Properties

Label 6033.2.a.d.1.19
Level $6033$
Weight $2$
Character 6033.1
Self dual yes
Analytic conductor $48.174$
Analytic rank $1$
Dimension $84$
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] = [6033,2,Mod(1,6033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6033, 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("6033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6033 = 3 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6033.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: \(48.1737475394\)
Analytic rank: \(1\)
Dimension: \(84\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 6033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.86532 q^{2} -1.00000 q^{3} +1.47943 q^{4} -0.830382 q^{5} +1.86532 q^{6} -1.56075 q^{7} +0.971032 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.86532 q^{2} -1.00000 q^{3} +1.47943 q^{4} -0.830382 q^{5} +1.86532 q^{6} -1.56075 q^{7} +0.971032 q^{8} +1.00000 q^{9} +1.54893 q^{10} -0.963587 q^{11} -1.47943 q^{12} +2.49116 q^{13} +2.91131 q^{14} +0.830382 q^{15} -4.77015 q^{16} -7.01663 q^{17} -1.86532 q^{18} +7.71862 q^{19} -1.22849 q^{20} +1.56075 q^{21} +1.79740 q^{22} +4.98467 q^{23} -0.971032 q^{24} -4.31047 q^{25} -4.64681 q^{26} -1.00000 q^{27} -2.30903 q^{28} -5.27328 q^{29} -1.54893 q^{30} +7.06097 q^{31} +6.95580 q^{32} +0.963587 q^{33} +13.0883 q^{34} +1.29602 q^{35} +1.47943 q^{36} -6.02292 q^{37} -14.3977 q^{38} -2.49116 q^{39} -0.806327 q^{40} -3.69659 q^{41} -2.91131 q^{42} -2.56589 q^{43} -1.42556 q^{44} -0.830382 q^{45} -9.29802 q^{46} +3.50021 q^{47} +4.77015 q^{48} -4.56405 q^{49} +8.04041 q^{50} +7.01663 q^{51} +3.68549 q^{52} +2.99589 q^{53} +1.86532 q^{54} +0.800146 q^{55} -1.51554 q^{56} -7.71862 q^{57} +9.83638 q^{58} +4.80183 q^{59} +1.22849 q^{60} +0.592250 q^{61} -13.1710 q^{62} -1.56075 q^{63} -3.43452 q^{64} -2.06861 q^{65} -1.79740 q^{66} +2.76615 q^{67} -10.3806 q^{68} -4.98467 q^{69} -2.41750 q^{70} -0.539467 q^{71} +0.971032 q^{72} +8.09331 q^{73} +11.2347 q^{74} +4.31047 q^{75} +11.4192 q^{76} +1.50392 q^{77} +4.64681 q^{78} +8.49130 q^{79} +3.96105 q^{80} +1.00000 q^{81} +6.89534 q^{82} -13.3674 q^{83} +2.30903 q^{84} +5.82649 q^{85} +4.78620 q^{86} +5.27328 q^{87} -0.935674 q^{88} -4.97649 q^{89} +1.54893 q^{90} -3.88808 q^{91} +7.37447 q^{92} -7.06097 q^{93} -6.52903 q^{94} -6.40940 q^{95} -6.95580 q^{96} -8.51266 q^{97} +8.51342 q^{98} -0.963587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86532 −1.31898 −0.659491 0.751712i \(-0.729228\pi\)
−0.659491 + 0.751712i \(0.729228\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.47943 0.739715
\(5\) −0.830382 −0.371358 −0.185679 0.982610i \(-0.559448\pi\)
−0.185679 + 0.982610i \(0.559448\pi\)
\(6\) 1.86532 0.761515
\(7\) −1.56075 −0.589910 −0.294955 0.955511i \(-0.595305\pi\)
−0.294955 + 0.955511i \(0.595305\pi\)
\(8\) 0.971032 0.343312
\(9\) 1.00000 0.333333
\(10\) 1.54893 0.489815
\(11\) −0.963587 −0.290532 −0.145266 0.989393i \(-0.546404\pi\)
−0.145266 + 0.989393i \(0.546404\pi\)
\(12\) −1.47943 −0.427075
\(13\) 2.49116 0.690922 0.345461 0.938433i \(-0.387723\pi\)
0.345461 + 0.938433i \(0.387723\pi\)
\(14\) 2.91131 0.778081
\(15\) 0.830382 0.214404
\(16\) −4.77015 −1.19254
\(17\) −7.01663 −1.70178 −0.850892 0.525341i \(-0.823938\pi\)
−0.850892 + 0.525341i \(0.823938\pi\)
\(18\) −1.86532 −0.439661
\(19\) 7.71862 1.77077 0.885386 0.464856i \(-0.153894\pi\)
0.885386 + 0.464856i \(0.153894\pi\)
\(20\) −1.22849 −0.274699
\(21\) 1.56075 0.340585
\(22\) 1.79740 0.383207
\(23\) 4.98467 1.03938 0.519688 0.854356i \(-0.326048\pi\)
0.519688 + 0.854356i \(0.326048\pi\)
\(24\) −0.971032 −0.198211
\(25\) −4.31047 −0.862093
\(26\) −4.64681 −0.911314
\(27\) −1.00000 −0.192450
\(28\) −2.30903 −0.436365
\(29\) −5.27328 −0.979224 −0.489612 0.871940i \(-0.662862\pi\)
−0.489612 + 0.871940i \(0.662862\pi\)
\(30\) −1.54893 −0.282795
\(31\) 7.06097 1.26819 0.634094 0.773256i \(-0.281373\pi\)
0.634094 + 0.773256i \(0.281373\pi\)
\(32\) 6.95580 1.22962
\(33\) 0.963587 0.167739
\(34\) 13.0883 2.24462
\(35\) 1.29602 0.219068
\(36\) 1.47943 0.246572
\(37\) −6.02292 −0.990163 −0.495081 0.868847i \(-0.664862\pi\)
−0.495081 + 0.868847i \(0.664862\pi\)
\(38\) −14.3977 −2.33562
\(39\) −2.49116 −0.398904
\(40\) −0.806327 −0.127492
\(41\) −3.69659 −0.577311 −0.288656 0.957433i \(-0.593208\pi\)
−0.288656 + 0.957433i \(0.593208\pi\)
\(42\) −2.91131 −0.449225
\(43\) −2.56589 −0.391294 −0.195647 0.980674i \(-0.562681\pi\)
−0.195647 + 0.980674i \(0.562681\pi\)
\(44\) −1.42556 −0.214911
\(45\) −0.830382 −0.123786
\(46\) −9.29802 −1.37092
\(47\) 3.50021 0.510558 0.255279 0.966867i \(-0.417833\pi\)
0.255279 + 0.966867i \(0.417833\pi\)
\(48\) 4.77015 0.688511
\(49\) −4.56405 −0.652006
\(50\) 8.04041 1.13709
\(51\) 7.01663 0.982525
\(52\) 3.68549 0.511085
\(53\) 2.99589 0.411516 0.205758 0.978603i \(-0.434034\pi\)
0.205758 + 0.978603i \(0.434034\pi\)
\(54\) 1.86532 0.253838
\(55\) 0.800146 0.107892
\(56\) −1.51554 −0.202523
\(57\) −7.71862 −1.02236
\(58\) 9.83638 1.29158
\(59\) 4.80183 0.625145 0.312573 0.949894i \(-0.398809\pi\)
0.312573 + 0.949894i \(0.398809\pi\)
\(60\) 1.22849 0.158598
