Properties

Label 8026.2.a.b.1.16
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $1$
Dimension $81$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, 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("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(1\)
Dimension: \(81\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.34885 q^{3} +1.00000 q^{4} +3.93410 q^{5} +2.34885 q^{6} -0.279699 q^{7} -1.00000 q^{8} +2.51708 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.34885 q^{3} +1.00000 q^{4} +3.93410 q^{5} +2.34885 q^{6} -0.279699 q^{7} -1.00000 q^{8} +2.51708 q^{9} -3.93410 q^{10} +0.973217 q^{11} -2.34885 q^{12} -0.411920 q^{13} +0.279699 q^{14} -9.24060 q^{15} +1.00000 q^{16} -1.47119 q^{17} -2.51708 q^{18} -7.83609 q^{19} +3.93410 q^{20} +0.656970 q^{21} -0.973217 q^{22} -2.84547 q^{23} +2.34885 q^{24} +10.4771 q^{25} +0.411920 q^{26} +1.13430 q^{27} -0.279699 q^{28} +4.82149 q^{29} +9.24060 q^{30} -5.14273 q^{31} -1.00000 q^{32} -2.28594 q^{33} +1.47119 q^{34} -1.10036 q^{35} +2.51708 q^{36} +4.41180 q^{37} +7.83609 q^{38} +0.967537 q^{39} -3.93410 q^{40} -3.33780 q^{41} -0.656970 q^{42} +5.27289 q^{43} +0.973217 q^{44} +9.90246 q^{45} +2.84547 q^{46} -1.59196 q^{47} -2.34885 q^{48} -6.92177 q^{49} -10.4771 q^{50} +3.45560 q^{51} -0.411920 q^{52} +10.2898 q^{53} -1.13430 q^{54} +3.82873 q^{55} +0.279699 q^{56} +18.4058 q^{57} -4.82149 q^{58} +3.83766 q^{59} -9.24060 q^{60} +11.1929 q^{61} +5.14273 q^{62} -0.704025 q^{63} +1.00000 q^{64} -1.62053 q^{65} +2.28594 q^{66} -7.74705 q^{67} -1.47119 q^{68} +6.68358 q^{69} +1.10036 q^{70} -0.378148 q^{71} -2.51708 q^{72} -11.8009 q^{73} -4.41180 q^{74} -24.6092 q^{75} -7.83609 q^{76} -0.272208 q^{77} -0.967537 q^{78} +0.341349 q^{79} +3.93410 q^{80} -10.2155 q^{81} +3.33780 q^{82} -10.7671 q^{83} +0.656970 q^{84} -5.78781 q^{85} -5.27289 q^{86} -11.3249 q^{87} -0.973217 q^{88} -3.35948 q^{89} -9.90246 q^{90} +0.115214 q^{91} -2.84547 q^{92} +12.0795 q^{93} +1.59196 q^{94} -30.8280 q^{95} +2.34885 q^{96} -0.405935 q^{97} +6.92177 q^{98} +2.44967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.34885 −1.35611 −0.678054 0.735012i \(-0.737176\pi\)
−0.678054 + 0.735012i \(0.737176\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.93410 1.75938 0.879692 0.475545i \(-0.157749\pi\)
0.879692 + 0.475545i \(0.157749\pi\)
\(6\) 2.34885 0.958913
\(7\) −0.279699 −0.105716 −0.0528581 0.998602i \(-0.516833\pi\)
−0.0528581 + 0.998602i \(0.516833\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.51708 0.839028
\(10\) −3.93410 −1.24407
\(11\) 0.973217 0.293436 0.146718 0.989178i \(-0.453129\pi\)
0.146718 + 0.989178i \(0.453129\pi\)
\(12\) −2.34885 −0.678054
\(13\) −0.411920 −0.114246 −0.0571230 0.998367i \(-0.518193\pi\)
−0.0571230 + 0.998367i \(0.518193\pi\)
\(14\) 0.279699 0.0747527
\(15\) −9.24060 −2.38591
\(16\) 1.00000 0.250000
\(17\) −1.47119 −0.356816 −0.178408 0.983957i \(-0.557095\pi\)
−0.178408 + 0.983957i \(0.557095\pi\)
\(18\) −2.51708 −0.593282
\(19\) −7.83609 −1.79772 −0.898862 0.438233i \(-0.855605\pi\)
−0.898862 + 0.438233i \(0.855605\pi\)
\(20\) 3.93410 0.879692
\(21\) 0.656970 0.143363
\(22\) −0.973217 −0.207491
\(23\) −2.84547 −0.593322 −0.296661 0.954983i \(-0.595873\pi\)
−0.296661 + 0.954983i \(0.595873\pi\)
\(24\) 2.34885 0.479456
\(25\) 10.4771 2.09543
\(26\) 0.411920 0.0807841
\(27\) 1.13430 0.218296
\(28\) −0.279699 −0.0528581
\(29\) 4.82149 0.895328 0.447664 0.894202i \(-0.352256\pi\)
0.447664 + 0.894202i \(0.352256\pi\)
\(30\) 9.24060 1.68709
\(31\) −5.14273 −0.923661 −0.461830 0.886968i \(-0.652807\pi\)
−0.461830 + 0.886968i \(0.652807\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.28594 −0.397931
\(34\) 1.47119 0.252307
\(35\) −1.10036 −0.185995
\(36\) 2.51708 0.419514
\(37\) 4.41180 0.725295 0.362647 0.931926i \(-0.381873\pi\)
0.362647 + 0.931926i \(0.381873\pi\)
\(38\) 7.83609 1.27118
\(39\) 0.967537 0.154930
\(40\) −3.93410 −0.622036
\(41\) −3.33780 −0.521277 −0.260639 0.965436i \(-0.583933\pi\)
−0.260639 + 0.965436i \(0.583933\pi\)
\(42\) −0.656970 −0.101373
\(43\) 5.27289 0.804108 0.402054 0.915616i \(-0.368296\pi\)
0.402054 + 0.915616i \(0.368296\pi\)
\(44\) 0.973217 0.146718
\(45\) 9.90246 1.47617
\(46\) 2.84547 0.419542
\(47\) −1.59196 −0.232211 −0.116105 0.993237i \(-0.537041\pi\)
−0.116105 + 0.993237i \(0.537041\pi\)
\(48\) −2.34885 −0.339027
\(49\) −6.92177 −0.988824
\(50\) −10.4771 −1.48169
\(51\) 3.45560 0.483881
\(52\) −0.411920 −0.0571230
\(53\) 10.2898 1.41342 0.706709 0.707504i \(-0.250179\pi\)
0.706709 + 0.707504i \(0.250179\pi\)
\(54\) −1.13430 −0.154358
\(55\) 3.82873 0.516266
\(56\) 0.279699 0.0373763
\(57\) 18.4058 2.43791
\(58\) −4.82149 −0.633092
\(59\) 3.83766 0.499621 0.249811 0.968295i \(-0.419632\pi\)
0.249811 + 0.968295i \(0.419632\pi\)
\(60\) −9.24060 −1.19296
\(61\) 11.1929 1.43310 0.716551 0.697535i \(-0.245720\pi\)
0.716551 + 0.697535i \(0.245720\pi\)
\(62\) 5.14273 0.653127
\(63\) −0.704025 −0.0886989
\(64\) 1.00000 0.125000
\(65\) −1.62053 −0.201003
\(66\) 2.28594 0.281380
\(67\) −7.74705 −0.946452 −0.473226 0.880941i \(-0.656911\pi\)
−0.473226 + 0.880941i \(0.656911\pi\)
