Properties

Label 8033.2.a.b.1.8
Level $8033$
Weight $2$
Character 8033.1
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.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: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59993 q^{2} -1.45421 q^{3} +4.75963 q^{4} -1.16680 q^{5} +3.78083 q^{6} +3.18169 q^{7} -7.17483 q^{8} -0.885282 q^{9} +O(q^{10})\) \(q-2.59993 q^{2} -1.45421 q^{3} +4.75963 q^{4} -1.16680 q^{5} +3.78083 q^{6} +3.18169 q^{7} -7.17483 q^{8} -0.885282 q^{9} +3.03360 q^{10} +3.09017 q^{11} -6.92148 q^{12} +1.04576 q^{13} -8.27216 q^{14} +1.69677 q^{15} +9.13479 q^{16} +4.29740 q^{17} +2.30167 q^{18} -6.83368 q^{19} -5.55355 q^{20} -4.62683 q^{21} -8.03422 q^{22} +3.18164 q^{23} +10.4337 q^{24} -3.63857 q^{25} -2.71889 q^{26} +5.65000 q^{27} +15.1436 q^{28} -1.00000 q^{29} -4.41149 q^{30} -2.55535 q^{31} -9.40013 q^{32} -4.49375 q^{33} -11.1729 q^{34} -3.71240 q^{35} -4.21361 q^{36} +4.84526 q^{37} +17.7671 q^{38} -1.52075 q^{39} +8.37161 q^{40} +10.0079 q^{41} +12.0294 q^{42} -2.22184 q^{43} +14.7081 q^{44} +1.03295 q^{45} -8.27203 q^{46} -3.69215 q^{47} -13.2839 q^{48} +3.12314 q^{49} +9.46002 q^{50} -6.24930 q^{51} +4.97741 q^{52} -11.8110 q^{53} -14.6896 q^{54} -3.60562 q^{55} -22.8281 q^{56} +9.93758 q^{57} +2.59993 q^{58} +7.12627 q^{59} +8.07600 q^{60} +2.04583 q^{61} +6.64373 q^{62} -2.81669 q^{63} +6.17009 q^{64} -1.22019 q^{65} +11.6834 q^{66} -9.49425 q^{67} +20.4540 q^{68} -4.62676 q^{69} +9.65198 q^{70} +0.524942 q^{71} +6.35175 q^{72} +13.5622 q^{73} -12.5973 q^{74} +5.29124 q^{75} -32.5258 q^{76} +9.83196 q^{77} +3.95383 q^{78} -12.2384 q^{79} -10.6585 q^{80} -5.56043 q^{81} -26.0199 q^{82} -5.35933 q^{83} -22.0220 q^{84} -5.01421 q^{85} +5.77663 q^{86} +1.45421 q^{87} -22.1714 q^{88} -14.1569 q^{89} -2.68559 q^{90} +3.32727 q^{91} +15.1434 q^{92} +3.71601 q^{93} +9.59932 q^{94} +7.97356 q^{95} +13.6697 q^{96} -12.9697 q^{97} -8.11994 q^{98} -2.73567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59993 −1.83843 −0.919213 0.393760i \(-0.871174\pi\)
−0.919213 + 0.393760i \(0.871174\pi\)
\(3\) −1.45421 −0.839587 −0.419793 0.907620i \(-0.637897\pi\)
−0.419793 + 0.907620i \(0.637897\pi\)
\(4\) 4.75963 2.37981
\(5\) −1.16680 −0.521810 −0.260905 0.965364i \(-0.584021\pi\)
−0.260905 + 0.965364i \(0.584021\pi\)
\(6\) 3.78083 1.54352
\(7\) 3.18169 1.20257 0.601283 0.799036i \(-0.294657\pi\)
0.601283 + 0.799036i \(0.294657\pi\)
\(8\) −7.17483 −2.53668
\(9\) −0.885282 −0.295094
\(10\) 3.03360 0.959310
\(11\) 3.09017 0.931722 0.465861 0.884858i \(-0.345745\pi\)
0.465861 + 0.884858i \(0.345745\pi\)
\(12\) −6.92148 −1.99806
\(13\) 1.04576 0.290041 0.145020 0.989429i \(-0.453675\pi\)
0.145020 + 0.989429i \(0.453675\pi\)
\(14\) −8.27216 −2.21083
\(15\) 1.69677 0.438105
\(16\) 9.13479 2.28370
\(17\) 4.29740 1.04227 0.521136 0.853474i \(-0.325509\pi\)
0.521136 + 0.853474i \(0.325509\pi\)
\(18\) 2.30167 0.542509
\(19\) −6.83368 −1.56775 −0.783877 0.620916i \(-0.786761\pi\)
−0.783877 + 0.620916i \(0.786761\pi\)
\(20\) −5.55355 −1.24181
\(21\) −4.62683 −1.00966
\(22\) −8.03422 −1.71290
\(23\) 3.18164 0.663417 0.331709 0.943382i \(-0.392375\pi\)
0.331709 + 0.943382i \(0.392375\pi\)
\(24\) 10.4337 2.12977
\(25\) −3.63857 −0.727714
\(26\) −2.71889 −0.533218
\(27\) 5.65000 1.08734
\(28\) 15.1436 2.86188
\(29\) −1.00000 −0.185695
\(30\) −4.41149 −0.805424
\(31\) −2.55535 −0.458955 −0.229477 0.973314i \(-0.573702\pi\)
−0.229477 + 0.973314i \(0.573702\pi\)
\(32\) −9.40013 −1.66172
\(33\) −4.49375 −0.782261
\(34\) −11.1729 −1.91614
\(35\) −3.71240 −0.627511
\(36\) −4.21361 −0.702269
\(37\) 4.84526 0.796555 0.398278 0.917265i \(-0.369608\pi\)
0.398278 + 0.917265i \(0.369608\pi\)
\(38\) 17.7671 2.88220
\(39\) −1.52075 −0.243514
\(40\) 8.37161 1.32367
\(41\) 10.0079 1.56298 0.781489 0.623919i \(-0.214460\pi\)
0.781489 + 0.623919i \(0.214460\pi\)
\(42\) 12.0294 1.85618
\(43\) −2.22184 −0.338828 −0.169414 0.985545i \(-0.554187\pi\)
−0.169414 + 0.985545i \(0.554187\pi\)
\(44\) 14.7081 2.21732
\(45\) 1.03295 0.153983
\(46\) −8.27203 −1.21964
\(47\) −3.69215 −0.538555 −0.269278 0.963063i \(-0.586785\pi\)
−0.269278 + 0.963063i \(0.586785\pi\)
\(48\) −13.2839 −1.91736
\(49\) 3.12314 0.446163
\(50\) 9.46002 1.33785
\(51\) −6.24930 −0.875077
\(52\) 4.97741 0.690242
\(53\) −11.8110 −1.62237 −0.811185 0.584789i \(-0.801177\pi\)
−0.811185 + 0.584789i \(0.801177\pi\)
\(54\) −14.6896 −1.99900
\(55\) −3.60562 −0.486182
\(56\) −22.8281 −3.05053
\(57\) 9.93758 1.31627
\(58\) 2.59993 0.341387
\(59\) 7.12627 0.927762 0.463881 0.885898i \(-0.346457\pi\)
0.463881 + 0.885898i \(0.346457\pi\)
\(60\) 8.07600 1.04261
\(61\) 2.04583 0.261942 0.130971 0.991386i \(-0.458190\pi\)
0.130971 + 0.991386i \(0.458190\pi\)
\(62\) 6.64373 0.843754
\(63\) −2.81669 −0.354870
\(64\) 6.17009 0.771261
\(65\) −1.22019 −0.151346
\(66\) 11.6834 1.43813
\(67\) −9.49425 −1.15991 −0.579954 0.814650i \(-0.696929\pi\)
−0.579954 + 0.814650i \(0.696929\pi\)
\(68\) 20.4540 2.48041
\(69\) −4.62676 −0.556996
\(70\) 9.65198 1.15363
