Properties

Label 4011.2.a.k.1.7
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $27$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.28891 q^{2} +1.00000 q^{3} -0.338712 q^{4} +0.716613 q^{5} -1.28891 q^{6} +1.00000 q^{7} +3.01439 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.28891 q^{2} +1.00000 q^{3} -0.338712 q^{4} +0.716613 q^{5} -1.28891 q^{6} +1.00000 q^{7} +3.01439 q^{8} +1.00000 q^{9} -0.923650 q^{10} +5.42521 q^{11} -0.338712 q^{12} +3.53458 q^{13} -1.28891 q^{14} +0.716613 q^{15} -3.20785 q^{16} +3.87656 q^{17} -1.28891 q^{18} +5.75190 q^{19} -0.242726 q^{20} +1.00000 q^{21} -6.99261 q^{22} -3.07639 q^{23} +3.01439 q^{24} -4.48647 q^{25} -4.55575 q^{26} +1.00000 q^{27} -0.338712 q^{28} +1.93227 q^{29} -0.923650 q^{30} +10.3463 q^{31} -1.89415 q^{32} +5.42521 q^{33} -4.99654 q^{34} +0.716613 q^{35} -0.338712 q^{36} +3.10093 q^{37} -7.41367 q^{38} +3.53458 q^{39} +2.16015 q^{40} +0.243689 q^{41} -1.28891 q^{42} +8.67240 q^{43} -1.83759 q^{44} +0.716613 q^{45} +3.96519 q^{46} +5.34819 q^{47} -3.20785 q^{48} +1.00000 q^{49} +5.78265 q^{50} +3.87656 q^{51} -1.19720 q^{52} -2.95325 q^{53} -1.28891 q^{54} +3.88778 q^{55} +3.01439 q^{56} +5.75190 q^{57} -2.49052 q^{58} -6.43358 q^{59} -0.242726 q^{60} -9.78399 q^{61} -13.3354 q^{62} +1.00000 q^{63} +8.85709 q^{64} +2.53292 q^{65} -6.99261 q^{66} +0.0125252 q^{67} -1.31304 q^{68} -3.07639 q^{69} -0.923650 q^{70} -1.56317 q^{71} +3.01439 q^{72} -15.4518 q^{73} -3.99682 q^{74} -4.48647 q^{75} -1.94824 q^{76} +5.42521 q^{77} -4.55575 q^{78} -5.55105 q^{79} -2.29879 q^{80} +1.00000 q^{81} -0.314093 q^{82} +12.6372 q^{83} -0.338712 q^{84} +2.77800 q^{85} -11.1779 q^{86} +1.93227 q^{87} +16.3537 q^{88} -10.2353 q^{89} -0.923650 q^{90} +3.53458 q^{91} +1.04201 q^{92} +10.3463 q^{93} -6.89333 q^{94} +4.12189 q^{95} -1.89415 q^{96} -18.5407 q^{97} -1.28891 q^{98} +5.42521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28891 −0.911397 −0.455698 0.890134i \(-0.650610\pi\)
−0.455698 + 0.890134i \(0.650610\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.338712 −0.169356
\(5\) 0.716613 0.320479 0.160240 0.987078i \(-0.448773\pi\)
0.160240 + 0.987078i \(0.448773\pi\)
\(6\) −1.28891 −0.526195
\(7\) 1.00000 0.377964
\(8\) 3.01439 1.06575
\(9\) 1.00000 0.333333
\(10\) −0.923650 −0.292084
\(11\) 5.42521 1.63576 0.817882 0.575386i \(-0.195148\pi\)
0.817882 + 0.575386i \(0.195148\pi\)
\(12\) −0.338712 −0.0977778
\(13\) 3.53458 0.980315 0.490157 0.871634i \(-0.336939\pi\)
0.490157 + 0.871634i \(0.336939\pi\)
\(14\) −1.28891 −0.344476
\(15\) 0.716613 0.185029
\(16\) −3.20785 −0.801962
\(17\) 3.87656 0.940204 0.470102 0.882612i \(-0.344217\pi\)
0.470102 + 0.882612i \(0.344217\pi\)
\(18\) −1.28891 −0.303799
\(19\) 5.75190 1.31958 0.659788 0.751452i \(-0.270646\pi\)
0.659788 + 0.751452i \(0.270646\pi\)
\(20\) −0.242726 −0.0542751
\(21\) 1.00000 0.218218
\(22\) −6.99261 −1.49083
\(23\) −3.07639 −0.641473 −0.320736 0.947169i \(-0.603930\pi\)
−0.320736 + 0.947169i \(0.603930\pi\)
\(24\) 3.01439 0.615309
\(25\) −4.48647 −0.897293
\(26\) −4.55575 −0.893456
\(27\) 1.00000 0.192450
\(28\) −0.338712 −0.0640106
\(29\) 1.93227 0.358814 0.179407 0.983775i \(-0.442582\pi\)
0.179407 + 0.983775i \(0.442582\pi\)
\(30\) −0.923650 −0.168635
\(31\) 10.3463 1.85824 0.929122 0.369774i \(-0.120565\pi\)
0.929122 + 0.369774i \(0.120565\pi\)
\(32\) −1.89415 −0.334841
\(33\) 5.42521 0.944409
\(34\) −4.99654 −0.856899
\(35\) 0.716613 0.121130
\(36\) −0.338712 −0.0564520
\(37\) 3.10093 0.509790 0.254895 0.966969i \(-0.417959\pi\)
0.254895 + 0.966969i \(0.417959\pi\)
\(38\) −7.41367 −1.20266
\(39\) 3.53458 0.565985
\(40\) 2.16015 0.341550
\(41\) 0.243689 0.0380578 0.0190289 0.999819i \(-0.493943\pi\)
0.0190289 + 0.999819i \(0.493943\pi\)
\(42\) −1.28891 −0.198883
\(43\) 8.67240 1.32253 0.661264 0.750153i \(-0.270020\pi\)
0.661264 + 0.750153i \(0.270020\pi\)
\(44\) −1.83759 −0.277027
\(45\) 0.716613 0.106826
\(46\) 3.96519 0.584636
\(47\) 5.34819 0.780113 0.390056 0.920791i \(-0.372455\pi\)
0.390056 + 0.920791i \(0.372455\pi\)
\(48\) −3.20785 −0.463013
\(49\) 1.00000 0.142857
\(50\) 5.78265 0.817790
\(51\) 3.87656 0.542827
\(52\) −1.19720 −0.166022
\(53\) −2.95325 −0.405661 −0.202830 0.979214i \(-0.565014\pi\)
−0.202830 + 0.979214i \(0.565014\pi\)
\(54\) −1.28891 −0.175398
\(55\) 3.88778 0.524228
\(56\) 3.01439 0.402815
\(57\) 5.75190 0.761857
\(58\) −2.49052 −0.327022
\(59\) −6.43358 −0.837581 −0.418790 0.908083i \(-0.637546\pi\)
−0.418790 + 0.908083i \(0.637546\pi\)
\(60\) −0.242726 −0.0313358
\(61\) −9.78399 −1.25271 −0.626356 0.779537i \(-0.715454\pi\)
−0.626356 + 0.779537i \(0.715454\pi\)
\(62\) −13.3354 −1.69360
\(63\) 1.00000 0.125988
\(64\) 8.85709 1.10714
\(65\) 2.53292 0.314171
\(66\) −6.99261 −0.860731
\(67\) 0.0125252 0.00153020 0.000765098 1.00000i \(-0.499756\pi\)
0.000765098 1.00000i \(0.499756\pi\)
\(68\) −1.31304 −0.159229
\(69\) −3.07639 −0.370354
\(70\) −0.923650 −0.110397
\(71\) −1.56317 −0.185514 −0.0927569 0.995689i \(-0.529568\pi\)
−0.0927569 + 0.995689i \(0.529568\pi\)
\(72\) 3.01439 0.355249
