Properties

Label 6015.2.a.i.1.7
Level $6015$
Weight $2$
Character 6015.1
Self dual yes
Analytic conductor $48.030$
Analytic rank $0$
Dimension $43$
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] = [6015,2,Mod(1,6015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6015.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: \(48.0300168158\)
Analytic rank: \(0\)
Dimension: \(43\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.07772 q^{2} +1.00000 q^{3} +2.31692 q^{4} +1.00000 q^{5} -2.07772 q^{6} -4.42665 q^{7} -0.658463 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.07772 q^{2} +1.00000 q^{3} +2.31692 q^{4} +1.00000 q^{5} -2.07772 q^{6} -4.42665 q^{7} -0.658463 q^{8} +1.00000 q^{9} -2.07772 q^{10} -1.48363 q^{11} +2.31692 q^{12} +6.43697 q^{13} +9.19733 q^{14} +1.00000 q^{15} -3.26573 q^{16} -0.558508 q^{17} -2.07772 q^{18} +2.52484 q^{19} +2.31692 q^{20} -4.42665 q^{21} +3.08256 q^{22} +7.03342 q^{23} -0.658463 q^{24} +1.00000 q^{25} -13.3742 q^{26} +1.00000 q^{27} -10.2562 q^{28} -1.58577 q^{29} -2.07772 q^{30} +1.47401 q^{31} +8.10220 q^{32} -1.48363 q^{33} +1.16042 q^{34} -4.42665 q^{35} +2.31692 q^{36} -4.72112 q^{37} -5.24591 q^{38} +6.43697 q^{39} -0.658463 q^{40} +1.86270 q^{41} +9.19733 q^{42} +2.32977 q^{43} -3.43744 q^{44} +1.00000 q^{45} -14.6135 q^{46} -2.29045 q^{47} -3.26573 q^{48} +12.5952 q^{49} -2.07772 q^{50} -0.558508 q^{51} +14.9139 q^{52} +7.52558 q^{53} -2.07772 q^{54} -1.48363 q^{55} +2.91479 q^{56} +2.52484 q^{57} +3.29478 q^{58} -0.844805 q^{59} +2.31692 q^{60} +12.7934 q^{61} -3.06259 q^{62} -4.42665 q^{63} -10.3026 q^{64} +6.43697 q^{65} +3.08256 q^{66} -2.81592 q^{67} -1.29402 q^{68} +7.03342 q^{69} +9.19733 q^{70} -6.45925 q^{71} -0.658463 q^{72} -14.8625 q^{73} +9.80916 q^{74} +1.00000 q^{75} +5.84985 q^{76} +6.56750 q^{77} -13.3742 q^{78} -12.2729 q^{79} -3.26573 q^{80} +1.00000 q^{81} -3.87016 q^{82} -15.5654 q^{83} -10.2562 q^{84} -0.558508 q^{85} -4.84062 q^{86} -1.58577 q^{87} +0.976915 q^{88} +3.07441 q^{89} -2.07772 q^{90} -28.4942 q^{91} +16.2959 q^{92} +1.47401 q^{93} +4.75891 q^{94} +2.52484 q^{95} +8.10220 q^{96} +1.79405 q^{97} -26.1693 q^{98} -1.48363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.07772 −1.46917 −0.734585 0.678517i \(-0.762623\pi\)
−0.734585 + 0.678517i \(0.762623\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.31692 1.15846
\(5\) 1.00000 0.447214
\(6\) −2.07772 −0.848225
\(7\) −4.42665 −1.67312 −0.836558 0.547878i \(-0.815436\pi\)
−0.836558 + 0.547878i \(0.815436\pi\)
\(8\) −0.658463 −0.232802
\(9\) 1.00000 0.333333
\(10\) −2.07772 −0.657032
\(11\) −1.48363 −0.447331 −0.223665 0.974666i \(-0.571802\pi\)
−0.223665 + 0.974666i \(0.571802\pi\)
\(12\) 2.31692 0.668836
\(13\) 6.43697 1.78529 0.892647 0.450757i \(-0.148846\pi\)
0.892647 + 0.450757i \(0.148846\pi\)
\(14\) 9.19733 2.45809
\(15\) 1.00000 0.258199
\(16\) −3.26573 −0.816433
\(17\) −0.558508 −0.135458 −0.0677290 0.997704i \(-0.521575\pi\)
−0.0677290 + 0.997704i \(0.521575\pi\)
\(18\) −2.07772 −0.489723
\(19\) 2.52484 0.579239 0.289619 0.957142i \(-0.406471\pi\)
0.289619 + 0.957142i \(0.406471\pi\)
\(20\) 2.31692 0.518078
\(21\) −4.42665 −0.965974
\(22\) 3.08256 0.657205
\(23\) 7.03342 1.46657 0.733285 0.679921i \(-0.237986\pi\)
0.733285 + 0.679921i \(0.237986\pi\)
\(24\) −0.658463 −0.134408
\(25\) 1.00000 0.200000
\(26\) −13.3742 −2.62290
\(27\) 1.00000 0.192450
\(28\) −10.2562 −1.93824
\(29\) −1.58577 −0.294469 −0.147235 0.989102i \(-0.547037\pi\)
−0.147235 + 0.989102i \(0.547037\pi\)
\(30\) −2.07772 −0.379338
\(31\) 1.47401 0.264741 0.132370 0.991200i \(-0.457741\pi\)
0.132370 + 0.991200i \(0.457741\pi\)
\(32\) 8.10220 1.43228
\(33\) −1.48363 −0.258267
\(34\) 1.16042 0.199011
\(35\) −4.42665 −0.748240
\(36\) 2.31692 0.386153
\(37\) −4.72112 −0.776147 −0.388074 0.921628i \(-0.626859\pi\)
−0.388074 + 0.921628i \(0.626859\pi\)
\(38\) −5.24591 −0.851000
\(39\) 6.43697 1.03074
\(40\) −0.658463 −0.104112
\(41\) 1.86270 0.290904 0.145452 0.989365i \(-0.453536\pi\)
0.145452 + 0.989365i \(0.453536\pi\)
\(42\) 9.19733 1.41918
\(43\) 2.32977 0.355287 0.177644 0.984095i \(-0.443153\pi\)
0.177644 + 0.984095i \(0.443153\pi\)
\(44\) −3.43744 −0.518214
\(45\) 1.00000 0.149071
\(46\) −14.6135 −2.15464
\(47\) −2.29045 −0.334096 −0.167048 0.985949i \(-0.553424\pi\)
−0.167048 + 0.985949i \(0.553424\pi\)
\(48\) −3.26573 −0.471368
\(49\) 12.5952 1.79932
\(50\) −2.07772 −0.293834
\(51\) −0.558508 −0.0782068
\(52\) 14.9139 2.06819
\(53\) 7.52558 1.03372 0.516859 0.856070i \(-0.327101\pi\)
0.516859 + 0.856070i \(0.327101\pi\)
\(54\) −2.07772 −0.282742
\(55\) −1.48363 −0.200052
\(56\) 2.91479 0.389505
\(57\) 2.52484 0.334424
\(58\) 3.29478 0.432625
\(59\) −0.844805 −0.109984 −0.0549921 0.998487i \(-0.517513\pi\)
−0.0549921 + 0.998487i \(0.517513\pi\)
\(60\) 2.31692 0.299113
\(61\) 12.7934 1.63803 0.819013 0.573775i \(-0.194522\pi\)
0.819013 + 0.573775i \(0.194522\pi\)
\(62\) −3.06259 −0.388949
\(63\) −4.42665 −0.557705
\(64\) −10.3026 −1.28783
\(65\) 6.43697 0.798407
\(66\) 3.08256 0.379437
\(67\) −2.81592 −0.344019 −0.172010 0.985095i \(-0.555026\pi\)
