825 −0.189413 0.981898i \(-0.560658\pi\)
−0.189413 + 0.981898i \(0.560658\pi\)
\(338\) 17.1231 0.931375
\(339\) 12.6316 0.686054
\(340\) 5.60220 0.303822
\(341\) 3.42503 0.185476
\(342\) 12.8717 0.696022
\(343\) −15.5312 −0.838607
\(344\) −2.33949 −0.126137
\(345\) 4.48936 0.241699
\(346\) −17.8769 −0.961071
\(347\) 2.71917 0.145973 0.0729863 0.997333i \(-0.476747\pi\)
0.0729863 + 0.997333i \(0.476747\pi\)
\(348\) 21.5746 1.15652
\(349\) 6.57908 0.352170 0.176085 0.984375i \(-0.443657\pi\)
0.176085 + 0.984375i \(0.443657\pi\)
\(350\) −2.00431 −0.107135
\(351\) −12.9105 −0.689114
\(352\) −1.09381 −0.0583001
\(353\) −17.9575 −0.955781 −0.477891 0.878419i \(-0.658598\pi\)
−0.477891 + 0.878419i \(0.658598\pi\)
\(354\) −14.7156 −0.782123
\(355\) 2.20028 0.116779
\(356\) 12.8515 0.681128
\(357\) 8.43816 0.446595
\(358\) 25.2144 1.33262
\(359\) −7.51102 −0.396416 −0.198208 0.980160i \(-0.563512\pi\)
−0.198208 + 0.980160i \(0.563512\pi\)
\(360\) −3.57763 −0.188558
\(361\) 24.9384 1.31255
\(362\) −24.1061 −1.26699
\(363\) 21.7936 1.14387
\(364\) −6.85134 −0.359108
\(365\) −2.54368 −0.133143
\(366\) 4.31672 0.225639
\(367\) 20.6962 1.08033 0.540166 0.841558i \(-0.318361\pi\)
0.540166 + 0.841558i \(0.318361\pi\)
\(368\) 1.09612 0.0571393
\(369\) 7.28296 0.379136
\(370\) −9.59944 −0.499051
\(371\) −7.11633 −0.369462
\(372\) 6.96095 0.360908
\(373\) −1.02232 −0.0529338 −0.0264669 0.999650i \(-0.508426\pi\)
−0.0264669 + 0.999650i \(0.508426\pi\)
\(374\) 3.32597 0.171982
\(375\) −27.0544 −1.39708
\(376\) −3.47861 −0.179395
\(377\) 53.2658 2.74333
\(378\) 2.93644 0.151034
\(379\) −27.1713 −1.39570 −0.697848 0.716246i \(-0.745859\pi\)
−0.697848 + 0.716246i \(0.745859\pi\)
\(380\) −12.2125 −0.626486
\(381\) −31.2995 −1.60352
\(382\) −2.26690 −0.115985
\(383\) −4.14476 −0.211787 −0.105894 0.994377i \(-0.533770\pi\)
−0.105894 + 0.994377i \(0.533770\pi\)
\(384\) −2.22303 −0.113443
\(385\) 2.51563 0.128209
\(386\) −19.5256 −0.993826
\(387\) −4.54293 −0.230930
\(388\) −4.57839 −0.232433
\(389\) −16.3646 −0.829721 −0.414860 0.909885i \(-0.636170\pi\)
−0.414860 + 0.909885i \(0.636170\pi\)
\(390\) −22.4789 −1.13826
\(391\) −3.33301 −0.168558
\(392\) −5.44170 −0.274847
\(393\) −43.2271 −2.18052
\(394\) 22.9860 1.15802
\(395\) 17.6018 0.885642
\(396\) −2.12400 −0.106735
\(397\) 23.8452 1.19676 0.598379 0.801213i \(-0.295812\pi\)
0.598379 + 0.801213i \(0.295812\pi\)
\(398\) 12.1639 0.609721
\(399\) −18.3947 −0.920886
\(400\) −1.60561 −0.0802803
\(401\) 13.7293 0.685610 0.342805 0.939407i \(-0.388623\pi\)
0.342805 + 0.939407i \(0.388623\pi\)
\(402\) −4.02690 −0.200843
\(403\) 17.1860 0.856094
\(404\) −11.0170 −0.548116
\(405\) 20.3672 1.01205
\(406\) −12.1150 −0.601259
\(407\) −5.69909 −0.282493
\(408\) 6.75962 0.334651
\(409\) 13.6374 0.674324 0.337162 0.941447i \(-0.390533\pi\)
0.337162 + 0.941447i \(0.390533\pi\)
\(410\) −6.90995 −0.341258
\(411\) −8.14151 −0.401591
\(412\) −11.5103 −0.567073
\(413\) 8.26339 0.406615
\(414\) 2.12850 0.104610
\(415\) −22.8770 −1.12299
\(416\) −5.48845 −0.269094
\(417\) 18.7484 0.918111
\(418\) −7.25041 −0.354629
