Properties

Label 4017.2.a.l.1.9
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $32$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.48812 q^{2} +1.00000 q^{3} +0.214502 q^{4} -3.58678 q^{5} -1.48812 q^{6} +0.0236485 q^{7} +2.65704 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.48812 q^{2} +1.00000 q^{3} +0.214502 q^{4} -3.58678 q^{5} -1.48812 q^{6} +0.0236485 q^{7} +2.65704 q^{8} +1.00000 q^{9} +5.33757 q^{10} -3.71531 q^{11} +0.214502 q^{12} -1.00000 q^{13} -0.0351918 q^{14} -3.58678 q^{15} -4.38299 q^{16} +2.38483 q^{17} -1.48812 q^{18} +1.67761 q^{19} -0.769373 q^{20} +0.0236485 q^{21} +5.52883 q^{22} -5.50028 q^{23} +2.65704 q^{24} +7.86502 q^{25} +1.48812 q^{26} +1.00000 q^{27} +0.00507265 q^{28} -1.60562 q^{29} +5.33757 q^{30} +2.89038 q^{31} +1.20835 q^{32} -3.71531 q^{33} -3.54891 q^{34} -0.0848220 q^{35} +0.214502 q^{36} -3.51029 q^{37} -2.49648 q^{38} -1.00000 q^{39} -9.53021 q^{40} -6.74954 q^{41} -0.0351918 q^{42} -0.758748 q^{43} -0.796942 q^{44} -3.58678 q^{45} +8.18507 q^{46} -4.08640 q^{47} -4.38299 q^{48} -6.99944 q^{49} -11.7041 q^{50} +2.38483 q^{51} -0.214502 q^{52} +7.86931 q^{53} -1.48812 q^{54} +13.3260 q^{55} +0.0628349 q^{56} +1.67761 q^{57} +2.38936 q^{58} -10.6800 q^{59} -0.769373 q^{60} -5.42985 q^{61} -4.30123 q^{62} +0.0236485 q^{63} +6.96782 q^{64} +3.58678 q^{65} +5.52883 q^{66} -9.67812 q^{67} +0.511550 q^{68} -5.50028 q^{69} +0.126225 q^{70} -2.86157 q^{71} +2.65704 q^{72} +15.1910 q^{73} +5.22374 q^{74} +7.86502 q^{75} +0.359850 q^{76} -0.0878616 q^{77} +1.48812 q^{78} +16.7621 q^{79} +15.7208 q^{80} +1.00000 q^{81} +10.0441 q^{82} -4.59132 q^{83} +0.00507265 q^{84} -8.55385 q^{85} +1.12911 q^{86} -1.60562 q^{87} -9.87172 q^{88} +9.99536 q^{89} +5.33757 q^{90} -0.0236485 q^{91} -1.17982 q^{92} +2.89038 q^{93} +6.08106 q^{94} -6.01721 q^{95} +1.20835 q^{96} -3.56186 q^{97} +10.4160 q^{98} -3.71531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.48812 −1.05226 −0.526130 0.850404i \(-0.676357\pi\)
−0.526130 + 0.850404i \(0.676357\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.214502 0.107251
\(5\) −3.58678 −1.60406 −0.802029 0.597285i \(-0.796246\pi\)
−0.802029 + 0.597285i \(0.796246\pi\)
\(6\) −1.48812 −0.607523
\(7\) 0.0236485 0.00893829 0.00446915 0.999990i \(-0.498577\pi\)
0.00446915 + 0.999990i \(0.498577\pi\)
\(8\) 2.65704 0.939404
\(9\) 1.00000 0.333333
\(10\) 5.33757 1.68789
\(11\) −3.71531 −1.12021 −0.560104 0.828422i \(-0.689239\pi\)
−0.560104 + 0.828422i \(0.689239\pi\)
\(12\) 0.214502 0.0619214
\(13\) −1.00000 −0.277350
\(14\) −0.0351918 −0.00940541
\(15\) −3.58678 −0.926103
\(16\) −4.38299 −1.09575
\(17\) 2.38483 0.578405 0.289203 0.957268i \(-0.406610\pi\)
0.289203 + 0.957268i \(0.406610\pi\)
\(18\) −1.48812 −0.350753
\(19\) 1.67761 0.384869 0.192435 0.981310i \(-0.438362\pi\)
0.192435 + 0.981310i \(0.438362\pi\)
\(20\) −0.769373 −0.172037
\(21\) 0.0236485 0.00516053
\(22\) 5.52883 1.17875
\(23\) −5.50028 −1.14689 −0.573443 0.819245i \(-0.694393\pi\)
−0.573443 + 0.819245i \(0.694393\pi\)
\(24\) 2.65704 0.542365
\(25\) 7.86502 1.57300
\(26\) 1.48812 0.291844
\(27\) 1.00000 0.192450
\(28\) 0.00507265 0.000958641 0
\(29\) −1.60562 −0.298156 −0.149078 0.988825i \(-0.547631\pi\)
−0.149078 + 0.988825i \(0.547631\pi\)
\(30\) 5.33757 0.974502
\(31\) 2.89038 0.519127 0.259563 0.965726i \(-0.416421\pi\)
0.259563 + 0.965726i \(0.416421\pi\)
\(32\) 1.20835 0.213608
\(33\) −3.71531 −0.646753
\(34\) −3.54891 −0.608633
\(35\) −0.0848220 −0.0143375
\(36\) 0.214502 0.0357504
\(37\) −3.51029 −0.577089 −0.288544 0.957467i \(-0.593171\pi\)
−0.288544 + 0.957467i \(0.593171\pi\)
\(38\) −2.49648 −0.404983
\(39\) −1.00000 −0.160128
\(40\) −9.53021 −1.50686
\(41\) −6.74954 −1.05410 −0.527051 0.849834i \(-0.676702\pi\)
−0.527051 + 0.849834i \(0.676702\pi\)
\(42\) −0.0351918 −0.00543021
\(43\) −0.758748 −0.115708 −0.0578540 0.998325i \(-0.518426\pi\)
−0.0578540 + 0.998325i \(0.518426\pi\)
\(44\) −0.796942 −0.120144
\(45\) −3.58678 −0.534686
\(46\) 8.18507 1.20682
\(47\) −4.08640 −0.596063 −0.298032 0.954556i \(-0.596330\pi\)
−0.298032 + 0.954556i \(0.596330\pi\)
\(48\) −4.38299 −0.632631
\(49\) −6.99944 −0.999920
\(50\) −11.7041 −1.65521
\(51\) 2.38483 0.333942
\(52\) −0.214502 −0.0297461
\(53\) 7.86931 1.08093 0.540466 0.841366i \(-0.318248\pi\)
0.540466 + 0.841366i \(0.318248\pi\)
\(54\) −1.48812 −0.202508
\(55\) 13.3260 1.79688
\(56\) 0.0628349 0.00839667
\(57\) 1.67761 0.222204
\(58\) 2.38936 0.313738
\(59\) −10.6800 −1.39042 −0.695209 0.718807i \(-0.744688\pi\)
−0.695209 + 0.718807i \(0.744688\pi\)
\(60\) −0.769373 −0.0993256
\(61\) −5.42985 −0.695221 −0.347611 0.937639i \(-0.613007\pi\)
−0.347611 + 0.937639i \(0.613007\pi\)
\(62\) −4.30123 −0.546256
\(63\) 0.0236485 0.00297943
\(64\) 6.96782 0.870977
\(65\) 3.58678 0.444886
\(66\) 5.52883 0.680552
\(67\) −9.67812 −1.18237 −0.591185 0.806536i \(-0.701340\pi\)
−0.591185 + 0.806536i \(0.701340\pi\)
\(68\) 0.511550 0.0620346
\(69\) −5.50028 −0.662156
\(70\) 0.126225 0.0150868
\(71\) −2.86157 −0.339606 −0.169803 0.985478i \(-0.554313\pi\)
−0.169803 + 0.985478i \(0.554313\pi\)
\(72\) 2.65704 0.313135