\(71\) 0.524942 0.0622992 0.0311496 0.999515i \(-0.490083\pi\)
0.0311496 + 0.999515i \(0.490083\pi\)
\(72\) 6.35175 0.748561
\(73\) 13.5622 1.58734 0.793669 0.608349i \(-0.208168\pi\)
0.793669 + 0.608349i \(0.208168\pi\)
\(74\) −12.5973 −1.46441
\(75\) 5.29124 0.610979
\(76\) −32.5258 −3.73096
\(77\) 9.83196 1.12046
\(78\) 3.95383 0.447683
\(79\) −12.2384 −1.37693 −0.688466 0.725269i \(-0.741715\pi\)
−0.688466 + 0.725269i \(0.741715\pi\)
\(80\) −10.6585 −1.19166
\(81\) −5.56043 −0.617825
\(82\) −26.0199 −2.87342
\(83\) −5.35933 −0.588263 −0.294131 0.955765i \(-0.595030\pi\)
−0.294131 + 0.955765i \(0.595030\pi\)
\(84\) −22.0220 −2.40280
\(85\) −5.01421 −0.543868
\(86\) 5.77663 0.622910
\(87\) 1.45421 0.155907
\(88\) −22.1714 −2.36348
\(89\) −14.1569 −1.50063 −0.750313 0.661083i \(-0.770097\pi\)
−0.750313 + 0.661083i \(0.770097\pi\)
\(90\) −2.68559 −0.283087
\(91\) 3.32727 0.348793
\(92\) 15.1434 1.57881
\(93\) 3.71601 0.385332
\(94\) 9.59932 0.990094
\(95\) 7.97356 0.818070
\(96\) 13.6697 1.39516
\(97\) −12.9697 −1.31687 −0.658436 0.752637i \(-0.728782\pi\)
−0.658436 + 0.752637i \(0.728782\pi\)
\(98\) −8.11994 −0.820238
\(99\) −2.73567 −0.274945
\(100\) −17.3182 −1.73182
\(101\) −5.99376 −0.596402 −0.298201 0.954503i \(-0.596386\pi\)
−0.298201 + 0.954503i \(0.596386\pi\)
\(102\) 16.2477 1.60877
\(103\) −15.7675 −1.55362 −0.776809 0.629736i \(-0.783163\pi\)
−0.776809 + 0.629736i \(0.783163\pi\)
\(104\) −7.50312 −0.735742
\(105\) 5.39860 0.526850
\(106\) 30.7079 2.98261
\(107\) 11.3386 1.09615 0.548073 0.836431i \(-0.315362\pi\)
0.548073 + 0.836431i \(0.315362\pi\)
\(108\) 26.8919 2.58767
\(109\) 9.73391 0.932340 0.466170 0.884695i \(-0.345634\pi\)
0.466170 + 0.884695i \(0.345634\pi\)
\(110\) 9.37435 0.893809
\(111\) −7.04601 −0.668777
\(112\) 29.0640 2.74629
\(113\) 18.2462 1.71646 0.858229 0.513266i \(-0.171565\pi\)
0.858229 + 0.513266i \(0.171565\pi\)
\(114\) −25.8370 −2.41986
\(115\) −3.71234 −0.346178
\(116\) −4.75963 −0.441920
\(117\) −0.925789 −0.0855893
\(118\) −18.5278 −1.70562
\(119\) 13.6730 1.25340
\(120\) −12.1741 −1.11133
\(121\) −1.45084 −0.131895
\(122\) −5.31902 −0.481561
\(123\) −14.5536 −1.31226
\(124\) −12.1625 −1.09223
\(125\) 10.0795 0.901539
\(126\) 7.32320 0.652402
\(127\) 5.97922 0.530570 0.265285 0.964170i \(-0.414534\pi\)
0.265285 + 0.964170i \(0.414534\pi\)
\(128\) 2.75847 0.243817
\(129\) 3.23102 0.284475
\(130\) 3.17241 0.278239
\(131\) 2.99339 0.261534 0.130767 0.991413i \(-0.458256\pi\)
0.130767 + 0.991413i \(0.458256\pi\)
\(132\) −21.3886 −1.86164
\(133\) −21.7426 −1.88533
\(134\) 24.6844 2.13240
\(135\) −6.59244 −0.567387
\(136\) −30.8331 −2.64391
\(137\) −21.1681 −1.80851 −0.904254 0.426994i \(-0.859573\pi\)
−0.904254 + 0.426994i \(0.859573\pi\)
\(138\) 12.0292 1.02400
\(139\) 0.825350 0.0700053 0.0350027 0.999387i \(-0.488856\pi\)
0.0350027 + 0.999387i \(0.488856\pi\)
\(140\) −17.6696 −1.49336
\(141\) 5.36915 0.452164
\(142\) −1.36481 −0.114532
\(143\) 3.23157 0.270237
\(144\) −8.08686 −0.673905
\(145\) 1.16680 0.0968977
\(146\) −35.2608 −2.91821
\(147\) −4.54169 −0.374592
\(148\) 23.0616 1.89565
\(149\) −7.01371 −0.574586 −0.287293 0.957843i \(-0.592755\pi\)
−0.287293 + 0.957843i \(0.592755\pi\)
\(150\) −13.7568 −1.12324
\(151\) 4.47562 0.364221 0.182110 0.983278i \(-0.441707\pi\)
0.182110 + 0.983278i \(0.441707\pi\)
\(152\) 49.0305 3.97690
\(153\) −3.80441 −0.307568
\(154\) −25.5624 −2.05988
\(155\) 2.98159 0.239487
\(156\) −7.23818 −0.579518
\(157\) −14.5569 −1.16177 −0.580884 0.813986i \(-0.697293\pi\)
−0.580884 + 0.813986i \(0.697293\pi\)
\(158\) 31.8190 2.53139
\(159\) 17.1757 1.36212
\(160\) 10.9681 0.867104
\(161\) 10.1230 0.797803
\(162\) 14.4567 1.13583
\(163\) −12.7429 −0.998099 −0.499049 0.866574i \(-0.666317\pi\)
−0.499049 + 0.866574i \(0.666317\pi\)
\(164\) 47.6341 3.71960
\(165\) 5.24332 0.408192
\(166\) 13.9339 1.08148
\(167\) −11.6489 −0.901418 −0.450709 0.892671i \(-0.648829\pi\)
−0.450709 + 0.892671i \(0.648829\pi\)
\(168\) 33.1967 2.56118
\(169\) −11.9064 −0.915876
\(170\) 13.0366 0.999861
\(171\) 6.04973 0.462635
\(172\) −10.5751 −0.806346
\(173\) −2.66418 −0.202554 −0.101277 0.994858i \(-0.532293\pi\)
−0.101277 + 0.994858i \(0.532293\pi\)
\(174\) −3.78083 −0.286624
\(175\) −11.5768 −0.875124
\(176\) 28.2280 2.12777
\(177\) −10.3631 −0.778936
\(178\) 36.8069 2.75879
\(179\) 5.69199 0.425439 0.212720 0.977113i \(-0.431768\pi\)
0.212720 + 0.977113i \(0.431768\pi\)
\(180\) 4.91645 0.366451
\(181\) −6.33227 −0.470674 −0.235337 0.971914i \(-0.575619\pi\)
−0.235337 + 0.971914i \(0.575619\pi\)
\(182\) −8.65066 −0.641230
\(183\) −2.97507 −0.219923
\(184\) −22.8277 −1.68288
\(185\) −5.65346 −0.415651
\(186\) −9.66136 −0.708405
\(187\) 13.2797 0.971107
\(188\) −17.5732 −1.28166
\(189\) 17.9766 1.30760
\(190\) −20.7307 −1.50396
\(191\) −10.1032 −0.731044 −0.365522 0.930803i \(-0.619110\pi\)
−0.365522 + 0.930803i \(0.619110\pi\)
\(192\) −8.97259 −0.647541
\(193\) 10.3090 0.742060 0.371030 0.928621i \(-0.379005\pi\)
0.371030 + 0.928621i \(0.379005\pi\)
\(194\) 33.7202 2.42097