\(419\) 12.3966 0.605612 0.302806 0.953052i \(-0.402077\pi\)
0.302806 + 0.953052i \(0.402077\pi\)
\(420\) 5.11271 0.249475
\(421\) 28.9782 1.41231 0.706156 0.708057i \(-0.250428\pi\)
0.706156 + 0.708057i \(0.250428\pi\)
\(422\) −11.0249 −0.536685
\(423\) −6.75491 −0.328435
\(424\) −5.70073 −0.276852
\(425\) 4.88221 0.236822
\(426\) 2.65486 0.128628
\(427\) −2.42402 −0.117306
\(428\) 10.6131 0.513005
\(429\) −13.3455 −0.644327
\(430\) 4.31025 0.207859
\(431\) −41.1783 −1.98349 −0.991746 0.128221i \(-0.959073\pi\)
−0.991746 + 0.128221i \(0.959073\pi\)
\(432\) 2.35231 0.113176
\(433\) 13.6220 0.654634 0.327317 0.944915i \(-0.393856\pi\)
0.327317 + 0.944915i \(0.393856\pi\)
\(434\) −3.90885 −0.187631
\(435\) −39.7488 −1.90581
\(436\) 10.3963 0.497891
\(437\) 7.26576 0.347568
\(438\) −3.06921 −0.146653
\(439\) −17.6779 −0.843718 −0.421859 0.906661i \(-0.638622\pi\)
−0.421859 + 0.906661i \(0.638622\pi\)
\(440\) 2.01522 0.0960717
\(441\) −10.5669 −0.503187
\(442\) 16.6889 0.793810
\(443\) −1.29910 −0.0617223 −0.0308612 0.999524i \(-0.509825\pi\)
−0.0308612 + 0.999524i \(0.509825\pi\)
\(444\) −11.5827 −0.549690
\(445\) −23.6774 −1.12242
\(446\) −21.8149 −1.03296
\(447\) 52.5660 2.48628
\(448\) 1.24832 0.0589776
\(449\) 3.37641 0.159342 0.0796712 0.996821i \(-0.474613\pi\)
0.0796712 + 0.996821i \(0.474613\pi\)
\(450\) −3.11784 −0.146976
\(451\) −4.10236 −0.193173
\(452\) −5.68217 −0.267267
\(453\) −29.4977 −1.38592
\(454\) 23.4640 1.10122
\(455\) 12.6228 0.591768
\(456\) −14.7356 −0.690056
\(457\) 41.0130 1.91851 0.959254 0.282544i \(-0.0911783\pi\)
0.959254 + 0.282544i \(0.0911783\pi\)
\(458\) −8.00993 −0.374279
\(459\) −7.15274 −0.333861
\(460\) −2.01948 −0.0941588
\(461\) 32.2201 1.50064 0.750320 0.661075i \(-0.229899\pi\)
0.750320 + 0.661075i \(0.229899\pi\)
\(462\) 3.03536 0.141218
\(463\) −19.7940 −0.919903 −0.459951 0.887944i \(-0.652133\pi\)
−0.459951 + 0.887944i \(0.652133\pi\)
\(464\) −9.70507 −0.450547
\(465\) −12.8248 −0.594734
\(466\) 14.4560 0.669659
\(467\) 3.15870 0.146167 0.0730835 0.997326i \(-0.476716\pi\)
0.0730835 + 0.997326i \(0.476716\pi\)
\(468\) −10.6577 −0.492653
\(469\) 2.26127 0.104416
\(470\) 6.40894 0.295623
\(471\) 7.11945 0.328047
\(472\) 6.61961 0.304692
\(473\) 2.55895 0.117661
\(474\) 21.2383 0.975508
\(475\) −10.6429 −0.488331
\(476\) −3.79580 −0.173980
\(477\) −11.0699 −0.506857
\(478\) 5.47930 0.250617
\(479\) 17.8792 0.816921 0.408460 0.912776i \(-0.366066\pi\)
0.408460 + 0.912776i \(0.366066\pi\)
\(480\) 4.09568 0.186941
\(481\) −28.5966 −1.30389
\(482\) 22.0387 1.00384
\(483\) −3.04179 −0.138406
\(484\) −9.80359 −0.445618
\(485\) 8.43517 0.383022
\(486\) 17.5181 0.794638
\(487\) 30.7020 1.39124 0.695621 0.718409i \(-0.255129\pi\)
0.695621 + 0.718409i \(0.255129\pi\)
\(488\) −1.94182 −0.0879022
\(489\) −18.6134 −0.841728
\(490\) 10.0257 0.452916
\(491\) −14.9541 −0.674870 −0.337435 0.941349i \(-0.609559\pi\)
−0.337435 + 0.941349i \(0.609559\pi\)
\(492\) −8.33754 −0.375885
\(493\) 29.5105 1.32909
\(494\) −36.3808 −1.63685
\(495\) 3.91323 0.175887
\(496\) −3.13129 −0.140599
\(497\) −1.49081 −0.0668720
\(498\) −27.6034 −1.23694
