Properties

Label 983.2.a.b.1.15
Level $983$
Weight $2$
Character 983.1
Self dual yes
Analytic conductor $7.849$
Analytic rank $0$
Dimension $54$
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] = [983,2,Mod(1,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, 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("983.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 983.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: \(7.84929451869\)
Analytic rank: \(0\)
Dimension: \(54\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 983.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.45073 q^{2} +1.34954 q^{3} +0.104610 q^{4} +3.00144 q^{5} -1.95782 q^{6} -1.88776 q^{7} +2.74969 q^{8} -1.17873 q^{9} +O(q^{10})\) \(q-1.45073 q^{2} +1.34954 q^{3} +0.104610 q^{4} +3.00144 q^{5} -1.95782 q^{6} -1.88776 q^{7} +2.74969 q^{8} -1.17873 q^{9} -4.35427 q^{10} +3.71907 q^{11} +0.141176 q^{12} +2.53528 q^{13} +2.73863 q^{14} +4.05057 q^{15} -4.19828 q^{16} +3.78744 q^{17} +1.71002 q^{18} -6.83647 q^{19} +0.313982 q^{20} -2.54762 q^{21} -5.39535 q^{22} +3.18416 q^{23} +3.71083 q^{24} +4.00862 q^{25} -3.67800 q^{26} -5.63938 q^{27} -0.197480 q^{28} +8.32393 q^{29} -5.87627 q^{30} +3.36062 q^{31} +0.591169 q^{32} +5.01904 q^{33} -5.49454 q^{34} -5.66600 q^{35} -0.123308 q^{36} +7.28659 q^{37} +9.91785 q^{38} +3.42147 q^{39} +8.25303 q^{40} +9.17250 q^{41} +3.69590 q^{42} -9.55198 q^{43} +0.389054 q^{44} -3.53789 q^{45} -4.61936 q^{46} -0.876620 q^{47} -5.66576 q^{48} -3.43635 q^{49} -5.81542 q^{50} +5.11131 q^{51} +0.265217 q^{52} -0.975272 q^{53} +8.18121 q^{54} +11.1625 q^{55} -5.19077 q^{56} -9.22611 q^{57} -12.0758 q^{58} -5.04391 q^{59} +0.423732 q^{60} -2.70474 q^{61} -4.87535 q^{62} +2.22517 q^{63} +7.53893 q^{64} +7.60948 q^{65} -7.28126 q^{66} -14.7687 q^{67} +0.396205 q^{68} +4.29717 q^{69} +8.21982 q^{70} +14.7189 q^{71} -3.24116 q^{72} +0.866554 q^{73} -10.5709 q^{74} +5.40981 q^{75} -0.715166 q^{76} -7.02072 q^{77} -4.96362 q^{78} +17.3763 q^{79} -12.6009 q^{80} -4.07439 q^{81} -13.3068 q^{82} +0.894889 q^{83} -0.266507 q^{84} +11.3677 q^{85} +13.8573 q^{86} +11.2335 q^{87} +10.2263 q^{88} +8.23898 q^{89} +5.13252 q^{90} -4.78600 q^{91} +0.333097 q^{92} +4.53531 q^{93} +1.27174 q^{94} -20.5192 q^{95} +0.797809 q^{96} -1.04131 q^{97} +4.98521 q^{98} -4.38379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45073 −1.02582 −0.512910 0.858443i \(-0.671432\pi\)
−0.512910 + 0.858443i \(0.671432\pi\)
\(3\) 1.34954 0.779159 0.389580 0.920993i \(-0.372620\pi\)
0.389580 + 0.920993i \(0.372620\pi\)
\(4\) 0.104610 0.0523052
\(5\) 3.00144 1.34228 0.671142 0.741329i \(-0.265804\pi\)
0.671142 + 0.741329i \(0.265804\pi\)
\(6\) −1.95782 −0.799276
\(7\) −1.88776 −0.713507 −0.356754 0.934199i \(-0.616116\pi\)
−0.356754 + 0.934199i \(0.616116\pi\)
\(8\) 2.74969 0.972164
\(9\) −1.17873 −0.392911
\(10\) −4.35427 −1.37694
\(11\) 3.71907 1.12134 0.560671 0.828039i \(-0.310543\pi\)
0.560671 + 0.828039i \(0.310543\pi\)
\(12\) 0.141176 0.0407541
\(13\) 2.53528 0.703160 0.351580 0.936158i \(-0.385645\pi\)
0.351580 + 0.936158i \(0.385645\pi\)
\(14\) 2.73863 0.731929
\(15\) 4.05057 1.04585
\(16\) −4.19828 −1.04957
\(17\) 3.78744 0.918588 0.459294 0.888284i \(-0.348102\pi\)
0.459294 + 0.888284i \(0.348102\pi\)
\(18\) 1.71002 0.403056
\(19\) −6.83647 −1.56839 −0.784197 0.620512i \(-0.786925\pi\)
−0.784197 + 0.620512i \(0.786925\pi\)
\(20\) 0.313982 0.0702084
\(21\) −2.54762 −0.555936
\(22\) −5.39535 −1.15029
\(23\) 3.18416 0.663944 0.331972 0.943289i \(-0.392286\pi\)
0.331972 + 0.943289i \(0.392286\pi\)
\(24\) 3.71083 0.757470
\(25\) 4.00862 0.801724
\(26\) −3.67800 −0.721315
\(27\) −5.63938 −1.08530
\(28\) −0.197480 −0.0373202
\(29\) 8.32393 1.54572 0.772858 0.634580i \(-0.218827\pi\)
0.772858 + 0.634580i \(0.218827\pi\)
\(30\) −5.87627 −1.07286
\(31\) 3.36062 0.603586 0.301793 0.953373i \(-0.402415\pi\)
0.301793 + 0.953373i \(0.402415\pi\)
\(32\) 0.591169 0.104505
\(33\) 5.01904 0.873703
\(34\) −5.49454 −0.942305
\(35\) −5.66600 −0.957729
\(36\) −0.123308 −0.0205513
\(37\) 7.28659 1.19791 0.598954 0.800783i \(-0.295583\pi\)
0.598954 + 0.800783i \(0.295583\pi\)
\(38\) 9.91785 1.60889
\(39\) 3.42147 0.547873
\(40\) 8.25303 1.30492
\(41\) 9.17250 1.43250 0.716252 0.697842i \(-0.245856\pi\)
0.716252 + 0.697842i \(0.245856\pi\)
\(42\) 3.69590 0.570290
\(43\) −9.55198 −1.45666 −0.728332 0.685225i \(-0.759704\pi\)
−0.728332 + 0.685225i \(0.759704\pi\)
\(44\) 0.389054 0.0586520
\(45\) −3.53789 −0.527398
\(46\) −4.61936 −0.681087
\(47\) −0.876620 −0.127868 −0.0639341 0.997954i \(-0.520365\pi\)
−0.0639341 + 0.997954i \(0.520365\pi\)
\(48\) −5.66576 −0.817782
\(49\) −3.43635 −0.490908
\(50\) −5.81542 −0.822424
\(51\) 5.11131 0.715726
\(52\) 0.265217 0.0367789
\(53\) −0.975272 −0.133964 −0.0669819 0.997754i \(-0.521337\pi\)
−0.0669819 + 0.997754i \(0.521337\pi\)
\(54\) 8.18121 1.11332
\(55\) 11.1625 1.50516
\(56\) −5.19077 −0.693646
\(57\) −9.22611 −1.22203
\(58\) −12.0758 −1.58562
\(59\) −5.04391 −0.656662 −0.328331 0.944563i \(-0.606486\pi\)
−0.328331 + 0.944563i \(0.606486\pi\)
\(60\) 0.423732 0.0547036