\(61\) 0.592250 0.0758298 0.0379149 0.999281i \(-0.487928\pi\)
0.0379149 + 0.999281i \(0.487928\pi\)
\(62\) −13.1710 −1.67272
\(63\) −1.56075 −0.196637
\(64\) −3.43452 −0.429315
\(65\) −2.06861 −0.256580
\(66\) −1.79740 −0.221245
\(67\) 2.76615 0.337939 0.168969 0.985621i \(-0.445956\pi\)
0.168969 + 0.985621i \(0.445956\pi\)
\(68\) −10.3806 −1.25883
\(69\) −4.98467 −0.600084
\(70\) −2.41750 −0.288947
\(71\) −0.539467 −0.0640229 −0.0320115 0.999488i \(-0.510191\pi\)
−0.0320115 + 0.999488i \(0.510191\pi\)
\(72\) 0.971032 0.114437
\(73\) 8.09331 0.947250 0.473625 0.880727i \(-0.342945\pi\)
0.473625 + 0.880727i \(0.342945\pi\)
\(74\) 11.2347 1.30601
\(75\) 4.31047 0.497730
\(76\) 11.4192 1.30987
\(77\) 1.50392 0.171388
\(78\) 4.64681 0.526148
\(79\) 8.49130 0.955346 0.477673 0.878538i \(-0.341480\pi\)
0.477673 + 0.878538i \(0.341480\pi\)
\(80\) 3.96105 0.442858
\(81\) 1.00000 0.111111
\(82\) 6.89534 0.761463
\(83\) −13.3674 −1.46726 −0.733632 0.679547i \(-0.762176\pi\)
−0.733632 + 0.679547i \(0.762176\pi\)
\(84\) 2.30903 0.251935
\(85\) 5.82649 0.631971
\(86\) 4.78620 0.516110
\(87\) 5.27328 0.565355
\(88\) −0.935674 −0.0997431
\(89\) −4.97649 −0.527507 −0.263753 0.964590i \(-0.584961\pi\)
−0.263753 + 0.964590i \(0.584961\pi\)
\(90\) 1.54893 0.163272
\(91\) −3.88808 −0.407582
\(92\) 7.37447 0.768841
\(93\) −7.06097 −0.732189
\(94\) −6.52903 −0.673418
\(95\) −6.40940 −0.657591
\(96\) −6.95580 −0.709924
\(97\) −8.51266 −0.864329 −0.432165 0.901795i \(-0.642250\pi\)
−0.432165 + 0.901795i \(0.642250\pi\)
\(98\) 8.51342 0.859985
\(99\) −0.963587 −0.0968441
\(100\) −6.37703 −0.637703
\(101\) 7.85984 0.782083 0.391042 0.920373i \(-0.372115\pi\)
0.391042 + 0.920373i \(0.372115\pi\)
\(102\) −13.0883 −1.29593
\(103\) −9.63873 −0.949732 −0.474866 0.880058i \(-0.657504\pi\)
−0.474866 + 0.880058i \(0.657504\pi\)
\(104\) 2.41899 0.237202
\(105\) −1.29602 −0.126479
\(106\) −5.58829 −0.542783
\(107\) −6.35949 −0.614795 −0.307398 0.951581i \(-0.599458\pi\)
−0.307398 + 0.951581i \(0.599458\pi\)
\(108\) −1.47943 −0.142358
\(109\) 14.1151 1.35198 0.675992 0.736909i \(-0.263715\pi\)
0.675992 + 0.736909i \(0.263715\pi\)
\(110\) −1.49253 −0.142307
\(111\) 6.02292 0.571671
\(112\) 7.44503 0.703489
\(113\) 1.62567 0.152931 0.0764653 0.997072i \(-0.475637\pi\)
0.0764653 + 0.997072i \(0.475637\pi\)
\(114\) 14.3977 1.34847
\(115\) −4.13918 −0.385981
\(116\) −7.80145 −0.724347
\(117\) 2.49116 0.230307
\(118\) −8.95696 −0.824555
\(119\) 10.9512 1.00390
\(120\) 0.806327 0.0736073
\(121\) −10.0715 −0.915591
\(122\) −1.10474 −0.100018
\(123\) 3.69659 0.333311
\(124\) 10.4462 0.938098
\(125\) 7.73124 0.691504
\(126\) 2.91131 0.259360
\(127\) 20.7987 1.84559 0.922793 0.385295i \(-0.125900\pi\)
0.922793 + 0.385295i \(0.125900\pi\)
\(128\) −7.50511 −0.663364
\(129\) 2.56589 0.225914
\(130\) 3.85863 0.338424
\(131\) −2.35111 −0.205417 −0.102709 0.994711i \(-0.532751\pi\)
−0.102709 + 0.994711i \(0.532751\pi\)
\(132\) 1.42556 0.124079
\(133\) −12.0469 −1.04460
\(134\) −5.15976 −0.445735
\(135\) 0.830382 0.0714679
\(136\) −6.81337 −0.584242
\(137\) −9.94169 −0.849376 −0.424688 0.905340i \(-0.639616\pi\)
−0.424688 + 0.905340i \(0.639616\pi\)
\(138\) 9.29802 0.791500
\(139\) 2.50975 0.212874 0.106437 0.994319i \(-0.466056\pi\)
0.106437 + 0.994319i \(0.466056\pi\)
\(140\) 1.91737 0.162048
\(141\) −3.50021 −0.294771
\(142\) 1.00628 0.0844451
\(143\) −2.40045 −0.200735
\(144\) −4.77015 −0.397512
\(145\) 4.37884 0.363643
\(146\) −15.0966 −1.24941
\(147\) 4.56405 0.376436
\(148\) −8.91049 −0.732438
\(149\) 11.2473 0.921417 0.460709 0.887551i \(-0.347595\pi\)
0.460709 + 0.887551i \(0.347595\pi\)
\(150\) −8.04041 −0.656497
\(151\) 11.9413 0.971765 0.485883 0.874024i \(-0.338498\pi\)
0.485883 + 0.874024i \(0.338498\pi\)
\(152\) 7.49502 0.607927
\(153\) −7.01663 −0.567261
\(154\) −2.80530 −0.226058
\(155\) −5.86331 −0.470952
\(156\) −3.68549 −0.295075
\(157\) 22.0003 1.75581 0.877907 0.478831i \(-0.158939\pi\)
0.877907 + 0.478831i \(0.158939\pi\)
\(158\) −15.8390 −1.26008
\(159\) −2.99589 −0.237589
\(160\) −5.77597 −0.456631
\(161\) −7.77984 −0.613138
\(162\) −1.86532 −0.146554
\(163\) −7.54504 −0.590973 −0.295487 0.955347i \(-0.595482\pi\)
−0.295487 + 0.955347i \(0.595482\pi\)
\(164\) −5.46885 −0.427046
\(165\) −0.800146 −0.0622912
\(166\) 24.9345 1.93529
\(167\) 13.4737 1.04262 0.521312 0.853366i \(-0.325443\pi\)
0.521312 + 0.853366i \(0.325443\pi\)
\(168\) 1.51554 0.116927
\(169\) −6.79414 −0.522626
\(170\) −10.8683 −0.833559
\(171\) 7.71862 0.590258
\(172\) −3.79605 −0.289446
\(173\) −20.0283 −1.52272 −0.761362 0.648327i \(-0.775469\pi\)
−0.761362 + 0.648327i \(0.775469\pi\)
\(174\) −9.83638 −0.745694
\(175\) 6.72758 0.508557
\(176\) 4.59645 0.346471
\(177\) −4.80183 −0.360928
\(178\) 9.28276 0.695772
\(179\) 8.16777 0.610488 0.305244 0.952274i \(-0.401262\pi\)
0.305244 + 0.952274i \(0.401262\pi\)
\(180\) −1.22849 −0.0915664
\(181\) 12.5430 0.932315 0.466158 0.884702i \(-0.345638\pi\)
0.466158 + 0.884702i \(0.345638\pi\)
\(182\) 7.25253 0.537593
\(183\) −0.592250 −0.0437804
\(184\) 4.84027 0.356830
\(185\) 5.00133 0.367705
\(186\) 13.1710 0.965744
\(187\) 6.76114 0.494423
