Properties

Label 1849.2.a.i.1.2
Level $1849$
Weight $2$
Character 1849.1
Self dual yes
Analytic conductor $14.764$
Analytic rank $1$
Dimension $3$
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] = [1849,2,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, 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("1849.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.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: \(14.7643393337\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.554958 q^{2} -0.198062 q^{3} -1.69202 q^{4} -2.00000 q^{5} +0.109916 q^{6} -2.55496 q^{7} +2.04892 q^{8} -2.96077 q^{9} +O(q^{10})\) \(q-0.554958 q^{2} -0.198062 q^{3} -1.69202 q^{4} -2.00000 q^{5} +0.109916 q^{6} -2.55496 q^{7} +2.04892 q^{8} -2.96077 q^{9} +1.10992 q^{10} +4.74094 q^{11} +0.335126 q^{12} +0.643104 q^{13} +1.41789 q^{14} +0.396125 q^{15} +2.24698 q^{16} +1.10992 q^{17} +1.64310 q^{18} +5.35690 q^{19} +3.38404 q^{20} +0.506041 q^{21} -2.63102 q^{22} +5.24698 q^{23} -0.405813 q^{24} -1.00000 q^{25} -0.356896 q^{26} +1.18060 q^{27} +4.32304 q^{28} -0.911854 q^{29} -0.219833 q^{30} +5.96077 q^{31} -5.34481 q^{32} -0.939001 q^{33} -0.615957 q^{34} +5.10992 q^{35} +5.00969 q^{36} -11.3937 q^{37} -2.97285 q^{38} -0.127375 q^{39} -4.09783 q^{40} -7.76271 q^{41} -0.280831 q^{42} -8.02177 q^{44} +5.92154 q^{45} -2.91185 q^{46} -1.00000 q^{47} -0.445042 q^{48} -0.472189 q^{49} +0.554958 q^{50} -0.219833 q^{51} -1.08815 q^{52} +7.74094 q^{53} -0.655186 q^{54} -9.48188 q^{55} -5.23490 q^{56} -1.06100 q^{57} +0.506041 q^{58} -8.33513 q^{59} -0.670251 q^{60} -7.89977 q^{61} -3.30798 q^{62} +7.56465 q^{63} -1.52781 q^{64} -1.28621 q^{65} +0.521106 q^{66} +0.466812 q^{67} -1.87800 q^{68} -1.03923 q^{69} -2.83579 q^{70} +9.48188 q^{71} -6.06638 q^{72} -12.6799 q^{73} +6.32304 q^{74} +0.198062 q^{75} -9.06398 q^{76} -12.1129 q^{77} +0.0706876 q^{78} -5.09783 q^{79} -4.49396 q^{80} +8.64848 q^{81} +4.30798 q^{82} +14.9215 q^{83} -0.856232 q^{84} -2.21983 q^{85} +0.180604 q^{87} +9.71379 q^{88} -17.0151 q^{89} -3.28621 q^{90} -1.64310 q^{91} -8.87800 q^{92} -1.18060 q^{93} +0.554958 q^{94} -10.7138 q^{95} +1.05861 q^{96} +16.5550 q^{97} +0.262045 q^{98} -14.0368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{2} - 5 q^{3} - 6 q^{5} + q^{6} - 8 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{2} - 5 q^{3} - 6 q^{5} + q^{6} - 8 q^{7} - 3 q^{8} + 4 q^{9} + 4 q^{10} + 6 q^{13} + 10 q^{14} + 10 q^{15} + 2 q^{16} + 4 q^{17} + 9 q^{18} + 12 q^{19} + 11 q^{21} + 7 q^{22} + 11 q^{23} + 12 q^{24} - 3 q^{25} + 3 q^{26} - 8 q^{27} - 7 q^{28} + q^{29} - 2 q^{30} + 5 q^{31} + 7 q^{32} + 7 q^{33} - 12 q^{34} + 16 q^{35} - 7 q^{36} - 2 q^{37} - 15 q^{38} - 17 q^{39} + 6 q^{40} - 6 q^{41} - 12 q^{42} - 21 q^{44} - 8 q^{45} - 5 q^{46} - 3 q^{47} - q^{48} + 5 q^{49} + 2 q^{50} - 2 q^{51} - 7 q^{52} + 9 q^{53} - 25 q^{54} + 8 q^{56} - 13 q^{57} + 11 q^{58} - 24 q^{59} - q^{61} - 15 q^{62} + q^{63} - 11 q^{64} - 12 q^{65} - 14 q^{66} - 2 q^{67} + 14 q^{68} - 16 q^{69} - 20 q^{70} - 25 q^{72} - 14 q^{73} - q^{74} + 5 q^{75} + 7 q^{76} + 7 q^{77} - 12 q^{78} + 3 q^{79} - 4 q^{80} + 27 q^{81} + 18 q^{82} + 19 q^{83} + 14 q^{84} - 8 q^{85} - 11 q^{87} + 21 q^{88} - 26 q^{89} - 18 q^{90} - 9 q^{91} - 7 q^{92} + 8 q^{93} + 2 q^{94} - 24 q^{95} - 28 q^{96} + 50 q^{97} - 29 q^{98} - 14 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.554958 −0.392415 −0.196207 0.980562i \(-0.562863\pi\)
−0.196207 + 0.980562i \(0.562863\pi\)
\(3\) −0.198062 −0.114351 −0.0571757 0.998364i \(-0.518210\pi\)
−0.0571757 + 0.998364i \(0.518210\pi\)
\(4\) −1.69202 −0.846011
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0.109916 0.0448731
\(7\) −2.55496 −0.965683 −0.482842 0.875708i \(-0.660395\pi\)
−0.482842 + 0.875708i \(0.660395\pi\)
\(8\) 2.04892 0.724402
\(9\) −2.96077 −0.986924
\(10\) 1.10992 0.350986
\(11\) 4.74094 1.42945 0.714723 0.699407i \(-0.246553\pi\)
0.714723 + 0.699407i \(0.246553\pi\)
\(12\) 0.335126 0.0967424
\(13\) 0.643104 0.178365 0.0891825 0.996015i \(-0.471575\pi\)
0.0891825 + 0.996015i \(0.471575\pi\)
\(14\) 1.41789 0.378948
\(15\) 0.396125 0.102279
\(16\) 2.24698 0.561745
\(17\) 1.10992 0.269194 0.134597 0.990900i \(-0.457026\pi\)
0.134597 + 0.990900i \(0.457026\pi\)
\(18\) 1.64310 0.387283
\(19\) 5.35690 1.22896 0.614478 0.788934i \(-0.289367\pi\)
0.614478 + 0.788934i \(0.289367\pi\)
\(20\) 3.38404 0.756695
\(21\) 0.506041 0.110427
\(22\) −2.63102 −0.560936
\(23\) 5.24698 1.09407 0.547035 0.837109i \(-0.315756\pi\)
0.547035 + 0.837109i \(0.315756\pi\)
\(24\) −0.405813 −0.0828363
\(25\) −1.00000 −0.200000
\(26\) −0.356896 −0.0699930
\(27\) 1.18060 0.227207
\(28\) 4.32304 0.816979
\(29\) −0.911854 −0.169327 −0.0846635 0.996410i \(-0.526982\pi\)
−0.0846635 + 0.996410i \(0.526982\pi\)
\(30\) −0.219833 −0.0401357
\(31\) 5.96077 1.07059 0.535293 0.844666i \(-0.320201\pi\)
0.535293 + 0.844666i \(0.320201\pi\)
\(32\) −5.34481 −0.944839
\(33\) −0.939001 −0.163459
\(34\) −0.615957 −0.105636
\(35\) 5.10992 0.863733
\(36\) 5.00969 0.834948
\(37\) −11.3937 −1.87312 −0.936559 0.350510i \(-0.886008\pi\)
−0.936559 + 0.350510i \(0.886008\pi\)
\(38\) −2.97285 −0.482260
\(39\) −0.127375 −0.0203963
\(40\) −4.09783 −0.647925
\(41\) −7.76271 −1.21233 −0.606166 0.795338i \(-0.707293\pi\)
