Properties

Label 8006.2.a.a.1.1
Level $8006$
Weight $2$
Character 8006.1
Self dual yes
Analytic conductor $63.928$
Analytic rank $1$
Dimension $69$
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] = [8006,2,Mod(1,8006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8006, 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("8006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8006.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: \(63.9282318582\)
Analytic rank: \(1\)
Dimension: \(69\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.36322 q^{3} +1.00000 q^{4} +3.90848 q^{5} -3.36322 q^{6} -1.71915 q^{7} +1.00000 q^{8} +8.31124 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.36322 q^{3} +1.00000 q^{4} +3.90848 q^{5} -3.36322 q^{6} -1.71915 q^{7} +1.00000 q^{8} +8.31124 q^{9} +3.90848 q^{10} -1.66701 q^{11} -3.36322 q^{12} -0.631638 q^{13} -1.71915 q^{14} -13.1451 q^{15} +1.00000 q^{16} +2.65196 q^{17} +8.31124 q^{18} -3.22088 q^{19} +3.90848 q^{20} +5.78186 q^{21} -1.66701 q^{22} +2.00580 q^{23} -3.36322 q^{24} +10.2762 q^{25} -0.631638 q^{26} -17.8629 q^{27} -1.71915 q^{28} -6.75737 q^{29} -13.1451 q^{30} -4.06395 q^{31} +1.00000 q^{32} +5.60653 q^{33} +2.65196 q^{34} -6.71924 q^{35} +8.31124 q^{36} -2.95478 q^{37} -3.22088 q^{38} +2.12434 q^{39} +3.90848 q^{40} +2.41376 q^{41} +5.78186 q^{42} +3.91405 q^{43} -1.66701 q^{44} +32.4843 q^{45} +2.00580 q^{46} -7.79943 q^{47} -3.36322 q^{48} -4.04454 q^{49} +10.2762 q^{50} -8.91911 q^{51} -0.631638 q^{52} -10.4966 q^{53} -17.8629 q^{54} -6.51548 q^{55} -1.71915 q^{56} +10.8325 q^{57} -6.75737 q^{58} -6.59901 q^{59} -13.1451 q^{60} +6.19818 q^{61} -4.06395 q^{62} -14.2882 q^{63} +1.00000 q^{64} -2.46874 q^{65} +5.60653 q^{66} -2.95815 q^{67} +2.65196 q^{68} -6.74593 q^{69} -6.71924 q^{70} +11.4309 q^{71} +8.31124 q^{72} -7.30030 q^{73} -2.95478 q^{74} -34.5611 q^{75} -3.22088 q^{76} +2.86584 q^{77} +2.12434 q^{78} -17.2392 q^{79} +3.90848 q^{80} +35.1431 q^{81} +2.41376 q^{82} +13.7900 q^{83} +5.78186 q^{84} +10.3651 q^{85} +3.91405 q^{86} +22.7265 q^{87} -1.66701 q^{88} +0.657803 q^{89} +32.4843 q^{90} +1.08588 q^{91} +2.00580 q^{92} +13.6680 q^{93} -7.79943 q^{94} -12.5888 q^{95} -3.36322 q^{96} -1.90755 q^{97} -4.04454 q^{98} -13.8549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 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
\(3\) −3.36322 −1.94176 −0.970878 0.239575i \(-0.922992\pi\)
−0.970878 + 0.239575i \(0.922992\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.90848 1.74792 0.873962 0.485994i \(-0.161542\pi\)
0.873962 + 0.485994i \(0.161542\pi\)
\(6\) −3.36322 −1.37303
\(7\) −1.71915 −0.649776 −0.324888 0.945753i \(-0.605327\pi\)
−0.324888 + 0.945753i \(0.605327\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.31124 2.77041
\(10\) 3.90848 1.23597
\(11\) −1.66701 −0.502623 −0.251312 0.967906i \(-0.580862\pi\)
−0.251312 + 0.967906i \(0.580862\pi\)
\(12\) −3.36322 −0.970878
\(13\) −0.631638 −0.175185 −0.0875924 0.996156i \(-0.527917\pi\)
−0.0875924 + 0.996156i \(0.527917\pi\)
\(14\) −1.71915 −0.459461
\(15\) −13.1451 −3.39404
\(16\) 1.00000 0.250000
\(17\) 2.65196 0.643194 0.321597 0.946877i \(-0.395780\pi\)
0.321597 + 0.946877i \(0.395780\pi\)
\(18\) 8.31124 1.95898
\(19\) −3.22088 −0.738922 −0.369461 0.929246i \(-0.620458\pi\)
−0.369461 + 0.929246i \(0.620458\pi\)
\(20\) 3.90848 0.873962
\(21\) 5.78186 1.26171
\(22\) −1.66701 −0.355408
\(23\) 2.00580 0.418237 0.209119 0.977890i \(-0.432940\pi\)
0.209119 + 0.977890i \(0.432940\pi\)
\(24\) −3.36322 −0.686514
\(25\) 10.2762 2.05524
\(26\) −0.631638 −0.123874
\(27\) −17.8629 −3.43771
\(28\) −1.71915 −0.324888
\(29\) −6.75737 −1.25481 −0.627406 0.778692i \(-0.715883\pi\)
−0.627406 + 0.778692i \(0.715883\pi\)
\(30\) −13.1451 −2.39995
\(31\) −4.06395 −0.729908 −0.364954 0.931026i \(-0.618915\pi\)
−0.364954 + 0.931026i \(0.618915\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.60653 0.975971
\(34\) 2.65196 0.454807
\(35\) −6.71924 −1.13576
\(36\) 8.31124 1.38521
\(37\) −2.95478 −0.485762 −0.242881 0.970056i \(-0.578093\pi\)
−0.242881 + 0.970056i \(0.578093\pi\)
\(38\) −3.22088 −0.522497
\(39\) 2.12434 0.340166
\(40\) 3.90848 0.617984
\(41\) 2.41376 0.376966 0.188483 0.982076i \(-0.439643\pi\)
0.188483 + 0.982076i \(0.439643\pi\)
\(42\) 5.78186 0.892161
\(43\) 3.91405 0.596887 0.298443 0.954427i \(-0.403533\pi\)
0.298443 + 0.954427i \(0.403533\pi\)
\(44\) −1.66701 −0.251312
\(45\) 32.4843 4.84247
\(46\) 2.00580 0.295739
\(47\) −7.79943 −1.13766 −0.568832 0.822454i \(-0.692605\pi\)
−0.568832 + 0.822454i \(0.692605\pi\)
\(48\) −3.36322 −0.485439
\(49\) −4.04454 −0.577791
\(50\) 10.2762 1.45327
\(51\) −8.91911 −1.24893
\(52\) −0.631638 −0.0875924
\(53\) −10.4966 −1.44182 −0.720911 0.693028i \(-0.756276\pi\)
−0.720911 + 0.693028i \(0.756276\pi\)
\(54\) −17.8629 −2.43083
\(55\) −6.51548 −0.878547
\(56\) −1.71915 −0.229730
\(57\) 10.8325 1.43481
\(58\) −6.75737 −0.887286
\(59\) −6.59901 −0.859117 −0.429559 0.903039i \(-0.641331\pi\)
−0.429559 + 0.903039i \(0.641331\pi\)
\(60\) −13.1451 −1.69702
\(61\) 6.19818 0.793595 0.396798 0.917906i \(-0.370122\pi\)