\(499\) 15.6608 0.701074 0.350537 0.936549i \(-0.385999\pi\)
0.350537 + 0.936549i \(0.385999\pi\)
\(500\) 12.1701 0.544263
\(501\) −8.76106 −0.391415
\(502\) 18.3170 0.817528
\(503\) −15.0646 −0.671697 −0.335849 0.941916i \(-0.609023\pi\)
−0.335849 + 0.941916i \(0.609023\pi\)
\(504\) 2.42404 0.107975
\(505\) 20.2976 0.903230
\(506\) −1.19895 −0.0532996
\(507\) −38.0651 −1.69053
\(508\) 14.0797 0.624686
\(509\) −26.4750 −1.17348 −0.586742 0.809774i \(-0.699590\pi\)
−0.586742 + 0.809774i \(0.699590\pi\)
\(510\) −12.4538 −0.551465
\(511\) 1.72349 0.0762426
\(512\) 1.00000 0.0441942
\(513\) 15.5925 0.688427
\(514\) 23.3720 1.03090
\(515\) 21.2065 0.934470
\(516\) 5.20075 0.228950
\(517\) 3.80492 0.167340
\(518\) 6.50415 0.285776
\(519\) 39.7409 1.74443
\(520\) 10.1119 0.443434
\(521\) 9.39227 0.411483 0.205741 0.978606i \(-0.434039\pi\)
0.205741 + 0.978606i \(0.434039\pi\)
\(522\) −18.8457 −0.824855
\(523\) −17.7326 −0.775390 −0.387695 0.921788i \(-0.626729\pi\)
−0.387695 + 0.921788i \(0.626729\pi\)
\(524\) 19.4452 0.849466
\(525\) 4.45563 0.194460
\(526\) 15.2298 0.664051
\(527\) 9.52141 0.414759
\(528\) 2.43156 0.105820
\(529\) −21.7985 −0.947762
\(530\) 10.5030 0.456219
\(531\) 12.8542 0.557826
\(532\) 8.27462 0.358750
\(533\) −20.5847 −0.891620
\(534\) −28.5692 −1.23631
\(535\) −19.5535 −0.845372
\(536\) 1.81145 0.0782426
\(537\) −56.0522 −2.41883
\(538\) 24.5727 1.05940
\(539\) 5.95217 0.256378
\(540\) −4.33387 −0.186500
\(541\) −10.4151 −0.447779 −0.223889 0.974615i \(-0.571875\pi\)
−0.223889 + 0.974615i \(0.571875\pi\)
\(542\) 0.531606 0.0228344
\(543\) 53.5885 2.29970
\(544\) −3.04073 −0.130370
\(545\) −19.1540 −0.820466
\(546\) 15.2307 0.651814
\(547\) 9.90374 0.423454 0.211727 0.977329i \(-0.432091\pi\)
0.211727 + 0.977329i \(0.432091\pi\)
\(548\) 3.66236 0.156448
\(549\) −3.77071 −0.160930
\(550\) 1.75622 0.0748856
\(551\) −64.3311 −2.74060
\(552\) −2.43671 −0.103713
\(553\) −11.9262 −0.507153
\(554\) 7.11143 0.302136
\(555\) 21.3398 0.905824
\(556\) −8.43371 −0.357669
\(557\) 8.02786 0.340152 0.170076 0.985431i \(-0.445599\pi\)
0.170076 + 0.985431i \(0.445599\pi\)
\(558\) −6.08048 −0.257407
\(559\) 12.8402 0.543082
\(560\) −2.29989 −0.0971880
\(561\) −7.39371 −0.312163
\(562\) 4.33769 0.182974
\(563\) 26.2504 1.10632 0.553161 0.833074i \(-0.313421\pi\)
0.553161 + 0.833074i \(0.313421\pi\)
\(564\) 7.73303 0.325619
\(565\) 10.4688 0.440424
\(566\) −2.76378 −0.116170
\(567\) −13.7999 −0.579541
\(568\) −1.19425 −0.0501098
\(569\) −14.3068 −0.599773 −0.299887 0.953975i \(-0.596949\pi\)
−0.299887 + 0.953975i \(0.596949\pi\)
\(570\) 27.1486 1.13713
\(571\) −19.3018 −0.807757 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(572\) 6.00331 0.251011
\(573\) 5.03937 0.210523
\(574\) 4.68187 0.195418
\(575\) −1.75994 −0.0733946
\(576\) 1.94184 0.0809101
\(577\) −23.5231 −0.979281 −0.489640 0.871924i \(-0.662872\pi\)
−0.489640 + 0.871924i \(0.662872\pi\)
\(578\) −7.75397 −0.322523
\(579\) 43.4059 1.80389
\(580\) 17.8805 0.742448
\(581\) 15.5004 0.643066
\(582\) 10.1779 0.421887
\(583\) 6.23550 0.258248
\(584\) 1.38065 0.0571315
\(585\) 19.6356 0.811834