−0.606166 + 0.795338i \(0.707293\pi\)
\(42\) −0.280831 −0.0433332
\(43\) 0 0
\(44\) −8.02177 −1.20933
\(45\) 5.92154 0.882731
\(46\) −2.91185 −0.429329
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) −0.445042 −0.0642363
\(49\) −0.472189 −0.0674556
\(50\) 0.554958 0.0784829
\(51\) −0.219833 −0.0307827
\(52\) −1.08815 −0.150899
\(53\) 7.74094 1.06330 0.531650 0.846964i \(-0.321572\pi\)
0.531650 + 0.846964i \(0.321572\pi\)
\(54\) −0.655186 −0.0891595
\(55\) −9.48188 −1.27854
\(56\) −5.23490 −0.699543
\(57\) −1.06100 −0.140533
\(58\) 0.506041 0.0664464
\(59\) −8.33513 −1.08514 −0.542570 0.840010i \(-0.682549\pi\)
−0.542570 + 0.840010i \(0.682549\pi\)
\(60\) −0.670251 −0.0865291
\(61\) −7.89977 −1.01146 −0.505731 0.862691i \(-0.668777\pi\)
−0.505731 + 0.862691i \(0.668777\pi\)
\(62\) −3.30798 −0.420114
\(63\) 7.56465 0.953056
\(64\) −1.52781 −0.190976
\(65\) −1.28621 −0.159535
\(66\) 0.521106 0.0641437
\(67\) 0.466812 0.0570302 0.0285151 0.999593i \(-0.490922\pi\)
0.0285151 + 0.999593i \(0.490922\pi\)
\(68\) −1.87800 −0.227741
\(69\) −1.03923 −0.125108
\(70\) −2.83579 −0.338942
\(71\) 9.48188 1.12529 0.562646 0.826698i \(-0.309783\pi\)
0.562646 + 0.826698i \(0.309783\pi\)
\(72\) −6.06638 −0.714929
\(73\) −12.6799 −1.48407 −0.742037 0.670359i \(-0.766140\pi\)
−0.742037 + 0.670359i \(0.766140\pi\)
\(74\) 6.32304 0.735039
\(75\) 0.198062 0.0228703
\(76\) −9.06398 −1.03971
\(77\) −12.1129 −1.38039
\(78\) 0.0706876 0.00800380
\(79\) −5.09783 −0.573551 −0.286776 0.957998i \(-0.592583\pi\)
−0.286776 + 0.957998i \(0.592583\pi\)
\(80\) −4.49396 −0.502440
\(81\) 8.64848 0.960942
\(82\) 4.30798 0.475737
\(83\) 14.9215 1.63785 0.818926 0.573899i \(-0.194570\pi\)
0.818926 + 0.573899i \(0.194570\pi\)
\(84\) −0.856232 −0.0934226
\(85\) −2.21983 −0.240775
\(86\) 0 0
\(87\) 0.180604 0.0193628
\(88\) 9.71379 1.03549
\(89\) −17.0151 −1.80359 −0.901797 0.432161i \(-0.857751\pi\)
−0.901797 + 0.432161i \(0.857751\pi\)
\(90\) −3.28621 −0.346397
\(91\) −1.64310 −0.172244
\(92\) −8.87800 −0.925596
\(93\) −1.18060 −0.122423
\(94\) 0.554958 0.0572396
\(95\) −10.7138 −1.09921
\(96\) 1.05861 0.108044
\(97\) 16.5550 1.68090 0.840451 0.541888i \(-0.182290\pi\)
0.840451 + 0.541888i \(0.182290\pi\)
\(98\) 0.262045 0.0264706
\(99\) −14.0368 −1.41076
\(100\) 1.69202 0.169202
\(101\) −3.79225 −0.377343 −0.188671 0.982040i \(-0.560418\pi\)
−0.188671 + 0.982040i \(0.560418\pi\)
\(102\) 0.121998 0.0120796
\(103\) −5.92154 −0.583467 −0.291733 0.956500i \(-0.594232\pi\)
−0.291733 + 0.956500i \(0.594232\pi\)
\(104\) 1.31767 0.129208
\(105\) −1.01208 −0.0987690
\(106\) −4.29590 −0.417254
\(107\) 1.96615 0.190075 0.0950374 0.995474i \(-0.469703\pi\)
0.0950374 + 0.995474i \(0.469703\pi\)
\(108\) −1.99761 −0.192220
\(109\) −8.32304 −0.797203 −0.398602 0.917124i \(-0.630504\pi\)
−0.398602 + 0.917124i \(0.630504\pi\)
\(110\) 5.26205 0.501716
\(111\) 2.25667 0.214193
\(112\) −5.74094 −0.542468
\(113\) −1.82908 −0.172066 −0.0860329 0.996292i \(-0.527419\pi\)
−0.0860329 + 0.996292i \(0.527419\pi\)
\(114\) 0.588810 0.0551471
\(115\) −10.4940 −0.978567
\(116\) 1.54288 0.143252
\(117\) −1.90408 −0.176033
\(118\) 4.62565 0.425825
\(119\) −2.83579 −0.259956
\(120\) 0.811626 0.0740910
\(121\) 11.4765 1.04332
\(122\) 4.38404 0.396913
\(123\) 1.53750 0.138632
\(124\) −10.0858 −0.905727
\(125\) 12.0000 1.07331
\(126\) −4.19806 −0.373993
\(127\) 2.96615 0.263203 0.131602 0.991303i \(-0.457988\pi\)
0.131602 + 0.991303i \(0.457988\pi\)
\(128\) 11.5375 1.01978
\(129\) 0 0
\(130\) 0.713792 0.0626037
\(131\) −7.10992 −0.621196 −0.310598 0.950541i \(-0.600529\pi\)
−0.310598 + 0.950541i \(0.600529\pi\)
\(132\) 1.58881 0.138288
\(133\) −13.6866 −1.18678
\(134\) −0.259061 −0.0223795
\(135\) −2.36121 −0.203220
\(136\) 2.27413 0.195005
\(137\) 8.32304 0.711086 0.355543 0.934660i \(-0.384296\pi\)
0.355543 + 0.934660i \(0.384296\pi\)
\(138\) 0.576728 0.0490944
\(139\) 6.03923 0.512241 0.256120 0.966645i \(-0.417556\pi\)
0.256120 + 0.966645i \(0.417556\pi\)
\(140\) −8.64609 −0.730728
\(141\) 0.198062 0.0166799
\(142\) −5.26205 −0.441581
\(143\) 3.04892 0.254963
\(144\) −6.65279 −0.554399
\(145\) 1.82371 0.151451
\(146\) 7.03684 0.582373
\(147\) 0.0935228 0.00771363
\(148\) 19.2784 1.58468
\(149\) 2.22521 0.182296 0.0911481 0.995837i \(-0.470946\pi\)
0.0911481 + 0.995837i \(0.470946\pi\)
\(150\) −0.109916 −0.00897463
\(151\) 0.493959 0.0401978 0.0200989 0.999798i \(-0.493602\pi\)
0.0200989 + 0.999798i \(0.493602\pi\)
\(152\) 10.9758 0.890258
\(153\) −3.28621 −0.265674
\(154\) 6.72215 0.541686
\(155\) −11.9215 −0.957561
\(156\) 0.215521 0.0172555
\(157\) −7.71140 −0.615437 −0.307718 0.951478i \(-0.599565\pi\)
−0.307718 + 0.951478i \(0.599565\pi\)
\(158\) 2.82908 0.225070
\(159\) −1.53319 −0.121590
\(160\) 10.6896 0.845089
\(161\) −13.4058 −1.05653
\(162\) −4.79954 −0.377088
\(163\) 0.975837 0.0764334 0.0382167 0.999269i \(-0.487832\pi\)
0.0382167 + 0.999269i \(0.487832\pi\)
\(164\) 13.1347 1.02565
\(165\) 1.87800 0.146202
\(166\) −8.28083 −0.642717
\(167\) −5.64848 −0.437093 −0.218546 0.975827i \(-0.570131\pi\)
−0.218546 + 0.975827i \(0.570131\pi\)
\(168\) 1.03684 0.0799936
\(169\) −12.5864 −0.968186
\(170\) 1.23191 0.0944835
\(171\) −15.8605 −1.21289
\(172\) 0 0
\(173\) −8.65279 −0.657860 −0.328930 0.944354i \(-0.606688\pi\)
