Properties

Label 539.2.e.j.67.2
Level $539$
Weight $2$
Character 539.67
Analytic conductor $4.304$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(67,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.e (of order \(3\), degree \(2\), not minimal)

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: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 539.67
Dual form 539.2.e.j.177.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.11803 + 1.93649i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-1.00000 - 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})\) \(q+(1.11803 + 1.93649i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-1.00000 - 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 - 6.47106i) q^{9} +(2.23607 - 3.87298i) q^{10} +(0.500000 - 0.866025i) q^{11} +(4.85410 + 8.40755i) q^{12} +1.23607 q^{13} -6.47214 q^{15} +(0.500000 + 0.866025i) q^{16} +(0.618034 - 1.07047i) q^{17} +(8.35410 - 14.4697i) q^{18} +(-1.23607 - 2.14093i) q^{19} +6.00000 q^{20} +2.23607 q^{22} +(3.23607 + 5.60503i) q^{23} +(-3.61803 + 6.26662i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.38197 + 2.39364i) q^{26} -14.4721 q^{27} -0.472136 q^{29} +(-7.23607 - 12.5332i) q^{30} +(-3.61803 + 6.26662i) q^{31} +(-3.35410 + 5.80948i) q^{32} +(-1.61803 - 2.80252i) q^{33} +2.76393 q^{34} +22.4164 q^{36} +(-0.236068 - 0.408882i) q^{37} +(2.76393 - 4.78727i) q^{38} +(2.00000 - 3.46410i) q^{39} +(2.23607 + 3.87298i) q^{40} +6.76393 q^{41} +8.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-7.47214 + 12.9421i) q^{45} +(-7.23607 + 12.5332i) q^{46} +(3.61803 + 6.26662i) q^{47} +3.23607 q^{48} +2.23607 q^{50} +(-2.00000 - 3.46410i) q^{51} +(-1.85410 + 3.21140i) q^{52} +(-4.23607 + 7.33708i) q^{53} +(-16.1803 - 28.0252i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-0.527864 - 0.914287i) q^{58} +(1.61803 - 2.80252i) q^{59} +(9.70820 - 16.8151i) q^{60} +(-1.38197 - 2.39364i) q^{61} -16.1803 q^{62} -13.0000 q^{64} +(-1.23607 - 2.14093i) q^{65} +(3.61803 - 6.26662i) q^{66} +(-2.76393 + 4.78727i) q^{67} +(1.85410 + 3.21140i) q^{68} +20.9443 q^{69} -1.52786 q^{71} +(8.35410 + 14.4697i) q^{72} +(-2.61803 + 4.53457i) q^{73} +(0.527864 - 0.914287i) q^{74} +(-1.61803 - 2.80252i) q^{75} +7.41641 q^{76} +8.94427 q^{78} +(-4.47214 - 7.74597i) q^{79} +(1.00000 - 1.73205i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(7.56231 + 13.0983i) q^{82} -15.4164 q^{83} -2.47214 q^{85} +(8.94427 + 15.4919i) q^{86} +(-0.763932 + 1.32317i) q^{87} +(-1.11803 + 1.93649i) q^{88} +(1.00000 + 1.73205i) q^{89} -33.4164 q^{90} -19.4164 q^{92} +(11.7082 + 20.2792i) q^{93} +(-8.09017 + 14.0126i) q^{94} +(-2.47214 + 4.28187i) q^{95} +(10.8541 + 18.7999i) q^{96} +9.41641 q^{97} -7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9} + 2 q^{11} + 6 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} + 20 q^{18} + 4 q^{19} + 24 q^{20} + 4 q^{23} - 10 q^{24} + 2 q^{25} + 10 q^{26} - 40 q^{27} + 16 q^{29} - 20 q^{30} - 10 q^{31} - 2 q^{33} + 20 q^{34} + 36 q^{36} + 8 q^{37} + 20 q^{38} + 8 q^{39} + 36 q^{41} + 32 q^{43} + 6 q^{44} - 12 q^{45} - 20 q^{46} + 10 q^{47} + 4 q^{48} - 8 q^{51} + 6 q^{52} - 8 q^{53} - 20 q^{54} - 8 q^{55} - 32 q^{57} - 20 q^{58} + 2 q^{59} + 12 q^{60} - 10 q^{61} - 20 q^{62} - 52 q^{64} + 4 q^{65} + 10 q^{66} - 20 q^{67} - 6 q^{68} + 48 q^{69} - 24 q^{71} + 20 q^{72} - 6 q^{73} + 20 q^{74} - 2 q^{75} - 24 q^{76} + 4 q^{80} - 22 q^{81} - 10 q^{82} - 8 q^{83} + 8 q^{85} - 12 q^{87} + 4 q^{89} - 80 q^{90} - 24 q^{92} + 20 q^{93} - 10 q^{94} + 8 q^{95} + 30 q^{96} - 16 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.11803 + 1.93649i 0.790569 + 1.36931i 0.925615 + 0.378467i \(0.123549\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) 1.61803 2.80252i 0.934172 1.61803i 0.158069 0.987428i \(-0.449473\pi\)
0.776103 0.630606i \(-0.217194\pi\)
\(4\) −1.50000 + 2.59808i −0.750000 + 1.29904i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 7.23607 2.95411
\(7\) 0 0
\(8\) −2.23607 −0.790569
\(9\) −3.73607 6.47106i −1.24536 2.15702i
\(10\) 2.23607 3.87298i 0.707107 1.22474i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 4.85410 + 8.40755i 1.40126 + 2.42705i
\(13\) 1.23607 0.342824 0.171412 0.985199i \(-0.445167\pi\)
0.171412 + 0.985199i \(0.445167\pi\)
\(14\) 0 0
\(15\) −6.47214 −1.67110
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0.618034 1.07047i 0.149895 0.259626i −0.781293 0.624164i \(-0.785440\pi\)
0.931189 + 0.364538i \(0.118773\pi\)
\(18\) 8.35410 14.4697i 1.96908 3.41055i
\(19\) −1.23607 2.14093i −0.283573 0.491164i 0.688689 0.725057i \(-0.258187\pi\)
−0.972262 + 0.233893i \(0.924853\pi\)
\(20\) 6.00000 1.34164
\(21\) 0 0
\(22\) 2.23607 0.476731
\(23\) 3.23607 + 5.60503i 0.674767 + 1.16873i 0.976537 + 0.215350i \(0.0690891\pi\)
−0.301770 + 0.953381i \(0.597578\pi\)
\(24\) −3.61803 + 6.26662i −0.738528 + 1.27917i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.38197 + 2.39364i 0.271026 + 0.469431i
\(27\) −14.4721 −2.78516
\(28\) 0 0
\(29\) −0.472136 −0.0876734 −0.0438367 0.999039i \(-0.513958\pi\)
−0.0438367 + 0.999039i \(0.513958\pi\)