\(61\) −2.70474 −0.346306 −0.173153 0.984895i \(-0.555396\pi\)
−0.173153 + 0.984895i \(0.555396\pi\)
\(62\) −4.87535 −0.619170
\(63\) 2.22517 0.280345
\(64\) 7.53893 0.942366
\(65\) 7.60948 0.943839
\(66\) −7.28126 −0.896262
\(67\) −14.7687 −1.80429 −0.902145 0.431434i \(-0.858008\pi\)
−0.902145 + 0.431434i \(0.858008\pi\)
\(68\) 0.396205 0.0480470
\(69\) 4.29717 0.517318
\(70\) 8.21982 0.982457
\(71\) 14.7189 1.74681 0.873407 0.486991i \(-0.161905\pi\)
0.873407 + 0.486991i \(0.161905\pi\)
\(72\) −3.24116 −0.381974
\(73\) 0.866554 0.101423 0.0507113 0.998713i \(-0.483851\pi\)
0.0507113 + 0.998713i \(0.483851\pi\)
\(74\) −10.5709 −1.22884
\(75\) 5.40981 0.624671
\(76\) −0.715166 −0.0820352
\(77\) −7.02072 −0.800085
\(78\) −4.96362 −0.562019
\(79\) 17.3763 1.95499 0.977495 0.210960i \(-0.0676591\pi\)
0.977495 + 0.210960i \(0.0676591\pi\)
\(80\) −12.6009 −1.40882
\(81\) −4.07439 −0.452710
\(82\) −13.3068 −1.46949
\(83\) 0.894889 0.0982269 0.0491134 0.998793i \(-0.484360\pi\)
0.0491134 + 0.998793i \(0.484360\pi\)
\(84\) −0.266507 −0.0290783
\(85\) 11.3677 1.23301
\(86\) 13.8573 1.49427
\(87\) 11.2335 1.20436
\(88\) 10.2263 1.09013
\(89\) 8.23898 0.873330 0.436665 0.899624i \(-0.356159\pi\)
0.436665 + 0.899624i \(0.356159\pi\)
\(90\) 5.13252 0.541015
\(91\) −4.78600 −0.501709
\(92\) 0.333097 0.0347278
\(93\) 4.53531 0.470289
\(94\) 1.27174 0.131170
\(95\) −20.5192 −2.10523
\(96\) 0.797809 0.0814260
\(97\) −1.04131 −0.105729 −0.0528643 0.998602i \(-0.516835\pi\)
−0.0528643 + 0.998602i \(0.516835\pi\)
\(98\) 4.98521 0.503582
\(99\) −4.38379 −0.440587
\(100\) 0.419344 0.0419344
\(101\) −7.70973 −0.767147 −0.383574 0.923510i \(-0.625307\pi\)
−0.383574 + 0.923510i \(0.625307\pi\)
\(102\) −7.41512 −0.734206
\(103\) 9.99278 0.984618 0.492309 0.870421i \(-0.336153\pi\)
0.492309 + 0.870421i \(0.336153\pi\)
\(104\) 6.97124 0.683586
\(105\) −7.64651 −0.746223
\(106\) 1.41485 0.137423
\(107\) 13.9840 1.35188 0.675941 0.736956i \(-0.263738\pi\)
0.675941 + 0.736956i \(0.263738\pi\)
\(108\) −0.589938 −0.0567668
\(109\) 3.47527 0.332870 0.166435 0.986052i \(-0.446774\pi\)
0.166435 + 0.986052i \(0.446774\pi\)
\(110\) −16.1938 −1.54402
\(111\) 9.83357 0.933361
\(112\) 7.92535 0.748875
\(113\) 19.1675 1.80313 0.901565 0.432643i \(-0.142419\pi\)
0.901565 + 0.432643i \(0.142419\pi\)
\(114\) 13.3846 1.25358
\(115\) 9.55707 0.891201
\(116\) 0.870770 0.0808490
\(117\) −2.98842 −0.276279
\(118\) 7.31735 0.673616
\(119\) −7.14978 −0.655419
\(120\) 11.1378 1.01674
\(121\) 2.83147 0.257406
\(122\) 3.92384 0.355248
\(123\) 12.3787 1.11615
\(124\) 0.351557 0.0315707
\(125\) −2.97556 −0.266142
\(126\) −3.22811 −0.287583
\(127\) 13.9984 1.24216 0.621078 0.783749i \(-0.286695\pi\)
0.621078 + 0.783749i \(0.286695\pi\)
\(128\) −12.1193 −1.07120
\(129\) −12.8908 −1.13497
\(130\) −11.0393 −0.968209
\(131\) −16.5816 −1.44874 −0.724372 0.689409i \(-0.757870\pi\)
−0.724372 + 0.689409i \(0.757870\pi\)
\(132\) 0.525045 0.0456993
\(133\) 12.9056 1.11906
\(134\) 21.4254 1.85087
\(135\) −16.9262 −1.45678
\(136\) 10.4143 0.893018
\(137\) −18.1996 −1.55489 −0.777447 0.628948i \(-0.783486\pi\)
−0.777447 + 0.628948i \(0.783486\pi\)
\(138\) −6.23402 −0.530675
\(139\) 2.55559 0.216763 0.108381 0.994109i \(-0.465433\pi\)
0.108381 + 0.994109i \(0.465433\pi\)
\(140\) −0.592723 −0.0500942
\(141\) −1.18304 −0.0996297
\(142\) −21.3531 −1.79192
\(143\) 9.42887 0.788482
\(144\) 4.94865 0.412387
\(145\) 24.9837 2.07479
\(146\) −1.25713 −0.104041
\(147\) −4.63751 −0.382495
\(148\) 0.762254 0.0626569
\(149\) −2.49663 −0.204532 −0.102266 0.994757i \(-0.532609\pi\)
−0.102266 + 0.994757i \(0.532609\pi\)
\(150\) −7.84816 −0.640799
\(151\) −12.5137 −1.01835 −0.509175 0.860663i \(-0.670049\pi\)
−0.509175 + 0.860663i \(0.670049\pi\)
\(152\) −18.7982 −1.52473
\(153\) −4.46438 −0.360923
\(154\) 10.1851 0.820743
\(155\) 10.0867 0.810183
\(156\) 0.357921 0.0286566
\(157\) −21.6510 −1.72793 −0.863967 0.503548i \(-0.832028\pi\)
−0.863967 + 0.503548i \(0.832028\pi\)
\(158\) −25.2083 −2.00547
\(159\) −1.31617 −0.104379
\(160\) 1.77436 0.140275
\(161\) −6.01095 −0.473729
\(162\) 5.91083 0.464399
\(163\) 16.8642 1.32091 0.660453 0.750867i \(-0.270364\pi\)
0.660453 + 0.750867i \(0.270364\pi\)
\(164\) 0.959540 0.0749275
\(165\) 15.0643 1.17276
\(166\) −1.29824 −0.100763
\(167\) 1.93831 0.149991 0.0749955 0.997184i \(-0.476106\pi\)
0.0749955 + 0.997184i \(0.476106\pi\)
\(168\) −7.00517 −0.540460
\(169\) −6.57237 −0.505567
\(170\) −16.4915 −1.26484
\(171\) 8.05837 0.616239
\(172\) −0.999237 −0.0761911
\(173\) −11.7282 −0.891682 −0.445841 0.895112i \(-0.647095\pi\)
−0.445841 + 0.895112i \(0.647095\pi\)
\(174\) −16.2968 −1.23545
\(175\) −7.56732 −0.572036
\(176\) −15.6137 −1.17693
\(177\) −6.80698 −0.511644
\(178\) −11.9525 −0.895879
\(179\) −4.38674 −0.327880 −0.163940 0.986470i \(-0.552420\pi\)
−0.163940 + 0.986470i \(0.552420\pi\)
\(180\) −0.370101 −0.0275857
\(181\) 7.45034 0.553780 0.276890 0.960902i \(-0.410696\pi\)
0.276890 + 0.960902i \(0.410696\pi\)
\(182\) 6.94319 0.514663
\(183\) −3.65016 −0.269828
\(184\) 8.75548 0.645462
\(185\) 21.8702 1.60793
\(186\) −6.57950 −0.482432
\(187\) 14.0857 1.03005