\(73\) 15.1910 1.77797 0.888986 0.457935i \(-0.151411\pi\)
0.888986 + 0.457935i \(0.151411\pi\)
\(74\) 5.22374 0.607247
\(75\) 7.86502 0.908174
\(76\) 0.359850 0.0412776
\(77\) −0.0878616 −0.0100128
\(78\) 1.48812 0.168496
\(79\) 16.7621 1.88589 0.942945 0.332950i \(-0.108044\pi\)
0.942945 + 0.332950i \(0.108044\pi\)
\(80\) 15.7208 1.75764
\(81\) 1.00000 0.111111
\(82\) 10.0441 1.10919
\(83\) −4.59132 −0.503963 −0.251982 0.967732i \(-0.581082\pi\)
−0.251982 + 0.967732i \(0.581082\pi\)
\(84\) 0.00507265 0.000553472 0
\(85\) −8.55385 −0.927796
\(86\) 1.12911 0.121755
\(87\) −1.60562 −0.172141
\(88\) −9.87172 −1.05233
\(89\) 9.99536 1.05951 0.529753 0.848152i \(-0.322285\pi\)
0.529753 + 0.848152i \(0.322285\pi\)
\(90\) 5.33757 0.562629
\(91\) −0.0236485 −0.00247904
\(92\) −1.17982 −0.123005
\(93\) 2.89038 0.299718
\(94\) 6.08106 0.627214
\(95\) −6.01721 −0.617353
\(96\) 1.20835 0.123327
\(97\) −3.56186 −0.361653 −0.180826 0.983515i \(-0.557877\pi\)
−0.180826 + 0.983515i \(0.557877\pi\)
\(98\) 10.4160 1.05218
\(99\) −3.71531 −0.373403
\(100\) 1.68706 0.168706
\(101\) 1.85275 0.184356 0.0921779 0.995743i \(-0.470617\pi\)
0.0921779 + 0.995743i \(0.470617\pi\)
\(102\) −3.54891 −0.351394
\(103\) −1.00000 −0.0985329
\(104\) −2.65704 −0.260544
\(105\) −0.0848220 −0.00827778
\(106\) −11.7105 −1.13742
\(107\) −1.21058 −0.117031 −0.0585155 0.998287i \(-0.518637\pi\)
−0.0585155 + 0.998287i \(0.518637\pi\)
\(108\) 0.214502 0.0206405
\(109\) −9.25070 −0.886057 −0.443028 0.896508i \(-0.646096\pi\)
−0.443028 + 0.896508i \(0.646096\pi\)
\(110\) −19.8307 −1.89079
\(111\) −3.51029 −0.333182
\(112\) −0.103651 −0.00979412
\(113\) −12.0437 −1.13297 −0.566487 0.824070i \(-0.691698\pi\)
−0.566487 + 0.824070i \(0.691698\pi\)
\(114\) −2.49648 −0.233817
\(115\) 19.7283 1.83967
\(116\) −0.344409 −0.0319776
\(117\) −1.00000 −0.0924500
\(118\) 15.8931 1.46308
\(119\) 0.0563975 0.00516995
\(120\) −9.53021 −0.869985
\(121\) 2.80355 0.254868
\(122\) 8.08027 0.731553
\(123\) −6.74954 −0.608586
\(124\) 0.619992 0.0556769
\(125\) −10.2762 −0.919130
\(126\) −0.0351918 −0.00313514
\(127\) 1.60892 0.142769 0.0713845 0.997449i \(-0.477258\pi\)
0.0713845 + 0.997449i \(0.477258\pi\)
\(128\) −12.7856 −1.13010
\(129\) −0.758748 −0.0668040
\(130\) −5.33757 −0.468135
\(131\) 5.67616 0.495928 0.247964 0.968769i \(-0.420238\pi\)
0.247964 + 0.968769i \(0.420238\pi\)
\(132\) −0.796942 −0.0693649
\(133\) 0.0396729 0.00344007
\(134\) 14.4022 1.24416
\(135\) −3.58678 −0.308701
\(136\) 6.33657 0.543356
\(137\) −13.8157 −1.18035 −0.590176 0.807275i \(-0.700942\pi\)
−0.590176 + 0.807275i \(0.700942\pi\)
\(138\) 8.18507 0.696760
\(139\) 13.2348 1.12256 0.561280 0.827626i \(-0.310309\pi\)
0.561280 + 0.827626i \(0.310309\pi\)
\(140\) −0.0181945 −0.00153772
\(141\) −4.08640 −0.344137
\(142\) 4.25836 0.357354
\(143\) 3.71531 0.310690
\(144\) −4.38299 −0.365249
\(145\) 5.75902 0.478260
\(146\) −22.6060 −1.87089
\(147\) −6.99944 −0.577304
\(148\) −0.752965 −0.0618934
\(149\) −3.91884 −0.321044 −0.160522 0.987032i \(-0.551318\pi\)
−0.160522 + 0.987032i \(0.551318\pi\)
\(150\) −11.7041 −0.955635
\(151\) 21.0997 1.71707 0.858534 0.512756i \(-0.171376\pi\)
0.858534 + 0.512756i \(0.171376\pi\)
\(152\) 4.45746 0.361548
\(153\) 2.38483 0.192802
\(154\) 0.130749 0.0105360
\(155\) −10.3672 −0.832710
\(156\) −0.214502 −0.0171739
\(157\) 9.31170 0.743155 0.371577 0.928402i \(-0.378817\pi\)
0.371577 + 0.928402i \(0.378817\pi\)
\(158\) −24.9441 −1.98445
\(159\) 7.86931 0.624077
\(160\) −4.33409 −0.342640
\(161\) −0.130073 −0.0102512
\(162\) −1.48812 −0.116918
\(163\) −3.01766 −0.236361 −0.118181 0.992992i \(-0.537706\pi\)
−0.118181 + 0.992992i \(0.537706\pi\)
\(164\) −1.44779 −0.113053
\(165\) 13.3260 1.03743
\(166\) 6.83244 0.530300
\(167\) 21.5065 1.66422 0.832111 0.554608i \(-0.187132\pi\)
0.832111 + 0.554608i \(0.187132\pi\)
\(168\) 0.0628349 0.00484782
\(169\) 1.00000 0.0769231
\(170\) 12.7292 0.976282
\(171\) 1.67761 0.128290
\(172\) −0.162753 −0.0124098
\(173\) 18.3177 1.39267 0.696334 0.717718i \(-0.254813\pi\)
0.696334 + 0.717718i \(0.254813\pi\)
\(174\) 2.38936 0.181137
\(175\) 0.185996 0.0140600
\(176\) 16.2842 1.22747
\(177\) −10.6800 −0.802759
\(178\) −14.8743 −1.11488
\(179\) 0.253741 0.0189655 0.00948273 0.999955i \(-0.496982\pi\)
0.00948273 + 0.999955i \(0.496982\pi\)
\(180\) −0.769373 −0.0573456
\(181\) −15.1376 −1.12517 −0.562584 0.826740i \(-0.690193\pi\)
−0.562584 + 0.826740i \(0.690193\pi\)
\(182\) 0.0351918 0.00260859
\(183\) −5.42985 −0.401386
\(184\) −14.6144 −1.07739
\(185\) 12.5907 0.925684
\(186\) −4.30123 −0.315381
\(187\) −8.86037 −0.647935
\(188\) −0.876542 −0.0639284
\(189\) 0.0236485 0.00172018
\(190\) 8.95434 0.649616
\(191\) 10.3023 0.745448 0.372724 0.927942i \(-0.378424\pi\)
0.372724 + 0.927942i \(0.378424\pi\)
\(192\) 6.96782 0.502859
\(193\) 6.08382 0.437923 0.218962 0.975733i \(-0.429733\pi\)
0.218962 + 0.975733i \(0.429733\pi\)
\(194\) 5.30048 0.380553
\(195\) 3.58678 0.256855
\(196\) −1.50139 −0.107242
\(197\) −15.6327 −1.11379 −0.556893 0.830584i \(-0.688007\pi\)
−0.556893 + 0.830584i \(0.688007\pi\)
\(198\) 5.52883 0.392917