\(30\) −7.23607 12.5332i −1.32112 2.28825i
\(31\) −3.61803 + 6.26662i −0.649818 + 1.12552i 0.333348 + 0.942804i \(0.391822\pi\)
−0.983166 + 0.182714i \(0.941512\pi\)
\(32\) −3.35410 + 5.80948i −0.592927 + 1.02698i
\(33\) −1.61803 2.80252i −0.281664 0.487856i
\(34\) 2.76393 0.474010
\(35\) 0 0
\(36\) 22.4164 3.73607
\(37\) −0.236068 0.408882i −0.0388093 0.0672197i 0.845968 0.533233i \(-0.179023\pi\)
−0.884778 + 0.466013i \(0.845690\pi\)
\(38\) 2.76393 4.78727i 0.448369 0.776598i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) 2.23607 + 3.87298i 0.353553 + 0.612372i
\(41\) 6.76393 1.05635 0.528174 0.849136i \(-0.322877\pi\)
0.528174 + 0.849136i \(0.322877\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) −7.47214 + 12.9421i −1.11388 + 1.92930i
\(46\) −7.23607 + 12.5332i −1.06690 + 1.84793i
\(47\) 3.61803 + 6.26662i 0.527744 + 0.914080i 0.999477 + 0.0323386i \(0.0102955\pi\)
−0.471732 + 0.881742i \(0.656371\pi\)
\(48\) 3.23607 0.467086
\(49\) 0 0
\(50\) 2.23607 0.316228
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) −1.85410 + 3.21140i −0.257118 + 0.445341i
\(53\) −4.23607 + 7.33708i −0.581869 + 1.00783i 0.413389 + 0.910554i \(0.364345\pi\)
−0.995258 + 0.0972717i \(0.968988\pi\)
\(54\) −16.1803 28.0252i −2.20187 3.81374i
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) −0.527864 0.914287i −0.0693119 0.120052i
\(59\) 1.61803 2.80252i 0.210650 0.364857i −0.741268 0.671209i \(-0.765775\pi\)
0.951918 + 0.306352i \(0.0991086\pi\)
\(60\) 9.70820 16.8151i 1.25332 2.17082i
\(61\) −1.38197 2.39364i −0.176943 0.306474i 0.763889 0.645347i \(-0.223287\pi\)
−0.940832 + 0.338874i \(0.889954\pi\)
\(62\) −16.1803 −2.05491
\(63\) 0 0
\(64\) −13.0000 −1.62500
\(65\) −1.23607 2.14093i −0.153315 0.265550i
\(66\) 3.61803 6.26662i 0.445349 0.771367i
\(67\) −2.76393 + 4.78727i −0.337668 + 0.584858i −0.983994 0.178204i \(-0.942971\pi\)
0.646326 + 0.763062i \(0.276305\pi\)
\(68\) 1.85410 + 3.21140i 0.224843 + 0.389439i
\(69\) 20.9443 2.52139
\(70\) 0 0
\(71\) −1.52786 −0.181324 −0.0906621 0.995882i \(-0.528898\pi\)
−0.0906621 + 0.995882i \(0.528898\pi\)
\(72\) 8.35410 + 14.4697i 0.984540 + 1.70527i
\(73\) −2.61803 + 4.53457i −0.306418 + 0.530731i −0.977576 0.210583i \(-0.932464\pi\)
0.671158 + 0.741314i \(0.265797\pi\)
\(74\) 0.527864 0.914287i 0.0613629 0.106284i
\(75\) −1.61803 2.80252i −0.186834 0.323607i
\(76\) 7.41641 0.850720
\(77\) 0 0
\(78\) 8.94427 1.01274
\(79\) −4.47214 7.74597i −0.503155 0.871489i −0.999993 0.00364646i \(-0.998839\pi\)
0.496839 0.867843i \(-0.334494\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) −12.2082 + 21.1452i −1.35647 + 2.34947i
\(82\) 7.56231 + 13.0983i 0.835117 + 1.44647i
\(83\) −15.4164 −1.69217 −0.846085 0.533048i \(-0.821047\pi\)
−0.846085 + 0.533048i \(0.821047\pi\)
\(84\) 0 0
\(85\) −2.47214 −0.268141
\(86\) 8.94427 + 15.4919i 0.964486 + 1.67054i
\(87\) −0.763932 + 1.32317i −0.0819021 + 0.141859i
\(88\) −1.11803 + 1.93649i −0.119183 + 0.206431i
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) −33.4164 −3.52240
\(91\) 0 0
\(92\) −19.4164 −2.02430
\(93\) 11.7082 + 20.2792i 1.21408 + 2.10286i
\(94\) −8.09017 + 14.0126i −0.834437 + 1.44529i
\(95\) −2.47214 + 4.28187i −0.253636 + 0.439310i
\(96\) 10.8541 + 18.7999i 1.10779 + 1.91875i
\(97\) 9.41641 0.956091 0.478046 0.878335i \(-0.341345\pi\)
0.478046 + 0.878335i \(0.341345\pi\)
\(98\) 0 0
\(99\) −7.47214 −0.750978
\(100\) 1.50000 + 2.59808i 0.150000 + 0.259808i
\(101\) −4.61803 + 7.99867i −0.459512 + 0.795897i −0.998935 0.0461372i \(-0.985309\pi\)
0.539424 + 0.842035i \(0.318642\pi\)
\(102\) 4.47214 7.74597i 0.442807 0.766965i
\(103\) −2.85410 4.94345i −0.281223 0.487093i 0.690463 0.723368i \(-0.257407\pi\)
−0.971686 + 0.236275i \(0.924073\pi\)
\(104\) −2.76393 −0.271026
\(105\) 0 0
\(106\) −18.9443 −1.84003
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 21.7082 37.5997i 2.08887 3.61803i
\(109\) −2.23607 + 3.87298i −0.214176 + 0.370965i −0.953018 0.302915i \(-0.902040\pi\)
0.738841 + 0.673880i \(0.235373\pi\)
\(110\) −2.23607 3.87298i −0.213201 0.369274i
\(111\) −1.52786 −0.145018
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −8.94427 15.4919i −0.837708 1.45095i
\(115\) 6.47214 11.2101i 0.603530 1.04534i
\(116\) 0.708204 1.22665i 0.0657551 0.113891i
\(117\) −4.61803 7.99867i −0.426937 0.739477i
\(118\) 7.23607 0.666134
\(119\) 0 0
\(120\) 14.4721 1.32112
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 3.09017 5.35233i 0.279771 0.484577i
\(123\) 10.9443 18.9560i 0.986812 1.70921i
\(124\) −10.8541 18.7999i −0.974727 1.68828i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 20.9443 1.85850 0.929252 0.369447i \(-0.120453\pi\)
0.929252 + 0.369447i \(0.120453\pi\)
\(128\) −7.82624 13.5554i −0.691748 1.19814i
\(129\) 12.9443 22.4201i 1.13968 1.97398i
\(130\) 2.76393 4.78727i 0.242413 0.419871i
\(131\) −6.94427 12.0278i −0.606724 1.05088i −0.991776 0.127982i \(-0.959150\pi\)
0.385053 0.922895i \(-0.374183\pi\)
\(132\) 9.70820 0.844991
\(133\) 0 0
\(134\) −12.3607 −1.06780
\(135\) 14.4721 + 25.0665i 1.24556 + 2.15738i