\(188\) −0.0917036 −0.00668818
\(189\) 10.6458 0.774369
\(190\) 29.7678 2.15958
\(191\) −8.59358 −0.621809 −0.310905 0.950441i \(-0.600632\pi\)
−0.310905 + 0.950441i \(0.600632\pi\)
\(192\) 10.1741 0.734253
\(193\) 10.9955 0.791471 0.395736 0.918364i \(-0.370490\pi\)
0.395736 + 0.918364i \(0.370490\pi\)
\(194\) 1.51065 0.108458
\(195\) 10.2693 0.735401
\(196\) −0.359479 −0.0256770
\(197\) 4.71964 0.336260 0.168130 0.985765i \(-0.446227\pi\)
0.168130 + 0.985765i \(0.446227\pi\)
\(198\) 6.35968 0.451963
\(199\) −14.3633 −1.01819 −0.509093 0.860712i \(-0.670019\pi\)
−0.509093 + 0.860712i \(0.670019\pi\)
\(200\) 11.0225 0.779407
\(201\) −19.9311 −1.40583
\(202\) 11.1847 0.786954
\(203\) −15.7136 −1.10288
\(204\) 0.534696 0.0374362
\(205\) 27.5307 1.92283
\(206\) −14.4968 −1.01004
\(207\) −3.75328 −0.260871
\(208\) −10.6438 −0.738015
\(209\) −25.4253 −1.75870
\(210\) 11.0930 0.765490
\(211\) −13.5723 −0.934353 −0.467177 0.884164i \(-0.654729\pi\)
−0.467177 + 0.884164i \(0.654729\pi\)
\(212\) −0.102024 −0.00700701
\(213\) 19.8638 1.36105
\(214\) −20.2869 −1.38679
\(215\) −28.6697 −1.95525
\(216\) −15.5066 −1.05509
\(217\) −6.34406 −0.430663
\(218\) −5.04167 −0.341465
\(219\) 1.16945 0.0790243
\(220\) 1.16772 0.0787276
\(221\) 9.60220 0.645914
\(222\) −14.2658 −0.957460
\(223\) −20.2102 −1.35338 −0.676689 0.736269i \(-0.736586\pi\)
−0.676689 + 0.736269i \(0.736586\pi\)
\(224\) −1.11599 −0.0745650
\(225\) −4.72509 −0.315006
\(226\) −27.8069 −1.84969
\(227\) −11.3411 −0.752733 −0.376367 0.926471i \(-0.622827\pi\)
−0.376367 + 0.926471i \(0.622827\pi\)
\(228\) −0.965148 −0.0639185
\(229\) −26.4406 −1.74724 −0.873622 0.486605i \(-0.838235\pi\)
−0.873622 + 0.486605i \(0.838235\pi\)
\(230\) −13.8647 −0.914211
\(231\) −9.47476 −0.623394
\(232\) 22.8883 1.50269
\(233\) 18.1239 1.18734 0.593668 0.804710i \(-0.297679\pi\)
0.593668 + 0.804710i \(0.297679\pi\)
\(234\) 4.33538 0.283412
\(235\) −2.63112 −0.171635
\(236\) −0.527646 −0.0343468
\(237\) 23.4501 1.52325
\(238\) 10.3724 0.672342
\(239\) −12.4814 −0.807355 −0.403678 0.914901i \(-0.632268\pi\)
−0.403678 + 0.914901i \(0.632268\pi\)
\(240\) −17.0054 −1.09769
\(241\) 27.2423 1.75483 0.877414 0.479734i \(-0.159267\pi\)
0.877414 + 0.479734i \(0.159267\pi\)
\(242\) −4.10769 −0.264052
\(243\) 11.4196 0.732566
\(244\) −0.282944 −0.0181136
\(245\) −10.3140 −0.658937
\(246\) −17.9581 −1.14497
\(247\) −17.3323 −1.10283
\(248\) 9.24069 0.586784
\(249\) 1.20769 0.0765344
\(250\) 4.31673 0.273014
\(251\) −6.05155 −0.381970 −0.190985 0.981593i \(-0.561168\pi\)
−0.190985 + 0.981593i \(0.561168\pi\)
\(252\) 0.232776 0.0146635
\(253\) 11.8421 0.744508
\(254\) −20.3078 −1.27423
\(255\) 15.3413 0.960707
\(256\) 2.50390 0.156494
\(257\) −4.35090 −0.271402 −0.135701 0.990750i \(-0.543329\pi\)
−0.135701 + 0.990750i \(0.543329\pi\)
\(258\) 18.7011 1.16428
\(259\) −13.7554 −0.854716
\(260\) 0.796031 0.0493677
\(261\) −9.81169 −0.607329
\(262\) 24.0554 1.48615
\(263\) 2.50475 0.154450 0.0772249 0.997014i \(-0.475394\pi\)
0.0772249 + 0.997014i \(0.475394\pi\)
\(264\) 13.8008 0.849383
\(265\) −2.92722 −0.179817
\(266\) −18.7226 −1.14795
\(267\) 11.1189 0.680463
\(268\) −1.54497 −0.0943738
\(269\) −22.2360 −1.35575 −0.677877 0.735175i \(-0.737100\pi\)
−0.677877 + 0.735175i \(0.737100\pi\)
\(270\) 24.5554 1.49439
\(271\) −26.7130 −1.62270 −0.811350 0.584560i \(-0.801267\pi\)
−0.811350 + 0.584560i \(0.801267\pi\)
\(272\) −15.9007 −0.964122
\(273\) −6.45892 −0.390911
\(274\) 26.4026 1.59504
\(275\) 14.9083 0.899006
\(276\) 0.449529 0.0270585
\(277\) −13.6054 −0.817470 −0.408735 0.912653i \(-0.634030\pi\)
−0.408735 + 0.912653i \(0.634030\pi\)
\(278\) −3.70747 −0.222359
\(279\) −3.96128 −0.237156
\(280\) −15.5798 −0.931069
\(281\) 15.6871 0.935812 0.467906 0.883778i \(-0.345008\pi\)
0.467906 + 0.883778i \(0.345008\pi\)
\(282\) 1.71626 0.102202
\(283\) −17.3203 −1.02958 −0.514792 0.857315i \(-0.672131\pi\)
−0.514792 + 0.857315i \(0.672131\pi\)
\(284\) 1.53975 0.0913675
\(285\) −27.6916 −1.64031
\(286\) −13.6787 −0.808840
\(287\) −17.3155 −1.02210
\(288\) −0.696831 −0.0410612
\(289\) −2.65533 −0.156196
\(290\) −36.2446 −2.12836
\(291\) −1.40529 −0.0823795
\(292\) 0.0906507 0.00530493
\(293\) −25.3088 −1.47856 −0.739278 0.673400i \(-0.764833\pi\)
−0.739278 + 0.673400i \(0.764833\pi\)
\(294\) 6.72776 0.392371
\(295\) −15.1390 −0.881426
\(296\) 20.0359 1.16456
\(297\) −20.9732 −1.21699
\(298\) 3.62194 0.209813
\(299\) 8.07274 0.466859
\(300\) 0.565922 0.0326735
\(301\) 18.0319 1.03934
\(302\) 18.1539 1.04464
\(303\) −10.4046 −0.597730
\(304\) 28.7014 1.64614
\(305\) −8.11810 −0.464841
\(306\) 6.47659 0.370242
\(307\) −23.1877 −1.32339 −0.661695 0.749773i \(-0.730163\pi\)
−0.661695 + 0.749773i \(0.730163\pi\)
\(308\) −0.734441 −0.0418486
\(309\) 13.4857 0.767174
\(310\) −14.6331 −0.831102
\(311\) 12.0104 0.681050 0.340525 0.940235i \(-0.389395\pi\)
0.340525 + 0.940235i \(0.389395\pi\)
\(312\) 9.40799 0.532622
\(313\) −22.6132 −1.27817 −0.639087 0.769135i \(-0.720688\pi\)
−0.639087 + 0.769135i \(0.720688\pi\)
\(314\) 31.4096 1.77255
\(315\) 6.67870 0.376302
\(316\) 1.81775 0.102256