\(199\) 17.8911 1.26827 0.634134 0.773223i \(-0.281357\pi\)
0.634134 + 0.773223i \(0.281357\pi\)
\(200\) 20.8976 1.47769
\(201\) −9.67812 −0.682642
\(202\) −2.75712 −0.193990
\(203\) −0.0379705 −0.00266501
\(204\) 0.511550 0.0358157
\(205\) 24.2091 1.69084
\(206\) 1.48812 0.103682
\(207\) −5.50028 −0.382296
\(208\) 4.38299 0.303906
\(209\) −6.23283 −0.431134
\(210\) 0.126225 0.00871038
\(211\) 3.09757 0.213245 0.106623 0.994300i \(-0.465996\pi\)
0.106623 + 0.994300i \(0.465996\pi\)
\(212\) 1.68798 0.115931
\(213\) −2.86157 −0.196071
\(214\) 1.80148 0.123147
\(215\) 2.72146 0.185602
\(216\) 2.65704 0.180788
\(217\) 0.0683530 0.00464011
\(218\) 13.7662 0.932362
\(219\) 15.1910 1.02651
\(220\) 2.85846 0.192717
\(221\) −2.38483 −0.160421
\(222\) 5.22374 0.350594
\(223\) 9.20720 0.616560 0.308280 0.951296i \(-0.400247\pi\)
0.308280 + 0.951296i \(0.400247\pi\)
\(224\) 0.0285757 0.00190929
\(225\) 7.86502 0.524334
\(226\) 17.9225 1.19218
\(227\) −16.1094 −1.06922 −0.534610 0.845099i \(-0.679541\pi\)
−0.534610 + 0.845099i \(0.679541\pi\)
\(228\) 0.359850 0.0238317
\(229\) 29.8683 1.97375 0.986875 0.161485i \(-0.0516284\pi\)
0.986875 + 0.161485i \(0.0516284\pi\)
\(230\) −29.3581 −1.93581
\(231\) −0.0878616 −0.00578087
\(232\) −4.26619 −0.280089
\(233\) 28.5167 1.86819 0.934094 0.357027i \(-0.116210\pi\)
0.934094 + 0.357027i \(0.116210\pi\)
\(234\) 1.48812 0.0972815
\(235\) 14.6570 0.956120
\(236\) −2.29088 −0.149124
\(237\) 16.7621 1.08882
\(238\) −0.0839263 −0.00544014
\(239\) 5.57306 0.360491 0.180246 0.983622i \(-0.442311\pi\)
0.180246 + 0.983622i \(0.442311\pi\)
\(240\) 15.7208 1.01478
\(241\) 5.03224 0.324155 0.162078 0.986778i \(-0.448181\pi\)
0.162078 + 0.986778i \(0.448181\pi\)
\(242\) −4.17202 −0.268187
\(243\) 1.00000 0.0641500
\(244\) −1.16471 −0.0745632
\(245\) 25.1055 1.60393
\(246\) 10.0441 0.640390
\(247\) −1.67761 −0.106744
\(248\) 7.67983 0.487670
\(249\) −4.59132 −0.290963
\(250\) 15.2922 0.967164
\(251\) −4.32041 −0.272702 −0.136351 0.990661i \(-0.543537\pi\)
−0.136351 + 0.990661i \(0.543537\pi\)
\(252\) 0.00507265 0.000319547 0
\(253\) 20.4352 1.28475
\(254\) −2.39427 −0.150230
\(255\) −8.55385 −0.535663
\(256\) 5.09095 0.318184
\(257\) 25.6635 1.60084 0.800422 0.599436i \(-0.204609\pi\)
0.800422 + 0.599436i \(0.204609\pi\)
\(258\) 1.12911 0.0702952
\(259\) −0.0830132 −0.00515819
\(260\) 0.769373 0.0477145
\(261\) −1.60562 −0.0993855
\(262\) −8.44681 −0.521846
\(263\) −10.3901 −0.640683 −0.320341 0.947302i \(-0.603798\pi\)
−0.320341 + 0.947302i \(0.603798\pi\)
\(264\) −9.87172 −0.607562
\(265\) −28.2255 −1.73388
\(266\) −0.0590380 −0.00361985
\(267\) 9.99536 0.611706
\(268\) −2.07598 −0.126810
\(269\) −6.11062 −0.372571 −0.186285 0.982496i \(-0.559645\pi\)
−0.186285 + 0.982496i \(0.559645\pi\)
\(270\) 5.33757 0.324834
\(271\) 6.66920 0.405125 0.202562 0.979269i \(-0.435073\pi\)
0.202562 + 0.979269i \(0.435073\pi\)
\(272\) −10.4527 −0.633786
\(273\) −0.0236485 −0.00143127
\(274\) 20.5594 1.24204
\(275\) −29.2210 −1.76209
\(276\) −1.17982 −0.0710169
\(277\) 31.3374 1.88288 0.941442 0.337174i \(-0.109471\pi\)
0.941442 + 0.337174i \(0.109471\pi\)
\(278\) −19.6949 −1.18122
\(279\) 2.89038 0.173042
\(280\) −0.225375 −0.0134687
\(281\) −29.0071 −1.73042 −0.865210 0.501410i \(-0.832815\pi\)
−0.865210 + 0.501410i \(0.832815\pi\)
\(282\) 6.08106 0.362122
\(283\) −8.88428 −0.528116 −0.264058 0.964507i \(-0.585061\pi\)
−0.264058 + 0.964507i \(0.585061\pi\)
\(284\) −0.613813 −0.0364231
\(285\) −6.01721 −0.356429
\(286\) −5.52883 −0.326927
\(287\) −0.159617 −0.00942186
\(288\) 1.20835 0.0712027
\(289\) −11.3126 −0.665447
\(290\) −8.57011 −0.503254
\(291\) −3.56186 −0.208800
\(292\) 3.25850 0.190689
\(293\) −10.7899 −0.630355 −0.315178 0.949033i \(-0.602064\pi\)
−0.315178 + 0.949033i \(0.602064\pi\)
\(294\) 10.4160 0.607474
\(295\) 38.3069 2.23031
\(296\) −9.32697 −0.542119
\(297\) −3.71531 −0.215584
\(298\) 5.83171 0.337822
\(299\) 5.50028 0.318089
\(300\) 1.68706 0.0974026
\(301\) −0.0179432 −0.00103423
\(302\) −31.3989 −1.80680
\(303\) 1.85275 0.106438
\(304\) −7.35294 −0.421720
\(305\) 19.4757 1.11518
\(306\) −3.54891 −0.202878
\(307\) −15.7118 −0.896722 −0.448361 0.893853i \(-0.647992\pi\)
−0.448361 + 0.893853i \(0.647992\pi\)
\(308\) −0.0188465 −0.00107388
\(309\) −1.00000 −0.0568880
\(310\) 15.4276 0.876227
\(311\) 10.8175 0.613405 0.306703 0.951805i \(-0.400774\pi\)
0.306703 + 0.951805i \(0.400774\pi\)
\(312\) −2.65704 −0.150425
\(313\) −11.1508 −0.630283 −0.315142 0.949045i \(-0.602052\pi\)
−0.315142 + 0.949045i \(0.602052\pi\)
\(314\) −13.8569 −0.781992
\(315\) −0.0848220 −0.00477918
\(316\) 3.59552 0.202264
\(317\) 11.1229 0.624727 0.312363 0.949963i \(-0.398879\pi\)
0.312363 + 0.949963i \(0.398879\pi\)
\(318\) −11.7105 −0.656691
\(319\) 5.96539 0.333998
\(320\) −24.9920 −1.39710
\(321\) −1.21058 −0.0675678
\(322\) 0.193565 0.0107869
\(323\) 4.00080 0.222610
\(324\) 0.214502 0.0119168
\(325\) −7.86502 −0.436273
\(326\) 4.49064 0.248713
\(327\) −9.25070 −0.511565
\(328\) −17.9338 −0.990227
\(329\) −0.0966373 −0.00532779
\(330\) −19.8307 −1.09165