\(136\) −1.38197 + 2.39364i −0.118503 + 0.205253i
\(137\) −3.76393 + 6.51932i −0.321574 + 0.556983i −0.980813 0.194951i \(-0.937545\pi\)
0.659239 + 0.751934i \(0.270879\pi\)
\(138\) 23.4164 + 40.5584i 1.99334 + 3.45256i
\(139\) 10.4721 0.888235 0.444117 0.895969i \(-0.353517\pi\)
0.444117 + 0.895969i \(0.353517\pi\)
\(140\) 0 0
\(141\) 23.4164 1.97202
\(142\) −1.70820 2.95870i −0.143349 0.248288i
\(143\) 0.618034 1.07047i 0.0516826 0.0895169i
\(144\) 3.73607 6.47106i 0.311339 0.539255i
\(145\) 0.472136 + 0.817763i 0.0392088 + 0.0679116i
\(146\) −11.7082 −0.968978
\(147\) 0 0
\(148\) 1.41641 0.116428
\(149\) −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i \(-0.972267\pi\)
0.422744 0.906249i \(-0.361067\pi\)
\(150\) 3.61803 6.26662i 0.295411 0.511667i
\(151\) 4.47214 7.74597i 0.363937 0.630358i −0.624668 0.780891i \(-0.714766\pi\)
0.988605 + 0.150533i \(0.0480989\pi\)
\(152\) 2.76393 + 4.78727i 0.224184 + 0.388299i
\(153\) −9.23607 −0.746692
\(154\) 0 0
\(155\) 14.4721 1.16243
\(156\) 6.00000 + 10.3923i 0.480384 + 0.832050i
\(157\) −3.47214 + 6.01392i −0.277107 + 0.479963i −0.970664 0.240438i \(-0.922709\pi\)
0.693558 + 0.720401i \(0.256042\pi\)
\(158\) 10.0000 17.3205i 0.795557 1.37795i
\(159\) 13.7082 + 23.7433i 1.08713 + 1.88297i
\(160\) 13.4164 1.06066
\(161\) 0 0
\(162\) −54.5967 −4.28953
\(163\) −11.7082 20.2792i −0.917057 1.58839i −0.803861 0.594817i \(-0.797224\pi\)
−0.113196 0.993573i \(-0.536109\pi\)
\(164\) −10.1459 + 17.5732i −0.792262 + 1.37224i
\(165\) −3.23607 + 5.60503i −0.251928 + 0.436351i
\(166\) −17.2361 29.8537i −1.33778 2.31710i
\(167\) 12.9443 1.00166 0.500829 0.865546i \(-0.333029\pi\)
0.500829 + 0.865546i \(0.333029\pi\)
\(168\) 0 0
\(169\) −11.4721 −0.882472
\(170\) −2.76393 4.78727i −0.211984 0.367167i
\(171\) −9.23607 + 15.9973i −0.706300 + 1.22335i
\(172\) −12.0000 + 20.7846i −0.914991 + 1.58481i
\(173\) −8.61803 14.9269i −0.655217 1.13487i −0.981839 0.189714i \(-0.939244\pi\)
0.326622 0.945155i \(-0.394089\pi\)
\(174\) −3.41641 −0.258997
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −5.23607 9.06914i −0.393567 0.681678i
\(178\) −2.23607 + 3.87298i −0.167600 + 0.290292i
\(179\) −4.47214 + 7.74597i −0.334263 + 0.578961i −0.983343 0.181760i \(-0.941821\pi\)
0.649080 + 0.760720i \(0.275154\pi\)
\(180\) −22.4164 38.8264i −1.67082 2.89395i
\(181\) −1.41641 −0.105281 −0.0526404 0.998614i \(-0.516764\pi\)
−0.0526404 + 0.998614i \(0.516764\pi\)
\(182\) 0 0
\(183\) −8.94427 −0.661180
\(184\) −7.23607 12.5332i −0.533450 0.923963i
\(185\) −0.472136 + 0.817763i −0.0347121 + 0.0601232i
\(186\) −26.1803 + 45.3457i −1.91964 + 3.32491i
\(187\) −0.618034 1.07047i −0.0451951 0.0782802i
\(188\) −21.7082 −1.58323
\(189\) 0 0
\(190\) −11.0557 −0.802067
\(191\) 10.4721 + 18.1383i 0.757737 + 1.31244i 0.944002 + 0.329940i \(0.107028\pi\)
−0.186265 + 0.982500i \(0.559638\pi\)
\(192\) −21.0344 + 36.4327i −1.51803 + 2.62931i
\(193\) 11.9443 20.6881i 0.859768 1.48916i −0.0123830 0.999923i \(-0.503942\pi\)
0.872151 0.489238i \(-0.162725\pi\)
\(194\) 10.5279 + 18.2348i 0.755857 + 1.30918i
\(195\) −8.00000 −0.572892
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −8.35410 14.4697i −0.593700 1.02832i
\(199\) 10.0902 17.4767i 0.715273 1.23889i −0.247581 0.968867i \(-0.579636\pi\)
0.962854 0.270022i \(-0.0870311\pi\)
\(200\) −1.11803 + 1.93649i −0.0790569 + 0.136931i
\(201\) 8.94427 + 15.4919i 0.630880 + 1.09272i
\(202\) −20.6525 −1.45310
\(203\) 0 0
\(204\) 12.0000 0.840168
\(205\) −6.76393 11.7155i −0.472414 0.818244i
\(206\) 6.38197 11.0539i 0.444653 0.770161i
\(207\) 24.1803 41.8816i 1.68065 2.91097i
\(208\) 0.618034 + 1.07047i 0.0428529 + 0.0742235i
\(209\) −2.47214 −0.171001
\(210\) 0 0
\(211\) 21.8885 1.50687 0.753435 0.657523i \(-0.228396\pi\)
0.753435 + 0.657523i \(0.228396\pi\)
\(212\) −12.7082 22.0113i −0.872803 1.51174i
\(213\) −2.47214 + 4.28187i −0.169388 + 0.293389i
\(214\) −4.47214 + 7.74597i −0.305709 + 0.529503i
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 32.3607 2.20187
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) 8.47214 + 14.6742i 0.572494 + 0.991589i
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) 0.763932 1.32317i 0.0513876 0.0890060i
\(222\) −1.70820 2.95870i −0.114647 0.198575i
\(223\) −12.1803 −0.815656 −0.407828 0.913059i \(-0.633714\pi\)
−0.407828 + 0.913059i \(0.633714\pi\)
\(224\) 0 0
\(225\) −7.47214 −0.498142
\(226\) 2.23607 + 3.87298i 0.148741 + 0.257627i
\(227\) −14.9443 + 25.8842i −0.991886 + 1.71800i −0.385846 + 0.922563i \(0.626090\pi\)
−0.606040 + 0.795434i \(0.707243\pi\)
\(228\) 12.0000 20.7846i 0.794719 1.37649i
\(229\) 2.23607 + 3.87298i 0.147764 + 0.255934i 0.930401 0.366544i \(-0.119459\pi\)
−0.782637 + 0.622478i \(0.786126\pi\)
\(230\) 28.9443 1.90853
\(231\) 0 0
\(232\) 1.05573 0.0693119
\(233\) 8.70820 + 15.0831i 0.570493 + 0.988124i 0.996515 + 0.0834107i \(0.0265813\pi\)
−0.426022 + 0.904713i \(0.640085\pi\)
\(234\) 10.3262 17.8856i 0.675047 1.16922i
\(235\) 7.23607 12.5332i 0.472029 0.817578i
\(236\) 4.85410 + 8.40755i 0.315975 + 0.547285i
\(237\) −28.9443 −1.88013
\(238\) 0 0