\(195\) 1.77441 0.127068
\(196\) 14.8650 1.06178
\(197\) −5.85194 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(198\) 7.11255 0.505467
\(199\) −1.27055 −0.0900667 −0.0450333 0.998985i \(-0.514339\pi\)
−0.0450333 + 0.998985i \(0.514339\pi\)
\(200\) 26.1061 1.84598
\(201\) 13.8066 0.973843
\(202\) 15.5833 1.09644
\(203\) −3.18169 −0.223311
\(204\) −29.7443 −2.08252
\(205\) −11.6773 −0.815578
\(206\) 40.9944 2.85621
\(207\) −2.81665 −0.195771
\(208\) 9.55276 0.662365
\(209\) −21.1172 −1.46071
\(210\) −14.0360 −0.968574
\(211\) 24.7393 1.70312 0.851561 0.524256i \(-0.175656\pi\)
0.851561 + 0.524256i \(0.175656\pi\)
\(212\) −56.2161 −3.86094
\(213\) −0.763375 −0.0523056
\(214\) −29.4796 −2.01518
\(215\) 2.59245 0.176804
\(216\) −40.5378 −2.75825
\(217\) −8.13033 −0.551923
\(218\) −25.3075 −1.71404
\(219\) −19.7223 −1.33271
\(220\) −17.1614 −1.15702
\(221\) 4.49403 0.302301
\(222\) 18.3191 1.22950
\(223\) −13.8366 −0.926565 −0.463283 0.886211i \(-0.653328\pi\)
−0.463283 + 0.886211i \(0.653328\pi\)
\(224\) −29.9083 −1.99833
\(225\) 3.22116 0.214744
\(226\) −47.4388 −3.15558
\(227\) −10.2707 −0.681688 −0.340844 0.940120i \(-0.610713\pi\)
−0.340844 + 0.940120i \(0.610713\pi\)
\(228\) 47.2992 3.13246
\(229\) −7.67566 −0.507222 −0.253611 0.967306i \(-0.581618\pi\)
−0.253611 + 0.967306i \(0.581618\pi\)
\(230\) 9.65183 0.636423
\(231\) −14.2977 −0.940720
\(232\) 7.17483 0.471051
\(233\) −0.0796221 −0.00521622 −0.00260811 0.999997i \(-0.500830\pi\)
−0.00260811 + 0.999997i \(0.500830\pi\)
\(234\) 2.40699 0.157350
\(235\) 4.30801 0.281024
\(236\) 33.9184 2.20790
\(237\) 17.7972 1.15605
\(238\) −35.5487 −2.30428
\(239\) 2.28804 0.148001 0.0740004 0.997258i \(-0.476423\pi\)
0.0740004 + 0.997258i \(0.476423\pi\)
\(240\) 15.4997 1.00050
\(241\) 12.2878 0.791528 0.395764 0.918352i \(-0.370480\pi\)
0.395764 + 0.918352i \(0.370480\pi\)
\(242\) 3.77209 0.242479
\(243\) −8.86400 −0.568626
\(244\) 9.73740 0.623373
\(245\) −3.64409 −0.232812
\(246\) 37.8384 2.41249
\(247\) −7.14636 −0.454712
\(248\) 18.3342 1.16422
\(249\) 7.79357 0.493898
\(250\) −26.2060 −1.65741
\(251\) 27.4924 1.73530 0.867652 0.497171i \(-0.165628\pi\)
0.867652 + 0.497171i \(0.165628\pi\)
\(252\) −13.4064 −0.844524
\(253\) 9.83180 0.618120
\(254\) −15.5455 −0.975414
\(255\) 7.29170 0.456624
\(256\) −19.5120 −1.21950
\(257\) −4.63962 −0.289412 −0.144706 0.989475i \(-0.546224\pi\)
−0.144706 + 0.989475i \(0.546224\pi\)
\(258\) −8.40041 −0.522987
\(259\) 15.4161 0.957910
\(260\) −5.80765 −0.360175
\(261\) 0.885282 0.0547976
\(262\) −7.78261 −0.480811
\(263\) −27.9900 −1.72594 −0.862969 0.505257i \(-0.831398\pi\)
−0.862969 + 0.505257i \(0.831398\pi\)
\(264\) 32.2419 1.98435
\(265\) 13.7812 0.846570
\(266\) 56.5293 3.46603
\(267\) 20.5870 1.25991
\(268\) −45.1891 −2.76036
\(269\) 21.8130 1.32996 0.664980 0.746861i \(-0.268440\pi\)
0.664980 + 0.746861i \(0.268440\pi\)
\(270\) 17.1399 1.04310
\(271\) −28.6765 −1.74197 −0.870987 0.491306i \(-0.836520\pi\)
−0.870987 + 0.491306i \(0.836520\pi\)
\(272\) 39.2558 2.38023
\(273\) −4.83854 −0.292842
\(274\) 55.0354 3.32481
\(275\) −11.2438 −0.678027
\(276\) −22.0216 −1.32555
\(277\) −1.00000 −0.0600842
\(278\) −2.14585 −0.128700
\(279\) 2.26221 0.135435
\(280\) 26.6359 1.59180
\(281\) 10.3356 0.616572 0.308286 0.951294i \(-0.400245\pi\)
0.308286 + 0.951294i \(0.400245\pi\)
\(282\) −13.9594 −0.831270
\(283\) −2.29188 −0.136238 −0.0681190 0.997677i \(-0.521700\pi\)
−0.0681190 + 0.997677i \(0.521700\pi\)
\(284\) 2.49853 0.148260
\(285\) −11.5952 −0.686840
\(286\) −8.40184 −0.496811
\(287\) 31.8422 1.87958
\(288\) 8.32177 0.490365
\(289\) 1.46760 0.0863297
\(290\) −3.03360 −0.178139
\(291\) 18.8606 1.10563
\(292\) 64.5511 3.77757
\(293\) 16.9457 0.989977 0.494989 0.868899i \(-0.335172\pi\)
0.494989 + 0.868899i \(0.335172\pi\)
\(294\) 11.8081 0.688661
\(295\) −8.31496 −0.484115
\(296\) −34.7639 −2.02061
\(297\) 17.4595 1.01310
\(298\) 18.2351 1.05633
\(299\) 3.32722 0.192418
\(300\) 25.1843 1.45402
\(301\) −7.06921 −0.407462
\(302\) −11.6363 −0.669593
\(303\) 8.71617 0.500731
\(304\) −62.4242 −3.58027
\(305\) −2.38708 −0.136684
\(306\) 9.89118 0.565441
\(307\) 15.0569 0.859342 0.429671 0.902985i \(-0.358629\pi\)
0.429671 + 0.902985i \(0.358629\pi\)
\(308\) 46.7965 2.66648
\(309\) 22.9292 1.30440
\(310\) −7.75192 −0.440280
\(311\) 10.4771 0.594101 0.297051 0.954862i \(-0.403997\pi\)
0.297051 + 0.954862i \(0.403997\pi\)
\(312\) 10.9111 0.617719
\(313\) 17.5449 0.991694 0.495847 0.868410i \(-0.334858\pi\)
0.495847 + 0.868410i \(0.334858\pi\)
\(314\) 37.8469 2.13582
\(315\) 3.28652 0.185175
\(316\) −58.2503 −3.27684
\(317\) 24.4682 1.37427 0.687135 0.726530i \(-0.258868\pi\)
0.687135 + 0.726530i \(0.258868\pi\)
\(318\) −44.6556 −2.50416
\(319\) −3.09017 −0.173016
\(320\) −7.19928 −0.402452
\(321\) −16.4887 −0.920309
\(322\) −26.3190 −1.46670
\(323\) −29.3670 −1.63402
\(324\) −26.4656 −1.47031
\(325\) −3.80506 −0.211067
\(326\) 33.1305 1.83493
\(327\) −14.1551 −0.782780
\(328\) −71.8053 −3.96478
\(329\) −11.7473 −0.647648
