Properties

Label 8002.2.a.e.1.25
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $0$
Dimension $77$
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: \(77\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.22439 q^{3} +1.00000 q^{4} -0.248249 q^{5} +1.22439 q^{6} +4.32372 q^{7} -1.00000 q^{8} -1.50087 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.22439 q^{3} +1.00000 q^{4} -0.248249 q^{5} +1.22439 q^{6} +4.32372 q^{7} -1.00000 q^{8} -1.50087 q^{9} +0.248249 q^{10} -3.72248 q^{11} -1.22439 q^{12} +3.31452 q^{13} -4.32372 q^{14} +0.303954 q^{15} +1.00000 q^{16} +4.48677 q^{17} +1.50087 q^{18} -1.51739 q^{19} -0.248249 q^{20} -5.29393 q^{21} +3.72248 q^{22} +6.11286 q^{23} +1.22439 q^{24} -4.93837 q^{25} -3.31452 q^{26} +5.51082 q^{27} +4.32372 q^{28} +7.04693 q^{29} -0.303954 q^{30} +1.22406 q^{31} -1.00000 q^{32} +4.55777 q^{33} -4.48677 q^{34} -1.07336 q^{35} -1.50087 q^{36} +4.45284 q^{37} +1.51739 q^{38} -4.05826 q^{39} +0.248249 q^{40} +1.02518 q^{41} +5.29393 q^{42} -12.1218 q^{43} -3.72248 q^{44} +0.372589 q^{45} -6.11286 q^{46} +11.9160 q^{47} -1.22439 q^{48} +11.6946 q^{49} +4.93837 q^{50} -5.49356 q^{51} +3.31452 q^{52} -8.22284 q^{53} -5.51082 q^{54} +0.924103 q^{55} -4.32372 q^{56} +1.85787 q^{57} -7.04693 q^{58} +5.21389 q^{59} +0.303954 q^{60} -9.22447 q^{61} -1.22406 q^{62} -6.48934 q^{63} +1.00000 q^{64} -0.822825 q^{65} -4.55777 q^{66} -8.76845 q^{67} +4.48677 q^{68} -7.48453 q^{69} +1.07336 q^{70} +5.36999 q^{71} +1.50087 q^{72} -0.386914 q^{73} -4.45284 q^{74} +6.04650 q^{75} -1.51739 q^{76} -16.0950 q^{77} +4.05826 q^{78} +1.57570 q^{79} -0.248249 q^{80} -2.24479 q^{81} -1.02518 q^{82} -1.96103 q^{83} -5.29393 q^{84} -1.11384 q^{85} +12.1218 q^{86} -8.62820 q^{87} +3.72248 q^{88} +0.276183 q^{89} -0.372589 q^{90} +14.3311 q^{91} +6.11286 q^{92} -1.49873 q^{93} -11.9160 q^{94} +0.376690 q^{95} +1.22439 q^{96} -1.72988 q^{97} -11.6946 q^{98} +5.58695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 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
\(3\) −1.22439 −0.706902 −0.353451 0.935453i \(-0.614992\pi\)
−0.353451 + 0.935453i \(0.614992\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.248249 −0.111020 −0.0555102 0.998458i \(-0.517679\pi\)
−0.0555102 + 0.998458i \(0.517679\pi\)
\(6\) 1.22439 0.499855
\(7\) 4.32372 1.63421 0.817107 0.576486i \(-0.195577\pi\)
0.817107 + 0.576486i \(0.195577\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.50087 −0.500289
\(10\) 0.248249 0.0785032
\(11\) −3.72248 −1.12237 −0.561185 0.827690i \(-0.689655\pi\)
−0.561185 + 0.827690i \(0.689655\pi\)
\(12\) −1.22439 −0.353451
\(13\) 3.31452 0.919282 0.459641 0.888105i \(-0.347978\pi\)
0.459641 + 0.888105i \(0.347978\pi\)
\(14\) −4.32372 −1.15556
\(15\) 0.303954 0.0784805
\(16\) 1.00000 0.250000
\(17\) 4.48677 1.08820 0.544101 0.839020i \(-0.316871\pi\)
0.544101 + 0.839020i \(0.316871\pi\)
\(18\) 1.50087 0.353758
\(19\) −1.51739 −0.348112 −0.174056 0.984736i \(-0.555687\pi\)
−0.174056 + 0.984736i \(0.555687\pi\)
\(20\) −0.248249 −0.0555102
\(21\) −5.29393 −1.15523
\(22\) 3.72248 0.793636
\(23\) 6.11286 1.27462 0.637310 0.770608i \(-0.280047\pi\)
0.637310 + 0.770608i \(0.280047\pi\)
\(24\) 1.22439 0.249928
\(25\) −4.93837 −0.987674
\(26\) −3.31452 −0.650030
\(27\) 5.51082 1.06056
\(28\) 4.32372 0.817107
\(29\) 7.04693 1.30858 0.654291 0.756243i \(-0.272967\pi\)
0.654291 + 0.756243i \(0.272967\pi\)
\(30\) −0.303954 −0.0554941
\(31\) 1.22406 0.219848 0.109924 0.993940i \(-0.464939\pi\)
0.109924 + 0.993940i \(0.464939\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.55777 0.793407
\(34\) −4.48677 −0.769475
\(35\) −1.07336 −0.181431
\(36\) −1.50087 −0.250145
\(37\) 4.45284 0.732043 0.366022 0.930606i \(-0.380720\pi\)
0.366022 + 0.930606i \(0.380720\pi\)
\(38\) 1.51739 0.246153
\(39\) −4.05826 −0.649842
\(40\) 0.248249 0.0392516
\(41\) 1.02518 0.160107 0.0800533 0.996791i \(-0.474491\pi\)
0.0800533 + 0.996791i \(0.474491\pi\)
\(42\) 5.29393 0.816871
\(43\) −12.1218 −1.84856 −0.924281 0.381713i \(-0.875334\pi\)
−0.924281 + 0.381713i \(0.875334\pi\)
\(44\) −3.72248 −0.561185
\(45\) 0.372589 0.0555423
\(46\) −6.11286 −0.901292
\(47\) 11.9160 1.73813 0.869064 0.494700i \(-0.164722\pi\)
0.869064 + 0.494700i \(0.164722\pi\)
\(48\) −1.22439 −0.176726
\(49\) 11.6946 1.67065
\(50\) 4.93837 0.698391
\(51\) −5.49356 −0.769252
\(52\) 3.31452 0.459641
\(53\) −8.22284 −1.12949 −0.564747 0.825264i \(-0.691026\pi\)
−0.564747 + 0.825264i \(0.691026\pi\)
\(54\) −5.51082 −0.749928
\(55\) 0.924103 0.124606
\(56\) −4.32372 −0.577782
\(57\) 1.85787 0.246081
\(58\) −7.04693 −0.925308
\(59\) 5.21389 0.678791 0.339395 0.940644i \(-0.389778\pi\)
0.339395 + 0.940644i \(0.389778\pi\)
\(60\) 0.303954 0.0392403
\(61\) −9.22447 −1.18107 −0.590536 0.807011i \(-0.701084\pi\)
−0.590536 + 0.807011i \(0.701084\pi\)
\(62\) −1.22406 −0.155456
\(63\) −6.48934 −0.817580
\(64\) 1.00000 0.125000
\(65\) −0.822825 −0.102059
\(66\) −4.55777 −0.561023
\(67\) −8.76845 −1.07124 −0.535618 0.844460i \(-0.679921\pi\)
−0.535618 + 0.844460i \(0.679921\pi\)
\(68\) 4.48677 0.544101
\(69\) −7.48453 −0.901032