\(239\) 25.8885 1.67459 0.837295 0.546751i \(-0.184136\pi\)
0.837295 + 0.546751i \(0.184136\pi\)
\(240\) −3.23607 5.60503i −0.208887 0.361803i
\(241\) 13.5623 23.4906i 0.873625 1.51316i 0.0154046 0.999881i \(-0.495096\pi\)
0.858220 0.513281i \(-0.171570\pi\)
\(242\) 1.11803 1.93649i 0.0718699 0.124482i
\(243\) 17.7984 + 30.8277i 1.14177 + 1.97760i
\(244\) 8.29180 0.530828
\(245\) 0 0
\(246\) 48.9443 3.12057
\(247\) −1.52786 2.64634i −0.0972157 0.168382i
\(248\) 8.09017 14.0126i 0.513726 0.889800i
\(249\) −24.9443 + 43.2047i −1.58078 + 2.73799i
\(250\) −13.4164 23.2379i −0.848528 1.46969i
\(251\) −17.7082 −1.11773 −0.558866 0.829258i \(-0.688763\pi\)
−0.558866 + 0.829258i \(0.688763\pi\)
\(252\) 0 0
\(253\) 6.47214 0.406900
\(254\) 23.4164 + 40.5584i 1.46928 + 2.54486i
\(255\) −4.00000 + 6.92820i −0.250490 + 0.433861i
\(256\) 4.50000 7.79423i 0.281250 0.487139i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 57.8885 3.60398
\(259\) 0 0
\(260\) 7.41641 0.459946
\(261\) 1.76393 + 3.05522i 0.109185 + 0.189113i
\(262\) 15.5279 26.8950i 0.959315 1.66158i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 3.61803 + 6.26662i 0.222675 + 0.385684i
\(265\) 16.9443 1.04088
\(266\) 0 0
\(267\) 6.47214 0.396088
\(268\) −8.29180 14.3618i −0.506502 0.877287i
\(269\) −6.70820 + 11.6190i −0.409006 + 0.708420i −0.994779 0.102056i \(-0.967458\pi\)
0.585772 + 0.810476i \(0.300791\pi\)
\(270\) −32.3607 + 56.0503i −1.96941 + 3.41112i
\(271\) −0.763932 1.32317i −0.0464056 0.0803768i 0.841890 0.539650i \(-0.181443\pi\)
−0.888295 + 0.459273i \(0.848110\pi\)
\(272\) 1.23607 0.0749476
\(273\) 0 0
\(274\) −16.8328 −1.01691
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) −31.4164 + 54.4148i −1.89105 + 3.27539i
\(277\) −7.94427 + 13.7599i −0.477325 + 0.826751i −0.999662 0.0259878i \(-0.991727\pi\)
0.522337 + 0.852739i \(0.325060\pi\)
\(278\) 11.7082 + 20.2792i 0.702211 + 1.21627i
\(279\) 54.0689 3.23702
\(280\) 0 0
\(281\) −12.4721 −0.744025 −0.372013 0.928228i \(-0.621332\pi\)
−0.372013 + 0.928228i \(0.621332\pi\)
\(282\) 26.1803 + 45.3457i 1.55902 + 2.70030i
\(283\) −2.94427 + 5.09963i −0.175019 + 0.303141i −0.940168 0.340712i \(-0.889332\pi\)
0.765149 + 0.643853i \(0.222665\pi\)
\(284\) 2.29180 3.96951i 0.135993 0.235547i
\(285\) 8.00000 + 13.8564i 0.473879 + 0.820783i
\(286\) 2.76393 0.163435
\(287\) 0 0
\(288\) 50.1246 2.95362
\(289\) 7.73607 + 13.3993i 0.455063 + 0.788192i
\(290\) −1.05573 + 1.82857i −0.0619945 + 0.107378i
\(291\) 15.2361 26.3896i 0.893154 1.54699i
\(292\) −7.85410 13.6037i −0.459627 0.796097i
\(293\) −15.1246 −0.883589 −0.441795 0.897116i \(-0.645658\pi\)
−0.441795 + 0.897116i \(0.645658\pi\)
\(294\) 0 0
\(295\) −6.47214 −0.376822
\(296\) 0.527864 + 0.914287i 0.0306815 + 0.0531419i
\(297\) −7.23607 + 12.5332i −0.419879 + 0.727252i
\(298\) 15.6525 27.1109i 0.906724 1.57049i
\(299\) 4.00000 + 6.92820i 0.231326 + 0.400668i
\(300\) 9.70820 0.560503
\(301\) 0 0
\(302\) 20.0000 1.15087
\(303\) 14.9443 + 25.8842i 0.858526 + 1.48701i
\(304\) 1.23607 2.14093i 0.0708934 0.122791i
\(305\) −2.76393 + 4.78727i −0.158262 + 0.274118i
\(306\) −10.3262 17.8856i −0.590312 1.02245i
\(307\) −8.94427 −0.510477 −0.255238 0.966878i \(-0.582154\pi\)
−0.255238 + 0.966878i \(0.582154\pi\)
\(308\) 0 0
\(309\) −18.4721 −1.05084
\(310\) 16.1803 + 28.0252i 0.918982 + 1.59172i
\(311\) −10.8541 + 18.7999i −0.615480 + 1.06604i 0.374820 + 0.927097i \(0.377704\pi\)
−0.990300 + 0.138945i \(0.955629\pi\)
\(312\) −4.47214 + 7.74597i −0.253185 + 0.438529i
\(313\) −1.47214 2.54981i −0.0832100 0.144124i 0.821417 0.570328i \(-0.193184\pi\)
−0.904627 + 0.426204i \(0.859851\pi\)
\(314\) −15.5279 −0.876288
\(315\) 0 0
\(316\) 26.8328 1.50946
\(317\) −7.00000 12.1244i −0.393159 0.680972i 0.599705 0.800221i \(-0.295285\pi\)
−0.992864 + 0.119249i \(0.961951\pi\)
\(318\) −30.6525 + 53.0916i −1.71891 + 2.97723i
\(319\) −0.236068 + 0.408882i −0.0132173 + 0.0228930i
\(320\) 13.0000 + 22.5167i 0.726722 + 1.25872i
\(321\) 12.9443 0.722479
\(322\) 0 0
\(323\) −3.05573 −0.170025
\(324\) −36.6246 63.4357i −2.03470 3.52420i
\(325\) 0.618034 1.07047i 0.0342824 0.0593788i
\(326\) 26.1803 45.3457i 1.44999 2.51146i
\(327\) 7.23607 + 12.5332i 0.400155 + 0.693090i
\(328\) −15.1246 −0.835117
\(329\) 0 0
\(330\) −14.4721 −0.796665
\(331\) −10.9443 18.9560i −0.601552 1.04192i −0.992586 0.121542i \(-0.961216\pi\)
0.391035 0.920376i \(-0.372117\pi\)
\(332\) 23.1246 40.0530i 1.26913 2.19819i
\(333\) −1.76393 + 3.05522i −0.0966629 + 0.167425i
\(334\) 14.4721 + 25.0665i 0.791880 + 1.37158i
\(335\) 11.0557 0.604039
\(336\) 0 0
\(337\) −20.4721 −1.11519 −0.557594 0.830114i \(-0.688275\pi\)
−0.557594 + 0.830114i \(0.688275\pi\)
\(338\) −12.8262 22.2157i −0.697655 1.20837i
\(339\) 3.23607 5.60503i 0.175759 0.304424i
\(340\) 3.70820 6.42280i 0.201106 0.348325i
\(341\) 3.61803 + 6.26662i 0.195928 + 0.339356i
\(342\) −41.3050 −2.23352
\(343\) 0 0
\(344\) −17.8885 −0.964486
\(345\) −20.9443 36.2765i −1.12760 1.95306i
\(346\) 19.2705 33.3775i 1.03599 1.79439i
\(347\) −1.52786 + 2.64634i −0.0820200 + 0.142063i −0.904118 0.427284i \(-0.859470\pi\)