0.396798 + 0.917906i \(0.370122\pi\)
\(62\) −4.06395 −0.516123
\(63\) −14.2882 −1.80015
\(64\) 1.00000 0.125000
\(65\) −2.46874 −0.306210
\(66\) 5.60653 0.690116
\(67\) −2.95815 −0.361395 −0.180698 0.983539i \(-0.557836\pi\)
−0.180698 + 0.983539i \(0.557836\pi\)
\(68\) 2.65196 0.321597
\(69\) −6.74593 −0.812115
\(70\) −6.71924 −0.803103
\(71\) 11.4309 1.35660 0.678302 0.734784i \(-0.262716\pi\)
0.678302 + 0.734784i \(0.262716\pi\)
\(72\) 8.31124 0.979490
\(73\) −7.30030 −0.854435 −0.427218 0.904149i \(-0.640506\pi\)
−0.427218 + 0.904149i \(0.640506\pi\)
\(74\) −2.95478 −0.343486
\(75\) −34.5611 −3.99077
\(76\) −3.22088 −0.369461
\(77\) 2.86584 0.326592
\(78\) 2.12434 0.240534
\(79\) −17.2392 −1.93957 −0.969783 0.243968i \(-0.921551\pi\)
−0.969783 + 0.243968i \(0.921551\pi\)
\(80\) 3.90848 0.436981
\(81\) 35.1431 3.90478
\(82\) 2.41376 0.266555
\(83\) 13.7900 1.51365 0.756823 0.653619i \(-0.226750\pi\)
0.756823 + 0.653619i \(0.226750\pi\)
\(84\) 5.78186 0.630853
\(85\) 10.3651 1.12425
\(86\) 3.91405 0.422063
\(87\) 22.7265 2.43654
\(88\) −1.66701 −0.177704
\(89\) 0.657803 0.0697269 0.0348635 0.999392i \(-0.488900\pi\)
0.0348635 + 0.999392i \(0.488900\pi\)
\(90\) 32.4843 3.42415
\(91\) 1.08588 0.113831
\(92\) 2.00580 0.209119
\(93\) 13.6680 1.41730
\(94\) −7.79943 −0.804450
\(95\) −12.5888 −1.29158
\(96\) −3.36322 −0.343257
\(97\) −1.90755 −0.193682 −0.0968410 0.995300i \(-0.530874\pi\)
−0.0968410 + 0.995300i \(0.530874\pi\)
\(98\) −4.04454 −0.408560
\(99\) −13.8549 −1.39247
\(100\) 10.2762 1.02762
\(101\) −15.8143 −1.57358 −0.786789 0.617221i \(-0.788258\pi\)
−0.786789 + 0.617221i \(0.788258\pi\)
\(102\) −8.91911 −0.883124
\(103\) 0.266726 0.0262813 0.0131406 0.999914i \(-0.495817\pi\)
0.0131406 + 0.999914i \(0.495817\pi\)
\(104\) −0.631638 −0.0619372
\(105\) 22.5983 2.20537
\(106\) −10.4966 −1.01952
\(107\) 0.701684 0.0678343 0.0339172 0.999425i \(-0.489202\pi\)
0.0339172 + 0.999425i \(0.489202\pi\)
\(108\) −17.8629 −1.71886
\(109\) −8.15785 −0.781381 −0.390690 0.920522i \(-0.627764\pi\)
−0.390690 + 0.920522i \(0.627764\pi\)
\(110\) −6.51548 −0.621226
\(111\) 9.93756 0.943232
\(112\) −1.71915 −0.162444
\(113\) −14.5249 −1.36638 −0.683192 0.730239i \(-0.739409\pi\)
−0.683192 + 0.730239i \(0.739409\pi\)
\(114\) 10.8325 1.01456
\(115\) 7.83961 0.731047
\(116\) −6.75737 −0.627406
\(117\) −5.24970 −0.485335
\(118\) −6.59901 −0.607488
\(119\) −4.55910 −0.417932
\(120\) −13.1451 −1.19997
\(121\) −8.22107 −0.747370
\(122\) 6.19818 0.561156
\(123\) −8.11800 −0.731975
\(124\) −4.06395 −0.364954
\(125\) 20.6219 1.84448
\(126\) −14.2882 −1.27290
\(127\) −10.1089 −0.897016 −0.448508 0.893779i \(-0.648044\pi\)
−0.448508 + 0.893779i \(0.648044\pi\)
\(128\) 1.00000 0.0883883
\(129\) −13.1638 −1.15901
\(130\) −2.46874 −0.216523
\(131\) 6.27545 0.548289 0.274144 0.961689i \(-0.411605\pi\)
0.274144 + 0.961689i \(0.411605\pi\)
\(132\) 5.60653 0.487986
\(133\) 5.53717 0.480133
\(134\) −2.95815 −0.255545
\(135\) −69.8167 −6.00886
\(136\) 2.65196 0.227403
\(137\) 8.02851 0.685922 0.342961 0.939350i \(-0.388570\pi\)
0.342961 + 0.939350i \(0.388570\pi\)
\(138\) −6.74593 −0.574252
\(139\) 19.1640 1.62547 0.812735 0.582633i \(-0.197977\pi\)
0.812735 + 0.582633i \(0.197977\pi\)
\(140\) −6.71924 −0.567879
\(141\) 26.2312 2.20907
\(142\) 11.4309 0.959263
\(143\) 1.05295 0.0880519
\(144\) 8.31124 0.692604
\(145\) −26.4110 −2.19332
\(146\) −7.30030 −0.604177
\(147\) 13.6027 1.12193
\(148\) −2.95478 −0.242881
\(149\) 19.4108 1.59019 0.795097 0.606482i \(-0.207420\pi\)
0.795097 + 0.606482i \(0.207420\pi\)
\(150\) −34.5611 −2.82190
\(151\) −16.5830 −1.34951 −0.674753 0.738044i \(-0.735750\pi\)
−0.674753 + 0.738044i \(0.735750\pi\)
\(152\) −3.22088 −0.261248
\(153\) 22.0411 1.78191
\(154\) 2.86584 0.230936
\(155\) −15.8839 −1.27582
\(156\) 2.12434 0.170083
\(157\) 5.27524 0.421010 0.210505 0.977593i \(-0.432489\pi\)
0.210505 + 0.977593i \(0.432489\pi\)
\(158\) −17.2392 −1.37148
\(159\) 35.3025 2.79967
\(160\) 3.90848 0.308992
\(161\) −3.44826 −0.271761
\(162\) 35.1431 2.76110
\(163\) 14.3426 1.12340 0.561700 0.827341i \(-0.310147\pi\)
0.561700 + 0.827341i \(0.310147\pi\)
\(164\) 2.41376 0.188483
\(165\) 21.9130 1.70592
\(166\) 13.7900 1.07031
\(167\) −9.09146 −0.703518 −0.351759 0.936091i \(-0.614416\pi\)
−0.351759 + 0.936091i \(0.614416\pi\)
\(168\) 5.78186 0.446080
\(169\) −12.6010 −0.969310
\(170\) 10.3651 0.794968
\(171\) −26.7696 −2.04712
\(172\) 3.91405 0.298443
\(173\) 8.30753 0.631610 0.315805 0.948824i \(-0.397725\pi\)
0.315805 + 0.948824i \(0.397725\pi\)
\(174\) 22.7265 1.72289
\(175\) −17.6663 −1.33544
\(176\) −1.66701 −0.125656
\(177\) 22.1939 1.66820
\(178\) 0.657803 0.0493044
\(179\) −17.8449 −1.33379 −0.666894 0.745153i \(-0.732377\pi\)
−0.666894 + 0.745153i \(0.732377\pi\)
\(180\) 32.4843 2.42124
\(181\) 6.30891 0.468938 0.234469 0.972124i \(-0.424665\pi\)
0.234469 + 0.972124i \(0.424665\pi\)
\(182\) 1.08588 0.0804906
\(183\) −20.8458 −1.54097
\(184\) 2.00580 0.147869
\(185\) −11.5487 −0.849076
\(186\) 13.6680 1.00218
\(187\) −4.42084 −0.323284
\(188\) −7.79943 −0.568832
