Properties

Label 983.2.a.b.1.17
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 1.17
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)
 
\(f(q)\) \(=\) \(q-1.13542 q^{2} -1.73773 q^{3} -0.710827 q^{4} -4.00726 q^{5} +1.97305 q^{6} +3.34589 q^{7} +3.07792 q^{8} +0.0197210 q^{9} +O(q^{10})\) \(q-1.13542 q^{2} -1.73773 q^{3} -0.710827 q^{4} -4.00726 q^{5} +1.97305 q^{6} +3.34589 q^{7} +3.07792 q^{8} +0.0197210 q^{9} +4.54991 q^{10} -4.42673 q^{11} +1.23523 q^{12} -5.98120 q^{13} -3.79899 q^{14} +6.96355 q^{15} -2.07307 q^{16} -5.87490 q^{17} -0.0223916 q^{18} -2.64412 q^{19} +2.84847 q^{20} -5.81427 q^{21} +5.02618 q^{22} -7.22232 q^{23} -5.34861 q^{24} +11.0581 q^{25} +6.79116 q^{26} +5.17893 q^{27} -2.37835 q^{28} -6.03703 q^{29} -7.90654 q^{30} +0.185465 q^{31} -3.80204 q^{32} +7.69248 q^{33} +6.67046 q^{34} -13.4079 q^{35} -0.0140182 q^{36} -11.0285 q^{37} +3.00218 q^{38} +10.3937 q^{39} -12.3340 q^{40} +2.46853 q^{41} +6.60163 q^{42} +6.27188 q^{43} +3.14664 q^{44} -0.0790273 q^{45} +8.20035 q^{46} +2.90363 q^{47} +3.60245 q^{48} +4.19500 q^{49} -12.5556 q^{50} +10.2090 q^{51} +4.25160 q^{52} +0.991456 q^{53} -5.88025 q^{54} +17.7390 q^{55} +10.2984 q^{56} +4.59478 q^{57} +6.85455 q^{58} +8.07947 q^{59} -4.94988 q^{60} -14.0732 q^{61} -0.210580 q^{62} +0.0659845 q^{63} +8.46304 q^{64} +23.9682 q^{65} -8.73417 q^{66} +8.15799 q^{67} +4.17604 q^{68} +12.5505 q^{69} +15.2235 q^{70} +1.43625 q^{71} +0.0606997 q^{72} -2.40711 q^{73} +12.5220 q^{74} -19.2161 q^{75} +1.87951 q^{76} -14.8114 q^{77} -11.8012 q^{78} +14.5102 q^{79} +8.30733 q^{80} -9.05877 q^{81} -2.80281 q^{82} -14.6046 q^{83} +4.13294 q^{84} +23.5422 q^{85} -7.12121 q^{86} +10.4908 q^{87} -13.6251 q^{88} -10.3503 q^{89} +0.0897289 q^{90} -20.0125 q^{91} +5.13382 q^{92} -0.322289 q^{93} -3.29683 q^{94} +10.5957 q^{95} +6.60694 q^{96} +13.1320 q^{97} -4.76308 q^{98} -0.0872996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13542 −0.802861 −0.401431 0.915889i \(-0.631487\pi\)
−0.401431 + 0.915889i \(0.631487\pi\)
\(3\) −1.73773 −1.00328 −0.501641 0.865076i \(-0.667270\pi\)
−0.501641 + 0.865076i \(0.667270\pi\)
\(4\) −0.710827 −0.355414
\(5\) −4.00726 −1.79210 −0.896051 0.443952i \(-0.853576\pi\)
−0.896051 + 0.443952i \(0.853576\pi\)
\(6\) 1.97305 0.805496
\(7\) 3.34589 1.26463 0.632314 0.774712i \(-0.282105\pi\)
0.632314 + 0.774712i \(0.282105\pi\)
\(8\) 3.07792 1.08821
\(9\) 0.0197210 0.00657368
\(10\) 4.54991 1.43881
\(11\) −4.42673 −1.33471 −0.667354 0.744741i \(-0.732573\pi\)
−0.667354 + 0.744741i \(0.732573\pi\)
\(12\) 1.23523 0.356580
\(13\) −5.98120 −1.65889 −0.829444 0.558591i \(-0.811342\pi\)
−0.829444 + 0.558591i \(0.811342\pi\)
\(14\) −3.79899 −1.01532
\(15\) 6.96355 1.79798
\(16\) −2.07307 −0.518268
\(17\) −5.87490 −1.42487 −0.712436 0.701737i \(-0.752408\pi\)
−0.712436 + 0.701737i \(0.752408\pi\)
\(18\) −0.0223916 −0.00527775
\(19\) −2.64412 −0.606603 −0.303302 0.952895i \(-0.598089\pi\)
−0.303302 + 0.952895i \(0.598089\pi\)
\(20\) 2.84847 0.636937
\(21\) −5.81427 −1.26878
\(22\) 5.02618 1.07159
\(23\) −7.22232 −1.50596 −0.752979 0.658045i \(-0.771384\pi\)
−0.752979 + 0.658045i \(0.771384\pi\)
\(24\) −5.34861 −1.09178
\(25\) 11.0581 2.21163
\(26\) 6.79116 1.33186
\(27\) 5.17893 0.996686
\(28\) −2.37835 −0.449466
\(29\) −6.03703 −1.12105 −0.560524 0.828138i \(-0.689400\pi\)
−0.560524 + 0.828138i \(0.689400\pi\)
\(30\) −7.90654 −1.44353
\(31\) 0.185465 0.0333105 0.0166553 0.999861i \(-0.494698\pi\)
0.0166553 + 0.999861i \(0.494698\pi\)
\(32\) −3.80204 −0.672112
\(33\) 7.69248 1.33909
\(34\) 6.67046 1.14397
\(35\) −13.4079 −2.26634
\(36\) −0.0140182 −0.00233637
\(37\) −11.0285 −1.81307 −0.906537 0.422126i \(-0.861284\pi\)
−0.906537 + 0.422126i \(0.861284\pi\)
\(38\) 3.00218 0.487018
\(39\) 10.3937 1.66433
\(40\) −12.3340 −1.95018
\(41\) 2.46853 0.385519 0.192759 0.981246i \(-0.438256\pi\)
0.192759 + 0.981246i \(0.438256\pi\)
\(42\) 6.60163 1.01865
\(43\) 6.27188 0.956453 0.478227 0.878236i \(-0.341280\pi\)
0.478227 + 0.878236i \(0.341280\pi\)
\(44\) 3.14664 0.474374
\(45\) −0.0790273 −0.0117807
\(46\) 8.20035 1.20908
\(47\) 2.90363 0.423537 0.211769 0.977320i \(-0.432078\pi\)
0.211769 + 0.977320i \(0.432078\pi\)
\(48\) 3.60245 0.519968
\(49\) 4.19500 0.599286
\(50\) −12.5556 −1.77563
\(51\) 10.2090 1.42955
\(52\) 4.25160 0.589591
\(53\) 0.991456 0.136187 0.0680935 0.997679i \(-0.478308\pi\)
0.0680935 + 0.997679i \(0.478308\pi\)
\(54\) −5.88025 −0.800201
\(55\) 17.7390 2.39193
\(56\) 10.2984 1.37618
\(57\) 4.59478 0.608594
\(58\) 6.85455 0.900046
\(59\) 8.07947 1.05186 0.525929 0.850529i \(-0.323718\pi\)
0.525929 + 0.850529i \(0.323718\pi\)
\(60\) −4.94988 −0.639027
\(61\) −14.0732 −1.80189 −0.900946 0.433932i \(-0.857126\pi\)
−0.900946 + 0.433932i \(0.857126\pi\)
\(62\) −0.210580 −0.0267437
\(63\) 0.0659845 0.00831326
\(64\) 8.46304 1.05788
\(65\) 23.9682 2.97289
\(66\) −8.73417 −1.07510
\(67\) 8.15799 0.996657 0.498328 0.866988i \(-0.333947\pi\)
0.498328 + 0.866988i \(0.333947\pi\)
\(68\) 4.17604 0.506419
\(69\) 12.5505 1.51090
\(70\) 15.2235 1.81956