\(73\) −15.4518 −1.80849 −0.904245 0.427013i \(-0.859566\pi\)
−0.904245 + 0.427013i \(0.859566\pi\)
\(74\) −3.99682 −0.464621
\(75\) −4.48647 −0.518052
\(76\) −1.94824 −0.223478
\(77\) 5.42521 0.618261
\(78\) −4.55575 −0.515837
\(79\) −5.55105 −0.624542 −0.312271 0.949993i \(-0.601090\pi\)
−0.312271 + 0.949993i \(0.601090\pi\)
\(80\) −2.29879 −0.257012
\(81\) 1.00000 0.111111
\(82\) −0.314093 −0.0346858
\(83\) 12.6372 1.38712 0.693559 0.720400i \(-0.256042\pi\)
0.693559 + 0.720400i \(0.256042\pi\)
\(84\) −0.338712 −0.0369565
\(85\) 2.77800 0.301316
\(86\) −11.1779 −1.20535
\(87\) 1.93227 0.207161
\(88\) 16.3537 1.74331
\(89\) −10.2353 −1.08494 −0.542472 0.840074i \(-0.682512\pi\)
−0.542472 + 0.840074i \(0.682512\pi\)
\(90\) −0.923650 −0.0973612
\(91\) 3.53458 0.370524
\(92\) 1.04201 0.108637
\(93\) 10.3463 1.07286
\(94\) −6.89333 −0.710992
\(95\) 4.12189 0.422897
\(96\) −1.89415 −0.193321
\(97\) −18.5407 −1.88252 −0.941260 0.337684i \(-0.890357\pi\)
−0.941260 + 0.337684i \(0.890357\pi\)
\(98\) −1.28891 −0.130200
\(99\) 5.42521 0.545255
\(100\) 1.51962 0.151962
\(101\) −5.99911 −0.596934 −0.298467 0.954420i \(-0.596475\pi\)
−0.298467 + 0.954420i \(0.596475\pi\)
\(102\) −4.99654 −0.494731
\(103\) −14.0429 −1.38368 −0.691842 0.722049i \(-0.743201\pi\)
−0.691842 + 0.722049i \(0.743201\pi\)
\(104\) 10.6546 1.04477
\(105\) 0.716613 0.0699343
\(106\) 3.80648 0.369718
\(107\) −20.0752 −1.94074 −0.970370 0.241623i \(-0.922320\pi\)
−0.970370 + 0.241623i \(0.922320\pi\)
\(108\) −0.338712 −0.0325926
\(109\) −5.64824 −0.541003 −0.270501 0.962720i \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(110\) −5.01100 −0.477780
\(111\) 3.10093 0.294327
\(112\) −3.20785 −0.303113
\(113\) 2.71733 0.255625 0.127812 0.991798i \(-0.459204\pi\)
0.127812 + 0.991798i \(0.459204\pi\)
\(114\) −7.41367 −0.694354
\(115\) −2.20459 −0.205579
\(116\) −0.654484 −0.0607673
\(117\) 3.53458 0.326772
\(118\) 8.29230 0.763368
\(119\) 3.87656 0.355364
\(120\) 2.16015 0.197194
\(121\) 18.4330 1.67572
\(122\) 12.6107 1.14172
\(123\) 0.243689 0.0219727
\(124\) −3.50441 −0.314705
\(125\) −6.79813 −0.608043
\(126\) −1.28891 −0.114825
\(127\) 0.0339105 0.00300907 0.00150453 0.999999i \(-0.499521\pi\)
0.00150453 + 0.999999i \(0.499521\pi\)
\(128\) −7.62768 −0.674198
\(129\) 8.67240 0.763562
\(130\) −3.26471 −0.286334
\(131\) 10.3981 0.908486 0.454243 0.890878i \(-0.349910\pi\)
0.454243 + 0.890878i \(0.349910\pi\)
\(132\) −1.83759 −0.159941
\(133\) 5.75190 0.498753
\(134\) −0.0161439 −0.00139462
\(135\) 0.716613 0.0616763
\(136\) 11.6855 1.00202
\(137\) 3.92674 0.335484 0.167742 0.985831i \(-0.446352\pi\)
0.167742 + 0.985831i \(0.446352\pi\)
\(138\) 3.96519 0.337540
\(139\) −14.8936 −1.26326 −0.631629 0.775271i \(-0.717613\pi\)
−0.631629 + 0.775271i \(0.717613\pi\)
\(140\) −0.242726 −0.0205141
\(141\) 5.34819 0.450398
\(142\) 2.01478 0.169077
\(143\) 19.1758 1.60356
\(144\) −3.20785 −0.267321
\(145\) 1.38469 0.114992
\(146\) 19.9159 1.64825
\(147\) 1.00000 0.0824786
\(148\) −1.05032 −0.0863360
\(149\) 19.9744 1.63637 0.818184 0.574957i \(-0.194981\pi\)
0.818184 + 0.574957i \(0.194981\pi\)
\(150\) 5.78265 0.472151
\(151\) 7.80032 0.634781 0.317391 0.948295i \(-0.397193\pi\)
0.317391 + 0.948295i \(0.397193\pi\)
\(152\) 17.3384 1.40633
\(153\) 3.87656 0.313401
\(154\) −6.99261 −0.563481
\(155\) 7.41427 0.595528
\(156\) −1.19720 −0.0958530
\(157\) −13.1463 −1.04919 −0.524595 0.851352i \(-0.675783\pi\)
−0.524595 + 0.851352i \(0.675783\pi\)
\(158\) 7.15481 0.569206
\(159\) −2.95325 −0.234208
\(160\) −1.35737 −0.107310
\(161\) −3.07639 −0.242454
\(162\) −1.28891 −0.101266
\(163\) −15.5010 −1.21414 −0.607068 0.794650i \(-0.707654\pi\)
−0.607068 + 0.794650i \(0.707654\pi\)
\(164\) −0.0825405 −0.00644533
\(165\) 3.88778 0.302663
\(166\) −16.2883 −1.26421
\(167\) 6.08456 0.470838 0.235419 0.971894i \(-0.424354\pi\)
0.235419 + 0.971894i \(0.424354\pi\)
\(168\) 3.01439 0.232565
\(169\) −0.506775 −0.0389827
\(170\) −3.58058 −0.274618
\(171\) 5.75190 0.439858
\(172\) −2.93745 −0.223978
\(173\) −9.91974 −0.754184 −0.377092 0.926176i \(-0.623076\pi\)
−0.377092 + 0.926176i \(0.623076\pi\)
\(174\) −2.49052 −0.188806
\(175\) −4.48647 −0.339145
\(176\) −17.4033 −1.31182
\(177\) −6.43358 −0.483578
\(178\) 13.1924 0.988814
\(179\) 4.88013 0.364758 0.182379 0.983228i \(-0.441620\pi\)
0.182379 + 0.983228i \(0.441620\pi\)
\(180\) −0.242726 −0.0180917
\(181\) −3.43394 −0.255243 −0.127621 0.991823i \(-0.540734\pi\)
−0.127621 + 0.991823i \(0.540734\pi\)
\(182\) −4.55575 −0.337695
\(183\) −9.78399 −0.723254
\(184\) −9.27345 −0.683648
\(185\) 2.22217 0.163377
\(186\) −13.3354 −0.977799
\(187\) 21.0312 1.53795
\(188\) −1.81150 −0.132117
\(189\) 1.00000 0.0727393
\(190\) −5.31274 −0.385426
\(191\) 1.00000 0.0723575
\(192\) 8.85709 0.639205
\(193\) −9.55231 −0.687590 −0.343795 0.939045i \(-0.611713\pi\)
−0.343795 + 0.939045i \(0.611713\pi\)
\(194\) 23.8972 1.71572
\(195\) 2.53292 0.181386
\(196\) −0.338712 −0.0241937
\(197\) 11.2246 0.799722 0.399861 0.916576i \(-0.369058\pi\)
0.399861 + 0.916576i \(0.369058\pi\)
\(198\) −6.99261 −0.496943