−0.172010 + 0.985095i \(0.555026\pi\)
\(68\) −1.29402 −0.156923
\(69\) 7.03342 0.846725
\(70\) 9.19733 1.09929
\(71\) −6.45925 −0.766572 −0.383286 0.923630i \(-0.625208\pi\)
−0.383286 + 0.923630i \(0.625208\pi\)
\(72\) −0.658463 −0.0776007
\(73\) −14.8625 −1.73952 −0.869761 0.493474i \(-0.835727\pi\)
−0.869761 + 0.493474i \(0.835727\pi\)
\(74\) 9.80916 1.14029
\(75\) 1.00000 0.115470
\(76\) 5.84985 0.671024
\(77\) 6.56750 0.748436
\(78\) −13.3742 −1.51433
\(79\) −12.2729 −1.38081 −0.690405 0.723423i \(-0.742568\pi\)
−0.690405 + 0.723423i \(0.742568\pi\)
\(80\) −3.26573 −0.365120
\(81\) 1.00000 0.111111
\(82\) −3.87016 −0.427387
\(83\) −15.5654 −1.70853 −0.854264 0.519839i \(-0.825992\pi\)
−0.854264 + 0.519839i \(0.825992\pi\)
\(84\) −10.2562 −1.11904
\(85\) −0.558508 −0.0605787
\(86\) −4.84062 −0.521977
\(87\) −1.58577 −0.170012
\(88\) 0.976915 0.104139
\(89\) 3.07441 0.325887 0.162943 0.986635i \(-0.447901\pi\)
0.162943 + 0.986635i \(0.447901\pi\)
\(90\) −2.07772 −0.219011
\(91\) −28.4942 −2.98700
\(92\) 16.2959 1.69896
\(93\) 1.47401 0.152848
\(94\) 4.75891 0.490844
\(95\) 2.52484 0.259043
\(96\) 8.10220 0.826927
\(97\) 1.79405 0.182158 0.0910791 0.995844i \(-0.470968\pi\)
0.0910791 + 0.995844i \(0.470968\pi\)
\(98\) −26.1693 −2.64350
\(99\) −1.48363 −0.149110
\(100\) 2.31692 0.231692
\(101\) 1.53032 0.152272 0.0761362 0.997097i \(-0.475742\pi\)
0.0761362 + 0.997097i \(0.475742\pi\)
\(102\) 1.16042 0.114899
\(103\) −5.23053 −0.515380 −0.257690 0.966228i \(-0.582961\pi\)
−0.257690 + 0.966228i \(0.582961\pi\)
\(104\) −4.23851 −0.415620
\(105\) −4.42665 −0.431997
\(106\) −15.6360 −1.51871
\(107\) 4.59052 0.443783 0.221891 0.975071i \(-0.428777\pi\)
0.221891 + 0.975071i \(0.428777\pi\)
\(108\) 2.31692 0.222945
\(109\) 15.6570 1.49966 0.749832 0.661628i \(-0.230134\pi\)
0.749832 + 0.661628i \(0.230134\pi\)
\(110\) 3.08256 0.293911
\(111\) −4.72112 −0.448109
\(112\) 14.4562 1.36599
\(113\) −2.49926 −0.235111 −0.117555 0.993066i \(-0.537506\pi\)
−0.117555 + 0.993066i \(0.537506\pi\)
\(114\) −5.24591 −0.491325
\(115\) 7.03342 0.655870
\(116\) −3.67409 −0.341131
\(117\) 6.43697 0.595098
\(118\) 1.75527 0.161585
\(119\) 2.47232 0.226637
\(120\) −0.658463 −0.0601092
\(121\) −8.79885 −0.799895
\(122\) −26.5811 −2.40654
\(123\) 1.86270 0.167954
\(124\) 3.41517 0.306691
\(125\) 1.00000 0.0894427
\(126\) 9.19733 0.819364
\(127\) 4.38227 0.388864 0.194432 0.980916i \(-0.437714\pi\)
0.194432 + 0.980916i \(0.437714\pi\)
\(128\) 5.20157 0.459759
\(129\) 2.32977 0.205125
\(130\) −13.3742 −1.17300
\(131\) −2.38767 −0.208612 −0.104306 0.994545i \(-0.533262\pi\)
−0.104306 + 0.994545i \(0.533262\pi\)
\(132\) −3.43744 −0.299191
\(133\) −11.1766 −0.969134
\(134\) 5.85069 0.505423
\(135\) 1.00000 0.0860663
\(136\) 0.367757 0.0315349
\(137\) −3.86352 −0.330082 −0.165041 0.986287i \(-0.552776\pi\)
−0.165041 + 0.986287i \(0.552776\pi\)
\(138\) −14.6135 −1.24398
\(139\) 21.5796 1.83036 0.915178 0.403050i \(-0.132050\pi\)
0.915178 + 0.403050i \(0.132050\pi\)
\(140\) −10.2562 −0.866805
\(141\) −2.29045 −0.192891
\(142\) 13.4205 1.12622
\(143\) −9.55007 −0.798617
\(144\) −3.26573 −0.272144
\(145\) −1.58577 −0.131691
\(146\) 30.8801 2.55565
\(147\) 12.5952 1.03884
\(148\) −10.9384 −0.899134
\(149\) 14.5330 1.19059 0.595296 0.803507i \(-0.297035\pi\)
0.595296 + 0.803507i \(0.297035\pi\)
\(150\) −2.07772 −0.169645
\(151\) 14.8051 1.20482 0.602411 0.798186i \(-0.294207\pi\)
0.602411 + 0.798186i \(0.294207\pi\)
\(152\) −1.66252 −0.134848
\(153\) −0.558508 −0.0451527
\(154\) −13.6454 −1.09958
\(155\) 1.47401 0.118396
\(156\) 14.9139 1.19407
\(157\) 12.3905 0.988866 0.494433 0.869216i \(-0.335376\pi\)
0.494433 + 0.869216i \(0.335376\pi\)
\(158\) 25.4997 2.02864
\(159\) 7.52558 0.596817
\(160\) 8.10220 0.640535
\(161\) −31.1345 −2.45374
\(162\) −2.07772 −0.163241
\(163\) −8.50867 −0.666450 −0.333225 0.942847i \(-0.608137\pi\)
−0.333225 + 0.942847i \(0.608137\pi\)
\(164\) 4.31571 0.337000
\(165\) −1.48363 −0.115500
\(166\) 32.3406 2.51012
\(167\) −9.85827 −0.762856 −0.381428 0.924399i \(-0.624568\pi\)
−0.381428 + 0.924399i \(0.624568\pi\)
\(168\) 2.91479 0.224881
\(169\) 28.4345 2.18727
\(170\) 1.16042 0.0890004
\(171\) 2.52484 0.193080
\(172\) 5.39789 0.411585
\(173\) −4.62289 −0.351472 −0.175736 0.984437i \(-0.556230\pi\)
−0.175736 + 0.984437i \(0.556230\pi\)
\(174\) 3.29478 0.249776
\(175\) −4.42665 −0.334623
\(176\) 4.84513 0.365216
\(177\) −0.844805 −0.0634994
\(178\) −6.38776 −0.478783
\(179\) −1.34249 −0.100343 −0.0501713 0.998741i \(-0.515977\pi\)
−0.0501713 + 0.998741i \(0.515977\pi\)
\(180\) 2.31692 0.172693
\(181\) 9.38498 0.697580 0.348790 0.937201i \(-0.386593\pi\)
0.348790 + 0.937201i \(0.386593\pi\)
\(182\) 59.2029 4.38841
\(183\) 12.7934 0.945714
\(184\) −4.63125 −0.341420
\(185\) −4.72112 −0.347104
\(186\) −3.06259 −0.224560
\(187\) 0.828618 0.0605946
\(188\) −5.30678 −0.387037
\(189\) −4.42665 −0.321991
\(190\) −5.24591 −0.380579
\(191\) −15.6325 −1.13113 −0.565563 0.824705i \(-0.691341\pi\)
−0.565563 + 0.824705i \(0.691341\pi\)
\(192\) −10.3026 −0.743528