\(189\) 30.7089 2.23374
\(190\) −12.5888 −0.913284
\(191\) 10.6681 0.771919 0.385960 0.922516i \(-0.373870\pi\)
0.385960 + 0.922516i \(0.373870\pi\)
\(192\) −3.36322 −0.242719
\(193\) 21.7456 1.56528 0.782641 0.622473i \(-0.213872\pi\)
0.782641 + 0.622473i \(0.213872\pi\)
\(194\) −1.90755 −0.136954
\(195\) 8.30292 0.594585
\(196\) −4.04454 −0.288896
\(197\) 14.0173 0.998691 0.499346 0.866403i \(-0.333574\pi\)
0.499346 + 0.866403i \(0.333574\pi\)
\(198\) −13.8549 −0.984628
\(199\) −25.7549 −1.82572 −0.912859 0.408274i \(-0.866131\pi\)
−0.912859 + 0.408274i \(0.866131\pi\)
\(200\) 10.2762 0.726637
\(201\) 9.94891 0.701742
\(202\) −15.8143 −1.11269
\(203\) 11.6169 0.815347
\(204\) −8.91911 −0.624463
\(205\) 9.43412 0.658907
\(206\) 0.266726 0.0185837
\(207\) 16.6707 1.15869
\(208\) −0.631638 −0.0437962
\(209\) 5.36925 0.371399
\(210\) 22.5983 1.55943
\(211\) 20.2343 1.39299 0.696495 0.717562i \(-0.254742\pi\)
0.696495 + 0.717562i \(0.254742\pi\)
\(212\) −10.4966 −0.720911
\(213\) −38.4448 −2.63419
\(214\) 0.701684 0.0479661
\(215\) 15.2980 1.04331
\(216\) −17.8629 −1.21542
\(217\) 6.98653 0.474276
\(218\) −8.15785 −0.552519
\(219\) 24.5525 1.65910
\(220\) −6.51548 −0.439273
\(221\) −1.67508 −0.112678
\(222\) 9.93756 0.666966
\(223\) 3.49374 0.233958 0.116979 0.993134i \(-0.462679\pi\)
0.116979 + 0.993134i \(0.462679\pi\)
\(224\) −1.71915 −0.114865
\(225\) 85.4080 5.69386
\(226\) −14.5249 −0.966179
\(227\) 5.78724 0.384113 0.192056 0.981384i \(-0.438484\pi\)
0.192056 + 0.981384i \(0.438484\pi\)
\(228\) 10.8325 0.717403
\(229\) 7.87808 0.520598 0.260299 0.965528i \(-0.416179\pi\)
0.260299 + 0.965528i \(0.416179\pi\)
\(230\) 7.83961 0.516929
\(231\) −9.63843 −0.634162
\(232\) −6.75737 −0.443643
\(233\) −17.0866 −1.11938 −0.559692 0.828701i \(-0.689080\pi\)
−0.559692 + 0.828701i \(0.689080\pi\)
\(234\) −5.24970 −0.343183
\(235\) −30.4839 −1.98855
\(236\) −6.59901 −0.429559
\(237\) 57.9794 3.76616
\(238\) −4.55910 −0.295522
\(239\) 6.15898 0.398391 0.199196 0.979960i \(-0.436167\pi\)
0.199196 + 0.979960i \(0.436167\pi\)
\(240\) −13.1451 −0.848510
\(241\) 1.72196 0.110921 0.0554607 0.998461i \(-0.482337\pi\)
0.0554607 + 0.998461i \(0.482337\pi\)
\(242\) −8.22107 −0.528470
\(243\) −64.6052 −4.14442
\(244\) 6.19818 0.396798
\(245\) −15.8080 −1.00994
\(246\) −8.11800 −0.517585
\(247\) 2.03443 0.129448
\(248\) −4.06395 −0.258061
\(249\) −46.3787 −2.93913
\(250\) 20.6219 1.30424
\(251\) −7.50315 −0.473594 −0.236797 0.971559i \(-0.576098\pi\)
−0.236797 + 0.971559i \(0.576098\pi\)
\(252\) −14.2882 −0.900074
\(253\) −3.34369 −0.210216
\(254\) −10.1089 −0.634286
\(255\) −34.8601 −2.18303
\(256\) 1.00000 0.0625000
\(257\) 6.17366 0.385102 0.192551 0.981287i \(-0.438324\pi\)
0.192551 + 0.981287i \(0.438324\pi\)
\(258\) −13.1638 −0.819542
\(259\) 5.07969 0.315637
\(260\) −2.46874 −0.153105
\(261\) −56.1622 −3.47635
\(262\) 6.27545 0.387699
\(263\) −13.7257 −0.846362 −0.423181 0.906045i \(-0.639087\pi\)
−0.423181 + 0.906045i \(0.639087\pi\)
\(264\) 5.60653 0.345058
\(265\) −41.0258 −2.52020
\(266\) 5.53717 0.339506
\(267\) −2.21233 −0.135393
\(268\) −2.95815 −0.180698
\(269\) −1.70806 −0.104142 −0.0520711 0.998643i \(-0.516582\pi\)
−0.0520711 + 0.998643i \(0.516582\pi\)
\(270\) −69.8167 −4.24891
\(271\) 13.4289 0.815748 0.407874 0.913038i \(-0.366270\pi\)
0.407874 + 0.913038i \(0.366270\pi\)
\(272\) 2.65196 0.160798
\(273\) −3.65204 −0.221032
\(274\) 8.02851 0.485020
\(275\) −17.1305 −1.03301
\(276\) −6.74593 −0.406057
\(277\) −24.5829 −1.47705 −0.738523 0.674228i \(-0.764476\pi\)
−0.738523 + 0.674228i \(0.764476\pi\)
\(278\) 19.1640 1.14938
\(279\) −33.7765 −2.02215
\(280\) −6.71924 −0.401551
\(281\) −29.0664 −1.73396 −0.866978 0.498347i \(-0.833941\pi\)
−0.866978 + 0.498347i \(0.833941\pi\)
\(282\) 26.2312 1.56205
\(283\) 11.1403 0.662222 0.331111 0.943592i \(-0.392576\pi\)
0.331111 + 0.943592i \(0.392576\pi\)
\(284\) 11.4309 0.678302
\(285\) 42.3387 2.50793
\(286\) 1.05295 0.0622621
\(287\) −4.14960 −0.244943
\(288\) 8.31124 0.489745
\(289\) −9.96713 −0.586302
\(290\) −26.4110 −1.55091
\(291\) 6.41549 0.376083
\(292\) −7.30030 −0.427218
\(293\) −17.0762 −0.997602 −0.498801 0.866717i \(-0.666226\pi\)
−0.498801 + 0.866717i \(0.666226\pi\)
\(294\) 13.6027 0.793324
\(295\) −25.7921 −1.50167
\(296\) −2.95478 −0.171743
\(297\) 29.7776 1.72787
\(298\) 19.4108 1.12444
\(299\) −1.26694 −0.0732689
\(300\) −34.5611 −1.99539
\(301\) −6.72882 −0.387843
\(302\) −16.5830 −0.954245
\(303\) 53.1869 3.05551
\(304\) −3.22088 −0.184730
\(305\) 24.2254 1.38714
\(306\) 22.0411 1.26000
\(307\) 13.5648 0.774187 0.387093 0.922041i \(-0.373479\pi\)
0.387093 + 0.922041i \(0.373479\pi\)
\(308\) 2.86584 0.163296
\(309\) −0.897058 −0.0510318
\(310\) −15.8839 −0.902143
\(311\) −8.01758 −0.454635 −0.227318 0.973821i \(-0.572996\pi\)
−0.227318 + 0.973821i \(0.572996\pi\)
\(312\) 2.12434 0.120267
\(313\) −4.93652 −0.279029 −0.139514 0.990220i \(-0.544554\pi\)
−0.139514 + 0.990220i \(0.544554\pi\)
\(314\) 5.27524 0.297699
\(315\) −55.8452 −3.14652
\(316\) −17.2392 −0.969783
\(317\) −8.73521 −0.490618 −0.245309 0.969445i \(-0.578889\pi\)