\(331\) 6.81134 0.374385 0.187193 0.982323i \(-0.440061\pi\)
0.187193 + 0.982323i \(0.440061\pi\)
\(332\) −0.984848 −0.0540506
\(333\) −3.51029 −0.192363
\(334\) −32.0043 −1.75120
\(335\) 34.7133 1.89659
\(336\) −0.103651 −0.00565464
\(337\) 7.54055 0.410760 0.205380 0.978682i \(-0.434157\pi\)
0.205380 + 0.978682i \(0.434157\pi\)
\(338\) −1.48812 −0.0809431
\(339\) −12.0437 −0.654123
\(340\) −1.83482 −0.0995071
\(341\) −10.7386 −0.581530
\(342\) −2.49648 −0.134994
\(343\) −0.331066 −0.0178759
\(344\) −2.01602 −0.108696
\(345\) 19.7283 1.06214
\(346\) −27.2589 −1.46545
\(347\) −0.978400 −0.0525233 −0.0262616 0.999655i \(-0.508360\pi\)
−0.0262616 + 0.999655i \(0.508360\pi\)
\(348\) −0.344409 −0.0184623
\(349\) 1.21341 0.0649522 0.0324761 0.999473i \(-0.489661\pi\)
0.0324761 + 0.999473i \(0.489661\pi\)
\(350\) −0.276784 −0.0147947
\(351\) −1.00000 −0.0533761
\(352\) −4.48940 −0.239286
\(353\) −5.19525 −0.276515 −0.138258 0.990396i \(-0.544150\pi\)
−0.138258 + 0.990396i \(0.544150\pi\)
\(354\) 15.8931 0.844711
\(355\) 10.2638 0.544747
\(356\) 2.14402 0.113633
\(357\) 0.0563975 0.00298487
\(358\) −0.377597 −0.0199566
\(359\) 36.8307 1.94385 0.971925 0.235291i \(-0.0756042\pi\)
0.971925 + 0.235291i \(0.0756042\pi\)
\(360\) −9.53021 −0.502286
\(361\) −16.1856 −0.851876
\(362\) 22.5266 1.18397
\(363\) 2.80355 0.147148
\(364\) −0.00507265 −0.000265879 0
\(365\) −54.4868 −2.85197
\(366\) 8.08027 0.422363
\(367\) 22.8942 1.19507 0.597534 0.801844i \(-0.296147\pi\)
0.597534 + 0.801844i \(0.296147\pi\)
\(368\) 24.1077 1.25670
\(369\) −6.74954 −0.351367
\(370\) −18.7364 −0.974060
\(371\) 0.186097 0.00966169
\(372\) 0.619992 0.0321451
\(373\) 25.3139 1.31070 0.655351 0.755324i \(-0.272521\pi\)
0.655351 + 0.755324i \(0.272521\pi\)
\(374\) 13.1853 0.681796
\(375\) −10.2762 −0.530660
\(376\) −10.8577 −0.559944
\(377\) 1.60562 0.0826937
\(378\) −0.0351918 −0.00181007
\(379\) 8.48624 0.435909 0.217955 0.975959i \(-0.430062\pi\)
0.217955 + 0.975959i \(0.430062\pi\)
\(380\) −1.29070 −0.0662117
\(381\) 1.60892 0.0824277
\(382\) −15.3311 −0.784405
\(383\) −3.24774 −0.165952 −0.0829759 0.996552i \(-0.526442\pi\)
−0.0829759 + 0.996552i \(0.526442\pi\)
\(384\) −12.7856 −0.652465
\(385\) 0.315140 0.0160610
\(386\) −9.05346 −0.460809
\(387\) −0.758748 −0.0385693
\(388\) −0.764028 −0.0387876
\(389\) 19.8931 1.00862 0.504311 0.863522i \(-0.331746\pi\)
0.504311 + 0.863522i \(0.331746\pi\)
\(390\) −5.33757 −0.270278
\(391\) −13.1172 −0.663365
\(392\) −18.5978 −0.939329
\(393\) 5.67616 0.286324
\(394\) 23.2634 1.17199
\(395\) −60.1222 −3.02508
\(396\) −0.796942 −0.0400479
\(397\) −11.7640 −0.590421 −0.295210 0.955432i \(-0.595390\pi\)
−0.295210 + 0.955432i \(0.595390\pi\)
\(398\) −26.6241 −1.33455
\(399\) 0.0396729 0.00198613
\(400\) −34.4723 −1.72362
\(401\) 16.2212 0.810050 0.405025 0.914306i \(-0.367263\pi\)
0.405025 + 0.914306i \(0.367263\pi\)
\(402\) 14.4022 0.718317
\(403\) −2.89038 −0.143980
\(404\) 0.397419 0.0197723
\(405\) −3.58678 −0.178229
\(406\) 0.0565047 0.00280428
\(407\) 13.0418 0.646460
\(408\) 6.33657 0.313707
\(409\) 29.6167 1.46445 0.732227 0.681061i \(-0.238481\pi\)
0.732227 + 0.681061i \(0.238481\pi\)
\(410\) −36.0261 −1.77920
\(411\) −13.8157 −0.681476
\(412\) −0.214502 −0.0105678
\(413\) −0.252566 −0.0124280
\(414\) 8.18507 0.402274
\(415\) 16.4681 0.808386
\(416\) −1.20835 −0.0592442
\(417\) 13.2348 0.648110
\(418\) 9.27521 0.453665
\(419\) 8.22298 0.401719 0.200859 0.979620i \(-0.435627\pi\)
0.200859 + 0.979620i \(0.435627\pi\)
\(420\) −0.0181945 −0.000887801 0
\(421\) −30.6539 −1.49398 −0.746989 0.664836i \(-0.768501\pi\)
−0.746989 + 0.664836i \(0.768501\pi\)
\(422\) −4.60955 −0.224389
\(423\) −4.08640 −0.198688
\(424\) 20.9090 1.01543
\(425\) 18.7567 0.909833
\(426\) 4.25836 0.206318
\(427\) −0.128408 −0.00621409
\(428\) −0.259671 −0.0125517
\(429\) 3.71531 0.179377
\(430\) −4.04987 −0.195302
\(431\) 21.8734 1.05361 0.526803 0.849987i \(-0.323391\pi\)
0.526803 + 0.849987i \(0.323391\pi\)
\(432\) −4.38299 −0.210877
\(433\) 11.9588 0.574704 0.287352 0.957825i \(-0.407225\pi\)
0.287352 + 0.957825i \(0.407225\pi\)
\(434\) −0.101718 −0.00488260
\(435\) 5.75902 0.276124
\(436\) −1.98430 −0.0950305
\(437\) −9.22730 −0.441402
\(438\) −22.6060 −1.08016
\(439\) −16.6422 −0.794290 −0.397145 0.917756i \(-0.629999\pi\)
−0.397145 + 0.917756i \(0.629999\pi\)
\(440\) 35.4077 1.68800
\(441\) −6.99944 −0.333307
\(442\) 3.54891 0.168804
\(443\) 12.2352 0.581312 0.290656 0.956828i \(-0.406126\pi\)
0.290656 + 0.956828i \(0.406126\pi\)
\(444\) −0.752965 −0.0357342
\(445\) −35.8512 −1.69951
\(446\) −13.7014 −0.648781
\(447\) −3.91884 −0.185355
\(448\) 0.164778 0.00778505
\(449\) −29.8011 −1.40640 −0.703200 0.710992i \(-0.748246\pi\)
−0.703200 + 0.710992i \(0.748246\pi\)
\(450\) −11.7041 −0.551736
\(451\) 25.0767 1.18081
\(452\) −2.58340 −0.121513
\(453\) 21.0997 0.991350
\(454\) 23.9727 1.12510
\(455\) 0.0848220 0.00397652
\(456\) 4.45746 0.208740
\(457\) 6.28598 0.294046 0.147023 0.989133i \(-0.453031\pi\)
0.147023 + 0.989133i \(0.453031\pi\)
\(458\) −44.4476 −2.07690
\(459\) 2.38483 0.111314
\(460\) 4.23176 0.197307