\(193\) −1.12574 −0.0810323 −0.0405161 0.999179i \(-0.512900\pi\)
−0.0405161 + 0.999179i \(0.512900\pi\)
\(194\) −3.72753 −0.267621
\(195\) 6.43697 0.460961
\(196\) 29.1821 2.08443
\(197\) −20.7500 −1.47838 −0.739189 0.673498i \(-0.764791\pi\)
−0.739189 + 0.673498i \(0.764791\pi\)
\(198\) 3.08256 0.219068
\(199\) 15.8179 1.12130 0.560649 0.828054i \(-0.310552\pi\)
0.560649 + 0.828054i \(0.310552\pi\)
\(200\) −0.658463 −0.0465604
\(201\) −2.81592 −0.198620
\(202\) −3.17957 −0.223714
\(203\) 7.01963 0.492682
\(204\) −1.29402 −0.0905993
\(205\) 1.86270 0.130096
\(206\) 10.8676 0.757180
\(207\) 7.03342 0.488857
\(208\) −21.0214 −1.45757
\(209\) −3.74593 −0.259111
\(210\) 9.19733 0.634676
\(211\) 26.4561 1.82131 0.910656 0.413166i \(-0.135577\pi\)
0.910656 + 0.413166i \(0.135577\pi\)
\(212\) 17.4361 1.19752
\(213\) −6.45925 −0.442580
\(214\) −9.53782 −0.651992
\(215\) 2.32977 0.158889
\(216\) −0.658463 −0.0448028
\(217\) −6.52494 −0.442942
\(218\) −32.5307 −2.20326
\(219\) −14.8625 −1.00431
\(220\) −3.43744 −0.231752
\(221\) −3.59510 −0.241832
\(222\) 9.80916 0.658348
\(223\) 24.2406 1.62327 0.811634 0.584167i \(-0.198579\pi\)
0.811634 + 0.584167i \(0.198579\pi\)
\(224\) −35.8656 −2.39637
\(225\) 1.00000 0.0666667
\(226\) 5.19276 0.345417
\(227\) −11.6881 −0.775766 −0.387883 0.921709i \(-0.626794\pi\)
−0.387883 + 0.921709i \(0.626794\pi\)
\(228\) 5.84985 0.387416
\(229\) 17.6754 1.16802 0.584012 0.811745i \(-0.301482\pi\)
0.584012 + 0.811745i \(0.301482\pi\)
\(230\) −14.6135 −0.963584
\(231\) 6.56750 0.432110
\(232\) 1.04417 0.0685531
\(233\) 22.3503 1.46422 0.732108 0.681189i \(-0.238537\pi\)
0.732108 + 0.681189i \(0.238537\pi\)
\(234\) −13.3742 −0.874299
\(235\) −2.29045 −0.149412
\(236\) −1.95734 −0.127412
\(237\) −12.2729 −0.797211
\(238\) −5.13678 −0.332968
\(239\) −3.42123 −0.221301 −0.110651 0.993859i \(-0.535293\pi\)
−0.110651 + 0.993859i \(0.535293\pi\)
\(240\) −3.26573 −0.210802
\(241\) 24.3443 1.56815 0.784077 0.620664i \(-0.213137\pi\)
0.784077 + 0.620664i \(0.213137\pi\)
\(242\) 18.2815 1.17518
\(243\) 1.00000 0.0641500
\(244\) 29.6412 1.89758
\(245\) 12.5952 0.804680
\(246\) −3.87016 −0.246752
\(247\) 16.2523 1.03411
\(248\) −0.970584 −0.0616321
\(249\) −15.5654 −0.986420
\(250\) −2.07772 −0.131406
\(251\) −28.3171 −1.78736 −0.893678 0.448708i \(-0.851884\pi\)
−0.893678 + 0.448708i \(0.851884\pi\)
\(252\) −10.2562 −0.646078
\(253\) −10.4350 −0.656042
\(254\) −9.10513 −0.571307
\(255\) −0.558508 −0.0349751
\(256\) 9.79785 0.612366
\(257\) −23.2754 −1.45188 −0.725941 0.687757i \(-0.758596\pi\)
−0.725941 + 0.687757i \(0.758596\pi\)
\(258\) −4.84062 −0.301364
\(259\) 20.8987 1.29858
\(260\) 14.9139 0.924922
\(261\) −1.58577 −0.0981565
\(262\) 4.96091 0.306486
\(263\) 21.2062 1.30763 0.653815 0.756654i \(-0.273167\pi\)
0.653815 + 0.756654i \(0.273167\pi\)
\(264\) 0.976915 0.0601250
\(265\) 7.52558 0.462293
\(266\) 23.2218 1.42382
\(267\) 3.07441 0.188151
\(268\) −6.52425 −0.398532
\(269\) 29.1884 1.77965 0.889824 0.456304i \(-0.150827\pi\)
0.889824 + 0.456304i \(0.150827\pi\)
\(270\) −2.07772 −0.126446
\(271\) 25.6360 1.55728 0.778638 0.627474i \(-0.215911\pi\)
0.778638 + 0.627474i \(0.215911\pi\)
\(272\) 1.82394 0.110592
\(273\) −28.4942 −1.72455
\(274\) 8.02730 0.484947
\(275\) −1.48363 −0.0894662
\(276\) 16.2959 0.980895
\(277\) −10.7203 −0.644118 −0.322059 0.946720i \(-0.604375\pi\)
−0.322059 + 0.946720i \(0.604375\pi\)
\(278\) −44.8363 −2.68910
\(279\) 1.47401 0.0882469
\(280\) 2.91479 0.174192
\(281\) 27.2623 1.62633 0.813166 0.582032i \(-0.197742\pi\)
0.813166 + 0.582032i \(0.197742\pi\)
\(282\) 4.75891 0.283389
\(283\) 5.89342 0.350327 0.175164 0.984539i \(-0.443955\pi\)
0.175164 + 0.984539i \(0.443955\pi\)
\(284\) −14.9655 −0.888041
\(285\) 2.52484 0.149559
\(286\) 19.8424 1.17330
\(287\) −8.24550 −0.486717
\(288\) 8.10220 0.477427
\(289\) −16.6881 −0.981651
\(290\) 3.29478 0.193476
\(291\) 1.79405 0.105169
\(292\) −34.4351 −2.01516
\(293\) 4.62191 0.270015 0.135008 0.990845i \(-0.456894\pi\)
0.135008 + 0.990845i \(0.456894\pi\)
\(294\) −26.1693 −1.52623
\(295\) −0.844805 −0.0491864
\(296\) 3.10868 0.180689
\(297\) −1.48363 −0.0860888
\(298\) −30.1955 −1.74918
\(299\) 45.2739 2.61826
\(300\) 2.31692 0.133767
\(301\) −10.3131 −0.594437
\(302\) −30.7608 −1.77009
\(303\) 1.53032 0.0879145
\(304\) −8.24546 −0.472909
\(305\) 12.7934 0.732547
\(306\) 1.16042 0.0663370
\(307\) 10.9881 0.627123 0.313561 0.949568i \(-0.398478\pi\)
0.313561 + 0.949568i \(0.398478\pi\)
\(308\) 15.2164 0.867032
\(309\) −5.23053 −0.297555
\(310\) −3.06259 −0.173943
\(311\) −0.114314 −0.00648215 −0.00324108 0.999995i \(-0.501032\pi\)
−0.00324108 + 0.999995i \(0.501032\pi\)
\(312\) −4.23851 −0.239958
\(313\) −5.70116 −0.322249 −0.161124 0.986934i \(-0.551512\pi\)
−0.161124 + 0.986934i \(0.551512\pi\)
\(314\) −25.7439 −1.45281
\(315\) −4.42665 −0.249413
\(316\) −28.4353 −1.59961
\(317\) 1.13763 0.0638958 0.0319479 0.999490i \(-0.489829\pi\)
0.0319479 + 0.999490i \(0.489829\pi\)
\(318\) −15.6360 −0.876826
\(319\) 2.35269 0.131725
\(320\) −10.3026 −0.575935
\(321\) 4.59052 0.256218