\(586\) 21.5468 0.890092
\(587\) −13.4255 −0.554130 −0.277065 0.960851i \(-0.589362\pi\)
−0.277065 + 0.960851i \(0.589362\pi\)
\(588\) 12.0970 0.498873
\(589\) −20.7561 −0.855240
\(590\) −12.1959 −0.502097
\(591\) −51.0985 −2.10191
\(592\) 5.21032 0.214143
\(593\) 39.7617 1.63282 0.816408 0.577476i \(-0.195962\pi\)
0.816408 + 0.577476i \(0.195962\pi\)
\(594\) −2.57297 −0.105570
\(595\) 6.99334 0.286699
\(596\) −23.6461 −0.968583
\(597\) −27.0407 −1.10670
\(598\) −6.01602 −0.246013
\(599\) 6.80413 0.278009 0.139005 0.990292i \(-0.455610\pi\)
0.139005 + 0.990292i \(0.455610\pi\)
\(600\) 3.56930 0.145716
\(601\) −7.62747 −0.311131 −0.155565 0.987826i \(-0.549720\pi\)
−0.155565 + 0.987826i \(0.549720\pi\)
\(602\) −2.92043 −0.119028
\(603\) 3.51755 0.143246
\(604\) 13.2692 0.539914
\(605\) 18.0620 0.734325
\(606\) 24.4910 0.994881
\(607\) 28.2126 1.14512 0.572558 0.819864i \(-0.305951\pi\)
0.572558 + 0.819864i \(0.305951\pi\)
\(608\) 6.62860 0.268825
\(609\) 26.9320 1.09134
\(610\) 3.57759 0.144852
\(611\) 19.0922 0.772387
\(612\) −5.90462 −0.238680
\(613\) 12.2578 0.495087 0.247544 0.968877i \(-0.420377\pi\)
0.247544 + 0.968877i \(0.420377\pi\)
\(614\) 26.9463 1.08746
\(615\) 15.3610 0.619415
\(616\) −1.36542 −0.0550143
\(617\) 0.151590 0.00610280 0.00305140 0.999995i \(-0.499029\pi\)
0.00305140 + 0.999995i \(0.499029\pi\)
\(618\) 25.5878 1.02929
\(619\) 25.5565 1.02720 0.513600 0.858030i \(-0.328311\pi\)
0.513600 + 0.858030i \(0.328311\pi\)
\(620\) 5.76906 0.231691
\(621\) 2.57842 0.103468
\(622\) 14.0062 0.561597
\(623\) 16.0428 0.642740
\(624\) 12.2010 0.488430
\(625\) −14.3940 −0.575760
\(626\) 4.91789 0.196558
\(627\) 16.1178 0.643685
\(628\) −3.20259 −0.127797
\(629\) −15.8432 −0.631709
\(630\) −4.46602 −0.177931
\(631\) −20.4424 −0.813798 −0.406899 0.913473i \(-0.633390\pi\)
−0.406899 + 0.913473i \(0.633390\pi\)
\(632\) −9.55379 −0.380029
\(633\) 24.5087 0.974134
\(634\) −17.5254 −0.696024
\(635\) −25.9403 −1.02941
\(636\) 12.6729 0.502512
\(637\) 29.8665 1.18335
\(638\) 10.6155 0.420270
\(639\) −2.31905 −0.0917403
\(640\) −1.84239 −0.0728268
\(641\) 23.8005 0.940064 0.470032 0.882649i \(-0.344242\pi\)
0.470032 + 0.882649i \(0.344242\pi\)
\(642\) −23.5933 −0.931152
\(643\) 35.6219 1.40479 0.702395 0.711787i \(-0.252114\pi\)
0.702395 + 0.711787i \(0.252114\pi\)
\(644\) 1.36831 0.0539190
\(645\) −9.58180 −0.377283
\(646\) −20.1558 −0.793019
\(647\) 32.4220 1.27464 0.637320 0.770599i \(-0.280043\pi\)
0.637320 + 0.770599i \(0.280043\pi\)
\(648\) −11.0548 −0.434273
\(649\) −7.24057 −0.284217
\(650\) 8.81230 0.345647
\(651\) 8.68948 0.340568
\(652\) 8.37302 0.327913
\(653\) 44.4779 1.74055 0.870277 0.492563i \(-0.163940\pi\)
0.870277 + 0.492563i \(0.163940\pi\)
\(654\) −23.1112 −0.903719
\(655\) −35.8255 −1.39982
\(656\) 3.75054 0.146434
\(657\) 2.68100 0.104596
\(658\) −4.34241 −0.169285
\(659\) 33.5473 1.30682 0.653409 0.757005i \(-0.273338\pi\)
0.653409 + 0.757005i \(0.273338\pi\)
\(660\) −4.47988 −0.174379
\(661\) 3.24064 0.126046 0.0630232 0.998012i \(-0.479926\pi\)
0.0630232 + 0.998012i \(0.479926\pi\)
\(662\) 22.9977 0.893832
\(663\) −37.0998 −1.44084