\(461\) −11.7732 −0.548332 −0.274166 0.961682i \(-0.588402\pi\)
−0.274166 + 0.961682i \(0.588402\pi\)
\(462\) 0.130749 0.00608297
\(463\) −25.6663 −1.19281 −0.596406 0.802683i \(-0.703405\pi\)
−0.596406 + 0.802683i \(0.703405\pi\)
\(464\) 7.03743 0.326704
\(465\) −10.3672 −0.480765
\(466\) −42.4362 −1.96582
\(467\) 27.1923 1.25831 0.629155 0.777280i \(-0.283401\pi\)
0.629155 + 0.777280i \(0.283401\pi\)
\(468\) −0.214502 −0.00991536
\(469\) −0.228873 −0.0105684
\(470\) −21.8115 −1.00609
\(471\) 9.31170 0.429060
\(472\) −28.3772 −1.30616
\(473\) 2.81898 0.129617
\(474\) −24.9441 −1.14572
\(475\) 13.1944 0.605401
\(476\) 0.0120974 0.000554483 0
\(477\) 7.86931 0.360311
\(478\) −8.29339 −0.379331
\(479\) 19.4778 0.889963 0.444981 0.895540i \(-0.353210\pi\)
0.444981 + 0.895540i \(0.353210\pi\)
\(480\) −4.33409 −0.197823
\(481\) 3.51029 0.160056
\(482\) −7.48858 −0.341096
\(483\) −0.130073 −0.00591854
\(484\) 0.601367 0.0273349
\(485\) 12.7756 0.580112
\(486\) −1.48812 −0.0675025
\(487\) −35.5437 −1.61064 −0.805319 0.592841i \(-0.798006\pi\)
−0.805319 + 0.592841i \(0.798006\pi\)
\(488\) −14.4273 −0.653094
\(489\) −3.01766 −0.136463
\(490\) −37.3600 −1.68775
\(491\) 25.9533 1.17126 0.585628 0.810580i \(-0.300848\pi\)
0.585628 + 0.810580i \(0.300848\pi\)
\(492\) −1.44779 −0.0652714
\(493\) −3.82913 −0.172455
\(494\) 2.49648 0.112322
\(495\) 13.3260 0.598960
\(496\) −12.6685 −0.568832
\(497\) −0.0676718 −0.00303550
\(498\) 6.83244 0.306169
\(499\) 14.5179 0.649911 0.324955 0.945729i \(-0.394651\pi\)
0.324955 + 0.945729i \(0.394651\pi\)
\(500\) −2.20426 −0.0985777
\(501\) 21.5065 0.960840
\(502\) 6.42929 0.286953
\(503\) 16.4003 0.731254 0.365627 0.930761i \(-0.380855\pi\)
0.365627 + 0.930761i \(0.380855\pi\)
\(504\) 0.0628349 0.00279889
\(505\) −6.64542 −0.295717
\(506\) −30.4101 −1.35189
\(507\) 1.00000 0.0444116
\(508\) 0.345118 0.0153121
\(509\) −0.273378 −0.0121172 −0.00605862 0.999982i \(-0.501929\pi\)
−0.00605862 + 0.999982i \(0.501929\pi\)
\(510\) 12.7292 0.563657
\(511\) 0.359244 0.0158920
\(512\) 17.9954 0.795290
\(513\) 1.67761 0.0740681
\(514\) −38.1904 −1.68450
\(515\) 3.58678 0.158053
\(516\) −0.162753 −0.00716480
\(517\) 15.1823 0.667715
\(518\) 0.123534 0.00542775
\(519\) 18.3177 0.804057
\(520\) 9.53021 0.417927
\(521\) 25.0865 1.09906 0.549529 0.835475i \(-0.314807\pi\)
0.549529 + 0.835475i \(0.314807\pi\)
\(522\) 2.38936 0.104579
\(523\) −38.2574 −1.67288 −0.836440 0.548058i \(-0.815367\pi\)
−0.836440 + 0.548058i \(0.815367\pi\)
\(524\) 1.21755 0.0531888
\(525\) 0.185996 0.00811752
\(526\) 15.4618 0.674165
\(527\) 6.89304 0.300266
\(528\) 16.2842 0.708678
\(529\) 7.25305 0.315350
\(530\) 42.0029 1.82449
\(531\) −10.6800 −0.463473
\(532\) 0.00850992 0.000368952 0
\(533\) 6.74954 0.292355
\(534\) −14.8743 −0.643674
\(535\) 4.34208 0.187724
\(536\) −25.7151 −1.11072
\(537\) 0.253741 0.0109497
\(538\) 9.09333 0.392041
\(539\) 26.0051 1.12012
\(540\) −0.769373 −0.0331085
\(541\) 20.3560 0.875172 0.437586 0.899177i \(-0.355834\pi\)
0.437586 + 0.899177i \(0.355834\pi\)
\(542\) −9.92457 −0.426297
\(543\) −15.1376 −0.649616
\(544\) 2.88170 0.123552
\(545\) 33.1803 1.42129
\(546\) 0.0351918 0.00150607
\(547\) 19.4491 0.831584 0.415792 0.909460i \(-0.363505\pi\)
0.415792 + 0.909460i \(0.363505\pi\)
\(548\) −2.96349 −0.126594
\(549\) −5.42985 −0.231740
\(550\) 43.4844 1.85418
\(551\) −2.69360 −0.114751
\(552\) −14.6144 −0.622032
\(553\) 0.396400 0.0168566
\(554\) −46.6339 −1.98128
\(555\) 12.5907 0.534444
\(556\) 2.83889 0.120396
\(557\) 4.82681 0.204518 0.102259 0.994758i \(-0.467393\pi\)
0.102259 + 0.994758i \(0.467393\pi\)
\(558\) −4.30123 −0.182085
\(559\) 0.758748 0.0320916
\(560\) 0.371774 0.0157103
\(561\) −8.86037 −0.374085
\(562\) 43.1661 1.82085
\(563\) −20.8748 −0.879768 −0.439884 0.898055i \(-0.644980\pi\)
−0.439884 + 0.898055i \(0.644980\pi\)
\(564\) −0.876542 −0.0369091
\(565\) 43.1981 1.81736
\(566\) 13.2209 0.555715
\(567\) 0.0236485 0.000993144 0
\(568\) −7.60329 −0.319027
\(569\) 7.59511 0.318404 0.159202 0.987246i \(-0.449108\pi\)
0.159202 + 0.987246i \(0.449108\pi\)
\(570\) 8.95434 0.375056
\(571\) 21.5156 0.900401 0.450200 0.892928i \(-0.351353\pi\)
0.450200 + 0.892928i \(0.351353\pi\)
\(572\) 0.796942 0.0333218
\(573\) 10.3023 0.430384
\(574\) 0.237529 0.00991425
\(575\) −43.2598 −1.80406
\(576\) 6.96782 0.290326
\(577\) 5.99567 0.249603 0.124801 0.992182i \(-0.460171\pi\)
0.124801 + 0.992182i \(0.460171\pi\)
\(578\) 16.8345 0.700224
\(579\) 6.08382 0.252835
\(580\) 1.23532 0.0512939
\(581\) −0.108578 −0.00450457
\(582\) 5.30048 0.219712
\(583\) −29.2369 −1.21087
\(584\) 40.3630 1.67023
\(585\) 3.58678 0.148295
\(586\) 16.0567 0.663297
\(587\) −12.3136 −0.508237 −0.254118 0.967173i \(-0.581785\pi\)
−0.254118 + 0.967173i \(0.581785\pi\)
\(588\) −1.50139 −0.0619165
\(589\) 4.84891 0.199796
\(590\) −57.0052 −2.34687
\(591\) −15.6327 −0.643045
\(592\) 15.3856 0.632344
\(593\) −33.3943 −1.37134 −0.685671 0.727912i \(-0.740491\pi\)
−0.685671 + 0.727912i \(0.740491\pi\)
\(594\) 5.52883 0.226851
\(595\) −0.202286 −0.00829291
\(596\) −0.840601 −0.0344323
\(597\) 17.8911 0.732235
\(598\) −8.18507 −0.334713