−0.328930 + 0.944354i \(0.606688\pi\)
\(174\) −0.100228 −0.00759823
\(175\) 2.55496 0.193137
\(176\) 10.6528 0.802984
\(177\) 1.65087 0.124087
\(178\) 9.44265 0.707756
\(179\) −1.99462 −0.149085 −0.0745426 0.997218i \(-0.523750\pi\)
−0.0745426 + 0.997218i \(0.523750\pi\)
\(180\) −10.0194 −0.746800
\(181\) −8.85623 −0.658279 −0.329139 0.944281i \(-0.606759\pi\)
−0.329139 + 0.944281i \(0.606759\pi\)
\(182\) 0.911854 0.0675911
\(183\) 1.56465 0.115662
\(184\) 10.7506 0.792547
\(185\) 22.7875 1.67537
\(186\) 0.655186 0.0480405
\(187\) 5.26205 0.384799
\(188\) 1.69202 0.123403
\(189\) −3.01639 −0.219410
\(190\) 5.94571 0.431347
\(191\) −7.54527 −0.545957 −0.272978 0.962020i \(-0.588009\pi\)
−0.272978 + 0.962020i \(0.588009\pi\)
\(192\) 0.302602 0.0218384
\(193\) −8.04221 −0.578891 −0.289446 0.957194i \(-0.593471\pi\)
−0.289446 + 0.957194i \(0.593471\pi\)
\(194\) −9.18731 −0.659610
\(195\) 0.254749 0.0182430
\(196\) 0.798954 0.0570681
\(197\) −19.3913 −1.38158 −0.690788 0.723058i \(-0.742736\pi\)
−0.690788 + 0.723058i \(0.742736\pi\)
\(198\) 7.78986 0.553601
\(199\) 22.6625 1.60650 0.803250 0.595642i \(-0.203102\pi\)
0.803250 + 0.595642i \(0.203102\pi\)
\(200\) −2.04892 −0.144880
\(201\) −0.0924579 −0.00652148
\(202\) 2.10454 0.148075
\(203\) 2.32975 0.163516
\(204\) 0.371961 0.0260425
\(205\) 15.5254 1.08434
\(206\) 3.28621 0.228961
\(207\) −15.5351 −1.07976
\(208\) 1.44504 0.100196
\(209\) 25.3967 1.75673
\(210\) 0.561663 0.0387584
\(211\) −16.4916 −1.13533 −0.567663 0.823261i \(-0.692152\pi\)
−0.567663 + 0.823261i \(0.692152\pi\)
\(212\) −13.0978 −0.899563
\(213\) −1.87800 −0.128679
\(214\) −1.09113 −0.0745881
\(215\) 0 0
\(216\) 2.41896 0.164589
\(217\) −15.2295 −1.03385
\(218\) 4.61894 0.312834
\(219\) 2.51142 0.169706
\(220\) 16.0435 1.08166
\(221\) 0.713792 0.0480148
\(222\) −1.25236 −0.0840527
\(223\) −1.50604 −0.100852 −0.0504260 0.998728i \(-0.516058\pi\)
−0.0504260 + 0.998728i \(0.516058\pi\)
\(224\) 13.6558 0.912415
\(225\) 2.96077 0.197385
\(226\) 1.01507 0.0675212
\(227\) −18.3599 −1.21859 −0.609294 0.792944i \(-0.708547\pi\)
−0.609294 + 0.792944i \(0.708547\pi\)
\(228\) 1.79523 0.118892
\(229\) 6.18359 0.408623 0.204311 0.978906i \(-0.434504\pi\)
0.204311 + 0.978906i \(0.434504\pi\)
\(230\) 5.82371 0.384004
\(231\) 2.39911 0.157850
\(232\) −1.86831 −0.122661
\(233\) 4.42088 0.289621 0.144811 0.989459i \(-0.453743\pi\)
0.144811 + 0.989459i \(0.453743\pi\)
\(234\) 1.05669 0.0690778
\(235\) 2.00000 0.130466
\(236\) 14.1032 0.918041
\(237\) 1.00969 0.0655863
\(238\) 1.57374 0.102011
\(239\) −10.4494 −0.675913 −0.337956 0.941162i \(-0.609736\pi\)
−0.337956 + 0.941162i \(0.609736\pi\)
\(240\) 0.890084 0.0574547
\(241\) 24.3002 1.56531 0.782657 0.622453i \(-0.213864\pi\)
0.782657 + 0.622453i \(0.213864\pi\)
\(242\) −6.36898 −0.409413
\(243\) −5.25475 −0.337092
\(244\) 13.3666 0.855708
\(245\) 0.944378 0.0603341
\(246\) −0.853248 −0.0544011
\(247\) 3.44504 0.219203
\(248\) 12.2131 0.775534
\(249\) −2.95539 −0.187291
\(250\) −6.65950 −0.421184
\(251\) −21.9269 −1.38401 −0.692007 0.721890i \(-0.743273\pi\)
−0.692007 + 0.721890i \(0.743273\pi\)
\(252\) −12.7995 −0.806296
\(253\) 24.8756 1.56392
\(254\) −1.64609 −0.103285
\(255\) 0.439665 0.0275329
\(256\) −3.34721 −0.209200
\(257\) −2.89546 −0.180614 −0.0903069 0.995914i \(-0.528785\pi\)
−0.0903069 + 0.995914i \(0.528785\pi\)
\(258\) 0 0
\(259\) 29.1105 1.80884
\(260\) 2.17629 0.134968
\(261\) 2.69979 0.167113
\(262\) 3.94571 0.243767
\(263\) −17.3744 −1.07135 −0.535674 0.844425i \(-0.679943\pi\)
−0.535674 + 0.844425i \(0.679943\pi\)
\(264\) −1.92394 −0.118410
\(265\) −15.4819 −0.951044
\(266\) 7.59551 0.465711
\(267\) 3.37004 0.206243
\(268\) −0.789856 −0.0482481
\(269\) −14.0707 −0.857905 −0.428952 0.903327i \(-0.641117\pi\)
−0.428952 + 0.903327i \(0.641117\pi\)
\(270\) 1.31037 0.0797467
\(271\) −2.14377 −0.130225 −0.0651123 0.997878i \(-0.520741\pi\)
−0.0651123 + 0.997878i \(0.520741\pi\)
\(272\) 2.49396 0.151218
\(273\) 0.325437 0.0196963
\(274\) −4.61894 −0.279040
\(275\) −4.74094 −0.285889
\(276\) 1.75840 0.105843
\(277\) −23.2597 −1.39754 −0.698769 0.715348i \(-0.746268\pi\)
−0.698769 + 0.715348i \(0.746268\pi\)
\(278\) −3.35152 −0.201011
\(279\) −17.6485 −1.05659
\(280\) 10.4698 0.625690
\(281\) −17.7342 −1.05794 −0.528968 0.848642i \(-0.677421\pi\)
−0.528968 + 0.848642i \(0.677421\pi\)
\(282\) −0.109916 −0.00654542
\(283\) 3.90946 0.232393 0.116197 0.993226i \(-0.462930\pi\)
0.116197 + 0.993226i \(0.462930\pi\)
\(284\) −16.0435 −0.952009
\(285\) 2.12200 0.125696
\(286\) −1.69202 −0.100051
\(287\) 19.8334 1.17073
\(288\) 15.8248 0.932484
\(289\) −15.7681 −0.927534
\(290\) −1.01208 −0.0594315
\(291\) −3.27891 −0.192213
\(292\) 21.4547 1.25554
\(293\) −28.0320 −1.63765 −0.818825 0.574043i \(-0.805374\pi\)
−0.818825 + 0.574043i \(0.805374\pi\)
\(294\) −0.0519012 −0.00302694
\(295\) 16.6703 0.970580
\(296\) −23.3448 −1.35689
\(297\) 5.59717 0.324781
\(298\) −1.23490 −0.0715357
\(299\) 3.37435 0.195144
\(300\) −0.335126 −0.0193485
\(301\) 0 0
\(302\) −0.274127 −0.0157742
\(303\) 0.751101 0.0431496
\(304\) 12.0368 0.690360
\(305\) 15.7995 0.904679
\(306\) 1.82371 0.104254
\(307\) −0.633415 −0.0361509 −0.0180755 0.999837i \(-0.505754\pi\)
−0.0180755 + 0.999837i \(0.505754\pi\)
\(308\) 20.4953 1.16783
\(309\) 1.17283 0.0667202