\(664\) 12.4170 0.481874
\(665\) −15.2451 −0.591178
\(666\) 10.1176 0.392050
\(667\) −10.6379 −0.411903
\(668\) 3.94105 0.152484
\(669\) 48.4950 1.87493
\(670\) −3.33739 −0.128935
\(671\) 2.12398 0.0819953
\(672\) −2.77505 −0.107050
\(673\) 7.17893 0.276727 0.138364 0.990381i \(-0.455816\pi\)
0.138364 + 0.990381i \(0.455816\pi\)
\(674\) −6.95431 −0.267870
\(675\) −3.77689 −0.145372
\(676\) 17.1231 0.658582
\(677\) 18.8176 0.723219 0.361609 0.932330i \(-0.382227\pi\)
0.361609 + 0.932330i \(0.382227\pi\)
\(678\) 12.6316 0.485114
\(679\) −5.71530 −0.219333
\(680\) 5.60220 0.214835
\(681\) −52.1612 −1.99882
\(682\) 3.42503 0.131151
\(683\) 18.4604 0.706369 0.353185 0.935554i \(-0.385099\pi\)
0.353185 + 0.935554i \(0.385099\pi\)
\(684\) 12.8717 0.492162
\(685\) −6.74748 −0.257808
\(686\) −15.5312 −0.592985
\(687\) 17.8063 0.679352
\(688\) −2.33949 −0.0891923
\(689\) 31.2882 1.19199
\(690\) 4.48936 0.170907
\(691\) −44.3311 −1.68643 −0.843217 0.537573i \(-0.819341\pi\)
−0.843217 + 0.537573i \(0.819341\pi\)
\(692\) −17.8769 −0.679580
\(693\) −2.65143 −0.100720
\(694\) 2.71917 0.103218
\(695\) 15.5382 0.589396
\(696\) 21.5746 0.817784
\(697\) −11.4044 −0.431971
\(698\) 6.57908 0.249022
\(699\) −32.1360 −1.21549
\(700\) −2.00431 −0.0757558
\(701\) 4.26690 0.161159 0.0805793 0.996748i \(-0.474323\pi\)
0.0805793 + 0.996748i \(0.474323\pi\)
\(702\) −12.9105 −0.487277
\(703\) 34.5372 1.30259
\(704\) −1.09381 −0.0412244
\(705\) −14.2472 −0.536582
\(706\) −17.9575 −0.675839
\(707\) −13.7527 −0.517224
\(708\) −14.7156 −0.553044
\(709\) 45.5587 1.71099 0.855497 0.517808i \(-0.173252\pi\)
0.855497 + 0.517808i \(0.173252\pi\)
\(710\) 2.20028 0.0825750
\(711\) −18.5520 −0.695753
\(712\) 12.8515 0.481630
\(713\) −3.43228 −0.128540
\(714\) 8.43816 0.315790
\(715\) −11.0604 −0.413636
\(716\) 25.2144 0.942306
\(717\) −12.1806 −0.454893
\(718\) −7.51102 −0.280309
\(719\) −38.0007 −1.41719 −0.708593 0.705617i \(-0.750670\pi\)
−0.708593 + 0.705617i \(0.750670\pi\)
\(720\) −3.57763 −0.133330
\(721\) −14.3686 −0.535113
\(722\) 24.9384 0.928111
\(723\) −48.9927 −1.82206
\(724\) −24.1061 −0.895896
\(725\) 15.5825 0.578720
\(726\) 21.7936 0.808837
\(727\) −52.7677 −1.95704 −0.978522 0.206142i \(-0.933909\pi\)
−0.978522 + 0.206142i \(0.933909\pi\)
\(728\) −6.85134 −0.253928
\(729\) −5.77890 −0.214033
\(730\) −2.54368 −0.0941460
\(731\) 7.11376 0.263112
\(732\) 4.31672 0.159551
\(733\) 20.5213 0.757970 0.378985 0.925403i \(-0.376273\pi\)
0.378985 + 0.925403i \(0.376273\pi\)
\(734\) 20.6962 0.763911
\(735\) −22.2874 −0.822084
\(736\) 1.09612 0.0404036
\(737\) −1.98137 −0.0729848
\(738\) 7.28296 0.268089
\(739\) −10.4308 −0.383705 −0.191852 0.981424i \(-0.561449\pi\)
−0.191852 + 0.981424i \(0.561449\pi\)
\(740\) −9.59944 −0.352882
\(741\) 80.8754 2.97103
\(742\) −7.11633 −0.261249
\(743\) −50.2175 −1.84230 −0.921151 0.389206i \(-0.872750\pi\)
−0.921151 + 0.389206i \(0.872750\pi\)
\(744\) 6.96095 0.255201
\(745\) 43.5653 1.59611
\(746\) −1.02232 −0.0374299
\(747\) 24.1119 0.882209
\(748\) 3.32597 0.121609
\(749\) 13.2486 0.484093
\(750\) −27.0544 −0.987888