\(71\) 1.43625 0.170452 0.0852259 0.996362i \(-0.472839\pi\)
0.0852259 + 0.996362i \(0.472839\pi\)
\(72\) 0.0606997 0.00715353
\(73\) −2.40711 −0.281731 −0.140865 0.990029i \(-0.544988\pi\)
−0.140865 + 0.990029i \(0.544988\pi\)
\(74\) 12.5220 1.45565
\(75\) −19.2161 −2.21888
\(76\) 1.87951 0.215595
\(77\) −14.8114 −1.68791
\(78\) −11.8012 −1.33623
\(79\) 14.5102 1.63253 0.816265 0.577678i \(-0.196041\pi\)
0.816265 + 0.577678i \(0.196041\pi\)
\(80\) 8.30733 0.928788
\(81\) −9.05877 −1.00653
\(82\) −2.80281 −0.309518
\(83\) −14.6046 −1.60306 −0.801530 0.597955i \(-0.795980\pi\)
−0.801530 + 0.597955i \(0.795980\pi\)
\(84\) 4.13294 0.450941
\(85\) 23.5422 2.55351
\(86\) −7.12121 −0.767900
\(87\) 10.4908 1.12473
\(88\) −13.6251 −1.45244
\(89\) −10.3503 −1.09713 −0.548567 0.836106i \(-0.684827\pi\)
−0.548567 + 0.836106i \(0.684827\pi\)
\(90\) 0.0897289 0.00945826
\(91\) −20.0125 −2.09788
\(92\) 5.13382 0.535238
\(93\) −0.322289 −0.0334198
\(94\) −3.29683 −0.340042
\(95\) 10.5957 1.08709
\(96\) 6.60694 0.674318
\(97\) 13.1320 1.33335 0.666677 0.745347i \(-0.267716\pi\)
0.666677 + 0.745347i \(0.267716\pi\)
\(98\) −4.76308 −0.481144
\(99\) −0.0872996 −0.00877394
\(100\) −7.86042 −0.786042
\(101\) 4.54533 0.452277 0.226139 0.974095i \(-0.427390\pi\)
0.226139 + 0.974095i \(0.427390\pi\)
\(102\) −11.5915 −1.14773
\(103\) −13.8304 −1.36275 −0.681374 0.731936i \(-0.738617\pi\)
−0.681374 + 0.731936i \(0.738617\pi\)
\(104\) −18.4097 −1.80522
\(105\) 23.2993 2.27378
\(106\) −1.12572 −0.109339
\(107\) 9.58532 0.926648 0.463324 0.886189i \(-0.346657\pi\)
0.463324 + 0.886189i \(0.346657\pi\)
\(108\) −3.68133 −0.354236
\(109\) −6.83430 −0.654607 −0.327304 0.944919i \(-0.606140\pi\)
−0.327304 + 0.944919i \(0.606140\pi\)
\(110\) −20.1412 −1.92039
\(111\) 19.1646 1.81902
\(112\) −6.93627 −0.655416
\(113\) −10.2635 −0.965509 −0.482755 0.875756i \(-0.660364\pi\)
−0.482755 + 0.875756i \(0.660364\pi\)
\(114\) −5.21700 −0.488617
\(115\) 28.9417 2.69883
\(116\) 4.29128 0.398436
\(117\) −0.117955 −0.0109050
\(118\) −9.17357 −0.844496
\(119\) −19.6568 −1.80193
\(120\) 21.4333 1.95658
\(121\) 8.59591 0.781446
\(122\) 15.9790 1.44667
\(123\) −4.28964 −0.386784
\(124\) −0.131834 −0.0118390
\(125\) −24.2765 −2.17136
\(126\) −0.0749199 −0.00667439
\(127\) −5.93782 −0.526896 −0.263448 0.964674i \(-0.584860\pi\)
−0.263448 + 0.964674i \(0.584860\pi\)
\(128\) −2.00501 −0.177219
\(129\) −10.8989 −0.959592
\(130\) −27.2139 −2.38682
\(131\) 2.42159 0.211576 0.105788 0.994389i \(-0.466264\pi\)
0.105788 + 0.994389i \(0.466264\pi\)
\(132\) −5.46802 −0.475930
\(133\) −8.84696 −0.767128
\(134\) −9.26272 −0.800177
\(135\) −20.7533 −1.78616
\(136\) −18.0825 −1.55056
\(137\) 0.957836 0.0818335 0.0409167 0.999163i \(-0.486972\pi\)
0.0409167 + 0.999163i \(0.486972\pi\)
\(138\) −14.2500 −1.21304
\(139\) 3.71094 0.314758 0.157379 0.987538i \(-0.449696\pi\)
0.157379 + 0.987538i \(0.449696\pi\)
\(140\) 9.53068 0.805489
\(141\) −5.04573 −0.424927
\(142\) −1.63075 −0.136849
\(143\) 26.4771 2.21413
\(144\) −0.0408831 −0.00340692
\(145\) 24.1919 2.00903
\(146\) 2.73307 0.226191
\(147\) −7.28980 −0.601253
\(148\) 7.83936 0.644391
\(149\) −8.61614 −0.705862 −0.352931 0.935649i \(-0.614815\pi\)
−0.352931 + 0.935649i \(0.614815\pi\)
\(150\) 21.8183 1.78146
\(151\) −9.01120 −0.733321 −0.366661 0.930355i \(-0.619499\pi\)
−0.366661 + 0.930355i \(0.619499\pi\)
\(152\) −8.13840 −0.660112
\(153\) −0.115859 −0.00936665
\(154\) 16.8171 1.35516
\(155\) −0.743207 −0.0596958
\(156\) −7.38815 −0.591526
\(157\) −2.92562 −0.233490 −0.116745 0.993162i \(-0.537246\pi\)
−0.116745 + 0.993162i \(0.537246\pi\)
\(158\) −16.4752 −1.31070
\(159\) −1.72289 −0.136634
\(160\) 15.2358 1.20449
\(161\) −24.1651 −1.90448
\(162\) 10.2855 0.808104
\(163\) −1.40921 −0.110378 −0.0551890 0.998476i \(-0.517576\pi\)
−0.0551890 + 0.998476i \(0.517576\pi\)
\(164\) −1.75470 −0.137019
\(165\) −30.8257 −2.39978
\(166\) 16.5823 1.28703
\(167\) 2.86088 0.221382 0.110691 0.993855i \(-0.464694\pi\)
0.110691 + 0.993855i \(0.464694\pi\)
\(168\) −17.8959 −1.38070
\(169\) 22.7748 1.75191
\(170\) −26.7303 −2.05012
\(171\) −0.0521448 −0.00398761
\(172\) −4.45823 −0.339937
\(173\) 13.1930 1.00305 0.501524 0.865144i \(-0.332773\pi\)
0.501524 + 0.865144i \(0.332773\pi\)
\(174\) −11.9114 −0.902999
\(175\) 36.9993 2.79689
\(176\) 9.17691 0.691736
\(177\) −14.0400 −1.05531
\(178\) 11.7520 0.880847
\(179\) −8.13143 −0.607771 −0.303886 0.952709i \(-0.598284\pi\)
−0.303886 + 0.952709i \(0.598284\pi\)
\(180\) 0.0561747 0.00418702
\(181\) −10.9771 −0.815924 −0.407962 0.912999i \(-0.633761\pi\)
−0.407962 + 0.912999i \(0.633761\pi\)
\(182\) 22.7225 1.68430
\(183\) 24.4555 1.80780
\(184\) −22.2297 −1.63880
\(185\) 44.1941 3.24921
\(186\) 0.365933 0.0268315
\(187\) 26.0066 1.90179
\(188\) −2.06398 −0.150531
\(189\) 17.3282 1.26044
\(190\) −12.0305 −0.872786
\(191\) −5.55812 −0.402172 −0.201086 0.979574i \(-0.564447\pi\)
−0.201086 + 0.979574i \(0.564447\pi\)
\(192\) −14.7065 −1.06135
\(193\) 13.1531 0.946782 0.473391 0.880852i \(-0.343030\pi\)
0.473391 + 0.880852i \(0.343030\pi\)