\(68\) −1.47119 −0.178408
\(69\) 6.68358 0.804609
\(70\) 1.10036 0.131519
\(71\) −0.378148 −0.0448780 −0.0224390 0.999748i \(-0.507143\pi\)
−0.0224390 + 0.999748i \(0.507143\pi\)
\(72\) −2.51708 −0.296641
\(73\) −11.8009 −1.38119 −0.690595 0.723242i \(-0.742651\pi\)
−0.690595 + 0.723242i \(0.742651\pi\)
\(74\) −4.41180 −0.512861
\(75\) −24.6092 −2.84163
\(76\) −7.83609 −0.898862
\(77\) −0.272208 −0.0310210
\(78\) −0.967537 −0.109552
\(79\) 0.341349 0.0384048 0.0192024 0.999816i \(-0.493887\pi\)
0.0192024 + 0.999816i \(0.493887\pi\)
\(80\) 3.93410 0.439846
\(81\) −10.2155 −1.13506
\(82\) 3.33780 0.368599
\(83\) −10.7671 −1.18184 −0.590921 0.806730i \(-0.701235\pi\)
−0.590921 + 0.806730i \(0.701235\pi\)
\(84\) 0.656970 0.0716813
\(85\) −5.78781 −0.627776
\(86\) −5.27289 −0.568590
\(87\) −11.3249 −1.21416
\(88\) −0.973217 −0.103745
\(89\) −3.35948 −0.356105 −0.178052 0.984021i \(-0.556980\pi\)
−0.178052 + 0.984021i \(0.556980\pi\)
\(90\) −9.90246 −1.04381
\(91\) 0.115214 0.0120777
\(92\) −2.84547 −0.296661
\(93\) 12.0795 1.25258
\(94\) 1.59196 0.164198
\(95\) −30.8280 −3.16288
\(96\) 2.34885 0.239728
\(97\) −0.405935 −0.0412165 −0.0206082 0.999788i \(-0.506560\pi\)
−0.0206082 + 0.999788i \(0.506560\pi\)
\(98\) 6.92177 0.699204
\(99\) 2.44967 0.246201
\(100\) 10.4771 1.04771
\(101\) 7.88785 0.784870 0.392435 0.919780i \(-0.371633\pi\)
0.392435 + 0.919780i \(0.371633\pi\)
\(102\) −3.45560 −0.342156
\(103\) −3.63531 −0.358197 −0.179099 0.983831i \(-0.557318\pi\)
−0.179099 + 0.983831i \(0.557318\pi\)
\(104\) 0.411920 0.0403921
\(105\) 2.58459 0.252230
\(106\) −10.2898 −0.999437
\(107\) 9.95348 0.962239 0.481120 0.876655i \(-0.340230\pi\)
0.481120 + 0.876655i \(0.340230\pi\)
\(108\) 1.13430 0.109148
\(109\) −5.47783 −0.524681 −0.262340 0.964975i \(-0.584494\pi\)
−0.262340 + 0.964975i \(0.584494\pi\)
\(110\) −3.82873 −0.365055
\(111\) −10.3626 −0.983578
\(112\) −0.279699 −0.0264291
\(113\) −7.48323 −0.703963 −0.351981 0.936007i \(-0.614492\pi\)
−0.351981 + 0.936007i \(0.614492\pi\)
\(114\) −18.4058 −1.72386
\(115\) −11.1944 −1.04388
\(116\) 4.82149 0.447664
\(117\) −1.03684 −0.0958556
\(118\) −3.83766 −0.353286
\(119\) 0.411490 0.0377213
\(120\) 9.24060 0.843547
\(121\) −10.0528 −0.913895
\(122\) −11.1929 −1.01336
\(123\) 7.83999 0.706908
\(124\) −5.14273 −0.461830
\(125\) 21.5476 1.92728
\(126\) 0.704025 0.0627196
\(127\) −0.276800 −0.0245621 −0.0122810 0.999925i \(-0.503909\pi\)
−0.0122810 + 0.999925i \(0.503909\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.3852 −1.09046
\(130\) 1.62053 0.142130
\(131\) 4.09617 0.357884 0.178942 0.983860i \(-0.442733\pi\)
0.178942 + 0.983860i \(0.442733\pi\)
\(132\) −2.28594 −0.198965
\(133\) 2.19175 0.190049
\(134\) 7.74705 0.669243
\(135\) 4.46244 0.384066
\(136\) 1.47119 0.126154
\(137\) 6.29922 0.538179 0.269089 0.963115i \(-0.413277\pi\)
0.269089 + 0.963115i \(0.413277\pi\)
\(138\) −6.68358 −0.568944
\(139\) −0.391750 −0.0332278 −0.0166139 0.999862i \(-0.505289\pi\)
−0.0166139 + 0.999862i \(0.505289\pi\)
\(140\) −1.10036 −0.0929977
\(141\) 3.73926 0.314903
\(142\) 0.378148 0.0317335
\(143\) −0.400888 −0.0335239
\(144\) 2.51708 0.209757
\(145\) 18.9682 1.57522
\(146\) 11.8009 0.976649
\(147\) 16.2582 1.34095
\(148\) 4.41180 0.362647
\(149\) −11.2133 −0.918626 −0.459313 0.888274i \(-0.651904\pi\)
−0.459313 + 0.888274i \(0.651904\pi\)
\(150\) 24.6092 2.00933
\(151\) −7.54365 −0.613894 −0.306947 0.951727i \(-0.599307\pi\)
−0.306947 + 0.951727i \(0.599307\pi\)
\(152\) 7.83609 0.635591
\(153\) −3.70311 −0.299379
\(154\) 0.272208 0.0219351
\(155\) −20.2320 −1.62507
\(156\) 0.967537 0.0774649
\(157\) −12.5208 −0.999272 −0.499636 0.866235i \(-0.666533\pi\)
−0.499636 + 0.866235i \(0.666533\pi\)
\(158\) −0.341349 −0.0271563
\(159\) −24.1693 −1.91675
\(160\) −3.93410 −0.311018
\(161\) 0.795876 0.0627238
\(162\) 10.2155 0.802609
\(163\) 3.30396 0.258786 0.129393 0.991593i \(-0.458697\pi\)
0.129393 + 0.991593i \(0.458697\pi\)
\(164\) −3.33780 −0.260639
\(165\) −8.99311 −0.700113
\(166\) 10.7671 0.835688
\(167\) −21.6536 −1.67561 −0.837804 0.545971i \(-0.816161\pi\)
−0.837804 + 0.545971i \(0.816161\pi\)
\(168\) −0.656970 −0.0506863
\(169\) −12.8303 −0.986948
\(170\) 5.78781 0.443905
\(171\) −19.7241 −1.50834
\(172\) 5.27289 0.402054
\(173\) 2.39732 0.182265 0.0911323 0.995839i \(-0.470951\pi\)
0.0911323 + 0.995839i \(0.470951\pi\)
\(174\) 11.3249 0.858541
\(175\) −2.93045 −0.221521
\(176\) 0.973217 0.0733590
\(177\) −9.01409 −0.677540
\(178\) 3.35948 0.251804
\(179\) 21.8559 1.63358 0.816792 0.576933i \(-0.195751\pi\)
0.816792 + 0.576933i \(0.195751\pi\)
\(180\) 9.90246 0.738086
\(181\) −5.04230 −0.374791 −0.187395 0.982285i \(-0.560005\pi\)
−0.187395 + 0.982285i \(0.560005\pi\)
\(182\) −0.115214 −0.00854019
\(183\) −26.2904 −1.94344
\(184\) 2.84547 0.209771
\(185\) 17.3564 1.27607
\(186\) −12.0795 −0.885710
\(187\) −1.43179 −0.104703
\(188\) −1.59196 −0.116105
\(189\) −0.317262 −0.0230774
\(190\) 30.8280 2.23650
\(191\) −18.2990 −1.32407 −0.662035 0.749473i \(-0.730307\pi\)
−0.662035 + 0.749473i \(0.730307\pi\)
\(192\) −2.34885 −0.169513