\(310\) 6.61596 0.375761
\(311\) −25.3666 −1.43841 −0.719204 0.694799i \(-0.755493\pi\)
−0.719204 + 0.694799i \(0.755493\pi\)
\(312\) −0.260980 −0.0147751
\(313\) 14.9463 0.844815 0.422407 0.906406i \(-0.361185\pi\)
0.422407 + 0.906406i \(0.361185\pi\)
\(314\) 4.27950 0.241506
\(315\) −15.1293 −0.852439
\(316\) 8.62565 0.485230
\(317\) −4.84548 −0.272149 −0.136075 0.990699i \(-0.543449\pi\)
−0.136075 + 0.990699i \(0.543449\pi\)
\(318\) 0.850855 0.0477136
\(319\) −4.32304 −0.242044
\(320\) 3.05562 0.170814
\(321\) −0.389420 −0.0217353
\(322\) 7.43967 0.414596
\(323\) 5.94571 0.330828
\(324\) −14.6334 −0.812968
\(325\) −0.643104 −0.0356730
\(326\) −0.541549 −0.0299936
\(327\) 1.64848 0.0911612
\(328\) −15.9051 −0.878215
\(329\) 2.55496 0.140859
\(330\) −1.04221 −0.0573719
\(331\) 12.3472 0.678664 0.339332 0.940667i \(-0.389799\pi\)
0.339332 + 0.940667i \(0.389799\pi\)
\(332\) −25.2476 −1.38564
\(333\) 33.7342 1.84862
\(334\) 3.13467 0.171522
\(335\) −0.933624 −0.0510093
\(336\) 1.13706 0.0620319
\(337\) 6.20344 0.337923 0.168961 0.985623i \(-0.445959\pi\)
0.168961 + 0.985623i \(0.445959\pi\)
\(338\) 6.98493 0.379930
\(339\) 0.362273 0.0196760
\(340\) 3.75600 0.203698
\(341\) 28.2597 1.53035
\(342\) 8.80194 0.475954
\(343\) 19.0911 1.03082
\(344\) 0 0
\(345\) 2.07846 0.111900
\(346\) 4.80194 0.258154
\(347\) 18.0901 0.971126 0.485563 0.874202i \(-0.338615\pi\)
0.485563 + 0.874202i \(0.338615\pi\)
\(348\) −0.305586 −0.0163811
\(349\) 7.25667 0.388441 0.194220 0.980958i \(-0.437782\pi\)
0.194220 + 0.980958i \(0.437782\pi\)
\(350\) −1.41789 −0.0757897
\(351\) 0.759251 0.0405258
\(352\) −25.3394 −1.35060
\(353\) 10.4397 0.555647 0.277824 0.960632i \(-0.410387\pi\)
0.277824 + 0.960632i \(0.410387\pi\)
\(354\) −0.916166 −0.0486937
\(355\) −18.9638 −1.00649
\(356\) 28.7899 1.52586
\(357\) 0.561663 0.0297264
\(358\) 1.10693 0.0585032
\(359\) −28.1347 −1.48489 −0.742446 0.669906i \(-0.766334\pi\)
−0.742446 + 0.669906i \(0.766334\pi\)
\(360\) 12.1328 0.639452
\(361\) 9.69633 0.510333
\(362\) 4.91484 0.258318
\(363\) −2.27306 −0.119305
\(364\) 2.78017 0.145720
\(365\) 25.3599 1.32740
\(366\) −0.868313 −0.0453875
\(367\) 16.4480 0.858580 0.429290 0.903167i \(-0.358764\pi\)
0.429290 + 0.903167i \(0.358764\pi\)
\(368\) 11.7899 0.614589
\(369\) 22.9836 1.19648
\(370\) −12.6461 −0.657439
\(371\) −19.7778 −1.02681
\(372\) 1.99761 0.103571
\(373\) −10.8062 −0.559526 −0.279763 0.960069i \(-0.590256\pi\)
−0.279763 + 0.960069i \(0.590256\pi\)
\(374\) −2.92021 −0.151001
\(375\) −2.37675 −0.122735
\(376\) −2.04892 −0.105665
\(377\) −0.586417 −0.0302020
\(378\) 1.67397 0.0860998
\(379\) −9.71917 −0.499240 −0.249620 0.968344i \(-0.580306\pi\)
−0.249620 + 0.968344i \(0.580306\pi\)
\(380\) 18.1280 0.929945
\(381\) −0.587482 −0.0300976
\(382\) 4.18731 0.214241
\(383\) −23.6407 −1.20798 −0.603992 0.796990i \(-0.706424\pi\)
−0.603992 + 0.796990i \(0.706424\pi\)
\(384\) −2.28514 −0.116613
\(385\) 24.2258 1.23466
\(386\) 4.46309 0.227165
\(387\) 0 0
\(388\) −28.0113 −1.42206
\(389\) −7.89307 −0.400194 −0.200097 0.979776i \(-0.564126\pi\)
−0.200097 + 0.979776i \(0.564126\pi\)
\(390\) −0.141375 −0.00715881
\(391\) 5.82371 0.294518
\(392\) −0.967476 −0.0488649
\(393\) 1.40821 0.0710346
\(394\) 10.7614 0.542151
\(395\) 10.1957 0.513000
\(396\) 23.7506 1.19351
\(397\) −25.5894 −1.28430 −0.642148 0.766581i \(-0.721956\pi\)
−0.642148 + 0.766581i \(0.721956\pi\)
\(398\) −12.5767 −0.630414
\(399\) 2.71081 0.135710
\(400\) −2.24698 −0.112349
\(401\) −8.70948 −0.434931 −0.217465 0.976068i \(-0.569779\pi\)
−0.217465 + 0.976068i \(0.569779\pi\)
\(402\) 0.0513102 0.00255912
\(403\) 3.83340 0.190955
\(404\) 6.41657 0.319236
\(405\) −17.2970 −0.859493
\(406\) −1.29291 −0.0641662
\(407\) −54.0170 −2.67752
\(408\) −0.450419 −0.0222990
\(409\) 13.2567 0.655500 0.327750 0.944764i \(-0.393710\pi\)
0.327750 + 0.944764i \(0.393710\pi\)
\(410\) −8.61596 −0.425512
\(411\) −1.64848 −0.0813136
\(412\) 10.0194 0.493619
\(413\) 21.2959 1.04790
\(414\) 8.62133 0.423715
\(415\) −29.8431 −1.46494
\(416\) −3.43727 −0.168526
\(417\) −1.19614 −0.0585754
\(418\) −14.0941 −0.689366
\(419\) 1.14138 0.0557598 0.0278799 0.999611i \(-0.491124\pi\)
0.0278799 + 0.999611i \(0.491124\pi\)
\(420\) 1.71246 0.0835597
\(421\) 3.33214 0.162399 0.0811993 0.996698i \(-0.474125\pi\)
0.0811993 + 0.996698i \(0.474125\pi\)
\(422\) 9.15213 0.445519
\(423\) 2.96077 0.143958
\(424\) 15.8605 0.770256
\(425\) −1.10992 −0.0538388
\(426\) 1.04221 0.0504954
\(427\) 20.1836 0.976752
\(428\) −3.32676 −0.160805
\(429\) −0.603875 −0.0291554
\(430\) 0 0
\(431\) 20.3515 0.980298 0.490149 0.871639i \(-0.336942\pi\)
0.490149 + 0.871639i \(0.336942\pi\)
\(432\) 2.65279 0.127633
\(433\) 9.96316 0.478799 0.239400 0.970921i \(-0.423049\pi\)
0.239400 + 0.970921i \(0.423049\pi\)
\(434\) 8.45175 0.405697
\(435\) −0.361208 −0.0173186
\(436\) 14.0828 0.674442
\(437\) 28.1075 1.34457
\(438\) −1.39373 −0.0665951
\(439\) 8.18731 0.390759 0.195379 0.980728i \(-0.437406\pi\)
0.195379 + 0.980728i \(0.437406\pi\)
\(440\) −19.4276 −0.926174
\(441\) 1.39804 0.0665735
\(442\) −0.396125 −0.0188417
\(443\) 30.4077 1.44471 0.722357 0.691520i \(-0.243059\pi\)
0.722357 + 0.691520i \(0.243059\pi\)
\(444\) −3.81833 −0.181210
\(445\) 34.0301 1.61318
\(446\) 0.835790 0.0395758