\(194\) −14.9103 −1.07050
\(195\) −41.6504 −2.98265
\(196\) −2.98192 −0.212995
\(197\) 16.6322 1.18500 0.592498 0.805572i \(-0.298142\pi\)
0.592498 + 0.805572i \(0.298142\pi\)
\(198\) 0.0991215 0.00704426
\(199\) 3.30876 0.234551 0.117276 0.993099i \(-0.462584\pi\)
0.117276 + 0.993099i \(0.462584\pi\)
\(200\) 34.0361 2.40671
\(201\) −14.1764 −0.999927
\(202\) −5.16085 −0.363116
\(203\) −20.1993 −1.41771
\(204\) −7.25684 −0.508081
\(205\) −9.89202 −0.690889
\(206\) 15.7032 1.09410
\(207\) −0.142432 −0.00989968
\(208\) 12.3995 0.859747
\(209\) 11.7048 0.809639
\(210\) −26.4544 −1.82553
\(211\) 8.50878 0.585768 0.292884 0.956148i \(-0.405385\pi\)
0.292884 + 0.956148i \(0.405385\pi\)
\(212\) −0.704754 −0.0484027
\(213\) −2.49582 −0.171011
\(214\) −10.8833 −0.743970
\(215\) −25.1331 −1.71406
\(216\) 15.9403 1.08460
\(217\) 0.620547 0.0421255
\(218\) 7.75979 0.525559
\(219\) 4.18292 0.282655
\(220\) −12.6094 −0.850125
\(221\) 35.1390 2.36370
\(222\) −21.7598 −1.46042
\(223\) −7.38436 −0.494493 −0.247247 0.968953i \(-0.579526\pi\)
−0.247247 + 0.968953i \(0.579526\pi\)
\(224\) −12.7212 −0.849973
\(225\) 0.218078 0.0145385
\(226\) 11.6534 0.775170
\(227\) 2.82859 0.187740 0.0938699 0.995584i \(-0.470076\pi\)
0.0938699 + 0.995584i \(0.470076\pi\)
\(228\) −3.26610 −0.216303
\(229\) −18.8778 −1.24748 −0.623739 0.781633i \(-0.714387\pi\)
−0.623739 + 0.781633i \(0.714387\pi\)
\(230\) −32.8609 −2.16679
\(231\) 25.7382 1.69345
\(232\) −18.5815 −1.21993
\(233\) 11.3943 0.746463 0.373231 0.927738i \(-0.378250\pi\)
0.373231 + 0.927738i \(0.378250\pi\)
\(234\) 0.133929 0.00875519
\(235\) −11.6356 −0.759022
\(236\) −5.74311 −0.373845
\(237\) −25.2150 −1.63789
\(238\) 22.3187 1.44670
\(239\) −6.61371 −0.427805 −0.213903 0.976855i \(-0.568618\pi\)
−0.213903 + 0.976855i \(0.568618\pi\)
\(240\) −14.4359 −0.931836
\(241\) −27.0082 −1.73975 −0.869875 0.493273i \(-0.835801\pi\)
−0.869875 + 0.493273i \(0.835801\pi\)
\(242\) −9.75995 −0.627393
\(243\) 0.204944 0.0131471
\(244\) 10.0036 0.640417
\(245\) −16.8105 −1.07398
\(246\) 4.87053 0.310534
\(247\) 15.8150 1.00629
\(248\) 0.570847 0.0362488
\(249\) 25.3789 1.60832
\(250\) 27.5640 1.74330
\(251\) −21.0115 −1.32624 −0.663118 0.748515i \(-0.730767\pi\)
−0.663118 + 0.748515i \(0.730767\pi\)
\(252\) −0.0469035 −0.00295465
\(253\) 31.9712 2.01001
\(254\) 6.74190 0.423025
\(255\) −40.9102 −2.56189
\(256\) −14.6496 −0.915598
\(257\) −15.3646 −0.958419 −0.479209 0.877701i \(-0.659077\pi\)
−0.479209 + 0.877701i \(0.659077\pi\)
\(258\) 12.3748 0.770419
\(259\) −36.9002 −2.29287
\(260\) −17.0373 −1.05661
\(261\) −0.119056 −0.00736940
\(262\) −2.74952 −0.169866
\(263\) −20.3976 −1.25777 −0.628884 0.777499i \(-0.716488\pi\)
−0.628884 + 0.777499i \(0.716488\pi\)
\(264\) 23.6768 1.45721
\(265\) −3.97302 −0.244061
\(266\) 10.0450 0.615898
\(267\) 17.9862 1.10073
\(268\) −5.79892 −0.354225
\(269\) 12.7051 0.774642 0.387321 0.921945i \(-0.373400\pi\)
0.387321 + 0.921945i \(0.373400\pi\)
\(270\) 23.5637 1.43404
\(271\) −8.76714 −0.532566 −0.266283 0.963895i \(-0.585796\pi\)
−0.266283 + 0.963895i \(0.585796\pi\)
\(272\) 12.1791 0.738465
\(273\) 34.7764 2.10476
\(274\) −1.08754 −0.0657009
\(275\) −48.9513 −2.95188
\(276\) −8.92122 −0.536994
\(277\) 30.1590 1.81208 0.906040 0.423193i \(-0.139091\pi\)
0.906040 + 0.423193i \(0.139091\pi\)
\(278\) −4.21347 −0.252707
\(279\) 0.00365756 0.000218973 0
\(280\) −41.2683 −2.46626
\(281\) −12.3546 −0.737015 −0.368508 0.929625i \(-0.620131\pi\)
−0.368508 + 0.929625i \(0.620131\pi\)
\(282\) 5.72901 0.341158
\(283\) 6.38400 0.379489 0.189745 0.981833i \(-0.439234\pi\)
0.189745 + 0.981833i \(0.439234\pi\)
\(284\) −1.02093 −0.0605809
\(285\) −18.4125 −1.09066
\(286\) −30.0626 −1.77764
\(287\) 8.25942 0.487538
\(288\) −0.0749802 −0.00441825
\(289\) 17.5144 1.03026
\(290\) −27.4679 −1.61297
\(291\) −22.8200 −1.33773
\(292\) 1.71104 0.100131
\(293\) 8.15051 0.476158 0.238079 0.971246i \(-0.423482\pi\)
0.238079 + 0.971246i \(0.423482\pi\)
\(294\) 8.27697 0.482723
\(295\) −32.3765 −1.88504
\(296\) −33.9449 −1.97300
\(297\) −22.9257 −1.33029
\(298\) 9.78292 0.566709
\(299\) 43.1982 2.49821
\(300\) 13.6593 0.788622
\(301\) 20.9851 1.20956
\(302\) 10.2315 0.588755
\(303\) −7.89858 −0.453761
\(304\) 5.48145 0.314383
\(305\) 56.3950 3.22917
\(306\) 0.131548 0.00752012
\(307\) −25.4382 −1.45183 −0.725917 0.687783i \(-0.758584\pi\)
−0.725917 + 0.687783i \(0.758584\pi\)
\(308\) 10.5283 0.599906
\(309\) 24.0335 1.36722
\(310\) 0.843850 0.0479275
\(311\) −7.39618 −0.419399 −0.209700 0.977766i \(-0.567249\pi\)
−0.209700 + 0.977766i \(0.567249\pi\)
\(312\) 31.9911 1.81114
\(313\) −11.5734 −0.654168 −0.327084 0.944995i \(-0.606066\pi\)
−0.327084 + 0.944995i \(0.606066\pi\)
\(314\) 3.32180 0.187460
\(315\) −0.264417 −0.0148982
\(316\) −10.3143 −0.580223
\(317\) 15.1402 0.850358 0.425179 0.905109i \(-0.360211\pi\)
0.425179 + 0.905109i \(0.360211\pi\)
\(318\) 1.95620 0.109698
\(319\) 26.7243 1.49627
\(320\) −33.9136 −1.89583
\(321\) −16.6567 −0.929689
\(322\) 27.4375 1.52903
\(323\) 15.5340 0.864332
\(324\) 6.43922 0.357735