−0.245309 + 0.969445i \(0.578889\pi\)
\(318\) 35.3025 1.97966
\(319\) 11.2646 0.630698
\(320\) 3.90848 0.218491
\(321\) −2.35992 −0.131718
\(322\) −3.44826 −0.192164
\(323\) −8.54165 −0.475270
\(324\) 35.1431 1.95239
\(325\) −6.49083 −0.360047
\(326\) 14.3426 0.794364
\(327\) 27.4366 1.51725
\(328\) 2.41376 0.133277
\(329\) 13.4084 0.739227
\(330\) 21.9130 1.20627
\(331\) −12.5613 −0.690433 −0.345216 0.938523i \(-0.612194\pi\)
−0.345216 + 0.938523i \(0.612194\pi\)
\(332\) 13.7900 0.756823
\(333\) −24.5579 −1.34576
\(334\) −9.09146 −0.497463
\(335\) −11.5619 −0.631692
\(336\) 5.78186 0.315426
\(337\) −9.26971 −0.504953 −0.252477 0.967603i \(-0.581245\pi\)
−0.252477 + 0.967603i \(0.581245\pi\)
\(338\) −12.6010 −0.685406
\(339\) 48.8503 2.65318
\(340\) 10.3651 0.562127
\(341\) 6.77466 0.366868
\(342\) −26.7696 −1.44753
\(343\) 18.9872 1.02521
\(344\) 3.91405 0.211031
\(345\) −26.3663 −1.41952
\(346\) 8.30753 0.446616
\(347\) −20.3167 −1.09066 −0.545330 0.838222i \(-0.683596\pi\)
−0.545330 + 0.838222i \(0.683596\pi\)
\(348\) 22.7265 1.21827
\(349\) −5.58689 −0.299060 −0.149530 0.988757i \(-0.547776\pi\)
−0.149530 + 0.988757i \(0.547776\pi\)
\(350\) −17.6663 −0.944302
\(351\) 11.2829 0.602235
\(352\) −1.66701 −0.0888520
\(353\) 24.3701 1.29709 0.648546 0.761176i \(-0.275377\pi\)
0.648546 + 0.761176i \(0.275377\pi\)
\(354\) 22.1939 1.17959
\(355\) 44.6776 2.37124
\(356\) 0.657803 0.0348635
\(357\) 15.3332 0.811522
\(358\) −17.8449 −0.943131
\(359\) −6.81820 −0.359851 −0.179925 0.983680i \(-0.557586\pi\)
−0.179925 + 0.983680i \(0.557586\pi\)
\(360\) 32.4843 1.71207
\(361\) −8.62590 −0.453995
\(362\) 6.30891 0.331589
\(363\) 27.6493 1.45121
\(364\) 1.08588 0.0569154
\(365\) −28.5331 −1.49349
\(366\) −20.8458 −1.08963
\(367\) −4.85785 −0.253578 −0.126789 0.991930i \(-0.540467\pi\)
−0.126789 + 0.991930i \(0.540467\pi\)
\(368\) 2.00580 0.104559
\(369\) 20.0613 1.04435
\(370\) −11.5487 −0.600387
\(371\) 18.0452 0.936861
\(372\) 13.6680 0.708651
\(373\) 4.02390 0.208350 0.104175 0.994559i \(-0.466780\pi\)
0.104175 + 0.994559i \(0.466780\pi\)
\(374\) −4.42084 −0.228596
\(375\) −69.3559 −3.58152
\(376\) −7.79943 −0.402225
\(377\) 4.26821 0.219824
\(378\) 30.7089 1.57949
\(379\) −7.91538 −0.406586 −0.203293 0.979118i \(-0.565164\pi\)
−0.203293 + 0.979118i \(0.565164\pi\)
\(380\) −12.5888 −0.645789
\(381\) 33.9983 1.74178
\(382\) 10.6681 0.545829
\(383\) 5.04462 0.257768 0.128884 0.991660i \(-0.458861\pi\)
0.128884 + 0.991660i \(0.458861\pi\)
\(384\) −3.36322 −0.171629
\(385\) 11.2011 0.570859
\(386\) 21.7456 1.10682
\(387\) 32.5306 1.65362
\(388\) −1.90755 −0.0968410
\(389\) 4.90941 0.248917 0.124459 0.992225i \(-0.460281\pi\)
0.124459 + 0.992225i \(0.460281\pi\)
\(390\) 8.30292 0.420435
\(391\) 5.31928 0.269008
\(392\) −4.04454 −0.204280
\(393\) −21.1057 −1.06464
\(394\) 14.0173 0.706181
\(395\) −67.3792 −3.39022
\(396\) −13.8549 −0.696237
\(397\) 7.90142 0.396561 0.198280 0.980145i \(-0.436464\pi\)
0.198280 + 0.980145i \(0.436464\pi\)
\(398\) −25.7549 −1.29098
\(399\) −18.6227 −0.932302
\(400\) 10.2762 0.513810
\(401\) −36.5778 −1.82661 −0.913304 0.407279i \(-0.866478\pi\)
−0.913304 + 0.407279i \(0.866478\pi\)
\(402\) 9.94891 0.496206
\(403\) 2.56695 0.127869
\(404\) −15.8143 −0.786789
\(405\) 137.356 6.82527
\(406\) 11.6169 0.576537
\(407\) 4.92565 0.244155
\(408\) −8.91911 −0.441562
\(409\) 23.6810 1.17095 0.585474 0.810691i \(-0.300908\pi\)
0.585474 + 0.810691i \(0.300908\pi\)
\(410\) 9.43412 0.465918
\(411\) −27.0017 −1.33189
\(412\) 0.266726 0.0131406
\(413\) 11.3447 0.558234
\(414\) 16.6707 0.819318
\(415\) 53.8978 2.64574
\(416\) −0.631638 −0.0309686
\(417\) −64.4528 −3.15627
\(418\) 5.36925 0.262619
\(419\) −6.30101 −0.307824 −0.153912 0.988085i \(-0.549187\pi\)
−0.153912 + 0.988085i \(0.549187\pi\)
\(420\) 22.5983 1.10268
\(421\) 40.7075 1.98396 0.991981 0.126390i \(-0.0403389\pi\)
0.991981 + 0.126390i \(0.0403389\pi\)
\(422\) 20.2343 0.984993
\(423\) −64.8230 −3.15180
\(424\) −10.4966 −0.509761
\(425\) 27.2520 1.32192
\(426\) −38.4448 −1.86265
\(427\) −10.6556 −0.515659
\(428\) 0.701684 0.0339172
\(429\) −3.54130 −0.170975
\(430\) 15.2980 0.737733
\(431\) −32.1445 −1.54834 −0.774172 0.632975i \(-0.781834\pi\)
−0.774172 + 0.632975i \(0.781834\pi\)
\(432\) −17.8629 −0.859428
\(433\) −27.3389 −1.31382 −0.656912 0.753967i \(-0.728138\pi\)
−0.656912 + 0.753967i \(0.728138\pi\)
\(434\) 6.98653 0.335364
\(435\) 88.8261 4.25889
\(436\) −8.15785 −0.390690
\(437\) −6.46044 −0.309045
\(438\) 24.5525 1.17316
\(439\) −7.46270 −0.356175 −0.178088 0.984015i \(-0.556991\pi\)
−0.178088 + 0.984015i \(0.556991\pi\)
\(440\) −6.51548 −0.310613
\(441\) −33.6152 −1.60072
\(442\) −1.67508 −0.0796753
\(443\) 25.9025 1.23066 0.615332 0.788268i \(-0.289022\pi\)
0.615332 + 0.788268i \(0.289022\pi\)
\(444\) 9.93756 0.471616
\(445\) 2.57101 0.121877
\(446\) 3.49374 0.165433
\(447\) −65.2828 −3.08777
\(448\) −1.71915 −0.0812220
\(449\) 5.51032 0.260048 0.130024 0.991511i \(-0.458495\pi\)
0.130024 + 0.991511i \(0.458495\pi\)
\(450\) 85.4080 4.02617
\(451\) −4.02376 −0.189472
\(452\) −14.5249 −0.683192
\(453\) 55.7723 2.62041