\(193\) 8.37506 0.602850 0.301425 0.953490i \(-0.402538\pi\)
0.301425 + 0.953490i \(0.402538\pi\)
\(194\) 0.405935 0.0291444
\(195\) 3.80639 0.272581
\(196\) −6.92177 −0.494412
\(197\) 10.9612 0.780952 0.390476 0.920613i \(-0.372311\pi\)
0.390476 + 0.920613i \(0.372311\pi\)
\(198\) −2.44967 −0.174090
\(199\) −20.8954 −1.48124 −0.740619 0.671925i \(-0.765468\pi\)
−0.740619 + 0.671925i \(0.765468\pi\)
\(200\) −10.4771 −0.740846
\(201\) 18.1966 1.28349
\(202\) −7.88785 −0.554987
\(203\) −1.34856 −0.0946507
\(204\) 3.45560 0.241941
\(205\) −13.1313 −0.917127
\(206\) 3.63531 0.253284
\(207\) −7.16229 −0.497814
\(208\) −0.411920 −0.0285615
\(209\) −7.62622 −0.527517
\(210\) −2.58459 −0.178353
\(211\) 20.1820 1.38939 0.694693 0.719306i \(-0.255540\pi\)
0.694693 + 0.719306i \(0.255540\pi\)
\(212\) 10.2898 0.706709
\(213\) 0.888213 0.0608593
\(214\) −9.95348 −0.680406
\(215\) 20.7441 1.41473
\(216\) −1.13430 −0.0771792
\(217\) 1.43841 0.0976460
\(218\) 5.47783 0.371005
\(219\) 27.7185 1.87304
\(220\) 3.82873 0.258133
\(221\) 0.606013 0.0407648
\(222\) 10.3626 0.695494
\(223\) 0.688835 0.0461278 0.0230639 0.999734i \(-0.492658\pi\)
0.0230639 + 0.999734i \(0.492658\pi\)
\(224\) 0.279699 0.0186882
\(225\) 26.3718 1.75812
\(226\) 7.48323 0.497777
\(227\) −28.0232 −1.85996 −0.929982 0.367606i \(-0.880178\pi\)
−0.929982 + 0.367606i \(0.880178\pi\)
\(228\) 18.4058 1.21895
\(229\) −4.68908 −0.309863 −0.154932 0.987925i \(-0.549516\pi\)
−0.154932 + 0.987925i \(0.549516\pi\)
\(230\) 11.1944 0.738135
\(231\) 0.639374 0.0420677
\(232\) −4.82149 −0.316546
\(233\) 7.02459 0.460196 0.230098 0.973167i \(-0.426095\pi\)
0.230098 + 0.973167i \(0.426095\pi\)
\(234\) 1.03684 0.0677801
\(235\) −6.26292 −0.408548
\(236\) 3.83766 0.249811
\(237\) −0.801777 −0.0520810
\(238\) −0.411490 −0.0266730
\(239\) −9.43944 −0.610587 −0.305293 0.952258i \(-0.598755\pi\)
−0.305293 + 0.952258i \(0.598755\pi\)
\(240\) −9.24060 −0.596478
\(241\) −21.0367 −1.35510 −0.677548 0.735479i \(-0.736957\pi\)
−0.677548 + 0.735479i \(0.736957\pi\)
\(242\) 10.0528 0.646222
\(243\) 20.5919 1.32097
\(244\) 11.1929 0.716551
\(245\) −27.2309 −1.73972
\(246\) −7.83999 −0.499860
\(247\) 3.22784 0.205383
\(248\) 5.14273 0.326563
\(249\) 25.2902 1.60270
\(250\) −21.5476 −1.36279
\(251\) 8.33760 0.526265 0.263132 0.964760i \(-0.415244\pi\)
0.263132 + 0.964760i \(0.415244\pi\)
\(252\) −0.704025 −0.0443494
\(253\) −2.76926 −0.174102
\(254\) 0.276800 0.0173680
\(255\) 13.5947 0.851332
\(256\) 1.00000 0.0625000
\(257\) −1.43675 −0.0896218 −0.0448109 0.998995i \(-0.514269\pi\)
−0.0448109 + 0.998995i \(0.514269\pi\)
\(258\) 12.3852 0.771069
\(259\) −1.23397 −0.0766754
\(260\) −1.62053 −0.100501
\(261\) 12.1361 0.751205
\(262\) −4.09617 −0.253062
\(263\) 23.1216 1.42574 0.712869 0.701297i \(-0.247395\pi\)
0.712869 + 0.701297i \(0.247395\pi\)
\(264\) 2.28594 0.140690
\(265\) 40.4812 2.48674
\(266\) −2.19175 −0.134385
\(267\) 7.89091 0.482916
\(268\) −7.74705 −0.473226
\(269\) −6.83237 −0.416577 −0.208289 0.978067i \(-0.566789\pi\)
−0.208289 + 0.978067i \(0.566789\pi\)
\(270\) −4.46244 −0.271576
\(271\) 13.4951 0.819771 0.409885 0.912137i \(-0.365569\pi\)
0.409885 + 0.912137i \(0.365569\pi\)
\(272\) −1.47119 −0.0892040
\(273\) −0.270619 −0.0163786
\(274\) −6.29922 −0.380550
\(275\) 10.1965 0.614874
\(276\) 6.68358 0.402304
\(277\) 9.70591 0.583171 0.291586 0.956545i \(-0.405817\pi\)
0.291586 + 0.956545i \(0.405817\pi\)
\(278\) 0.391750 0.0234956
\(279\) −12.9447 −0.774977
\(280\) 1.10036 0.0657593
\(281\) 10.9873 0.655447 0.327723 0.944774i \(-0.393719\pi\)
0.327723 + 0.944774i \(0.393719\pi\)
\(282\) −3.73926 −0.222670
\(283\) −22.9974 −1.36706 −0.683528 0.729924i \(-0.739555\pi\)
−0.683528 + 0.729924i \(0.739555\pi\)
\(284\) −0.378148 −0.0224390
\(285\) 72.4102 4.28921
\(286\) 0.400888 0.0237050
\(287\) 0.933580 0.0551075
\(288\) −2.51708 −0.148321
\(289\) −14.8356 −0.872682
\(290\) −18.9682 −1.11385
\(291\) 0.953479 0.0558940
\(292\) −11.8009 −0.690595
\(293\) 18.7803 1.09715 0.548577 0.836100i \(-0.315170\pi\)
0.548577 + 0.836100i \(0.315170\pi\)
\(294\) −16.2582 −0.948196
\(295\) 15.0978 0.879025
\(296\) −4.41180 −0.256430
\(297\) 1.10392 0.0640558
\(298\) 11.2133 0.649567
\(299\) 1.17211 0.0677847
\(300\) −24.6092 −1.42081
\(301\) −1.47482 −0.0850072
\(302\) 7.54365 0.434089
\(303\) −18.5274 −1.06437
\(304\) −7.83609 −0.449431
\(305\) 44.0339 2.52137
\(306\) 3.70311 0.211693
\(307\) −2.16399 −0.123506 −0.0617529 0.998091i \(-0.519669\pi\)
−0.0617529 + 0.998091i \(0.519669\pi\)
\(308\) −0.272208 −0.0155105
\(309\) 8.53878 0.485754
\(310\) 20.2320 1.14910
\(311\) 0.454201 0.0257554 0.0128777 0.999917i \(-0.495901\pi\)
0.0128777 + 0.999917i \(0.495901\pi\)
\(312\) −0.967537 −0.0547760
\(313\) 13.9830 0.790365 0.395183 0.918603i \(-0.370681\pi\)
0.395183 + 0.918603i \(0.370681\pi\)
\(314\) 12.5208 0.706592
\(315\) −2.76971 −0.156055
\(316\) 0.341349 0.0192024
\(317\) 20.2358 1.13655 0.568277 0.822837i \(-0.307610\pi\)
0.568277 + 0.822837i \(0.307610\pi\)
\(318\) 24.1693 1.35534
\(319\) 4.69235 0.262721
\(320\) 3.93410 0.219923
\(321\) −23.3792 −1.30490
\(322\) −0.795876 −0.0443524