\(188\) 5.17832 0.377668
\(189\) 1.56075 0.113528
\(190\) 11.9556 0.867351
\(191\) 8.52547 0.616881 0.308441 0.951244i \(-0.400193\pi\)
0.308441 + 0.951244i \(0.400193\pi\)
\(192\) 3.43452 0.247865
\(193\) 4.74772 0.341748 0.170874 0.985293i \(-0.445341\pi\)
0.170874 + 0.985293i \(0.445341\pi\)
\(194\) 15.8789 1.14004
\(195\) 2.06861 0.148136
\(196\) −6.75218 −0.482299
\(197\) 8.15451 0.580985 0.290492 0.956877i \(-0.406181\pi\)
0.290492 + 0.956877i \(0.406181\pi\)
\(198\) 1.79740 0.127736
\(199\) −0.508875 −0.0360732 −0.0180366 0.999837i \(-0.505742\pi\)
−0.0180366 + 0.999837i \(0.505742\pi\)
\(200\) −4.18560 −0.295967
\(201\) −2.76615 −0.195109
\(202\) −14.6611 −1.03155
\(203\) 8.23030 0.577654
\(204\) 10.3806 0.726788
\(205\) 3.06959 0.214389
\(206\) 17.9793 1.25268
\(207\) 4.98467 0.346458
\(208\) −11.8832 −0.823950
\(209\) −7.43756 −0.514467
\(210\) 2.41750 0.166823
\(211\) 3.64195 0.250722 0.125361 0.992111i \(-0.459991\pi\)
0.125361 + 0.992111i \(0.459991\pi\)
\(212\) 4.43220 0.304405
\(213\) 0.539467 0.0369637
\(214\) 11.8625 0.810904
\(215\) 2.13067 0.145310
\(216\) −0.971032 −0.0660703
\(217\) −11.0204 −0.748117
\(218\) −26.3293 −1.78324
\(219\) −8.09331 −0.546895
\(220\) 1.18376 0.0798090
\(221\) −17.4795 −1.17580
\(222\) −11.2347 −0.754024
\(223\) 19.2756 1.29079 0.645396 0.763848i \(-0.276692\pi\)
0.645396 + 0.763848i \(0.276692\pi\)
\(224\) −10.8563 −0.725367
\(225\) −4.31047 −0.287364
\(226\) −3.03241 −0.201713
\(227\) −15.2177 −1.01003 −0.505017 0.863109i \(-0.668514\pi\)
−0.505017 + 0.863109i \(0.668514\pi\)
\(228\) −11.4192 −0.756252
\(229\) −20.4128 −1.34892 −0.674458 0.738313i \(-0.735623\pi\)
−0.674458 + 0.738313i \(0.735623\pi\)
\(230\) 7.72091 0.509102
\(231\) −1.50392 −0.0989509
\(232\) −5.12053 −0.336179
\(233\) 8.60588 0.563790 0.281895 0.959445i \(-0.409037\pi\)
0.281895 + 0.959445i \(0.409037\pi\)
\(234\) −4.64681 −0.303771
\(235\) −2.90651 −0.189600
\(236\) 7.10397 0.462429
\(237\) −8.49130 −0.551569
\(238\) −20.4276 −1.32412
\(239\) −10.2583 −0.663556 −0.331778 0.943358i \(-0.607648\pi\)
−0.331778 + 0.943358i \(0.607648\pi\)
\(240\) −3.96105 −0.255684
\(241\) −14.6332 −0.942608 −0.471304 0.881971i \(-0.656216\pi\)
−0.471304 + 0.881971i \(0.656216\pi\)
\(242\) 18.7866 1.20765
\(243\) −1.00000 −0.0641500
\(244\) 0.876192 0.0560924
\(245\) 3.78990 0.242128
\(246\) −6.89534 −0.439631
\(247\) 19.2283 1.22347
\(248\) 6.85643 0.435384
\(249\) 13.3674 0.847125
\(250\) −14.4213 −0.912081
\(251\) −16.7486 −1.05716 −0.528582 0.848882i \(-0.677276\pi\)
−0.528582 + 0.848882i \(0.677276\pi\)
\(252\) −2.30903 −0.145455
\(253\) −4.80316 −0.301972
\(254\) −38.7963 −2.43430
\(255\) −5.82649 −0.364869
\(256\) 20.8685 1.30428
\(257\) 4.89131 0.305111 0.152556 0.988295i \(-0.451250\pi\)
0.152556 + 0.988295i \(0.451250\pi\)
\(258\) −4.78620 −0.297976
\(259\) 9.40031 0.584107
\(260\) −3.06036 −0.189796
\(261\) −5.27328 −0.326408
\(262\) 4.38558 0.270942
\(263\) 1.80979 0.111596 0.0557982 0.998442i \(-0.482230\pi\)
0.0557982 + 0.998442i \(0.482230\pi\)
\(264\) 0.935674 0.0575867
\(265\) −2.48773 −0.152820
\(266\) 22.4713 1.37780
\(267\) 4.97649 0.304556
\(268\) 4.09232 0.249978
\(269\) 3.71262 0.226363 0.113181 0.993574i \(-0.463896\pi\)
0.113181 + 0.993574i \(0.463896\pi\)
\(270\) −1.54893 −0.0942649
\(271\) −4.45630 −0.270701 −0.135350 0.990798i \(-0.543216\pi\)
−0.135350 + 0.990798i \(0.543216\pi\)
\(272\) 33.4704 2.02944
\(273\) 3.88808 0.235317
\(274\) 18.5445 1.12031
\(275\) 4.15351 0.250466
\(276\) −7.37447 −0.443891
\(277\) 9.13295 0.548746 0.274373 0.961623i \(-0.411530\pi\)
0.274373 + 0.961623i \(0.411530\pi\)
\(278\) −4.68150 −0.280778
\(279\) 7.06097 0.422729
\(280\) 1.25848 0.0752085
\(281\) −22.5769 −1.34682 −0.673412 0.739267i \(-0.735172\pi\)
−0.673412 + 0.739267i \(0.735172\pi\)
\(282\) 6.52903 0.388798
\(283\) −6.41224 −0.381168 −0.190584 0.981671i \(-0.561038\pi\)
−0.190584 + 0.981671i \(0.561038\pi\)
\(284\) −0.798103 −0.0473587
\(285\) 6.40940 0.379660
\(286\) 4.47761 0.264766
\(287\) 5.76948 0.340561
\(288\) 6.95580 0.409875
\(289\) 32.2331 1.89607
\(290\) −8.16795 −0.479639
\(291\) 8.51266 0.499021
\(292\) 11.9735 0.700695
\(293\) −3.55312 −0.207576 −0.103788 0.994599i \(-0.533096\pi\)
−0.103788 + 0.994599i \(0.533096\pi\)
\(294\) −8.51342 −0.496513
\(295\) −3.98735 −0.232153
\(296\) −5.84845 −0.339934
\(297\) 0.963587 0.0559130
\(298\) −20.9799 −1.21533
\(299\) 12.4176 0.718128
\(300\) 6.37703 0.368178
\(301\) 4.00472 0.230828
\(302\) −22.2743 −1.28174
\(303\) −7.85984 −0.451536
\(304\) −36.8189 −2.11171
\(305\) −0.491794 −0.0281600
\(306\) 13.0883 0.748207
\(307\) −27.0815 −1.54562 −0.772812 0.634635i \(-0.781150\pi\)
−0.772812 + 0.634635i \(0.781150\pi\)
\(308\) 2.22495 0.126778
\(309\) 9.63873 0.548328
\(310\) 10.9370 0.621178
\(311\) 17.1629 0.973219 0.486609 0.873620i \(-0.338233\pi\)
0.486609 + 0.873620i \(0.338233\pi\)
\(312\) −2.41899 −0.136948
\(313\) −4.58545 −0.259185 −0.129593 0.991567i \(-0.541367\pi\)
−0.129593 + 0.991567i \(0.541367\pi\)
\(314\) −41.0377 −2.31589
\(315\) 1.29602 0.0730226
\(316\) 12.5623 0.706683
\(317\) −24.8545 −1.39597 −0.697984 0.716113i \(-0.745919\pi\)