\(454\) 5.78724 0.271609
\(455\) 4.24413 0.198968
\(456\) 10.8325 0.507280
\(457\) −15.4448 −0.722478 −0.361239 0.932473i \(-0.617646\pi\)
−0.361239 + 0.932473i \(0.617646\pi\)
\(458\) 7.87808 0.368118
\(459\) −47.3716 −2.21112
\(460\) 7.83961 0.365524
\(461\) −37.5298 −1.74794 −0.873969 0.485982i \(-0.838462\pi\)
−0.873969 + 0.485982i \(0.838462\pi\)
\(462\) −9.63843 −0.448421
\(463\) −28.0159 −1.30201 −0.651004 0.759074i \(-0.725652\pi\)
−0.651004 + 0.759074i \(0.725652\pi\)
\(464\) −6.75737 −0.313703
\(465\) 53.4209 2.47734
\(466\) −17.0866 −0.791523
\(467\) −18.2634 −0.845131 −0.422565 0.906332i \(-0.638870\pi\)
−0.422565 + 0.906332i \(0.638870\pi\)
\(468\) −5.24970 −0.242667
\(469\) 5.08549 0.234826
\(470\) −30.4839 −1.40612
\(471\) −17.7418 −0.817499
\(472\) −6.59901 −0.303744
\(473\) −6.52476 −0.300009
\(474\) 57.9794 2.66308
\(475\) −33.0984 −1.51866
\(476\) −4.55910 −0.208966
\(477\) −87.2400 −3.99445
\(478\) 6.15898 0.281705
\(479\) −26.7325 −1.22144 −0.610721 0.791846i \(-0.709120\pi\)
−0.610721 + 0.791846i \(0.709120\pi\)
\(480\) −13.1451 −0.599987
\(481\) 1.86635 0.0850982
\(482\) 1.72196 0.0784333
\(483\) 11.5972 0.527693
\(484\) −8.22107 −0.373685
\(485\) −7.45560 −0.338541
\(486\) −64.6052 −2.93055
\(487\) 30.5225 1.38311 0.691553 0.722326i \(-0.256927\pi\)
0.691553 + 0.722326i \(0.256927\pi\)
\(488\) 6.19818 0.280578
\(489\) −48.2374 −2.18137
\(490\) −15.8080 −0.714132
\(491\) −27.7964 −1.25443 −0.627216 0.778845i \(-0.715806\pi\)
−0.627216 + 0.778845i \(0.715806\pi\)
\(492\) −8.11800 −0.365988
\(493\) −17.9203 −0.807088
\(494\) 2.03443 0.0915335
\(495\) −54.1517 −2.43394
\(496\) −4.06395 −0.182477
\(497\) −19.6514 −0.881488
\(498\) −46.3787 −2.07828
\(499\) −28.3537 −1.26929 −0.634644 0.772805i \(-0.718853\pi\)
−0.634644 + 0.772805i \(0.718853\pi\)
\(500\) 20.6219 0.922238
\(501\) 30.5766 1.36606
\(502\) −7.50315 −0.334882
\(503\) −26.6814 −1.18967 −0.594833 0.803850i \(-0.702782\pi\)
−0.594833 + 0.803850i \(0.702782\pi\)
\(504\) −14.2882 −0.636449
\(505\) −61.8097 −2.75050
\(506\) −3.34369 −0.148645
\(507\) 42.3800 1.88216
\(508\) −10.1089 −0.448508
\(509\) −26.2488 −1.16346 −0.581728 0.813383i \(-0.697623\pi\)
−0.581728 + 0.813383i \(0.697623\pi\)
\(510\) −34.8601 −1.54363
\(511\) 12.5503 0.555192
\(512\) 1.00000 0.0441942
\(513\) 57.5343 2.54020
\(514\) 6.17366 0.272309
\(515\) 1.04249 0.0459377
\(516\) −13.1638 −0.579504
\(517\) 13.0017 0.571816
\(518\) 5.07969 0.223189
\(519\) −27.9401 −1.22643
\(520\) −2.46874 −0.108262
\(521\) 4.04006 0.176998 0.0884991 0.996076i \(-0.471793\pi\)
0.0884991 + 0.996076i \(0.471793\pi\)
\(522\) −56.1622 −2.45815
\(523\) 20.9331 0.915342 0.457671 0.889122i \(-0.348684\pi\)
0.457671 + 0.889122i \(0.348684\pi\)
\(524\) 6.27545 0.274144
\(525\) 59.4155 2.59311
\(526\) −13.7257 −0.598468
\(527\) −10.7774 −0.469472
\(528\) 5.60653 0.243993
\(529\) −18.9768 −0.825077
\(530\) −41.0258 −1.78205
\(531\) −54.8460 −2.38011
\(532\) 5.53717 0.240067
\(533\) −1.52462 −0.0660387
\(534\) −2.21233 −0.0957371
\(535\) 2.74251 0.118569
\(536\) −2.95815 −0.127773
\(537\) 60.0162 2.58989
\(538\) −1.70806 −0.0736397
\(539\) 6.74230 0.290411
\(540\) −69.8167 −3.00443
\(541\) 4.38341 0.188458 0.0942289 0.995551i \(-0.469961\pi\)
0.0942289 + 0.995551i \(0.469961\pi\)
\(542\) 13.4289 0.576821
\(543\) −21.2182 −0.910562
\(544\) 2.65196 0.113702
\(545\) −31.8848 −1.36579
\(546\) −3.65204 −0.156293
\(547\) 0.715201 0.0305798 0.0152899 0.999883i \(-0.495133\pi\)
0.0152899 + 0.999883i \(0.495133\pi\)
\(548\) 8.02851 0.342961
\(549\) 51.5145 2.19859
\(550\) −17.1305 −0.730449
\(551\) 21.7647 0.927208
\(552\) −6.74593 −0.287126
\(553\) 29.6368 1.26028
\(554\) −24.5829 −1.04443
\(555\) 38.8407 1.64870
\(556\) 19.1640 0.812735
\(557\) 27.7402 1.17539 0.587694 0.809083i \(-0.300036\pi\)
0.587694 + 0.809083i \(0.300036\pi\)
\(558\) −33.7765 −1.42987
\(559\) −2.47226 −0.104565
\(560\) −6.71924 −0.283940
\(561\) 14.8683 0.627739
\(562\) −29.0664 −1.22609
\(563\) 32.3622 1.36391 0.681953 0.731396i \(-0.261131\pi\)
0.681953 + 0.731396i \(0.261131\pi\)
\(564\) 26.2312 1.10453
\(565\) −56.7701 −2.38834
\(566\) 11.1403 0.468262
\(567\) −60.4160 −2.53723
\(568\) 11.4309 0.479632
\(569\) −16.0787 −0.674055 −0.337028 0.941495i \(-0.609422\pi\)
−0.337028 + 0.941495i \(0.609422\pi\)
\(570\) 42.3387 1.77337
\(571\) 30.1474 1.26163 0.630814 0.775934i \(-0.282721\pi\)
0.630814 + 0.775934i \(0.282721\pi\)
\(572\) 1.05295 0.0440260
\(573\) −35.8793 −1.49888
\(574\) −4.14960 −0.173201
\(575\) 20.6120 0.859578
\(576\) 8.31124 0.346302
\(577\) −39.7986 −1.65684 −0.828419 0.560110i \(-0.810759\pi\)
−0.828419 + 0.560110i \(0.810759\pi\)
\(578\) −9.96713 −0.414578
\(579\) −73.1352 −3.03940
\(580\) −26.4110 −1.09666
\(581\) −23.7070 −0.983531
\(582\) 6.41549 0.265931
\(583\) 17.4980 0.724693
\(584\) −7.30030 −0.302089
\(585\) −20.5183 −0.848328
\(586\) −17.0762 −0.705411
\(587\) −16.7439 −0.691095 −0.345548 0.938401i \(-0.612307\pi\)
−0.345548 + 0.938401i \(0.612307\pi\)
\(588\) 13.6027 0.560965
\(589\) 13.0895 0.539344
\(590\) −25.7921 −1.06184
\(591\) −47.1433 −1.93921