\(599\) −30.9686 −1.26534 −0.632672 0.774420i \(-0.718042\pi\)
−0.632672 + 0.774420i \(0.718042\pi\)
\(600\) 20.8976 0.853142
\(601\) 31.0693 1.26734 0.633672 0.773601i \(-0.281547\pi\)
0.633672 + 0.773601i \(0.281547\pi\)
\(602\) 0.0267017 0.00108828
\(603\) −9.67812 −0.394124
\(604\) 4.52593 0.184157
\(605\) −10.0557 −0.408823
\(606\) −2.75712 −0.112000
\(607\) −5.04927 −0.204944 −0.102472 0.994736i \(-0.532675\pi\)
−0.102472 + 0.994736i \(0.532675\pi\)
\(608\) 2.02714 0.0822112
\(609\) −0.0379705 −0.00153864
\(610\) −28.9822 −1.17345
\(611\) 4.08640 0.165318
\(612\) 0.511550 0.0206782
\(613\) 17.5767 0.709915 0.354958 0.934882i \(-0.384495\pi\)
0.354958 + 0.934882i \(0.384495\pi\)
\(614\) 23.3811 0.943584
\(615\) 24.2091 0.976207
\(616\) −0.233451 −0.00940602
\(617\) 1.63595 0.0658608 0.0329304 0.999458i \(-0.489516\pi\)
0.0329304 + 0.999458i \(0.489516\pi\)
\(618\) 1.48812 0.0598610
\(619\) 0.779525 0.0313318 0.0156659 0.999877i \(-0.495013\pi\)
0.0156659 + 0.999877i \(0.495013\pi\)
\(620\) −2.22378 −0.0893090
\(621\) −5.50028 −0.220719
\(622\) −16.0978 −0.645462
\(623\) 0.236375 0.00947017
\(624\) 4.38299 0.175460
\(625\) −2.46661 −0.0986645
\(626\) 16.5938 0.663222
\(627\) −6.23283 −0.248915
\(628\) 1.99738 0.0797041
\(629\) −8.37144 −0.333791
\(630\) 0.126225 0.00502894
\(631\) −23.5978 −0.939412 −0.469706 0.882823i \(-0.655640\pi\)
−0.469706 + 0.882823i \(0.655640\pi\)
\(632\) 44.5376 1.77161
\(633\) 3.09757 0.123117
\(634\) −16.5523 −0.657375
\(635\) −5.77086 −0.229010
\(636\) 1.68798 0.0669329
\(637\) 6.99944 0.277328
\(638\) −8.87721 −0.351452
\(639\) −2.86157 −0.113202
\(640\) 45.8594 1.81275
\(641\) −38.6884 −1.52810 −0.764051 0.645156i \(-0.776792\pi\)
−0.764051 + 0.645156i \(0.776792\pi\)
\(642\) 1.80148 0.0710989
\(643\) −23.2538 −0.917039 −0.458519 0.888684i \(-0.651620\pi\)
−0.458519 + 0.888684i \(0.651620\pi\)
\(644\) −0.0279010 −0.00109945
\(645\) 2.72146 0.107158
\(646\) −5.95367 −0.234244
\(647\) 14.5221 0.570924 0.285462 0.958390i \(-0.407853\pi\)
0.285462 + 0.958390i \(0.407853\pi\)
\(648\) 2.65704 0.104378
\(649\) 39.6796 1.55756
\(650\) 11.7041 0.459072
\(651\) 0.0683530 0.00267897
\(652\) −0.647294 −0.0253500
\(653\) −0.348559 −0.0136402 −0.00682008 0.999977i \(-0.502171\pi\)
−0.00682008 + 0.999977i \(0.502171\pi\)
\(654\) 13.7662 0.538299
\(655\) −20.3592 −0.795498
\(656\) 29.5832 1.15503
\(657\) 15.1910 0.592657
\(658\) 0.143808 0.00560622
\(659\) −11.2477 −0.438148 −0.219074 0.975708i \(-0.570304\pi\)
−0.219074 + 0.975708i \(0.570304\pi\)
\(660\) 2.85846 0.111265
\(661\) 36.4348 1.41715 0.708574 0.705637i \(-0.249339\pi\)
0.708574 + 0.705637i \(0.249339\pi\)
\(662\) −10.1361 −0.393951
\(663\) −2.38483 −0.0926189
\(664\) −12.1993 −0.473425
\(665\) −0.142298 −0.00551808
\(666\) 5.22374 0.202416
\(667\) 8.83136 0.341952
\(668\) 4.61319 0.178490
\(669\) 9.20720 0.355971
\(670\) −51.6576 −1.99571
\(671\) 20.1736 0.778793
\(672\) 0.0285757 0.00110233
\(673\) −43.6019 −1.68073 −0.840366 0.542020i \(-0.817660\pi\)
−0.840366 + 0.542020i \(0.817660\pi\)
\(674\) −11.2212 −0.432226
\(675\) 7.86502 0.302725
\(676\) 0.214502 0.00825008
\(677\) 20.9648 0.805741 0.402871 0.915257i \(-0.368012\pi\)
0.402871 + 0.915257i \(0.368012\pi\)
\(678\) 17.9225 0.688308
\(679\) −0.0842328 −0.00323256
\(680\) −22.7279 −0.871575
\(681\) −16.1094 −0.617314
\(682\) 15.9804 0.611921
\(683\) 12.3760 0.473554 0.236777 0.971564i \(-0.423909\pi\)
0.236777 + 0.971564i \(0.423909\pi\)
\(684\) 0.359850 0.0137592
\(685\) 49.5538 1.89335
\(686\) 0.492666 0.0188101
\(687\) 29.8683 1.13955
\(688\) 3.32559 0.126787
\(689\) −7.86931 −0.299797
\(690\) −29.3581 −1.11764
\(691\) −32.3780 −1.23172 −0.615859 0.787857i \(-0.711191\pi\)
−0.615859 + 0.787857i \(0.711191\pi\)
\(692\) 3.92918 0.149365
\(693\) −0.0878616 −0.00333758
\(694\) 1.45598 0.0552681
\(695\) −47.4703 −1.80065
\(696\) −4.26619 −0.161710
\(697\) −16.0965 −0.609698
\(698\) −1.80570 −0.0683466
\(699\) 28.5167 1.07860
\(700\) 0.0398965 0.00150795
\(701\) 33.1812 1.25324 0.626618 0.779327i \(-0.284439\pi\)
0.626618 + 0.779327i \(0.284439\pi\)
\(702\) 1.48812 0.0561655
\(703\) −5.88889 −0.222104
\(704\) −25.8876 −0.975676
\(705\) 14.6570 0.552016
\(706\) 7.73115 0.290966
\(707\) 0.0438148 0.00164783
\(708\) −2.29088 −0.0860967
\(709\) 48.9104 1.83687 0.918434 0.395575i \(-0.129455\pi\)
0.918434 + 0.395575i \(0.129455\pi\)
\(710\) −15.2738 −0.573216
\(711\) 16.7621 0.628630
\(712\) 26.5580 0.995304
\(713\) −15.8979 −0.595380
\(714\) −0.0839263 −0.00314086
\(715\) −13.3260 −0.498365
\(716\) 0.0544279 0.00203407
\(717\) 5.57306 0.208130
\(718\) −54.8085 −2.04544
\(719\) −50.7176 −1.89145 −0.945725 0.324969i \(-0.894646\pi\)
−0.945725 + 0.324969i \(0.894646\pi\)
\(720\) 15.7208 0.585881
\(721\) −0.0236485 −0.000880716 0
\(722\) 24.0862 0.896395
\(723\) 5.03224 0.187151
\(724\) −3.24705 −0.120676
\(725\) −12.6282 −0.469001
\(726\) −4.17202 −0.154838
\(727\) 17.6824 0.655805 0.327903 0.944712i \(-0.393658\pi\)
0.327903 + 0.944712i \(0.393658\pi\)
\(728\) −0.0628349 −0.00232882
\(729\) 1.00000 0.0370370
\(730\) 81.0829 3.00101
\(731\) −1.80948 −0.0669261