0.822097 + 0.569347i \(0.192804\pi\)
\(348\) −2.29180 3.96951i −0.122853 0.212788i
\(349\) 2.76393 0.147950 0.0739749 0.997260i \(-0.476432\pi\)
0.0739749 + 0.997260i \(0.476432\pi\)
\(350\) 0 0
\(351\) −17.8885 −0.954820
\(352\) 3.35410 + 5.80948i 0.178774 + 0.309646i
\(353\) −7.94427 + 13.7599i −0.422831 + 0.732365i −0.996215 0.0869220i \(-0.972297\pi\)
0.573384 + 0.819287i \(0.305630\pi\)
\(354\) 11.7082 20.2792i 0.622284 1.07783i
\(355\) 1.52786 + 2.64634i 0.0810906 + 0.140453i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) 3.52786 + 6.11044i 0.186194 + 0.322497i 0.943978 0.330008i \(-0.107052\pi\)
−0.757785 + 0.652505i \(0.773718\pi\)
\(360\) 16.7082 28.9395i 0.880600 1.52524i
\(361\) 6.44427 11.1618i 0.339172 0.587463i
\(362\) −1.58359 2.74286i −0.0832318 0.144162i
\(363\) −3.23607 −0.169850
\(364\) 0 0
\(365\) 10.4721 0.548137
\(366\) −10.0000 17.3205i −0.522708 0.905357i
\(367\) 8.56231 14.8303i 0.446949 0.774138i −0.551237 0.834349i \(-0.685844\pi\)
0.998186 + 0.0602108i \(0.0191773\pi\)
\(368\) −3.23607 + 5.60503i −0.168692 + 0.292183i
\(369\) −25.2705 43.7698i −1.31553 2.27857i
\(370\) −2.11146 −0.109769
\(371\) 0 0
\(372\) −70.2492 −3.64225
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 1.38197 2.39364i 0.0714598 0.123772i
\(375\) −19.4164 + 33.6302i −1.00266 + 1.73666i
\(376\) −8.09017 14.0126i −0.417219 0.722644i
\(377\) −0.583592 −0.0300565
\(378\) 0 0
\(379\) −25.3050 −1.29983 −0.649914 0.760008i \(-0.725195\pi\)
−0.649914 + 0.760008i \(0.725195\pi\)
\(380\) −7.41641 12.8456i −0.380454 0.658965i
\(381\) 33.8885 58.6967i 1.73616 3.00712i
\(382\) −23.4164 + 40.5584i −1.19809 + 2.07515i
\(383\) 13.3262 + 23.0817i 0.680939 + 1.17942i 0.974695 + 0.223540i \(0.0717614\pi\)
−0.293756 + 0.955881i \(0.594905\pi\)
\(384\) −50.6525 −2.58485
\(385\) 0 0
\(386\) 53.4164 2.71882
\(387\) −29.8885 51.7685i −1.51932 2.63154i
\(388\) −14.1246 + 24.4645i −0.717069 + 1.24200i
\(389\) 9.94427 17.2240i 0.504195 0.873291i −0.495794 0.868440i \(-0.665123\pi\)
0.999988 0.00485030i \(-0.00154390\pi\)
\(390\) −8.94427 15.4919i −0.452911 0.784465i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) −44.9443 −2.26714
\(394\) −2.23607 3.87298i −0.112651 0.195118i
\(395\) −8.94427 + 15.4919i −0.450035 + 0.779484i
\(396\) 11.2082 19.4132i 0.563233 0.975549i
\(397\) −0.0557281 0.0965239i −0.00279691 0.00484439i 0.864624 0.502420i \(-0.167557\pi\)
−0.867420 + 0.497576i \(0.834224\pi\)
\(398\) 45.1246 2.26189
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −2.52786 4.37839i −0.126236 0.218646i 0.795980 0.605323i \(-0.206956\pi\)
−0.922215 + 0.386677i \(0.873623\pi\)
\(402\) −20.0000 + 34.6410i −0.997509 + 1.72774i
\(403\) −4.47214 + 7.74597i −0.222773 + 0.385854i
\(404\) −13.8541 23.9960i −0.689267 1.19385i
\(405\) 48.8328 2.42652
\(406\) 0 0
\(407\) −0.472136 −0.0234029
\(408\) 4.47214 + 7.74597i 0.221404 + 0.383482i
\(409\) −15.5623 + 26.9547i −0.769507 + 1.33282i 0.168324 + 0.985732i \(0.446164\pi\)
−0.937831 + 0.347093i \(0.887169\pi\)
\(410\) 15.1246 26.1966i 0.746951 1.29376i
\(411\) 12.1803 + 21.0970i 0.600812 + 1.04064i
\(412\) 17.1246 0.843669
\(413\) 0 0
\(414\) 108.138 5.31468
\(415\) 15.4164 + 26.7020i 0.756762 + 1.31075i
\(416\) −4.14590 + 7.18091i −0.203269 + 0.352073i
\(417\) 16.9443 29.3483i 0.829765 1.43719i
\(418\) −2.76393 4.78727i −0.135188 0.234153i
\(419\) 6.65248 0.324995 0.162497 0.986709i \(-0.448045\pi\)
0.162497 + 0.986709i \(0.448045\pi\)
\(420\) 0 0
\(421\) −22.3607 −1.08979 −0.544896 0.838503i \(-0.683431\pi\)
−0.544896 + 0.838503i \(0.683431\pi\)
\(422\) 24.4721 + 42.3870i 1.19128 + 2.06337i
\(423\) 27.0344 46.8250i 1.31446 2.27671i
\(424\) 9.47214 16.4062i 0.460008 0.796757i
\(425\) −0.618034 1.07047i −0.0299791 0.0519252i
\(426\) −11.0557 −0.535652
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −2.00000 3.46410i −0.0965609 0.167248i
\(430\) 17.8885 30.9839i 0.862662 1.49417i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) −7.23607 12.5332i −0.348145 0.603006i
\(433\) −0.472136 −0.0226894 −0.0113447 0.999936i \(-0.503611\pi\)
−0.0113447 + 0.999936i \(0.503611\pi\)
\(434\) 0 0
\(435\) 3.05573 0.146511
\(436\) −6.70820 11.6190i −0.321265 0.556447i
\(437\) 8.00000 13.8564i 0.382692 0.662842i
\(438\) −18.9443 + 32.8124i −0.905192 + 1.56784i
\(439\) 0.763932 + 1.32317i 0.0364605 + 0.0631514i 0.883680 0.468092i \(-0.155058\pi\)
−0.847219 + 0.531243i \(0.821725\pi\)
\(440\) 4.47214 0.213201
\(441\) 0 0
\(442\) 3.41641 0.162502
\(443\) 3.52786 + 6.11044i 0.167614 + 0.290316i 0.937580 0.347768i \(-0.113060\pi\)
−0.769967 + 0.638084i \(0.779727\pi\)
\(444\) 2.29180 3.96951i 0.108764 0.188384i
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) −13.6180 23.5871i −0.644833 1.11688i
\(447\) −45.3050 −2.14285
\(448\) 0 0
\(449\) −19.5279 −0.921577 −0.460788 0.887510i \(-0.652433\pi\)
−0.460788 + 0.887510i \(0.652433\pi\)
\(450\) −8.35410 14.4697i −0.393816 0.682110i
\(451\) 3.38197 5.85774i 0.159251 0.275830i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −14.4721 25.0665i −0.679960 1.17773i
\(454\) −66.8328 −3.13662