\(330\) −13.6322 −0.750431
\(331\) 23.5168 1.29260 0.646300 0.763083i \(-0.276315\pi\)
0.646300 + 0.763083i \(0.276315\pi\)
\(332\) −25.5084 −1.39996
\(333\) −4.28942 −0.235059
\(334\) 30.2863 1.65719
\(335\) 11.0779 0.605251
\(336\) −42.2651 −2.30575
\(337\) −8.71267 −0.474609 −0.237305 0.971435i \(-0.576264\pi\)
−0.237305 + 0.971435i \(0.576264\pi\)
\(338\) 30.9558 1.68377
\(339\) −26.5338 −1.44112
\(340\) −23.8658 −1.29430
\(341\) −7.89647 −0.427618
\(342\) −15.7289 −0.850520
\(343\) −12.3350 −0.666025
\(344\) 15.9413 0.859499
\(345\) 5.39852 0.290646
\(346\) 6.92667 0.372380
\(347\) 16.2624 0.873013 0.436507 0.899701i \(-0.356216\pi\)
0.436507 + 0.899701i \(0.356216\pi\)
\(348\) 6.92148 0.371030
\(349\) −3.94679 −0.211267 −0.105633 0.994405i \(-0.533687\pi\)
−0.105633 + 0.994405i \(0.533687\pi\)
\(350\) 30.0988 1.60885
\(351\) 5.90853 0.315374
\(352\) −29.0480 −1.54826
\(353\) −18.3963 −0.979136 −0.489568 0.871965i \(-0.662845\pi\)
−0.489568 + 0.871965i \(0.662845\pi\)
\(354\) 26.9433 1.43202
\(355\) −0.612504 −0.0325083
\(356\) −67.3815 −3.57121
\(357\) −19.8833 −1.05234
\(358\) −14.7988 −0.782139
\(359\) 24.8085 1.30934 0.654672 0.755913i \(-0.272807\pi\)
0.654672 + 0.755913i \(0.272807\pi\)
\(360\) −7.41124 −0.390606
\(361\) 27.6992 1.45785
\(362\) 16.4635 0.865300
\(363\) 2.10983 0.110737
\(364\) 15.8366 0.830061
\(365\) −15.8244 −0.828289
\(366\) 7.73496 0.404313
\(367\) 26.6310 1.39012 0.695062 0.718950i \(-0.255377\pi\)
0.695062 + 0.718950i \(0.255377\pi\)
\(368\) 29.0636 1.51504
\(369\) −8.85985 −0.461226
\(370\) 14.6986 0.764143
\(371\) −37.5790 −1.95101
\(372\) 17.6868 0.917019
\(373\) 3.53801 0.183191 0.0915956 0.995796i \(-0.470803\pi\)
0.0915956 + 0.995796i \(0.470803\pi\)
\(374\) −34.5262 −1.78531
\(375\) −14.6577 −0.756920
\(376\) 26.4905 1.36615
\(377\) −1.04576 −0.0538592
\(378\) −46.7377 −2.40393
\(379\) −0.0570090 −0.00292836 −0.00146418 0.999999i \(-0.500466\pi\)
−0.00146418 + 0.999999i \(0.500466\pi\)
\(380\) 37.9511 1.94685
\(381\) −8.69502 −0.445459
\(382\) 26.2677 1.34397
\(383\) 3.12056 0.159453 0.0797265 0.996817i \(-0.474595\pi\)
0.0797265 + 0.996817i \(0.474595\pi\)
\(384\) −4.01139 −0.204705
\(385\) −11.4720 −0.584665
\(386\) −26.8027 −1.36422
\(387\) 1.96696 0.0999860
\(388\) −61.7308 −3.13391
\(389\) −2.32042 −0.117650 −0.0588249 0.998268i \(-0.518735\pi\)
−0.0588249 + 0.998268i \(0.518735\pi\)
\(390\) −4.61334 −0.233606
\(391\) 13.6728 0.691461
\(392\) −22.4080 −1.13177
\(393\) −4.35301 −0.219581
\(394\) 15.2146 0.766502
\(395\) 14.2798 0.718497
\(396\) −13.0208 −0.654319
\(397\) −22.7613 −1.14236 −0.571178 0.820826i \(-0.693513\pi\)
−0.571178 + 0.820826i \(0.693513\pi\)
\(398\) 3.30333 0.165581
\(399\) 31.6183 1.58289
\(400\) −33.2376 −1.66188
\(401\) 5.70620 0.284954 0.142477 0.989798i \(-0.454493\pi\)
0.142477 + 0.989798i \(0.454493\pi\)
\(402\) −35.8962 −1.79034
\(403\) −2.67227 −0.133115
\(404\) −28.5281 −1.41932
\(405\) 6.48792 0.322388
\(406\) 8.27216 0.410540
\(407\) 14.9727 0.742168
\(408\) 44.8377 2.21980
\(409\) −6.29813 −0.311423 −0.155711 0.987803i \(-0.549767\pi\)
−0.155711 + 0.987803i \(0.549767\pi\)
\(410\) 30.3601 1.49938
\(411\) 30.7827 1.51840
\(412\) −75.0474 −3.69732
\(413\) 22.6736 1.11569
\(414\) 7.32308 0.359910
\(415\) 6.25328 0.306962
\(416\) −9.83025 −0.481967
\(417\) −1.20023 −0.0587755
\(418\) 54.9033 2.68541
\(419\) −12.6515 −0.618065 −0.309032 0.951052i \(-0.600005\pi\)
−0.309032 + 0.951052i \(0.600005\pi\)
\(420\) 25.6953 1.25380
\(421\) −19.0787 −0.929837 −0.464919 0.885353i \(-0.653916\pi\)
−0.464919 + 0.885353i \(0.653916\pi\)
\(422\) −64.3203 −3.13106
\(423\) 3.26859 0.158924
\(424\) 84.7422 4.11544
\(425\) −15.6364 −0.758476
\(426\) 1.98472 0.0961599
\(427\) 6.50920 0.315002
\(428\) 53.9676 2.60862
\(429\) −4.69937 −0.226887
\(430\) −6.74018 −0.325041
\(431\) 27.9122 1.34448 0.672241 0.740332i \(-0.265332\pi\)
0.672241 + 0.740332i \(0.265332\pi\)
\(432\) 51.6116 2.48316
\(433\) −20.2979 −0.975453 −0.487727 0.872996i \(-0.662174\pi\)
−0.487727 + 0.872996i \(0.662174\pi\)
\(434\) 21.1383 1.01467
\(435\) −1.69677 −0.0813540
\(436\) 46.3298 2.21879
\(437\) −21.7423 −1.04007
\(438\) 51.2765 2.45009
\(439\) −6.96865 −0.332596 −0.166298 0.986076i \(-0.553181\pi\)
−0.166298 + 0.986076i \(0.553181\pi\)
\(440\) 25.8697 1.23329
\(441\) −2.76486 −0.131660
\(442\) −11.6841 −0.555758
\(443\) 30.3877 1.44376 0.721880 0.692018i \(-0.243278\pi\)
0.721880 + 0.692018i \(0.243278\pi\)
\(444\) −33.5364 −1.59157
\(445\) 16.5183 0.783042
\(446\) 35.9741 1.70342
\(447\) 10.1994 0.482414
\(448\) 19.6313 0.927492
\(449\) 19.5846 0.924255 0.462127 0.886814i \(-0.347086\pi\)
0.462127 + 0.886814i \(0.347086\pi\)
\(450\) −8.37479 −0.394791
\(451\) 30.9263 1.45626
\(452\) 86.8451 4.08485
\(453\) −6.50848 −0.305795
\(454\) 26.7030 1.25323
\(455\) −3.88227 −0.182004
\(456\) −71.3005 −3.33895
\(457\) −10.7321 −0.502027 −0.251014 0.967984i \(-0.580764\pi\)
−0.251014 + 0.967984i \(0.580764\pi\)
\(458\) 19.9562 0.932491
\(459\) 24.2803 1.13331
\(460\) −17.6694 −0.823839