\(323\) 11.5284 0.641457
\(324\) −10.2155 −0.567530
\(325\) −4.31574 −0.239394
\(326\) −3.30396 −0.182989
\(327\) 12.8666 0.711524
\(328\) 3.33780 0.184299
\(329\) 0.445269 0.0245484
\(330\) 8.99311 0.495054
\(331\) −16.1563 −0.888030 −0.444015 0.896019i \(-0.646446\pi\)
−0.444015 + 0.896019i \(0.646446\pi\)
\(332\) −10.7671 −0.590921
\(333\) 11.1049 0.608542
\(334\) 21.6536 1.18483
\(335\) −30.4777 −1.66517
\(336\) 0.656970 0.0358406
\(337\) 6.64099 0.361758 0.180879 0.983505i \(-0.442106\pi\)
0.180879 + 0.983505i \(0.442106\pi\)
\(338\) 12.8303 0.697878
\(339\) 17.5770 0.954649
\(340\) −5.78781 −0.313888
\(341\) −5.00499 −0.271035
\(342\) 19.7241 1.06656
\(343\) 3.89390 0.210251
\(344\) −5.27289 −0.284295
\(345\) 26.2939 1.41561
\(346\) −2.39732 −0.128881
\(347\) 22.8869 1.22863 0.614317 0.789060i \(-0.289432\pi\)
0.614317 + 0.789060i \(0.289432\pi\)
\(348\) −11.3249 −0.607080
\(349\) 8.68372 0.464829 0.232414 0.972617i \(-0.425337\pi\)
0.232414 + 0.972617i \(0.425337\pi\)
\(350\) 2.93045 0.156639
\(351\) −0.467240 −0.0249394
\(352\) −0.973217 −0.0518726
\(353\) −29.6885 −1.58016 −0.790080 0.613004i \(-0.789961\pi\)
−0.790080 + 0.613004i \(0.789961\pi\)
\(354\) 9.01409 0.479093
\(355\) −1.48767 −0.0789575
\(356\) −3.35948 −0.178052
\(357\) −0.966528 −0.0511541
\(358\) −21.8559 −1.15512
\(359\) −20.9634 −1.10641 −0.553203 0.833047i \(-0.686595\pi\)
−0.553203 + 0.833047i \(0.686595\pi\)
\(360\) −9.90246 −0.521905
\(361\) 42.4044 2.23181
\(362\) 5.04230 0.265017
\(363\) 23.6126 1.23934
\(364\) 0.115214 0.00603883
\(365\) −46.4259 −2.43004
\(366\) 26.2904 1.37422
\(367\) 12.5856 0.656964 0.328482 0.944510i \(-0.393463\pi\)
0.328482 + 0.944510i \(0.393463\pi\)
\(368\) −2.84547 −0.148331
\(369\) −8.40153 −0.437366
\(370\) −17.3564 −0.902319
\(371\) −2.87806 −0.149421
\(372\) 12.0795 0.626292
\(373\) −20.6444 −1.06892 −0.534462 0.845192i \(-0.679486\pi\)
−0.534462 + 0.845192i \(0.679486\pi\)
\(374\) 1.43179 0.0740360
\(375\) −50.6121 −2.61360
\(376\) 1.59196 0.0820989
\(377\) −1.98607 −0.102288
\(378\) 0.317262 0.0163182
\(379\) −36.4215 −1.87085 −0.935424 0.353528i \(-0.884982\pi\)
−0.935424 + 0.353528i \(0.884982\pi\)
\(380\) −30.8280 −1.58144
\(381\) 0.650162 0.0333088
\(382\) 18.2990 0.936258
\(383\) −28.6532 −1.46411 −0.732056 0.681244i \(-0.761439\pi\)
−0.732056 + 0.681244i \(0.761439\pi\)
\(384\) 2.34885 0.119864
\(385\) −1.07089 −0.0545777
\(386\) −8.37506 −0.426279
\(387\) 13.2723 0.674669
\(388\) −0.405935 −0.0206082
\(389\) 23.4401 1.18846 0.594231 0.804294i \(-0.297457\pi\)
0.594231 + 0.804294i \(0.297457\pi\)
\(390\) −3.80639 −0.192744
\(391\) 4.18623 0.211707
\(392\) 6.92177 0.349602
\(393\) −9.62127 −0.485329
\(394\) −10.9612 −0.552216
\(395\) 1.34290 0.0675687
\(396\) 2.44967 0.123100
\(397\) −8.53221 −0.428219 −0.214110 0.976810i \(-0.568685\pi\)
−0.214110 + 0.976810i \(0.568685\pi\)
\(398\) 20.8954 1.04739
\(399\) −5.14808 −0.257726
\(400\) 10.4771 0.523857
\(401\) −6.88659 −0.343900 −0.171950 0.985106i \(-0.555007\pi\)
−0.171950 + 0.985106i \(0.555007\pi\)
\(402\) −18.1966 −0.907565
\(403\) 2.11839 0.105525
\(404\) 7.88785 0.392435
\(405\) −40.1890 −1.99701
\(406\) 1.34856 0.0669281
\(407\) 4.29364 0.212828
\(408\) −3.45560 −0.171078
\(409\) 6.40048 0.316483 0.158242 0.987400i \(-0.449417\pi\)
0.158242 + 0.987400i \(0.449417\pi\)
\(410\) 13.1313 0.648506
\(411\) −14.7959 −0.729828
\(412\) −3.63531 −0.179099
\(413\) −1.07339 −0.0528181
\(414\) 7.16229 0.352007
\(415\) −42.3588 −2.07931
\(416\) 0.411920 0.0201960
\(417\) 0.920160 0.0450604
\(418\) 7.62622 0.373011
\(419\) −28.9035 −1.41203 −0.706013 0.708199i \(-0.749508\pi\)
−0.706013 + 0.708199i \(0.749508\pi\)
\(420\) 2.58459 0.126115
\(421\) −37.0768 −1.80701 −0.903507 0.428574i \(-0.859016\pi\)
−0.903507 + 0.428574i \(0.859016\pi\)
\(422\) −20.1820 −0.982444
\(423\) −4.00709 −0.194831
\(424\) −10.2898 −0.499719
\(425\) −15.4139 −0.747683
\(426\) −0.888213 −0.0430340
\(427\) −3.13064 −0.151502
\(428\) 9.95348 0.481120
\(429\) 0.941623 0.0454620
\(430\) −20.7441 −1.00037
\(431\) 21.4172 1.03163 0.515816 0.856699i \(-0.327489\pi\)
0.515816 + 0.856699i \(0.327489\pi\)
\(432\) 1.13430 0.0545739
\(433\) −11.0724 −0.532106 −0.266053 0.963958i \(-0.585720\pi\)
−0.266053 + 0.963958i \(0.585720\pi\)
\(434\) −1.43841 −0.0690461
\(435\) −44.5534 −2.13617
\(436\) −5.47783 −0.262340
\(437\) 22.2974 1.06663
\(438\) −27.7185 −1.32444
\(439\) −14.9576 −0.713890 −0.356945 0.934125i \(-0.616182\pi\)
−0.356945 + 0.934125i \(0.616182\pi\)
\(440\) −3.82873 −0.182528
\(441\) −17.4227 −0.829651
\(442\) −0.606013 −0.0288251
\(443\) 11.7114 0.556427 0.278214 0.960519i \(-0.410258\pi\)
0.278214 + 0.960519i \(0.410258\pi\)
\(444\) −10.3626 −0.491789
\(445\) −13.2165 −0.626524
\(446\) −0.688835 −0.0326173
\(447\) 26.3382 1.24576
\(448\) −0.279699 −0.0132145
\(449\) −4.90126 −0.231305 −0.115652 0.993290i \(-0.536896\pi\)
−0.115652 + 0.993290i \(0.536896\pi\)
\(450\) −26.3718 −1.24318
\(451\) −3.24841 −0.152962
\(452\) −7.48323 −0.351981
\(453\) 17.7189 0.832506
\(454\) 28.0232 1.31519
\(455\) 0.453262 0.0212492
\(456\) −18.4058 −0.861930