\(70\) 1.07336 0.128291
\(71\) 5.36999 0.637300 0.318650 0.947872i \(-0.396770\pi\)
0.318650 + 0.947872i \(0.396770\pi\)
\(72\) 1.50087 0.176879
\(73\) −0.386914 −0.0452849 −0.0226424 0.999744i \(-0.507208\pi\)
−0.0226424 + 0.999744i \(0.507208\pi\)
\(74\) −4.45284 −0.517633
\(75\) 6.04650 0.698189
\(76\) −1.51739 −0.174056
\(77\) −16.0950 −1.83419
\(78\) 4.05826 0.459508
\(79\) 1.57570 0.177280 0.0886398 0.996064i \(-0.471748\pi\)
0.0886398 + 0.996064i \(0.471748\pi\)
\(80\) −0.248249 −0.0277551
\(81\) −2.24479 −0.249421
\(82\) −1.02518 −0.113212
\(83\) −1.96103 −0.215251 −0.107625 0.994192i \(-0.534325\pi\)
−0.107625 + 0.994192i \(0.534325\pi\)
\(84\) −5.29393 −0.577615
\(85\) −1.11384 −0.120812
\(86\) 12.1218 1.30713
\(87\) −8.62820 −0.925040
\(88\) 3.72248 0.396818
\(89\) 0.276183 0.0292754 0.0146377 0.999893i \(-0.495341\pi\)
0.0146377 + 0.999893i \(0.495341\pi\)
\(90\) −0.372589 −0.0392743
\(91\) 14.3311 1.50230
\(92\) 6.11286 0.637310
\(93\) −1.49873 −0.155411
\(94\) −11.9160 −1.22904
\(95\) 0.376690 0.0386475
\(96\) 1.22439 0.124964
\(97\) −1.72988 −0.175643 −0.0878216 0.996136i \(-0.527991\pi\)
−0.0878216 + 0.996136i \(0.527991\pi\)
\(98\) −11.6946 −1.18133
\(99\) 5.58695 0.561510
\(100\) −4.93837 −0.493837
\(101\) 16.4714 1.63897 0.819484 0.573102i \(-0.194260\pi\)
0.819484 + 0.573102i \(0.194260\pi\)
\(102\) 5.49356 0.543943
\(103\) 13.3695 1.31733 0.658667 0.752435i \(-0.271121\pi\)
0.658667 + 0.752435i \(0.271121\pi\)
\(104\) −3.31452 −0.325015
\(105\) 1.31421 0.128254
\(106\) 8.22284 0.798673
\(107\) −11.6495 −1.12620 −0.563098 0.826390i \(-0.690390\pi\)
−0.563098 + 0.826390i \(0.690390\pi\)
\(108\) 5.51082 0.530279
\(109\) 11.4514 1.09685 0.548423 0.836201i \(-0.315228\pi\)
0.548423 + 0.836201i \(0.315228\pi\)
\(110\) −0.924103 −0.0881097
\(111\) −5.45202 −0.517483
\(112\) 4.32372 0.408553
\(113\) 16.3565 1.53869 0.769344 0.638835i \(-0.220583\pi\)
0.769344 + 0.638835i \(0.220583\pi\)
\(114\) −1.85787 −0.174006
\(115\) −1.51751 −0.141509
\(116\) 7.04693 0.654291
\(117\) −4.97465 −0.459907
\(118\) −5.21389 −0.479978
\(119\) 19.3996 1.77835
\(120\) −0.303954 −0.0277470
\(121\) 2.85688 0.259716
\(122\) 9.22447 0.835144
\(123\) −1.25522 −0.113180
\(124\) 1.22406 0.109924
\(125\) 2.46719 0.220672
\(126\) 6.48934 0.578116
\(127\) 15.0082 1.33176 0.665882 0.746057i \(-0.268055\pi\)
0.665882 + 0.746057i \(0.268055\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 14.8419 1.30675
\(130\) 0.822825 0.0721666
\(131\) 5.86352 0.512298 0.256149 0.966637i \(-0.417546\pi\)
0.256149 + 0.966637i \(0.417546\pi\)
\(132\) 4.55777 0.396703
\(133\) −6.56076 −0.568890
\(134\) 8.76845 0.757479
\(135\) −1.36806 −0.117743
\(136\) −4.48677 −0.384737
\(137\) −15.9745 −1.36479 −0.682395 0.730983i \(-0.739062\pi\)
−0.682395 + 0.730983i \(0.739062\pi\)
\(138\) 7.48453 0.637126
\(139\) −15.9939 −1.35658 −0.678291 0.734793i \(-0.737279\pi\)
−0.678291 + 0.734793i \(0.737279\pi\)
\(140\) −1.07336 −0.0907155
\(141\) −14.5898 −1.22869
\(142\) −5.36999 −0.450639
\(143\) −12.3382 −1.03177
\(144\) −1.50087 −0.125072
\(145\) −1.74939 −0.145279
\(146\) 0.386914 0.0320212
\(147\) −14.3187 −1.18099
\(148\) 4.45284 0.366022
\(149\) −22.3966 −1.83480 −0.917399 0.397968i \(-0.869716\pi\)
−0.917399 + 0.397968i \(0.869716\pi\)
\(150\) −6.04650 −0.493694
\(151\) 19.1383 1.55745 0.778727 0.627363i \(-0.215866\pi\)
0.778727 + 0.627363i \(0.215866\pi\)
\(152\) 1.51739 0.123076
\(153\) −6.73405 −0.544416
\(154\) 16.0950 1.29697
\(155\) −0.303872 −0.0244076
\(156\) −4.05826 −0.324921
\(157\) −23.6945 −1.89102 −0.945512 0.325588i \(-0.894438\pi\)
−0.945512 + 0.325588i \(0.894438\pi\)
\(158\) −1.57570 −0.125356
\(159\) 10.0680 0.798442
\(160\) 0.248249 0.0196258
\(161\) 26.4303 2.08300
\(162\) 2.24479 0.176368
\(163\) −0.879204 −0.0688646 −0.0344323 0.999407i \(-0.510962\pi\)
−0.0344323 + 0.999407i \(0.510962\pi\)
\(164\) 1.02518 0.0800533
\(165\) −1.13146 −0.0880842
\(166\) 1.96103 0.152205
\(167\) −11.6716 −0.903177 −0.451588 0.892226i \(-0.649142\pi\)
−0.451588 + 0.892226i \(0.649142\pi\)
\(168\) 5.29393 0.408435
\(169\) −2.01398 −0.154921
\(170\) 1.11384 0.0854273
\(171\) 2.27740 0.174157
\(172\) −12.1218 −0.924281
\(173\) 7.76573 0.590417 0.295209 0.955433i \(-0.404611\pi\)
0.295209 + 0.955433i \(0.404611\pi\)
\(174\) 8.62820 0.654102
\(175\) −21.3522 −1.61407
\(176\) −3.72248 −0.280593
\(177\) −6.38384 −0.479839
\(178\) −0.276183 −0.0207008
\(179\) 17.2220 1.28723 0.643616 0.765348i \(-0.277433\pi\)
0.643616 + 0.765348i \(0.277433\pi\)
\(180\) 0.372589 0.0277711
\(181\) −11.3054 −0.840321 −0.420161 0.907450i \(-0.638026\pi\)
−0.420161 + 0.907450i \(0.638026\pi\)
\(182\) −14.3311 −1.06229
\(183\) 11.2943 0.834902
\(184\) −6.11286 −0.450646
\(185\) −1.10541 −0.0812716
\(186\) 1.49873 0.109892
\(187\) −16.7019 −1.22137
\(188\) 11.9160 0.869064
\(189\) 23.8273 1.73318
\(190\) −0.376690 −0.0273279
\(191\) 8.44189 0.610834 0.305417 0.952219i \(-0.401204\pi\)
0.305417 + 0.952219i \(0.401204\pi\)
\(192\) −1.22439 −0.0883628
\(193\) 4.44258 0.319784 0.159892 0.987135i \(-0.448885\pi\)
0.159892 + 0.987135i \(0.448885\pi\)