\(751\) 15.7490 0.574688 0.287344 0.957827i \(-0.407228\pi\)
0.287344 + 0.957827i \(0.407228\pi\)
\(752\) −3.47861 −0.126852
\(753\) −40.7192 −1.48389
\(754\) 53.2658 1.93983
\(755\) −24.4469 −0.889715
\(756\) 2.93644 0.106797
\(757\) −18.5723 −0.675023 −0.337512 0.941321i \(-0.609585\pi\)
−0.337512 + 0.941321i \(0.609585\pi\)
\(758\) −27.1713 −0.986906
\(759\) 2.66529 0.0967438
\(760\) −12.2125 −0.442992
\(761\) −11.0537 −0.400698 −0.200349 0.979725i \(-0.564208\pi\)
−0.200349 + 0.979725i \(0.564208\pi\)
\(762\) −31.2995 −1.13386
\(763\) 12.9779 0.469830
\(764\) −2.26690 −0.0820135
\(765\) 10.8786 0.393316
\(766\) −4.14476 −0.149756
\(767\) −36.3314 −1.31185
\(768\) −2.22303 −0.0802165
\(769\) −8.33985 −0.300743 −0.150371 0.988630i \(-0.548047\pi\)
−0.150371 + 0.988630i \(0.548047\pi\)
\(770\) 2.51563 0.0906571
\(771\) −51.9566 −1.87117
\(772\) −19.5256 −0.702741
\(773\) 44.4344 1.59819 0.799096 0.601203i \(-0.205312\pi\)
0.799096 + 0.601203i \(0.205312\pi\)
\(774\) −4.54293 −0.163292
\(775\) 5.02763 0.180598
\(776\) −4.57839 −0.164355
\(777\) −14.4589 −0.518710
\(778\) −16.3646 −0.586701
\(779\) 24.8608 0.890732
\(780\) −22.4789 −0.804875
\(781\) 1.30628 0.0467425
\(782\) −3.33301 −0.119188
\(783\) −22.8293 −0.815854
\(784\) −5.44170 −0.194346
\(785\) 5.90042 0.210595
\(786\) −43.2271 −1.54186
\(787\) 18.2782 0.651548 0.325774 0.945448i \(-0.394375\pi\)
0.325774 + 0.945448i \(0.394375\pi\)
\(788\) 22.9860 0.818842
\(789\) −33.8563 −1.20531
\(790\) 17.6018 0.626243
\(791\) −7.09316 −0.252204
\(792\) −2.12400 −0.0754731
\(793\) 10.6576 0.378463
\(794\) 23.8452 0.846235
\(795\) −23.3483 −0.828080
\(796\) 12.1639 0.431138
\(797\) 12.5359 0.444045 0.222022 0.975042i \(-0.428734\pi\)
0.222022 + 0.975042i \(0.428734\pi\)
\(798\) −18.3947 −0.651165
\(799\) 10.5775 0.374205
\(800\) −1.60561 −0.0567668
\(801\) 24.9556 0.881762
\(802\) 13.7293 0.484799
\(803\) −1.51016 −0.0532924
\(804\) −4.02690 −0.142018
\(805\) −2.52096 −0.0888521
\(806\) 17.1860 0.605350
\(807\) −54.6257 −1.92291
\(808\) −11.0170 −0.387576
\(809\) −26.5633 −0.933915 −0.466957 0.884280i \(-0.654650\pi\)
−0.466957 + 0.884280i \(0.654650\pi\)
\(810\) 20.3672 0.715630
\(811\) −10.4591 −0.367270 −0.183635 0.982994i \(-0.558786\pi\)
−0.183635 + 0.982994i \(0.558786\pi\)
\(812\) −12.1150 −0.425154
\(813\) −1.18177 −0.0414466
\(814\) −5.69909 −0.199753
\(815\) −15.4263 −0.540361
\(816\) 6.75962 0.236634
\(817\) −15.5076 −0.542541
\(818\) 13.6374 0.476819
\(819\) −13.3042 −0.464888
\(820\) −6.90995 −0.241306
\(821\) −38.3478 −1.33835 −0.669175 0.743105i \(-0.733352\pi\)
−0.669175 + 0.743105i \(0.733352\pi\)
\(822\) −8.14151 −0.283968
\(823\) 16.6549 0.580552 0.290276 0.956943i \(-0.406253\pi\)
0.290276 + 0.956943i \(0.406253\pi\)
\(824\) −11.5103 −0.400981
\(825\) −3.90413 −0.135924
\(826\) 8.26339 0.287520
\(827\) −12.6346 −0.439347 −0.219673 0.975573i \(-0.570499\pi\)
−0.219673 + 0.975573i \(0.570499\pi\)
\(828\) 2.12850 0.0739704
\(829\) 5.97838 0.207638 0.103819 0.994596i \(-0.466894\pi\)
0.103819 + 0.994596i \(0.466894\pi\)
\(830\) −22.8770 −0.794072
\(831\) −15.8089 −0.548404
\(832\) −5.48845 −0.190278