\(457\) −3.76798 −0.176259 −0.0881293 0.996109i \(-0.528089\pi\)
−0.0881293 + 0.996109i \(0.528089\pi\)
\(458\) 4.68908 0.219106
\(459\) −1.66877 −0.0778914
\(460\) −11.1944 −0.521940
\(461\) −20.9688 −0.976615 −0.488307 0.872672i \(-0.662385\pi\)
−0.488307 + 0.872672i \(0.662385\pi\)
\(462\) −0.639374 −0.0297464
\(463\) 25.8109 1.19953 0.599767 0.800175i \(-0.295260\pi\)
0.599767 + 0.800175i \(0.295260\pi\)
\(464\) 4.82149 0.223832
\(465\) 47.5219 2.20377
\(466\) −7.02459 −0.325408
\(467\) −11.4599 −0.530302 −0.265151 0.964207i \(-0.585422\pi\)
−0.265151 + 0.964207i \(0.585422\pi\)
\(468\) −1.03684 −0.0479278
\(469\) 2.16684 0.100055
\(470\) 6.26292 0.288887
\(471\) 29.4096 1.35512
\(472\) −3.83766 −0.176643
\(473\) 5.13166 0.235954
\(474\) 0.801777 0.0368268
\(475\) −82.0999 −3.76700
\(476\) 0.411490 0.0188606
\(477\) 25.9004 1.18590
\(478\) 9.43944 0.431750
\(479\) −0.722672 −0.0330197 −0.0165099 0.999864i \(-0.505255\pi\)
−0.0165099 + 0.999864i \(0.505255\pi\)
\(480\) 9.24060 0.421774
\(481\) −1.81731 −0.0828620
\(482\) 21.0367 0.958197
\(483\) −1.86939 −0.0850602
\(484\) −10.0528 −0.456948
\(485\) −1.59699 −0.0725155
\(486\) −20.5919 −0.934065
\(487\) 24.3721 1.10441 0.552203 0.833710i \(-0.313787\pi\)
0.552203 + 0.833710i \(0.313787\pi\)
\(488\) −11.1929 −0.506678
\(489\) −7.76050 −0.350942
\(490\) 27.2309 1.23017
\(491\) −21.6203 −0.975713 −0.487856 0.872924i \(-0.662221\pi\)
−0.487856 + 0.872924i \(0.662221\pi\)
\(492\) 7.83999 0.353454
\(493\) −7.09333 −0.319467
\(494\) −3.22784 −0.145228
\(495\) 9.63724 0.433162
\(496\) −5.14273 −0.230915
\(497\) 0.105768 0.00474433
\(498\) −25.2902 −1.13328
\(499\) −9.82237 −0.439710 −0.219855 0.975533i \(-0.570558\pi\)
−0.219855 + 0.975533i \(0.570558\pi\)
\(500\) 21.5476 0.963639
\(501\) 50.8611 2.27231
\(502\) −8.33760 −0.372125
\(503\) 3.54808 0.158201 0.0791006 0.996867i \(-0.474795\pi\)
0.0791006 + 0.996867i \(0.474795\pi\)
\(504\) 0.704025 0.0313598
\(505\) 31.0316 1.38089
\(506\) 2.76926 0.123109
\(507\) 30.1365 1.33841
\(508\) −0.276800 −0.0122810
\(509\) 23.3137 1.03336 0.516681 0.856178i \(-0.327167\pi\)
0.516681 + 0.856178i \(0.327167\pi\)
\(510\) −13.5947 −0.601983
\(511\) 3.30070 0.146014
\(512\) −1.00000 −0.0441942
\(513\) −8.88847 −0.392435
\(514\) 1.43675 0.0633722
\(515\) −14.3017 −0.630206
\(516\) −12.3852 −0.545228
\(517\) −1.54932 −0.0681390
\(518\) 1.23397 0.0542177
\(519\) −5.63093 −0.247170
\(520\) 1.62053 0.0710651
\(521\) −17.0410 −0.746579 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(522\) −12.1361 −0.531182
\(523\) 40.1166 1.75418 0.877088 0.480329i \(-0.159483\pi\)
0.877088 + 0.480329i \(0.159483\pi\)
\(524\) 4.09617 0.178942
\(525\) 6.88317 0.300406
\(526\) −23.1216 −1.00815
\(527\) 7.56593 0.329577
\(528\) −2.28594 −0.0994827
\(529\) −14.9033 −0.647969
\(530\) −40.4812 −1.75839
\(531\) 9.65972 0.419196
\(532\) 2.19175 0.0950243
\(533\) 1.37491 0.0595539
\(534\) −7.89091 −0.341473
\(535\) 39.1580 1.69295
\(536\) 7.74705 0.334621
\(537\) −51.3361 −2.21531
\(538\) 6.83237 0.294565
\(539\) −6.73638 −0.290157
\(540\) 4.46244 0.192033
\(541\) −6.69422 −0.287807 −0.143904 0.989592i \(-0.545965\pi\)
−0.143904 + 0.989592i \(0.545965\pi\)
\(542\) −13.4951 −0.579665
\(543\) 11.8436 0.508257
\(544\) 1.47119 0.0630768
\(545\) −21.5503 −0.923115
\(546\) 0.270619 0.0115814
\(547\) −6.03681 −0.258116 −0.129058 0.991637i \(-0.541195\pi\)
−0.129058 + 0.991637i \(0.541195\pi\)
\(548\) 6.29922 0.269089
\(549\) 28.1734 1.20241
\(550\) −10.1965 −0.434782
\(551\) −37.7816 −1.60955
\(552\) −6.68358 −0.284472
\(553\) −0.0954750 −0.00406001
\(554\) −9.70591 −0.412364
\(555\) −40.7676 −1.73049
\(556\) −0.391750 −0.0166139
\(557\) 4.83205 0.204740 0.102370 0.994746i \(-0.467357\pi\)
0.102370 + 0.994746i \(0.467357\pi\)
\(558\) 12.9447 0.547992
\(559\) −2.17201 −0.0918661
\(560\) −1.10036 −0.0464988
\(561\) 3.36305 0.141988
\(562\) −10.9873 −0.463471
\(563\) 0.793724 0.0334515 0.0167257 0.999860i \(-0.494676\pi\)
0.0167257 + 0.999860i \(0.494676\pi\)
\(564\) 3.73926 0.157451
\(565\) −29.4398 −1.23854
\(566\) 22.9974 0.966655
\(567\) 2.85728 0.119994
\(568\) 0.378148 0.0158668
\(569\) 0.829034 0.0347549 0.0173774 0.999849i \(-0.494468\pi\)
0.0173774 + 0.999849i \(0.494468\pi\)
\(570\) −72.4102 −3.03293
\(571\) −9.07103 −0.379611 −0.189805 0.981822i \(-0.560786\pi\)
−0.189805 + 0.981822i \(0.560786\pi\)
\(572\) −0.400888 −0.0167619
\(573\) 42.9816 1.79558
\(574\) −0.933580 −0.0389669
\(575\) −29.8124 −1.24326
\(576\) 2.51708 0.104878
\(577\) 22.3568 0.930725 0.465362 0.885120i \(-0.345924\pi\)
0.465362 + 0.885120i \(0.345924\pi\)
\(578\) 14.8356 0.617080
\(579\) −19.6717 −0.817529
\(580\) 18.9682 0.787612
\(581\) 3.01154 0.124940
\(582\) −0.953479 −0.0395230
\(583\) 10.0142 0.414748
\(584\) 11.8009 0.488325
\(585\) −4.07902 −0.168647
\(586\) −18.7803 −0.775806
\(587\) −34.6229 −1.42904 −0.714520 0.699615i \(-0.753355\pi\)
−0.714520 + 0.699615i \(0.753355\pi\)
\(588\) 16.2582 0.670476
\(589\) 40.2989 1.66049
\(590\) −15.0978 −0.621565
\(591\) −25.7461 −1.05905
\(592\) 4.41180 0.181324
\(593\) −13.1463 −0.539855 −0.269928 0.962881i \(-0.587000\pi\)
−0.269928 + 0.962881i \(0.587000\pi\)