\(194\) 1.72988 0.124198
\(195\) 1.00746 0.0721457
\(196\) 11.6946 0.835327
\(197\) 6.69132 0.476736 0.238368 0.971175i \(-0.423387\pi\)
0.238368 + 0.971175i \(0.423387\pi\)
\(198\) −5.58695 −0.397048
\(199\) −12.3570 −0.875964 −0.437982 0.898984i \(-0.644307\pi\)
−0.437982 + 0.898984i \(0.644307\pi\)
\(200\) 4.93837 0.349196
\(201\) 10.7360 0.757260
\(202\) −16.4714 −1.15893
\(203\) 30.4690 2.13850
\(204\) −5.49356 −0.384626
\(205\) −0.254500 −0.0177751
\(206\) −13.3695 −0.931495
\(207\) −9.17460 −0.637679
\(208\) 3.31452 0.229820
\(209\) 5.64844 0.390711
\(210\) −1.31421 −0.0906892
\(211\) 10.2881 0.708261 0.354131 0.935196i \(-0.384777\pi\)
0.354131 + 0.935196i \(0.384777\pi\)
\(212\) −8.22284 −0.564747
\(213\) −6.57496 −0.450509
\(214\) 11.6495 0.796340
\(215\) 3.00923 0.205228
\(216\) −5.51082 −0.374964
\(217\) 5.29251 0.359279
\(218\) −11.4514 −0.775587
\(219\) 0.473734 0.0320120
\(220\) 0.924103 0.0623030
\(221\) 14.8715 1.00036
\(222\) 5.45202 0.365916
\(223\) 11.2371 0.752490 0.376245 0.926520i \(-0.377215\pi\)
0.376245 + 0.926520i \(0.377215\pi\)
\(224\) −4.32372 −0.288891
\(225\) 7.41184 0.494123
\(226\) −16.3565 −1.08802
\(227\) −5.84329 −0.387833 −0.193916 0.981018i \(-0.562119\pi\)
−0.193916 + 0.981018i \(0.562119\pi\)
\(228\) 1.85787 0.123041
\(229\) 24.3768 1.61087 0.805433 0.592687i \(-0.201933\pi\)
0.805433 + 0.592687i \(0.201933\pi\)
\(230\) 1.51751 0.100062
\(231\) 19.7066 1.29660
\(232\) −7.04693 −0.462654
\(233\) −0.658244 −0.0431230 −0.0215615 0.999768i \(-0.506864\pi\)
−0.0215615 + 0.999768i \(0.506864\pi\)
\(234\) 4.97465 0.325203
\(235\) −2.95814 −0.192967
\(236\) 5.21389 0.339395
\(237\) −1.92927 −0.125319
\(238\) −19.3996 −1.25749
\(239\) 20.6017 1.33261 0.666305 0.745679i \(-0.267875\pi\)
0.666305 + 0.745679i \(0.267875\pi\)
\(240\) 0.303954 0.0196201
\(241\) −10.4957 −0.676090 −0.338045 0.941130i \(-0.609766\pi\)
−0.338045 + 0.941130i \(0.609766\pi\)
\(242\) −2.85688 −0.183647
\(243\) −13.7840 −0.884241
\(244\) −9.22447 −0.590536
\(245\) −2.90317 −0.185477
\(246\) 1.25522 0.0800301
\(247\) −5.02940 −0.320013
\(248\) −1.22406 −0.0777281
\(249\) 2.40106 0.152161
\(250\) −2.46719 −0.156039
\(251\) −27.7384 −1.75083 −0.875416 0.483369i \(-0.839413\pi\)
−0.875416 + 0.483369i \(0.839413\pi\)
\(252\) −6.48934 −0.408790
\(253\) −22.7550 −1.43060
\(254\) −15.0082 −0.941699
\(255\) 1.36377 0.0854026
\(256\) 1.00000 0.0625000
\(257\) −19.7192 −1.23005 −0.615024 0.788509i \(-0.710854\pi\)
−0.615024 + 0.788509i \(0.710854\pi\)
\(258\) −14.8419 −0.924013
\(259\) 19.2529 1.19631
\(260\) −0.822825 −0.0510295
\(261\) −10.5765 −0.654670
\(262\) −5.86352 −0.362250
\(263\) −21.9558 −1.35385 −0.676925 0.736052i \(-0.736688\pi\)
−0.676925 + 0.736052i \(0.736688\pi\)
\(264\) −4.55777 −0.280512
\(265\) 2.04131 0.125397
\(266\) 6.56076 0.402266
\(267\) −0.338156 −0.0206948
\(268\) −8.76845 −0.535618
\(269\) 22.8909 1.39568 0.697842 0.716252i \(-0.254144\pi\)
0.697842 + 0.716252i \(0.254144\pi\)
\(270\) 1.36806 0.0832572
\(271\) −10.7632 −0.653820 −0.326910 0.945056i \(-0.606007\pi\)
−0.326910 + 0.945056i \(0.606007\pi\)
\(272\) 4.48677 0.272050
\(273\) −17.5468 −1.06198
\(274\) 15.9745 0.965053
\(275\) 18.3830 1.10854
\(276\) −7.48453 −0.450516
\(277\) 1.48199 0.0890444 0.0445222 0.999008i \(-0.485823\pi\)
0.0445222 + 0.999008i \(0.485823\pi\)
\(278\) 15.9939 0.959248
\(279\) −1.83716 −0.109988
\(280\) 1.07336 0.0641455
\(281\) 18.5237 1.10503 0.552515 0.833503i \(-0.313668\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(282\) 14.5898 0.868813
\(283\) −7.04766 −0.418940 −0.209470 0.977815i \(-0.567174\pi\)
−0.209470 + 0.977815i \(0.567174\pi\)
\(284\) 5.36999 0.318650
\(285\) −0.461215 −0.0273200
\(286\) 12.3382 0.729575
\(287\) 4.43260 0.261648
\(288\) 1.50087 0.0884395
\(289\) 3.13111 0.184183
\(290\) 1.74939 0.102728
\(291\) 2.11805 0.124163
\(292\) −0.386914 −0.0226424
\(293\) 24.4395 1.42777 0.713886 0.700262i \(-0.246933\pi\)
0.713886 + 0.700262i \(0.246933\pi\)
\(294\) 14.3187 0.835086
\(295\) −1.29434 −0.0753596
\(296\) −4.45284 −0.258816
\(297\) −20.5139 −1.19034
\(298\) 22.3966 1.29740
\(299\) 20.2612 1.17173
\(300\) 6.04650 0.349095
\(301\) −52.4114 −3.02094
\(302\) −19.1383 −1.10129
\(303\) −20.1675 −1.15859
\(304\) −1.51739 −0.0870281
\(305\) 2.28996 0.131123
\(306\) 6.73405 0.384960
\(307\) −13.4958 −0.770246 −0.385123 0.922865i \(-0.625841\pi\)
−0.385123 + 0.922865i \(0.625841\pi\)
\(308\) −16.0950 −0.917097
\(309\) −16.3695 −0.931226
\(310\) 0.303872 0.0172588
\(311\) −14.1036 −0.799739 −0.399870 0.916572i \(-0.630945\pi\)
−0.399870 + 0.916572i \(0.630945\pi\)
\(312\) 4.05826 0.229754
\(313\) 17.1577 0.969812 0.484906 0.874566i \(-0.338854\pi\)
0.484906 + 0.874566i \(0.338854\pi\)
\(314\) 23.6945 1.33716
\(315\) 1.61097 0.0907679
\(316\) 1.57570 0.0886398
\(317\) −5.02832 −0.282419 −0.141209 0.989980i \(-0.545099\pi\)
−0.141209 + 0.989980i \(0.545099\pi\)
\(318\) −10.0680 −0.564583
\(319\) −26.2321 −1.46871
\(320\) −0.248249 −0.0138775
\(321\) 14.2635 0.796110
\(322\) −26.4303 −1.47290
\(323\) −6.80816 −0.378816
\(324\) −2.24479 −0.124711