\(461\) 39.7219 1.85003 0.925016 0.379928i \(-0.124051\pi\)
0.925016 + 0.379928i \(0.124051\pi\)
\(462\) 37.1730 1.72944
\(463\) 1.53215 0.0712050 0.0356025 0.999366i \(-0.488665\pi\)
0.0356025 + 0.999366i \(0.488665\pi\)
\(464\) −9.13479 −0.424072
\(465\) −4.33585 −0.201070
\(466\) 0.207012 0.00958963
\(467\) 27.7463 1.28394 0.641972 0.766728i \(-0.278116\pi\)
0.641972 + 0.766728i \(0.278116\pi\)
\(468\) −4.40641 −0.203686
\(469\) −30.2077 −1.39486
\(470\) −11.2005 −0.516641
\(471\) 21.1688 0.975405
\(472\) −51.1298 −2.35344
\(473\) −6.86587 −0.315693
\(474\) −46.2715 −2.12532
\(475\) 24.8648 1.14088
\(476\) 65.0782 2.98286
\(477\) 10.4561 0.478752
\(478\) −5.94874 −0.272089
\(479\) −8.55476 −0.390877 −0.195438 0.980716i \(-0.562613\pi\)
−0.195438 + 0.980716i \(0.562613\pi\)
\(480\) −15.9499 −0.728009
\(481\) 5.06696 0.231033
\(482\) −31.9475 −1.45517
\(483\) −14.7209 −0.669825
\(484\) −6.90548 −0.313885
\(485\) 15.1331 0.687157
\(486\) 23.0458 1.04538
\(487\) −37.0106 −1.67711 −0.838555 0.544817i \(-0.816599\pi\)
−0.838555 + 0.544817i \(0.816599\pi\)
\(488\) −14.6785 −0.664465
\(489\) 18.5308 0.837990
\(490\) 9.47437 0.428008
\(491\) −0.724907 −0.0327146 −0.0163573 0.999866i \(-0.505207\pi\)
−0.0163573 + 0.999866i \(0.505207\pi\)
\(492\) −69.2698 −3.12292
\(493\) −4.29740 −0.193545
\(494\) 18.5800 0.835955
\(495\) 3.19199 0.143469
\(496\) −23.3426 −1.04811
\(497\) 1.67020 0.0749188
\(498\) −20.2627 −0.907995
\(499\) −37.2504 −1.66756 −0.833778 0.552099i \(-0.813827\pi\)
−0.833778 + 0.552099i \(0.813827\pi\)
\(500\) 47.9747 2.14549
\(501\) 16.9399 0.756819
\(502\) −71.4783 −3.19023
\(503\) 13.9476 0.621893 0.310946 0.950427i \(-0.399354\pi\)
0.310946 + 0.950427i \(0.399354\pi\)
\(504\) 20.2093 0.900193
\(505\) 6.99354 0.311208
\(506\) −25.5620 −1.13637
\(507\) 17.3144 0.768958
\(508\) 28.4588 1.26266
\(509\) −36.4195 −1.61427 −0.807134 0.590368i \(-0.798983\pi\)
−0.807134 + 0.590368i \(0.798983\pi\)
\(510\) −18.9579 −0.839470
\(511\) 43.1508 1.90888
\(512\) 45.2129 1.99815
\(513\) −38.6103 −1.70469
\(514\) 12.0627 0.532062
\(515\) 18.3976 0.810693
\(516\) 15.3784 0.676998
\(517\) −11.4094 −0.501784
\(518\) −40.0808 −1.76105
\(519\) 3.87427 0.170061
\(520\) 8.75466 0.383917
\(521\) 12.4780 0.546669 0.273335 0.961919i \(-0.411873\pi\)
0.273335 + 0.961919i \(0.411873\pi\)
\(522\) −2.30167 −0.100741
\(523\) −18.2832 −0.799468 −0.399734 0.916631i \(-0.630898\pi\)
−0.399734 + 0.916631i \(0.630898\pi\)
\(524\) 14.2474 0.622402
\(525\) 16.8351 0.734742
\(526\) 72.7720 3.17301
\(527\) −10.9814 −0.478355
\(528\) −41.0494 −1.78645
\(529\) −12.8772 −0.559877
\(530\) −35.8300 −1.55636
\(531\) −6.30876 −0.273777
\(532\) −103.487 −4.48672
\(533\) 10.4659 0.453327
\(534\) −53.5248 −2.31624
\(535\) −13.2299 −0.571980
\(536\) 68.1196 2.94232
\(537\) −8.27733 −0.357193
\(538\) −56.7122 −2.44504
\(539\) 9.65104 0.415700
\(540\) −31.3776 −1.35027
\(541\) 15.7038 0.675160 0.337580 0.941297i \(-0.390392\pi\)
0.337580 + 0.941297i \(0.390392\pi\)
\(542\) 74.5569 3.20249
\(543\) 9.20844 0.395172
\(544\) −40.3961 −1.73197
\(545\) −11.3576 −0.486504
\(546\) 12.5799 0.538368
\(547\) −4.80939 −0.205635 −0.102817 0.994700i \(-0.532786\pi\)
−0.102817 + 0.994700i \(0.532786\pi\)
\(548\) −100.752 −4.30391
\(549\) −1.81114 −0.0772976
\(550\) 29.2331 1.24650
\(551\) 6.83368 0.291125
\(552\) 33.1962 1.41292
\(553\) −38.9389 −1.65585
\(554\) 2.59993 0.110460
\(555\) 8.22130 0.348975
\(556\) 3.92836 0.166600
\(557\) −22.3816 −0.948340 −0.474170 0.880433i \(-0.657252\pi\)
−0.474170 + 0.880433i \(0.657252\pi\)
\(558\) −5.88157 −0.248987
\(559\) −2.32350 −0.0982738
\(560\) −33.9120 −1.43304
\(561\) −19.3114 −0.815328
\(562\) −26.8719 −1.13352
\(563\) 24.7258 1.04207 0.521035 0.853535i \(-0.325546\pi\)
0.521035 + 0.853535i \(0.325546\pi\)
\(564\) 25.5551 1.07607
\(565\) −21.2897 −0.895666
\(566\) 5.95872 0.250464
\(567\) −17.6916 −0.742975
\(568\) −3.76637 −0.158033
\(569\) −23.1811 −0.971801 −0.485900 0.874014i \(-0.661508\pi\)
−0.485900 + 0.874014i \(0.661508\pi\)
\(570\) 30.1467 1.26271
\(571\) 14.8743 0.622472 0.311236 0.950333i \(-0.399257\pi\)
0.311236 + 0.950333i \(0.399257\pi\)
\(572\) 15.3810 0.643114
\(573\) 14.6922 0.613775
\(574\) −82.7873 −3.45548
\(575\) −11.5766 −0.482778
\(576\) −5.46227 −0.227595
\(577\) 17.8376 0.742591 0.371295 0.928515i \(-0.378914\pi\)
0.371295 + 0.928515i \(0.378914\pi\)
\(578\) −3.81567 −0.158711
\(579\) −14.9915 −0.623024
\(580\) 5.55355 0.230598
\(581\) −17.0517 −0.707424
\(582\) −49.0362 −2.03262
\(583\) −36.4981 −1.51160
\(584\) −97.3067 −4.02658
\(585\) 1.08021 0.0446613
\(586\) −44.0575 −1.82000
\(587\) −33.7389 −1.39255 −0.696276 0.717774i \(-0.745161\pi\)
−0.696276 + 0.717774i \(0.745161\pi\)
\(588\) −21.6168 −0.891460
\(589\) 17.4625 0.719528
\(590\) 21.6183 0.890011
\(591\) 8.50993 0.350052
\(592\) 44.2604 1.81909
\(593\) −13.0912 −0.537590 −0.268795 0.963197i \(-0.586625\pi\)
−0.268795 + 0.963197i \(0.586625\pi\)
\(594\) −45.3934 −1.86251
\(595\) −15.9537 −0.654036
\(596\) −33.3826 −1.36741