\(447\) −0.440730 −0.0208458
\(448\) 3.90349 0.184423
\(449\) −22.2000 −1.04768 −0.523841 0.851816i \(-0.675501\pi\)
−0.523841 + 0.851816i \(0.675501\pi\)
\(450\) −1.64310 −0.0774567
\(451\) −36.8025 −1.73296
\(452\) 3.09485 0.145570
\(453\) −0.0978347 −0.00459667
\(454\) 10.1890 0.478192
\(455\) 3.28621 0.154060
\(456\) −2.17390 −0.101802
\(457\) 11.2185 0.524780 0.262390 0.964962i \(-0.415489\pi\)
0.262390 + 0.964962i \(0.415489\pi\)
\(458\) −3.43163 −0.160350
\(459\) 1.31037 0.0611629
\(460\) 17.7560 0.827878
\(461\) −34.5459 −1.60896 −0.804481 0.593979i \(-0.797556\pi\)
−0.804481 + 0.593979i \(0.797556\pi\)
\(462\) −1.33140 −0.0619426
\(463\) 10.1806 0.473133 0.236566 0.971615i \(-0.423978\pi\)
0.236566 + 0.971615i \(0.423978\pi\)
\(464\) −2.04892 −0.0951186
\(465\) 2.36121 0.109498
\(466\) −2.45340 −0.113652
\(467\) 14.9782 0.693110 0.346555 0.938030i \(-0.387351\pi\)
0.346555 + 0.938030i \(0.387351\pi\)
\(468\) 3.22175 0.148926
\(469\) −1.19269 −0.0550731
\(470\) −1.10992 −0.0511966
\(471\) 1.52734 0.0703760
\(472\) −17.0780 −0.786078
\(473\) 0 0
\(474\) −0.560335 −0.0257370
\(475\) −5.35690 −0.245791
\(476\) 4.79822 0.219926
\(477\) −22.9191 −1.04940
\(478\) 5.79895 0.265238
\(479\) 29.0573 1.32766 0.663830 0.747883i \(-0.268930\pi\)
0.663830 + 0.747883i \(0.268930\pi\)
\(480\) −2.11721 −0.0966371
\(481\) −7.32736 −0.334099
\(482\) −13.4856 −0.614252
\(483\) 2.65519 0.120815
\(484\) −19.4185 −0.882658
\(485\) −33.1099 −1.50344
\(486\) 2.91617 0.132280
\(487\) −23.8810 −1.08215 −0.541075 0.840974i \(-0.681983\pi\)
−0.541075 + 0.840974i \(0.681983\pi\)
\(488\) −16.1860 −0.732705
\(489\) −0.193276 −0.00874026
\(490\) −0.524090 −0.0236760
\(491\) −0.675628 −0.0304907 −0.0152453 0.999884i \(-0.504853\pi\)
−0.0152453 + 0.999884i \(0.504853\pi\)
\(492\) −2.60148 −0.117284
\(493\) −1.01208 −0.0455819
\(494\) −1.91185 −0.0860184
\(495\) 28.0737 1.26182
\(496\) 13.3937 0.601396
\(497\) −24.2258 −1.08668
\(498\) 1.64012 0.0734955
\(499\) 32.1943 1.44122 0.720608 0.693342i \(-0.243863\pi\)
0.720608 + 0.693342i \(0.243863\pi\)
\(500\) −20.3043 −0.908034
\(501\) 1.11875 0.0499821
\(502\) 12.1685 0.543108
\(503\) −23.1491 −1.03217 −0.516085 0.856538i \(-0.672611\pi\)
−0.516085 + 0.856538i \(0.672611\pi\)
\(504\) 15.4993 0.690395
\(505\) 7.58450 0.337506
\(506\) −13.8049 −0.613704
\(507\) 2.49289 0.110713
\(508\) −5.01879 −0.222673
\(509\) −29.2010 −1.29431 −0.647157 0.762357i \(-0.724042\pi\)
−0.647157 + 0.762357i \(0.724042\pi\)
\(510\) −0.243996 −0.0108043
\(511\) 32.3967 1.43315
\(512\) −21.2174 −0.937687
\(513\) 6.32437 0.279228
\(514\) 1.60686 0.0708755
\(515\) 11.8431 0.521869
\(516\) 0 0
\(517\) −4.74094 −0.208506
\(518\) −16.1551 −0.709815
\(519\) 1.71379 0.0752271
\(520\) −2.63533 −0.115567
\(521\) 0.948690 0.0415629 0.0207814 0.999784i \(-0.493385\pi\)
0.0207814 + 0.999784i \(0.493385\pi\)
\(522\) −1.49827 −0.0655775
\(523\) −36.8853 −1.61288 −0.806441 0.591315i \(-0.798609\pi\)
−0.806441 + 0.591315i \(0.798609\pi\)
\(524\) 12.0301 0.525539
\(525\) −0.506041 −0.0220854
\(526\) 9.64204 0.420413
\(527\) 6.61596 0.288196
\(528\) −2.10992 −0.0918223
\(529\) 4.53079 0.196991
\(530\) 8.59179 0.373204
\(531\) 24.6784 1.07095
\(532\) 23.1581 1.00403
\(533\) −4.99223 −0.216237
\(534\) −1.87023 −0.0809329
\(535\) −3.93230 −0.170008
\(536\) 0.956459 0.0413128
\(537\) 0.395060 0.0170481
\(538\) 7.80864 0.336654
\(539\) −2.23862 −0.0964241
\(540\) 3.99521 0.171927
\(541\) −17.5157 −0.753060 −0.376530 0.926404i \(-0.622883\pi\)
−0.376530 + 0.926404i \(0.622883\pi\)
\(542\) 1.18970 0.0511021
\(543\) 1.75409 0.0752750
\(544\) −5.93230 −0.254345
\(545\) 16.6461 0.713040
\(546\) −0.180604 −0.00772913
\(547\) 16.1032 0.688524 0.344262 0.938874i \(-0.388129\pi\)
0.344262 + 0.938874i \(0.388129\pi\)
\(548\) −14.0828 −0.601586
\(549\) 23.3894 0.998236
\(550\) 2.63102 0.112187
\(551\) −4.88471 −0.208096
\(552\) −2.12929 −0.0906288
\(553\) 13.0248 0.553869
\(554\) 12.9081 0.548414
\(555\) −4.51334 −0.191580
\(556\) −10.2185 −0.433361
\(557\) 5.46788 0.231681 0.115841 0.993268i \(-0.463044\pi\)
0.115841 + 0.993268i \(0.463044\pi\)
\(558\) 9.79417 0.414620
\(559\) 0 0
\(560\) 11.4819 0.485198
\(561\) −1.04221 −0.0440022
\(562\) 9.84176 0.415149
\(563\) 34.9874 1.47454 0.737272 0.675595i \(-0.236113\pi\)
0.737272 + 0.675595i \(0.236113\pi\)
\(564\) −0.335126 −0.0141113
\(565\) 3.65817 0.153900
\(566\) −2.16959 −0.0911946
\(567\) −22.0965 −0.927966
\(568\) 19.4276 0.815163
\(569\) −6.32245 −0.265051 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(570\) −1.17762 −0.0493251
\(571\) 19.6606 0.822769 0.411384 0.911462i \(-0.365045\pi\)
0.411384 + 0.911462i \(0.365045\pi\)
\(572\) −5.15883 −0.215702
\(573\) 1.49443 0.0624308
\(574\) −11.0067 −0.459411
\(575\) −5.24698 −0.218814
\(576\) 4.52350 0.188479
\(577\) 15.1377 0.630189 0.315094 0.949060i \(-0.397964\pi\)
0.315094 + 0.949060i \(0.397964\pi\)
\(578\) 8.75063 0.363978
\(579\) 1.59286 0.0661970
\(580\) −3.08575 −0.128129
\(581\) −38.1239 −1.58165
\(582\) 1.81966 0.0754273
\(583\) 36.6993 1.51993
\(584\) −25.9801 −1.07507
\(585\) 3.80817 0.157448
\(586\) 15.5566 0.642638
\(587\) −6.02416 −0.248644 −0.124322 0.992242i \(-0.539676\pi\)
−0.124322 + 0.992242i \(0.539676\pi\)
\(588\) −0.158243 −0.00652582
\(589\) 31.9312 1.31570
\(590\) −9.25129 −0.380870