\(317\) 12.8214 0.720122 0.360061 0.932929i \(-0.382756\pi\)
0.360061 + 0.932929i \(0.382756\pi\)
\(318\) 1.90941 0.107074
\(319\) 30.9573 1.73327
\(320\) 22.6276 1.26492
\(321\) 18.8720 1.05333
\(322\) 8.72025 0.485960
\(323\) −25.8927 −1.44071
\(324\) −0.426224 −0.0236791
\(325\) 10.1630 0.563740
\(326\) −24.4654 −1.35501
\(327\) 4.69002 0.259359
\(328\) 25.2216 1.39263
\(329\) 1.65485 0.0912349
\(330\) −21.8543 −1.20304
\(331\) −29.0189 −1.59502 −0.797512 0.603303i \(-0.793851\pi\)
−0.797512 + 0.603303i \(0.793851\pi\)
\(332\) 0.0936148 0.00513778
\(333\) −8.58895 −0.470671
\(334\) −2.81196 −0.153864
\(335\) −44.3274 −2.42187
\(336\) 10.6956 0.583493
\(337\) 10.1690 0.553940 0.276970 0.960879i \(-0.410670\pi\)
0.276970 + 0.960879i \(0.410670\pi\)
\(338\) 9.53471 0.518620
\(339\) 25.8674 1.40493
\(340\) 1.18919 0.0644926
\(341\) 12.4984 0.676826
\(342\) −11.6905 −0.632150
\(343\) 19.7014 1.06377
\(344\) −26.2650 −1.41611
\(345\) 12.8977 0.694388
\(346\) 17.0145 0.914705
\(347\) 3.37958 0.181426 0.0907128 0.995877i \(-0.471085\pi\)
0.0907128 + 0.995877i \(0.471085\pi\)
\(348\) 1.17514 0.0629942
\(349\) 11.1240 0.595453 0.297727 0.954651i \(-0.403772\pi\)
0.297727 + 0.954651i \(0.403772\pi\)
\(350\) 10.9781 0.586805
\(351\) −14.2974 −0.763139
\(352\) 2.19860 0.117186
\(353\) 12.2734 0.653245 0.326623 0.945155i \(-0.394089\pi\)
0.326623 + 0.945155i \(0.394089\pi\)
\(354\) 9.87507 0.524854
\(355\) 44.1779 2.34472
\(356\) 0.861884 0.0456797
\(357\) −9.64894 −0.510676
\(358\) 6.36396 0.336346
\(359\) 12.7857 0.674802 0.337401 0.941361i \(-0.390452\pi\)
0.337401 + 0.941361i \(0.390452\pi\)
\(360\) −9.72812 −0.512717
\(361\) 27.7373 1.45986
\(362\) −10.8084 −0.568078
\(363\) 3.82119 0.200560
\(364\) −0.500666 −0.0262420
\(365\) 2.60091 0.136138
\(366\) 5.29539 0.276794
\(367\) −16.8725 −0.880739 −0.440369 0.897817i \(-0.645152\pi\)
−0.440369 + 0.897817i \(0.645152\pi\)
\(368\) −13.3680 −0.696856
\(369\) −10.8119 −0.562847
\(370\) −31.7278 −1.64945
\(371\) 1.84108 0.0955842
\(372\) 0.474441 0.0245986
\(373\) 25.0777 1.29847 0.649236 0.760587i \(-0.275089\pi\)
0.649236 + 0.760587i \(0.275089\pi\)
\(374\) −20.4346 −1.05665
\(375\) −4.01565 −0.207367
\(376\) −2.41044 −0.124309
\(377\) 21.1035 1.08688
\(378\) −15.4442 −0.794363
\(379\) −20.7014 −1.06336 −0.531679 0.846946i \(-0.678439\pi\)
−0.531679 + 0.846946i \(0.678439\pi\)
\(380\) −2.14653 −0.110114
\(381\) 18.8914 0.967837
\(382\) 12.4669 0.637864
\(383\) −4.51458 −0.230684 −0.115342 0.993326i \(-0.536796\pi\)
−0.115342 + 0.993326i \(0.536796\pi\)
\(384\) −16.3555 −0.834637
\(385\) −21.0722 −1.07394
\(386\) −15.9514 −0.811907
\(387\) 11.2592 0.572339
\(388\) −0.108932 −0.00553016
\(389\) 5.10467 0.258817 0.129408 0.991591i \(-0.458692\pi\)
0.129408 + 0.991591i \(0.458692\pi\)
\(390\) −14.8980 −0.754389
\(391\) 12.0598 0.609891
\(392\) −9.44892 −0.477242
\(393\) −22.3776 −1.12880
\(394\) −6.84691 −0.344942
\(395\) 52.1539 2.62415
\(396\) −0.458590 −0.0230450
\(397\) −9.63939 −0.483787 −0.241893 0.970303i \(-0.577768\pi\)
−0.241893 + 0.970303i \(0.577768\pi\)
\(398\) 20.8372 1.04447
\(399\) 17.4167 0.871926
\(400\) −16.8293 −0.841465
\(401\) −31.9040 −1.59321 −0.796605 0.604500i \(-0.793373\pi\)
−0.796605 + 0.604500i \(0.793373\pi\)
\(402\) 28.9145 1.44213
\(403\) 8.52012 0.424417
\(404\) −0.806519 −0.0401258
\(405\) −12.2290 −0.607665
\(406\) 22.7962 1.13135
\(407\) 27.0993 1.34326
\(408\) 14.0545 0.695803
\(409\) −1.73766 −0.0859217 −0.0429609 0.999077i \(-0.513679\pi\)
−0.0429609 + 0.999077i \(0.513679\pi\)
\(410\) −39.9395 −1.97247
\(411\) −24.5611 −1.21151
\(412\) 1.04535 0.0515007
\(413\) 9.52171 0.468533
\(414\) 5.44499 0.267607
\(415\) 2.68595 0.131848
\(416\) 1.49878 0.0734837
\(417\) 3.44889 0.168893
\(418\) 36.8852 1.80411
\(419\) 14.5746 0.712015 0.356008 0.934483i \(-0.384138\pi\)
0.356008 + 0.934483i \(0.384138\pi\)
\(420\) −0.799905 −0.0390314
\(421\) −11.9750 −0.583624 −0.291812 0.956476i \(-0.594258\pi\)
−0.291812 + 0.956476i \(0.594258\pi\)
\(422\) 19.6897 0.958478
\(423\) 1.03330 0.0502408
\(424\) −2.68170 −0.130235
\(425\) 15.1824 0.736454
\(426\) −28.8170 −1.39619
\(427\) 5.10590 0.247092
\(428\) 1.46287 0.0707105
\(429\) 12.7247 0.614353
\(430\) 41.5919 2.00574
\(431\) −27.2432 −1.31226 −0.656128 0.754649i \(-0.727807\pi\)
−0.656128 + 0.754649i \(0.727807\pi\)
\(432\) 23.6757 1.13910
\(433\) 7.04691 0.338653 0.169326 0.985560i \(-0.445841\pi\)
0.169326 + 0.985560i \(0.445841\pi\)
\(434\) 9.20350 0.441782
\(435\) 33.7166 1.61659
\(436\) 0.363549 0.0174109
\(437\) −21.7684 −1.04133
\(438\) −1.69656 −0.0810646
\(439\) −3.95251 −0.188643 −0.0943214 0.995542i \(-0.530068\pi\)
−0.0943214 + 0.995542i \(0.530068\pi\)
\(440\) 30.6936 1.46326
\(441\) 4.05054 0.192883
\(442\) −13.9302 −0.662591
\(443\) 27.4494 1.30416 0.652080 0.758150i \(-0.273896\pi\)
0.652080 + 0.758150i \(0.273896\pi\)
\(444\) 1.02869 0.0488197
\(445\) 24.7288 1.17226
\(446\) 29.3195 1.38832
\(447\) −3.36932 −0.159363
\(448\) −14.2317 −0.672385
\(449\) −30.1810 −1.42433 −0.712166 0.702011i \(-0.752286\pi\)
−0.712166 + 0.702011i \(0.752286\pi\)
\(450\) 6.85482 0.323139
\(451\) 34.1132 1.60633