\(325\) −66.1409 −3.66884
\(326\) 1.60004 0.0886183
\(327\) 11.8762 0.656756
\(328\) 7.59793 0.419525
\(329\) 9.71522 0.535617
\(330\) 35.0001 1.92669
\(331\) 3.53220 0.194147 0.0970735 0.995277i \(-0.469052\pi\)
0.0970735 + 0.995277i \(0.469052\pi\)
\(332\) 10.3813 0.569749
\(333\) −0.217493 −0.0119186
\(334\) −3.24830 −0.177739
\(335\) −32.6912 −1.78611
\(336\) 12.0534 0.657567
\(337\) 8.06868 0.439529 0.219764 0.975553i \(-0.429471\pi\)
0.219764 + 0.975553i \(0.429471\pi\)
\(338\) −25.8589 −1.40654
\(339\) 17.8352 0.968678
\(340\) −16.7345 −0.907554
\(341\) −0.821004 −0.0444598
\(342\) 0.0592061 0.00320150
\(343\) −9.38522 −0.506754
\(344\) 19.3044 1.04082
\(345\) −50.2930 −2.70768
\(346\) −14.9796 −0.805309
\(347\) −5.99108 −0.321618 −0.160809 0.986986i \(-0.551410\pi\)
−0.160809 + 0.986986i \(0.551410\pi\)
\(348\) −7.45711 −0.399743
\(349\) −17.1178 −0.916295 −0.458147 0.888876i \(-0.651487\pi\)
−0.458147 + 0.888876i \(0.651487\pi\)
\(350\) −42.0097 −2.24551
\(351\) −30.9762 −1.65339
\(352\) 16.8306 0.897074
\(353\) 9.77501 0.520271 0.260136 0.965572i \(-0.416233\pi\)
0.260136 + 0.965572i \(0.416233\pi\)
\(354\) 15.9412 0.847267
\(355\) −5.75544 −0.305467
\(356\) 7.35731 0.389937
\(357\) 34.1583 1.80785
\(358\) 9.23256 0.487956
\(359\) −24.0383 −1.26869 −0.634347 0.773048i \(-0.718731\pi\)
−0.634347 + 0.773048i \(0.718731\pi\)
\(360\) −0.243240 −0.0128199
\(361\) −12.0086 −0.632032
\(362\) 12.4636 0.655074
\(363\) −14.9374 −0.784011
\(364\) 14.2254 0.745614
\(365\) 9.64591 0.504890
\(366\) −27.7672 −1.45142
\(367\) −11.4894 −0.599743 −0.299872 0.953980i \(-0.596944\pi\)
−0.299872 + 0.953980i \(0.596944\pi\)
\(368\) 14.9724 0.780489
\(369\) 0.0486819 0.00253428
\(370\) −50.1787 −2.60867
\(371\) 3.31731 0.172226
\(372\) 0.229092 0.0118779
\(373\) 28.3635 1.46860 0.734302 0.678823i \(-0.237510\pi\)
0.734302 + 0.678823i \(0.237510\pi\)
\(374\) −29.5283 −1.52687
\(375\) 42.1861 2.17848
\(376\) 8.93713 0.460897
\(377\) 36.1087 1.85969
\(378\) −19.6747 −1.01196
\(379\) 26.1006 1.34070 0.670350 0.742045i \(-0.266144\pi\)
0.670350 + 0.742045i \(0.266144\pi\)
\(380\) −7.53170 −0.386368
\(381\) 10.3184 0.528625
\(382\) 6.31079 0.322888
\(383\) 32.3936 1.65524 0.827619 0.561291i \(-0.189695\pi\)
0.827619 + 0.561291i \(0.189695\pi\)
\(384\) 3.48417 0.177801
\(385\) 59.3530 3.02491
\(386\) −14.9343 −0.760135
\(387\) 0.123688 0.00628741
\(388\) −9.33459 −0.473892
\(389\) 7.66199 0.388478 0.194239 0.980954i \(-0.437776\pi\)
0.194239 + 0.980954i \(0.437776\pi\)
\(390\) 47.2906 2.39465
\(391\) 42.4304 2.14580
\(392\) 12.9119 0.652149
\(393\) −4.20809 −0.212270
\(394\) −18.8845 −0.951388
\(395\) −58.1463 −2.92566
\(396\) 0.0620549 0.00311838
\(397\) −16.9437 −0.850379 −0.425189 0.905104i \(-0.639792\pi\)
−0.425189 + 0.905104i \(0.639792\pi\)
\(398\) −3.75682 −0.188312
\(399\) 15.3737 0.769646
\(400\) −22.9243 −1.14621
\(401\) −9.87337 −0.493053 −0.246526 0.969136i \(-0.579289\pi\)
−0.246526 + 0.969136i \(0.579289\pi\)
\(402\) 16.0962 0.802803
\(403\) −1.10930 −0.0552584
\(404\) −3.23094 −0.160746
\(405\) 36.3009 1.80380
\(406\) 22.9346 1.13822
\(407\) 48.8202 2.41993
\(408\) 31.4225 1.55565
\(409\) 13.2558 0.655458 0.327729 0.944772i \(-0.393717\pi\)
0.327729 + 0.944772i \(0.393717\pi\)
\(410\) 11.2316 0.554688
\(411\) −1.66446 −0.0821020
\(412\) 9.83101 0.484339
\(413\) 27.0331 1.33021
\(414\) 0.161719 0.00794807
\(415\) 58.5243 2.87284
\(416\) 22.7408 1.11496
\(417\) −6.44863 −0.315791
\(418\) −13.2898 −0.650028
\(419\) −25.2387 −1.23299 −0.616496 0.787358i \(-0.711448\pi\)
−0.616496 + 0.787358i \(0.711448\pi\)
\(420\) −16.5618 −0.808132
\(421\) 14.4226 0.702916 0.351458 0.936204i \(-0.385686\pi\)
0.351458 + 0.936204i \(0.385686\pi\)
\(422\) −9.66101 −0.470291
\(423\) 0.0572625 0.00278420
\(424\) 3.05162 0.148200
\(425\) −64.9654 −3.15128
\(426\) 2.83380 0.137298
\(427\) −47.0875 −2.27872
\(428\) −6.81351 −0.329343
\(429\) −46.0103 −2.22140
\(430\) 28.5365 1.37615
\(431\) −14.4106 −0.694136 −0.347068 0.937840i \(-0.612823\pi\)
−0.347068 + 0.937840i \(0.612823\pi\)
\(432\) −10.7363 −0.516550
\(433\) −24.6812 −1.18610 −0.593051 0.805165i \(-0.702077\pi\)
−0.593051 + 0.805165i \(0.702077\pi\)
\(434\) −0.704580 −0.0338209
\(435\) −42.0392 −2.01562
\(436\) 4.85801 0.232656
\(437\) 19.0967 0.913519
\(438\) −4.74936 −0.226933
\(439\) −29.4671 −1.40639 −0.703194 0.710998i \(-0.748244\pi\)
−0.703194 + 0.710998i \(0.748244\pi\)
\(440\) 54.5994 2.60292
\(441\) 0.0827298 0.00393951
\(442\) −39.8974 −1.89772
\(443\) 4.51884 0.214697 0.107348 0.994221i \(-0.465764\pi\)
0.107348 + 0.994221i \(0.465764\pi\)
\(444\) −13.6227 −0.646506
\(445\) 41.4765 1.96618
\(446\) 8.38433 0.397010
\(447\) 14.9726 0.708178
\(448\) 28.3164 1.33783
\(449\) 6.82816 0.322241 0.161120 0.986935i \(-0.448489\pi\)
0.161120 + 0.986935i \(0.448489\pi\)
\(450\) −0.247609 −0.0116724
\(451\) −10.9275 −0.514555
\(452\) 7.29558 0.343155
\(453\) 15.6591 0.735727
\(454\) −3.21162 −0.150729
\(455\) 80.1952 3.75961
\(456\) 14.1424 0.662278
\(457\) −18.3271 −0.857304 −0.428652 0.903470i \(-0.641011\pi\)