\(325\) −16.3683 −0.907951
\(326\) 0.879204 0.0486946
\(327\) −14.0210 −0.775363
\(328\) −1.02518 −0.0566062
\(329\) 51.5215 2.84047
\(330\) 1.13146 0.0622850
\(331\) −10.9441 −0.601543 −0.300771 0.953696i \(-0.597244\pi\)
−0.300771 + 0.953696i \(0.597244\pi\)
\(332\) −1.96103 −0.107625
\(333\) −6.68313 −0.366233
\(334\) 11.6716 0.638642
\(335\) 2.17676 0.118929
\(336\) −5.29393 −0.288807
\(337\) 8.73457 0.475802 0.237901 0.971289i \(-0.423541\pi\)
0.237901 + 0.971289i \(0.423541\pi\)
\(338\) 2.01398 0.109546
\(339\) −20.0267 −1.08770
\(340\) −1.11384 −0.0604062
\(341\) −4.55655 −0.246751
\(342\) −2.27740 −0.123147
\(343\) 20.2981 1.09599
\(344\) 12.1218 0.653565
\(345\) 1.85803 0.100033
\(346\) −7.76573 −0.417488
\(347\) 29.6761 1.59309 0.796547 0.604577i \(-0.206658\pi\)
0.796547 + 0.604577i \(0.206658\pi\)
\(348\) −8.62820 −0.462520
\(349\) 1.27149 0.0680610 0.0340305 0.999421i \(-0.489166\pi\)
0.0340305 + 0.999421i \(0.489166\pi\)
\(350\) 21.3522 1.14132
\(351\) 18.2657 0.974951
\(352\) 3.72248 0.198409
\(353\) −9.27511 −0.493664 −0.246832 0.969058i \(-0.579390\pi\)
−0.246832 + 0.969058i \(0.579390\pi\)
\(354\) 6.38384 0.339297
\(355\) −1.33309 −0.0707533
\(356\) 0.276183 0.0146377
\(357\) −23.7526 −1.25712
\(358\) −17.2220 −0.910211
\(359\) 17.0690 0.900867 0.450433 0.892810i \(-0.351270\pi\)
0.450433 + 0.892810i \(0.351270\pi\)
\(360\) −0.372589 −0.0196372
\(361\) −16.6975 −0.878818
\(362\) 11.3054 0.594197
\(363\) −3.49794 −0.183594
\(364\) 14.3311 0.751151
\(365\) 0.0960510 0.00502754
\(366\) −11.2943 −0.590365
\(367\) 8.70871 0.454591 0.227296 0.973826i \(-0.427012\pi\)
0.227296 + 0.973826i \(0.427012\pi\)
\(368\) 6.11286 0.318655
\(369\) −1.53866 −0.0800996
\(370\) 1.10541 0.0574677
\(371\) −35.5533 −1.84583
\(372\) −1.49873 −0.0777056
\(373\) 24.9428 1.29149 0.645745 0.763553i \(-0.276547\pi\)
0.645745 + 0.763553i \(0.276547\pi\)
\(374\) 16.7019 0.863636
\(375\) −3.02080 −0.155994
\(376\) −11.9160 −0.614521
\(377\) 23.3572 1.20296
\(378\) −23.8273 −1.22554
\(379\) −23.6900 −1.21687 −0.608437 0.793602i \(-0.708203\pi\)
−0.608437 + 0.793602i \(0.708203\pi\)
\(380\) 0.376690 0.0193238
\(381\) −18.3759 −0.941427
\(382\) −8.44189 −0.431925
\(383\) −4.57618 −0.233832 −0.116916 0.993142i \(-0.537301\pi\)
−0.116916 + 0.993142i \(0.537301\pi\)
\(384\) 1.22439 0.0624819
\(385\) 3.99556 0.203633
\(386\) −4.44258 −0.226121
\(387\) 18.1933 0.924815
\(388\) −1.72988 −0.0878216
\(389\) 0.0324068 0.00164309 0.000821546 1.00000i \(-0.499738\pi\)
0.000821546 1.00000i \(0.499738\pi\)
\(390\) −1.00746 −0.0510147
\(391\) 27.4270 1.38704
\(392\) −11.6946 −0.590666
\(393\) −7.17924 −0.362145
\(394\) −6.69132 −0.337104
\(395\) −0.391165 −0.0196816
\(396\) 5.58695 0.280755
\(397\) −2.85169 −0.143122 −0.0715610 0.997436i \(-0.522798\pi\)
−0.0715610 + 0.997436i \(0.522798\pi\)
\(398\) 12.3570 0.619400
\(399\) 8.03293 0.402150
\(400\) −4.93837 −0.246919
\(401\) 17.5491 0.876362 0.438181 0.898887i \(-0.355623\pi\)
0.438181 + 0.898887i \(0.355623\pi\)
\(402\) −10.7360 −0.535463
\(403\) 4.05718 0.202102
\(404\) 16.4714 0.819484
\(405\) 0.557268 0.0276908
\(406\) −30.4690 −1.51215
\(407\) −16.5756 −0.821624
\(408\) 5.49356 0.271972
\(409\) −2.30656 −0.114052 −0.0570259 0.998373i \(-0.518162\pi\)
−0.0570259 + 0.998373i \(0.518162\pi\)
\(410\) 0.254500 0.0125689
\(411\) 19.5590 0.964773
\(412\) 13.3695 0.658667
\(413\) 22.5434 1.10929
\(414\) 9.17460 0.450907
\(415\) 0.486823 0.0238972
\(416\) −3.31452 −0.162508
\(417\) 19.5827 0.958971
\(418\) −5.64844 −0.276274
\(419\) 11.6974 0.571458 0.285729 0.958310i \(-0.407764\pi\)
0.285729 + 0.958310i \(0.407764\pi\)
\(420\) 1.31421 0.0641270
\(421\) −0.852363 −0.0415416 −0.0207708 0.999784i \(-0.506612\pi\)
−0.0207708 + 0.999784i \(0.506612\pi\)
\(422\) −10.2881 −0.500816
\(423\) −17.8843 −0.869567
\(424\) 8.22284 0.399336
\(425\) −22.1573 −1.07479
\(426\) 6.57496 0.318558
\(427\) −39.8840 −1.93012
\(428\) −11.6495 −0.563098
\(429\) 15.1068 0.729364
\(430\) −3.00923 −0.145118
\(431\) 13.1994 0.635793 0.317897 0.948125i \(-0.397023\pi\)
0.317897 + 0.948125i \(0.397023\pi\)
\(432\) 5.51082 0.265139
\(433\) 0.224106 0.0107698 0.00538492 0.999986i \(-0.498286\pi\)
0.00538492 + 0.999986i \(0.498286\pi\)
\(434\) −5.29251 −0.254049
\(435\) 2.14194 0.102698
\(436\) 11.4514 0.548423
\(437\) −9.27557 −0.443711
\(438\) −0.473734 −0.0226359
\(439\) 0.963307 0.0459761 0.0229881 0.999736i \(-0.492682\pi\)
0.0229881 + 0.999736i \(0.492682\pi\)
\(440\) −0.924103 −0.0440549
\(441\) −17.5520 −0.835811
\(442\) −14.8715 −0.707364
\(443\) 17.3974 0.826575 0.413287 0.910601i \(-0.364381\pi\)
0.413287 + 0.910601i \(0.364381\pi\)
\(444\) −5.45202 −0.258741
\(445\) −0.0685622 −0.00325016
\(446\) −11.2371 −0.532091
\(447\) 27.4222 1.29702
\(448\) 4.32372 0.204277
\(449\) 26.4577 1.24862 0.624309 0.781177i \(-0.285381\pi\)
0.624309 + 0.781177i \(0.285381\pi\)
\(450\) −7.41184 −0.349398
\(451\) −3.81622 −0.179699
\(452\) 16.3565 0.769344
\(453\) −23.4328 −1.10097
\(454\) 5.84329 0.274239
\(455\) −3.55767 −0.166786
\(456\) −1.85787 −0.0870029
\(457\) −3.63016 −0.169812 −0.0849059 0.996389i \(-0.527059\pi\)