\(732\) −1.16471 −0.0430491
\(733\) −15.0161 −0.554632 −0.277316 0.960779i \(-0.589445\pi\)
−0.277316 + 0.960779i \(0.589445\pi\)
\(734\) −34.0693 −1.25752
\(735\) 25.1055 0.926030
\(736\) −6.64626 −0.244984
\(737\) 35.9572 1.32450
\(738\) 10.0441 0.369730
\(739\) 28.7271 1.05674 0.528372 0.849013i \(-0.322803\pi\)
0.528372 + 0.849013i \(0.322803\pi\)
\(740\) 2.70072 0.0992806
\(741\) −1.67761 −0.0616284
\(742\) −0.276935 −0.0101666
\(743\) 50.5855 1.85580 0.927900 0.372829i \(-0.121612\pi\)
0.927900 + 0.372829i \(0.121612\pi\)
\(744\) 7.67983 0.281556
\(745\) 14.0560 0.514974
\(746\) −37.6701 −1.37920
\(747\) −4.59132 −0.167988
\(748\) −1.90057 −0.0694917
\(749\) −0.0286283 −0.00104606
\(750\) 15.2922 0.558392
\(751\) −25.9645 −0.947457 −0.473728 0.880671i \(-0.657092\pi\)
−0.473728 + 0.880671i \(0.657092\pi\)
\(752\) 17.9107 0.653135
\(753\) −4.32041 −0.157444
\(754\) −2.38936 −0.0870153
\(755\) −75.6800 −2.75428
\(756\) 0.00507265 0.000184491 0
\(757\) 34.2130 1.24349 0.621746 0.783219i \(-0.286423\pi\)
0.621746 + 0.783219i \(0.286423\pi\)
\(758\) −12.6286 −0.458690
\(759\) 20.4352 0.741753
\(760\) −15.9879 −0.579944
\(761\) 51.7887 1.87734 0.938670 0.344816i \(-0.112059\pi\)
0.938670 + 0.344816i \(0.112059\pi\)
\(762\) −2.39427 −0.0867354
\(763\) −0.218765 −0.00791983
\(764\) 2.20986 0.0799501
\(765\) −8.55385 −0.309265
\(766\) 4.83303 0.174624
\(767\) 10.6800 0.385633
\(768\) 5.09095 0.183704
\(769\) −11.0760 −0.399409 −0.199705 0.979856i \(-0.563998\pi\)
−0.199705 + 0.979856i \(0.563998\pi\)
\(770\) −0.468967 −0.0169004
\(771\) 25.6635 0.924248
\(772\) 1.30499 0.0469677
\(773\) −20.8839 −0.751143 −0.375571 0.926794i \(-0.622553\pi\)
−0.375571 + 0.926794i \(0.622553\pi\)
\(774\) 1.12911 0.0405849
\(775\) 22.7328 0.816588
\(776\) −9.46400 −0.339738
\(777\) −0.0830132 −0.00297808
\(778\) −29.6034 −1.06133
\(779\) −11.3231 −0.405691
\(780\) 0.769373 0.0275480
\(781\) 10.6316 0.380429
\(782\) 19.5200 0.698033
\(783\) −1.60562 −0.0573802
\(784\) 30.6785 1.09566
\(785\) −33.3991 −1.19206
\(786\) −8.44681 −0.301288
\(787\) −2.13144 −0.0759775 −0.0379888 0.999278i \(-0.512095\pi\)
−0.0379888 + 0.999278i \(0.512095\pi\)
\(788\) −3.35326 −0.119455
\(789\) −10.3901 −0.369898
\(790\) 89.4691 3.18317
\(791\) −0.284815 −0.0101269
\(792\) −9.87172 −0.350776
\(793\) 5.42985 0.192820
\(794\) 17.5063 0.621276
\(795\) −28.2255 −1.00106
\(796\) 3.83768 0.136023
\(797\) −55.9046 −1.98024 −0.990121 0.140214i \(-0.955221\pi\)
−0.990121 + 0.140214i \(0.955221\pi\)
\(798\) −0.0590380 −0.00208992
\(799\) −9.74536 −0.344766
\(800\) 9.50369 0.336006
\(801\) 9.99536 0.353169
\(802\) −24.1392 −0.852383
\(803\) −56.4393 −1.99170
\(804\) −2.07598 −0.0732141
\(805\) 0.466545 0.0164435
\(806\) 4.30123 0.151504
\(807\) −6.11062 −0.215104
\(808\) 4.92283 0.173184
\(809\) −20.7727 −0.730330 −0.365165 0.930943i \(-0.618987\pi\)
−0.365165 + 0.930943i \(0.618987\pi\)
\(810\) 5.33757 0.187543
\(811\) 27.3891 0.961762 0.480881 0.876786i \(-0.340317\pi\)
0.480881 + 0.876786i \(0.340317\pi\)
\(812\) −0.00814476 −0.000285825 0
\(813\) 6.66920 0.233899
\(814\) −19.4078 −0.680244
\(815\) 10.8237 0.379137
\(816\) −10.4527 −0.365917
\(817\) −1.27288 −0.0445324
\(818\) −44.0733 −1.54099
\(819\) −0.0236485 −0.000826345 0
\(820\) 5.19291 0.181344
\(821\) −8.56521 −0.298928 −0.149464 0.988767i \(-0.547755\pi\)
−0.149464 + 0.988767i \(0.547755\pi\)
\(822\) 20.5594 0.717090
\(823\) −4.04383 −0.140959 −0.0704794 0.997513i \(-0.522453\pi\)
−0.0704794 + 0.997513i \(0.522453\pi\)
\(824\) −2.65704 −0.0925622
\(825\) −29.2210 −1.01734
\(826\) 0.375849 0.0130775
\(827\) 26.2429 0.912555 0.456278 0.889837i \(-0.349182\pi\)
0.456278 + 0.889837i \(0.349182\pi\)
\(828\) −1.17982 −0.0410016
\(829\) 9.21308 0.319984 0.159992 0.987118i \(-0.448853\pi\)
0.159992 + 0.987118i \(0.448853\pi\)
\(830\) −24.5065 −0.850633
\(831\) 31.3374 1.08708
\(832\) −6.96782 −0.241566
\(833\) −16.6924 −0.578359
\(834\) −19.6949 −0.681980
\(835\) −77.1392 −2.66951
\(836\) −1.33696 −0.0462396
\(837\) 2.89038 0.0999060
\(838\) −12.2368 −0.422712
\(839\) −52.0976 −1.79861 −0.899304 0.437325i \(-0.855926\pi\)
−0.899304 + 0.437325i \(0.855926\pi\)
\(840\) −0.225375 −0.00777618
\(841\) −26.4220 −0.911103
\(842\) 45.6166 1.57205
\(843\) −29.0071 −0.999059
\(844\) 0.664434 0.0228708
\(845\) −3.58678 −0.123389
\(846\) 6.08106 0.209071
\(847\) 0.0662997 0.00227809
\(848\) −34.4911 −1.18443
\(849\) −8.88428 −0.304908
\(850\) −27.9122 −0.957381
\(851\) 19.3076 0.661855
\(852\) −0.613813 −0.0210289
\(853\) 16.5563 0.566878 0.283439 0.958990i \(-0.408525\pi\)
0.283439 + 0.958990i \(0.408525\pi\)
\(854\) 0.191086 0.00653884
\(855\) −6.01721 −0.205784
\(856\) −3.21655 −0.109939
\(857\) 2.19005 0.0748108 0.0374054 0.999300i \(-0.488091\pi\)
0.0374054 + 0.999300i \(0.488091\pi\)
\(858\) −5.52883 −0.188751
\(859\) −35.4959 −1.21110 −0.605552 0.795805i \(-0.707048\pi\)
−0.605552 + 0.795805i \(0.707048\pi\)
\(860\) 0.583760 0.0199060
\(861\) −0.159617 −0.00543972
\(862\) −32.5503 −1.10867
\(863\) 0.00343611 0.000116967 0 5.84833e−5 1.00000i \(-0.499981\pi\)
5.84833e−5 1.00000i \(0.499981\pi\)