\(452\) 2.00513 0.0943132
\(453\) −16.8878 −0.793456
\(454\) 16.4528 0.772168
\(455\) −14.3649 −0.673436
\(456\) −25.3690 −1.18801
\(457\) −16.0684 −0.751648 −0.375824 0.926691i \(-0.622640\pi\)
−0.375824 + 0.926691i \(0.622640\pi\)
\(458\) 38.3581 1.79236
\(459\) −21.3588 −0.996943
\(460\) 0.999769 0.0466145
\(461\) 0.892613 0.0415731 0.0207866 0.999784i \(-0.493383\pi\)
0.0207866 + 0.999784i \(0.493383\pi\)
\(462\) 13.7453 0.639489
\(463\) 42.3928 1.97016 0.985081 0.172090i \(-0.0550519\pi\)
0.985081 + 0.172090i \(0.0550519\pi\)
\(464\) −34.9462 −1.62234
\(465\) 13.6124 0.631262
\(466\) −26.2928 −1.21799
\(467\) −32.4692 −1.50250 −0.751248 0.660020i \(-0.770548\pi\)
−0.751248 + 0.660020i \(0.770548\pi\)
\(468\) −0.312620 −0.0144508
\(469\) 27.8799 1.28737
\(470\) 3.81704 0.176067
\(471\) −29.2189 −1.34634
\(472\) −13.8692 −0.638383
\(473\) −35.5245 −1.63342
\(474\) −34.0197 −1.56258
\(475\) −27.4048 −1.25742
\(476\) −0.747942 −0.0342819
\(477\) 1.14959 0.0526359
\(478\) 18.1071 0.828200
\(479\) 14.1845 0.648106 0.324053 0.946039i \(-0.394954\pi\)
0.324053 + 0.946039i \(0.394954\pi\)
\(480\) 2.39457 0.109297
\(481\) 18.4735 0.842321
\(482\) −39.5211 −1.80014
\(483\) −8.11203 −0.369110
\(484\) 0.296201 0.0134637
\(485\) −3.12542 −0.141918
\(486\) −16.5667 −0.751481
\(487\) −23.8548 −1.08096 −0.540482 0.841356i \(-0.681758\pi\)
−0.540482 + 0.841356i \(0.681758\pi\)
\(488\) −7.43720 −0.336666
\(489\) 22.7590 1.02920
\(490\) 14.9628 0.675950
\(491\) 22.9375 1.03515 0.517576 0.855637i \(-0.326834\pi\)
0.517576 + 0.855637i \(0.326834\pi\)
\(492\) 1.29494 0.0583804
\(493\) 31.5264 1.41988
\(494\) 25.1445 1.13131
\(495\) −13.1577 −0.591393
\(496\) −14.1088 −0.633505
\(497\) −27.7858 −1.24636
\(498\) −1.75203 −0.0785104
\(499\) 22.1577 0.991917 0.495958 0.868346i \(-0.334817\pi\)
0.495958 + 0.868346i \(0.334817\pi\)
\(500\) −0.311275 −0.0139206
\(501\) 2.61583 0.116867
\(502\) 8.77915 0.391832
\(503\) 13.4364 0.599100 0.299550 0.954081i \(-0.403164\pi\)
0.299550 + 0.954081i \(0.403164\pi\)
\(504\) 6.11853 0.272541
\(505\) −23.1403 −1.02973
\(506\) −17.1797 −0.763731
\(507\) −8.86969 −0.393917
\(508\) 1.46438 0.0649712
\(509\) 4.24178 0.188014 0.0940068 0.995572i \(-0.470032\pi\)
0.0940068 + 0.995572i \(0.470032\pi\)
\(510\) −22.2560 −0.985512
\(511\) −1.63585 −0.0723657
\(512\) 20.6061 0.910668
\(513\) 38.5534 1.70218
\(514\) 6.31197 0.278409
\(515\) 29.9927 1.32164
\(516\) −1.34851 −0.0593650
\(517\) −3.26021 −0.143384
\(518\) 19.9553 0.876785
\(519\) −15.8278 −0.694762
\(520\) 20.9237 0.917566
\(521\) −0.576744 −0.0252676 −0.0126338 0.999920i \(-0.504022\pi\)
−0.0126338 + 0.999920i \(0.504022\pi\)
\(522\) 14.2341 0.623009
\(523\) −1.02123 −0.0446554 −0.0223277 0.999751i \(-0.507108\pi\)
−0.0223277 + 0.999751i \(0.507108\pi\)
\(524\) −1.73461 −0.0757769
\(525\) −10.2124 −0.445707
\(526\) −3.63372 −0.158438
\(527\) 12.7281 0.554447
\(528\) −21.0713 −0.917012
\(529\) −12.8611 −0.559178
\(530\) 4.24659 0.184460
\(531\) 5.94543 0.258010
\(532\) 1.35006 0.0585327
\(533\) 23.2548 1.00728
\(534\) −16.1304 −0.698032
\(535\) 41.9720 1.81461
\(536\) −40.6095 −1.75406
\(537\) −5.92009 −0.255471
\(538\) 32.2584 1.39076
\(539\) −12.7800 −0.550475
\(540\) −1.77066 −0.0761972
\(541\) −15.6894 −0.674539 −0.337269 0.941408i \(-0.609503\pi\)
−0.337269 + 0.941408i \(0.609503\pi\)
\(542\) 38.7533 1.66460
\(543\) 10.0546 0.431482
\(544\) 2.23902 0.0959970
\(545\) 10.4308 0.446806
\(546\) 9.37013 0.401005
\(547\) −11.2159 −0.479557 −0.239779 0.970828i \(-0.577075\pi\)
−0.239779 + 0.970828i \(0.577075\pi\)
\(548\) −1.90387 −0.0813292
\(549\) 3.18816 0.136068
\(550\) −21.6279 −0.922218
\(551\) −56.9063 −2.42429
\(552\) 11.8159 0.502918
\(553\) −32.8024 −1.39490
\(554\) 19.7377 0.838577
\(555\) 29.5148 1.25284
\(556\) 0.267342 0.0113378
\(557\) 14.3333 0.607322 0.303661 0.952780i \(-0.401791\pi\)
0.303661 + 0.952780i \(0.401791\pi\)
\(558\) 5.74674 0.243279
\(559\) −24.2169 −1.02427
\(560\) 23.7874 1.00520
\(561\) 19.0093 0.802573
\(562\) −22.7577 −0.959975
\(563\) 26.9834 1.13722 0.568608 0.822609i \(-0.307482\pi\)
0.568608 + 0.822609i \(0.307482\pi\)
\(564\) −0.123758 −0.00521115
\(565\) 57.5302 2.42031
\(566\) 25.1270 1.05617
\(567\) 7.69148 0.323012
\(568\) 40.4725 1.69819
\(569\) 3.08488 0.129325 0.0646625 0.997907i \(-0.479403\pi\)
0.0646625 + 0.997907i \(0.479403\pi\)
\(570\) 40.1729 1.68266
\(571\) −8.77746 −0.367325 −0.183663 0.982989i \(-0.558795\pi\)
−0.183663 + 0.982989i \(0.558795\pi\)
\(572\) 0.986359 0.0412417
\(573\) −11.5974 −0.484488
\(574\) 25.1201 1.04849
\(575\) 12.7641 0.532300
\(576\) −8.88639 −0.370266
\(577\) 26.3403 1.09656 0.548280 0.836295i \(-0.315283\pi\)
0.548280 + 0.836295i \(0.315283\pi\)
\(578\) 3.85216 0.160229
\(579\) 14.8389 0.616682
\(580\) 2.61356 0.108522
\(581\) −1.68934 −0.0700856
\(582\) 2.03869 0.0845064
\(583\) −3.62710 −0.150219
\(584\) 2.38276 0.0985993
\(585\) −8.96954 −0.370845
\(586\) 36.7162 1.51673
\(587\) 4.65092 0.191964 0.0959820 0.995383i \(-0.469401\pi\)
0.0959820 + 0.995383i \(0.469401\pi\)
\(588\) −0.485132 −0.0200065
\(589\) −22.9748 −0.946660
\(590\) 21.9625 0.904184
\(591\) 6.36936 0.262000