\(591\) 3.84069 0.157985
\(592\) −25.6015 −1.05221
\(593\) 40.7894 1.67502 0.837510 0.546423i \(-0.184011\pi\)
0.837510 + 0.546423i \(0.184011\pi\)
\(594\) −3.10620 −0.127449
\(595\) 5.67158 0.232512
\(596\) −3.76510 −0.154225
\(597\) −4.48858 −0.183705
\(598\) −1.87263 −0.0765773
\(599\) −22.9293 −0.936866 −0.468433 0.883499i \(-0.655181\pi\)
−0.468433 + 0.883499i \(0.655181\pi\)
\(600\) 0.405813 0.0165673
\(601\) −11.6974 −0.477147 −0.238573 0.971124i \(-0.576680\pi\)
−0.238573 + 0.971124i \(0.576680\pi\)
\(602\) 0 0
\(603\) −1.38212 −0.0562844
\(604\) −0.835790 −0.0340078
\(605\) −22.9530 −0.933172
\(606\) −0.416830 −0.0169326
\(607\) −15.8659 −0.643978 −0.321989 0.946743i \(-0.604351\pi\)
−0.321989 + 0.946743i \(0.604351\pi\)
\(608\) −28.6316 −1.16117
\(609\) −0.461435 −0.0186983
\(610\) −8.76809 −0.355009
\(611\) −0.643104 −0.0260172
\(612\) 5.56033 0.224763
\(613\) 32.6461 1.31856 0.659282 0.751896i \(-0.270861\pi\)
0.659282 + 0.751896i \(0.270861\pi\)
\(614\) 0.351519 0.0141862
\(615\) −3.07500 −0.123996
\(616\) −24.8183 −0.999959
\(617\) 36.0575 1.45162 0.725811 0.687894i \(-0.241465\pi\)
0.725811 + 0.687894i \(0.241465\pi\)
\(618\) −0.650874 −0.0261820
\(619\) 9.03577 0.363178 0.181589 0.983374i \(-0.441876\pi\)
0.181589 + 0.983374i \(0.441876\pi\)
\(620\) 20.1715 0.810107
\(621\) 6.19460 0.248581
\(622\) 14.0774 0.564452
\(623\) 43.4728 1.74170
\(624\) −0.286208 −0.0114575
\(625\) −19.0000 −0.760000
\(626\) −8.29457 −0.331518
\(627\) −5.03013 −0.200884
\(628\) 13.0479 0.520666
\(629\) −12.6461 −0.504233
\(630\) 8.39612 0.334510
\(631\) 17.0224 0.677650 0.338825 0.940850i \(-0.389971\pi\)
0.338825 + 0.940850i \(0.389971\pi\)
\(632\) −10.4450 −0.415481
\(633\) 3.26636 0.129826
\(634\) 2.68904 0.106795
\(635\) −5.93230 −0.235416
\(636\) 2.59419 0.102866
\(637\) −0.303667 −0.0120317
\(638\) 2.39911 0.0949816
\(639\) −28.0737 −1.11058
\(640\) −23.0750 −0.912119
\(641\) −5.35152 −0.211372 −0.105686 0.994400i \(-0.533704\pi\)
−0.105686 + 0.994400i \(0.533704\pi\)
\(642\) 0.216112 0.00852925
\(643\) −18.5241 −0.730519 −0.365259 0.930906i \(-0.619020\pi\)
−0.365259 + 0.930906i \(0.619020\pi\)
\(644\) 22.6829 0.893832
\(645\) 0 0
\(646\) −3.29962 −0.129822
\(647\) 21.3357 0.838794 0.419397 0.907803i \(-0.362242\pi\)
0.419397 + 0.907803i \(0.362242\pi\)
\(648\) 17.7200 0.696108
\(649\) −39.5163 −1.55115
\(650\) 0.356896 0.0139986
\(651\) 3.01639 0.118222
\(652\) −1.65114 −0.0646635
\(653\) 34.6698 1.35673 0.678367 0.734724i \(-0.262688\pi\)
0.678367 + 0.734724i \(0.262688\pi\)
\(654\) −0.914838 −0.0357730
\(655\) 14.2198 0.555615
\(656\) −17.4426 −0.681021
\(657\) 37.5424 1.46467
\(658\) −1.41789 −0.0552753
\(659\) 46.9124 1.82745 0.913725 0.406334i \(-0.133193\pi\)
0.913725 + 0.406334i \(0.133193\pi\)
\(660\) −3.17762 −0.123689
\(661\) 14.1062 0.548667 0.274334 0.961635i \(-0.411543\pi\)
0.274334 + 0.961635i \(0.411543\pi\)
\(662\) −6.85218 −0.266318
\(663\) −0.141375 −0.00549056
\(664\) 30.5730 1.18646
\(665\) 27.3733 1.06149
\(666\) −18.7211 −0.725427
\(667\) −4.78448 −0.185256
\(668\) 9.55735 0.369785
\(669\) 0.298290 0.0115326
\(670\) 0.518122 0.0200168
\(671\) −37.4523 −1.44583
\(672\) −2.70469 −0.104336
\(673\) 24.3207 0.937492 0.468746 0.883333i \(-0.344706\pi\)
0.468746 + 0.883333i \(0.344706\pi\)
\(674\) −3.44265 −0.132606
\(675\) −1.18060 −0.0454415
\(676\) 21.2965 0.819096
\(677\) −34.6571 −1.33198 −0.665990 0.745960i \(-0.731991\pi\)
−0.665990 + 0.745960i \(0.731991\pi\)
\(678\) −0.201046 −0.00772113
\(679\) −42.2972 −1.62322
\(680\) −4.54825 −0.174418
\(681\) 3.63640 0.139347
\(682\) −15.6829 −0.600530
\(683\) −29.2790 −1.12033 −0.560165 0.828381i \(-0.689262\pi\)
−0.560165 + 0.828381i \(0.689262\pi\)
\(684\) 26.8364 1.02611
\(685\) −16.6461 −0.636014
\(686\) −10.5948 −0.404510
\(687\) −1.22474 −0.0467266
\(688\) 0 0
\(689\) 4.97823 0.189655
\(690\) −1.15346 −0.0439113
\(691\) 4.59956 0.174976 0.0874878 0.996166i \(-0.472116\pi\)
0.0874878 + 0.996166i \(0.472116\pi\)
\(692\) 14.6407 0.556556
\(693\) 35.8635 1.36234
\(694\) −10.0392 −0.381084
\(695\) −12.0785 −0.458162
\(696\) 0.370042 0.0140264
\(697\) −8.61596 −0.326353
\(698\) −4.02715 −0.152430
\(699\) −0.875609 −0.0331186
\(700\) −4.32304 −0.163396
\(701\) 3.77373 0.142532 0.0712658 0.997457i \(-0.477296\pi\)
0.0712658 + 0.997457i \(0.477296\pi\)
\(702\) −0.421353 −0.0159029
\(703\) −61.0350 −2.30198
\(704\) −7.24326 −0.272991
\(705\) −0.396125 −0.0149189
\(706\) −5.79358 −0.218044
\(707\) 9.68904 0.364394
\(708\) −2.79331 −0.104979
\(709\) 4.86353 0.182654 0.0913268 0.995821i \(-0.470889\pi\)
0.0913268 + 0.995821i \(0.470889\pi\)
\(710\) 10.5241 0.394962
\(711\) 15.0935 0.566051
\(712\) −34.8625 −1.30653
\(713\) 31.2760 1.17130
\(714\) −0.311699 −0.0116651
\(715\) −6.09783 −0.228046
\(716\) 3.37495 0.126128
\(717\) 2.06962 0.0772915
\(718\) 15.6136 0.582693
\(719\) −12.2911 −0.458381 −0.229191 0.973382i \(-0.573608\pi\)
−0.229191 + 0.973382i \(0.573608\pi\)
\(720\) 13.3056 0.495870
\(721\) 15.1293 0.563444
\(722\) −5.38106 −0.200262
\(723\) −4.81295 −0.178996
\(724\) 14.9849 0.556911
\(725\) 0.911854 0.0338654
\(726\) 1.26145 0.0468170
\(727\) 43.2127 1.60267 0.801334 0.598217i \(-0.204124\pi\)
0.801334 + 0.598217i \(0.204124\pi\)
\(728\) −3.36658 −0.124774
\(729\) −24.9047 −0.922395