\(322\) 64.6887 3.60496
\(323\) −1.41015 −0.0784626
\(324\) 2.31692 0.128718
\(325\) 6.43697 0.357059
\(326\) 17.6786 0.979128
\(327\) 15.6570 0.865831
\(328\) −1.22652 −0.0677231
\(329\) 10.1390 0.558982
\(330\) 3.08256 0.169690
\(331\) −2.00858 −0.110402 −0.0552008 0.998475i \(-0.517580\pi\)
−0.0552008 + 0.998475i \(0.517580\pi\)
\(332\) −36.0638 −1.97926
\(333\) −4.72112 −0.258716
\(334\) 20.4827 1.12076
\(335\) −2.81592 −0.153850
\(336\) 14.4562 0.788653
\(337\) −17.3508 −0.945160 −0.472580 0.881288i \(-0.656677\pi\)
−0.472580 + 0.881288i \(0.656677\pi\)
\(338\) −59.0790 −3.21347
\(339\) −2.49926 −0.135741
\(340\) −1.29402 −0.0701779
\(341\) −2.18689 −0.118427
\(342\) −5.24591 −0.283667
\(343\) −24.7681 −1.33735
\(344\) −1.53407 −0.0827116
\(345\) 7.03342 0.378667
\(346\) 9.60507 0.516372
\(347\) 15.4484 0.829313 0.414657 0.909978i \(-0.363902\pi\)
0.414657 + 0.909978i \(0.363902\pi\)
\(348\) −3.67409 −0.196952
\(349\) −26.3636 −1.41121 −0.705607 0.708604i \(-0.749325\pi\)
−0.705607 + 0.708604i \(0.749325\pi\)
\(350\) 9.19733 0.491618
\(351\) 6.43697 0.343580
\(352\) −12.0207 −0.640703
\(353\) 4.81739 0.256404 0.128202 0.991748i \(-0.459079\pi\)
0.128202 + 0.991748i \(0.459079\pi\)
\(354\) 1.75527 0.0932914
\(355\) −6.45925 −0.342821
\(356\) 7.12315 0.377526
\(357\) 2.47232 0.130849
\(358\) 2.78932 0.147420
\(359\) −30.8062 −1.62589 −0.812943 0.582343i \(-0.802136\pi\)
−0.812943 + 0.582343i \(0.802136\pi\)
\(360\) −0.658463 −0.0347041
\(361\) −12.6252 −0.664483
\(362\) −19.4994 −1.02486
\(363\) −8.79885 −0.461820
\(364\) −66.0187 −3.46032
\(365\) −14.8625 −0.777938
\(366\) −26.5811 −1.38941
\(367\) −2.06412 −0.107746 −0.0538732 0.998548i \(-0.517157\pi\)
−0.0538732 + 0.998548i \(0.517157\pi\)
\(368\) −22.9693 −1.19736
\(369\) 1.86270 0.0969681
\(370\) 9.80916 0.509954
\(371\) −33.3131 −1.72953
\(372\) 3.41517 0.177068
\(373\) 22.1308 1.14589 0.572945 0.819594i \(-0.305801\pi\)
0.572945 + 0.819594i \(0.305801\pi\)
\(374\) −1.72164 −0.0890237
\(375\) 1.00000 0.0516398
\(376\) 1.50818 0.0777783
\(377\) −10.2075 −0.525714
\(378\) 9.19733 0.473060
\(379\) 21.3004 1.09413 0.547063 0.837092i \(-0.315746\pi\)
0.547063 + 0.837092i \(0.315746\pi\)
\(380\) 5.84985 0.300091
\(381\) 4.38227 0.224511
\(382\) 32.4799 1.66181
\(383\) −16.4144 −0.838735 −0.419368 0.907816i \(-0.637748\pi\)
−0.419368 + 0.907816i \(0.637748\pi\)
\(384\) 5.20157 0.265442
\(385\) 6.56750 0.334711
\(386\) 2.33896 0.119050
\(387\) 2.32977 0.118429
\(388\) 4.15666 0.211023
\(389\) 15.1829 0.769805 0.384903 0.922957i \(-0.374235\pi\)
0.384903 + 0.922957i \(0.374235\pi\)
\(390\) −13.3742 −0.677229
\(391\) −3.92822 −0.198659
\(392\) −8.29350 −0.418885
\(393\) −2.38767 −0.120442
\(394\) 43.1127 2.17199
\(395\) −12.2729 −0.617517
\(396\) −3.43744 −0.172738
\(397\) 7.22477 0.362601 0.181301 0.983428i \(-0.441969\pi\)
0.181301 + 0.983428i \(0.441969\pi\)
\(398\) −32.8651 −1.64738
\(399\) −11.1766 −0.559530
\(400\) −3.26573 −0.163287
\(401\) 1.00000 0.0499376
\(402\) 5.85069 0.291806
\(403\) 9.48817 0.472640
\(404\) 3.54562 0.176401
\(405\) 1.00000 0.0496904
\(406\) −14.5848 −0.723833
\(407\) 7.00439 0.347195
\(408\) 0.367757 0.0182067
\(409\) 6.69677 0.331134 0.165567 0.986199i \(-0.447055\pi\)
0.165567 + 0.986199i \(0.447055\pi\)
\(410\) −3.87016 −0.191133
\(411\) −3.86352 −0.190573
\(412\) −12.1187 −0.597046
\(413\) 3.73965 0.184016
\(414\) −14.6135 −0.718213
\(415\) −15.5654 −0.764077
\(416\) 52.1536 2.55704
\(417\) 21.5796 1.05676
\(418\) 7.78299 0.380678
\(419\) −3.57582 −0.174690 −0.0873451 0.996178i \(-0.527838\pi\)
−0.0873451 + 0.996178i \(0.527838\pi\)
\(420\) −10.2562 −0.500450
\(421\) −2.99153 −0.145798 −0.0728991 0.997339i \(-0.523225\pi\)
−0.0728991 + 0.997339i \(0.523225\pi\)
\(422\) −54.9683 −2.67581
\(423\) −2.29045 −0.111365
\(424\) −4.95532 −0.240652
\(425\) −0.558508 −0.0270916
\(426\) 13.4205 0.650225
\(427\) −56.6318 −2.74061
\(428\) 10.6359 0.514104
\(429\) −9.55007 −0.461082
\(430\) −4.84062 −0.233435
\(431\) 5.97384 0.287750 0.143875 0.989596i \(-0.454044\pi\)
0.143875 + 0.989596i \(0.454044\pi\)
\(432\) −3.26573 −0.157123
\(433\) 16.2663 0.781711 0.390855 0.920452i \(-0.372179\pi\)
0.390855 + 0.920452i \(0.372179\pi\)
\(434\) 13.5570 0.650756
\(435\) −1.58577 −0.0760317
\(436\) 36.2758 1.73730
\(437\) 17.7583 0.849494
\(438\) 30.8801 1.47551
\(439\) −36.4207 −1.73827 −0.869134 0.494577i \(-0.835323\pi\)
−0.869134 + 0.494577i \(0.835323\pi\)
\(440\) 0.976915 0.0465726
\(441\) 12.5952 0.599773
\(442\) 7.46960 0.355293
\(443\) 8.11596 0.385601 0.192801 0.981238i \(-0.438243\pi\)
0.192801 + 0.981238i \(0.438243\pi\)
\(444\) −10.9384 −0.519115
\(445\) 3.07441 0.145741
\(446\) −50.3651 −2.38485
\(447\) 14.5330 0.687388
\(448\) 45.6061 2.15469
\(449\) −18.8078 −0.887597 −0.443799 0.896127i \(-0.646369\pi\)
−0.443799 + 0.896127i \(0.646369\pi\)
\(450\) −2.07772 −0.0979446
\(451\) −2.76355 −0.130130
\(452\) −5.79058 −0.272366
\(453\) 14.8051 0.695604
\(454\) 24.2846 1.13973
\(455\) −28.4942 −1.33583
\(456\) −1.66252 −0.0778545
\(457\) 28.8194 1.34811 0.674057 0.738680i \(-0.264550\pi\)