\(592\) −30.5911 −1.25729
\(593\) 23.3624 0.959380 0.479690 0.877438i \(-0.340749\pi\)
0.479690 + 0.877438i \(0.340749\pi\)
\(594\) 30.4265 1.24841
\(595\) −21.4596 −0.879758
\(596\) −0.261174 −0.0106981
\(597\) −19.3839 −0.793329
\(598\) −11.7113 −0.478913
\(599\) −35.6661 −1.45728 −0.728638 0.684899i \(-0.759846\pi\)
−0.728638 + 0.684899i \(0.759846\pi\)
\(600\) 14.8753 0.607282
\(601\) 38.0829 1.55343 0.776717 0.629850i \(-0.216883\pi\)
0.776717 + 0.629850i \(0.216883\pi\)
\(602\) −26.1593 −1.06617
\(603\) 17.4084 0.708925
\(604\) −1.30906 −0.0532650
\(605\) 8.49847 0.345512
\(606\) 15.0943 0.613163
\(607\) 32.9253 1.33640 0.668199 0.743983i \(-0.267065\pi\)
0.668199 + 0.743983i \(0.267065\pi\)
\(608\) −4.04151 −0.163905
\(609\) −21.2062 −0.859318
\(610\) 11.7771 0.476843
\(611\) −2.22248 −0.0899117
\(612\) −0.467020 −0.0188782
\(613\) 33.2601 1.34336 0.671680 0.740841i \(-0.265573\pi\)
0.671680 + 0.740841i \(0.265573\pi\)
\(614\) 33.6390 1.35756
\(615\) 37.1538 1.49819
\(616\) −19.3048 −0.777814
\(617\) 25.9173 1.04339 0.521695 0.853132i \(-0.325300\pi\)
0.521695 + 0.853132i \(0.325300\pi\)
\(618\) −19.5641 −0.786982
\(619\) −36.2632 −1.45754 −0.728771 0.684758i \(-0.759908\pi\)
−0.728771 + 0.684758i \(0.759908\pi\)
\(620\) 1.05517 0.0423768
\(621\) −17.9567 −0.720578
\(622\) −17.4239 −0.698634
\(623\) −15.5532 −0.623127
\(624\) −14.3643 −0.575031
\(625\) −28.9741 −1.15896
\(626\) 32.8056 1.31118
\(627\) −34.3125 −1.37031
\(628\) −2.26492 −0.0903800
\(629\) 27.5975 1.10038
\(630\) −9.68898 −0.386018
\(631\) 26.2694 1.04577 0.522884 0.852404i \(-0.324856\pi\)
0.522884 + 0.852404i \(0.324856\pi\)
\(632\) 47.7796 1.90057
\(633\) −18.3164 −0.728010
\(634\) −18.6004 −0.738715
\(635\) 42.0152 1.66732
\(636\) −0.137685 −0.00545958
\(637\) −8.71211 −0.345186
\(638\) −44.9106 −1.77803
\(639\) −17.3497 −0.686343
\(640\) −36.3752 −1.43786
\(641\) 1.87771 0.0741651 0.0370826 0.999312i \(-0.488194\pi\)
0.0370826 + 0.999312i \(0.488194\pi\)
\(642\) −27.3781 −1.08053
\(643\) −38.7911 −1.52977 −0.764886 0.644165i \(-0.777205\pi\)
−0.764886 + 0.644165i \(0.777205\pi\)
\(644\) −0.628808 −0.0247785
\(645\) −38.6909 −1.52345
\(646\) 37.5632 1.47791
\(647\) −14.5299 −0.571227 −0.285614 0.958345i \(-0.592197\pi\)
−0.285614 + 0.958345i \(0.592197\pi\)
\(648\) −11.2033 −0.440108
\(649\) −18.7587 −0.736342
\(650\) −14.7437 −0.578295
\(651\) −8.56158 −0.335555
\(652\) 1.76417 0.0690904
\(653\) −44.2710 −1.73246 −0.866230 0.499646i \(-0.833464\pi\)
−0.866230 + 0.499646i \(0.833464\pi\)
\(654\) −6.80395 −0.266055
\(655\) −49.7687 −1.94463
\(656\) −38.5087 −1.50351
\(657\) −1.02144 −0.0398500
\(658\) −2.40074 −0.0935905
\(659\) 31.8325 1.24002 0.620009 0.784595i \(-0.287129\pi\)
0.620009 + 0.784595i \(0.287129\pi\)
\(660\) 1.57589 0.0613413
\(661\) 12.3380 0.479892 0.239946 0.970786i \(-0.422870\pi\)
0.239946 + 0.970786i \(0.422870\pi\)
\(662\) 42.0986 1.63621
\(663\) 12.9586 0.503270
\(664\) 2.46067 0.0954926
\(665\) 38.7354 1.50210
\(666\) 12.4602 0.482824
\(667\) 26.5048 1.02627
\(668\) 0.202768 0.00784531
\(669\) −27.2746 −1.05450
\(670\) 64.3070 2.48440
\(671\) −10.0591 −0.388327
\(672\) −1.50607 −0.0580980
\(673\) −44.0425 −1.69771 −0.848856 0.528624i \(-0.822708\pi\)
−0.848856 + 0.528624i \(0.822708\pi\)
\(674\) −14.7524 −0.568243
\(675\) −22.6061 −0.870111
\(676\) −0.687538 −0.0264438
\(677\) 50.5185 1.94158 0.970792 0.239921i \(-0.0771216\pi\)
0.970792 + 0.239921i \(0.0771216\pi\)
\(678\) −37.5266 −1.44120
\(679\) 1.96574 0.0754382
\(680\) 31.2578 1.19868
\(681\) −15.3053 −0.586499
\(682\) −18.1318 −0.694301
\(683\) 33.9742 1.29999 0.649993 0.759941i \(-0.274772\pi\)
0.649993 + 0.759941i \(0.274772\pi\)
\(684\) 0.842990 0.0322325
\(685\) −54.6249 −2.08711
\(686\) −28.5813 −1.09124
\(687\) −35.6827 −1.36138
\(688\) 40.1019 1.52887
\(689\) −2.47259 −0.0941980
\(690\) −18.7110 −0.712316
\(691\) −33.8904 −1.28925 −0.644626 0.764498i \(-0.722987\pi\)
−0.644626 + 0.764498i \(0.722987\pi\)
\(692\) −1.22690 −0.0466396
\(693\) 8.27555 0.314362
\(694\) −4.90285 −0.186110
\(695\) 7.67046 0.290957
\(696\) 30.8887 1.17083
\(697\) 34.7403 1.31588
\(698\) −16.1379 −0.610827
\(699\) 24.4590 0.925124
\(700\) −0.791621 −0.0299205
\(701\) −16.8977 −0.638216 −0.319108 0.947718i \(-0.603383\pi\)
−0.319108 + 0.947718i \(0.603383\pi\)
\(702\) 20.7416 0.782842
\(703\) −49.8146 −1.87879
\(704\) 28.0378 1.05671
\(705\) −3.55081 −0.133731
\(706\) −17.8053 −0.670111
\(707\) 14.5541 0.547365
\(708\) −0.712082 −0.0267617
\(709\) −1.62126 −0.0608879 −0.0304439 0.999536i \(-0.509692\pi\)
−0.0304439 + 0.999536i \(0.509692\pi\)
\(710\) −64.0901 −2.40526
\(711\) −20.4820 −0.768137
\(712\) 22.6547 0.849020
\(713\) 10.7008 0.400747
\(714\) 13.9980 0.523861
\(715\) 28.3002 1.05837
\(716\) −0.458899 −0.0171499
\(717\) −16.8442 −0.629058
\(718\) −18.5485 −0.692225
\(719\) 1.96204 0.0731718 0.0365859 0.999331i \(-0.488352\pi\)
0.0365859 + 0.999331i \(0.488352\pi\)
\(720\) 14.8531 0.553541
\(721\) −18.8640 −0.702532
\(722\) −40.2393 −1.49755
\(723\) 36.7646 1.36729
\(724\) 0.779384 0.0289656
\(725\) 33.3675 1.23924
\(726\) −5.54350 −0.205739