−0.697984 + 0.716113i \(0.745919\pi\)
\(318\) 5.58829 0.313376
\(319\) 5.08127 0.284496
\(320\) 2.85197 0.159430
\(321\) 6.35949 0.354952
\(322\) 14.5119 0.808718
\(323\) −54.1587 −3.01347
\(324\) 1.47943 0.0821905
\(325\) −10.7380 −0.595639
\(326\) 14.0739 0.779483
\(327\) −14.1151 −0.780569
\(328\) −3.58951 −0.198198
\(329\) −5.46297 −0.301183
\(330\) 1.49253 0.0821611
\(331\) −23.1335 −1.27153 −0.635765 0.771882i \(-0.719315\pi\)
−0.635765 + 0.771882i \(0.719315\pi\)
\(332\) −19.7761 −1.08536
\(333\) −6.02292 −0.330054
\(334\) −25.1327 −1.37520
\(335\) −2.29696 −0.125496
\(336\) −7.44503 −0.406160
\(337\) 13.9613 0.760522 0.380261 0.924879i \(-0.375834\pi\)
0.380261 + 0.924879i \(0.375834\pi\)
\(338\) 12.6733 0.689335
\(339\) −1.62567 −0.0882945
\(340\) 8.61988 0.467478
\(341\) −6.80386 −0.368450
\(342\) −14.3977 −0.778539
\(343\) 18.0486 0.974535
\(344\) −2.49156 −0.134336
\(345\) 4.13918 0.222846
\(346\) 37.3593 2.00845
\(347\) −13.3009 −0.714032 −0.357016 0.934098i \(-0.616206\pi\)
−0.357016 + 0.934098i \(0.616206\pi\)
\(348\) 7.80145 0.418202
\(349\) 25.4322 1.36136 0.680678 0.732583i \(-0.261685\pi\)
0.680678 + 0.732583i \(0.261685\pi\)
\(350\) −12.5491 −0.670778
\(351\) −2.49116 −0.132968
\(352\) −6.70252 −0.357246
\(353\) −27.3285 −1.45455 −0.727273 0.686348i \(-0.759213\pi\)
−0.727273 + 0.686348i \(0.759213\pi\)
\(354\) 8.95696 0.476057
\(355\) 0.447964 0.0237754
\(356\) −7.36237 −0.390205
\(357\) −10.9512 −0.579601
\(358\) −15.2355 −0.805223
\(359\) 4.39233 0.231818 0.115909 0.993260i \(-0.463022\pi\)
0.115909 + 0.993260i \(0.463022\pi\)
\(360\) −0.806327 −0.0424972
\(361\) 40.5771 2.13564
\(362\) −23.3968 −1.22971
\(363\) 10.0715 0.528617
\(364\) −5.75214 −0.301494
\(365\) −6.72054 −0.351769
\(366\) 1.10474 0.0577455
\(367\) 27.9324 1.45806 0.729029 0.684482i \(-0.239972\pi\)
0.729029 + 0.684482i \(0.239972\pi\)
\(368\) −23.7776 −1.23949
\(369\) −3.69659 −0.192437
\(370\) −9.32909 −0.484997
\(371\) −4.67584 −0.242758
\(372\) −10.4462 −0.541611
\(373\) −5.12249 −0.265232 −0.132616 0.991167i \(-0.542338\pi\)
−0.132616 + 0.991167i \(0.542338\pi\)
\(374\) −12.6117 −0.652136
\(375\) −7.73124 −0.399240
\(376\) 3.39882 0.175281
\(377\) −13.1366 −0.676568
\(378\) −2.91131 −0.149742
\(379\) 13.9046 0.714230 0.357115 0.934060i \(-0.383760\pi\)
0.357115 + 0.934060i \(0.383760\pi\)
\(380\) −9.48226 −0.486430
\(381\) −20.7987 −1.06555
\(382\) −15.9028 −0.813656
\(383\) −5.78300 −0.295498 −0.147749 0.989025i \(-0.547203\pi\)
−0.147749 + 0.989025i \(0.547203\pi\)
\(384\) 7.50511 0.382994
\(385\) −1.24883 −0.0636463
\(386\) −8.85603 −0.450760
\(387\) −2.56589 −0.130431
\(388\) −12.5939 −0.639357
\(389\) −21.4651 −1.08832 −0.544161 0.838981i \(-0.683152\pi\)
−0.544161 + 0.838981i \(0.683152\pi\)
\(390\) −3.85863 −0.195389
\(391\) −34.9756 −1.76879
\(392\) −4.43183 −0.223841
\(393\) 2.35111 0.118598
\(394\) −15.2108 −0.766309
\(395\) −7.05102 −0.354775
\(396\) −1.42556 −0.0716371
\(397\) −11.1495 −0.559577 −0.279788 0.960062i \(-0.590264\pi\)
−0.279788 + 0.960062i \(0.590264\pi\)
\(398\) 0.949216 0.0475799
\(399\) 12.0469 0.603098
\(400\) 20.5616 1.02808
\(401\) 26.8528 1.34096 0.670482 0.741926i \(-0.266087\pi\)
0.670482 + 0.741926i \(0.266087\pi\)
\(402\) 5.15976 0.257345
\(403\) 17.5900 0.876220
\(404\) 11.6281 0.578519
\(405\) −0.830382 −0.0412620
\(406\) −15.3522 −0.761915
\(407\) 5.80361 0.287674
\(408\) 6.81337 0.337312
\(409\) 12.3151 0.608943 0.304472 0.952521i \(-0.401520\pi\)
0.304472 + 0.952521i \(0.401520\pi\)
\(410\) −5.72577 −0.282776
\(411\) 9.94169 0.490387
\(412\) −14.2598 −0.702531
\(413\) −7.49448 −0.368779
\(414\) −9.29802 −0.456973
\(415\) 11.1001 0.544880
\(416\) 17.3280 0.849574
\(417\) −2.50975 −0.122903
\(418\) 13.8735 0.678573
\(419\) −0.482802 −0.0235864 −0.0117932 0.999930i \(-0.503754\pi\)
−0.0117932 + 0.999930i \(0.503754\pi\)
\(420\) −1.91737 −0.0935583
\(421\) 4.20660 0.205017 0.102509 0.994732i \(-0.467313\pi\)
0.102509 + 0.994732i \(0.467313\pi\)
\(422\) −6.79341 −0.330698
\(423\) 3.50021 0.170186
\(424\) 2.90910 0.141278
\(425\) 30.2450 1.46710
\(426\) −1.00628 −0.0487544
\(427\) −0.924357 −0.0447328
\(428\) −9.40842 −0.454773
\(429\) 2.40045 0.115895
\(430\) −3.97438 −0.191662
\(431\) −37.7930 −1.82043 −0.910213 0.414141i \(-0.864082\pi\)
−0.910213 + 0.414141i \(0.864082\pi\)
\(432\) 4.77015 0.229504
\(433\) 26.2119 1.25966 0.629832 0.776731i \(-0.283124\pi\)
0.629832 + 0.776731i \(0.283124\pi\)
\(434\) 20.5567 0.986753
\(435\) −4.37884 −0.209949
\(436\) 20.8823 1.00008
\(437\) 38.4748 1.84050
\(438\) 15.0966 0.721345
\(439\) −2.27776 −0.108712 −0.0543558 0.998522i \(-0.517311\pi\)
−0.0543558 + 0.998522i \(0.517311\pi\)
\(440\) 0.776967 0.0370404
\(441\) −4.56405 −0.217335
\(442\) 32.6050 1.55086
\(443\) −32.7283 −1.55497 −0.777485 0.628901i \(-0.783505\pi\)
−0.777485 + 0.628901i \(0.783505\pi\)
\(444\) 8.91049 0.422873
\(445\) 4.13239 0.195894
\(446\) −35.9553 −1.70253
\(447\) −11.2473 −0.531980
\(448\) 5.36045 0.253257
\(449\) −3.52134 −0.166182 −0.0830911 0.996542i \(-0.526479\pi\)
−0.0830911 + 0.996542i \(0.526479\pi\)
\(450\) 8.04041 0.379029
\(451\) 3.56199 0.167728
\(452\) 2.40507 0.113125