0.674057 + 0.738680i \(0.264550\pi\)
\(458\) −36.7246 −1.71603
\(459\) −0.558508 −0.0260689
\(460\) 16.2959 0.759798
\(461\) −42.2802 −1.96919 −0.984593 0.174864i \(-0.944051\pi\)
−0.984593 + 0.174864i \(0.944051\pi\)
\(462\) −13.6454 −0.634843
\(463\) −20.6245 −0.958503 −0.479252 0.877678i \(-0.659092\pi\)
−0.479252 + 0.877678i \(0.659092\pi\)
\(464\) 5.17869 0.240414
\(465\) 1.47401 0.0683557
\(466\) −46.4376 −2.15118
\(467\) 3.42075 0.158294 0.0791468 0.996863i \(-0.474780\pi\)
0.0791468 + 0.996863i \(0.474780\pi\)
\(468\) 14.9139 0.689396
\(469\) 12.4651 0.575585
\(470\) 4.75891 0.219512
\(471\) 12.3905 0.570922
\(472\) 0.556273 0.0256045
\(473\) −3.45652 −0.158931
\(474\) 25.4997 1.17124
\(475\) 2.52484 0.115848
\(476\) 5.72816 0.262550
\(477\) 7.52558 0.344573
\(478\) 7.10836 0.325129
\(479\) 30.4454 1.39109 0.695543 0.718485i \(-0.255164\pi\)
0.695543 + 0.718485i \(0.255164\pi\)
\(480\) 8.10220 0.369813
\(481\) −30.3897 −1.38565
\(482\) −50.5806 −2.30388
\(483\) −31.1345 −1.41667
\(484\) −20.3862 −0.926645
\(485\) 1.79405 0.0814636
\(486\) −2.07772 −0.0942473
\(487\) −16.9043 −0.766008 −0.383004 0.923747i \(-0.625110\pi\)
−0.383004 + 0.923747i \(0.625110\pi\)
\(488\) −8.42398 −0.381336
\(489\) −8.50867 −0.384775
\(490\) −26.1693 −1.18221
\(491\) 36.1062 1.62945 0.814724 0.579848i \(-0.196888\pi\)
0.814724 + 0.579848i \(0.196888\pi\)
\(492\) 4.31571 0.194567
\(493\) 0.885663 0.0398883
\(494\) −33.7678 −1.51928
\(495\) −1.48363 −0.0666841
\(496\) −4.81373 −0.216143
\(497\) 28.5928 1.28256
\(498\) 32.3406 1.44922
\(499\) 2.69002 0.120422 0.0602110 0.998186i \(-0.480823\pi\)
0.0602110 + 0.998186i \(0.480823\pi\)
\(500\) 2.31692 0.103616
\(501\) −9.85827 −0.440435
\(502\) 58.8349 2.62593
\(503\) 21.4498 0.956399 0.478199 0.878251i \(-0.341290\pi\)
0.478199 + 0.878251i \(0.341290\pi\)
\(504\) 2.91479 0.129835
\(505\) 1.53032 0.0680983
\(506\) 21.6810 0.963837
\(507\) 28.4345 1.26282
\(508\) 10.1534 0.450482
\(509\) −8.21098 −0.363945 −0.181973 0.983304i \(-0.558248\pi\)
−0.181973 + 0.983304i \(0.558248\pi\)
\(510\) 1.16042 0.0513844
\(511\) 65.7910 2.91042
\(512\) −30.7603 −1.35943
\(513\) 2.52484 0.111475
\(514\) 48.3598 2.13306
\(515\) −5.23053 −0.230485
\(516\) 5.39789 0.237629
\(517\) 3.39817 0.149452
\(518\) −43.4217 −1.90784
\(519\) −4.62289 −0.202922
\(520\) −4.23851 −0.185871
\(521\) 10.3035 0.451405 0.225703 0.974196i \(-0.427532\pi\)
0.225703 + 0.974196i \(0.427532\pi\)
\(522\) 3.29478 0.144208
\(523\) 27.9991 1.22432 0.612158 0.790736i \(-0.290302\pi\)
0.612158 + 0.790736i \(0.290302\pi\)
\(524\) −5.53204 −0.241668
\(525\) −4.42665 −0.193195
\(526\) −44.0605 −1.92113
\(527\) −0.823248 −0.0358613
\(528\) 4.84513 0.210857
\(529\) 26.4690 1.15083
\(530\) −15.6360 −0.679186
\(531\) −0.844805 −0.0366614
\(532\) −25.8952 −1.12270
\(533\) 11.9901 0.519349
\(534\) −6.38776 −0.276426
\(535\) 4.59052 0.198466
\(536\) 1.85418 0.0800884
\(537\) −1.34249 −0.0579328
\(538\) −60.6453 −2.61460
\(539\) −18.6866 −0.804890
\(540\) 2.31692 0.0997042
\(541\) 33.0225 1.41975 0.709874 0.704329i \(-0.248752\pi\)
0.709874 + 0.704329i \(0.248752\pi\)
\(542\) −53.2644 −2.28790
\(543\) 9.38498 0.402748
\(544\) −4.52514 −0.194014
\(545\) 15.6570 0.670670
\(546\) 59.2029 2.53365
\(547\) 4.82015 0.206095 0.103047 0.994676i \(-0.467141\pi\)
0.103047 + 0.994676i \(0.467141\pi\)
\(548\) −8.95144 −0.382387
\(549\) 12.7934 0.546008
\(550\) 3.08256 0.131441
\(551\) −4.00381 −0.170568
\(552\) −4.63125 −0.197119
\(553\) 54.3279 2.31026
\(554\) 22.2737 0.946319
\(555\) −4.72112 −0.200400
\(556\) 49.9981 2.12039
\(557\) −29.0822 −1.23225 −0.616127 0.787647i \(-0.711299\pi\)
−0.616127 + 0.787647i \(0.711299\pi\)
\(558\) −3.06259 −0.129650
\(559\) 14.9967 0.634292
\(560\) 14.4562 0.610888
\(561\) 0.828618 0.0349843
\(562\) −56.6434 −2.38936
\(563\) −26.7323 −1.12663 −0.563315 0.826242i \(-0.690474\pi\)
−0.563315 + 0.826242i \(0.690474\pi\)
\(564\) −5.30678 −0.223456
\(565\) −2.49926 −0.105145
\(566\) −12.2449 −0.514690
\(567\) −4.42665 −0.185902
\(568\) 4.25318 0.178459
\(569\) −19.0470 −0.798491 −0.399246 0.916844i \(-0.630728\pi\)
−0.399246 + 0.916844i \(0.630728\pi\)
\(570\) −5.24591 −0.219727
\(571\) −9.76891 −0.408816 −0.204408 0.978886i \(-0.565527\pi\)
−0.204408 + 0.978886i \(0.565527\pi\)
\(572\) −22.1267 −0.925164
\(573\) −15.6325 −0.653055
\(574\) 17.1318 0.715069
\(575\) 7.03342 0.293314
\(576\) −10.3026 −0.429276
\(577\) 23.3735 0.973050 0.486525 0.873667i \(-0.338264\pi\)
0.486525 + 0.873667i \(0.338264\pi\)
\(578\) 34.6731 1.44221
\(579\) −1.12574 −0.0467840
\(580\) −3.67409 −0.152558
\(581\) 68.9027 2.85857
\(582\) −3.72753 −0.154511
\(583\) −11.1652 −0.462414
\(584\) 9.78640 0.404964
\(585\) 6.43697 0.266136
\(586\) −9.60304 −0.396698
\(587\) −5.74205 −0.237000 −0.118500 0.992954i \(-0.537809\pi\)
−0.118500 + 0.992954i \(0.537809\pi\)
\(588\) 29.1821 1.20345
\(589\) 3.72165 0.153348
\(590\) 1.75527 0.0722632
\(591\) −20.7500 −0.853542
\(592\) 15.4179 0.633672
\(593\) 30.6567 1.25892 0.629459 0.777033i \(-0.283276\pi\)
0.629459 + 0.777033i \(0.283276\pi\)
\(594\) 3.08256 0.126479