\(592\) −2.95478 −0.121441
\(593\) 3.03276 0.124541 0.0622703 0.998059i \(-0.480166\pi\)
0.0622703 + 0.998059i \(0.480166\pi\)
\(594\) 29.7776 1.22179
\(595\) −17.8191 −0.730513
\(596\) 19.4108 0.795097
\(597\) 86.6195 3.54510
\(598\) −1.26694 −0.0518089
\(599\) −8.84889 −0.361556 −0.180778 0.983524i \(-0.557862\pi\)
−0.180778 + 0.983524i \(0.557862\pi\)
\(600\) −34.5611 −1.41095
\(601\) −46.1425 −1.88219 −0.941095 0.338141i \(-0.890202\pi\)
−0.941095 + 0.338141i \(0.890202\pi\)
\(602\) −6.72882 −0.274246
\(603\) −24.5859 −1.00122
\(604\) −16.5830 −0.674753
\(605\) −32.1319 −1.30635
\(606\) 53.1869 2.16057
\(607\) 21.6279 0.877850 0.438925 0.898524i \(-0.355359\pi\)
0.438925 + 0.898524i \(0.355359\pi\)
\(608\) −3.22088 −0.130624
\(609\) −39.0702 −1.58320
\(610\) 24.2254 0.980859
\(611\) 4.92642 0.199301
\(612\) 22.0411 0.890957
\(613\) −0.159695 −0.00645002 −0.00322501 0.999995i \(-0.501027\pi\)
−0.00322501 + 0.999995i \(0.501027\pi\)
\(614\) 13.5648 0.547433
\(615\) −31.7290 −1.27944
\(616\) 2.86584 0.115468
\(617\) 28.1834 1.13462 0.567311 0.823504i \(-0.307984\pi\)
0.567311 + 0.823504i \(0.307984\pi\)
\(618\) −0.897058 −0.0360849
\(619\) −1.85877 −0.0747103 −0.0373551 0.999302i \(-0.511893\pi\)
−0.0373551 + 0.999302i \(0.511893\pi\)
\(620\) −15.8839 −0.637911
\(621\) −35.8293 −1.43778
\(622\) −8.01758 −0.321476
\(623\) −1.13086 −0.0453069
\(624\) 2.12434 0.0850415
\(625\) 29.2192 1.16877
\(626\) −4.93652 −0.197303
\(627\) −18.0580 −0.721166
\(628\) 5.27524 0.210505
\(629\) −7.83594 −0.312439
\(630\) −55.8452 −2.22493
\(631\) 4.29589 0.171017 0.0855083 0.996337i \(-0.472749\pi\)
0.0855083 + 0.996337i \(0.472749\pi\)
\(632\) −17.2392 −0.685740
\(633\) −68.0525 −2.70485
\(634\) −8.73521 −0.346920
\(635\) −39.5102 −1.56792
\(636\) 35.3025 1.39983
\(637\) 2.55468 0.101220
\(638\) 11.2646 0.445971
\(639\) 95.0054 3.75835
\(640\) 3.90848 0.154496
\(641\) −48.7776 −1.92660 −0.963300 0.268427i \(-0.913496\pi\)
−0.963300 + 0.268427i \(0.913496\pi\)
\(642\) −2.35992 −0.0931385
\(643\) 31.3870 1.23778 0.618891 0.785477i \(-0.287582\pi\)
0.618891 + 0.785477i \(0.287582\pi\)
\(644\) −3.44826 −0.135880
\(645\) −51.4504 −2.02586
\(646\) −8.54165 −0.336067
\(647\) −41.4036 −1.62774 −0.813872 0.581044i \(-0.802644\pi\)
−0.813872 + 0.581044i \(0.802644\pi\)
\(648\) 35.1431 1.38055
\(649\) 11.0006 0.431812
\(650\) −6.49083 −0.254591
\(651\) −23.4972 −0.920929
\(652\) 14.3426 0.561700
\(653\) 36.0006 1.40881 0.704407 0.709796i \(-0.251213\pi\)
0.704407 + 0.709796i \(0.251213\pi\)
\(654\) 27.4366 1.07286
\(655\) 24.5275 0.958368
\(656\) 2.41376 0.0942414
\(657\) −60.6746 −2.36714
\(658\) 13.4084 0.522712
\(659\) −7.06885 −0.275363 −0.137682 0.990477i \(-0.543965\pi\)
−0.137682 + 0.990477i \(0.543965\pi\)
\(660\) 21.9130 0.852962
\(661\) 7.26222 0.282468 0.141234 0.989976i \(-0.454893\pi\)
0.141234 + 0.989976i \(0.454893\pi\)
\(662\) −12.5613 −0.488210
\(663\) 5.63365 0.218793
\(664\) 13.7900 0.535155
\(665\) 21.6419 0.839237
\(666\) −24.5579 −0.951598
\(667\) −13.5539 −0.524810
\(668\) −9.09146 −0.351759
\(669\) −11.7502 −0.454289
\(670\) −11.5619 −0.446674
\(671\) −10.3324 −0.398879
\(672\) 5.78186 0.223040
\(673\) 9.74807 0.375760 0.187880 0.982192i \(-0.439838\pi\)
0.187880 + 0.982192i \(0.439838\pi\)
\(674\) −9.26971 −0.357056
\(675\) −183.562 −7.06532
\(676\) −12.6010 −0.484655
\(677\) −12.6333 −0.485538 −0.242769 0.970084i \(-0.578056\pi\)
−0.242769 + 0.970084i \(0.578056\pi\)
\(678\) 48.8503 1.87608
\(679\) 3.27935 0.125850
\(680\) 10.3651 0.397484
\(681\) −19.4638 −0.745853
\(682\) 6.77466 0.259415
\(683\) 10.6884 0.408980 0.204490 0.978869i \(-0.434446\pi\)
0.204490 + 0.978869i \(0.434446\pi\)
\(684\) −26.7696 −1.02356
\(685\) 31.3793 1.19894
\(686\) 18.9872 0.724933
\(687\) −26.4957 −1.01087
\(688\) 3.91405 0.149222
\(689\) 6.63007 0.252585
\(690\) −26.3663 −1.00375
\(691\) 15.5769 0.592574 0.296287 0.955099i \(-0.404252\pi\)
0.296287 + 0.955099i \(0.404252\pi\)
\(692\) 8.30753 0.315805
\(693\) 23.8187 0.904796
\(694\) −20.3167 −0.771213
\(695\) 74.9021 2.84120
\(696\) 22.7265 0.861447
\(697\) 6.40118 0.242462
\(698\) −5.58689 −0.211467
\(699\) 57.4661 2.17357
\(700\) −17.6663 −0.667722
\(701\) 12.2139 0.461313 0.230656 0.973035i \(-0.425913\pi\)
0.230656 + 0.973035i \(0.425913\pi\)
\(702\) 11.2829 0.425845
\(703\) 9.51700 0.358940
\(704\) −1.66701 −0.0628279
\(705\) 102.524 3.86128
\(706\) 24.3701 0.917182
\(707\) 27.1870 1.02247
\(708\) 22.1939 0.834098
\(709\) 3.03355 0.113927 0.0569636 0.998376i \(-0.481858\pi\)
0.0569636 + 0.998376i \(0.481858\pi\)
\(710\) 44.6776 1.67672
\(711\) −143.280 −5.37340
\(712\) 0.657803 0.0246522
\(713\) −8.15146 −0.305275
\(714\) 15.3332 0.573832
\(715\) 4.11542 0.153908
\(716\) −17.8449 −0.666894
\(717\) −20.7140 −0.773578
\(718\) −6.81820 −0.254453
\(719\) 52.2647 1.94914 0.974572 0.224075i \(-0.0719360\pi\)
0.974572 + 0.224075i \(0.0719360\pi\)
\(720\) 32.4843 1.21062
\(721\) −0.458540 −0.0170769
\(722\) −8.62590 −0.321023
\(723\) −5.79134 −0.215382
\(724\) 6.30891 0.234469
\(725\) −69.4401 −2.57894
\(726\) 27.6493 1.02616
\(727\) −18.4591 −0.684610 −0.342305 0.939589i \(-0.611208\pi\)