−0.428652 + 0.903470i \(0.641011\pi\)
\(458\) 21.4341 1.00155
\(459\) −30.4257 −1.42015
\(460\) −20.5726 −0.959201
\(461\) −30.0207 −1.39820 −0.699101 0.715023i \(-0.746416\pi\)
−0.699101 + 0.715023i \(0.746416\pi\)
\(462\) −29.2236 −1.35961
\(463\) 27.1507 1.26180 0.630901 0.775864i \(-0.282686\pi\)
0.630901 + 0.775864i \(0.282686\pi\)
\(464\) 12.5152 0.581003
\(465\) 1.29150 0.0598917
\(466\) −12.9372 −0.599306
\(467\) 2.08061 0.0962791 0.0481396 0.998841i \(-0.484671\pi\)
0.0481396 + 0.998841i \(0.484671\pi\)
\(468\) 0.0838459 0.00387578
\(469\) 27.2958 1.26040
\(470\) 13.2112 0.609389
\(471\) 5.08394 0.234256
\(472\) 24.8680 1.14464
\(473\) −27.7639 −1.27659
\(474\) 28.6295 1.31500
\(475\) −29.2391 −1.34158
\(476\) 13.9726 0.640432
\(477\) 0.0195525 0.000895249 0
\(478\) 7.50932 0.343468
\(479\) −2.25809 −0.103175 −0.0515873 0.998668i \(-0.516428\pi\)
−0.0515873 + 0.998668i \(0.516428\pi\)
\(480\) −26.4757 −1.20845
\(481\) 65.9637 3.00769
\(482\) 30.6656 1.39678
\(483\) 41.9926 1.91073
\(484\) −6.11021 −0.277737
\(485\) −52.6234 −2.38951
\(486\) −0.232697 −0.0105553
\(487\) 5.19372 0.235350 0.117675 0.993052i \(-0.462456\pi\)
0.117675 + 0.993052i \(0.462456\pi\)
\(488\) −43.3163 −1.96083
\(489\) 2.44884 0.110740
\(490\) 19.0869 0.862258
\(491\) 1.50929 0.0681135 0.0340567 0.999420i \(-0.489157\pi\)
0.0340567 + 0.999420i \(0.489157\pi\)
\(492\) 3.04919 0.137468
\(493\) 35.4669 1.59735
\(494\) −17.9567 −0.807909
\(495\) 0.349832 0.0157238
\(496\) −0.384482 −0.0172638
\(497\) 4.80555 0.215558
\(498\) −28.8156 −1.29126
\(499\) 16.7473 0.749714 0.374857 0.927083i \(-0.377692\pi\)
0.374857 + 0.927083i \(0.377692\pi\)
\(500\) 17.2564 0.771730
\(501\) −4.97145 −0.222108
\(502\) 23.8569 1.06478
\(503\) 16.8253 0.750204 0.375102 0.926984i \(-0.377608\pi\)
0.375102 + 0.926984i \(0.377608\pi\)
\(504\) 0.203095 0.00904657
\(505\) −18.2143 −0.810527
\(506\) −36.3007 −1.61376
\(507\) −39.5765 −1.75766
\(508\) 4.22076 0.187266
\(509\) −11.7317 −0.519999 −0.259999 0.965609i \(-0.583722\pi\)
−0.259999 + 0.965609i \(0.583722\pi\)
\(510\) 46.4501 2.05685
\(511\) −8.05393 −0.356285
\(512\) 20.6434 0.912317
\(513\) −13.6937 −0.604593
\(514\) 17.4453 0.769477
\(515\) 55.4219 2.44218
\(516\) 7.74721 0.341052
\(517\) −12.8536 −0.565299
\(518\) 41.8971 1.84085
\(519\) −22.9260 −1.00634
\(520\) 73.7723 3.23513
\(521\) −35.9580 −1.57535 −0.787675 0.616091i \(-0.788715\pi\)
−0.787675 + 0.616091i \(0.788715\pi\)
\(522\) 0.135179 0.00591661
\(523\) 6.13225 0.268145 0.134072 0.990972i \(-0.457195\pi\)
0.134072 + 0.990972i \(0.457195\pi\)
\(524\) −1.72133 −0.0751968
\(525\) −64.2950 −2.80606
\(526\) 23.1597 1.00981
\(527\) −1.08959 −0.0474632
\(528\) −15.9470 −0.694006
\(529\) 29.1619 1.26791
\(530\) 4.51104 0.195947
\(531\) 0.159335 0.00691457
\(532\) 6.28866 0.272648
\(533\) −14.7648 −0.639532
\(534\) −20.4218 −0.883738
\(535\) −38.4109 −1.66065
\(536\) 25.1096 1.08457
\(537\) 14.1303 0.609766
\(538\) −14.4256 −0.621930
\(539\) −18.5701 −0.799872
\(540\) 14.7520 0.634826
\(541\) −29.5854 −1.27197 −0.635987 0.771700i \(-0.719407\pi\)
−0.635987 + 0.771700i \(0.719407\pi\)
\(542\) 9.95436 0.427577
\(543\) 19.0754 0.818602
\(544\) 22.3366 0.957674
\(545\) 27.3868 1.17312
\(546\) −39.4857 −1.68983
\(547\) 36.6644 1.56765 0.783827 0.620979i \(-0.213265\pi\)
0.783827 + 0.620979i \(0.213265\pi\)
\(548\) −0.680856 −0.0290847
\(549\) −0.277538 −0.0118450
\(550\) 55.5802 2.36995
\(551\) 15.9626 0.680032
\(552\) 38.6294 1.64417
\(553\) 48.5497 2.06454
\(554\) −34.2431 −1.45485
\(555\) −76.7976 −3.25987
\(556\) −2.63784 −0.111869
\(557\) −13.0289 −0.552052 −0.276026 0.961150i \(-0.589018\pi\)
−0.276026 + 0.961150i \(0.589018\pi\)
\(558\) −0.00415286 −0.000175805 0
\(559\) −37.5134 −1.58665
\(560\) 27.7954 1.17457
\(561\) −45.1925 −1.90803
\(562\) 14.0277 0.591721
\(563\) −29.6497 −1.24959 −0.624793 0.780790i \(-0.714817\pi\)
−0.624793 + 0.780790i \(0.714817\pi\)
\(564\) 3.58664 0.151025
\(565\) 41.1285 1.73029
\(566\) −7.24850 −0.304677
\(567\) −30.3097 −1.27289
\(568\) 4.42067 0.185487
\(569\) −26.5214 −1.11183 −0.555916 0.831238i \(-0.687633\pi\)
−0.555916 + 0.831238i \(0.687633\pi\)
\(570\) 20.9059 0.875650
\(571\) −37.2859 −1.56037 −0.780183 0.625552i \(-0.784874\pi\)
−0.780183 + 0.625552i \(0.784874\pi\)
\(572\) −18.8207 −0.786932
\(573\) 9.65854 0.403491
\(574\) −9.37789 −0.391426
\(575\) −79.8654 −3.33062
\(576\) 0.166900 0.00695416
\(577\) 1.03258 0.0429868 0.0214934 0.999769i \(-0.493158\pi\)
0.0214934 + 0.999769i \(0.493158\pi\)
\(578\) −19.8862 −0.827156
\(579\) −22.8566 −0.949889
\(580\) −17.1963 −0.714037
\(581\) −48.8653 −2.02727
\(582\) 25.9102 1.07401
\(583\) −4.38891 −0.181770
\(584\) −7.40889 −0.306582
\(585\) 0.472678 0.0195428
\(586\) −9.25423 −0.382289
\(587\) −29.6501 −1.22379 −0.611895 0.790939i \(-0.709593\pi\)
−0.611895 + 0.790939i \(0.709593\pi\)
\(588\) 5.18179 0.213693
\(589\) −0.490393 −0.0202063
\(590\) 36.7609 1.51342
\(591\) −28.9024 −1.18888
\(592\) 22.8629 0.939658
\(593\) −3.38488 −0.139000 −0.0695002 0.997582i \(-0.522140\pi\)
−0.0695002 + 0.997582i \(0.522140\pi\)