−0.0849059 + 0.996389i \(0.527059\pi\)
\(458\) −24.3768 −1.13905
\(459\) 24.7258 1.15410
\(460\) −1.51751 −0.0707543
\(461\) 15.7254 0.732404 0.366202 0.930535i \(-0.380658\pi\)
0.366202 + 0.930535i \(0.380658\pi\)
\(462\) −19.7066 −0.916832
\(463\) −23.0730 −1.07229 −0.536146 0.844125i \(-0.680120\pi\)
−0.536146 + 0.844125i \(0.680120\pi\)
\(464\) 7.04693 0.327146
\(465\) 0.372058 0.0172538
\(466\) 0.658244 0.0304926
\(467\) −13.1775 −0.609780 −0.304890 0.952387i \(-0.598620\pi\)
−0.304890 + 0.952387i \(0.598620\pi\)
\(468\) −4.97465 −0.229953
\(469\) −37.9124 −1.75063
\(470\) 2.95814 0.136449
\(471\) 29.0113 1.33677
\(472\) −5.21389 −0.239989
\(473\) 45.1233 2.07477
\(474\) 1.92927 0.0886142
\(475\) 7.49342 0.343822
\(476\) 19.3996 0.889177
\(477\) 12.3414 0.565074
\(478\) −20.6017 −0.942298
\(479\) 6.21942 0.284173 0.142086 0.989854i \(-0.454619\pi\)
0.142086 + 0.989854i \(0.454619\pi\)
\(480\) −0.303954 −0.0138735
\(481\) 14.7590 0.672954
\(482\) 10.4957 0.478068
\(483\) −32.3610 −1.47248
\(484\) 2.85688 0.129858
\(485\) 0.429442 0.0195000
\(486\) 13.7840 0.625253
\(487\) 9.26111 0.419661 0.209830 0.977738i \(-0.432709\pi\)
0.209830 + 0.977738i \(0.432709\pi\)
\(488\) 9.22447 0.417572
\(489\) 1.07649 0.0486805
\(490\) 2.90317 0.131152
\(491\) 39.7962 1.79598 0.897989 0.440017i \(-0.145028\pi\)
0.897989 + 0.440017i \(0.145028\pi\)
\(492\) −1.25522 −0.0565898
\(493\) 31.6180 1.42400
\(494\) 5.02940 0.226283
\(495\) −1.38696 −0.0623390
\(496\) 1.22406 0.0549620
\(497\) 23.2183 1.04149
\(498\) −2.40106 −0.107594
\(499\) −6.82565 −0.305558 −0.152779 0.988260i \(-0.548822\pi\)
−0.152779 + 0.988260i \(0.548822\pi\)
\(500\) 2.46719 0.110336
\(501\) 14.2906 0.638458
\(502\) 27.7384 1.23803
\(503\) 25.4730 1.13579 0.567893 0.823102i \(-0.307759\pi\)
0.567893 + 0.823102i \(0.307759\pi\)
\(504\) 6.48934 0.289058
\(505\) −4.08901 −0.181959
\(506\) 22.7550 1.01158
\(507\) 2.46590 0.109514
\(508\) 15.0082 0.665882
\(509\) 14.7446 0.653543 0.326772 0.945103i \(-0.394039\pi\)
0.326772 + 0.945103i \(0.394039\pi\)
\(510\) −1.36377 −0.0603888
\(511\) −1.67291 −0.0740051
\(512\) −1.00000 −0.0441942
\(513\) −8.36204 −0.369193
\(514\) 19.7192 0.869775
\(515\) −3.31896 −0.146251
\(516\) 14.8419 0.653376
\(517\) −44.3571 −1.95082
\(518\) −19.2529 −0.845922
\(519\) −9.50828 −0.417367
\(520\) 0.822825 0.0360833
\(521\) 17.1824 0.752776 0.376388 0.926462i \(-0.377166\pi\)
0.376388 + 0.926462i \(0.377166\pi\)
\(522\) 10.5765 0.462921
\(523\) 40.1178 1.75423 0.877115 0.480281i \(-0.159465\pi\)
0.877115 + 0.480281i \(0.159465\pi\)
\(524\) 5.86352 0.256149
\(525\) 26.1434 1.14099
\(526\) 21.9558 0.957317
\(527\) 5.49209 0.239239
\(528\) 4.55777 0.198352
\(529\) 14.3671 0.624656
\(530\) −2.04131 −0.0886689
\(531\) −7.82536 −0.339592
\(532\) −6.56076 −0.284445
\(533\) 3.39798 0.147183
\(534\) 0.338156 0.0146335
\(535\) 2.89196 0.125031
\(536\) 8.76845 0.378739
\(537\) −21.0865 −0.909948
\(538\) −22.8909 −0.986897
\(539\) −43.5329 −1.87509
\(540\) −1.36806 −0.0588717
\(541\) −7.71991 −0.331905 −0.165952 0.986134i \(-0.553070\pi\)
−0.165952 + 0.986134i \(0.553070\pi\)
\(542\) 10.7632 0.462320
\(543\) 13.8422 0.594025
\(544\) −4.48677 −0.192369
\(545\) −2.84280 −0.121772
\(546\) 17.5468 0.750934
\(547\) 29.0251 1.24102 0.620512 0.784197i \(-0.286925\pi\)
0.620512 + 0.784197i \(0.286925\pi\)
\(548\) −15.9745 −0.682395
\(549\) 13.8447 0.590878
\(550\) −18.3830 −0.783854
\(551\) −10.6929 −0.455534
\(552\) 7.48453 0.318563
\(553\) 6.81287 0.289713
\(554\) −1.48199 −0.0629639
\(555\) 1.35346 0.0574511
\(556\) −15.9939 −0.678291
\(557\) −14.3046 −0.606105 −0.303053 0.952974i \(-0.598006\pi\)
−0.303053 + 0.952974i \(0.598006\pi\)
\(558\) 1.83716 0.0777730
\(559\) −40.1780 −1.69935
\(560\) −1.07336 −0.0453577
\(561\) 20.4497 0.863386
\(562\) −18.5237 −0.781374
\(563\) 15.2574 0.643022 0.321511 0.946906i \(-0.395809\pi\)
0.321511 + 0.946906i \(0.395809\pi\)
\(564\) −14.5898 −0.614343
\(565\) −4.06048 −0.170826
\(566\) 7.04766 0.296235
\(567\) −9.70586 −0.407608
\(568\) −5.36999 −0.225320
\(569\) −28.0678 −1.17666 −0.588332 0.808619i \(-0.700215\pi\)
−0.588332 + 0.808619i \(0.700215\pi\)
\(570\) 0.461215 0.0193182
\(571\) 8.96499 0.375173 0.187587 0.982248i \(-0.439933\pi\)
0.187587 + 0.982248i \(0.439933\pi\)
\(572\) −12.3382 −0.515887
\(573\) −10.3362 −0.431800
\(574\) −4.43260 −0.185013
\(575\) −30.1876 −1.25891
\(576\) −1.50087 −0.0625362
\(577\) 12.2395 0.509539 0.254769 0.967002i \(-0.418000\pi\)
0.254769 + 0.967002i \(0.418000\pi\)
\(578\) −3.13111 −0.130237
\(579\) −5.43945 −0.226056
\(580\) −1.74939 −0.0726396
\(581\) −8.47894 −0.351766
\(582\) −2.11805 −0.0877962
\(583\) 30.6094 1.26771
\(584\) 0.386914 0.0160106
\(585\) 1.23495 0.0510590
\(586\) −24.4395 −1.00959
\(587\) 24.7196 1.02029 0.510144 0.860089i \(-0.329592\pi\)
0.510144 + 0.860089i \(0.329592\pi\)
\(588\) −14.3187 −0.590495
\(589\) −1.85738 −0.0765318
\(590\) 1.29434 0.0532873
\(591\) −8.19278 −0.337006
\(592\) 4.45284 0.183011
\(593\) −40.4198 −1.65984 −0.829922 0.557880i \(-0.811615\pi\)
−0.829922 + 0.557880i \(0.811615\pi\)