\(455\) 0 0
\(456\) 17.8885 0.837708
\(457\) −12.4164 21.5058i −0.580815 1.00600i −0.995383 0.0959828i \(-0.969401\pi\)
0.414568 0.910018i \(-0.363933\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) −8.94427 + 15.4919i −0.417483 + 0.723102i
\(460\) 19.4164 + 33.6302i 0.905295 + 1.56802i
\(461\) −10.1803 −0.474146 −0.237073 0.971492i \(-0.576188\pi\)
−0.237073 + 0.971492i \(0.576188\pi\)
\(462\) 0 0
\(463\) −14.4721 −0.672577 −0.336289 0.941759i \(-0.609172\pi\)
−0.336289 + 0.941759i \(0.609172\pi\)
\(464\) −0.236068 0.408882i −0.0109592 0.0189819i
\(465\) 23.4164 40.5584i 1.08591 1.88085i
\(466\) −19.4721 + 33.7267i −0.902029 + 1.56236i
\(467\) −17.0344 29.5045i −0.788260 1.36531i −0.927032 0.374982i \(-0.877649\pi\)
0.138772 0.990324i \(-0.455684\pi\)
\(468\) 27.7082 1.28081
\(469\) 0 0
\(470\) 32.3607 1.49269
\(471\) 11.2361 + 19.4614i 0.517731 + 0.896736i
\(472\) −3.61803 + 6.26662i −0.166534 + 0.288445i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) −32.3607 56.0503i −1.48638 2.57448i
\(475\) −2.47214 −0.113429
\(476\) 0 0
\(477\) 63.3050 2.89853
\(478\) 28.9443 + 50.1329i 1.32388 + 2.29303i
\(479\) 11.2361 19.4614i 0.513389 0.889216i −0.486490 0.873686i \(-0.661723\pi\)
0.999879 0.0155300i \(-0.00494354\pi\)
\(480\) 21.7082 37.5997i 0.990839 1.71618i
\(481\) −0.291796 0.505406i −0.0133048 0.0230445i
\(482\) 60.6525 2.76264
\(483\) 0 0
\(484\) 3.00000 0.136364
\(485\) −9.41641 16.3097i −0.427577 0.740585i
\(486\) −39.7984 + 68.9328i −1.80529 + 3.12686i
\(487\) −4.18034 + 7.24056i −0.189429 + 0.328101i −0.945060 0.326897i \(-0.893997\pi\)
0.755631 + 0.654998i \(0.227330\pi\)
\(488\) 3.09017 + 5.35233i 0.139885 + 0.242289i
\(489\) −75.7771 −3.42676
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 32.8328 + 56.8681i 1.48022 + 2.56381i
\(493\) −0.291796 + 0.505406i −0.0131418 + 0.0227623i
\(494\) 3.41641 5.91739i 0.153711 0.266236i
\(495\) 7.47214 + 12.9421i 0.335848 + 0.581705i
\(496\) −7.23607 −0.324909
\(497\) 0 0
\(498\) −111.554 −4.99886
\(499\) −5.23607 9.06914i −0.234399 0.405990i 0.724699 0.689065i \(-0.241979\pi\)
−0.959098 + 0.283075i \(0.908645\pi\)
\(500\) 18.0000 31.1769i 0.804984 1.39427i
\(501\) 20.9443 36.2765i 0.935721 1.62072i
\(502\) −19.7984 34.2918i −0.883645 1.53052i
\(503\) 3.41641 0.152330 0.0761650 0.997095i \(-0.475732\pi\)
0.0761650 + 0.997095i \(0.475732\pi\)
\(504\) 0 0
\(505\) 18.4721 0.821999
\(506\) 7.23607 + 12.5332i 0.321682 + 0.557170i
\(507\) −18.5623 + 32.1509i −0.824381 + 1.42787i
\(508\) −31.4164 + 54.4148i −1.39388 + 2.41427i
\(509\) 15.7639 + 27.3039i 0.698724 + 1.21023i 0.968909 + 0.247417i \(0.0795818\pi\)
−0.270185 + 0.962808i \(0.587085\pi\)
\(510\) −17.8885 −0.792118
\(511\) 0 0
\(512\) −11.1803 −0.494106
\(513\) 17.8885 + 30.9839i 0.789799 + 1.36797i
\(514\) 6.70820 11.6190i 0.295886 0.512490i
\(515\) −5.70820 + 9.88690i −0.251534 + 0.435669i
\(516\) 38.8328 + 67.2604i 1.70952 + 2.96097i
\(517\) 7.23607 0.318242
\(518\) 0 0
\(519\) −55.7771 −2.44834
\(520\) 2.76393 + 4.78727i 0.121206 + 0.209936i
\(521\) −7.18034 + 12.4367i −0.314576 + 0.544862i −0.979347 0.202185i \(-0.935196\pi\)
0.664771 + 0.747047i \(0.268529\pi\)
\(522\) −3.94427 + 6.83168i −0.172636 + 0.299014i
\(523\) 22.0000 + 38.1051i 0.961993 + 1.66622i 0.717486 + 0.696573i \(0.245293\pi\)
0.244507 + 0.969648i \(0.421374\pi\)
\(524\) 41.6656 1.82017
\(525\) 0 0
\(526\) 0 0
\(527\) 4.47214 + 7.74597i 0.194809 + 0.337420i
\(528\) 1.61803 2.80252i 0.0704159 0.121964i
\(529\) −9.44427 + 16.3580i −0.410621 + 0.711216i
\(530\) 18.9443 + 32.8124i 0.822887 + 1.42528i
\(531\) −24.1803 −1.04934
\(532\) 0 0
\(533\) 8.36068 0.362141
\(534\) 7.23607 + 12.5332i 0.313135 + 0.542366i
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) 6.18034 10.7047i 0.266950 0.462371i
\(537\) 14.4721 + 25.0665i 0.624519 + 1.08170i
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) −86.8328 −3.73669
\(541\) 16.4164 + 28.4341i 0.705797 + 1.22248i 0.966403 + 0.257030i \(0.0827440\pi\)
−0.260607 + 0.965445i \(0.583923\pi\)
\(542\) 1.70820 2.95870i 0.0733736 0.127087i
\(543\) −2.29180 + 3.96951i −0.0983504 + 0.170348i
\(544\) 4.14590 + 7.18091i 0.177754 + 0.307879i
\(545\) 8.94427 0.383131
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −11.2918 19.5580i −0.482362 0.835475i
\(549\) −10.3262 + 17.8856i −0.440713 + 0.763337i
\(550\) 1.11803 1.93649i 0.0476731 0.0825723i
\(551\) 0.583592 + 1.01081i 0.0248619 + 0.0430620i
\(552\) −46.8328 −1.99334
\(553\) 0 0
\(554\) −35.5279 −1.50943
\(555\) 1.52786 + 2.64634i 0.0648542 + 0.112331i
\(556\) −15.7082 + 27.2074i −0.666176 + 1.15385i
\(557\) 10.5279 18.2348i 0.446080 0.772633i −0.552047 0.833813i \(-0.686153\pi\)
0.998127 + 0.0611800i \(0.0194864\pi\)
\(558\) 60.4508 + 104.704i 2.55909 + 4.43247i
\(559\) 9.88854 0.418241
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −13.9443 24.1522i −0.588204 1.01880i
\(563\) 19.7082 34.1356i 0.830602 1.43864i −0.0669600 0.997756i \(-0.521330\pi\)
0.897562 0.440889i \(-0.145337\pi\)
\(564\) −35.1246 + 60.8376i −1.47901 + 2.56173i
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) −13.1672 −0.553458