\(594\) 26.0303 1.06803
\(595\) 78.7698 3.22925
\(596\) 6.12459 0.250873
\(597\) −5.74974 −0.235321
\(598\) −49.0479 −2.00572
\(599\) 3.31033 0.135256 0.0676281 0.997711i \(-0.478457\pi\)
0.0676281 + 0.997711i \(0.478457\pi\)
\(600\) −59.1456 −2.41461
\(601\) 38.6413 1.57621 0.788107 0.615539i \(-0.211061\pi\)
0.788107 + 0.615539i \(0.211061\pi\)
\(602\) −23.8268 −0.971108
\(603\) 0.160884 0.00655170
\(604\) 6.40541 0.260632
\(605\) −34.4460 −1.40043
\(606\) 8.96818 0.364307
\(607\) −42.5467 −1.72692 −0.863458 0.504420i \(-0.831706\pi\)
−0.863458 + 0.504420i \(0.831706\pi\)
\(608\) 10.0531 0.407706
\(609\) 35.1009 1.42236
\(610\) −64.0319 −2.59258
\(611\) −17.3672 −0.702600
\(612\) 0.0823557 0.00332903
\(613\) −31.8355 −1.28583 −0.642913 0.765939i \(-0.722274\pi\)
−0.642913 + 0.765939i \(0.722274\pi\)
\(614\) 28.8830 1.16562
\(615\) 17.1897 0.693156
\(616\) −45.5882 −1.83680
\(617\) −4.30232 −0.173205 −0.0866024 0.996243i \(-0.527601\pi\)
−0.0866024 + 0.996243i \(0.527601\pi\)
\(618\) −27.2881 −1.09769
\(619\) 28.5222 1.14641 0.573203 0.819413i \(-0.305701\pi\)
0.573203 + 0.819413i \(0.305701\pi\)
\(620\) 0.528292 0.0212167
\(621\) −37.4039 −1.50097
\(622\) 8.39776 0.336719
\(623\) −34.6312 −1.38747
\(624\) −21.5470 −0.862568
\(625\) 41.9916 1.67966
\(626\) 13.1407 0.525206
\(627\) −20.3399 −0.812296
\(628\) 2.07961 0.0829854
\(629\) 64.7913 2.58340
\(630\) 0.300223 0.0119612
\(631\) 12.2527 0.487773 0.243887 0.969804i \(-0.421578\pi\)
0.243887 + 0.969804i \(0.421578\pi\)
\(632\) 44.6614 1.77653
\(633\) −14.7860 −0.587691
\(634\) −17.1904 −0.682720
\(635\) 23.7944 0.944252
\(636\) 1.22468 0.0485615
\(637\) −25.0912 −0.994148
\(638\) −30.3432 −1.20130
\(639\) 0.0283244 0.00112049
\(640\) 8.03458 0.317595
\(641\) 10.4682 0.413468 0.206734 0.978397i \(-0.433716\pi\)
0.206734 + 0.978397i \(0.433716\pi\)
\(642\) 18.9124 0.746411
\(643\) −29.7777 −1.17432 −0.587159 0.809471i \(-0.699754\pi\)
−0.587159 + 0.809471i \(0.699754\pi\)
\(644\) 17.1772 0.676877
\(645\) 43.6746 1.71969
\(646\) −17.6375 −0.693939
\(647\) 36.4269 1.43209 0.716045 0.698054i \(-0.245951\pi\)
0.716045 + 0.698054i \(0.245951\pi\)
\(648\) −27.8822 −1.09532
\(649\) −35.7656 −1.40392
\(650\) 75.0976 2.94557
\(651\) −1.07835 −0.0422637
\(652\) 1.00171 0.0392299
\(653\) 43.7870 1.71352 0.856759 0.515717i \(-0.172474\pi\)
0.856759 + 0.515717i \(0.172474\pi\)
\(654\) −13.4844 −0.527284
\(655\) −9.70395 −0.379165
\(656\) −5.11743 −0.199802
\(657\) −0.0474707 −0.00185201
\(658\) −11.0308 −0.430027
\(659\) 47.6225 1.85511 0.927554 0.373690i \(-0.121907\pi\)
0.927554 + 0.373690i \(0.121907\pi\)
\(660\) 21.9118 0.852915
\(661\) −40.4025 −1.57147 −0.785737 0.618560i \(-0.787716\pi\)
−0.785737 + 0.618560i \(0.787716\pi\)
\(662\) −4.01052 −0.155873
\(663\) −61.0622 −2.37146
\(664\) −44.9517 −1.74446
\(665\) 35.4520 1.37477
\(666\) 0.246946 0.00956895
\(667\) 43.6013 1.68825
\(668\) −2.03359 −0.0786821
\(669\) 12.8321 0.496116
\(670\) 37.1181 1.43400
\(671\) 62.2983 2.40500
\(672\) 22.1061 0.852762
\(673\) 50.1686 1.93386 0.966928 0.255048i \(-0.0820913\pi\)
0.966928 + 0.255048i \(0.0820913\pi\)
\(674\) −9.16132 −0.352881
\(675\) 57.2693 2.20430
\(676\) −16.1889 −0.622651
\(677\) −29.5797 −1.13684 −0.568421 0.822738i \(-0.692445\pi\)
−0.568421 + 0.822738i \(0.692445\pi\)
\(678\) −20.2505 −0.777714
\(679\) 43.9383 1.68620
\(680\) 72.4612 2.77876
\(681\) −4.91533 −0.188356
\(682\) 0.932182 0.0356951
\(683\) −21.1259 −0.808359 −0.404179 0.914680i \(-0.632443\pi\)
−0.404179 + 0.914680i \(0.632443\pi\)
\(684\) 0.0370660 0.00141725
\(685\) −3.83830 −0.146654
\(686\) 10.6561 0.406853
\(687\) 32.8045 1.25157
\(688\) −13.0021 −0.495699
\(689\) −5.93010 −0.225919
\(690\) 57.1036 2.17390
\(691\) 8.14572 0.309878 0.154939 0.987924i \(-0.450482\pi\)
0.154939 + 0.987924i \(0.450482\pi\)
\(692\) −9.37798 −0.356497
\(693\) −0.292095 −0.0110958
\(694\) 6.80238 0.258215
\(695\) −14.8707 −0.564078
\(696\) 32.2897 1.22394
\(697\) −14.5023 −0.549315
\(698\) 19.4358 0.735657
\(699\) −19.8002 −0.748912
\(700\) −26.3001 −0.994052
\(701\) 24.2564 0.916152 0.458076 0.888913i \(-0.348539\pi\)
0.458076 + 0.888913i \(0.348539\pi\)
\(702\) 35.1710 1.32744
\(703\) 29.1607 1.09982
\(704\) −37.4636 −1.41196
\(705\) 20.2195 0.761512
\(706\) −11.0987 −0.417706
\(707\) 15.2082 0.571963
\(708\) 9.98000 0.375071
\(709\) 32.2235 1.21018 0.605089 0.796158i \(-0.293138\pi\)
0.605089 + 0.796158i \(0.293138\pi\)
\(710\) 6.53482 0.245247
\(711\) 0.286157 0.0107317
\(712\) −31.8575 −1.19391
\(713\) −1.33949 −0.0501643
\(714\) −38.7839 −1.45145
\(715\) −106.101 −3.96795
\(716\) 5.78004 0.216010
\(717\) 11.4929 0.429209
\(718\) 27.2935 1.01859
\(719\) 38.1364 1.42225 0.711124 0.703066i \(-0.248186\pi\)
0.711124 + 0.703066i \(0.248186\pi\)
\(720\) 0.163829 0.00610555
\(721\) −46.2750 −1.72337
\(722\) 13.6348 0.507434
\(723\) 46.9330 1.74546
\(724\) 7.80285 0.289991
\(725\) −66.7582 −2.47934
\(726\) 16.9602 0.629452
\(727\) 3.55446 0.131828 0.0659138 0.997825i \(-0.479004\pi\)
0.0659138 + 0.997825i \(0.479004\pi\)
\(728\) −61.5968 −2.28293