\(453\) −11.9413 −0.561049
\(454\) 28.3859 1.33222
\(455\) 3.22859 0.151359
\(456\) −7.49502 −0.350987
\(457\) 35.8412 1.67658 0.838290 0.545224i \(-0.183556\pi\)
0.838290 + 0.545224i \(0.183556\pi\)
\(458\) 38.0765 1.77920
\(459\) 7.01663 0.327508
\(460\) −6.12363 −0.285516
\(461\) −34.6163 −1.61224 −0.806121 0.591750i \(-0.798437\pi\)
−0.806121 + 0.591750i \(0.798437\pi\)
\(462\) 2.80530 0.130514
\(463\) −36.0446 −1.67513 −0.837567 0.546334i \(-0.816023\pi\)
−0.837567 + 0.546334i \(0.816023\pi\)
\(464\) 25.1543 1.16776
\(465\) 5.86331 0.271904
\(466\) −16.0527 −0.743629
\(467\) −0.946926 −0.0438185 −0.0219092 0.999760i \(-0.506974\pi\)
−0.0219092 + 0.999760i \(0.506974\pi\)
\(468\) 3.68549 0.170362
\(469\) −4.31728 −0.199353
\(470\) 5.42159 0.250079
\(471\) −22.0003 −1.01372
\(472\) 4.66273 0.214620
\(473\) 2.47245 0.113684
\(474\) 15.8390 0.727510
\(475\) −33.2708 −1.52657
\(476\) 16.2016 0.742599
\(477\) 2.99589 0.137172
\(478\) 19.1351 0.875218
\(479\) −12.7304 −0.581667 −0.290834 0.956774i \(-0.593933\pi\)
−0.290834 + 0.956774i \(0.593933\pi\)
\(480\) 5.77597 0.263636
\(481\) −15.0040 −0.684125
\(482\) 27.2957 1.24328
\(483\) 7.77984 0.353995
\(484\) −14.9001 −0.677276
\(485\) 7.06876 0.320976
\(486\) 1.86532 0.0846128
\(487\) −35.9217 −1.62777 −0.813885 0.581027i \(-0.802651\pi\)
−0.813885 + 0.581027i \(0.802651\pi\)
\(488\) 0.575093 0.0260333
\(489\) 7.54504 0.341198
\(490\) −7.06939 −0.319363
\(491\) 34.4343 1.55400 0.776999 0.629502i \(-0.216741\pi\)
0.776999 + 0.629502i \(0.216741\pi\)
\(492\) 5.46885 0.246555
\(493\) 37.0007 1.66643
\(494\) −35.8670 −1.61373
\(495\) 0.800146 0.0359639
\(496\) −33.6819 −1.51236
\(497\) 0.841975 0.0377678
\(498\) −24.9345 −1.11734
\(499\) −18.8783 −0.845111 −0.422555 0.906337i \(-0.638867\pi\)
−0.422555 + 0.906337i \(0.638867\pi\)
\(500\) 11.4378 0.511515
\(501\) −13.4737 −0.601959
\(502\) 31.2416 1.39438
\(503\) −19.3504 −0.862794 −0.431397 0.902162i \(-0.641979\pi\)
−0.431397 + 0.902162i \(0.641979\pi\)
\(504\) −1.51554 −0.0675076
\(505\) −6.52667 −0.290433
\(506\) 8.95945 0.398296
\(507\) 6.79414 0.301739
\(508\) 30.7702 1.36521
\(509\) 21.1614 0.937961 0.468981 0.883208i \(-0.344621\pi\)
0.468981 + 0.883208i \(0.344621\pi\)
\(510\) 10.8683 0.481255
\(511\) −12.6317 −0.558792
\(512\) −23.9163 −1.05696
\(513\) −7.71862 −0.340785
\(514\) −9.12387 −0.402436
\(515\) 8.00383 0.352691
\(516\) 3.79605 0.167112
\(517\) −3.37276 −0.148334
\(518\) −17.5346 −0.770426
\(519\) 20.0283 0.879145
\(520\) −2.00869 −0.0880868
\(521\) −1.70720 −0.0747938 −0.0373969 0.999300i \(-0.511907\pi\)
−0.0373969 + 0.999300i \(0.511907\pi\)
\(522\) 9.83638 0.430527
\(523\) −34.0337 −1.48819 −0.744095 0.668073i \(-0.767119\pi\)
−0.744095 + 0.668073i \(0.767119\pi\)
\(524\) −3.47830 −0.151950
\(525\) −6.72758 −0.293616
\(526\) −3.37584 −0.147194
\(527\) −49.5443 −2.15818
\(528\) −4.59645 −0.200035
\(529\) 1.84692 0.0803010
\(530\) 4.64042 0.201567
\(531\) 4.80183 0.208382
\(532\) −17.8225 −0.772703
\(533\) −9.20879 −0.398877
\(534\) −9.28276 −0.401704
\(535\) 5.28081 0.228309
\(536\) 2.68602 0.116018
\(537\) −8.16777 −0.352465
\(538\) −6.92524 −0.298568
\(539\) 4.39786 0.189429
\(540\) 1.22849 0.0528659
\(541\) −19.5570 −0.840822 −0.420411 0.907334i \(-0.638114\pi\)
−0.420411 + 0.907334i \(0.638114\pi\)
\(542\) 8.31243 0.357050
\(543\) −12.5430 −0.538272
\(544\) −48.8063 −2.09255
\(545\) −11.7210 −0.502070
\(546\) −7.25253 −0.310380
\(547\) 18.2043 0.778361 0.389180 0.921162i \(-0.372758\pi\)
0.389180 + 0.921162i \(0.372758\pi\)
\(548\) −14.7080 −0.628296
\(549\) 0.592250 0.0252766
\(550\) −7.74764 −0.330360
\(551\) −40.7025 −1.73398
\(552\) −4.84027 −0.206016
\(553\) −13.2528 −0.563568
\(554\) −17.0359 −0.723786
\(555\) −5.00133 −0.212295
\(556\) 3.71300 0.157466
\(557\) −27.1202 −1.14912 −0.574559 0.818463i \(-0.694826\pi\)
−0.574559 + 0.818463i \(0.694826\pi\)
\(558\) −13.1710 −0.557573
\(559\) −6.39202 −0.270354
\(560\) −6.18222 −0.261246
\(561\) −6.76114 −0.285455
\(562\) 42.1132 1.77644
\(563\) −33.3968 −1.40751 −0.703753 0.710445i \(-0.748494\pi\)
−0.703753 + 0.710445i \(0.748494\pi\)
\(564\) −5.17832 −0.218047
\(565\) −1.34993 −0.0567920
\(566\) 11.9609 0.502754
\(567\) −1.56075 −0.0655455
\(568\) −0.523839 −0.0219798
\(569\) 1.70655 0.0715423 0.0357712 0.999360i \(-0.488611\pi\)
0.0357712 + 0.999360i \(0.488611\pi\)
\(570\) −11.9556 −0.500765
\(571\) −13.1200 −0.549056 −0.274528 0.961579i \(-0.588522\pi\)
−0.274528 + 0.961579i \(0.588522\pi\)
\(572\) −3.55129 −0.148487
\(573\) −8.52547 −0.356157
\(574\) −10.7619 −0.449195
\(575\) −21.4862 −0.896038
\(576\) −3.43452 −0.143105
\(577\) −26.7845 −1.11505 −0.557526 0.830159i \(-0.688249\pi\)
−0.557526 + 0.830159i \(0.688249\pi\)
\(578\) −60.1252 −2.50088
\(579\) −4.74772 −0.197308
\(580\) 6.47819 0.268992
\(581\) 20.8632 0.865553
\(582\) −15.8789 −0.658200
\(583\) −2.88680 −0.119559
\(584\) 7.85886 0.325202
\(585\) −2.06861 −0.0855265
\(586\) 6.62772 0.273788
\(587\) 15.6518 0.646019 0.323009 0.946396i \(-0.395305\pi\)
0.323009 + 0.946396i \(0.395305\pi\)
\(588\) 6.75218 0.278455
\(589\) 54.5010 2.24567
\(590\) 7.43770 0.306205