\(567\) 0 0
\(568\) 3.41641 0.143349
\(569\) −8.23607 14.2653i −0.345274 0.598032i 0.640130 0.768267i \(-0.278881\pi\)
−0.985403 + 0.170235i \(0.945547\pi\)
\(570\) −17.8885 + 30.9839i −0.749269 + 1.29777i
\(571\) 16.4721 28.5306i 0.689337 1.19397i −0.282715 0.959204i \(-0.591235\pi\)
0.972053 0.234764i \(-0.0754316\pi\)
\(572\) 1.85410 + 3.21140i 0.0775239 + 0.134275i
\(573\) 67.7771 2.83143
\(574\) 0 0
\(575\) 6.47214 0.269907
\(576\) 48.5689 + 84.1238i 2.02370 + 3.50516i
\(577\) −14.2361 + 24.6576i −0.592655 + 1.02651i 0.401218 + 0.915983i \(0.368587\pi\)
−0.993873 + 0.110526i \(0.964746\pi\)
\(578\) −17.2984 + 29.9617i −0.719517 + 1.24624i
\(579\) −38.6525 66.9481i −1.60634 2.78227i
\(580\) −2.83282 −0.117626
\(581\) 0 0
\(582\) 68.1378 2.82440
\(583\) 4.23607 + 7.33708i 0.175440 + 0.303871i
\(584\) 5.85410 10.1396i 0.242244 0.419580i
\(585\) −9.23607 + 15.9973i −0.381864 + 0.661409i
\(586\) −16.9098 29.2887i −0.698539 1.20990i
\(587\) 13.1246 0.541711 0.270855 0.962620i \(-0.412693\pi\)
0.270855 + 0.962620i \(0.412693\pi\)
\(588\) 0 0
\(589\) 17.8885 0.737085
\(590\) −7.23607 12.5332i −0.297904 0.515985i
\(591\) −3.23607 + 5.60503i −0.133114 + 0.230560i
\(592\) 0.236068 0.408882i 0.00970233 0.0168049i
\(593\) −16.1459 27.9655i −0.663033 1.14841i −0.979815 0.199908i \(-0.935936\pi\)
0.316782 0.948498i \(-0.397398\pi\)
\(594\) −32.3607 −1.32777
\(595\) 0 0
\(596\) 42.0000 1.72039
\(597\) −32.6525 56.5557i −1.33638 2.31467i
\(598\) −8.94427 + 15.4919i −0.365758 + 0.633512i
\(599\) −1.70820 + 2.95870i −0.0697953 + 0.120889i −0.898811 0.438336i \(-0.855568\pi\)
0.829016 + 0.559225i \(0.188901\pi\)
\(600\) 3.61803 + 6.26662i 0.147706 + 0.255834i
\(601\) −3.12461 −0.127456 −0.0637278 0.997967i \(-0.520299\pi\)
−0.0637278 + 0.997967i \(0.520299\pi\)
\(602\) 0 0
\(603\) 41.3050 1.68207
\(604\) 13.4164 + 23.2379i 0.545906 + 0.945537i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −33.4164 + 57.8789i −1.35745 + 2.35117i
\(607\) −2.47214 4.28187i −0.100341 0.173796i 0.811484 0.584374i \(-0.198660\pi\)
−0.911825 + 0.410579i \(0.865327\pi\)
\(608\) 16.5836 0.672553
\(609\) 0 0
\(610\) −12.3607 −0.500469
\(611\) 4.47214 + 7.74597i 0.180923 + 0.313368i
\(612\) 13.8541 23.9960i 0.560019 0.969981i
\(613\) 23.6525 40.9673i 0.955315 1.65465i 0.221668 0.975122i \(-0.428850\pi\)
0.733647 0.679531i \(-0.237817\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) −43.7771 −1.76526
\(616\) 0 0
\(617\) 33.4164 1.34529 0.672647 0.739964i \(-0.265157\pi\)
0.672647 + 0.739964i \(0.265157\pi\)
\(618\) −20.6525 35.7711i −0.830764 1.43893i
\(619\) −14.5623 + 25.2227i −0.585308 + 1.01378i 0.409528 + 0.912297i \(0.365693\pi\)
−0.994837 + 0.101487i \(0.967640\pi\)
\(620\) −21.7082 + 37.5997i −0.871822 + 1.51004i
\(621\) −46.8328 81.1168i −1.87934 3.25511i
\(622\) −48.5410 −1.94632
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 3.29180 5.70156i 0.131567 0.227880i
\(627\) −4.00000 + 6.92820i −0.159745 + 0.276686i
\(628\) −10.4164 18.0417i −0.415660 0.719944i
\(629\) −0.583592 −0.0232693
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 10.0000 + 17.3205i 0.397779 + 0.688973i
\(633\) 35.4164 61.3430i 1.40768 2.43817i
\(634\) 15.6525 27.1109i 0.621639 1.07671i
\(635\) −20.9443 36.2765i −0.831148 1.43959i
\(636\) −82.2492 −3.26139
\(637\) 0 0
\(638\) −1.05573 −0.0417967
\(639\) 5.70820 + 9.88690i 0.225813 + 0.391120i
\(640\) −15.6525 + 27.1109i −0.618718 + 1.07165i
\(641\) 12.2361 21.1935i 0.483296 0.837093i −0.516520 0.856275i \(-0.672773\pi\)
0.999816 + 0.0191823i \(0.00610630\pi\)
\(642\) 14.4721 + 25.0665i 0.571170 + 0.989295i
\(643\) 29.1246 1.14856 0.574281 0.818658i \(-0.305282\pi\)
0.574281 + 0.818658i \(0.305282\pi\)
\(644\) 0 0
\(645\) −51.7771 −2.03872
\(646\) −3.41641 5.91739i −0.134417 0.232817i
\(647\) −11.0344 + 19.1122i −0.433809 + 0.751379i −0.997198 0.0748132i \(-0.976164\pi\)
0.563389 + 0.826192i \(0.309497\pi\)
\(648\) 27.2984 47.2822i 1.07238 1.85742i
\(649\) −1.61803 2.80252i −0.0635134 0.110008i
\(650\) 2.76393 0.108410
\(651\) 0 0
\(652\) 70.2492 2.75117
\(653\) −21.4721 37.1908i −0.840270 1.45539i −0.889667 0.456610i \(-0.849063\pi\)
0.0493971 0.998779i \(-0.484270\pi\)
\(654\) −16.1803 + 28.0252i −0.632701 + 1.09587i
\(655\) −13.8885 + 24.0557i −0.542670 + 0.939933i
\(656\) 3.38197 + 5.85774i 0.132044 + 0.228706i
\(657\) 39.1246 1.52640
\(658\) 0 0
\(659\) 17.8885 0.696839 0.348419 0.937339i \(-0.386719\pi\)
0.348419 + 0.937339i \(0.386719\pi\)
\(660\) −9.70820 16.8151i −0.377891 0.654527i
\(661\) 6.41641 11.1135i 0.249569 0.432267i −0.713837 0.700312i \(-0.753044\pi\)
0.963406 + 0.268045i \(0.0863776\pi\)
\(662\) 24.4721 42.3870i 0.951137 1.64742i
\(663\) −2.47214 4.28187i −0.0960098 0.166294i
\(664\) 34.4721 1.33778
\(665\) 0 0
\(666\) −7.88854 −0.305675
\(667\) −1.52786 2.64634i −0.0591591 0.102467i
\(668\) −19.4164 + 33.6302i −0.751243 + 1.30119i
\(669\) −19.7082 + 34.1356i −0.761963 + 1.31976i
\(670\) 12.3607 + 21.4093i 0.477535 + 0.827114i
\(671\) −2.76393 −0.106700
\(672\) 0 0
\(673\) 5.41641 0.208787 0.104394 0.994536i \(-0.466710\pi\)