\(595\) 2.47232 0.101355
\(596\) 33.6718 1.37925
\(597\) 15.8179 0.647382
\(598\) −94.0665 −3.84666
\(599\) 8.95067 0.365715 0.182857 0.983139i \(-0.441465\pi\)
0.182857 + 0.983139i \(0.441465\pi\)
\(600\) −0.658463 −0.0268817
\(601\) 23.5695 0.961419 0.480710 0.876880i \(-0.340379\pi\)
0.480710 + 0.876880i \(0.340379\pi\)
\(602\) 21.4277 0.873328
\(603\) −2.81592 −0.114673
\(604\) 34.3022 1.39574
\(605\) −8.79885 −0.357724
\(606\) −3.17957 −0.129161
\(607\) 17.9509 0.728604 0.364302 0.931281i \(-0.381308\pi\)
0.364302 + 0.931281i \(0.381308\pi\)
\(608\) 20.4568 0.829632
\(609\) 7.01963 0.284450
\(610\) −26.5811 −1.07624
\(611\) −14.7435 −0.596460
\(612\) −1.29402 −0.0523075
\(613\) −0.187178 −0.00756003 −0.00378002 0.999993i \(-0.501203\pi\)
−0.00378002 + 0.999993i \(0.501203\pi\)
\(614\) −22.8301 −0.921349
\(615\) 1.86270 0.0751111
\(616\) −4.32446 −0.174237
\(617\) 21.2845 0.856880 0.428440 0.903570i \(-0.359063\pi\)
0.428440 + 0.903570i \(0.359063\pi\)
\(618\) 10.8676 0.437158
\(619\) 26.4776 1.06422 0.532112 0.846674i \(-0.321398\pi\)
0.532112 + 0.846674i \(0.321398\pi\)
\(620\) 3.41517 0.137156
\(621\) 7.03342 0.282242
\(622\) 0.237512 0.00952338
\(623\) −13.6093 −0.545247
\(624\) −21.0214 −0.841529
\(625\) 1.00000 0.0400000
\(626\) 11.8454 0.473438
\(627\) −3.74593 −0.149598
\(628\) 28.7076 1.14556
\(629\) 2.63678 0.105135
\(630\) 9.19733 0.366431
\(631\) −15.3672 −0.611757 −0.305878 0.952071i \(-0.598950\pi\)
−0.305878 + 0.952071i \(0.598950\pi\)
\(632\) 8.08127 0.321455
\(633\) 26.4561 1.05153
\(634\) −2.36368 −0.0938738
\(635\) 4.38227 0.173905
\(636\) 17.4361 0.691388
\(637\) 81.0750 3.21231
\(638\) −4.88822 −0.193527
\(639\) −6.45925 −0.255524
\(640\) 5.20157 0.205610
\(641\) 21.2377 0.838839 0.419420 0.907792i \(-0.362234\pi\)
0.419420 + 0.907792i \(0.362234\pi\)
\(642\) −9.53782 −0.376428
\(643\) −9.46684 −0.373336 −0.186668 0.982423i \(-0.559769\pi\)
−0.186668 + 0.982423i \(0.559769\pi\)
\(644\) −72.1360 −2.84256
\(645\) 2.32977 0.0917348
\(646\) 2.92989 0.115275
\(647\) −13.4251 −0.527796 −0.263898 0.964551i \(-0.585008\pi\)
−0.263898 + 0.964551i \(0.585008\pi\)
\(648\) −0.658463 −0.0258669
\(649\) 1.25338 0.0491993
\(650\) −13.3742 −0.524580
\(651\) −6.52494 −0.255733
\(652\) −19.7139 −0.772055
\(653\) 29.2982 1.14653 0.573264 0.819371i \(-0.305677\pi\)
0.573264 + 0.819371i \(0.305677\pi\)
\(654\) −32.5307 −1.27205
\(655\) −2.38767 −0.0932941
\(656\) −6.08306 −0.237504
\(657\) −14.8625 −0.579840
\(658\) −21.0660 −0.821239
\(659\) −32.2265 −1.25537 −0.627684 0.778468i \(-0.715997\pi\)
−0.627684 + 0.778468i \(0.715997\pi\)
\(660\) −3.43744 −0.133802
\(661\) −4.95749 −0.192824 −0.0964121 0.995342i \(-0.530737\pi\)
−0.0964121 + 0.995342i \(0.530737\pi\)
\(662\) 4.17327 0.162199
\(663\) −3.59510 −0.139622
\(664\) 10.2493 0.397749
\(665\) −11.1766 −0.433410
\(666\) 9.80916 0.380097
\(667\) −11.1534 −0.431860
\(668\) −22.8408 −0.883737
\(669\) 24.2406 0.937194
\(670\) 5.85069 0.226032
\(671\) −18.9806 −0.732739
\(672\) −35.8656 −1.38355
\(673\) 7.51400 0.289644 0.144822 0.989458i \(-0.453739\pi\)
0.144822 + 0.989458i \(0.453739\pi\)
\(674\) 36.0501 1.38860
\(675\) 1.00000 0.0384900
\(676\) 65.8804 2.53386
\(677\) 32.9678 1.26706 0.633528 0.773720i \(-0.281606\pi\)
0.633528 + 0.773720i \(0.281606\pi\)
\(678\) 5.19276 0.199427
\(679\) −7.94163 −0.304772
\(680\) 0.367757 0.0141028
\(681\) −11.6881 −0.447889
\(682\) 4.54374 0.173989
\(683\) 29.6082 1.13293 0.566463 0.824087i \(-0.308311\pi\)
0.566463 + 0.824087i \(0.308311\pi\)
\(684\) 5.84985 0.223675
\(685\) −3.86352 −0.147617
\(686\) 51.4612 1.96480
\(687\) 17.6754 0.674359
\(688\) −7.60841 −0.290068
\(689\) 48.4419 1.84549
\(690\) −14.6135 −0.556326
\(691\) −11.6840 −0.444480 −0.222240 0.974992i \(-0.571337\pi\)
−0.222240 + 0.974992i \(0.571337\pi\)
\(692\) −10.7109 −0.407166
\(693\) 6.56750 0.249479
\(694\) −32.0974 −1.21840
\(695\) 21.5796 0.818560
\(696\) 1.04417 0.0395791
\(697\) −1.04033 −0.0394053
\(698\) 54.7762 2.07331
\(699\) 22.3503 0.845365
\(700\) −10.2562 −0.387647
\(701\) 36.6032 1.38248 0.691242 0.722623i \(-0.257064\pi\)
0.691242 + 0.722623i \(0.257064\pi\)
\(702\) −13.3742 −0.504777
\(703\) −11.9201 −0.449574
\(704\) 15.2853 0.576085
\(705\) −2.29045 −0.0862633
\(706\) −10.0092 −0.376700
\(707\) −6.77419 −0.254770
\(708\) −1.95734 −0.0735614
\(709\) −32.2651 −1.21174 −0.605871 0.795563i \(-0.707175\pi\)
−0.605871 + 0.795563i \(0.707175\pi\)
\(710\) 13.4205 0.503662
\(711\) −12.2729 −0.460270
\(712\) −2.02439 −0.0758671
\(713\) 10.3674 0.388261
\(714\) −5.13678 −0.192239
\(715\) −9.55007 −0.357152
\(716\) −3.11044 −0.116243
\(717\) −3.42123 −0.127768
\(718\) 64.0065 2.38870
\(719\) 0.320817 0.0119645 0.00598223 0.999982i \(-0.498096\pi\)
0.00598223 + 0.999982i \(0.498096\pi\)
\(720\) −3.26573 −0.121707
\(721\) 23.1537 0.862290
\(722\) 26.2316 0.976237
\(723\) 24.3443 0.905374
\(724\) 21.7442 0.808118
\(725\) −1.58577 −0.0588939
\(726\) 18.2815 0.678491
\(727\) −6.07116 −0.225167 −0.112583 0.993642i \(-0.535913\pi\)
−0.112583 + 0.993642i \(0.535913\pi\)
\(728\) 18.7624 0.695380