\(864\) 1.20835 0.0411089
\(865\) −65.7015 −2.23392
\(866\) −17.7962 −0.604738
\(867\) −11.3126 −0.384196
\(868\) 0.0146619 0.000497656 0
\(869\) −62.2766 −2.11259
\(870\) −8.57011 −0.290554
\(871\) 9.67812 0.327931
\(872\) −24.5794 −0.832365
\(873\) −3.56186 −0.120551
\(874\) 13.7313 0.464469
\(875\) −0.243016 −0.00821545
\(876\) 3.25850 0.110095
\(877\) 31.7336 1.07157 0.535784 0.844355i \(-0.320016\pi\)
0.535784 + 0.844355i \(0.320016\pi\)
\(878\) 24.7656 0.835800
\(879\) −10.7899 −0.363936
\(880\) −58.4079 −1.96893
\(881\) 33.8906 1.14180 0.570901 0.821019i \(-0.306594\pi\)
0.570901 + 0.821019i \(0.306594\pi\)
\(882\) 10.4160 0.350725
\(883\) −14.9095 −0.501744 −0.250872 0.968020i \(-0.580717\pi\)
−0.250872 + 0.968020i \(0.580717\pi\)
\(884\) −0.511550 −0.0172053
\(885\) 38.3069 1.28767
\(886\) −18.2075 −0.611692
\(887\) 5.81841 0.195363 0.0976815 0.995218i \(-0.468857\pi\)
0.0976815 + 0.995218i \(0.468857\pi\)
\(888\) −9.32697 −0.312993
\(889\) 0.0380487 0.00127611
\(890\) 53.3509 1.78832
\(891\) −3.71531 −0.124468
\(892\) 1.97496 0.0661267
\(893\) −6.85538 −0.229407
\(894\) 5.83171 0.195042
\(895\) −0.910113 −0.0304217
\(896\) −0.302361 −0.0101012
\(897\) 5.50028 0.183649
\(898\) 44.3476 1.47990
\(899\) −4.64085 −0.154781
\(900\) 1.68706 0.0562354
\(901\) 18.7669 0.625217
\(902\) −37.3171 −1.24252
\(903\) −0.0179432 −0.000597114 0
\(904\) −32.0005 −1.06432
\(905\) 54.2953 1.80484
\(906\) −31.3989 −1.04316
\(907\) −11.9288 −0.396090 −0.198045 0.980193i \(-0.563459\pi\)
−0.198045 + 0.980193i \(0.563459\pi\)
\(908\) −3.45550 −0.114675
\(909\) 1.85275 0.0614519
\(910\) −0.126225 −0.00418433
\(911\) −38.6204 −1.27955 −0.639775 0.768562i \(-0.720973\pi\)
−0.639775 + 0.768562i \(0.720973\pi\)
\(912\) −7.35294 −0.243480
\(913\) 17.0582 0.564544
\(914\) −9.35429 −0.309412
\(915\) 19.4757 0.643847
\(916\) 6.40680 0.211687
\(917\) 0.134233 0.00443275
\(918\) −3.54891 −0.117131
\(919\) −28.0457 −0.925142 −0.462571 0.886582i \(-0.653073\pi\)
−0.462571 + 0.886582i \(0.653073\pi\)
\(920\) 52.4188 1.72820
\(921\) −15.7118 −0.517723
\(922\) 17.5199 0.576988
\(923\) 2.86157 0.0941897
\(924\) −0.0188465 −0.000620004 0
\(925\) −27.6085 −0.907762
\(926\) 38.1945 1.25515
\(927\) −1.00000 −0.0328443
\(928\) −1.94015 −0.0636886
\(929\) 28.3527 0.930221 0.465110 0.885253i \(-0.346015\pi\)
0.465110 + 0.885253i \(0.346015\pi\)
\(930\) 15.4276 0.505890
\(931\) −11.7423 −0.384839
\(932\) 6.11688 0.200365
\(933\) 10.8175 0.354150
\(934\) −40.4654 −1.32407
\(935\) 31.7802 1.03932
\(936\) −2.65704 −0.0868479
\(937\) 2.23335 0.0729605 0.0364803 0.999334i \(-0.488385\pi\)
0.0364803 + 0.999334i \(0.488385\pi\)
\(938\) 0.340591 0.0111207
\(939\) −11.1508 −0.363894
\(940\) 3.14397 0.102545
\(941\) 21.9982 0.717122 0.358561 0.933506i \(-0.383268\pi\)
0.358561 + 0.933506i \(0.383268\pi\)
\(942\) −13.8569 −0.451483
\(943\) 37.1243 1.20893
\(944\) 46.8104 1.52355
\(945\) −0.0848220 −0.00275926
\(946\) −4.19499 −0.136391
\(947\) 1.67200 0.0543327 0.0271663 0.999631i \(-0.491352\pi\)
0.0271663 + 0.999631i \(0.491352\pi\)
\(948\) 3.59552 0.116777
\(949\) −15.1910 −0.493121
\(950\) −19.6349 −0.637039
\(951\) 11.1229 0.360686
\(952\) 0.149850 0.00485668
\(953\) 31.1056 1.00761 0.503805 0.863818i \(-0.331933\pi\)
0.503805 + 0.863818i \(0.331933\pi\)
\(954\) −11.7105 −0.379141
\(955\) −36.9521 −1.19574
\(956\) 1.19543 0.0386631
\(957\) 5.96539 0.192834
\(958\) −28.9853 −0.936472
\(959\) −0.326720 −0.0105503
\(960\) −24.9920 −0.806615
\(961\) −22.6457 −0.730507
\(962\) −5.22374 −0.168420
\(963\) −1.21058 −0.0390103
\(964\) 1.07943 0.0347660
\(965\) −21.8214 −0.702454
\(966\) 0.193565 0.00622784
\(967\) −35.1720 −1.13105 −0.565527 0.824730i \(-0.691327\pi\)
−0.565527 + 0.824730i \(0.691327\pi\)
\(968\) 7.44913 0.239424
\(969\) 4.00080 0.128524
\(970\) −19.0117 −0.610428
\(971\) −26.7524 −0.858524 −0.429262 0.903180i \(-0.641226\pi\)
−0.429262 + 0.903180i \(0.641226\pi\)
\(972\) 0.214502 0.00688016
\(973\) 0.312983 0.0100338
\(974\) 52.8933 1.69481
\(975\) −7.86502 −0.251882
\(976\) 23.7990 0.761787
\(977\) −11.5874 −0.370715 −0.185357 0.982671i \(-0.559344\pi\)
−0.185357 + 0.982671i \(0.559344\pi\)
\(978\) 4.49064 0.143595
\(979\) −37.1359 −1.18687
\(980\) 5.38518 0.172023
\(981\) −9.25070 −0.295352
\(982\) −38.6216 −1.23247
\(983\) 0.844719 0.0269424 0.0134712 0.999909i \(-0.495712\pi\)
0.0134712 + 0.999909i \(0.495712\pi\)
\(984\) −17.9338 −0.571708
\(985\) 56.0712 1.78658
\(986\) 5.69820 0.181468
\(987\) −0.0966373 −0.00307600
\(988\) −0.359850 −0.0114484
\(989\) 4.17332 0.132704
\(990\) −19.8307 −0.630262
\(991\) 45.4221 1.44288 0.721440 0.692477i \(-0.243481\pi\)
0.721440 + 0.692477i \(0.243481\pi\)
\(992\) 3.49258 0.110890
\(993\) 6.81134 0.216151
\(994\) 0.100704 0.00319413
\(995\) −64.1716 −2.03438
\(996\) −0.984848 −0.0312061
\(997\) −27.0049 −0.855254 −0.427627 0.903955i \(-0.640650\pi\)
−0.427627 + 0.903955i \(0.640650\pi\)
\(998\) −21.6044 −0.683875
\(999\) −3.51029 −0.111061
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 4017.2.a.l.1.9 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.l.1.9 32 1.1 even 1 trivial