\(727\) −20.1524 −0.747411 −0.373706 0.927547i \(-0.621913\pi\)
−0.373706 + 0.927547i \(0.621913\pi\)
\(728\) −13.1600 −0.487744
\(729\) 27.6344 1.02350
\(730\) −3.77321 −0.139653
\(731\) −36.1775 −1.33807
\(732\) −0.381845 −0.0141134
\(733\) −29.6504 −1.09516 −0.547581 0.836753i \(-0.684451\pi\)
−0.547581 + 0.836753i \(0.684451\pi\)
\(734\) 24.4774 0.903479
\(735\) −13.9192 −0.513417
\(736\) 1.88238 0.0693855
\(737\) −54.9260 −2.02322
\(738\) 15.6852 0.577379
\(739\) −25.6486 −0.943498 −0.471749 0.881733i \(-0.656377\pi\)
−0.471749 + 0.881733i \(0.656377\pi\)
\(740\) 2.28786 0.0841033
\(741\) −23.3908 −0.859281
\(742\) −2.67091 −0.0980521
\(743\) 15.5400 0.570106 0.285053 0.958512i \(-0.407989\pi\)
0.285053 + 0.958512i \(0.407989\pi\)
\(744\) 12.4707 0.457198
\(745\) −7.49349 −0.274540
\(746\) −36.3809 −1.33200
\(747\) −1.05484 −0.0385944
\(748\) 1.47352 0.0538770
\(749\) −26.3984 −0.964577
\(750\) 5.82561 0.212721
\(751\) −18.9200 −0.690401 −0.345201 0.938529i \(-0.612189\pi\)
−0.345201 + 0.938529i \(0.612189\pi\)
\(752\) 3.68029 0.134207
\(753\) −8.16682 −0.297616
\(754\) −30.6154 −1.11495
\(755\) −37.5590 −1.36691
\(756\) 1.11366 0.0405035
\(757\) 11.1265 0.404401 0.202200 0.979344i \(-0.435191\pi\)
0.202200 + 0.979344i \(0.435191\pi\)
\(758\) 30.0321 1.09081
\(759\) 15.9815 0.580090
\(760\) −56.4216 −2.04663
\(761\) 33.0965 1.19975 0.599874 0.800094i \(-0.295217\pi\)
0.599874 + 0.800094i \(0.295217\pi\)
\(762\) −27.4063 −0.992825
\(763\) −6.56048 −0.237505
\(764\) −0.898978 −0.0325239
\(765\) −13.3995 −0.484461
\(766\) 6.54943 0.236641
\(767\) −12.7877 −0.461738
\(768\) 3.37912 0.121934
\(769\) −5.34626 −0.192791 −0.0963956 0.995343i \(-0.530731\pi\)
−0.0963956 + 0.995343i \(0.530731\pi\)
\(770\) 30.5701 1.10167
\(771\) −5.87173 −0.211465
\(772\) 1.15024 0.0413981
\(773\) −29.8702 −1.07436 −0.537178 0.843469i \(-0.680510\pi\)
−0.537178 + 0.843469i \(0.680510\pi\)
\(774\) −16.3341 −0.587116
\(775\) 13.4715 0.483909
\(776\) −2.86327 −0.102786
\(777\) −18.5634 −0.665960
\(778\) −7.40548 −0.265499
\(779\) −62.7075 −2.24673
\(780\) 1.07428 0.0384653
\(781\) 54.7407 1.95877
\(782\) −17.4955 −0.625638
\(783\) −46.9418 −1.67756
\(784\) 14.4268 0.515242
\(785\) −64.9840 −2.31938
\(786\) 32.4639 1.15795
\(787\) −0.289779 −0.0103295 −0.00516474 0.999987i \(-0.501644\pi\)
−0.00516474 + 0.999987i \(0.501644\pi\)
\(788\) 0.493724 0.0175882
\(789\) 3.38027 0.120341
\(790\) −75.6611 −2.69190
\(791\) −36.1838 −1.28655
\(792\) −12.0541 −0.428323
\(793\) −6.85726 −0.243509
\(794\) 13.9841 0.496278
\(795\) −3.95041 −0.140106
\(796\) −1.50255 −0.0532564
\(797\) 18.9669 0.671842 0.335921 0.941890i \(-0.390952\pi\)
0.335921 + 0.941890i \(0.390952\pi\)
\(798\) −25.2669 −0.894438
\(799\) −3.32014 −0.117458
\(800\) 2.36977 0.0837842
\(801\) −9.71156 −0.343141
\(802\) 46.2840 1.63435
\(803\) 3.22277 0.113729
\(804\) −2.08500 −0.0735322
\(805\) −18.0415 −0.635878
\(806\) −12.3604 −0.435375
\(807\) −30.0085 −1.05635
\(808\) −21.1994 −0.745793
\(809\) −10.5686 −0.371572 −0.185786 0.982590i \(-0.559483\pi\)
−0.185786 + 0.982590i \(0.559483\pi\)
\(810\) 17.7410 0.623354
\(811\) −2.54431 −0.0893427 −0.0446714 0.999002i \(-0.514224\pi\)
−0.0446714 + 0.999002i \(0.514224\pi\)
\(812\) −1.64381 −0.0576863
\(813\) −36.0504 −1.26434
\(814\) −39.3138 −1.37795
\(815\) 50.6169 1.77303
\(816\) −21.4587 −0.751204
\(817\) 65.3018 2.28462
\(818\) 2.52087 0.0881402
\(819\) 5.64142 0.197127
\(820\) 2.88000 0.100574
\(821\) −7.11300 −0.248246 −0.124123 0.992267i \(-0.539612\pi\)
−0.124123 + 0.992267i \(0.539612\pi\)
\(822\) 35.6315 1.24279
\(823\) 27.0899 0.944294 0.472147 0.881520i \(-0.343479\pi\)
0.472147 + 0.881520i \(0.343479\pi\)
\(824\) 27.4771 0.957210
\(825\) 20.1194 0.700469
\(826\) −13.8134 −0.480630
\(827\) 31.8819 1.10864 0.554321 0.832303i \(-0.312978\pi\)
0.554321 + 0.832303i \(0.312978\pi\)
\(828\) −0.392632 −0.0136449
\(829\) 14.9781 0.520210 0.260105 0.965580i \(-0.416243\pi\)
0.260105 + 0.965580i \(0.416243\pi\)
\(830\) −3.89659 −0.135252
\(831\) −18.3611 −0.636939
\(832\) 19.1133 0.662634
\(833\) −13.0150 −0.450942
\(834\) −5.00339 −0.173253
\(835\) 5.81772 0.201330
\(836\) −2.65975 −0.0919894
\(837\) −18.9518 −0.655071
\(838\) −21.1438 −0.730399
\(839\) −42.8497 −1.47934 −0.739669 0.672971i \(-0.765018\pi\)
−0.739669 + 0.672971i \(0.765018\pi\)
\(840\) −21.0256 −0.725451
\(841\) 40.2878 1.38924
\(842\) 17.3724 0.598692
\(843\) 21.1704 0.729147
\(844\) −1.41980 −0.0488716
\(845\) −19.7265 −0.678614
\(846\) −1.49904 −0.0515380
\(847\) −5.34514 −0.183661
\(848\) 4.09446 0.140604
\(849\) −23.3745 −0.802210
\(850\) −22.0255 −0.755469
\(851\) 23.2017 0.795344
\(852\) 2.07796 0.0711899
\(853\) 27.5834 0.944438 0.472219 0.881481i \(-0.343453\pi\)
0.472219 + 0.881481i \(0.343453\pi\)
\(854\) −7.40727 −0.253472
\(855\) 24.1867 0.827167
\(856\) 38.4516 1.31425
\(857\) 29.6751 1.01368 0.506842 0.862039i \(-0.330813\pi\)
0.506842 + 0.862039i \(0.330813\pi\)
\(858\) −18.4600 −0.630215
\(859\) 32.9086 1.12283 0.561414 0.827535i \(-0.310257\pi\)
0.561414 + 0.827535i \(0.310257\pi\)
\(860\) −2.99915 −0.102270
\(861\) −23.3680 −0.796380
\(862\) 39.5224 1.34614