\(597\) 1.84764 0.0756188
\(598\) −8.65053 −0.353746
\(599\) −2.02815 −0.0828678 −0.0414339 0.999141i \(-0.513193\pi\)
−0.0414339 + 0.999141i \(0.513193\pi\)
\(600\) −37.9637 −1.54986
\(601\) 26.4789 1.08010 0.540048 0.841634i \(-0.318406\pi\)
0.540048 + 0.841634i \(0.318406\pi\)
\(602\) 18.3794 0.749089
\(603\) 8.40509 0.342282
\(604\) 21.3023 0.866778
\(605\) 1.69285 0.0688241
\(606\) −22.6614 −0.920557
\(607\) −15.0367 −0.610323 −0.305161 0.952301i \(-0.598710\pi\)
−0.305161 + 0.952301i \(0.598710\pi\)
\(608\) 64.2375 2.60517
\(609\) 4.62683 0.187489
\(610\) 6.20625 0.251284
\(611\) −3.86109 −0.156203
\(612\) −18.1076 −0.731954
\(613\) 36.8835 1.48971 0.744856 0.667225i \(-0.232518\pi\)
0.744856 + 0.667225i \(0.232518\pi\)
\(614\) −39.1468 −1.57984
\(615\) 16.9812 0.684748
\(616\) −70.5426 −2.84224
\(617\) −44.6051 −1.79573 −0.897866 0.440268i \(-0.854883\pi\)
−0.897866 + 0.440268i \(0.854883\pi\)
\(618\) −59.6143 −2.39804
\(619\) −9.59984 −0.385850 −0.192925 0.981213i \(-0.561797\pi\)
−0.192925 + 0.981213i \(0.561797\pi\)
\(620\) 14.1913 0.569935
\(621\) 17.9763 0.721363
\(622\) −27.2397 −1.09221
\(623\) −45.0428 −1.80460
\(624\) −13.8917 −0.556113
\(625\) 6.43205 0.257282
\(626\) −45.6154 −1.82316
\(627\) 30.7088 1.22639
\(628\) −69.2854 −2.76479
\(629\) 20.8220 0.830227
\(630\) −8.54473 −0.340430
\(631\) −32.9749 −1.31271 −0.656355 0.754452i \(-0.727903\pi\)
−0.656355 + 0.754452i \(0.727903\pi\)
\(632\) 87.8086 3.49284
\(633\) −35.9760 −1.42992
\(634\) −63.6155 −2.52649
\(635\) −6.97657 −0.276857
\(636\) 81.7499 3.24159
\(637\) 3.26604 0.129405
\(638\) 8.03422 0.318078
\(639\) −0.464722 −0.0183841
\(640\) −3.21859 −0.127226
\(641\) −2.81895 −0.111342 −0.0556709 0.998449i \(-0.517730\pi\)
−0.0556709 + 0.998449i \(0.517730\pi\)
\(642\) 42.8694 1.69192
\(643\) −18.3449 −0.723454 −0.361727 0.932284i \(-0.617813\pi\)
−0.361727 + 0.932284i \(0.617813\pi\)
\(644\) 48.1816 1.89862
\(645\) −3.76996 −0.148442
\(646\) 76.3521 3.00403
\(647\) −15.3799 −0.604647 −0.302323 0.953205i \(-0.597762\pi\)
−0.302323 + 0.953205i \(0.597762\pi\)
\(648\) 39.8951 1.56723
\(649\) 22.0214 0.864416
\(650\) 9.89288 0.388031
\(651\) 11.8232 0.463387
\(652\) −60.6513 −2.37529
\(653\) −40.2577 −1.57540 −0.787702 0.616057i \(-0.788729\pi\)
−0.787702 + 0.616057i \(0.788729\pi\)
\(654\) 36.8023 1.43908
\(655\) −3.49270 −0.136471
\(656\) 91.4204 3.56937
\(657\) −12.0064 −0.468414
\(658\) 30.5420 1.19065
\(659\) 39.0552 1.52138 0.760688 0.649118i \(-0.224862\pi\)
0.760688 + 0.649118i \(0.224862\pi\)
\(660\) 24.9562 0.971420
\(661\) 40.8793 1.59002 0.795010 0.606596i \(-0.207465\pi\)
0.795010 + 0.606596i \(0.207465\pi\)
\(662\) −61.1420 −2.37635
\(663\) −6.53525 −0.253808
\(664\) 38.4523 1.49224
\(665\) 25.3694 0.983782
\(666\) 11.1522 0.432138
\(667\) −3.18164 −0.123194
\(668\) −55.4443 −2.14521
\(669\) 20.1212 0.777932
\(670\) −28.8018 −1.11271
\(671\) 6.32197 0.244057
\(672\) 43.4928 1.67777
\(673\) −36.2824 −1.39858 −0.699292 0.714836i \(-0.746501\pi\)
−0.699292 + 0.714836i \(0.746501\pi\)
\(674\) 22.6523 0.872534
\(675\) −20.5579 −0.791276
\(676\) −56.6700 −2.17961
\(677\) 13.7005 0.526553 0.263277 0.964720i \(-0.415197\pi\)
0.263277 + 0.964720i \(0.415197\pi\)
\(678\) 68.9859 2.64939
\(679\) −41.2655 −1.58362
\(680\) 35.9761 1.37962
\(681\) 14.9357 0.572337
\(682\) 20.5303 0.786144
\(683\) 11.0145 0.421459 0.210730 0.977544i \(-0.432416\pi\)
0.210730 + 0.977544i \(0.432416\pi\)
\(684\) 28.7945 1.10098
\(685\) 24.6989 0.943698
\(686\) 32.0700 1.22444
\(687\) 11.1620 0.425857
\(688\) −20.2960 −0.773779
\(689\) −12.3515 −0.470553
\(690\) −14.0358 −0.534332
\(691\) −8.43574 −0.320911 −0.160455 0.987043i \(-0.551296\pi\)
−0.160455 + 0.987043i \(0.551296\pi\)
\(692\) −12.6805 −0.482040
\(693\) −8.70406 −0.330640
\(694\) −42.2812 −1.60497
\(695\) −0.963021 −0.0365295
\(696\) −10.4337 −0.395488
\(697\) 43.0081 1.62905
\(698\) 10.2614 0.388399
\(699\) 0.115787 0.00437947
\(700\) −55.1012 −2.08263
\(701\) −38.9674 −1.47178 −0.735889 0.677102i \(-0.763236\pi\)
−0.735889 + 0.677102i \(0.763236\pi\)
\(702\) −15.3617 −0.579792
\(703\) −33.1109 −1.24880
\(704\) 19.0666 0.718601
\(705\) −6.26474 −0.235944
\(706\) 47.8290 1.80007
\(707\) −19.0703 −0.717212
\(708\) −49.3244 −1.85372
\(709\) −11.3186 −0.425079 −0.212539 0.977152i \(-0.568173\pi\)
−0.212539 + 0.977152i \(0.568173\pi\)
\(710\) 1.59247 0.0597642
\(711\) 10.8345 0.406324
\(712\) 101.573 3.80662
\(713\) −8.13020 −0.304478
\(714\) 51.6952 1.93465
\(715\) −3.77060 −0.141012
\(716\) 27.0917 1.01247
\(717\) −3.32728 −0.124260
\(718\) −64.5004 −2.40713
\(719\) 5.63486 0.210145 0.105072 0.994465i \(-0.466493\pi\)
0.105072 + 0.994465i \(0.466493\pi\)
\(720\) 9.43577 0.351651
\(721\) −50.1673 −1.86833
\(722\) −72.0159 −2.68015
\(723\) −17.8690 −0.664557
\(724\) −30.1393 −1.12012
\(725\) 3.63857 0.135133
\(726\) −5.48540 −0.203582
\(727\) −3.75437 −0.139242 −0.0696210 0.997574i \(-0.522179\pi\)
−0.0696210 + 0.997574i \(0.522179\pi\)
\(728\) −23.8726 −0.884777
\(729\) 29.5714 1.09524