\(594\) 20.5139 0.841697
\(595\) −4.81592 −0.197433
\(596\) −22.3966 −0.917399
\(597\) 15.1298 0.619221
\(598\) −20.2612 −0.828541
\(599\) −15.4101 −0.629639 −0.314819 0.949152i \(-0.601944\pi\)
−0.314819 + 0.949152i \(0.601944\pi\)
\(600\) −6.04650 −0.246847
\(601\) −22.2557 −0.907830 −0.453915 0.891045i \(-0.649973\pi\)
−0.453915 + 0.891045i \(0.649973\pi\)
\(602\) 52.4114 2.13613
\(603\) 13.1603 0.535928
\(604\) 19.1383 0.778727
\(605\) −0.709218 −0.0288338
\(606\) 20.1675 0.819247
\(607\) −13.2148 −0.536370 −0.268185 0.963367i \(-0.586424\pi\)
−0.268185 + 0.963367i \(0.586424\pi\)
\(608\) 1.51739 0.0615381
\(609\) −37.3059 −1.51171
\(610\) −2.28996 −0.0927179
\(611\) 39.4958 1.59783
\(612\) −6.73405 −0.272208
\(613\) 19.7996 0.799700 0.399850 0.916581i \(-0.369062\pi\)
0.399850 + 0.916581i \(0.369062\pi\)
\(614\) 13.4958 0.544646
\(615\) 0.311608 0.0125652
\(616\) 16.0950 0.648486
\(617\) −11.9802 −0.482304 −0.241152 0.970487i \(-0.577525\pi\)
−0.241152 + 0.970487i \(0.577525\pi\)
\(618\) 16.3695 0.658476
\(619\) 49.0668 1.97216 0.986081 0.166268i \(-0.0531718\pi\)
0.986081 + 0.166268i \(0.0531718\pi\)
\(620\) −0.303872 −0.0122038
\(621\) 33.6869 1.35181
\(622\) 14.1036 0.565501
\(623\) 1.19414 0.0478422
\(624\) −4.05826 −0.162461
\(625\) 24.0794 0.963175
\(626\) −17.1577 −0.685761
\(627\) −6.91590 −0.276195
\(628\) −23.6945 −0.945512
\(629\) 19.9789 0.796611
\(630\) −1.61097 −0.0641826
\(631\) 3.11727 0.124097 0.0620484 0.998073i \(-0.480237\pi\)
0.0620484 + 0.998073i \(0.480237\pi\)
\(632\) −1.57570 −0.0626778
\(633\) −12.5966 −0.500671
\(634\) 5.02832 0.199700
\(635\) −3.72577 −0.147853
\(636\) 10.0680 0.399221
\(637\) 38.7619 1.53580
\(638\) 26.2321 1.03854
\(639\) −8.05964 −0.318835
\(640\) 0.248249 0.00981290
\(641\) 3.41858 0.135026 0.0675128 0.997718i \(-0.478494\pi\)
0.0675128 + 0.997718i \(0.478494\pi\)
\(642\) −14.2635 −0.562935
\(643\) 25.2786 0.996890 0.498445 0.866921i \(-0.333905\pi\)
0.498445 + 0.866921i \(0.333905\pi\)
\(644\) 26.4303 1.04150
\(645\) −3.68447 −0.145076
\(646\) 6.80816 0.267864
\(647\) 10.2230 0.401910 0.200955 0.979601i \(-0.435596\pi\)
0.200955 + 0.979601i \(0.435596\pi\)
\(648\) 2.24479 0.0881838
\(649\) −19.4086 −0.761855
\(650\) 16.3683 0.642018
\(651\) −6.48010 −0.253975
\(652\) −0.879204 −0.0344323
\(653\) 45.8179 1.79299 0.896497 0.443049i \(-0.146103\pi\)
0.896497 + 0.443049i \(0.146103\pi\)
\(654\) 14.0210 0.548264
\(655\) −1.45561 −0.0568755
\(656\) 1.02518 0.0400266
\(657\) 0.580707 0.0226555
\(658\) −51.5215 −2.00852
\(659\) 17.5979 0.685519 0.342759 0.939423i \(-0.388638\pi\)
0.342759 + 0.939423i \(0.388638\pi\)
\(660\) −1.13146 −0.0440421
\(661\) −40.7498 −1.58498 −0.792492 0.609882i \(-0.791217\pi\)
−0.792492 + 0.609882i \(0.791217\pi\)
\(662\) 10.9441 0.425355
\(663\) −18.2085 −0.707159
\(664\) 1.96103 0.0761026
\(665\) 1.62870 0.0631583
\(666\) 6.68313 0.258966
\(667\) 43.0769 1.66795
\(668\) −11.6716 −0.451588
\(669\) −13.7586 −0.531937
\(670\) −2.17676 −0.0840955
\(671\) 34.3379 1.32560
\(672\) 5.29393 0.204218
\(673\) 49.5901 1.91156 0.955778 0.294088i \(-0.0950158\pi\)
0.955778 + 0.294088i \(0.0950158\pi\)
\(674\) −8.73457 −0.336443
\(675\) −27.2145 −1.04749
\(676\) −2.01398 −0.0774607
\(677\) −11.7471 −0.451479 −0.225740 0.974188i \(-0.572480\pi\)
−0.225740 + 0.974188i \(0.572480\pi\)
\(678\) 20.0267 0.769121
\(679\) −7.47954 −0.287038
\(680\) 1.11384 0.0427137
\(681\) 7.15447 0.274160
\(682\) 4.55655 0.174479
\(683\) 8.28016 0.316831 0.158416 0.987373i \(-0.449361\pi\)
0.158416 + 0.987373i \(0.449361\pi\)
\(684\) 2.27740 0.0870784
\(685\) 3.96564 0.151519
\(686\) −20.2981 −0.774984
\(687\) −29.8467 −1.13872
\(688\) −12.1218 −0.462140
\(689\) −27.2547 −1.03832
\(690\) −1.85803 −0.0707339
\(691\) 18.3635 0.698580 0.349290 0.937015i \(-0.386423\pi\)
0.349290 + 0.937015i \(0.386423\pi\)
\(692\) 7.76573 0.295209
\(693\) 24.1564 0.917628
\(694\) −29.6761 −1.12649
\(695\) 3.97046 0.150608
\(696\) 8.62820 0.327051
\(697\) 4.59976 0.174228
\(698\) −1.27149 −0.0481264
\(699\) 0.805947 0.0304837
\(700\) −21.3522 −0.807036
\(701\) 39.5504 1.49380 0.746899 0.664938i \(-0.231542\pi\)
0.746899 + 0.664938i \(0.231542\pi\)
\(702\) −18.2657 −0.689395
\(703\) −6.75668 −0.254833
\(704\) −3.72248 −0.140296
\(705\) 3.62191 0.136409
\(706\) 9.27511 0.349073
\(707\) 71.2179 2.67842
\(708\) −6.38384 −0.239919
\(709\) −46.4479 −1.74439 −0.872193 0.489162i \(-0.837303\pi\)
−0.872193 + 0.489162i \(0.837303\pi\)
\(710\) 1.33309 0.0500301
\(711\) −2.36491 −0.0886911
\(712\) −0.276183 −0.0103504
\(713\) 7.48253 0.280223
\(714\) 23.7526 0.888920
\(715\) 3.06295 0.114548
\(716\) 17.2220 0.643616
\(717\) −25.2245 −0.942026
\(718\) −17.0690 −0.637009
\(719\) 7.80352 0.291022 0.145511 0.989357i \(-0.453517\pi\)
0.145511 + 0.989357i \(0.453517\pi\)
\(720\) 0.372589 0.0138856
\(721\) 57.8059 2.15280
\(722\) 16.6975 0.621418
\(723\) 12.8509 0.477930
\(724\) −11.3054 −0.420161
\(725\) −34.8004 −1.29245
\(726\) 3.49794 0.129821
\(727\) −33.7186 −1.25055 −0.625277 0.780403i \(-0.715014\pi\)
−0.625277 + 0.780403i \(0.715014\pi\)
\(728\) −14.3311 −0.531144