\(863\) −16.3490 −0.556526 −0.278263 0.960505i \(-0.589759\pi\)
−0.278263 + 0.960505i \(0.589759\pi\)
\(864\) −3.33383 −0.113419
\(865\) −35.2016 −1.19689
\(866\) −10.2231 −0.347397
\(867\) −3.58348 −0.121701
\(868\) −0.663655 −0.0225259
\(869\) 64.6237 2.19221
\(870\) −48.9137 −1.65833
\(871\) −37.4429 −1.26870
\(872\) 9.55592 0.323604
\(873\) 1.22742 0.0415420
\(874\) 31.5801 1.06821
\(875\) 5.61715 0.189894
\(876\) 0.122337 0.00413338
\(877\) −2.26530 −0.0764937 −0.0382469 0.999268i \(-0.512177\pi\)
−0.0382469 + 0.999268i \(0.512177\pi\)
\(878\) 5.73401 0.193514
\(879\) −34.1553 −1.15203
\(880\) −46.8635 −1.57977
\(881\) −15.7439 −0.530424 −0.265212 0.964190i \(-0.585442\pi\)
−0.265212 + 0.964190i \(0.585442\pi\)
\(882\) −5.87623 −0.197863
\(883\) −33.7073 −1.13434 −0.567170 0.823601i \(-0.691962\pi\)
−0.567170 + 0.823601i \(0.691962\pi\)
\(884\) 1.00449 0.0337847
\(885\) −20.4307 −0.686771
\(886\) −39.8216 −1.33783
\(887\) 15.1671 0.509260 0.254630 0.967039i \(-0.418046\pi\)
0.254630 + 0.967039i \(0.418046\pi\)
\(888\) 27.0393 0.907380
\(889\) −26.4256 −0.886287
\(890\) −35.8747 −1.20252
\(891\) −15.1529 −0.507642
\(892\) −2.11420 −0.0707887
\(893\) 5.99299 0.200548
\(894\) 4.88796 0.163478
\(895\) −13.1665 −0.440108
\(896\) 22.8783 0.764311
\(897\) 10.8945 0.363757
\(898\) 43.7845 1.46111
\(899\) 27.9736 0.932972
\(900\) −0.494294 −0.0164765
\(901\) −3.69378 −0.123058
\(902\) −49.4889 −1.64780
\(903\) 24.3348 0.809811
\(904\) 52.7049 1.75294
\(905\) 22.3617 0.743329
\(906\) 24.4995 0.813943
\(907\) 1.18154 0.0392325 0.0196162 0.999808i \(-0.493756\pi\)
0.0196162 + 0.999808i \(0.493756\pi\)
\(908\) −1.18639 −0.0393719
\(909\) 9.08772 0.301421
\(910\) 20.8395 0.690824
\(911\) 11.1032 0.367867 0.183934 0.982939i \(-0.441117\pi\)
0.183934 + 0.982939i \(0.441117\pi\)
\(912\) 38.7338 1.28260
\(913\) 3.32815 0.110146
\(914\) 23.3109 0.771055
\(915\) −10.9557 −0.362185
\(916\) −2.76596 −0.0913900
\(917\) 31.3022 1.03369
\(918\) 30.9858 1.02268
\(919\) −35.2464 −1.16267 −0.581336 0.813664i \(-0.697470\pi\)
−0.581336 + 0.813664i \(0.697470\pi\)
\(920\) 26.2790 0.866393
\(921\) −31.2928 −1.03113
\(922\) −1.29494 −0.0426465
\(923\) 37.3165 1.22829
\(924\) −0.991159 −0.0326067
\(925\) 29.2092 0.960392
\(926\) −61.5005 −2.02103
\(927\) −11.7788 −0.386867
\(928\) 4.92085 0.161535
\(929\) 11.9488 0.392028 0.196014 0.980601i \(-0.437200\pi\)
0.196014 + 0.980601i \(0.437200\pi\)
\(930\) −19.7479 −0.647560
\(931\) 23.4925 0.769936
\(932\) 1.89595 0.0621039
\(933\) 16.2086 0.530646
\(934\) 47.1040 1.54129
\(935\) 42.2774 1.38262
\(936\) −8.21723 −0.268589
\(937\) −15.5796 −0.508964 −0.254482 0.967078i \(-0.581905\pi\)
−0.254482 + 0.967078i \(0.581905\pi\)
\(938\) −40.4461 −1.32061
\(939\) −30.5175 −0.995901
\(940\) −0.275243 −0.00897743
\(941\) −14.4050 −0.469591 −0.234795 0.972045i \(-0.575442\pi\)
−0.234795 + 0.972045i \(0.575442\pi\)
\(942\) 42.3887 1.38110
\(943\) 29.2067 0.951103
\(944\) 21.1758 0.689212
\(945\) 31.9527 1.03942
\(946\) 51.5363 1.67559
\(947\) 44.5130 1.44648 0.723240 0.690597i \(-0.242652\pi\)
0.723240 + 0.690597i \(0.242652\pi\)
\(948\) 2.45313 0.0796738
\(949\) 2.19696 0.0713162
\(950\) 39.7569 1.28988
\(951\) 17.3030 0.561090
\(952\) −19.6597 −0.637175
\(953\) −26.4208 −0.855852 −0.427926 0.903814i \(-0.640756\pi\)
−0.427926 + 0.903814i \(0.640756\pi\)
\(954\) −1.66773 −0.0539949
\(955\) −25.7931 −0.834644
\(956\) −1.30569 −0.0422289
\(957\) 41.7782 1.35050
\(958\) −20.5778 −0.664840
\(959\) 34.3565 1.10943
\(960\) 30.5369 0.985576
\(961\) −19.7062 −0.635684
\(962\) −26.8001 −0.864069
\(963\) −16.4834 −0.531169
\(964\) 2.84983 0.0917867
\(965\) 33.0022 1.06238
\(966\) 11.7683 0.378640
\(967\) 43.1537 1.38773 0.693864 0.720106i \(-0.255907\pi\)
0.693864 + 0.720106i \(0.255907\pi\)
\(968\) 7.78567 0.250241
\(969\) −34.9433 −1.12254
\(970\) 4.53413 0.145582
\(971\) 11.9071 0.382115 0.191058 0.981579i \(-0.438808\pi\)
0.191058 + 0.981579i \(0.438808\pi\)
\(972\) 1.19461 0.0383171
\(973\) −4.82436 −0.154662
\(974\) 34.6068 1.10887
\(975\) 13.7154 0.439243
\(976\) 11.3552 0.363472
\(977\) 9.60316 0.307232 0.153616 0.988131i \(-0.450908\pi\)
0.153616 + 0.988131i \(0.450908\pi\)
\(978\) −33.0171 −1.05577
\(979\) 30.6413 0.979301
\(980\) −1.07895 −0.0344659
\(981\) −4.09641 −0.130788
\(982\) −33.2760 −1.06188
\(983\) 1.00000 0.0318950
\(984\) 34.0376 1.08508
\(985\) 14.1657 0.451357
\(986\) −45.7361 −1.45654
\(987\) 2.23329 0.0710865
\(988\) −1.81315 −0.0576838
\(989\) −30.4151 −0.967143
\(990\) 19.0882 0.606662
\(991\) 34.4460 1.09421 0.547106 0.837063i \(-0.315729\pi\)
0.547106 + 0.837063i \(0.315729\pi\)
\(992\) 1.98670 0.0630777
\(993\) −39.1623 −1.24278
\(994\) 40.3097 1.27854
\(995\) −43.1105 −1.36669
\(996\) 0.126337 0.00400315
\(997\) −30.7018 −0.972337 −0.486168 0.873865i \(-0.661606\pi\)
−0.486168 + 0.873865i \(0.661606\pi\)
\(998\) −32.1449 −1.01753
\(999\) −41.0919 −1.30009
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 983.2.a.b.1.15 54
3.2 odd 2 8847.2.a.g.1.40 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.2.a.b.1.15 54 1.1 even 1 trivial
8847.2.a.g.1.40 54 3.2 odd 2