\(730\) −14.0737 −0.520890
\(731\) 0 0
\(732\) −2.64742 −0.0978513
\(733\) −26.7590 −0.988366 −0.494183 0.869358i \(-0.664533\pi\)
−0.494183 + 0.869358i \(0.664533\pi\)
\(734\) −9.12797 −0.336919
\(735\) −0.187046 −0.00689928
\(736\) −28.0441 −1.03372
\(737\) 2.21313 0.0815216
\(738\) −12.7549 −0.469516
\(739\) 10.9535 0.402930 0.201465 0.979496i \(-0.435430\pi\)
0.201465 + 0.979496i \(0.435430\pi\)
\(740\) −38.5569 −1.41738
\(741\) −0.682333 −0.0250661
\(742\) 10.9758 0.402936
\(743\) −39.1661 −1.43687 −0.718433 0.695596i \(-0.755140\pi\)
−0.718433 + 0.695596i \(0.755140\pi\)
\(744\) −2.41896 −0.0886834
\(745\) −4.45042 −0.163051
\(746\) 5.99702 0.219566
\(747\) −44.1793 −1.61644
\(748\) −8.90349 −0.325544
\(749\) −5.02343 −0.183552
\(750\) 1.31900 0.0481629
\(751\) 11.4131 0.416470 0.208235 0.978079i \(-0.433228\pi\)
0.208235 + 0.978079i \(0.433228\pi\)
\(752\) −2.24698 −0.0819389
\(753\) 4.34290 0.158264
\(754\) 0.325437 0.0118517
\(755\) −0.987918 −0.0359540
\(756\) 5.10380 0.185624
\(757\) −27.9995 −1.01766 −0.508830 0.860867i \(-0.669922\pi\)
−0.508830 + 0.860867i \(0.669922\pi\)
\(758\) 5.39373 0.195909
\(759\) −4.92692 −0.178836
\(760\) −21.9517 −0.796271
\(761\) −31.0659 −1.12614 −0.563069 0.826410i \(-0.690379\pi\)
−0.563069 + 0.826410i \(0.690379\pi\)
\(762\) 0.326028 0.0118107
\(763\) 21.2650 0.769846
\(764\) 12.7668 0.461885
\(765\) 6.57242 0.237626
\(766\) 13.1196 0.474031
\(767\) −5.36035 −0.193551
\(768\) 0.662955 0.0239223
\(769\) −10.6267 −0.383209 −0.191604 0.981472i \(-0.561369\pi\)
−0.191604 + 0.981472i \(0.561369\pi\)
\(770\) −13.4443 −0.484499
\(771\) 0.573481 0.0206534
\(772\) 13.6076 0.489748
\(773\) −26.4359 −0.950835 −0.475417 0.879760i \(-0.657703\pi\)
−0.475417 + 0.879760i \(0.657703\pi\)
\(774\) 0 0
\(775\) −5.96077 −0.214117
\(776\) 33.9197 1.21765
\(777\) −5.76569 −0.206843
\(778\) 4.38032 0.157042
\(779\) −41.5840 −1.48990
\(780\) −0.431041 −0.0154338
\(781\) 44.9530 1.60854
\(782\) −3.23191 −0.115573
\(783\) −1.07654 −0.0384723
\(784\) −1.06100 −0.0378928
\(785\) 15.4228 0.550463
\(786\) −0.781495 −0.0278750
\(787\) −16.6517 −0.593570 −0.296785 0.954944i \(-0.595914\pi\)
−0.296785 + 0.954944i \(0.595914\pi\)
\(788\) 32.8106 1.16883
\(789\) 3.44120 0.122510
\(790\) −5.65817 −0.201309
\(791\) 4.67324 0.166161
\(792\) −28.7603 −1.02195
\(793\) −5.08038 −0.180409
\(794\) 14.2010 0.503976
\(795\) 3.06638 0.108753
\(796\) −38.3454 −1.35912
\(797\) −7.39612 −0.261984 −0.130992 0.991383i \(-0.541816\pi\)
−0.130992 + 0.991383i \(0.541816\pi\)
\(798\) −1.50438 −0.0532546
\(799\) −1.10992 −0.0392660
\(800\) 5.34481 0.188968
\(801\) 50.3777 1.78001
\(802\) 4.83340 0.170673
\(803\) −60.1148 −2.12141
\(804\) 0.156441 0.00551724
\(805\) 26.8116 0.944986
\(806\) −2.12737 −0.0749336
\(807\) 2.78687 0.0981025
\(808\) −7.77000 −0.273348
\(809\) 25.5687 0.898947 0.449474 0.893294i \(-0.351612\pi\)
0.449474 + 0.893294i \(0.351612\pi\)
\(810\) 9.59909 0.337278
\(811\) −23.1166 −0.811734 −0.405867 0.913932i \(-0.633030\pi\)
−0.405867 + 0.913932i \(0.633030\pi\)
\(812\) −3.94198 −0.138337
\(813\) 0.424600 0.0148914
\(814\) 29.9772 1.05070
\(815\) −1.95167 −0.0683641
\(816\) −0.493959 −0.0172920
\(817\) 0 0
\(818\) −7.35690 −0.257228
\(819\) 4.86486 0.169992
\(820\) −26.2693 −0.917365
\(821\) −15.8619 −0.553583 −0.276792 0.960930i \(-0.589271\pi\)
−0.276792 + 0.960930i \(0.589271\pi\)
\(822\) 0.914838 0.0319086
\(823\) −17.6209 −0.614225 −0.307112 0.951673i \(-0.599363\pi\)
−0.307112 + 0.951673i \(0.599363\pi\)
\(824\) −12.1328 −0.422664
\(825\) 0.939001 0.0326918
\(826\) −11.8183 −0.411212
\(827\) 28.6552 0.996438 0.498219 0.867051i \(-0.333987\pi\)
0.498219 + 0.867051i \(0.333987\pi\)
\(828\) 26.2857 0.913492
\(829\) −13.9011 −0.482805 −0.241403 0.970425i \(-0.577607\pi\)
−0.241403 + 0.970425i \(0.577607\pi\)
\(830\) 16.5617 0.574864
\(831\) 4.60686 0.159810
\(832\) −0.982542 −0.0340635
\(833\) −0.524090 −0.0181586
\(834\) 0.663809 0.0229858
\(835\) 11.2970 0.390947
\(836\) −42.9718 −1.48621
\(837\) 7.03731 0.243245
\(838\) −0.633415 −0.0218810
\(839\) −25.2131 −0.870454 −0.435227 0.900321i \(-0.643332\pi\)
−0.435227 + 0.900321i \(0.643332\pi\)
\(840\) −2.07367 −0.0715485
\(841\) −28.1685 −0.971328
\(842\) −1.84920 −0.0637276
\(843\) 3.51248 0.120976
\(844\) 27.9041 0.960498
\(845\) 25.1728 0.865972
\(846\) −1.64310 −0.0564911
\(847\) −29.3220 −1.00752
\(848\) 17.3937 0.597303
\(849\) −0.774317 −0.0265745
\(850\) 0.615957 0.0211272
\(851\) −59.7827 −2.04932
\(852\) 3.17762 0.108863
\(853\) 21.9135 0.750304 0.375152 0.926963i \(-0.377590\pi\)
0.375152 + 0.926963i \(0.377590\pi\)
\(854\) −11.2010 −0.383292
\(855\) 31.7211 1.08484
\(856\) 4.02848 0.137690
\(857\) 13.8804 0.474145 0.237073 0.971492i \(-0.423812\pi\)
0.237073 + 0.971492i \(0.423812\pi\)
\(858\) 0.335126 0.0114410
\(859\) −31.4959 −1.07463 −0.537313 0.843383i \(-0.680561\pi\)
−0.537313 + 0.843383i \(0.680561\pi\)
\(860\) 0 0
\(861\) −3.92825 −0.133874
\(862\) −11.2942 −0.384683
\(863\) −48.7958 −1.66103 −0.830515 0.556997i \(-0.811954\pi\)
−0.830515 + 0.556997i \(0.811954\pi\)
\(864\) −6.31011 −0.214674
\(865\) 17.3056 0.588408
\(866\) −5.52914 −0.187888
\(867\) 3.12306 0.106065
\(868\) 25.7687 0.874646
\(869\) −24.1685 −0.819861
\(870\) 0.200455 0.00679607
\(871\) 0.300209 0.0101722