\(730\) 41.1424 1.52275
\(731\) −9.54813 −0.353150
\(732\) −14.1602 −0.523376
\(733\) −21.2979 −0.786655 −0.393327 0.919399i \(-0.628676\pi\)
−0.393327 + 0.919399i \(0.628676\pi\)
\(734\) −69.2386 −2.55564
\(735\) 5.29926 0.195466
\(736\) −29.9078 −1.10242
\(737\) −29.3389 −1.08071
\(738\) 23.0350 0.847929
\(739\) −10.8813 −0.400274 −0.200137 0.979768i \(-0.564139\pi\)
−0.200137 + 0.979768i \(0.564139\pi\)
\(740\) −26.9084 −0.989171
\(741\) 10.3923 0.381770
\(742\) 97.7028 3.58678
\(743\) 25.5938 0.938945 0.469472 0.882947i \(-0.344444\pi\)
0.469472 + 0.882947i \(0.344444\pi\)
\(744\) −26.6617 −0.977467
\(745\) 8.18362 0.299825
\(746\) −9.19857 −0.336783
\(747\) 4.74452 0.173593
\(748\) 63.2063 2.31105
\(749\) 36.0760 1.31819
\(750\) 38.1089 1.39154
\(751\) −8.97244 −0.327409 −0.163705 0.986509i \(-0.552344\pi\)
−0.163705 + 0.986509i \(0.552344\pi\)
\(752\) −33.7270 −1.22990
\(753\) −39.9796 −1.45694
\(754\) 2.71889 0.0990162
\(755\) −5.22217 −0.190054
\(756\) 85.5617 3.11185
\(757\) −42.7727 −1.55460 −0.777301 0.629129i \(-0.783412\pi\)
−0.777301 + 0.629129i \(0.783412\pi\)
\(758\) 0.148219 0.00538357
\(759\) −14.2975 −0.518966
\(760\) −57.2089 −2.07518
\(761\) 29.8120 1.08068 0.540342 0.841446i \(-0.318295\pi\)
0.540342 + 0.841446i \(0.318295\pi\)
\(762\) 22.6064 0.818944
\(763\) 30.9703 1.12120
\(764\) −48.0876 −1.73975
\(765\) 4.43899 0.160492
\(766\) −8.11322 −0.293143
\(767\) 7.45234 0.269089
\(768\) 28.3745 1.02388
\(769\) 14.5679 0.525333 0.262666 0.964887i \(-0.415398\pi\)
0.262666 + 0.964887i \(0.415398\pi\)
\(770\) 29.8263 1.07486
\(771\) 6.74697 0.242986
\(772\) 49.0671 1.76597
\(773\) −25.5344 −0.918409 −0.459204 0.888331i \(-0.651865\pi\)
−0.459204 + 0.888331i \(0.651865\pi\)
\(774\) −5.11394 −0.183817
\(775\) 9.29783 0.333988
\(776\) 93.0552 3.34049
\(777\) −22.4182 −0.804248
\(778\) 6.03292 0.216290
\(779\) −68.3911 −2.45036
\(780\) 8.44553 0.302399
\(781\) 1.62216 0.0580455
\(782\) −35.5482 −1.27120
\(783\) −5.65000 −0.201915
\(784\) 28.5292 1.01890
\(785\) 16.9850 0.606222
\(786\) 11.3175 0.403683
\(787\) 17.7630 0.633182 0.316591 0.948562i \(-0.397462\pi\)
0.316591 + 0.948562i \(0.397462\pi\)
\(788\) −27.8531 −0.992224
\(789\) 40.7033 1.44907
\(790\) −37.1265 −1.32090
\(791\) 58.0537 2.06415
\(792\) 19.6280 0.697450
\(793\) 2.13944 0.0759739
\(794\) 59.1777 2.10014
\(795\) −20.0407 −0.710769
\(796\) −6.04733 −0.214342
\(797\) −16.4074 −0.581179 −0.290589 0.956848i \(-0.593851\pi\)
−0.290589 + 0.956848i \(0.593851\pi\)
\(798\) −82.2053 −2.91004
\(799\) −15.8666 −0.561321
\(800\) 34.2030 1.20926
\(801\) 12.5328 0.442826
\(802\) −14.8357 −0.523867
\(803\) 41.9096 1.47896
\(804\) 65.7143 2.31756
\(805\) −11.8115 −0.416301
\(806\) 6.94772 0.244723
\(807\) −31.7206 −1.11662
\(808\) 43.0042 1.51288
\(809\) −51.6436 −1.81569 −0.907846 0.419303i \(-0.862274\pi\)
−0.907846 + 0.419303i \(0.862274\pi\)
\(810\) −16.8681 −0.592686
\(811\) −15.4385 −0.542119 −0.271060 0.962563i \(-0.587374\pi\)
−0.271060 + 0.962563i \(0.587374\pi\)
\(812\) −15.1436 −0.531438
\(813\) 41.7016 1.46254
\(814\) −38.9279 −1.36442
\(815\) 14.8684 0.520818
\(816\) −57.0860 −1.99841
\(817\) 15.1833 0.531198
\(818\) 16.3747 0.572528
\(819\) −2.94557 −0.102927
\(820\) −55.5796 −1.94092
\(821\) −27.7562 −0.968697 −0.484349 0.874875i \(-0.660943\pi\)
−0.484349 + 0.874875i \(0.660943\pi\)
\(822\) −80.0329 −2.79147
\(823\) −13.2744 −0.462717 −0.231358 0.972869i \(-0.574317\pi\)
−0.231358 + 0.972869i \(0.574317\pi\)
\(824\) 113.129 3.94104
\(825\) 16.3508 0.569263
\(826\) −58.9497 −2.05112
\(827\) 18.7618 0.652411 0.326206 0.945299i \(-0.394230\pi\)
0.326206 + 0.945299i \(0.394230\pi\)
\(828\) −13.4062 −0.465897
\(829\) −25.3072 −0.878955 −0.439477 0.898254i \(-0.644836\pi\)
−0.439477 + 0.898254i \(0.644836\pi\)
\(830\) −16.2581 −0.564326
\(831\) 1.45421 0.0504459
\(832\) 6.45241 0.223697
\(833\) 13.4214 0.465023
\(834\) 3.12051 0.108054
\(835\) 13.5920 0.470369
\(836\) −100.510 −3.47622
\(837\) −14.4377 −0.499041
\(838\) 32.8929 1.13627
\(839\) −32.6367 −1.12674 −0.563371 0.826204i \(-0.690496\pi\)
−0.563371 + 0.826204i \(0.690496\pi\)
\(840\) −38.7340 −1.33645
\(841\) 1.00000 0.0344828
\(842\) 49.6032 1.70944
\(843\) −15.0302 −0.517666
\(844\) 117.750 4.05311
\(845\) 13.8924 0.477914
\(846\) −8.49811 −0.292171
\(847\) −4.61614 −0.158612
\(848\) −107.891 −3.70500
\(849\) 3.33286 0.114384
\(850\) 40.6535 1.39440
\(851\) 15.4159 0.528449
\(852\) −3.63338 −0.124477
\(853\) −14.3527 −0.491427 −0.245713 0.969343i \(-0.579022\pi\)
−0.245713 + 0.969343i \(0.579022\pi\)
\(854\) −16.9235 −0.579109
\(855\) −7.05885 −0.241407
\(856\) −81.3527 −2.78058
\(857\) −58.2887 −1.99111 −0.995553 0.0942080i \(-0.969968\pi\)
−0.995553 + 0.0942080i \(0.969968\pi\)
\(858\) 12.2180 0.417116
\(859\) −37.0161 −1.26297 −0.631486 0.775387i \(-0.717555\pi\)
−0.631486 + 0.775387i \(0.717555\pi\)
\(860\) 12.3391 0.420760
\(861\) −46.3051 −1.57807
\(862\) −72.5696 −2.47173
\(863\) −52.5341 −1.78828 −0.894141 0.447786i \(-0.852213\pi\)
−0.894141 + 0.447786i \(0.852213\pi\)