\(591\) −8.15451 −0.335432
\(592\) 28.7302 1.18081
\(593\) −28.9905 −1.19050 −0.595249 0.803541i \(-0.702947\pi\)
−0.595249 + 0.803541i \(0.702947\pi\)
\(594\) −1.79740 −0.0737483
\(595\) −9.09371 −0.372806
\(596\) 16.6396 0.681586
\(597\) 0.508875 0.0208269
\(598\) −23.1628 −0.947198
\(599\) −31.6792 −1.29438 −0.647188 0.762330i \(-0.724055\pi\)
−0.647188 + 0.762330i \(0.724055\pi\)
\(600\) 4.18560 0.170876
\(601\) −18.5474 −0.756565 −0.378283 0.925690i \(-0.623485\pi\)
−0.378283 + 0.925690i \(0.623485\pi\)
\(602\) −7.47009 −0.304458
\(603\) 2.76615 0.112646
\(604\) 17.6662 0.718829
\(605\) 8.36319 0.340012
\(606\) 14.6611 0.595568
\(607\) −44.8061 −1.81862 −0.909312 0.416115i \(-0.863391\pi\)
−0.909312 + 0.416115i \(0.863391\pi\)
\(608\) 53.6892 2.17738
\(609\) −8.23030 −0.333509
\(610\) 0.917354 0.0371426
\(611\) 8.71957 0.352756
\(612\) −10.3806 −0.419611
\(613\) −8.42647 −0.340342 −0.170171 0.985415i \(-0.554432\pi\)
−0.170171 + 0.985415i \(0.554432\pi\)
\(614\) 50.5158 2.03865
\(615\) −3.06959 −0.123778
\(616\) 1.46036 0.0588395
\(617\) 10.1002 0.406618 0.203309 0.979115i \(-0.434830\pi\)
0.203309 + 0.979115i \(0.434830\pi\)
\(618\) −17.9793 −0.723235
\(619\) 15.9945 0.642874 0.321437 0.946931i \(-0.395834\pi\)
0.321437 + 0.946931i \(0.395834\pi\)
\(620\) −8.67435 −0.348370
\(621\) −4.98467 −0.200028
\(622\) −32.0144 −1.28366
\(623\) 7.76708 0.311181
\(624\) 11.8832 0.475708
\(625\) 15.1324 0.605298
\(626\) 8.55335 0.341861
\(627\) 7.43756 0.297028
\(628\) 32.5479 1.29880
\(629\) 42.2606 1.68504
\(630\) −2.41750 −0.0963155
\(631\) −47.1827 −1.87831 −0.939157 0.343488i \(-0.888391\pi\)
−0.939157 + 0.343488i \(0.888391\pi\)
\(632\) 8.24532 0.327981
\(633\) −3.64195 −0.144754
\(634\) 46.3617 1.84126
\(635\) −17.2709 −0.685374
\(636\) −4.43220 −0.175748
\(637\) −11.3697 −0.450486
\(638\) −9.47821 −0.375246
\(639\) −0.539467 −0.0213410
\(640\) 6.23211 0.246346
\(641\) −12.9023 −0.509608 −0.254804 0.966993i \(-0.582011\pi\)
−0.254804 + 0.966993i \(0.582011\pi\)
\(642\) −11.8625 −0.468176
\(643\) −24.7744 −0.977005 −0.488503 0.872562i \(-0.662457\pi\)
−0.488503 + 0.872562i \(0.662457\pi\)
\(644\) −11.5097 −0.453547
\(645\) −2.13067 −0.0838949
\(646\) 101.023 3.97472
\(647\) 32.0696 1.26079 0.630394 0.776275i \(-0.282893\pi\)
0.630394 + 0.776275i \(0.282893\pi\)
\(648\) 0.971032 0.0381457
\(649\) −4.62698 −0.181625
\(650\) 20.0299 0.785638
\(651\) 11.0204 0.431925
\(652\) −11.1624 −0.437152
\(653\) −35.0193 −1.37041 −0.685205 0.728350i \(-0.740287\pi\)
−0.685205 + 0.728350i \(0.740287\pi\)
\(654\) 26.3293 1.02956
\(655\) 1.95232 0.0762835
\(656\) 17.6333 0.688465
\(657\) 8.09331 0.315750
\(658\) 10.1902 0.397256
\(659\) −44.2560 −1.72397 −0.861985 0.506933i \(-0.830779\pi\)
−0.861985 + 0.506933i \(0.830779\pi\)
\(660\) −1.18376 −0.0460778
\(661\) 50.3174 1.95712 0.978560 0.205962i \(-0.0660323\pi\)
0.978560 + 0.205962i \(0.0660323\pi\)
\(662\) 43.1514 1.67713
\(663\) 17.4795 0.678848
\(664\) −12.9802 −0.503729
\(665\) 10.0035 0.387919
\(666\) 11.2347 0.435336
\(667\) −26.2856 −1.01778
\(668\) 19.9333 0.771244
\(669\) −19.2756 −0.745240
\(670\) 4.28457 0.165527
\(671\) −0.570684 −0.0220310
\(672\) 10.8563 0.418791
\(673\) −44.4153 −1.71209 −0.856043 0.516905i \(-0.827084\pi\)
−0.856043 + 0.516905i \(0.827084\pi\)
\(674\) −26.0424 −1.00312
\(675\) 4.31047 0.165910
\(676\) −10.0515 −0.386595
\(677\) −21.3928 −0.822192 −0.411096 0.911592i \(-0.634854\pi\)
−0.411096 + 0.911592i \(0.634854\pi\)
\(678\) 3.03241 0.116459
\(679\) 13.2862 0.509876
\(680\) 5.65770 0.216963
\(681\) 15.2177 0.583143
\(682\) 12.6914 0.485979
\(683\) 15.4896 0.592693 0.296347 0.955080i \(-0.404232\pi\)
0.296347 + 0.955080i \(0.404232\pi\)
\(684\) 11.4192 0.436622
\(685\) 8.25540 0.315423
\(686\) −33.6665 −1.28539
\(687\) 20.4128 0.778798
\(688\) 12.2397 0.466632
\(689\) 7.46322 0.284326
\(690\) −7.72091 −0.293930
\(691\) −0.436168 −0.0165926 −0.00829630 0.999966i \(-0.502641\pi\)
−0.00829630 + 0.999966i \(0.502641\pi\)
\(692\) −29.6305 −1.12638
\(693\) 1.50392 0.0571293
\(694\) 24.8106 0.941796
\(695\) −2.08405 −0.0790527
\(696\) 5.12053 0.194093
\(697\) 25.9376 0.982458
\(698\) −47.4393 −1.79560
\(699\) −8.60588 −0.325504
\(700\) 9.95298 0.376187
\(701\) 47.9348 1.81047 0.905237 0.424908i \(-0.139694\pi\)
0.905237 + 0.424908i \(0.139694\pi\)
\(702\) 4.64681 0.175383
\(703\) −46.4887 −1.75335
\(704\) 3.30946 0.124730
\(705\) 2.90651 0.109466
\(706\) 50.9764 1.91852
\(707\) −12.2673 −0.461358
\(708\) −7.10397 −0.266984
\(709\) 49.0171 1.84088 0.920438 0.390888i \(-0.127832\pi\)
0.920438 + 0.390888i \(0.127832\pi\)
\(710\) −0.835597 −0.0313594
\(711\) 8.49130 0.318449
\(712\) −4.83233 −0.181099
\(713\) 35.1966 1.31812
\(714\) 20.4276 0.764484
\(715\) 1.99329 0.0745447
\(716\) 12.0836 0.451587
\(717\) 10.2583 0.383104
\(718\) −8.19312 −0.305764
\(719\) −21.7427 −0.810868 −0.405434 0.914124i \(-0.632880\pi\)
−0.405434 + 0.914124i \(0.632880\pi\)
\(720\) 3.96105 0.147619
\(721\) 15.0437 0.560256
\(722\) −75.6893 −2.81687
\(723\) 14.6332 0.544215
\(724\) 18.5565 0.689647
\(725\) 22.7303 0.844182
\(726\) −18.7866 −0.697236
\(727\) −5.78142 −0.214421 −0.107211 0.994236i \(-0.534192\pi\)