\(729\) 23.6113 0.874494
\(730\) −0.0960510 −0.00355501
\(731\) −54.3879 −2.01161
\(732\) 11.2943 0.417451
\(733\) 3.09009 0.114135 0.0570675 0.998370i \(-0.481825\pi\)
0.0570675 + 0.998370i \(0.481825\pi\)
\(734\) −8.70871 −0.321444
\(735\) 3.55461 0.131114
\(736\) −6.11286 −0.225323
\(737\) 32.6404 1.20233
\(738\) 1.53866 0.0566390
\(739\) 24.3931 0.897313 0.448657 0.893704i \(-0.351903\pi\)
0.448657 + 0.893704i \(0.351903\pi\)
\(740\) −1.10541 −0.0406358
\(741\) 6.15795 0.226218
\(742\) 35.5533 1.30520
\(743\) −9.21427 −0.338039 −0.169019 0.985613i \(-0.554060\pi\)
−0.169019 + 0.985613i \(0.554060\pi\)
\(744\) 1.49873 0.0549461
\(745\) 5.55993 0.203700
\(746\) −24.9428 −0.913222
\(747\) 2.94324 0.107688
\(748\) −16.7019 −0.610683
\(749\) −50.3690 −1.84044
\(750\) 3.02080 0.110304
\(751\) 42.6684 1.55699 0.778496 0.627650i \(-0.215983\pi\)
0.778496 + 0.627650i \(0.215983\pi\)
\(752\) 11.9160 0.434532
\(753\) 33.9626 1.23767
\(754\) −23.3572 −0.850618
\(755\) −4.75106 −0.172909
\(756\) 23.8273 0.866589
\(757\) 24.8955 0.904843 0.452422 0.891804i \(-0.350560\pi\)
0.452422 + 0.891804i \(0.350560\pi\)
\(758\) 23.6900 0.860459
\(759\) 27.8610 1.01129
\(760\) −0.376690 −0.0136640
\(761\) −0.296409 −0.0107448 −0.00537242 0.999986i \(-0.501710\pi\)
−0.00537242 + 0.999986i \(0.501710\pi\)
\(762\) 18.3759 0.665689
\(763\) 49.5127 1.79248
\(764\) 8.44189 0.305417
\(765\) 1.67172 0.0604412
\(766\) 4.57618 0.165344
\(767\) 17.2815 0.624000
\(768\) −1.22439 −0.0441814
\(769\) 38.0258 1.37124 0.685622 0.727958i \(-0.259530\pi\)
0.685622 + 0.727958i \(0.259530\pi\)
\(770\) −3.99556 −0.143990
\(771\) 24.1440 0.869523
\(772\) 4.44258 0.159892
\(773\) −34.7634 −1.25035 −0.625177 0.780483i \(-0.714973\pi\)
−0.625177 + 0.780483i \(0.714973\pi\)
\(774\) −18.1933 −0.653943
\(775\) −6.04488 −0.217138
\(776\) 1.72988 0.0620992
\(777\) −23.5730 −0.845678
\(778\) −0.0324068 −0.00116184
\(779\) −1.55560 −0.0557351
\(780\) 1.00746 0.0360728
\(781\) −19.9897 −0.715287
\(782\) −27.4270 −0.980788
\(783\) 38.8344 1.38783
\(784\) 11.6946 0.417664
\(785\) 5.88212 0.209942
\(786\) 7.17924 0.256075
\(787\) 6.82652 0.243339 0.121670 0.992571i \(-0.461175\pi\)
0.121670 + 0.992571i \(0.461175\pi\)
\(788\) 6.69132 0.238368
\(789\) 26.8824 0.957040
\(790\) 0.391165 0.0139170
\(791\) 70.7208 2.51454
\(792\) −5.58695 −0.198524
\(793\) −30.5746 −1.08574
\(794\) 2.85169 0.101203
\(795\) −2.49936 −0.0886432
\(796\) −12.3570 −0.437982
\(797\) 21.5899 0.764754 0.382377 0.924006i \(-0.375106\pi\)
0.382377 + 0.924006i \(0.375106\pi\)
\(798\) −8.03293 −0.284363
\(799\) 53.4644 1.89143
\(800\) 4.93837 0.174598
\(801\) −0.414515 −0.0146462
\(802\) −17.5491 −0.619681
\(803\) 1.44028 0.0508264
\(804\) 10.7360 0.378630
\(805\) −6.56130 −0.231255
\(806\) −4.05718 −0.142908
\(807\) −28.0274 −0.986612
\(808\) −16.4714 −0.579463
\(809\) −29.9123 −1.05166 −0.525830 0.850590i \(-0.676245\pi\)
−0.525830 + 0.850590i \(0.676245\pi\)
\(810\) −0.557268 −0.0195804
\(811\) −28.7896 −1.01094 −0.505470 0.862844i \(-0.668681\pi\)
−0.505470 + 0.862844i \(0.668681\pi\)
\(812\) 30.4690 1.06925
\(813\) 13.1784 0.462187
\(814\) 16.5756 0.580976
\(815\) 0.218262 0.00764537
\(816\) −5.49356 −0.192313
\(817\) 18.3935 0.643507
\(818\) 2.30656 0.0806469
\(819\) −21.5090 −0.751586
\(820\) −0.254500 −0.00888754
\(821\) −22.8651 −0.797997 −0.398999 0.916952i \(-0.630642\pi\)
−0.398999 + 0.916952i \(0.630642\pi\)
\(822\) −19.5590 −0.682198
\(823\) −6.57694 −0.229258 −0.114629 0.993408i \(-0.536568\pi\)
−0.114629 + 0.993408i \(0.536568\pi\)
\(824\) −13.3695 −0.465748
\(825\) −22.5080 −0.783627
\(826\) −22.5434 −0.784386
\(827\) −25.3271 −0.880708 −0.440354 0.897824i \(-0.645147\pi\)
−0.440354 + 0.897824i \(0.645147\pi\)
\(828\) −9.17460 −0.318839
\(829\) −33.7966 −1.17380 −0.586901 0.809658i \(-0.699652\pi\)
−0.586901 + 0.809658i \(0.699652\pi\)
\(830\) −0.486823 −0.0168979
\(831\) −1.81454 −0.0629457
\(832\) 3.31452 0.114910
\(833\) 52.4709 1.81801
\(834\) −19.5827 −0.678095
\(835\) 2.89747 0.100271
\(836\) 5.64844 0.195356
\(837\) 6.74559 0.233162
\(838\) −11.6974 −0.404082
\(839\) 33.5138 1.15703 0.578513 0.815673i \(-0.303633\pi\)
0.578513 + 0.815673i \(0.303633\pi\)
\(840\) −1.31421 −0.0453446
\(841\) 20.6593 0.712388
\(842\) 0.852363 0.0293744
\(843\) −22.6802 −0.781148
\(844\) 10.2881 0.354131
\(845\) 0.499968 0.0171994
\(846\) 17.8843 0.614876
\(847\) 12.3524 0.424432
\(848\) −8.22284 −0.282373
\(849\) 8.62909 0.296150
\(850\) 22.1573 0.759991
\(851\) 27.2196 0.933077
\(852\) −6.57496 −0.225255
\(853\) −20.5431 −0.703382 −0.351691 0.936116i \(-0.614393\pi\)
−0.351691 + 0.936116i \(0.614393\pi\)
\(854\) 39.8840 1.36480
\(855\) −0.565361 −0.0193349
\(856\) 11.6495 0.398170
\(857\) 1.77537 0.0606453 0.0303227 0.999540i \(-0.490347\pi\)
0.0303227 + 0.999540i \(0.490347\pi\)
\(858\) −15.1068 −0.515738
\(859\) 25.5058 0.870245 0.435123 0.900371i \(-0.356705\pi\)
0.435123 + 0.900371i \(0.356705\pi\)
\(860\) 3.00923 0.102614
\(861\) −5.42724 −0.184960
\(862\) −13.1994 −0.449574
\(863\) −31.4835 −1.07171 −0.535856 0.844309i \(-0.680011\pi\)