\(594\) −1.10392 −0.0452943
\(595\) 1.61884 0.0663661
\(596\) −11.2133 −0.459313
\(597\) 49.0802 2.00872
\(598\) −1.17211 −0.0479310
\(599\) −20.8726 −0.852833 −0.426416 0.904527i \(-0.640224\pi\)
−0.426416 + 0.904527i \(0.640224\pi\)
\(600\) 24.6092 1.00467
\(601\) −1.94377 −0.0792878 −0.0396439 0.999214i \(-0.512622\pi\)
−0.0396439 + 0.999214i \(0.512622\pi\)
\(602\) 1.47482 0.0601092
\(603\) −19.5000 −0.794100
\(604\) −7.54365 −0.306947
\(605\) −39.5489 −1.60789
\(606\) 18.5274 0.752622
\(607\) −38.2873 −1.55403 −0.777016 0.629480i \(-0.783268\pi\)
−0.777016 + 0.629480i \(0.783268\pi\)
\(608\) 7.83609 0.317796
\(609\) 3.16757 0.128356
\(610\) −44.0339 −1.78288
\(611\) 0.655759 0.0265292
\(612\) −3.70311 −0.149689
\(613\) −43.7352 −1.76645 −0.883224 0.468950i \(-0.844632\pi\)
−0.883224 + 0.468950i \(0.844632\pi\)
\(614\) 2.16399 0.0873317
\(615\) 30.8433 1.24372
\(616\) 0.272208 0.0109676
\(617\) −13.7553 −0.553770 −0.276885 0.960903i \(-0.589302\pi\)
−0.276885 + 0.960903i \(0.589302\pi\)
\(618\) −8.53878 −0.343480
\(619\) −2.96219 −0.119061 −0.0595303 0.998226i \(-0.518960\pi\)
−0.0595303 + 0.998226i \(0.518960\pi\)
\(620\) −20.2320 −0.812537
\(621\) −3.22761 −0.129520
\(622\) −0.454201 −0.0182118
\(623\) 0.939644 0.0376460
\(624\) 0.967537 0.0387325
\(625\) 32.3848 1.29539
\(626\) −13.9830 −0.558873
\(627\) 17.9128 0.715369
\(628\) −12.5208 −0.499636
\(629\) −6.49059 −0.258797
\(630\) 2.76971 0.110348
\(631\) −18.8091 −0.748778 −0.374389 0.927272i \(-0.622148\pi\)
−0.374389 + 0.927272i \(0.622148\pi\)
\(632\) −0.341349 −0.0135781
\(633\) −47.4044 −1.88416
\(634\) −20.2358 −0.803666
\(635\) −1.08896 −0.0432141
\(636\) −24.1693 −0.958373
\(637\) 2.85121 0.112969
\(638\) −4.69235 −0.185772
\(639\) −0.951831 −0.0376538
\(640\) −3.93410 −0.155509
\(641\) −29.1444 −1.15113 −0.575567 0.817755i \(-0.695219\pi\)
−0.575567 + 0.817755i \(0.695219\pi\)
\(642\) 23.3792 0.922704
\(643\) 4.57593 0.180457 0.0902286 0.995921i \(-0.471240\pi\)
0.0902286 + 0.995921i \(0.471240\pi\)
\(644\) 0.795876 0.0313619
\(645\) −48.7246 −1.91853
\(646\) −11.5284 −0.453578
\(647\) 19.3417 0.760403 0.380201 0.924904i \(-0.375855\pi\)
0.380201 + 0.924904i \(0.375855\pi\)
\(648\) 10.2155 0.401304
\(649\) 3.73488 0.146607
\(650\) 4.31574 0.169277
\(651\) −3.37862 −0.132418
\(652\) 3.30396 0.129393
\(653\) −36.2160 −1.41724 −0.708620 0.705590i \(-0.750682\pi\)
−0.708620 + 0.705590i \(0.750682\pi\)
\(654\) −12.8666 −0.503123
\(655\) 16.1147 0.629655
\(656\) −3.33780 −0.130319
\(657\) −29.7038 −1.15886
\(658\) −0.445269 −0.0173584
\(659\) 11.5159 0.448596 0.224298 0.974521i \(-0.427991\pi\)
0.224298 + 0.974521i \(0.427991\pi\)
\(660\) −8.99311 −0.350056
\(661\) −2.88262 −0.112121 −0.0560605 0.998427i \(-0.517854\pi\)
−0.0560605 + 0.998427i \(0.517854\pi\)
\(662\) 16.1563 0.627932
\(663\) −1.42343 −0.0552815
\(664\) 10.7671 0.417844
\(665\) 8.62255 0.334368
\(666\) −11.1049 −0.430304
\(667\) −13.7194 −0.531218
\(668\) −21.6536 −0.837804
\(669\) −1.61797 −0.0625543
\(670\) 30.4777 1.17745
\(671\) 10.8931 0.420523
\(672\) −0.656970 −0.0253432
\(673\) 34.4693 1.32869 0.664347 0.747424i \(-0.268710\pi\)
0.664347 + 0.747424i \(0.268710\pi\)
\(674\) −6.64099 −0.255801
\(675\) 11.8842 0.457423
\(676\) −12.8303 −0.493474
\(677\) −1.17801 −0.0452744 −0.0226372 0.999744i \(-0.507206\pi\)
−0.0226372 + 0.999744i \(0.507206\pi\)
\(678\) −17.5770 −0.675039
\(679\) 0.113540 0.00435725
\(680\) 5.78781 0.221952
\(681\) 65.8222 2.52231
\(682\) 5.00499 0.191651
\(683\) 3.20480 0.122628 0.0613141 0.998119i \(-0.480471\pi\)
0.0613141 + 0.998119i \(0.480471\pi\)
\(684\) −19.7241 −0.754170
\(685\) 24.7818 0.946863
\(686\) −3.89390 −0.148670
\(687\) 11.0139 0.420208
\(688\) 5.27289 0.201027
\(689\) −4.23859 −0.161477
\(690\) −26.2939 −1.00099
\(691\) −13.5900 −0.516988 −0.258494 0.966013i \(-0.583226\pi\)
−0.258494 + 0.966013i \(0.583226\pi\)
\(692\) 2.39732 0.0911323
\(693\) −0.685170 −0.0260274
\(694\) −22.8869 −0.868775
\(695\) −1.54118 −0.0584604
\(696\) 11.3249 0.429271
\(697\) 4.91055 0.186000
\(698\) −8.68372 −0.328684
\(699\) −16.4997 −0.624076
\(700\) −2.93045 −0.110760
\(701\) 11.3833 0.429942 0.214971 0.976620i \(-0.431034\pi\)
0.214971 + 0.976620i \(0.431034\pi\)
\(702\) 0.467240 0.0176348
\(703\) −34.5712 −1.30388
\(704\) 0.973217 0.0366795
\(705\) 14.7106 0.554035
\(706\) 29.6885 1.11734
\(707\) −2.20622 −0.0829736
\(708\) −9.01409 −0.338770
\(709\) −37.5605 −1.41061 −0.705307 0.708902i \(-0.749191\pi\)
−0.705307 + 0.708902i \(0.749191\pi\)
\(710\) 1.48767 0.0558314
\(711\) 0.859204 0.0322227
\(712\) 3.35948 0.125902
\(713\) 14.6335 0.548028
\(714\) 0.966528 0.0361714
\(715\) −1.57713 −0.0589814
\(716\) 21.8559 0.816792
\(717\) 22.1718 0.828021
\(718\) 20.9634 0.782347
\(719\) −10.9029 −0.406611 −0.203305 0.979115i \(-0.565168\pi\)
−0.203305 + 0.979115i \(0.565168\pi\)
\(720\) 9.90246 0.369043
\(721\) 1.01679 0.0378673
\(722\) −42.4044 −1.57813
\(723\) 49.4121 1.83766
\(724\) −5.04230 −0.187395
\(725\) 50.5154 1.87610
\(726\) −23.6126 −0.876346
\(727\) 6.85830 0.254360 0.127180 0.991880i \(-0.459407\pi\)
0.127180 + 0.991880i \(0.459407\pi\)