−0.342305 + 0.939589i \(0.611208\pi\)
\(728\) 1.08588 0.0402453
\(729\) 111.852 4.14267
\(730\) −28.5331 −1.05606
\(731\) 10.3799 0.383914
\(732\) −20.8458 −0.770484
\(733\) −0.903406 −0.0333681 −0.0166840 0.999861i \(-0.505311\pi\)
−0.0166840 + 0.999861i \(0.505311\pi\)
\(734\) −4.85785 −0.179307
\(735\) 53.1657 1.96105
\(736\) 2.00580 0.0739346
\(737\) 4.93127 0.181646
\(738\) 20.0613 0.738468
\(739\) −10.4273 −0.383573 −0.191787 0.981437i \(-0.561428\pi\)
−0.191787 + 0.981437i \(0.561428\pi\)
\(740\) −11.5487 −0.424538
\(741\) −6.84224 −0.251356
\(742\) 18.0452 0.662461
\(743\) 12.8836 0.472654 0.236327 0.971674i \(-0.424056\pi\)
0.236327 + 0.971674i \(0.424056\pi\)
\(744\) 13.6680 0.501092
\(745\) 75.8667 2.77954
\(746\) 4.02390 0.147325
\(747\) 114.612 4.19343
\(748\) −4.42084 −0.161642
\(749\) −1.20630 −0.0440771
\(750\) −69.3559 −2.53252
\(751\) −23.7808 −0.867773 −0.433886 0.900968i \(-0.642858\pi\)
−0.433886 + 0.900968i \(0.642858\pi\)
\(752\) −7.79943 −0.284416
\(753\) 25.2347 0.919605
\(754\) 4.26821 0.155439
\(755\) −64.8143 −2.35883
\(756\) 30.7089 1.11687
\(757\) −8.15142 −0.296268 −0.148134 0.988967i \(-0.547327\pi\)
−0.148134 + 0.988967i \(0.547327\pi\)
\(758\) −7.91538 −0.287500
\(759\) 11.2456 0.408188
\(760\) −12.5888 −0.456642
\(761\) −31.4531 −1.14017 −0.570087 0.821585i \(-0.693090\pi\)
−0.570087 + 0.821585i \(0.693090\pi\)
\(762\) 33.9983 1.23163
\(763\) 14.0245 0.507722
\(764\) 10.6681 0.385960
\(765\) 86.1470 3.11465
\(766\) 5.04462 0.182269
\(767\) 4.16818 0.150504
\(768\) −3.36322 −0.121360
\(769\) 17.6032 0.634787 0.317394 0.948294i \(-0.397192\pi\)
0.317394 + 0.948294i \(0.397192\pi\)
\(770\) 11.2011 0.403658
\(771\) −20.7634 −0.747775
\(772\) 21.7456 0.782641
\(773\) −0.721276 −0.0259425 −0.0129712 0.999916i \(-0.504129\pi\)
−0.0129712 + 0.999916i \(0.504129\pi\)
\(774\) 32.5306 1.16929
\(775\) −41.7620 −1.50013
\(776\) −1.90755 −0.0684769
\(777\) −17.0841 −0.612889
\(778\) 4.90941 0.176011
\(779\) −7.77444 −0.278548
\(780\) 8.30292 0.297292
\(781\) −19.0555 −0.681860
\(782\) 5.31928 0.190217
\(783\) 120.706 4.31369
\(784\) −4.04454 −0.144448
\(785\) 20.6182 0.735894
\(786\) −21.1057 −0.752816
\(787\) −2.58409 −0.0921128 −0.0460564 0.998939i \(-0.514665\pi\)
−0.0460564 + 0.998939i \(0.514665\pi\)
\(788\) 14.0173 0.499346
\(789\) 46.1625 1.64343
\(790\) −67.3792 −2.39724
\(791\) 24.9703 0.887843
\(792\) −13.8549 −0.492314
\(793\) −3.91500 −0.139026
\(794\) 7.90142 0.280411
\(795\) 137.979 4.89360
\(796\) −25.7549 −0.912859
\(797\) −10.7106 −0.379390 −0.189695 0.981843i \(-0.560750\pi\)
−0.189695 + 0.981843i \(0.560750\pi\)
\(798\) −18.6227 −0.659237
\(799\) −20.6838 −0.731739
\(800\) 10.2762 0.363318
\(801\) 5.46716 0.193173
\(802\) −36.5778 −1.29161
\(803\) 12.1697 0.429459
\(804\) 9.94891 0.350871
\(805\) −13.4774 −0.475017
\(806\) 2.56695 0.0904168
\(807\) 5.74458 0.202219
\(808\) −15.8143 −0.556344
\(809\) 25.2088 0.886295 0.443148 0.896449i \(-0.353862\pi\)
0.443148 + 0.896449i \(0.353862\pi\)
\(810\) 137.356 4.82619
\(811\) −10.3146 −0.362194 −0.181097 0.983465i \(-0.557965\pi\)
−0.181097 + 0.983465i \(0.557965\pi\)
\(812\) 11.6169 0.407673
\(813\) −45.1643 −1.58398
\(814\) 4.92565 0.172644
\(815\) 56.0578 1.96362
\(816\) −8.91911 −0.312231
\(817\) −12.6067 −0.441052
\(818\) 23.6810 0.827986
\(819\) 9.02499 0.315359
\(820\) 9.43412 0.329454
\(821\) 18.5346 0.646861 0.323430 0.946252i \(-0.395164\pi\)
0.323430 + 0.946252i \(0.395164\pi\)
\(822\) −27.0017 −0.941791
\(823\) 38.3771 1.33774 0.668871 0.743378i \(-0.266778\pi\)
0.668871 + 0.743378i \(0.266778\pi\)
\(824\) 0.266726 0.00929184
\(825\) 57.6138 2.00585
\(826\) 11.3447 0.394731
\(827\) −50.5317 −1.75716 −0.878580 0.477595i \(-0.841509\pi\)
−0.878580 + 0.477595i \(0.841509\pi\)
\(828\) 16.6707 0.579346
\(829\) 43.9252 1.52558 0.762792 0.646644i \(-0.223828\pi\)
0.762792 + 0.646644i \(0.223828\pi\)
\(830\) 53.8978 1.87082
\(831\) 82.6778 2.86806
\(832\) −0.631638 −0.0218981
\(833\) −10.7259 −0.371632
\(834\) −64.4528 −2.23182
\(835\) −35.5338 −1.22970
\(836\) 5.36925 0.185700
\(837\) 72.5939 2.50921
\(838\) −6.30101 −0.217665
\(839\) 44.7174 1.54382 0.771908 0.635735i \(-0.219303\pi\)
0.771908 + 0.635735i \(0.219303\pi\)
\(840\) 22.5983 0.779715
\(841\) 16.6621 0.574554
\(842\) 40.7075 1.40287
\(843\) 97.7566 3.36692
\(844\) 20.2343 0.696495
\(845\) −49.2509 −1.69428
\(846\) −64.8230 −2.22866
\(847\) 14.1332 0.485623
\(848\) −10.4966 −0.360456
\(849\) −37.4673 −1.28587
\(850\) 27.2520 0.934736
\(851\) −5.92668 −0.203164
\(852\) −38.4448 −1.31710
\(853\) −7.21418 −0.247009 −0.123504 0.992344i \(-0.539413\pi\)
−0.123504 + 0.992344i \(0.539413\pi\)
\(854\) −10.6556 −0.364626
\(855\) −104.628 −3.57821
\(856\) 0.701684 0.0239831
\(857\) −1.41440 −0.0483149 −0.0241574 0.999708i \(-0.507690\pi\)
−0.0241574 + 0.999708i \(0.507690\pi\)
\(858\) −3.54130 −0.120898
\(859\) −8.15761 −0.278334 −0.139167 0.990269i \(-0.544443\pi\)
−0.139167 + 0.990269i \(0.544443\pi\)
\(860\) 15.2980 0.521656
\(861\) 13.9560 0.475620
\(862\) −32.1445 −1.09484
\(863\) 53.0919 1.80727 0.903635 0.428303i \(-0.140888\pi\)