−0.535856 + 0.844309i \(0.680011\pi\)
\(864\) −5.51082 −0.187482
\(865\) −1.92783 −0.0655483
\(866\) −0.224106 −0.00761543
\(867\) −3.83371 −0.130199
\(868\) 5.29251 0.179639
\(869\) −5.86550 −0.198973
\(870\) −2.14194 −0.0726186
\(871\) −29.0632 −0.984768
\(872\) −11.4514 −0.387793
\(873\) 2.59633 0.0878724
\(874\) 9.27557 0.313751
\(875\) 10.6674 0.360626
\(876\) 0.473734 0.0160060
\(877\) −39.1735 −1.32279 −0.661397 0.750036i \(-0.730036\pi\)
−0.661397 + 0.750036i \(0.730036\pi\)
\(878\) −0.963307 −0.0325100
\(879\) −29.9235 −1.00930
\(880\) 0.924103 0.0311515
\(881\) 34.6580 1.16766 0.583828 0.811877i \(-0.301554\pi\)
0.583828 + 0.811877i \(0.301554\pi\)
\(882\) 17.5520 0.591007
\(883\) 39.1964 1.31906 0.659532 0.751677i \(-0.270755\pi\)
0.659532 + 0.751677i \(0.270755\pi\)
\(884\) 14.8715 0.500182
\(885\) 1.58478 0.0532718
\(886\) −17.3974 −0.584477
\(887\) 33.3120 1.11851 0.559253 0.828997i \(-0.311088\pi\)
0.559253 + 0.828997i \(0.311088\pi\)
\(888\) 5.45202 0.182958
\(889\) 64.8914 2.17639
\(890\) 0.0685622 0.00229821
\(891\) 8.35620 0.279943
\(892\) 11.2371 0.376245
\(893\) −18.0812 −0.605064
\(894\) −27.4222 −0.917134
\(895\) −4.27534 −0.142909
\(896\) −4.32372 −0.144445
\(897\) −24.8076 −0.828302
\(898\) −26.4577 −0.882906
\(899\) 8.62589 0.287689
\(900\) 7.41184 0.247061
\(901\) −36.8940 −1.22912
\(902\) 3.81622 0.127066
\(903\) 64.1721 2.13551
\(904\) −16.3565 −0.544008
\(905\) 2.80655 0.0932927
\(906\) 23.4328 0.778501
\(907\) 22.4933 0.746878 0.373439 0.927655i \(-0.378178\pi\)
0.373439 + 0.927655i \(0.378178\pi\)
\(908\) −5.84329 −0.193916
\(909\) −24.7214 −0.819958
\(910\) 3.55767 0.117936
\(911\) 12.1245 0.401701 0.200851 0.979622i \(-0.435629\pi\)
0.200851 + 0.979622i \(0.435629\pi\)
\(912\) 1.85787 0.0615203
\(913\) 7.29989 0.241591
\(914\) 3.63016 0.120075
\(915\) −2.80381 −0.0926911
\(916\) 24.3768 0.805433
\(917\) 25.3523 0.837205
\(918\) −24.7258 −0.816073
\(919\) 23.0906 0.761689 0.380845 0.924639i \(-0.375633\pi\)
0.380845 + 0.924639i \(0.375633\pi\)
\(920\) 1.51751 0.0500309
\(921\) 16.5241 0.544489
\(922\) −15.7254 −0.517888
\(923\) 17.7989 0.585859
\(924\) 19.7066 0.648298
\(925\) −21.9898 −0.723020
\(926\) 23.0730 0.758225
\(927\) −20.0658 −0.659048
\(928\) −7.04693 −0.231327
\(929\) 38.6985 1.26966 0.634828 0.772654i \(-0.281071\pi\)
0.634828 + 0.772654i \(0.281071\pi\)
\(930\) −0.372058 −0.0122003
\(931\) −17.7452 −0.581575
\(932\) −0.658244 −0.0215615
\(933\) 17.2683 0.565338
\(934\) 13.1775 0.431180
\(935\) 4.14624 0.135596
\(936\) 4.97465 0.162602
\(937\) −33.4369 −1.09233 −0.546167 0.837676i \(-0.683914\pi\)
−0.546167 + 0.837676i \(0.683914\pi\)
\(938\) 37.9124 1.23788
\(939\) −21.0078 −0.685562
\(940\) −2.95814 −0.0964837
\(941\) −1.60120 −0.0521977 −0.0260988 0.999659i \(-0.508308\pi\)
−0.0260988 + 0.999659i \(0.508308\pi\)
\(942\) −29.0113 −0.945238
\(943\) 6.26680 0.204075
\(944\) 5.21389 0.169698
\(945\) −5.91509 −0.192418
\(946\) −45.1233 −1.46709
\(947\) −22.7702 −0.739932 −0.369966 0.929045i \(-0.620631\pi\)
−0.369966 + 0.929045i \(0.620631\pi\)
\(948\) −1.92927 −0.0626597
\(949\) −1.28243 −0.0416295
\(950\) −7.49342 −0.243119
\(951\) 6.15663 0.199642
\(952\) −19.3996 −0.628743
\(953\) −33.6497 −1.09002 −0.545011 0.838429i \(-0.683475\pi\)
−0.545011 + 0.838429i \(0.683475\pi\)
\(954\) −12.3414 −0.399567
\(955\) −2.09569 −0.0678150
\(956\) 20.6017 0.666305
\(957\) 32.1183 1.03824
\(958\) −6.21942 −0.200940
\(959\) −69.0692 −2.23036
\(960\) 0.303954 0.00981006
\(961\) −29.5017 −0.951667
\(962\) −14.7590 −0.475850
\(963\) 17.4843 0.563423
\(964\) −10.4957 −0.338045
\(965\) −1.10287 −0.0355025
\(966\) 32.3610 1.04120
\(967\) 22.0176 0.708037 0.354019 0.935238i \(-0.384815\pi\)
0.354019 + 0.935238i \(0.384815\pi\)
\(968\) −2.85688 −0.0918236
\(969\) 8.33585 0.267786
\(970\) −0.429442 −0.0137886
\(971\) 44.6273 1.43216 0.716079 0.698019i \(-0.245935\pi\)
0.716079 + 0.698019i \(0.245935\pi\)
\(972\) −13.7840 −0.442121
\(973\) −69.1530 −2.21694
\(974\) −9.26111 −0.296745
\(975\) 20.0412 0.641833
\(976\) −9.22447 −0.295268
\(977\) 27.5899 0.882678 0.441339 0.897340i \(-0.354504\pi\)
0.441339 + 0.897340i \(0.354504\pi\)
\(978\) −1.07649 −0.0344223
\(979\) −1.02809 −0.0328578
\(980\) −2.90317 −0.0927383
\(981\) −17.1870 −0.548740
\(982\) −39.7962 −1.26995
\(983\) 7.57649 0.241652 0.120826 0.992674i \(-0.461446\pi\)
0.120826 + 0.992674i \(0.461446\pi\)
\(984\) 1.25522 0.0400151
\(985\) −1.66111 −0.0529274
\(986\) −31.6180 −1.00692
\(987\) −63.0824 −2.00794
\(988\) −5.02940 −0.160007
\(989\) −74.0991 −2.35621
\(990\) 1.38696 0.0440803
\(991\) 31.2023 0.991174 0.495587 0.868558i \(-0.334953\pi\)
0.495587 + 0.868558i \(0.334953\pi\)
\(992\) −1.22406 −0.0388640
\(993\) 13.3999 0.425232
\(994\) −23.2183 −0.736441
\(995\) 3.06761 0.0972497
\(996\) 2.40106 0.0760806
\(997\) −5.73538 −0.181641 −0.0908207 0.995867i \(-0.528949\pi\)
−0.0908207 + 0.995867i \(0.528949\pi\)
\(998\) 6.82565 0.216062
\(999\) 24.5388 0.776374
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.e.1.25 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.e.1.25 77 1.1 even 1 trivial