\(864\) −53.1108 −1.80687
\(865\) 3.10857 0.105695
\(866\) 52.7730 1.79330
\(867\) −2.13420 −0.0724813
\(868\) −38.6973 −1.31347
\(869\) −37.8188 −1.28292
\(870\) 4.41149 0.149563
\(871\) −9.92867 −0.336420
\(872\) −69.8392 −2.36505
\(873\) 11.4818 0.388601
\(874\) 56.5284 1.91210
\(875\) 32.0699 1.08416
\(876\) −93.8707 −3.17160
\(877\) −16.9002 −0.570678 −0.285339 0.958427i \(-0.592106\pi\)
−0.285339 + 0.958427i \(0.592106\pi\)
\(878\) 18.1180 0.611453
\(879\) −24.6425 −0.831172
\(880\) −32.9366 −1.11029
\(881\) 13.3438 0.449564 0.224782 0.974409i \(-0.427833\pi\)
0.224782 + 0.974409i \(0.427833\pi\)
\(882\) 7.18844 0.242047
\(883\) 17.8576 0.600957 0.300478 0.953789i \(-0.402854\pi\)
0.300478 + 0.953789i \(0.402854\pi\)
\(884\) 21.3899 0.719420
\(885\) 12.0917 0.406457
\(886\) −79.0057 −2.65425
\(887\) −36.5187 −1.22618 −0.613088 0.790014i \(-0.710073\pi\)
−0.613088 + 0.790014i \(0.710073\pi\)
\(888\) 50.5539 1.69648
\(889\) 19.0240 0.638045
\(890\) −42.9464 −1.43957
\(891\) −17.1827 −0.575641
\(892\) −65.8569 −2.20505
\(893\) 25.2310 0.844322
\(894\) −26.5177 −0.886884
\(895\) −6.64143 −0.221998
\(896\) 8.77660 0.293206
\(897\) −4.83846 −0.161552
\(898\) −50.9186 −1.69917
\(899\) 2.55535 0.0852257
\(900\) 15.3315 0.511051
\(901\) −50.7567 −1.69095
\(902\) −80.4060 −2.67723
\(903\) 10.2801 0.342100
\(904\) −130.913 −4.35412
\(905\) 7.38852 0.245603
\(906\) 16.9216 0.562182
\(907\) −7.04560 −0.233945 −0.116973 0.993135i \(-0.537319\pi\)
−0.116973 + 0.993135i \(0.537319\pi\)
\(908\) −48.8846 −1.62229
\(909\) 5.30617 0.175995
\(910\) 10.0936 0.334600
\(911\) −6.57859 −0.217958 −0.108979 0.994044i \(-0.534758\pi\)
−0.108979 + 0.994044i \(0.534758\pi\)
\(912\) 90.7777 3.00595
\(913\) −16.5612 −0.548097
\(914\) 27.9027 0.922940
\(915\) 3.47131 0.114758
\(916\) −36.5333 −1.20709
\(917\) 9.52405 0.314512
\(918\) −63.1270 −2.08350
\(919\) −34.0885 −1.12448 −0.562239 0.826975i \(-0.690060\pi\)
−0.562239 + 0.826975i \(0.690060\pi\)
\(920\) 26.6354 0.878144
\(921\) −21.8958 −0.721493
\(922\) −103.274 −3.40115
\(923\) 0.548962 0.0180693
\(924\) −68.0517 −2.23874
\(925\) −17.6298 −0.579665
\(926\) −3.98348 −0.130905
\(927\) 13.9587 0.458463
\(928\) 9.40013 0.308574
\(929\) 18.3288 0.601347 0.300674 0.953727i \(-0.402789\pi\)
0.300674 + 0.953727i \(0.402789\pi\)
\(930\) 11.2729 0.369653
\(931\) −21.3425 −0.699473
\(932\) −0.378971 −0.0124136
\(933\) −15.2359 −0.498800
\(934\) −72.1383 −2.36044
\(935\) −15.4948 −0.506733
\(936\) 6.64238 0.217113
\(937\) −3.22158 −0.105244 −0.0526222 0.998614i \(-0.516758\pi\)
−0.0526222 + 0.998614i \(0.516758\pi\)
\(938\) 78.5380 2.56436
\(939\) −25.5139 −0.832613
\(940\) 20.5045 0.668784
\(941\) 39.5939 1.29072 0.645362 0.763877i \(-0.276707\pi\)
0.645362 + 0.763877i \(0.276707\pi\)
\(942\) −55.0372 −1.79321
\(943\) 31.8417 1.03691
\(944\) 65.0970 2.11873
\(945\) −20.9751 −0.682320
\(946\) 17.8508 0.580378
\(947\) 14.8190 0.481552 0.240776 0.970581i \(-0.422598\pi\)
0.240776 + 0.970581i \(0.422598\pi\)
\(948\) 84.7081 2.75119
\(949\) 14.1828 0.460393
\(950\) −64.6468 −2.09742
\(951\) −35.5818 −1.15382
\(952\) −98.1012 −3.17948
\(953\) −38.5610 −1.24911 −0.624556 0.780980i \(-0.714720\pi\)
−0.624556 + 0.780980i \(0.714720\pi\)
\(954\) −27.1851 −0.880150
\(955\) 11.7885 0.381466
\(956\) 10.8902 0.352214
\(957\) 4.49375 0.145262
\(958\) 22.2417 0.718598
\(959\) −67.3501 −2.17485
\(960\) 10.4692 0.337893
\(961\) −24.4702 −0.789361
\(962\) −13.1737 −0.424738
\(963\) −10.0379 −0.323466
\(964\) 58.4854 1.88369
\(965\) −12.0286 −0.387215
\(966\) 38.2733 1.23142
\(967\) −18.0298 −0.579798 −0.289899 0.957057i \(-0.593622\pi\)
−0.289899 + 0.957057i \(0.593622\pi\)
\(968\) 10.4096 0.334576
\(969\) 42.7057 1.37191
\(970\) −39.3449 −1.26329
\(971\) 12.7974 0.410688 0.205344 0.978690i \(-0.434169\pi\)
0.205344 + 0.978690i \(0.434169\pi\)
\(972\) −42.1893 −1.35322
\(973\) 2.62601 0.0841859
\(974\) 96.2249 3.08324
\(975\) 5.53334 0.177209
\(976\) 18.6883 0.598196
\(977\) −26.6219 −0.851711 −0.425855 0.904791i \(-0.640027\pi\)
−0.425855 + 0.904791i \(0.640027\pi\)
\(978\) −48.1787 −1.54058
\(979\) −43.7472 −1.39817
\(980\) −17.3445 −0.554050
\(981\) −8.61726 −0.275128
\(982\) 1.88471 0.0601434
\(983\) 6.85150 0.218529 0.109264 0.994013i \(-0.465150\pi\)
0.109264 + 0.994013i \(0.465150\pi\)
\(984\) 104.420 3.32878
\(985\) 6.82806 0.217560
\(986\) 11.1729 0.355818
\(987\) 17.0830 0.543757
\(988\) −34.0140 −1.08213
\(989\) −7.06909 −0.224784
\(990\) −8.29895 −0.263758
\(991\) 56.5802 1.79733 0.898665 0.438636i \(-0.144538\pi\)
0.898665 + 0.438636i \(0.144538\pi\)
\(992\) 24.0206 0.762656
\(993\) −34.1983 −1.08525
\(994\) −4.34241 −0.137733
\(995\) 1.48248 0.0469977
\(996\) 37.0945 1.17538
\(997\) 45.0507 1.42677 0.713385 0.700773i \(-0.247161\pi\)
0.713385 + 0.700773i \(0.247161\pi\)
\(998\) 96.8483 3.06568
\(999\) 27.3757 0.866130
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 8033.2.a.b.1.8 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8033.2.a.b.1.8 153 1.1 even 1 trivial