\(729\) 26.8202 0.993340
\(730\) −10.9521 −0.405357
\(731\) −36.8467 −1.36282
\(732\) −17.3836 −0.642518
\(733\) −2.38315 −0.0880236 −0.0440118 0.999031i \(-0.514014\pi\)
−0.0440118 + 0.999031i \(0.514014\pi\)
\(734\) 13.0453 0.481511
\(735\) 29.2121 1.07751
\(736\) 27.4596 1.01217
\(737\) −36.1132 −1.33025
\(738\) −0.0552742 −0.00203467
\(739\) −45.3722 −1.66904 −0.834522 0.550974i \(-0.814256\pi\)
−0.834522 + 0.550974i \(0.814256\pi\)
\(740\) −31.4144 −1.15481
\(741\) −27.4823 −1.00959
\(742\) −3.76653 −0.138274
\(743\) −7.70430 −0.282643 −0.141322 0.989964i \(-0.545135\pi\)
−0.141322 + 0.989964i \(0.545135\pi\)
\(744\) −0.991981 −0.0363678
\(745\) 34.5271 1.26498
\(746\) −32.2044 −1.17909
\(747\) −0.288017 −0.0105380
\(748\) −18.4862 −0.675922
\(749\) 32.0715 1.17187
\(750\) −47.8989 −1.74902
\(751\) −44.9613 −1.64066 −0.820331 0.571889i \(-0.806211\pi\)
−0.820331 + 0.571889i \(0.806211\pi\)
\(752\) −6.01942 −0.219506
\(753\) 36.5125 1.33059
\(754\) −40.9984 −1.49307
\(755\) 36.1102 1.31419
\(756\) −12.3173 −0.447977
\(757\) 4.92035 0.178833 0.0894165 0.995994i \(-0.471500\pi\)
0.0894165 + 0.995994i \(0.471500\pi\)
\(758\) −29.6351 −1.07640
\(759\) −55.5575 −2.01661
\(760\) 32.6127 1.18299
\(761\) −15.7194 −0.569828 −0.284914 0.958553i \(-0.591965\pi\)
−0.284914 + 0.958553i \(0.591965\pi\)
\(762\) −11.7156 −0.424413
\(763\) −22.8669 −0.827836
\(764\) 3.95086 0.142937
\(765\) 0.464277 0.0167860
\(766\) −36.7803 −1.32893
\(767\) −48.3250 −1.74491
\(768\) 25.4571 0.918603
\(769\) 45.1212 1.62711 0.813556 0.581487i \(-0.197529\pi\)
0.813556 + 0.581487i \(0.197529\pi\)
\(770\) −67.3904 −2.42858
\(771\) 26.6996 0.961564
\(772\) −9.34960 −0.336499
\(773\) 21.3169 0.766716 0.383358 0.923600i \(-0.374768\pi\)
0.383358 + 0.923600i \(0.374768\pi\)
\(774\) −0.140438 −0.00504792
\(775\) 2.05090 0.0736704
\(776\) 40.4193 1.45097
\(777\) 64.1227 2.30039
\(778\) −8.69955 −0.311894
\(779\) −6.52709 −0.233857
\(780\) 29.6063 1.06007
\(781\) −6.35790 −0.227503
\(782\) −48.1762 −1.72278
\(783\) −31.2654 −1.11733
\(784\) −8.69654 −0.310591
\(785\) 11.7237 0.418437
\(786\) 4.77793 0.170423
\(787\) 27.4495 0.978470 0.489235 0.872152i \(-0.337276\pi\)
0.489235 + 0.872152i \(0.337276\pi\)
\(788\) −11.8226 −0.421164
\(789\) 35.4455 1.26189
\(790\) 66.0203 2.34890
\(791\) −34.3406 −1.22101
\(792\) −0.268701 −0.00954788
\(793\) 84.1748 2.98913
\(794\) 19.2381 0.682736
\(795\) 6.90406 0.244862
\(796\) −2.35195 −0.0833628
\(797\) 6.11326 0.216543 0.108271 0.994121i \(-0.465468\pi\)
0.108271 + 0.994121i \(0.465468\pi\)
\(798\) −17.4555 −0.617919
\(799\) −17.0585 −0.603486
\(800\) −42.0435 −1.48646
\(801\) −0.204119 −0.00721221
\(802\) 11.2104 0.395853
\(803\) 10.6556 0.376029
\(804\) 10.0770 0.355388
\(805\) 96.8359 3.41302
\(806\) 1.25952 0.0443648
\(807\) −22.0780 −0.777184
\(808\) 13.9902 0.492172
\(809\) −15.9722 −0.561551 −0.280776 0.959773i \(-0.590592\pi\)
−0.280776 + 0.959773i \(0.590592\pi\)
\(810\) −41.2166 −1.44820
\(811\) −22.7644 −0.799367 −0.399684 0.916653i \(-0.630880\pi\)
−0.399684 + 0.916653i \(0.630880\pi\)
\(812\) 14.3582 0.503873
\(813\) 15.2350 0.534313
\(814\) −55.4313 −1.94286
\(815\) 5.64708 0.197809
\(816\) −21.1640 −0.740888
\(817\) −16.5836 −0.580188
\(818\) −15.0509 −0.526242
\(819\) −0.394666 −0.0137908
\(820\) 7.03152 0.245551
\(821\) −17.5222 −0.611528 −0.305764 0.952107i \(-0.598912\pi\)
−0.305764 + 0.952107i \(0.598912\pi\)
\(822\) 1.88986 0.0659165
\(823\) −5.85303 −0.204024 −0.102012 0.994783i \(-0.532528\pi\)
−0.102012 + 0.994783i \(0.532528\pi\)
\(824\) −42.5688 −1.48295
\(825\) 85.0644 2.96156
\(826\) −30.6938 −1.06797
\(827\) 47.7861 1.66168 0.830842 0.556508i \(-0.187859\pi\)
0.830842 + 0.556508i \(0.187859\pi\)
\(828\) 0.101244 0.00351848
\(829\) −28.5195 −0.990523 −0.495261 0.868744i \(-0.664928\pi\)
−0.495261 + 0.868744i \(0.664928\pi\)
\(830\) −66.4495 −2.30650
\(831\) −52.4083 −1.81803
\(832\) −50.6192 −1.75490
\(833\) −24.6452 −0.853906
\(834\) 7.32189 0.253536
\(835\) −11.4643 −0.396738
\(836\) −8.32010 −0.287757
\(837\) 0.960512 0.0332001
\(838\) 28.6565 0.989921
\(839\) 8.65980 0.298970 0.149485 0.988764i \(-0.452238\pi\)
0.149485 + 0.988764i \(0.452238\pi\)
\(840\) 71.7134 2.47435
\(841\) 7.44570 0.256748
\(842\) −16.3757 −0.564344
\(843\) 21.4691 0.739434
\(844\) −6.04827 −0.208190
\(845\) −91.2645 −3.13959
\(846\) −0.0650168 −0.00223532
\(847\) 28.7610 0.988240
\(848\) −2.05536 −0.0705813
\(849\) −11.0937 −0.380735
\(850\) 73.7628 2.53004
\(851\) 79.6514 2.73041
\(852\) 1.77410 0.0607797
\(853\) 6.46300 0.221289 0.110644 0.993860i \(-0.464709\pi\)
0.110644 + 0.993860i \(0.464709\pi\)
\(854\) 53.4640 1.82950
\(855\) 0.208958 0.00714621
\(856\) 29.5029 1.00839
\(857\) 28.1294 0.960881 0.480441 0.877027i \(-0.340477\pi\)
0.480441 + 0.877027i \(0.340477\pi\)
\(858\) 52.2408 1.78347
\(859\) −12.9481 −0.441785 −0.220893 0.975298i \(-0.570897\pi\)
−0.220893 + 0.975298i \(0.570897\pi\)
\(860\) 17.8653 0.609201
\(861\) −14.3527 −0.489138
\(862\) 16.3621 0.557295
\(863\) −7.32424 −0.249320 −0.124660 0.992200i \(-0.539784\pi\)