\(729\) 1.00000 0.0370370
\(730\) 30.8801 1.14292
\(731\) −1.30120 −0.0481265
\(732\) 29.6412 1.09557
\(733\) −39.7977 −1.46996 −0.734982 0.678087i \(-0.762809\pi\)
−0.734982 + 0.678087i \(0.762809\pi\)
\(734\) 4.28867 0.158298
\(735\) 12.5952 0.464582
\(736\) 56.9862 2.10054
\(737\) 4.17778 0.153891
\(738\) −3.87016 −0.142462
\(739\) −10.5971 −0.389821 −0.194910 0.980821i \(-0.562442\pi\)
−0.194910 + 0.980821i \(0.562442\pi\)
\(740\) −10.9384 −0.402105
\(741\) 16.2523 0.597044
\(742\) 69.2153 2.54097
\(743\) −45.3111 −1.66230 −0.831152 0.556045i \(-0.812318\pi\)
−0.831152 + 0.556045i \(0.812318\pi\)
\(744\) −0.970584 −0.0355833
\(745\) 14.5330 0.532449
\(746\) −45.9816 −1.68351
\(747\) −15.5654 −0.569510
\(748\) 1.91984 0.0701963
\(749\) −20.3206 −0.742500
\(750\) −2.07772 −0.0758676
\(751\) 3.56157 0.129964 0.0649818 0.997886i \(-0.479301\pi\)
0.0649818 + 0.997886i \(0.479301\pi\)
\(752\) 7.47999 0.272767
\(753\) −28.3171 −1.03193
\(754\) 21.2084 0.772363
\(755\) 14.8051 0.538813
\(756\) −10.2562 −0.373014
\(757\) 22.7490 0.826826 0.413413 0.910544i \(-0.364337\pi\)
0.413413 + 0.910544i \(0.364337\pi\)
\(758\) −44.2561 −1.60746
\(759\) −10.4350 −0.378766
\(760\) −1.66252 −0.0603058
\(761\) 43.4393 1.57467 0.787336 0.616524i \(-0.211460\pi\)
0.787336 + 0.616524i \(0.211460\pi\)
\(762\) −9.10513 −0.329844
\(763\) −69.3078 −2.50911
\(764\) −36.2191 −1.31036
\(765\) −0.558508 −0.0201929
\(766\) 34.1045 1.23224
\(767\) −5.43798 −0.196354
\(768\) 9.79785 0.353549
\(769\) 51.0460 1.84076 0.920382 0.391020i \(-0.127878\pi\)
0.920382 + 0.391020i \(0.127878\pi\)
\(770\) −13.6454 −0.491747
\(771\) −23.2754 −0.838245
\(772\) −2.60824 −0.0938725
\(773\) −24.1477 −0.868533 −0.434266 0.900785i \(-0.642992\pi\)
−0.434266 + 0.900785i \(0.642992\pi\)
\(774\) −4.84062 −0.173992
\(775\) 1.47401 0.0529481
\(776\) −1.18132 −0.0424068
\(777\) 20.8987 0.749738
\(778\) −31.5459 −1.13097
\(779\) 4.70301 0.168503
\(780\) 14.9139 0.534004
\(781\) 9.58312 0.342911
\(782\) 8.16174 0.291863
\(783\) −1.58577 −0.0566707
\(784\) −41.1326 −1.46902
\(785\) 12.3905 0.442234
\(786\) 4.96091 0.176950
\(787\) 50.3061 1.79322 0.896610 0.442821i \(-0.146022\pi\)
0.896610 + 0.442821i \(0.146022\pi\)
\(788\) −48.0761 −1.71264
\(789\) 21.2062 0.754961
\(790\) 25.4997 0.907237
\(791\) 11.0633 0.393367
\(792\) 0.976915 0.0347132
\(793\) 82.3506 2.92436
\(794\) −15.0111 −0.532722
\(795\) 7.52558 0.266905
\(796\) 36.6487 1.29898
\(797\) 46.9664 1.66364 0.831818 0.555049i \(-0.187300\pi\)
0.831818 + 0.555049i \(0.187300\pi\)
\(798\) 23.2218 0.822044
\(799\) 1.27923 0.0452560
\(800\) 8.10220 0.286456
\(801\) 3.07441 0.108629
\(802\) −2.07772 −0.0733668
\(803\) 22.0504 0.778141
\(804\) −6.52425 −0.230093
\(805\) −31.1345 −1.09735
\(806\) −19.7138 −0.694387
\(807\) 29.1884 1.02748
\(808\) −1.00766 −0.0354493
\(809\) 46.2457 1.62591 0.812956 0.582326i \(-0.197857\pi\)
0.812956 + 0.582326i \(0.197857\pi\)
\(810\) −2.07772 −0.0730036
\(811\) 19.8260 0.696186 0.348093 0.937460i \(-0.386829\pi\)
0.348093 + 0.937460i \(0.386829\pi\)
\(812\) 16.2639 0.570751
\(813\) 25.6360 0.899093
\(814\) −14.5531 −0.510087
\(815\) −8.50867 −0.298046
\(816\) 1.82394 0.0638506
\(817\) 5.88231 0.205796
\(818\) −13.9140 −0.486492
\(819\) −28.4942 −0.995668
\(820\) 4.31571 0.150711
\(821\) 38.3828 1.33957 0.669784 0.742556i \(-0.266387\pi\)
0.669784 + 0.742556i \(0.266387\pi\)
\(822\) 8.02730 0.279984
\(823\) −21.1217 −0.736256 −0.368128 0.929775i \(-0.620001\pi\)
−0.368128 + 0.929775i \(0.620001\pi\)
\(824\) 3.44411 0.119981
\(825\) −1.48363 −0.0516533
\(826\) −7.76995 −0.270351
\(827\) 12.2201 0.424936 0.212468 0.977168i \(-0.431850\pi\)
0.212468 + 0.977168i \(0.431850\pi\)
\(828\) 16.2959 0.566320
\(829\) 4.75174 0.165035 0.0825174 0.996590i \(-0.473704\pi\)
0.0825174 + 0.996590i \(0.473704\pi\)
\(830\) 32.3406 1.12256
\(831\) −10.7203 −0.371882
\(832\) −66.3177 −2.29915
\(833\) −7.03454 −0.243732
\(834\) −44.8363 −1.55255
\(835\) −9.85827 −0.341160
\(836\) −8.67900 −0.300170
\(837\) 1.47401 0.0509493
\(838\) 7.42955 0.256649
\(839\) −5.57124 −0.192340 −0.0961702 0.995365i \(-0.530659\pi\)
−0.0961702 + 0.995365i \(0.530659\pi\)
\(840\) 2.91479 0.100570
\(841\) −26.4853 −0.913288
\(842\) 6.21556 0.214202
\(843\) 27.2623 0.938963
\(844\) 61.2965 2.10991
\(845\) 28.4345 0.978178
\(846\) 4.75891 0.163615
\(847\) 38.9494 1.33832
\(848\) −24.5765 −0.843961
\(849\) 5.89342 0.202262
\(850\) 1.16042 0.0398022
\(851\) −33.2056 −1.13827
\(852\) −14.9655 −0.512711
\(853\) 30.6515 1.04949 0.524744 0.851260i \(-0.324161\pi\)
0.524744 + 0.851260i \(0.324161\pi\)
\(854\) 117.665 4.02642
\(855\) 2.52484 0.0863478
\(856\) −3.02269 −0.103313
\(857\) −8.67392 −0.296295 −0.148148 0.988965i \(-0.547331\pi\)
−0.148148 + 0.988965i \(0.547331\pi\)
\(858\) 19.8424 0.677407
\(859\) 4.22187 0.144048 0.0720242 0.997403i \(-0.477054\pi\)
0.0720242 + 0.997403i \(0.477054\pi\)
\(860\) 5.39789 0.184067
\(861\) −8.24550 −0.281006
\(862\) −12.4120 −0.422753
\(863\) 6.39200 0.217586 0.108793 0.994064i \(-0.465301\pi\)
0.108793 + 0.994064i \(0.465301\pi\)