\(728\) −0.115214 −0.00427010
\(729\) −17.7205 −0.656314
\(730\) 46.4259 1.71830
\(731\) −7.75742 −0.286919
\(732\) −26.2904 −0.971720
\(733\) −15.4801 −0.571770 −0.285885 0.958264i \(-0.592287\pi\)
−0.285885 + 0.958264i \(0.592287\pi\)
\(734\) −12.5856 −0.464543
\(735\) 63.9613 2.35925
\(736\) 2.84547 0.104886
\(737\) −7.53956 −0.277723
\(738\) 8.40153 0.309265
\(739\) −16.4301 −0.604392 −0.302196 0.953246i \(-0.597720\pi\)
−0.302196 + 0.953246i \(0.597720\pi\)
\(740\) 17.3564 0.638036
\(741\) −7.58171 −0.278521
\(742\) 2.87806 0.105657
\(743\) 24.8397 0.911280 0.455640 0.890164i \(-0.349410\pi\)
0.455640 + 0.890164i \(0.349410\pi\)
\(744\) −12.0795 −0.442855
\(745\) −44.1141 −1.61622
\(746\) 20.6444 0.755844
\(747\) −27.1016 −0.991597
\(748\) −1.43179 −0.0523514
\(749\) −2.78398 −0.101724
\(750\) 50.6121 1.84809
\(751\) 9.02626 0.329373 0.164686 0.986346i \(-0.447339\pi\)
0.164686 + 0.986346i \(0.447339\pi\)
\(752\) −1.59196 −0.0580527
\(753\) −19.5838 −0.713672
\(754\) 1.98607 0.0723283
\(755\) −29.6775 −1.08007
\(756\) −0.317262 −0.0115387
\(757\) 38.8981 1.41377 0.706887 0.707327i \(-0.250099\pi\)
0.706887 + 0.707327i \(0.250099\pi\)
\(758\) 36.4215 1.32289
\(759\) 6.50458 0.236101
\(760\) 30.8280 1.11825
\(761\) 1.55368 0.0563209 0.0281604 0.999603i \(-0.491035\pi\)
0.0281604 + 0.999603i \(0.491035\pi\)
\(762\) −0.650162 −0.0235529
\(763\) 1.53214 0.0554673
\(764\) −18.2990 −0.662035
\(765\) −14.5684 −0.526722
\(766\) 28.6532 1.03528
\(767\) −1.58081 −0.0570797
\(768\) −2.34885 −0.0847567
\(769\) −26.9405 −0.971499 −0.485750 0.874098i \(-0.661453\pi\)
−0.485750 + 0.874098i \(0.661453\pi\)
\(770\) 1.07089 0.0385923
\(771\) 3.37470 0.121537
\(772\) 8.37506 0.301425
\(773\) −51.8772 −1.86589 −0.932947 0.360013i \(-0.882772\pi\)
−0.932947 + 0.360013i \(0.882772\pi\)
\(774\) −13.2723 −0.477063
\(775\) −53.8811 −1.93547
\(776\) 0.405935 0.0145722
\(777\) 2.89842 0.103980
\(778\) −23.4401 −0.840369
\(779\) 26.1553 0.937112
\(780\) 3.80639 0.136291
\(781\) −0.368020 −0.0131688
\(782\) −4.18623 −0.149699
\(783\) 5.46900 0.195446
\(784\) −6.92177 −0.247206
\(785\) −49.2583 −1.75810
\(786\) 9.62127 0.343179
\(787\) 46.1091 1.64361 0.821806 0.569767i \(-0.192966\pi\)
0.821806 + 0.569767i \(0.192966\pi\)
\(788\) 10.9612 0.390476
\(789\) −54.3091 −1.93345
\(790\) −1.34290 −0.0477783
\(791\) 2.09305 0.0744203
\(792\) −2.44967 −0.0870452
\(793\) −4.61057 −0.163726
\(794\) 8.53221 0.302797
\(795\) −95.0843 −3.37229
\(796\) −20.8954 −0.740619
\(797\) −6.85170 −0.242700 −0.121350 0.992610i \(-0.538722\pi\)
−0.121350 + 0.992610i \(0.538722\pi\)
\(798\) 5.14808 0.182240
\(799\) 2.34207 0.0828566
\(800\) −10.4771 −0.370423
\(801\) −8.45610 −0.298782
\(802\) 6.88659 0.243174
\(803\) −11.4848 −0.405291
\(804\) 18.1966 0.641746
\(805\) 3.13105 0.110355
\(806\) −2.11839 −0.0746172
\(807\) 16.0482 0.564923
\(808\) −7.88785 −0.277494
\(809\) −30.3448 −1.06687 −0.533433 0.845842i \(-0.679098\pi\)
−0.533433 + 0.845842i \(0.679098\pi\)
\(810\) 40.1890 1.41210
\(811\) 5.96595 0.209493 0.104746 0.994499i \(-0.466597\pi\)
0.104746 + 0.994499i \(0.466597\pi\)
\(812\) −1.34856 −0.0473253
\(813\) −31.6980 −1.11170
\(814\) −4.29364 −0.150492
\(815\) 12.9981 0.455304
\(816\) 3.45560 0.120970
\(817\) −41.3188 −1.44556
\(818\) −6.40048 −0.223788
\(819\) 0.290002 0.0101335
\(820\) −13.1313 −0.458563
\(821\) 36.8966 1.28770 0.643851 0.765151i \(-0.277336\pi\)
0.643851 + 0.765151i \(0.277336\pi\)
\(822\) 14.7959 0.516067
\(823\) −47.2113 −1.64568 −0.822841 0.568271i \(-0.807613\pi\)
−0.822841 + 0.568271i \(0.807613\pi\)
\(824\) 3.63531 0.126642
\(825\) −23.9501 −0.833836
\(826\) 1.07339 0.0373480
\(827\) 30.9725 1.07702 0.538510 0.842619i \(-0.318987\pi\)
0.538510 + 0.842619i \(0.318987\pi\)
\(828\) −7.16229 −0.248907
\(829\) −19.9418 −0.692607 −0.346303 0.938123i \(-0.612563\pi\)
−0.346303 + 0.938123i \(0.612563\pi\)
\(830\) 42.3588 1.47029
\(831\) −22.7977 −0.790843
\(832\) −0.411920 −0.0142808
\(833\) 10.1832 0.352828
\(834\) −0.920160 −0.0318625
\(835\) −85.1876 −2.94804
\(836\) −7.62622 −0.263758
\(837\) −5.83338 −0.201631
\(838\) 28.9035 0.998453
\(839\) 11.2315 0.387753 0.193877 0.981026i \(-0.437894\pi\)
0.193877 + 0.981026i \(0.437894\pi\)
\(840\) −2.58459 −0.0891767
\(841\) −5.75327 −0.198389
\(842\) 37.0768 1.27775
\(843\) −25.8075 −0.888857
\(844\) 20.1820 0.694693
\(845\) −50.4758 −1.73642
\(846\) 4.00709 0.137767
\(847\) 2.81177 0.0966136
\(848\) 10.2898 0.353354
\(849\) 54.0175 1.85388
\(850\) 15.4139 0.528692
\(851\) −12.5536 −0.430333
\(852\) 0.888213 0.0304297
\(853\) 33.8446 1.15882 0.579409 0.815037i \(-0.303283\pi\)
0.579409 + 0.815037i \(0.303283\pi\)
\(854\) 3.13064 0.107128
\(855\) −77.5966 −2.65375
\(856\) −9.95348 −0.340203
\(857\) −53.5592 −1.82955 −0.914774 0.403966i \(-0.867631\pi\)
−0.914774 + 0.403966i \(0.867631\pi\)
\(858\) −0.941623 −0.0321465
\(859\) −2.49569 −0.0851517 −0.0425758 0.999093i \(-0.513556\pi\)
−0.0425758 + 0.999093i \(0.513556\pi\)
\(860\) 20.7441 0.707367
\(861\) −2.19284 −0.0747317
\(862\) −21.4172 −0.729474
\(863\) 22.6794 0.772015 0.386008 0.922496i \(-0.373854\pi\)