0.903635 + 0.428303i \(0.140888\pi\)
\(864\) −17.8629 −0.607708
\(865\) 32.4698 1.10401
\(866\) −27.3389 −0.929014
\(867\) 33.5216 1.13845
\(868\) 6.98653 0.237138
\(869\) 28.7380 0.974871
\(870\) 88.8261 3.01149
\(871\) 1.86848 0.0633110
\(872\) −8.15785 −0.276260
\(873\) −15.8541 −0.536579
\(874\) −6.46044 −0.218528
\(875\) −35.4520 −1.19850
\(876\) 24.5525 0.829552
\(877\) −22.1155 −0.746789 −0.373394 0.927673i \(-0.621806\pi\)
−0.373394 + 0.927673i \(0.621806\pi\)
\(878\) −7.46270 −0.251854
\(879\) 57.4310 1.93710
\(880\) −6.51548 −0.219637
\(881\) −28.8797 −0.972981 −0.486490 0.873686i \(-0.661723\pi\)
−0.486490 + 0.873686i \(0.661723\pi\)
\(882\) −33.6152 −1.13188
\(883\) 30.2326 1.01741 0.508704 0.860942i \(-0.330125\pi\)
0.508704 + 0.860942i \(0.330125\pi\)
\(884\) −1.67508 −0.0563389
\(885\) 86.7444 2.91588
\(886\) 25.9025 0.870211
\(887\) 14.7967 0.496824 0.248412 0.968655i \(-0.420091\pi\)
0.248412 + 0.968655i \(0.420091\pi\)
\(888\) 9.93756 0.333483
\(889\) 17.3786 0.582859
\(890\) 2.57101 0.0861803
\(891\) −58.5839 −1.96263
\(892\) 3.49374 0.116979
\(893\) 25.1211 0.840645
\(894\) −65.2828 −2.18338
\(895\) −69.7463 −2.33136
\(896\) −1.71915 −0.0574326
\(897\) 4.26099 0.142270
\(898\) 5.51032 0.183882
\(899\) 27.4616 0.915897
\(900\) 85.4080 2.84693
\(901\) −27.8366 −0.927371
\(902\) −4.02376 −0.133977
\(903\) 22.6305 0.753095
\(904\) −14.5249 −0.483090
\(905\) 24.6582 0.819667
\(906\) 55.7723 1.85291
\(907\) −23.3848 −0.776480 −0.388240 0.921558i \(-0.626917\pi\)
−0.388240 + 0.921558i \(0.626917\pi\)
\(908\) 5.78724 0.192056
\(909\) −131.436 −4.35947
\(910\) 4.24413 0.140691
\(911\) −1.29699 −0.0429712 −0.0214856 0.999769i \(-0.506840\pi\)
−0.0214856 + 0.999769i \(0.506840\pi\)
\(912\) 10.8325 0.358701
\(913\) −22.9881 −0.760794
\(914\) −15.4448 −0.510869
\(915\) −81.4754 −2.69349
\(916\) 7.87808 0.260299
\(917\) −10.7884 −0.356265
\(918\) −47.3716 −1.56350
\(919\) 4.20700 0.138776 0.0693880 0.997590i \(-0.477895\pi\)
0.0693880 + 0.997590i \(0.477895\pi\)
\(920\) 7.83961 0.258464
\(921\) −45.6216 −1.50328
\(922\) −37.5298 −1.23598
\(923\) −7.22022 −0.237656
\(924\) −9.63843 −0.317081
\(925\) −30.3639 −0.998358
\(926\) −28.0159 −0.920659
\(927\) 2.21682 0.0728100
\(928\) −6.75737 −0.221822
\(929\) 12.1176 0.397564 0.198782 0.980044i \(-0.436301\pi\)
0.198782 + 0.980044i \(0.436301\pi\)
\(930\) 53.4209 1.75174
\(931\) 13.0270 0.426943
\(932\) −17.0866 −0.559692
\(933\) 26.9649 0.882790
\(934\) −18.2634 −0.597598
\(935\) −17.2788 −0.565076
\(936\) −5.24970 −0.171592
\(937\) 18.2879 0.597439 0.298719 0.954341i \(-0.403441\pi\)
0.298719 + 0.954341i \(0.403441\pi\)
\(938\) 5.08549 0.166047
\(939\) 16.6026 0.541806
\(940\) −30.4839 −0.994275
\(941\) 0.0297097 0.000968509 0 0.000484254 1.00000i \(-0.499846\pi\)
0.000484254 1.00000i \(0.499846\pi\)
\(942\) −17.7418 −0.578059
\(943\) 4.84151 0.157661
\(944\) −6.59901 −0.214779
\(945\) 120.025 3.90441
\(946\) −6.52476 −0.212138
\(947\) −7.28252 −0.236650 −0.118325 0.992975i \(-0.537752\pi\)
−0.118325 + 0.992975i \(0.537752\pi\)
\(948\) 57.9794 1.88308
\(949\) 4.61115 0.149684
\(950\) −33.0984 −1.07385
\(951\) 29.3784 0.952661
\(952\) −4.55910 −0.147761
\(953\) −39.5165 −1.28007 −0.640033 0.768348i \(-0.721079\pi\)
−0.640033 + 0.768348i \(0.721079\pi\)
\(954\) −87.2400 −2.82450
\(955\) 41.6962 1.34926
\(956\) 6.15898 0.199196
\(957\) −37.8854 −1.22466
\(958\) −26.7325 −0.863689
\(959\) −13.8022 −0.445696
\(960\) −13.1451 −0.424255
\(961\) −14.4843 −0.467235
\(962\) 1.86635 0.0601735
\(963\) 5.83186 0.187929
\(964\) 1.72196 0.0554607
\(965\) 84.9922 2.73599
\(966\) 11.5972 0.373135
\(967\) 0.783289 0.0251889 0.0125944 0.999921i \(-0.495991\pi\)
0.0125944 + 0.999921i \(0.495991\pi\)
\(968\) −8.22107 −0.264235
\(969\) 28.7274 0.922858
\(970\) −7.45560 −0.239385
\(971\) −35.8632 −1.15091 −0.575453 0.817835i \(-0.695174\pi\)
−0.575453 + 0.817835i \(0.695174\pi\)
\(972\) −64.6052 −2.07221
\(973\) −32.9457 −1.05619
\(974\) 30.5225 0.978004
\(975\) 21.8301 0.699123
\(976\) 6.19818 0.198399
\(977\) 45.6513 1.46051 0.730257 0.683172i \(-0.239400\pi\)
0.730257 + 0.683172i \(0.239400\pi\)
\(978\) −48.2374 −1.54246
\(979\) −1.09656 −0.0350464
\(980\) −15.8080 −0.504968
\(981\) −67.8019 −2.16475
\(982\) −27.7964 −0.887018
\(983\) −19.2422 −0.613730 −0.306865 0.951753i \(-0.599280\pi\)
−0.306865 + 0.951753i \(0.599280\pi\)
\(984\) −8.11800 −0.258792
\(985\) 54.7863 1.74564
\(986\) −17.9203 −0.570697
\(987\) −45.0952 −1.43540
\(988\) 2.03443 0.0647239
\(989\) 7.85078 0.249640
\(990\) −54.1517 −1.72106
\(991\) 41.4527 1.31679 0.658395 0.752673i \(-0.271236\pi\)
0.658395 + 0.752673i \(0.271236\pi\)
\(992\) −4.06395 −0.129031
\(993\) 42.2465 1.34065
\(994\) −19.6514 −0.623306
\(995\) −100.663 −3.19122
\(996\) −46.3787 −1.46957
\(997\) 55.6727 1.76317 0.881586 0.472023i \(-0.156476\pi\)
0.881586 + 0.472023i \(0.156476\pi\)
\(998\) −28.3537 −0.897522
\(999\) 52.7808 1.66991
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 8006.2.a.a.1.1 69
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8006.2.a.a.1.1 69 1.1 even 1 trivial