\(872\) −17.0532 −0.577495
\(873\) −49.0154 −1.65892
\(874\) −15.5985 −0.527627
\(875\) −30.6595 −1.03648
\(876\) −4.24937 −0.143573
\(877\) 0.398517 0.0134570 0.00672849 0.999977i \(-0.497858\pi\)
0.00672849 + 0.999977i \(0.497858\pi\)
\(878\) −4.54361 −0.153340
\(879\) 5.55209 0.187267
\(880\) −21.3056 −0.718211
\(881\) 20.7651 0.699594 0.349797 0.936826i \(-0.386251\pi\)
0.349797 + 0.936826i \(0.386251\pi\)
\(882\) −0.775856 −0.0261244
\(883\) 21.3840 0.719630 0.359815 0.933024i \(-0.382840\pi\)
0.359815 + 0.933024i \(0.382840\pi\)
\(884\) −1.20775 −0.0406211
\(885\) −3.30175 −0.110987
\(886\) −16.8750 −0.566927
\(887\) −39.8659 −1.33857 −0.669283 0.743007i \(-0.733399\pi\)
−0.669283 + 0.743007i \(0.733399\pi\)
\(888\) 4.62373 0.155162
\(889\) −7.57838 −0.254171
\(890\) −18.8853 −0.633037
\(891\) 41.0019 1.37362
\(892\) 2.54825 0.0853218
\(893\) −5.35690 −0.179262
\(894\) 0.244587 0.00818020
\(895\) 3.98925 0.133346
\(896\) −29.4778 −0.984785
\(897\) −0.668332 −0.0223150
\(898\) 12.3201 0.411126
\(899\) −5.43535 −0.181279
\(900\) −5.00969 −0.166990
\(901\) 8.59179 0.286234
\(902\) 20.4239 0.680040
\(903\) 0 0
\(904\) −3.74764 −0.124645
\(905\) 17.7125 0.588782
\(906\) 0.0542942 0.00180380
\(907\) 3.90217 0.129569 0.0647846 0.997899i \(-0.479364\pi\)
0.0647846 + 0.997899i \(0.479364\pi\)
\(908\) 31.0653 1.03094
\(909\) 11.2280 0.372409
\(910\) −1.82371 −0.0604553
\(911\) −47.1667 −1.56270 −0.781352 0.624091i \(-0.785469\pi\)
−0.781352 + 0.624091i \(0.785469\pi\)
\(912\) −2.38404 −0.0789436
\(913\) 70.7421 2.34122
\(914\) −6.22580 −0.205931
\(915\) −3.12929 −0.103451
\(916\) −10.4628 −0.345699
\(917\) 18.1655 0.599879
\(918\) −0.727201 −0.0240012
\(919\) −5.53511 −0.182586 −0.0912932 0.995824i \(-0.529100\pi\)
−0.0912932 + 0.995824i \(0.529100\pi\)
\(920\) −21.5013 −0.708875
\(921\) 0.125456 0.00413391
\(922\) 19.1715 0.631380
\(923\) 6.09783 0.200713
\(924\) −4.05934 −0.133543
\(925\) 11.3937 0.374624
\(926\) −5.64981 −0.185664
\(927\) 17.5323 0.575837
\(928\) 4.87369 0.159987
\(929\) −33.9541 −1.11400 −0.556998 0.830514i \(-0.688047\pi\)
−0.556998 + 0.830514i \(0.688047\pi\)
\(930\) −1.31037 −0.0429688
\(931\) −2.52947 −0.0828999
\(932\) −7.48022 −0.245023
\(933\) 5.02416 0.164484
\(934\) −8.31229 −0.271986
\(935\) −10.5241 −0.344175
\(936\) −3.90131 −0.127518
\(937\) 9.20775 0.300804 0.150402 0.988625i \(-0.451943\pi\)
0.150402 + 0.988625i \(0.451943\pi\)
\(938\) 0.661890 0.0216115
\(939\) −2.96030 −0.0966057
\(940\) −3.38404 −0.110375
\(941\) −39.0307 −1.27237 −0.636183 0.771539i \(-0.719487\pi\)
−0.636183 + 0.771539i \(0.719487\pi\)
\(942\) −0.847608 −0.0276166
\(943\) −40.7308 −1.32638
\(944\) −18.7289 −0.609572
\(945\) 6.03279 0.196247
\(946\) 0 0
\(947\) 18.4166 0.598458 0.299229 0.954181i \(-0.403271\pi\)
0.299229 + 0.954181i \(0.403271\pi\)
\(948\) −1.70841 −0.0554867
\(949\) −8.15452 −0.264707
\(950\) 2.97285 0.0964521
\(951\) 0.959706 0.0311206
\(952\) −5.81030 −0.188313
\(953\) 9.60819 0.311240 0.155620 0.987817i \(-0.450263\pi\)
0.155620 + 0.987817i \(0.450263\pi\)
\(954\) 12.7192 0.411798
\(955\) 15.0905 0.488318
\(956\) 17.6805 0.571829
\(957\) 0.856232 0.0276780
\(958\) −16.1256 −0.520994
\(959\) −21.2650 −0.686684
\(960\) −0.605203 −0.0195329
\(961\) 4.53079 0.146155
\(962\) 4.06638 0.131105
\(963\) −5.82132 −0.187589
\(964\) −41.1165 −1.32427
\(965\) 16.0844 0.517776
\(966\) −1.47352 −0.0474096
\(967\) −58.7235 −1.88842 −0.944210 0.329344i \(-0.893172\pi\)
−0.944210 + 0.329344i \(0.893172\pi\)
\(968\) 23.5144 0.755781
\(969\) −1.17762 −0.0378306
\(970\) 18.3746 0.589973
\(971\) −46.0887 −1.47906 −0.739529 0.673125i \(-0.764952\pi\)
−0.739529 + 0.673125i \(0.764952\pi\)
\(972\) 8.89115 0.285184
\(973\) −15.4300 −0.494662
\(974\) 13.2529 0.424652
\(975\) 0.127375 0.00407925
\(976\) −17.7506 −0.568184
\(977\) 11.7963 0.377397 0.188699 0.982035i \(-0.439573\pi\)
0.188699 + 0.982035i \(0.439573\pi\)
\(978\) 0.107260 0.00342981
\(979\) −80.6674 −2.57814
\(980\) −1.59791 −0.0510433
\(981\) 24.6426 0.786779
\(982\) 0.374945 0.0119650
\(983\) −1.78581 −0.0569584 −0.0284792 0.999594i \(-0.509066\pi\)
−0.0284792 + 0.999594i \(0.509066\pi\)
\(984\) 3.15021 0.100425
\(985\) 38.7827 1.23572
\(986\) 0.561663 0.0178870
\(987\) −0.506041 −0.0161075
\(988\) −5.82908 −0.185448
\(989\) 0 0
\(990\) −15.5797 −0.495156
\(991\) 48.0334 1.52583 0.762915 0.646498i \(-0.223767\pi\)
0.762915 + 0.646498i \(0.223767\pi\)
\(992\) −31.8592 −1.01153
\(993\) −2.44552 −0.0776061
\(994\) 13.4443 0.426427
\(995\) −45.3250 −1.43690
\(996\) 5.00059 0.158450
\(997\) 9.12690 0.289052 0.144526 0.989501i \(-0.453834\pi\)
0.144526 + 0.989501i \(0.453834\pi\)
\(998\) −17.8665 −0.565555
\(999\) −13.4515 −0.425586
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 1849.2.a.i.1.2 3
43.16 even 7 43.2.e.b.41.1 yes 6
43.35 even 7 43.2.e.b.21.1 6
43.42 odd 2 1849.2.a.l.1.2 3
129.35 odd 14 387.2.u.a.64.1 6
129.59 odd 14 387.2.u.a.127.1 6
172.35 odd 14 688.2.u.c.193.1 6
172.59 odd 14 688.2.u.c.385.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.2.e.b.21.1 6 43.35 even 7
43.2.e.b.41.1 yes 6 43.16 even 7
387.2.u.a.64.1 6 129.35 odd 14
387.2.u.a.127.1 6 129.59 odd 14
688.2.u.c.193.1 6 172.35 odd 14
688.2.u.c.385.1 6 172.59 odd 14
1849.2.a.i.1.2 3 1.1 even 1 trivial
1849.2.a.l.1.2 3 43.42 odd 2