0.386008 + 0.922496i \(0.373854\pi\)
\(864\) −1.13430 −0.0385896
\(865\) 9.43128 0.320673
\(866\) 11.0724 0.376256
\(867\) 34.8466 1.18345
\(868\) 1.43841 0.0488230
\(869\) 0.332207 0.0112693
\(870\) 44.5534 1.51050
\(871\) 3.19116 0.108128
\(872\) 5.47783 0.185503
\(873\) −1.02177 −0.0345818
\(874\) −22.2974 −0.754221
\(875\) −6.02685 −0.203745
\(876\) 27.7185 0.936521
\(877\) −17.1912 −0.580505 −0.290252 0.956950i \(-0.593739\pi\)
−0.290252 + 0.956950i \(0.593739\pi\)
\(878\) 14.9576 0.504796
\(879\) −44.1120 −1.48786
\(880\) 3.82873 0.129067
\(881\) −26.6406 −0.897543 −0.448772 0.893647i \(-0.648138\pi\)
−0.448772 + 0.893647i \(0.648138\pi\)
\(882\) 17.4227 0.586652
\(883\) 38.0916 1.28188 0.640942 0.767589i \(-0.278544\pi\)
0.640942 + 0.767589i \(0.278544\pi\)
\(884\) 0.606013 0.0203824
\(885\) −35.4623 −1.19205
\(886\) −11.7114 −0.393454
\(887\) 24.0173 0.806422 0.403211 0.915107i \(-0.367894\pi\)
0.403211 + 0.915107i \(0.367894\pi\)
\(888\) 10.3626 0.347747
\(889\) 0.0774208 0.00259661
\(890\) 13.2165 0.443020
\(891\) −9.94194 −0.333068
\(892\) 0.688835 0.0230639
\(893\) 12.4747 0.417451
\(894\) −26.3382 −0.880883
\(895\) 85.9831 2.87410
\(896\) 0.279699 0.00934408
\(897\) −2.75310 −0.0919233
\(898\) 4.90126 0.163557
\(899\) −24.7956 −0.826979
\(900\) 26.3718 0.879061
\(901\) −15.1383 −0.504330
\(902\) 3.24841 0.108160
\(903\) 3.46413 0.115279
\(904\) 7.48323 0.248888
\(905\) −19.8369 −0.659401
\(906\) −17.7189 −0.588671
\(907\) 14.3891 0.477782 0.238891 0.971046i \(-0.423216\pi\)
0.238891 + 0.971046i \(0.423216\pi\)
\(908\) −28.0232 −0.929982
\(909\) 19.8544 0.658528
\(910\) −0.453262 −0.0150255
\(911\) 9.39761 0.311357 0.155678 0.987808i \(-0.450244\pi\)
0.155678 + 0.987808i \(0.450244\pi\)
\(912\) 18.4058 0.609477
\(913\) −10.4787 −0.346795
\(914\) 3.76798 0.124634
\(915\) −103.429 −3.41925
\(916\) −4.68908 −0.154932
\(917\) −1.14569 −0.0378341
\(918\) 1.66877 0.0550776
\(919\) −17.8134 −0.587610 −0.293805 0.955865i \(-0.594922\pi\)
−0.293805 + 0.955865i \(0.594922\pi\)
\(920\) 11.1944 0.369068
\(921\) 5.08289 0.167487
\(922\) 20.9688 0.690571
\(923\) 0.155767 0.00512713
\(924\) 0.639374 0.0210339
\(925\) 46.2230 1.51980
\(926\) −25.8109 −0.848198
\(927\) −9.15037 −0.300538
\(928\) −4.82149 −0.158273
\(929\) −43.8538 −1.43880 −0.719398 0.694598i \(-0.755582\pi\)
−0.719398 + 0.694598i \(0.755582\pi\)
\(930\) −47.5219 −1.55830
\(931\) 54.2396 1.77763
\(932\) 7.02459 0.230098
\(933\) −1.06685 −0.0349270
\(934\) 11.4599 0.374980
\(935\) −5.63280 −0.184212
\(936\) 1.03684 0.0338901
\(937\) −14.2223 −0.464622 −0.232311 0.972642i \(-0.574629\pi\)
−0.232311 + 0.972642i \(0.574629\pi\)
\(938\) −2.16684 −0.0707498
\(939\) −32.8439 −1.07182
\(940\) −6.26292 −0.204274
\(941\) −38.8780 −1.26739 −0.633694 0.773584i \(-0.718462\pi\)
−0.633694 + 0.773584i \(0.718462\pi\)
\(942\) −29.4096 −0.958215
\(943\) 9.49763 0.309285
\(944\) 3.83766 0.124905
\(945\) −1.24814 −0.0406020
\(946\) −5.13166 −0.166845
\(947\) −16.4489 −0.534516 −0.267258 0.963625i \(-0.586118\pi\)
−0.267258 + 0.963625i \(0.586118\pi\)
\(948\) −0.801777 −0.0260405
\(949\) 4.86102 0.157795
\(950\) 82.0999 2.66367
\(951\) −47.5308 −1.54129
\(952\) −0.411490 −0.0133365
\(953\) 30.9997 1.00418 0.502090 0.864815i \(-0.332565\pi\)
0.502090 + 0.864815i \(0.332565\pi\)
\(954\) −25.9004 −0.838556
\(955\) −71.9901 −2.32955
\(956\) −9.43944 −0.305293
\(957\) −11.0216 −0.356278
\(958\) 0.722672 0.0233485
\(959\) −1.76188 −0.0568942
\(960\) −9.24060 −0.298239
\(961\) −4.55236 −0.146850
\(962\) 1.81731 0.0585923
\(963\) 25.0537 0.807346
\(964\) −21.0367 −0.677548
\(965\) 32.9483 1.06064
\(966\) 1.86939 0.0601466
\(967\) −10.4119 −0.334824 −0.167412 0.985887i \(-0.553541\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(968\) 10.0528 0.323111
\(969\) −27.0784 −0.869884
\(970\) 1.59699 0.0512762
\(971\) 32.5080 1.04323 0.521616 0.853180i \(-0.325329\pi\)
0.521616 + 0.853180i \(0.325329\pi\)
\(972\) 20.5919 0.660484
\(973\) 0.109572 0.00351271
\(974\) −24.3721 −0.780933
\(975\) 10.1370 0.324645
\(976\) 11.1929 0.358275
\(977\) 14.1647 0.453169 0.226584 0.973992i \(-0.427244\pi\)
0.226584 + 0.973992i \(0.427244\pi\)
\(978\) 7.76050 0.248153
\(979\) −3.26951 −0.104494
\(980\) −27.2309 −0.869860
\(981\) −13.7882 −0.440222
\(982\) 21.6203 0.689933
\(983\) −37.2717 −1.18878 −0.594392 0.804176i \(-0.702607\pi\)
−0.594392 + 0.804176i \(0.702607\pi\)
\(984\) −7.83999 −0.249930
\(985\) 43.1224 1.37399
\(986\) 7.09333 0.225898
\(987\) −1.04587 −0.0332903
\(988\) 3.22784 0.102691
\(989\) −15.0039 −0.477095
\(990\) −9.63724 −0.306292
\(991\) −16.1211 −0.512105 −0.256052 0.966663i \(-0.582422\pi\)
−0.256052 + 0.966663i \(0.582422\pi\)
\(992\) 5.14273 0.163282
\(993\) 37.9486 1.20426
\(994\) −0.105768 −0.00335475
\(995\) −82.2048 −2.60607
\(996\) 25.2902 0.801352
\(997\) 39.0214 1.23582 0.617910 0.786249i \(-0.287980\pi\)
0.617910 + 0.786249i \(0.287980\pi\)
\(998\) 9.82237 0.310922
\(999\) 5.00429 0.158329
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 8026.2.a.b.1.16 81
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.b.1.16 81 1.1 even 1 trivial