\(864\) 8.10220 0.275642
\(865\) −4.62289 −0.157183
\(866\) −33.7969 −1.14847
\(867\) −16.6881 −0.566757
\(868\) −15.1177 −0.513130
\(869\) 18.2084 0.617679
\(870\) 3.29478 0.111703
\(871\) −18.1260 −0.614176
\(872\) −10.3095 −0.349125
\(873\) 1.79405 0.0607194
\(874\) −36.8967 −1.24805
\(875\) −4.42665 −0.149648
\(876\) −34.4351 −1.16345
\(877\) −48.5065 −1.63795 −0.818974 0.573830i \(-0.805457\pi\)
−0.818974 + 0.573830i \(0.805457\pi\)
\(878\) 75.6721 2.55381
\(879\) 4.62191 0.155893
\(880\) 4.84513 0.163329
\(881\) −45.1632 −1.52159 −0.760794 0.648993i \(-0.775190\pi\)
−0.760794 + 0.648993i \(0.775190\pi\)
\(882\) −26.1693 −0.881168
\(883\) 41.8945 1.40986 0.704931 0.709275i \(-0.250978\pi\)
0.704931 + 0.709275i \(0.250978\pi\)
\(884\) −8.32954 −0.280153
\(885\) −0.844805 −0.0283978
\(886\) −16.8627 −0.566513
\(887\) −0.865938 −0.0290754 −0.0145377 0.999894i \(-0.504628\pi\)
−0.0145377 + 0.999894i \(0.504628\pi\)
\(888\) 3.10868 0.104321
\(889\) −19.3988 −0.650614
\(890\) −6.38776 −0.214118
\(891\) −1.48363 −0.0497034
\(892\) 56.1633 1.88049
\(893\) −5.78302 −0.193521
\(894\) −30.1955 −1.00989
\(895\) −1.34249 −0.0448746
\(896\) −23.0255 −0.769229
\(897\) 45.2739 1.51165
\(898\) 39.0774 1.30403
\(899\) −2.33744 −0.0779580
\(900\) 2.31692 0.0772305
\(901\) −4.20310 −0.140025
\(902\) 5.74188 0.191184
\(903\) −10.3131 −0.343198
\(904\) 1.64567 0.0547342
\(905\) 9.38498 0.311967
\(906\) −30.7608 −1.02196
\(907\) 18.2532 0.606088 0.303044 0.952977i \(-0.401997\pi\)
0.303044 + 0.952977i \(0.401997\pi\)
\(908\) −27.0803 −0.898692
\(909\) 1.53032 0.0507575
\(910\) 59.2029 1.96256
\(911\) −4.37970 −0.145106 −0.0725530 0.997365i \(-0.523115\pi\)
−0.0725530 + 0.997365i \(0.523115\pi\)
\(912\) −8.24546 −0.273034
\(913\) 23.0933 0.764278
\(914\) −59.8785 −1.98061
\(915\) 12.7934 0.422936
\(916\) 40.9525 1.35311
\(917\) 10.5694 0.349032
\(918\) 1.16042 0.0382997
\(919\) 9.08279 0.299614 0.149807 0.988715i \(-0.452135\pi\)
0.149807 + 0.988715i \(0.452135\pi\)
\(920\) −4.63125 −0.152688
\(921\) 10.9881 0.362069
\(922\) 87.8464 2.89307
\(923\) −41.5780 −1.36856
\(924\) 15.2164 0.500581
\(925\) −4.72112 −0.155229
\(926\) 42.8520 1.40820
\(927\) −5.23053 −0.171793
\(928\) −12.8482 −0.421763
\(929\) 15.3679 0.504205 0.252103 0.967700i \(-0.418878\pi\)
0.252103 + 0.967700i \(0.418878\pi\)
\(930\) −3.06259 −0.100426
\(931\) 31.8010 1.04223
\(932\) 51.7837 1.69623
\(933\) −0.114314 −0.00374247
\(934\) −7.10736 −0.232560
\(935\) 0.828618 0.0270987
\(936\) −4.23851 −0.138540
\(937\) −35.4554 −1.15828 −0.579139 0.815229i \(-0.696611\pi\)
−0.579139 + 0.815229i \(0.696611\pi\)
\(938\) −25.8990 −0.845631
\(939\) −5.70116 −0.186050
\(940\) −5.30678 −0.173088
\(941\) −30.3805 −0.990375 −0.495187 0.868786i \(-0.664901\pi\)
−0.495187 + 0.868786i \(0.664901\pi\)
\(942\) −25.7439 −0.838781
\(943\) 13.1011 0.426631
\(944\) 2.75890 0.0897947
\(945\) −4.42665 −0.143999
\(946\) 7.18167 0.233496
\(947\) −23.5258 −0.764487 −0.382243 0.924062i \(-0.624848\pi\)
−0.382243 + 0.924062i \(0.624848\pi\)
\(948\) −28.4353 −0.923536
\(949\) −95.6693 −3.10556
\(950\) −5.24591 −0.170200
\(951\) 1.13763 0.0368903
\(952\) −1.62793 −0.0527616
\(953\) −45.2597 −1.46610 −0.733052 0.680172i \(-0.761905\pi\)
−0.733052 + 0.680172i \(0.761905\pi\)
\(954\) −15.6360 −0.506236
\(955\) −15.6325 −0.505855
\(956\) −7.92671 −0.256368
\(957\) 2.35269 0.0760516
\(958\) −63.2570 −2.04374
\(959\) 17.1024 0.552266
\(960\) −10.3026 −0.332516
\(961\) −28.8273 −0.929912
\(962\) 63.1412 2.03575
\(963\) 4.59052 0.147928
\(964\) 56.4037 1.81664
\(965\) −1.12574 −0.0362387
\(966\) 64.6887 2.08133
\(967\) −28.1933 −0.906634 −0.453317 0.891349i \(-0.649759\pi\)
−0.453317 + 0.891349i \(0.649759\pi\)
\(968\) 5.79372 0.186217
\(969\) −1.41015 −0.0453004
\(970\) −3.72753 −0.119684
\(971\) −24.9658 −0.801192 −0.400596 0.916255i \(-0.631197\pi\)
−0.400596 + 0.916255i \(0.631197\pi\)
\(972\) 2.31692 0.0743151
\(973\) −95.5252 −3.06240
\(974\) 35.1224 1.12540
\(975\) 6.43697 0.206148
\(976\) −41.7798 −1.33734
\(977\) −8.55294 −0.273633 −0.136816 0.990596i \(-0.543687\pi\)
−0.136816 + 0.990596i \(0.543687\pi\)
\(978\) 17.6786 0.565300
\(979\) −4.56128 −0.145779
\(980\) 29.1821 0.932188
\(981\) 15.6570 0.499888
\(982\) −75.0185 −2.39394
\(983\) −39.1357 −1.24824 −0.624118 0.781330i \(-0.714541\pi\)
−0.624118 + 0.781330i \(0.714541\pi\)
\(984\) −1.22652 −0.0390999
\(985\) −20.7500 −0.661151
\(986\) −1.84016 −0.0586026
\(987\) 10.1390 0.322728
\(988\) 37.6553 1.19797
\(989\) 16.3863 0.521054
\(990\) 3.08256 0.0979703
\(991\) 13.2902 0.422178 0.211089 0.977467i \(-0.432299\pi\)
0.211089 + 0.977467i \(0.432299\pi\)
\(992\) 11.9427 0.379183
\(993\) −2.00858 −0.0637404
\(994\) −59.4079 −1.88430
\(995\) 15.8179 0.501460
\(996\) −36.0638 −1.14273
\(997\) −21.4461 −0.679205 −0.339603 0.940569i \(-0.610293\pi\)
−0.339603 + 0.940569i \(0.610293\pi\)
\(998\) −5.58911 −0.176920
\(999\) −4.72112 −0.149370
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 6015.2.a.i.1.7 43
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6015.2.a.i.1.7 43 1.1 even 1 trivial