\(833\) 16.5467 0.573310
\(834\) 18.7484 0.649202
\(835\) −7.26094 −0.251275
\(836\) −7.25041 −0.250761
\(837\) −7.36577 −0.254598
\(838\) 12.3966 0.428232
\(839\) −51.7914 −1.78804 −0.894019 0.448030i \(-0.852126\pi\)
−0.894019 + 0.448030i \(0.852126\pi\)
\(840\) 5.11271 0.176405
\(841\) 65.1884 2.24788
\(842\) 28.9782 0.998655
\(843\) −9.64280 −0.332116
\(844\) −11.0249 −0.379494
\(845\) −31.5474 −1.08526
\(846\) −6.75491 −0.232239
\(847\) −12.2380 −0.420503
\(848\) −5.70073 −0.195764
\(849\) 6.14395 0.210860
\(850\) 4.88221 0.167459
\(851\) 5.71115 0.195776
\(852\) 2.65486 0.0909539
\(853\) 20.9895 0.718667 0.359333 0.933209i \(-0.383004\pi\)
0.359333 + 0.933209i \(0.383004\pi\)
\(854\) −2.42402 −0.0829481
\(855\) −23.7147 −0.811025
\(856\) 10.6131 0.362749
\(857\) 6.19696 0.211684 0.105842 0.994383i \(-0.466246\pi\)
0.105842 + 0.994383i \(0.466246\pi\)
\(858\) −13.3455 −0.455608
\(859\) 18.2766 0.623589 0.311794 0.950150i \(-0.399070\pi\)
0.311794 + 0.950150i \(0.399070\pi\)
\(860\) 4.31025 0.146978
\(861\) −10.4079 −0.354701
\(862\) −41.1783 −1.40254
\(863\) −57.2359 −1.94833 −0.974166 0.225835i \(-0.927489\pi\)
−0.974166 + 0.225835i \(0.927489\pi\)
\(864\) 2.35231 0.0800272
\(865\) 32.9363 1.11987
\(866\) 13.6220 0.462896
\(867\) 17.2373 0.585409
\(868\) −3.90885 −0.132675
\(869\) 10.4500 0.354492
\(870\) −39.7488 −1.34761
\(871\) −9.94205 −0.336873
\(872\) 10.3963 0.352062
\(873\) −8.89052 −0.300898
\(874\) 7.26576 0.245768
\(875\) 15.1922 0.513589
\(876\) −3.06921 −0.103699
\(877\) −24.0244 −0.811248 −0.405624 0.914040i \(-0.632946\pi\)
−0.405624 + 0.914040i \(0.632946\pi\)
\(878\) −17.6779 −0.596599
\(879\) −47.8992 −1.61560
\(880\) 2.01522 0.0679329
\(881\) −2.27997 −0.0768141 −0.0384071 0.999262i \(-0.512228\pi\)
−0.0384071 + 0.999262i \(0.512228\pi\)
\(882\) −10.5669 −0.355807
\(883\) 30.1165 1.01350 0.506750 0.862093i \(-0.330847\pi\)
0.506750 + 0.862093i \(0.330847\pi\)
\(884\) 16.6889 0.561308
\(885\) 27.1118 0.911352
\(886\) −1.29910 −0.0436443
\(887\) 4.08912 0.137299 0.0686496 0.997641i \(-0.478131\pi\)
0.0686496 + 0.997641i \(0.478131\pi\)
\(888\) −11.5827 −0.388689
\(889\) 17.5760 0.589479
\(890\) −23.6774 −0.793669
\(891\) 12.0918 0.405090
\(892\) −21.8149 −0.730416
\(893\) −23.0583 −0.771617
\(894\) 52.5660 1.75807
\(895\) −46.4547 −1.55281
\(896\) 1.24832 0.0417034
\(897\) 13.3738 0.446537
\(898\) 3.37641 0.112672
\(899\) 30.3894 1.01354
\(900\) −3.11784 −0.103928
\(901\) 17.3344 0.577492
\(902\) −4.10236 −0.136594
\(903\) 6.49220 0.216047
\(904\) −5.68217 −0.188986
\(905\) 44.4128 1.47633
\(906\) −29.4977 −0.979995
\(907\) −28.6341 −0.950780 −0.475390 0.879775i \(-0.657693\pi\)
−0.475390 + 0.879775i \(0.657693\pi\)
\(908\) 23.4640 0.778682
\(909\) −21.3933 −0.709569
\(910\) 12.6228 0.418443
\(911\) −9.73535 −0.322546 −0.161273 0.986910i \(-0.551560\pi\)
−0.161273 + 0.986910i \(0.551560\pi\)
\(912\) −14.7356 −0.487943
\(913\) −13.5818 −0.449493
\(914\) 41.0130 1.35659
\(915\) −7.95308 −0.262921
\(916\) −8.00993 −0.264655
\(917\) 24.2738 0.801591
\(918\) −7.15274 −0.236075
\(919\) −48.4606 −1.59857 −0.799285 0.600953i \(-0.794788\pi\)