−0.107211 + 0.994236i \(0.534192\pi\)
\(728\) −3.77545 −0.139928
\(729\) 1.00000 0.0370370
\(730\) 12.5360 0.463977
\(731\) 18.0039 0.665897
\(732\) −0.876192 −0.0323850
\(733\) −31.0088 −1.14534 −0.572668 0.819788i \(-0.694091\pi\)
−0.572668 + 0.819788i \(0.694091\pi\)
\(734\) −52.1029 −1.92315
\(735\) −3.78990 −0.139793
\(736\) 34.6724 1.27804
\(737\) −2.66542 −0.0981821
\(738\) 6.89534 0.253821
\(739\) 47.3776 1.74281 0.871406 0.490563i \(-0.163209\pi\)
0.871406 + 0.490563i \(0.163209\pi\)
\(740\) 7.39912 0.271997
\(741\) −19.2283 −0.706369
\(742\) 8.72195 0.320193
\(743\) −23.4684 −0.860972 −0.430486 0.902597i \(-0.641658\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(744\) −6.85643 −0.251369
\(745\) −9.33958 −0.342176
\(746\) 9.55509 0.349837
\(747\) −13.3674 −0.489088
\(748\) 10.0026 0.365732
\(749\) 9.92560 0.362674
\(750\) 14.4213 0.526590
\(751\) 10.5901 0.386437 0.193218 0.981156i \(-0.438107\pi\)
0.193218 + 0.981156i \(0.438107\pi\)
\(752\) −16.6965 −0.608860
\(753\) 16.7486 0.610354
\(754\) 24.5039 0.892381
\(755\) −9.91580 −0.360873
\(756\) 2.30903 0.0839785
\(757\) −44.7414 −1.62615 −0.813076 0.582157i \(-0.802209\pi\)
−0.813076 + 0.582157i \(0.802209\pi\)
\(758\) −25.9365 −0.942057
\(759\) 4.80316 0.174344
\(760\) −6.22373 −0.225759
\(761\) −37.1182 −1.34553 −0.672767 0.739855i \(-0.734894\pi\)
−0.672767 + 0.739855i \(0.734894\pi\)
\(762\) 38.7963 1.40544
\(763\) −22.0303 −0.797549
\(764\) 12.6128 0.456316
\(765\) 5.82649 0.210657
\(766\) 10.7872 0.389756
\(767\) 11.9621 0.431927
\(768\) −20.8685 −0.753027
\(769\) −31.4382 −1.13369 −0.566845 0.823825i \(-0.691836\pi\)
−0.566845 + 0.823825i \(0.691836\pi\)
\(770\) 2.32947 0.0839484
\(771\) −4.89131 −0.176156
\(772\) 7.02392 0.252796
\(773\) −16.5463 −0.595129 −0.297564 0.954702i \(-0.596174\pi\)
−0.297564 + 0.954702i \(0.596174\pi\)
\(774\) 4.78620 0.172037
\(775\) −30.4361 −1.09330
\(776\) −8.26606 −0.296734
\(777\) −9.40031 −0.337234
\(778\) 40.0393 1.43548
\(779\) −28.5326 −1.02229
\(780\) 3.06036 0.109579
\(781\) 0.519823 0.0186007
\(782\) 65.2408 2.33301
\(783\) 5.27328 0.188452
\(784\) 21.7712 0.777542
\(785\) −18.2687 −0.652036
\(786\) −4.38558 −0.156428
\(787\) −13.6570 −0.486818 −0.243409 0.969924i \(-0.578266\pi\)
−0.243409 + 0.969924i \(0.578266\pi\)
\(788\) 12.0640 0.429763
\(789\) −1.80979 −0.0644302
\(790\) 13.1524 0.467943
\(791\) −2.53728 −0.0902153
\(792\) −0.935674 −0.0332477
\(793\) 1.47539 0.0523925
\(794\) 20.7974 0.738072
\(795\) 2.48773 0.0882307
\(796\) −0.752845 −0.0266839
\(797\) −27.4397 −0.971962 −0.485981 0.873969i \(-0.661538\pi\)
−0.485981 + 0.873969i \(0.661538\pi\)
\(798\) −22.4713 −0.795475
\(799\) −24.5597 −0.868860
\(800\) −29.9827 −1.06005
\(801\) −4.97649 −0.175836
\(802\) −50.0891 −1.76871
\(803\) −7.79861 −0.275207
\(804\) −4.09232 −0.144325
\(805\) 6.46024 0.227694
\(806\) −32.8110 −1.15572
\(807\) −3.71262 −0.130691
\(808\) 7.63215 0.268498
\(809\) −3.14162 −0.110454 −0.0552268 0.998474i \(-0.517588\pi\)
−0.0552268 + 0.998474i \(0.517588\pi\)
\(810\) 1.54893 0.0544239
\(811\) −50.4489 −1.77150 −0.885750 0.464162i \(-0.846356\pi\)
−0.885750 + 0.464162i \(0.846356\pi\)
\(812\) 12.1762 0.427299
\(813\) 4.45630 0.156289
\(814\) −10.8256 −0.379437
\(815\) 6.26527 0.219463
\(816\) −33.4704 −1.17170
\(817\) −19.8051 −0.692892
\(818\) −22.9717 −0.803185
\(819\) −3.88808 −0.135861
\(820\) 4.54124 0.158587
\(821\) −13.8898 −0.484758 −0.242379 0.970182i \(-0.577928\pi\)
−0.242379 + 0.970182i \(0.577928\pi\)
\(822\) −18.5445 −0.646812
\(823\) 34.1194 1.18933 0.594664 0.803974i \(-0.297285\pi\)
0.594664 + 0.803974i \(0.297285\pi\)
\(824\) −9.35951 −0.326054
\(825\) −4.15351 −0.144607
\(826\) 13.9796 0.486413
\(827\) 47.0110 1.63473 0.817366 0.576119i \(-0.195433\pi\)
0.817366 + 0.576119i \(0.195433\pi\)
\(828\) 7.37447 0.256280
\(829\) 9.52320 0.330754 0.165377 0.986230i \(-0.447116\pi\)
0.165377 + 0.986230i \(0.447116\pi\)
\(830\) −20.7052 −0.718688
\(831\) −9.13295 −0.316819
\(832\) −8.55593 −0.296623
\(833\) 32.0242 1.10957
\(834\) 4.68150 0.162107
\(835\) −11.1883 −0.387187
\(836\) −11.0033 −0.380559
\(837\) −7.06097 −0.244063
\(838\) 0.900582 0.0311101
\(839\) 25.9901 0.897277 0.448639 0.893713i \(-0.351909\pi\)
0.448639 + 0.893713i \(0.351909\pi\)
\(840\) −1.25848 −0.0434217
\(841\) −1.19248 −0.0411199
\(842\) −7.84666 −0.270414
\(843\) 22.5769 0.777589
\(844\) 5.38801 0.185463
\(845\) 5.64174 0.194082
\(846\) −6.52903 −0.224473
\(847\) 15.7191 0.540116
\(848\) −14.2908 −0.490749
\(849\) 6.41224 0.220068
\(850\) −56.4166 −1.93507
\(851\) −30.0223 −1.02915
\(852\) 0.798103 0.0273426
\(853\) −40.4602 −1.38533 −0.692666 0.721259i \(-0.743564\pi\)
−0.692666 + 0.721259i \(0.743564\pi\)
\(854\) 1.72422 0.0590017
\(855\) −6.40940 −0.219197
\(856\) −6.17527 −0.211066
\(857\) −12.6625 −0.432541 −0.216271 0.976333i \(-0.569389\pi\)
−0.216271 + 0.976333i \(0.569389\pi\)
\(858\) −4.47761 −0.152863
\(859\) −34.0940 −1.16327 −0.581636 0.813449i \(-0.697587\pi\)
−0.581636 + 0.813449i \(0.697587\pi\)
\(860\) 3.15217 0.107488
\(861\) −5.76948 −0.196623
\(862\) 70.4962 2.40111
\(863\) −18.1693 −0.618490 −0.309245 0.950982i \(-0.600076\pi\)