\(199\) 17.0021 1.20525 0.602624 0.798025i \(-0.294122\pi\)
0.602624 + 0.798025i \(0.294122\pi\)
\(200\) −13.5239 −0.956288
\(201\) 0.0125252 0.000883460 0
\(202\) 7.73231 0.544044
\(203\) 1.93227 0.135619
\(204\) −1.31304 −0.0919311
\(205\) 0.174631 0.0121967
\(206\) 18.1000 1.26108
\(207\) −3.07639 −0.213824
\(208\) −11.3384 −0.786176
\(209\) 31.2053 2.15851
\(210\) −0.923650 −0.0637379
\(211\) 11.2161 0.772146 0.386073 0.922468i \(-0.373831\pi\)
0.386073 + 0.922468i \(0.373831\pi\)
\(212\) 1.00030 0.0687011
\(213\) −1.56317 −0.107106
\(214\) 25.8751 1.76878
\(215\) 6.21476 0.423843
\(216\) 3.01439 0.205103
\(217\) 10.3463 0.702350
\(218\) 7.28007 0.493068
\(219\) −15.4518 −1.04413
\(220\) −1.31684 −0.0887813
\(221\) 13.7020 0.921696
\(222\) −3.99682 −0.268249
\(223\) −28.2613 −1.89252 −0.946258 0.323413i \(-0.895170\pi\)
−0.946258 + 0.323413i \(0.895170\pi\)
\(224\) −1.89415 −0.126558
\(225\) −4.48647 −0.299098
\(226\) −3.50239 −0.232976
\(227\) 14.8970 0.988750 0.494375 0.869249i \(-0.335397\pi\)
0.494375 + 0.869249i \(0.335397\pi\)
\(228\) −1.94824 −0.129025
\(229\) −19.6728 −1.30002 −0.650009 0.759926i \(-0.725235\pi\)
−0.650009 + 0.759926i \(0.725235\pi\)
\(230\) 2.84151 0.187364
\(231\) 5.42521 0.356953
\(232\) 5.82462 0.382405
\(233\) −5.32816 −0.349059 −0.174530 0.984652i \(-0.555840\pi\)
−0.174530 + 0.984652i \(0.555840\pi\)
\(234\) −4.55575 −0.297819
\(235\) 3.83258 0.250010
\(236\) 2.17913 0.141849
\(237\) −5.55105 −0.360580
\(238\) −4.99654 −0.323877
\(239\) −3.27976 −0.212150 −0.106075 0.994358i \(-0.533828\pi\)
−0.106075 + 0.994358i \(0.533828\pi\)
\(240\) −2.29879 −0.148386
\(241\) 11.7854 0.759165 0.379582 0.925158i \(-0.376068\pi\)
0.379582 + 0.925158i \(0.376068\pi\)
\(242\) −23.7584 −1.52725
\(243\) 1.00000 0.0641500
\(244\) 3.31396 0.212154
\(245\) 0.716613 0.0457827
\(246\) −0.314093 −0.0200259
\(247\) 20.3305 1.29360
\(248\) 31.1877 1.98042
\(249\) 12.6372 0.800853
\(250\) 8.76217 0.554168
\(251\) −14.6941 −0.927485 −0.463743 0.885970i \(-0.653494\pi\)
−0.463743 + 0.885970i \(0.653494\pi\)
\(252\) −0.338712 −0.0213369
\(253\) −16.6901 −1.04930
\(254\) −0.0437075 −0.00274245
\(255\) 2.77800 0.173965
\(256\) −7.88278 −0.492674
\(257\) 12.1910 0.760455 0.380228 0.924893i \(-0.375846\pi\)
0.380228 + 0.924893i \(0.375846\pi\)
\(258\) −11.1779 −0.695908
\(259\) 3.10093 0.192682
\(260\) −0.857932 −0.0532067
\(261\) 1.93227 0.119605
\(262\) −13.4022 −0.827991
\(263\) 2.82742 0.174346 0.0871730 0.996193i \(-0.472217\pi\)
0.0871730 + 0.996193i \(0.472217\pi\)
\(264\) 16.3537 1.00650
\(265\) −2.11634 −0.130006
\(266\) −7.41367 −0.454561
\(267\) −10.2353 −0.626393
\(268\) −0.00424244 −0.000259148 0
\(269\) −19.8290 −1.20900 −0.604498 0.796607i \(-0.706626\pi\)
−0.604498 + 0.796607i \(0.706626\pi\)
\(270\) −0.923650 −0.0562115
\(271\) 22.0669 1.34047 0.670233 0.742151i \(-0.266194\pi\)
0.670233 + 0.742151i \(0.266194\pi\)
\(272\) −12.4354 −0.754008
\(273\) 3.53458 0.213922
\(274\) −5.06122 −0.305759
\(275\) −24.3400 −1.46776
\(276\) 1.04201 0.0627218
\(277\) 6.98114 0.419456 0.209728 0.977760i \(-0.432742\pi\)
0.209728 + 0.977760i \(0.432742\pi\)
\(278\) 19.1965 1.15133
\(279\) 10.3463 0.619415
\(280\) 2.16015 0.129094
\(281\) 26.5918 1.58633 0.793166 0.609006i \(-0.208431\pi\)
0.793166 + 0.609006i \(0.208431\pi\)
\(282\) −6.89333 −0.410492
\(283\) 15.2797 0.908287 0.454143 0.890929i \(-0.349945\pi\)
0.454143 + 0.890929i \(0.349945\pi\)
\(284\) 0.529464 0.0314179
\(285\) 4.12189 0.244159
\(286\) −24.7159 −1.46148
\(287\) 0.243689 0.0143845
\(288\) −1.89415 −0.111614
\(289\) −1.97228 −0.116016
\(290\) −1.78474 −0.104804
\(291\) −18.5407 −1.08687
\(292\) 5.23370 0.306279
\(293\) 25.8528 1.51034 0.755168 0.655531i \(-0.227555\pi\)
0.755168 + 0.655531i \(0.227555\pi\)
\(294\) −1.28891 −0.0751707
\(295\) −4.61039 −0.268427
\(296\) 9.34741 0.543307
\(297\) 5.42521 0.314803
\(298\) −25.7452 −1.49138
\(299\) −10.8737 −0.628845
\(300\) 1.51962 0.0877353
\(301\) 8.67240 0.499869
\(302\) −10.0539 −0.578538
\(303\) −5.99911 −0.344640
\(304\) −18.4512 −1.05825
\(305\) −7.01134 −0.401468
\(306\) −4.99654 −0.285633
\(307\) −23.8691 −1.36228 −0.681140 0.732154i \(-0.738515\pi\)
−0.681140 + 0.732154i \(0.738515\pi\)
\(308\) −1.83759 −0.104706
\(309\) −14.0429 −0.798870
\(310\) −9.55632 −0.542763
\(311\) −13.5790 −0.769996 −0.384998 0.922917i \(-0.625798\pi\)
−0.384998 + 0.922917i \(0.625798\pi\)
\(312\) 10.6546 0.603197
\(313\) 16.4100 0.927546 0.463773 0.885954i \(-0.346495\pi\)
0.463773 + 0.885954i \(0.346495\pi\)
\(314\) 16.9444 0.956228
\(315\) 0.716613 0.0403766
\(316\) 1.88021 0.105770
\(317\) 6.08345 0.341681 0.170840 0.985299i \(-0.445352\pi\)
0.170840 + 0.985299i \(0.445352\pi\)
\(318\) 3.80648 0.213457
\(319\) 10.4830 0.586934
\(320\) 6.34711 0.354814
\(321\) −20.0752 −1.12049
\(322\) 3.96519 0.220972
\(323\) 22.2976 1.24067
\(324\) −0.338712 −0.0188173
\(325\) −15.8578 −0.879630
\(326\) 19.9795 1.10656
\(327\) −5.64824 −0.312348
\(328\) 0.734574 0.0405600
\(329\) 5.34819 0.294855
\(330\) −5.01100 −0.275846
\(331\) −22.8441 −1.25563 −0.627814 0.778364i \(-0.716050\pi\)