−0.799285 + 0.600953i \(0.794788\pi\)
\(920\) −2.01948 −0.0665804
\(921\) −59.9023 −1.97385
\(922\) 32.2201 1.06111
\(923\) 6.55460 0.215747
\(924\) 3.03536 0.0998561
\(925\) −8.36573 −0.275063
\(926\) −19.7940 −0.650470
\(927\) −22.3513 −0.734111
\(928\) −9.70507 −0.318585
\(929\) −14.2020 −0.465953 −0.232977 0.972482i \(-0.574847\pi\)
−0.232977 + 0.972482i \(0.574847\pi\)
\(930\) −12.8248 −0.420540
\(931\) −36.0709 −1.18217
\(932\) 14.4560 0.473521
\(933\) −31.1361 −1.01935
\(934\) 3.15870 0.103356
\(935\) −6.12772 −0.200398
\(936\) −10.6577 −0.348358
\(937\) −51.0903 −1.66905 −0.834523 0.550972i \(-0.814257\pi\)
−0.834523 + 0.550972i \(0.814257\pi\)
\(938\) 2.26127 0.0738330
\(939\) −10.9326 −0.356772
\(940\) 6.40894 0.209037
\(941\) −42.9275 −1.39940 −0.699699 0.714438i \(-0.746683\pi\)
−0.699699 + 0.714438i \(0.746683\pi\)
\(942\) 7.11945 0.231964
\(943\) 4.11105 0.133874
\(944\) 6.61961 0.215450
\(945\) −5.41005 −0.175989
\(946\) 2.55895 0.0831987
\(947\) −41.7163 −1.35560 −0.677798 0.735248i \(-0.737066\pi\)
−0.677798 + 0.735248i \(0.737066\pi\)
\(948\) 21.2383 0.689788
\(949\) −7.57761 −0.245980
\(950\) −10.6429 −0.345302
\(951\) 38.9595 1.26335
\(952\) −3.79580 −0.123023
\(953\) −33.4503 −1.08356 −0.541781 0.840519i \(-0.682250\pi\)
−0.541781 + 0.840519i \(0.682250\pi\)
\(954\) −11.0699 −0.358402
\(955\) 4.17651 0.135149
\(956\) 5.47930 0.177213
\(957\) −23.5985 −0.762830
\(958\) 17.8792 0.577650
\(959\) 4.57179 0.147631
\(960\) 4.09568 0.132187
\(961\) −21.1950 −0.683710
\(962\) −28.5966 −0.921992
\(963\) 20.6090 0.664117
\(964\) 22.0387 0.709820
\(965\) 35.9737 1.15803
\(966\) −3.04179 −0.0978680
\(967\) −35.2559 −1.13375 −0.566877 0.823802i \(-0.691849\pi\)
−0.566877 + 0.823802i \(0.691849\pi\)
\(968\) −9.80359 −0.315099
\(969\) 44.8068 1.43940
\(970\) 8.43517 0.270837
\(971\) −10.4410 −0.335066 −0.167533 0.985866i \(-0.553580\pi\)
−0.167533 + 0.985866i \(0.553580\pi\)
\(972\) 17.5181 0.561894
\(973\) −10.5280 −0.337511
\(974\) 30.7020 0.983757
\(975\) −19.5900 −0.627381
\(976\) −1.94182 −0.0621562
\(977\) 33.7498 1.07975 0.539877 0.841744i \(-0.318471\pi\)
0.539877 + 0.841744i \(0.318471\pi\)
\(978\) −18.6134 −0.595192
\(979\) −14.0570 −0.449265
\(980\) 10.0257 0.320260
\(981\) 20.1879 0.644551
\(982\) −14.9541 −0.477205
\(983\) −15.4362 −0.492339 −0.246170 0.969227i \(-0.579172\pi\)
−0.246170 + 0.969227i \(0.579172\pi\)
\(984\) −8.33754 −0.265791
\(985\) −42.3491 −1.34936
\(986\) 29.5105 0.939805
\(987\) 9.65329 0.307268
\(988\) −36.3808 −1.15743
\(989\) −2.56437 −0.0815422
\(990\) 3.91323 0.124371
\(991\) 29.4620 0.935890 0.467945 0.883758i \(-0.344995\pi\)
0.467945 + 0.883758i \(0.344995\pi\)
\(992\) −3.13129 −0.0994187
\(993\) −51.1245 −1.62239
\(994\) −1.49081 −0.0472856
\(995\) −22.4106 −0.710465
\(996\) −27.6034 −0.874647
\(997\) 40.9987 1.29844 0.649220 0.760600i \(-0.275095\pi\)
0.649220 + 0.760600i \(0.275095\pi\)
\(998\) 15.6608 0.495734
\(999\) 12.2563 0.387772
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 8002.2.a.g.1.16 95
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.g.1.16 95 1.1 even 1 trivial