−0.309245 + 0.950982i \(0.600076\pi\)
\(864\) −6.95580 −0.236641
\(865\) 16.6311 0.565476
\(866\) −48.8937 −1.66148
\(867\) −32.2331 −1.09469
\(868\) −16.3040 −0.553393
\(869\) −8.18211 −0.277559
\(870\) 8.16795 0.276920
\(871\) 6.89090 0.233489
\(872\) 13.7062 0.464152
\(873\) −8.51266 −0.288110
\(874\) −71.7678 −2.42758
\(875\) −12.0666 −0.407925
\(876\) −11.9735 −0.404546
\(877\) −26.5456 −0.896381 −0.448190 0.893938i \(-0.647931\pi\)
−0.448190 + 0.893938i \(0.647931\pi\)
\(878\) 4.24876 0.143389
\(879\) 3.55312 0.119844
\(880\) −3.81681 −0.128665
\(881\) −36.1912 −1.21931 −0.609657 0.792665i \(-0.708693\pi\)
−0.609657 + 0.792665i \(0.708693\pi\)
\(882\) 8.51342 0.286662
\(883\) 2.52755 0.0850587 0.0425293 0.999095i \(-0.486458\pi\)
0.0425293 + 0.999095i \(0.486458\pi\)
\(884\) −25.8597 −0.869757
\(885\) 3.98735 0.134033
\(886\) 61.0489 2.05098
\(887\) 6.35333 0.213324 0.106662 0.994295i \(-0.465984\pi\)
0.106662 + 0.994295i \(0.465984\pi\)
\(888\) 5.84845 0.196261
\(889\) −32.4617 −1.08873
\(890\) −7.70824 −0.258381
\(891\) −0.963587 −0.0322814
\(892\) 28.5170 0.954819
\(893\) 27.0168 0.904083
\(894\) 20.9799 0.701673
\(895\) −6.78237 −0.226710
\(896\) 11.7136 0.391325
\(897\) −12.4176 −0.414611
\(898\) 6.56844 0.219192
\(899\) −37.2345 −1.24184
\(900\) −6.37703 −0.212568
\(901\) −21.0210 −0.700312
\(902\) −6.64426 −0.221230
\(903\) −4.00472 −0.133269
\(904\) 1.57858 0.0525028
\(905\) −10.4155 −0.346223
\(906\) 22.2743 0.740014
\(907\) −24.3919 −0.809919 −0.404960 0.914335i \(-0.632714\pi\)
−0.404960 + 0.914335i \(0.632714\pi\)
\(908\) −22.5135 −0.747137
\(909\) 7.85984 0.260694
\(910\) −6.02237 −0.199640
\(911\) −10.3397 −0.342569 −0.171285 0.985222i \(-0.554792\pi\)
−0.171285 + 0.985222i \(0.554792\pi\)
\(912\) 36.8189 1.21920
\(913\) 12.8807 0.426288
\(914\) −66.8554 −2.21138
\(915\) 0.491794 0.0162582
\(916\) −30.1993 −0.997814
\(917\) 3.66951 0.121178
\(918\) −13.0883 −0.431978
\(919\) 0.529162 0.0174555 0.00872773 0.999962i \(-0.497222\pi\)
0.00872773 + 0.999962i \(0.497222\pi\)
\(920\) −4.01927 −0.132512
\(921\) 27.0815 0.892366
\(922\) 64.5706 2.12652
\(923\) −1.34390 −0.0442349
\(924\) −2.22495 −0.0731954
\(925\) 25.9616 0.853612
\(926\) 67.2348 2.20947
\(927\) −9.63873 −0.316577
\(928\) −36.6799 −1.20408
\(929\) 49.8368 1.63509 0.817546 0.575863i \(-0.195334\pi\)
0.817546 + 0.575863i \(0.195334\pi\)
\(930\) −10.9370 −0.358637
\(931\) −35.2281 −1.15456
\(932\) 12.7318 0.417044
\(933\) −17.1629 −0.561888
\(934\) 1.76632 0.0577958
\(935\) −5.61433 −0.183608
\(936\) 2.41899 0.0790672
\(937\) 14.9564 0.488605 0.244302 0.969699i \(-0.421441\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(938\) 8.05311 0.262944
\(939\) 4.58545 0.149641
\(940\) −4.29998 −0.140250
\(941\) −6.38382 −0.208106 −0.104053 0.994572i \(-0.533181\pi\)
−0.104053 + 0.994572i \(0.533181\pi\)
\(942\) 41.0377 1.33708
\(943\) −18.4263 −0.600043
\(944\) −22.9054 −0.745508
\(945\) −1.29602 −0.0421596
\(946\) −4.61193 −0.149947
\(947\) 15.8841 0.516164 0.258082 0.966123i \(-0.416910\pi\)
0.258082 + 0.966123i \(0.416910\pi\)
\(948\) −12.5623 −0.408004
\(949\) 20.1617 0.654476
\(950\) 62.0609 2.01352
\(951\) 24.8545 0.805963
\(952\) 10.6340 0.344650
\(953\) −12.9998 −0.421104 −0.210552 0.977583i \(-0.567526\pi\)
−0.210552 + 0.977583i \(0.567526\pi\)
\(954\) −5.58829 −0.180928
\(955\) −7.07940 −0.229084
\(956\) −15.1765 −0.490842
\(957\) −5.08127 −0.164254
\(958\) 23.7463 0.767209
\(959\) 15.5165 0.501055
\(960\) −2.85197 −0.0920468
\(961\) 18.8574 0.608302
\(962\) 27.9874 0.902350
\(963\) −6.35949 −0.204932
\(964\) −21.6488 −0.697261
\(965\) −3.94242 −0.126911
\(966\) −14.5119 −0.466913
\(967\) −11.7867 −0.379036 −0.189518 0.981877i \(-0.560693\pi\)
−0.189518 + 0.981877i \(0.560693\pi\)
\(968\) −9.77975 −0.314333
\(969\) 54.1587 1.73983
\(970\) −13.1855 −0.423361
\(971\) 24.1526 0.775095 0.387548 0.921850i \(-0.373322\pi\)
0.387548 + 0.921850i \(0.373322\pi\)
\(972\) −1.47943 −0.0474527
\(973\) −3.91711 −0.125577
\(974\) 67.0056 2.14700
\(975\) 10.7380 0.343893
\(976\) −2.82512 −0.0904299
\(977\) 15.4450 0.494129 0.247065 0.968999i \(-0.420534\pi\)
0.247065 + 0.968999i \(0.420534\pi\)
\(978\) −14.0739 −0.450035
\(979\) 4.79528 0.153258
\(980\) 5.60689 0.179106
\(981\) 14.1151 0.450661
\(982\) −64.2311 −2.04970
\(983\) −11.3002 −0.360421 −0.180210 0.983628i \(-0.557678\pi\)
−0.180210 + 0.983628i \(0.557678\pi\)
\(984\) 3.58951 0.114429
\(985\) −6.77136 −0.215753
\(986\) −69.0182 −2.19799
\(987\) 5.46297 0.173888
\(988\) 28.4469 0.905016
\(989\) −12.7901 −0.406701
\(990\) −1.49253 −0.0474357
\(991\) −39.0925 −1.24182 −0.620908 0.783884i \(-0.713236\pi\)
−0.620908 + 0.783884i \(0.713236\pi\)
\(992\) 49.1147 1.55939
\(993\) 23.1335 0.734119
\(994\) −1.57056 −0.0498150
\(995\) 0.422561 0.0133961
\(996\) 19.7761 0.626631
\(997\) −17.8388 −0.564962 −0.282481 0.959273i \(-0.591157\pi\)
−0.282481 + 0.959273i \(0.591157\pi\)
\(998\) 35.2142 1.11469
\(999\) 6.02292 0.190557
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 6033.2.a.d.1.19 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6033.2.a.d.1.19 84 1.1 even 1 trivial