−0.627814 + 0.778364i \(0.716050\pi\)
\(332\) −4.28039 −0.234917
\(333\) 3.10093 0.169930
\(334\) −7.84245 −0.429120
\(335\) 0.00897573 0.000490396 0
\(336\) −3.20785 −0.175003
\(337\) −1.12003 −0.0610119 −0.0305059 0.999535i \(-0.509712\pi\)
−0.0305059 + 0.999535i \(0.509712\pi\)
\(338\) 0.653187 0.0355287
\(339\) 2.71733 0.147585
\(340\) −0.940941 −0.0510297
\(341\) 56.1307 3.03965
\(342\) −7.41367 −0.400886
\(343\) 1.00000 0.0539949
\(344\) 26.1420 1.40948
\(345\) −2.20459 −0.118691
\(346\) 12.7856 0.687360
\(347\) −4.30026 −0.230850 −0.115425 0.993316i \(-0.536823\pi\)
−0.115425 + 0.993316i \(0.536823\pi\)
\(348\) −0.654484 −0.0350840
\(349\) 17.0512 0.912728 0.456364 0.889793i \(-0.349151\pi\)
0.456364 + 0.889793i \(0.349151\pi\)
\(350\) 5.78265 0.309096
\(351\) 3.53458 0.188662
\(352\) −10.2762 −0.547721
\(353\) 0.0960293 0.00511112 0.00255556 0.999997i \(-0.499187\pi\)
0.00255556 + 0.999997i \(0.499187\pi\)
\(354\) 8.29230 0.440731
\(355\) −1.12019 −0.0594533
\(356\) 3.46683 0.183742
\(357\) 3.87656 0.205169
\(358\) −6.29004 −0.332439
\(359\) −30.5766 −1.61377 −0.806885 0.590709i \(-0.798848\pi\)
−0.806885 + 0.590709i \(0.798848\pi\)
\(360\) 2.16015 0.113850
\(361\) 14.0843 0.741279
\(362\) 4.42604 0.232627
\(363\) 18.4330 0.967479
\(364\) −1.19720 −0.0627505
\(365\) −11.0729 −0.579584
\(366\) 12.6107 0.659171
\(367\) 32.4082 1.69169 0.845847 0.533425i \(-0.179095\pi\)
0.845847 + 0.533425i \(0.179095\pi\)
\(368\) 9.86861 0.514437
\(369\) 0.243689 0.0126859
\(370\) −2.86417 −0.148901
\(371\) −2.95325 −0.153325
\(372\) −3.50441 −0.181695
\(373\) −15.3890 −0.796811 −0.398406 0.917209i \(-0.630436\pi\)
−0.398406 + 0.917209i \(0.630436\pi\)
\(374\) −27.1073 −1.40168
\(375\) −6.79813 −0.351054
\(376\) 16.1215 0.831403
\(377\) 6.82976 0.351750
\(378\) −1.28891 −0.0662944
\(379\) 8.37059 0.429968 0.214984 0.976618i \(-0.431030\pi\)
0.214984 + 0.976618i \(0.431030\pi\)
\(380\) −1.39613 −0.0716201
\(381\) 0.0339105 0.00173729
\(382\) −1.28891 −0.0659463
\(383\) −17.0519 −0.871314 −0.435657 0.900113i \(-0.643484\pi\)
−0.435657 + 0.900113i \(0.643484\pi\)
\(384\) −7.62768 −0.389249
\(385\) 3.88778 0.198140
\(386\) 12.3121 0.626667
\(387\) 8.67240 0.440843
\(388\) 6.27995 0.318816
\(389\) 20.4796 1.03835 0.519177 0.854667i \(-0.326238\pi\)
0.519177 + 0.854667i \(0.326238\pi\)
\(390\) −3.26471 −0.165315
\(391\) −11.9258 −0.603115
\(392\) 3.01439 0.152250
\(393\) 10.3981 0.524515
\(394\) −14.4675 −0.728864
\(395\) −3.97796 −0.200153
\(396\) −1.83759 −0.0923422
\(397\) −18.3972 −0.923331 −0.461665 0.887054i \(-0.652748\pi\)
−0.461665 + 0.887054i \(0.652748\pi\)
\(398\) −21.9142 −1.09846
\(399\) 5.75190 0.287955
\(400\) 14.3919 0.719595
\(401\) −25.6981 −1.28330 −0.641650 0.766998i \(-0.721750\pi\)
−0.641650 + 0.766998i \(0.721750\pi\)
\(402\) −0.0161439 −0.000805182 0
\(403\) 36.5696 1.82166
\(404\) 2.03197 0.101094
\(405\) 0.716613 0.0356088
\(406\) −2.49052 −0.123603
\(407\) 16.8232 0.833896
\(408\) 11.6855 0.578516
\(409\) −0.688587 −0.0340485 −0.0170242 0.999855i \(-0.505419\pi\)
−0.0170242 + 0.999855i \(0.505419\pi\)
\(410\) −0.225083 −0.0111161
\(411\) 3.92674 0.193692
\(412\) 4.75649 0.234335
\(413\) −6.43358 −0.316576
\(414\) 3.96519 0.194879
\(415\) 9.05602 0.444542
\(416\) −6.69501 −0.328250
\(417\) −14.8936 −0.729343
\(418\) −40.2208 −1.96726
\(419\) −3.66524 −0.179059 −0.0895293 0.995984i \(-0.528536\pi\)
−0.0895293 + 0.995984i \(0.528536\pi\)
\(420\) −0.242726 −0.0118438
\(421\) −13.6438 −0.664959 −0.332479 0.943111i \(-0.607885\pi\)
−0.332479 + 0.943111i \(0.607885\pi\)
\(422\) −14.4565 −0.703731
\(423\) 5.34819 0.260038
\(424\) −8.90226 −0.432332
\(425\) −17.3921 −0.843639
\(426\) 2.01478 0.0976165
\(427\) −9.78399 −0.473481
\(428\) 6.79971 0.328676
\(429\) 19.1758 0.925818
\(430\) −8.01026 −0.386289
\(431\) −4.25103 −0.204765 −0.102382 0.994745i \(-0.532647\pi\)
−0.102382 + 0.994745i \(0.532647\pi\)
\(432\) −3.20785 −0.154338
\(433\) −36.6191 −1.75980 −0.879902 0.475156i \(-0.842392\pi\)
−0.879902 + 0.475156i \(0.842392\pi\)
\(434\) −13.3354 −0.640119
\(435\) 1.38469 0.0663909
\(436\) 1.91313 0.0916221
\(437\) −17.6951 −0.846471
\(438\) 19.9159 0.951619
\(439\) 7.26399 0.346691 0.173346 0.984861i \(-0.444542\pi\)
0.173346 + 0.984861i \(0.444542\pi\)
\(440\) 11.7193 0.558695
\(441\) 1.00000 0.0476190
\(442\) −17.6606 −0.840031
\(443\) 32.9289 1.56450 0.782251 0.622964i \(-0.214072\pi\)
0.782251 + 0.622964i \(0.214072\pi\)
\(444\) −1.05032 −0.0498461
\(445\) −7.33478 −0.347702
\(446\) 36.4262 1.72483
\(447\) 19.9744 0.944757
\(448\) 8.85709 0.418458
\(449\) −9.19664 −0.434016 −0.217008 0.976170i \(-0.569630\pi\)
−0.217008 + 0.976170i \(0.569630\pi\)
\(450\) 5.78265 0.272597
\(451\) 1.32207 0.0622536
\(452\) −0.920392 −0.0432916
\(453\) 7.80032 0.366491
\(454\) −19.2009 −0.901143
\(455\) 2.53292 0.118745
\(456\) 17.3384 0.811947
\(457\) −13.9780 −0.653864 −0.326932 0.945048i \(-0.606015\pi\)
−0.326932 + 0.945048i \(0.606015\pi\)
\(458\) 25.3565 1.18483
\(459\) 3.87656 0.180942
\(460\) 0.746720 0.0348160
\(461\) 38.4887 1.79260 0.896299 0.443450i \(-0.146246\pi\)