−0.124660 + 0.992200i \(0.539784\pi\)
\(864\) −19.6905 −0.669885
\(865\) −52.8680 −1.79756
\(866\) 28.0235 0.952276
\(867\) −30.4354 −1.03364
\(868\) −0.441102 −0.0149720
\(869\) −64.2329 −2.17895
\(870\) 47.7320 1.61827
\(871\) −48.7946 −1.65334
\(872\) −21.0354 −0.712350
\(873\) 0.258977 0.00876504
\(874\) −21.6827 −0.733429
\(875\) −81.2266 −2.74596
\(876\) −2.97333 −0.100460
\(877\) 7.11657 0.240310 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(878\) 33.4575 1.12914
\(879\) −14.1634 −0.477720
\(880\) −36.7743 −1.23966
\(881\) 4.35498 0.146723 0.0733615 0.997305i \(-0.476627\pi\)
0.0733615 + 0.997305i \(0.476627\pi\)
\(882\) −0.0939328 −0.00316288
\(883\) −9.97198 −0.335584 −0.167792 0.985822i \(-0.553664\pi\)
−0.167792 + 0.985822i \(0.553664\pi\)
\(884\) −24.9777 −0.840092
\(885\) 56.2618 1.89122
\(886\) −5.13077 −0.172372
\(887\) 34.5329 1.15950 0.579751 0.814794i \(-0.303150\pi\)
0.579751 + 0.814794i \(0.303150\pi\)
\(888\) 58.9871 1.97948
\(889\) −19.8673 −0.666328
\(890\) −47.0932 −1.57857
\(891\) 40.1007 1.34342
\(892\) 5.24901 0.175750
\(893\) −7.67754 −0.256919
\(894\) −17.0001 −0.568569
\(895\) 32.5847 1.08919
\(896\) −6.70853 −0.224116
\(897\) −75.0669 −2.50641
\(898\) −7.75281 −0.258715
\(899\) −1.11966 −0.0373427
\(900\) −0.155016 −0.00516719
\(901\) −5.82470 −0.194049
\(902\) 12.4073 0.413117
\(903\) −36.4665 −1.21353
\(904\) −31.5903 −1.05068
\(905\) 43.9883 1.46222
\(906\) −17.7796 −0.590687
\(907\) −40.9405 −1.35941 −0.679703 0.733487i \(-0.737891\pi\)
−0.679703 + 0.733487i \(0.737891\pi\)
\(908\) −2.01064 −0.0667253
\(909\) 0.0896386 0.00297312
\(910\) −91.0550 −3.01844
\(911\) −3.82522 −0.126735 −0.0633676 0.997990i \(-0.520184\pi\)
−0.0633676 + 0.997990i \(0.520184\pi\)
\(912\) −9.52531 −0.315415
\(913\) 64.6504 2.13962
\(914\) 20.8089 0.688296
\(915\) −97.9996 −3.23977
\(916\) 13.4188 0.443371
\(917\) 8.10239 0.267565
\(918\) 34.5459 1.14018
\(919\) 7.29380 0.240600 0.120300 0.992738i \(-0.461614\pi\)
0.120300 + 0.992738i \(0.461614\pi\)
\(920\) 89.0803 2.93689
\(921\) 44.2048 1.45660
\(922\) 34.0860 1.12256
\(923\) −8.59051 −0.282760
\(924\) −18.2954 −0.601875
\(925\) −121.955 −4.00984
\(926\) −30.8274 −1.01305
\(927\) −0.272749 −0.00895826
\(928\) 22.9530 0.753470
\(929\) 8.47518 0.278062 0.139031 0.990288i \(-0.455601\pi\)
0.139031 + 0.990288i \(0.455601\pi\)
\(930\) −1.46639 −0.0480848
\(931\) −11.0921 −0.363529
\(932\) −8.09935 −0.265303
\(933\) 12.8526 0.420775
\(934\) −2.36236 −0.0772988
\(935\) −104.215 −3.40820
\(936\) −0.363057 −0.0118669
\(937\) −24.0951 −0.787152 −0.393576 0.919292i \(-0.628762\pi\)
−0.393576 + 0.919292i \(0.628762\pi\)
\(938\) −30.9921 −1.01193
\(939\) 20.1115 0.656315
\(940\) 8.27089 0.269767
\(941\) 41.4426 1.35099 0.675494 0.737365i \(-0.263930\pi\)
0.675494 + 0.737365i \(0.263930\pi\)
\(942\) −5.77240 −0.188075
\(943\) −17.8285 −0.580575
\(944\) −16.7493 −0.545144
\(945\) −69.4384 −2.25883
\(946\) 31.5236 1.02492
\(947\) 32.9840 1.07184 0.535919 0.844270i \(-0.319965\pi\)
0.535919 + 0.844270i \(0.319965\pi\)
\(948\) 17.9235 0.582127
\(949\) 14.3974 0.467360
\(950\) 33.1985 1.07710
\(951\) −26.3096 −0.853149
\(952\) −60.5020 −1.96088
\(953\) −18.1979 −0.589488 −0.294744 0.955576i \(-0.595234\pi\)
−0.294744 + 0.955576i \(0.595234\pi\)
\(954\) −0.0222003 −0.000718761 0
\(955\) 22.2728 0.720732
\(956\) 4.70121 0.152048
\(957\) −46.4397 −1.50118
\(958\) 2.56387 0.0828349
\(959\) 3.20482 0.103489
\(960\) 58.9329 1.90205
\(961\) −30.9656 −0.998890
\(962\) −74.8963 −2.41475
\(963\) 0.189032 0.00609148
\(964\) 19.1981 0.618331
\(965\) −52.7080 −1.69673
\(966\) −47.6791 −1.53405
\(967\) 33.2473 1.06916 0.534580 0.845118i \(-0.320470\pi\)
0.534580 + 0.845118i \(0.320470\pi\)
\(968\) 26.4575 0.850377
\(969\) −26.9939 −0.867169
\(970\) 59.7495 1.91844
\(971\) 37.0654 1.18949 0.594743 0.803916i \(-0.297254\pi\)
0.594743 + 0.803916i \(0.297254\pi\)
\(972\) −0.145679 −0.00467267
\(973\) 12.4164 0.398052
\(974\) −5.89704 −0.188953
\(975\) 114.935 3.68088
\(976\) 29.1748 0.933862
\(977\) 13.9196 0.445328 0.222664 0.974895i \(-0.428525\pi\)
0.222664 + 0.974895i \(0.428525\pi\)
\(978\) −2.78045 −0.0889091
\(979\) 45.8182 1.46435
\(980\) 11.9493 0.381708
\(981\) −0.134779 −0.00430318
\(982\) −1.71368 −0.0546857
\(983\) 1.00000 0.0318950
\(984\) −13.2032 −0.420902
\(985\) −66.6496 −2.12363
\(986\) −40.2698 −1.28245
\(987\) −16.8825 −0.537375
\(988\) −11.2418 −0.357648
\(989\) −45.2976 −1.44038
\(990\) −0.397206 −0.0126240
\(991\) 2.58781 0.0822045 0.0411023 0.999155i \(-0.486913\pi\)
0.0411023 + 0.999155i \(0.486913\pi\)
\(992\) −0.705146 −0.0223884
\(993\) −6.13802 −0.194784
\(994\) −5.45630 −0.173063
\(995\) −13.2590 −0.420340
\(996\) −18.0400 −0.571619
\(997\) 0.514953 0.0163087 0.00815436 0.999967i \(-0.497404\pi\)
0.00815436 + 0.999967i \(0.497404\pi\)
\(998\) −19.0152 −0.601917
\(999\) −57.1159 −1.80707
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.1.17 54
3.2 odd 2 8847.2.a.g.1.38 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.2.a.b.1.17 54 1.1 even 1 trivial
8847.2.a.g.1.38 54 3.2 odd 2