0.896299 + 0.443450i \(0.146246\pi\)
\(462\) −6.99261 −0.325326
\(463\) 19.0064 0.883303 0.441652 0.897187i \(-0.354393\pi\)
0.441652 + 0.897187i \(0.354393\pi\)
\(464\) −6.19843 −0.287755
\(465\) 7.41427 0.343829
\(466\) 6.86751 0.318131
\(467\) −25.2053 −1.16636 −0.583182 0.812342i \(-0.698193\pi\)
−0.583182 + 0.812342i \(0.698193\pi\)
\(468\) −1.19720 −0.0553408
\(469\) 0.0125252 0.000578360 0
\(470\) −4.93985 −0.227858
\(471\) −13.1463 −0.605750
\(472\) −19.3933 −0.892650
\(473\) 47.0496 2.16334
\(474\) 7.15481 0.328631
\(475\) −25.8057 −1.18405
\(476\) −1.31304 −0.0601830
\(477\) −2.95325 −0.135220
\(478\) 4.22731 0.193353
\(479\) −5.20589 −0.237863 −0.118932 0.992902i \(-0.537947\pi\)
−0.118932 + 0.992902i \(0.537947\pi\)
\(480\) −1.35737 −0.0619553
\(481\) 10.9605 0.499754
\(482\) −15.1903 −0.691900
\(483\) −3.07639 −0.139981
\(484\) −6.24347 −0.283794
\(485\) −13.2865 −0.603308
\(486\) −1.28891 −0.0584661
\(487\) −11.7313 −0.531596 −0.265798 0.964029i \(-0.585635\pi\)
−0.265798 + 0.964029i \(0.585635\pi\)
\(488\) −29.4928 −1.33507
\(489\) −15.5010 −0.700982
\(490\) −0.923650 −0.0417262
\(491\) 39.1571 1.76713 0.883567 0.468304i \(-0.155135\pi\)
0.883567 + 0.468304i \(0.155135\pi\)
\(492\) −0.0825405 −0.00372121
\(493\) 7.49057 0.337358
\(494\) −26.2042 −1.17898
\(495\) 3.88778 0.174743
\(496\) −33.1893 −1.49024
\(497\) −1.56317 −0.0701176
\(498\) −16.2883 −0.729895
\(499\) −34.4988 −1.54438 −0.772188 0.635394i \(-0.780838\pi\)
−0.772188 + 0.635394i \(0.780838\pi\)
\(500\) 2.30261 0.102976
\(501\) 6.08456 0.271838
\(502\) 18.9394 0.845307
\(503\) 28.0256 1.24960 0.624800 0.780785i \(-0.285181\pi\)
0.624800 + 0.780785i \(0.285181\pi\)
\(504\) 3.01439 0.134272
\(505\) −4.29904 −0.191305
\(506\) 21.5120 0.956326
\(507\) −0.506775 −0.0225067
\(508\) −0.0114859 −0.000509604 0
\(509\) −37.8404 −1.67725 −0.838623 0.544712i \(-0.816639\pi\)
−0.838623 + 0.544712i \(0.816639\pi\)
\(510\) −3.58058 −0.158551
\(511\) −15.4518 −0.683545
\(512\) 25.4156 1.12322
\(513\) 5.75190 0.253952
\(514\) −15.7131 −0.693076
\(515\) −10.0633 −0.443442
\(516\) −2.93745 −0.129314
\(517\) 29.0151 1.27608
\(518\) −3.99682 −0.175610
\(519\) −9.91974 −0.435428
\(520\) 7.63522 0.334826
\(521\) −22.6377 −0.991777 −0.495889 0.868386i \(-0.665158\pi\)
−0.495889 + 0.868386i \(0.665158\pi\)
\(522\) −2.49052 −0.109007
\(523\) 17.9243 0.783777 0.391889 0.920013i \(-0.371822\pi\)
0.391889 + 0.920013i \(0.371822\pi\)
\(524\) −3.52196 −0.153858
\(525\) −4.48647 −0.195805
\(526\) −3.64428 −0.158898
\(527\) 40.1079 1.74713
\(528\) −17.4033 −0.757380
\(529\) −13.5358 −0.588513
\(530\) 2.72777 0.118487
\(531\) −6.43358 −0.279194
\(532\) −1.94824 −0.0844668
\(533\) 0.861338 0.0373087
\(534\) 13.1924 0.570892
\(535\) −14.3861 −0.621967
\(536\) 0.0377558 0.00163080
\(537\) 4.88013 0.210593
\(538\) 25.5578 1.10187
\(539\) 5.42521 0.233681
\(540\) −0.242726 −0.0104453
\(541\) −19.7848 −0.850614 −0.425307 0.905049i \(-0.639834\pi\)
−0.425307 + 0.905049i \(0.639834\pi\)
\(542\) −28.4422 −1.22170
\(543\) −3.43394 −0.147365
\(544\) −7.34278 −0.314819
\(545\) −4.04760 −0.173380
\(546\) −4.55575 −0.194968
\(547\) −39.3259 −1.68145 −0.840726 0.541460i \(-0.817872\pi\)
−0.840726 + 0.541460i \(0.817872\pi\)
\(548\) −1.33004 −0.0568163
\(549\) −9.78399 −0.417571
\(550\) 31.3721 1.33771
\(551\) 11.1142 0.473482
\(552\) −9.27345 −0.394704
\(553\) −5.55105 −0.236055
\(554\) −8.99806 −0.382291
\(555\) 2.22217 0.0943258
\(556\) 5.04464 0.213941
\(557\) −1.55498 −0.0658864 −0.0329432 0.999457i \(-0.510488\pi\)
−0.0329432 + 0.999457i \(0.510488\pi\)
\(558\) −13.3354 −0.564532
\(559\) 30.6532 1.29649
\(560\) −2.29879 −0.0971415
\(561\) 21.0312 0.887937
\(562\) −34.2744 −1.44578
\(563\) 11.9985 0.505677 0.252838 0.967509i \(-0.418636\pi\)
0.252838 + 0.967509i \(0.418636\pi\)
\(564\) −1.81150 −0.0762777
\(565\) 1.94727 0.0819224
\(566\) −19.6942 −0.827809
\(567\) 1.00000 0.0419961
\(568\) −4.71199 −0.197711
\(569\) −10.1682 −0.426272 −0.213136 0.977023i \(-0.568368\pi\)
−0.213136 + 0.977023i \(0.568368\pi\)
\(570\) −5.31274 −0.222526
\(571\) 10.6798 0.446934 0.223467 0.974711i \(-0.428262\pi\)
0.223467 + 0.974711i \(0.428262\pi\)
\(572\) −6.49509 −0.271573
\(573\) 1.00000 0.0417756
\(574\) −0.314093 −0.0131100
\(575\) 13.8021 0.575589
\(576\) 8.85709 0.369045
\(577\) 46.7618 1.94672 0.973359 0.229286i \(-0.0736390\pi\)
0.973359 + 0.229286i \(0.0736390\pi\)
\(578\) 2.54209 0.105737
\(579\) −9.55231 −0.396980
\(580\) −0.469012 −0.0194747
\(581\) 12.6372 0.524281
\(582\) 23.8972 0.990572
\(583\) −16.0220 −0.663565
\(584\) −46.5776 −1.92739
\(585\) 2.53292 0.104724
\(586\) −33.3219 −1.37652
\(587\) −13.8301 −0.570828 −0.285414 0.958404i \(-0.592131\pi\)
−0.285414 + 0.958404i \(0.592131\pi\)
\(588\) −0.338712 −0.0139683
\(589\) 59.5106 2.45209
\(590\) 5.94238 0.244644
\(591\) 11.2246 0.461720
\(592\) −9.94732 −0.408832
\(593\) 24.6222 1.01111 0.505556 0.862794i \(-0.331287\pi\)
0.505556 + 0.862794i \(0.331287\pi\)
\(594\) −6.99261 −0.286910
\(595\) 2.77800 0.113887
\(596\) −6.76558 −0.277129
\(597\) 17.0021 0.695851
\(598\) 14.0153 0.573127
\(599\) 43.7878 1.78912 0.894560 0.446948i \(-0.147489\pi\)
0.894560 + 0.446948i \(0.147489\pi\)
\(600\) −13.5239 −0.552113
\(601\) 3.54445 0.144581 0.0722906 0.997384i \(-0.476969\pi\)
0.0722906 + 0.997384i \(0.476969\pi\)
\(602\) −11.1779 −0.455579
\(603\) 0.0125252 0.000510066 0
\(604\) −2.64206 −0.107504
\(605\) 13.2093 0.537034
\(606\) 7.73231 0.314104
\(607\) 26.4064 1.07180 0.535901 0.844281i \(-0.319972\pi\)
0.535901 + 0.844281i \(0.319972\pi\)
\(608\) −10.8949 −0.441848
\(609\) 1.93227 0.0782996
\(610\) 9.03698 0.365897
\(611\) 18.9036 0.764756
\(612\) −1.31304 −0.0530764
\(613\) 21.7769 0.879559 0.439780 0.898106i \(-0.355057\pi\)
0.439780 + 0.898106i \(0.355057\pi\)
\(614\) 30.7651 1.24158
\(615\) 0.174631 0.00704180
\(616\) 16.3537 0.658910
\(617\) 5.59619 0.225294 0.112647 0.993635i \(-0.464067\pi\)
0.112647 + 0.993635i \(0.464067\pi\)
\(618\) 18.1000 0.728088
\(619\) −31.5824 −1.26941 −0.634703 0.772756i \(-0.718878\pi\)
−0.634703 + 0.772756i \(0.718878\pi\)
\(620\) −2.51130 −0.100856
\(621\) −3.07639 −0.123451
\(622\) 17.5021 0.701772
\(623\) −10.2353 −0.410070
\(624\) −11.3384 −0.453899
\(625\) 17.5607 0.702428
\(626\) −21.1510 −0.845363
\(627\) 31.2053 1.24622
\(628\) 4.45281 0.177687
\(629\) 12.0209 0.479306
\(630\) −0.923650 −0.0367991
\(631\) 33.1442 1.31945 0.659724 0.751508i \(-0.270673\pi\)
0.659724 + 0.751508i \(0.270673\pi\)
\(632\) −16.7330 −0.665604
\(633\) 11.2161 0.445799
\(634\) −7.84102 −0.311407
\(635\) 0.0243007 0.000964344 0
\(636\) 1.00030 0.0396646
\(637\) 3.53458 0.140045
\(638\) −13.5116 −0.534930
\(639\) −1.56317 −0.0618379
\(640\) −5.46610 −0.216067
\(641\) 7.28068 0.287569 0.143785 0.989609i \(-0.454073\pi\)
0.143785 + 0.989609i \(0.454073\pi\)
\(642\) 25.8751 1.02121
\(643\) −20.9999 −0.828156 −0.414078 0.910241i \(-0.635896\pi\)
−0.414078 + 0.910241i \(0.635896\pi\)
\(644\) 1.04201 0.0410610
\(645\) 6.21476 0.244706
\(646\) −28.7396 −1.13074
\(647\) −6.15247 −0.241879 −0.120939 0.992660i \(-0.538591\pi\)
−0.120939 + 0.992660i \(0.538591\pi\)
\(648\) 3.01439 0.118416
\(649\) −34.9036 −1.37008
\(650\) 20.4392 0.801692
\(651\) 10.3463 0.405502
\(652\) 5.25039 0.205621
\(653\) 0.236684 0.00926217 0.00463109 0.999989i \(-0.498526\pi\)
0.00463109 + 0.999989i \(0.498526\pi\)
\(654\) 7.28007 0.284673
\(655\) 7.45142 0.291151
\(656\) −0.781718 −0.0305210
\(657\) −15.4518 −0.602830
\(658\) −6.89333 −0.268730
\(659\) 8.67219 0.337821 0.168910 0.985631i \(-0.445975\pi\)
0.168910 + 0.985631i \(0.445975\pi\)
\(660\) −1.31684 −0.0512579
\(661\) 27.7143 1.07796 0.538980 0.842319i \(-0.318810\pi\)
0.538980 + 0.842319i \(0.318810\pi\)
\(662\) 29.4440 1.14437
\(663\) 13.7020 0.532141
\(664\) 38.0936 1.47832
\(665\) 4.12189 0.159840
\(666\) −3.99682 −0.154874
\(667\) −5.94443 −0.230169
\(668\) −2.06092 −0.0797393
\(669\) −28.2613 −1.09264
\(670\) −0.0115689 −0.000446946 0
\(671\) −53.0803 −2.04914
\(672\) −1.89415 −0.0730684
\(673\) −6.39286 −0.246427 −0.123213 0.992380i \(-0.539320\pi\)
−0.123213 + 0.992380i \(0.539320\pi\)
\(674\) 1.44362 0.0556060
\(675\) −4.48647 −0.172684
\(676\) 0.171651 0.00660196
\(677\) 33.3563 1.28199 0.640994 0.767546i \(-0.278522\pi\)
0.640994 + 0.767546i \(0.278522\pi\)
\(678\) −3.50239 −0.134509
\(679\) −18.5407 −0.711525
\(680\) 8.37396 0.321127
\(681\) 14.8970 0.570855
\(682\) −72.3474 −2.77032
\(683\) 26.5556 1.01612 0.508060 0.861322i \(-0.330363\pi\)
0.508060 + 0.861322i \(0.330363\pi\)
\(684\) −1.94824 −0.0744927
\(685\) 2.81396 0.107516
\(686\) −1.28891 −0.0492108
\(687\) −19.6728 −0.750566
\(688\) −27.8197 −1.06062
\(689\) −10.4385 −0.397675
\(690\) 2.84151 0.108174
\(691\) −19.3607 −0.736515 −0.368257 0.929724i \(-0.620045\pi\)
−0.368257 + 0.929724i \(0.620045\pi\)
\(692\) 3.35994 0.127726
\(693\) 5.42521 0.206087
\(694\) 5.54265 0.210396
\(695\) −10.6729 −0.404848
\(696\) 5.82462 0.220781
\(697\) 0.944676 0.0357821
\(698\) −21.9774 −0.831857
\(699\) −5.32816 −0.201529
\(700\) 1.51962 0.0574363
\(701\) −29.2639 −1.10528 −0.552642 0.833419i \(-0.686380\pi\)
−0.552642 + 0.833419i \(0.686380\pi\)
\(702\) −4.55575 −0.171946
\(703\) 17.8362 0.672706
\(704\) 48.0516 1.81101
\(705\) 3.83258 0.144343
\(706\) −0.123773 −0.00465826
\(707\) −5.99911 −0.225620
\(708\) 2.17913 0.0818968
\(709\) −17.6673 −0.663511 −0.331755 0.943365i \(-0.607641\pi\)
−0.331755 + 0.943365i \(0.607641\pi\)
\(710\) 1.44382 0.0541856
\(711\) −5.55105 −0.208181
\(712\) −30.8533 −1.15628
\(713\) −31.8292 −1.19201
\(714\) −4.99654 −0.186991
\(715\) 13.7417 0.513909
\(716\) −1.65296 −0.0617739
\(717\) −3.27976 −0.122485
\(718\) 39.4104 1.47078
\(719\) 10.3621 0.386441 0.193220 0.981155i \(-0.438107\pi\)
0.193220 + 0.981155i \(0.438107\pi\)
\(720\) −2.29879 −0.0856708
\(721\) −14.0429 −0.522983
\(722\) −18.1534 −0.675599
\(723\) 11.7854 0.438304
\(724\) 1.16312 0.0432269
\(725\) −8.66907 −0.321961
\(726\) −23.7584 −0.881757
\(727\) −4.85081 −0.179907 −0.0899534 0.995946i \(-0.528672\pi\)
−0.0899534 + 0.995946i \(0.528672\pi\)
\(728\) 10.6546 0.394885
\(729\) 1.00000 0.0370370
\(730\) 14.2720 0.528231
\(731\) 33.6191 1.24345
\(732\) 3.31396 0.122487
\(733\) −2.36363 −0.0873026 −0.0436513 0.999047i \(-0.513899\pi\)
−0.0436513 + 0.999047i \(0.513899\pi\)
\(734\) −41.7713 −1.54181
\(735\) 0.716613 0.0264327
\(736\) 5.82715 0.214792
\(737\) 0.0679519 0.00250304
\(738\) −0.314093 −0.0115619
\(739\) 5.61438 0.206528 0.103264 0.994654i \(-0.467071\pi\)
0.103264 + 0.994654i \(0.467071\pi\)
\(740\) −0.752675 −0.0276689
\(741\) 20.3305 0.746860
\(742\) 3.80648 0.139740
\(743\) −2.27545 −0.0834782 −0.0417391 0.999129i \(-0.513290\pi\)
−0.0417391 + 0.999129i \(0.513290\pi\)
\(744\) 31.1877 1.14339
\(745\) 14.3139 0.524422
\(746\) 19.8350 0.726211
\(747\) 12.6372 0.462373
\(748\) −7.12352 −0.260462
\(749\) −20.0752 −0.733531
\(750\) 8.76217 0.319949
\(751\) −4.50828 −0.164509 −0.0822546 0.996611i \(-0.526212\pi\)
−0.0822546 + 0.996611i \(0.526212\pi\)
\(752\) −17.1562 −0.625621
\(753\) −14.6941 −0.535484
\(754\) −8.80294 −0.320584
\(755\) 5.58982 0.203434
\(756\) −0.338712 −0.0123188
\(757\) 38.5415 1.40081 0.700407 0.713744i \(-0.253002\pi\)
0.700407 + 0.713744i \(0.253002\pi\)
\(758\) −10.7889 −0.391872
\(759\) −16.6901 −0.605812
\(760\) 12.4250 0.450701
\(761\) 34.5119 1.25106 0.625528 0.780202i \(-0.284884\pi\)
0.625528 + 0.780202i \(0.284884\pi\)
\(762\) −0.0437075 −0.00158336
\(763\) −5.64824 −0.204480
\(764\) −0.338712 −0.0122542
\(765\) 2.77800 0.100439
\(766\) 21.9784 0.794112
\(767\) −22.7400 −0.821093
\(768\) −7.88278 −0.284445
\(769\) −35.7693 −1.28988 −0.644938 0.764235i \(-0.723117\pi\)
−0.644938 + 0.764235i \(0.723117\pi\)
\(770\) −5.01100 −0.180584
\(771\) 12.1910 0.439049
\(772\) 3.23548 0.116448
\(773\) −8.79838 −0.316456 −0.158228 0.987403i \(-0.550578\pi\)
−0.158228 + 0.987403i \(0.550578\pi\)
\(774\) −11.1779 −0.401783
\(775\) −46.4181 −1.66739
\(776\) −55.8888 −2.00629
\(777\) 3.10093 0.111245
\(778\) −26.3963 −0.946353
\(779\) 1.40167 0.0502202
\(780\) −0.857932 −0.0307189
\(781\) −8.48052 −0.303457
\(782\) 15.3713 0.549677
\(783\) 1.93227 0.0690537
\(784\) −3.20785 −0.114566
\(785\) −9.42082 −0.336243
\(786\) −13.4022 −0.478041
\(787\) −34.3816 −1.22557 −0.612785 0.790250i \(-0.709951\pi\)
−0.612785 + 0.790250i \(0.709951\pi\)
\(788\) −3.80192 −0.135438
\(789\) 2.82742 0.100659
\(790\) 5.12723 0.182419
\(791\) 2.71733 0.0966171
\(792\) 16.3537 0.581104
\(793\) −34.5823 −1.22805
\(794\) 23.7124 0.841521
\(795\) −2.11634 −0.0750589
\(796\) −5.75883 −0.204116
\(797\) −17.5399 −0.621294 −0.310647 0.950525i \(-0.600546\pi\)
−0.310647 + 0.950525i \(0.600546\pi\)
\(798\) −7.41367 −0.262441
\(799\) 20.7326 0.733465
\(800\) 8.49803 0.300451
\(801\) −10.2353 −0.361648
\(802\) 33.1225 1.16960
\(803\) −83.8291 −2.95826
\(804\) −0.00424244 −0.000149619 0
\(805\) −2.20459 −0.0777014
\(806\) −47.1350 −1.66026
\(807\) −19.8290 −0.698014
\(808\) −18.0837 −0.636181
\(809\) −43.3301 −1.52341 −0.761703 0.647926i \(-0.775637\pi\)
−0.761703 + 0.647926i \(0.775637\pi\)
\(810\) −0.923650 −0.0324537
\(811\) −14.1553 −0.497060 −0.248530 0.968624i \(-0.579947\pi\)
−0.248530 + 0.968624i \(0.579947\pi\)
\(812\) −0.654484 −0.0229679
\(813\) 22.0669 0.773918
\(814\) −21.6836 −0.760010
\(815\) −11.1083 −0.389105
\(816\) −12.4354 −0.435327
\(817\) 49.8827 1.74518
\(818\) 0.887527 0.0310316
\(819\) 3.53458 0.123508
\(820\) −0.0591496 −0.00206559
\(821\) −31.7951 −1.10966 −0.554829 0.831965i \(-0.687216\pi\)
−0.554829 + 0.831965i \(0.687216\pi\)
\(822\) −5.06122 −0.176530
\(823\) 11.2600 0.392499 0.196250 0.980554i \(-0.437124\pi\)
0.196250 + 0.980554i \(0.437124\pi\)
\(824\) −42.3306 −1.47466
\(825\) −24.3400 −0.847411
\(826\) 8.29230 0.288526
\(827\) 4.18435 0.145504 0.0727521 0.997350i \(-0.476822\pi\)
0.0727521 + 0.997350i \(0.476822\pi\)
\(828\) 1.04201 0.0362124
\(829\) 20.3502 0.706791 0.353395 0.935474i \(-0.385027\pi\)
0.353395 + 0.935474i \(0.385027\pi\)
\(830\) −11.6724 −0.405154
\(831\) 6.98114 0.242173
\(832\) 31.3060 1.08534
\(833\) 3.87656 0.134315
\(834\) 19.1965 0.664720
\(835\) 4.36028 0.150894
\(836\) −10.5696 −0.365557
\(837\) 10.3463 0.357619
\(838\) 4.72416 0.163193
\(839\) 16.5287 0.570634 0.285317 0.958433i \(-0.407901\pi\)
0.285317 + 0.958433i \(0.407901\pi\)
\(840\) 2.16015 0.0745323
\(841\) −25.2663 −0.871253
\(842\) 17.5856 0.606041
\(843\) 26.5918 0.915869
\(844\) −3.79902 −0.130768
\(845\) −0.363162 −0.0124931
\(846\) −6.89333 −0.236997
\(847\) 18.4330 0.633364
\(848\) 9.47360 0.325325
\(849\) 15.2797 0.524400
\(850\) 22.4168 0.768889
\(851\) −9.53968 −0.327016
\(852\) 0.529464 0.0181391
\(853\) −20.1898 −0.691286 −0.345643 0.938366i \(-0.612339\pi\)
−0.345643 + 0.938366i \(0.612339\pi\)
\(854\) 12.6107 0.431529
\(855\) 4.12189 0.140966
\(856\) −60.5144 −2.06834
\(857\) 42.9661 1.46769 0.733847 0.679315i \(-0.237723\pi\)
0.733847 + 0.679315i \(0.237723\pi\)
\(858\) −24.7159 −0.843787
\(859\) −31.6244 −1.07901 −0.539505 0.841983i \(-0.681388\pi\)
−0.539505 + 0.841983i \(0.681388\pi\)
\(860\) −2.10501 −0.0717804
\(861\) 0.243689 0.00830490
\(862\) 5.47919 0.186622
\(863\) −22.8383 −0.777424 −0.388712 0.921359i \(-0.627080\pi\)
−0.388712 + 0.921359i \(0.627080\pi\)
\(864\) −1.89415 −0.0644403
\(865\) −7.10862 −0.241700
\(866\) 47.1987 1.60388
\(867\) −1.97228 −0.0669820
\(868\) −3.50441 −0.118947
\(869\) −30.1157 −1.02160
\(870\) −1.78474 −0.0605084
\(871\) 0.0442713 0.00150007
\(872\) −17.0260 −0.576572
\(873\) −18.5407 −0.627506
\(874\) 22.8074 0.771471
\(875\) −6.79813 −0.229819
\(876\) 5.23370 0.176830
\(877\) 6.92005 0.233673 0.116837 0.993151i \(-0.462725\pi\)
0.116837 + 0.993151i \(0.462725\pi\)
\(878\) −9.36262 −0.315973
\(879\) 25.8528 0.871993
\(880\) −12.4714 −0.420411
\(881\) −6.28431 −0.211724 −0.105862 0.994381i \(-0.533760\pi\)
−0.105862 + 0.994381i \(0.533760\pi\)
\(882\) −1.28891 −0.0433998
\(883\) −34.4540 −1.15947 −0.579735 0.814805i \(-0.696844\pi\)
−0.579735 + 0.814805i \(0.696844\pi\)
\(884\) −4.64103 −0.156095
\(885\) −4.61039 −0.154977
\(886\) −42.4424 −1.42588
\(887\) −21.0920 −0.708200 −0.354100 0.935208i \(-0.615213\pi\)
−0.354100 + 0.935208i \(0.615213\pi\)
\(888\) 9.34741 0.313678
\(889\) 0.0339105 0.00113732
\(890\) 9.45387 0.316894
\(891\) 5.42521 0.181752
\(892\) 9.57244 0.320509
\(893\) 30.7622 1.02942
\(894\) −25.7452 −0.861049
\(895\) 3.49716 0.116897
\(896\) −7.62768 −0.254823
\(897\) −10.8737 −0.363064
\(898\) 11.8536 0.395561
\(899\) 19.9918 0.666763
\(900\) 1.51962 0.0506540
\(901\) −11.4485 −0.381404
\(902\) −1.70402 −0.0567378
\(903\) 8.67240 0.288599
\(904\) 8.19108 0.272431
\(905\) −2.46081 −0.0818000
\(906\) −10.0539 −0.334019
\(907\) −53.5819 −1.77916 −0.889580 0.456780i \(-0.849003\pi\)
−0.889580 + 0.456780i \(0.849003\pi\)
\(908\) −5.04580 −0.167451
\(909\) −5.99911 −0.198978
\(910\) −3.26471 −0.108224
\(911\) 36.9670 1.22477 0.612386 0.790559i \(-0.290210\pi\)
0.612386 + 0.790559i \(0.290210\pi\)
\(912\) −18.4512 −0.610981
\(913\) 68.5598 2.26900
\(914\) 18.0164 0.595930
\(915\) −7.01134 −0.231788
\(916\) 6.66343 0.220166
\(917\) 10.3981 0.343376
\(918\) −4.99654 −0.164910
\(919\) 21.1835 0.698778 0.349389 0.936978i \(-0.386389\pi\)
0.349389 + 0.936978i \(0.386389\pi\)
\(920\) −6.64548 −0.219095
\(921\) −23.8691 −0.786512
\(922\) −49.6085 −1.63377
\(923\) −5.52513 −0.181862
\(924\) −1.83759 −0.0604522
\(925\) −13.9122 −0.457431
\(926\) −24.4976 −0.805040
\(927\) −14.0429 −0.461228
\(928\) −3.66001 −0.120146
\(929\) −31.1858 −1.02317 −0.511586 0.859232i \(-0.670942\pi\)
−0.511586 + 0.859232i \(0.670942\pi\)
\(930\) −9.55632 −0.313364
\(931\) 5.75190 0.188511
\(932\) 1.80471 0.0591153
\(933\) −13.5790 −0.444557
\(934\) 32.4874 1.06302
\(935\) 15.0712 0.492882
\(936\) 10.6546 0.348256
\(937\) 28.4722 0.930145 0.465072 0.885273i \(-0.346028\pi\)
0.465072 + 0.885273i \(0.346028\pi\)
\(938\) −0.0161439 −0.000527115 0
\(939\) 16.4100 0.535519
\(940\) −1.29814 −0.0423407
\(941\) −34.2874 −1.11774 −0.558868 0.829257i \(-0.688764\pi\)
−0.558868 + 0.829257i \(0.688764\pi\)
\(942\) 16.9444 0.552078
\(943\) −0.749684 −0.0244131
\(944\) 20.6380 0.671708
\(945\) 0.716613 0.0233114
\(946\) −60.6427 −1.97166
\(947\) −53.9405 −1.75283 −0.876415 0.481557i \(-0.840071\pi\)
−0.876415 + 0.481557i \(0.840071\pi\)
\(948\) 1.88021 0.0610664
\(949\) −54.6154 −1.77289
\(950\) 33.2612 1.07914
\(951\) 6.08345 0.197270
\(952\) 11.6855 0.378728
\(953\) 10.4268 0.337756 0.168878 0.985637i \(-0.445986\pi\)
0.168878 + 0.985637i \(0.445986\pi\)
\(954\) 3.80648 0.123239
\(955\) 0.716613 0.0231891
\(956\) 1.11089 0.0359289
\(957\) 10.4830 0.338867
\(958\) 6.70992 0.216788
\(959\) 3.92674 0.126801
\(960\) 6.34711 0.204852
\(961\) 76.0451 2.45307
\(962\) −14.1271 −0.455475
\(963\) −20.0752 −0.646913
\(964\) −3.99186 −0.128569
\(965\) −6.84531 −0.220358
\(966\) 3.96519 0.127578
\(967\) −24.5004 −0.787881 −0.393940 0.919136i \(-0.628888\pi\)
−0.393940 + 0.919136i \(0.628888\pi\)
\(968\) 55.5641 1.78590
\(969\) 22.2976 0.716301
\(970\) 17.1251 0.549853
\(971\) 25.9523 0.832848 0.416424 0.909170i \(-0.363283\pi\)
0.416424 + 0.909170i \(0.363283\pi\)
\(972\) −0.338712 −0.0108642
\(973\) −14.8936 −0.477467
\(974\) 15.1206 0.484495
\(975\) −15.8578 −0.507854
\(976\) 31.3856 1.00463
\(977\) 20.8782 0.667951 0.333976 0.942582i \(-0.391610\pi\)
0.333976 + 0.942582i \(0.391610\pi\)
\(978\) 19.9795 0.638872
\(979\) −55.5289 −1.77471
\(980\) −0.242726 −0.00775359
\(981\) −5.64824 −0.180334
\(982\) −50.4699 −1.61056
\(983\) 32.5924 1.03954 0.519768 0.854308i \(-0.326019\pi\)
0.519768 + 0.854308i \(0.326019\pi\)
\(984\) 0.734574 0.0234174
\(985\) 8.04372 0.256294
\(986\) −9.65466 −0.307467
\(987\) 5.34819 0.170235
\(988\) −6.88619 −0.219079
\(989\) −26.6797 −0.848366
\(990\) −5.01100 −0.159260
\(991\) −30.6977 −0.975144 −0.487572 0.873083i \(-0.662117\pi\)
−0.487572 + 0.873083i \(0.662117\pi\)
\(992\) −19.5974 −0.622217
\(993\) −22.8441 −0.724937
\(994\) 2.01478 0.0639050
\(995\) 12.1840 0.386257
\(996\) −4.28039 −0.135629
\(997\) −2.51877 −0.0797702 −0.0398851 0.999204i \(-0.512699\pi\)
−0.0398851 + 0.999204i \(0.512699\pi\)
\(998\) 44.4658 1.40754
\(999\) 3.10093 0.0981091
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 4011.2.a.k.1.7 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.k.1.7 27 1.1 even 1 trivial