0.104394 + 0.994536i \(0.466710\pi\)
\(674\) −22.8885 39.6441i −0.881634 1.52703i
\(675\) −7.23607 + 12.5332i −0.278516 + 0.482405i
\(676\) 17.2082 29.8055i 0.661854 1.14636i
\(677\) 1.85410 + 3.21140i 0.0712589 + 0.123424i 0.899453 0.437017i \(-0.143965\pi\)
−0.828194 + 0.560441i \(0.810632\pi\)
\(678\) 14.4721 0.555799
\(679\) 0 0
\(680\) 5.52786 0.211984
\(681\) 48.3607 + 83.7632i 1.85319 + 3.20981i
\(682\) −8.09017 + 14.0126i −0.309789 + 0.536570i
\(683\) −14.9443 + 25.8842i −0.571827 + 0.990433i 0.424552 + 0.905404i \(0.360432\pi\)
−0.996378 + 0.0850292i \(0.972902\pi\)
\(684\) −27.7082 47.9920i −1.05945 1.83502i
\(685\) 15.0557 0.575250
\(686\) 0 0
\(687\) 14.4721 0.552146
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −5.23607 + 9.06914i −0.199478 + 0.345507i
\(690\) 46.8328 81.1168i 1.78289 3.08806i
\(691\) −24.2705 42.0378i −0.923294 1.59919i −0.794283 0.607548i \(-0.792153\pi\)
−0.129011 0.991643i \(-0.541180\pi\)
\(692\) 51.7082 1.96565
\(693\) 0 0
\(694\) −6.83282 −0.259370
\(695\) −10.4721 18.1383i −0.397231 0.688024i
\(696\) 1.70820 2.95870i 0.0647493 0.112149i
\(697\) 4.18034 7.24056i 0.158342 0.274256i
\(698\) 3.09017 + 5.35233i 0.116965 + 0.202589i
\(699\) 56.3607 2.13176
\(700\) 0 0
\(701\) −24.4721 −0.924300 −0.462150 0.886802i \(-0.652922\pi\)
−0.462150 + 0.886802i \(0.652922\pi\)
\(702\) −20.0000 34.6410i −0.754851 1.30744i
\(703\) −0.583592 + 1.01081i −0.0220106 + 0.0381235i
\(704\) −6.50000 + 11.2583i −0.244978 + 0.424314i
\(705\) −23.4164 40.5584i −0.881913 1.52752i
\(706\) −35.5279 −1.33711
\(707\) 0 0
\(708\) 31.4164 1.18070
\(709\) −1.47214 2.54981i −0.0552872 0.0957603i 0.837057 0.547115i \(-0.184274\pi\)
−0.892344 + 0.451355i \(0.850941\pi\)
\(710\) −3.41641 + 5.91739i −0.128216 + 0.222076i
\(711\) −33.4164 + 57.8789i −1.25321 + 2.17063i
\(712\) −2.23607 3.87298i −0.0838002 0.145146i
\(713\) −46.8328 −1.75390
\(714\) 0 0
\(715\) −2.47214 −0.0924526
\(716\) −13.4164 23.2379i −0.501395 0.868441i
\(717\) 41.8885 72.5531i 1.56436 2.70954i
\(718\) −7.88854 + 13.6634i −0.294398 + 0.509912i
\(719\) 16.7426 + 28.9991i 0.624395 + 1.08148i 0.988657 + 0.150188i \(0.0479879\pi\)
−0.364262 + 0.931296i \(0.618679\pi\)
\(720\) −14.9443 −0.556940
\(721\) 0 0
\(722\) 28.8197 1.07256
\(723\) −43.8885 76.0172i −1.63223 2.82711i
\(724\) 2.12461 3.67994i 0.0789606 0.136764i
\(725\) −0.236068 + 0.408882i −0.00876734 + 0.0151855i
\(726\) −3.61803 6.26662i −0.134278 0.232576i
\(727\) 51.0132 1.89197 0.945987 0.324206i \(-0.105097\pi\)
0.945987 + 0.324206i \(0.105097\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 11.7082 + 20.2792i 0.433340 + 0.750567i
\(731\) 4.94427 8.56373i 0.182871 0.316741i
\(732\) 13.4164 23.2379i 0.495885 0.858898i
\(733\) 6.61803 + 11.4628i 0.244443 + 0.423387i 0.961975 0.273138i \(-0.0880617\pi\)
−0.717532 + 0.696525i \(0.754728\pi\)
\(734\) 38.2918 1.41338
\(735\) 0 0
\(736\) −43.4164 −1.60035
\(737\) 2.76393 + 4.78727i 0.101811 + 0.176341i
\(738\) 56.5066 97.8723i 2.08004 3.60273i
\(739\) −3.52786 + 6.11044i −0.129775 + 0.224776i −0.923589 0.383384i \(-0.874759\pi\)
0.793815 + 0.608160i \(0.208092\pi\)
\(740\) −1.41641 2.45329i −0.0520682 0.0901847i
\(741\) −9.88854 −0.363265
\(742\) 0 0
\(743\) −33.8885 −1.24325 −0.621625 0.783315i \(-0.713527\pi\)
−0.621625 + 0.783315i \(0.713527\pi\)
\(744\) −26.1803 45.3457i −0.959818 1.66245i
\(745\) −14.0000 + 24.2487i −0.512920 + 0.888404i
\(746\) 6.70820 11.6190i 0.245605 0.425400i
\(747\) 57.5967 + 99.7605i 2.10735 + 3.65005i
\(748\) 3.70820 0.135585
\(749\) 0 0
\(750\) −86.8328 −3.17069
\(751\) −19.2361 33.3178i −0.701934 1.21579i −0.967787 0.251772i \(-0.918987\pi\)
0.265853 0.964014i \(-0.414347\pi\)
\(752\) −3.61803 + 6.26662i −0.131936 + 0.228520i
\(753\) −28.6525 + 49.6275i −1.04415 + 1.80853i
\(754\) −0.652476 1.13012i −0.0237618 0.0411566i
\(755\) −17.8885 −0.651031
\(756\) 0 0
\(757\) −19.8885 −0.722861 −0.361431 0.932399i \(-0.617712\pi\)
−0.361431 + 0.932399i \(0.617712\pi\)
\(758\) −28.2918 49.0028i −1.02760 1.77986i
\(759\) 10.4721 18.1383i 0.380114 0.658378i
\(760\) 5.52786 9.57454i 0.200517 0.347305i
\(761\) 8.79837 + 15.2392i 0.318941 + 0.552422i 0.980267 0.197676i \(-0.0633395\pi\)
−0.661327 + 0.750098i \(0.730006\pi\)
\(762\) 151.554 5.49023
\(763\) 0 0
\(764\) −62.8328 −2.27321
\(765\) 9.23607 + 15.9973i 0.333931 + 0.578385i
\(766\) −29.7984 + 51.6123i −1.07666 + 1.86483i
\(767\) 2.00000 3.46410i 0.0722158 0.125081i
\(768\) −14.5623 25.2227i −0.525472 0.910144i
\(769\) −31.7082 −1.14343 −0.571714 0.820453i \(-0.693721\pi\)
−0.571714 + 0.820453i \(0.693721\pi\)
\(770\) 0 0
\(771\) −19.4164 −0.699265
\(772\) 35.8328 + 62.0643i 1.28965 + 2.23374i
\(773\) 3.18034 5.50851i 0.114389 0.198127i −0.803146 0.595782i \(-0.796842\pi\)
0.917535 + 0.397654i \(0.130176\pi\)
\(774\) 66.8328 115.758i 2.40226 4.16083i
\(775\) 3.61803 + 6.26662i 0.129964 + 0.225104i
\(776\) −21.0557 −0.755857
\(777\) 0 0
\(778\) 44.4721 1.59440
\(779\) −8.36068 14.4811i −0.299552 0.518840i
\(780\) 12.0000 20.7846i 0.429669 0.744208i
\(781\) −0.763932 + 1.32317i −0.0273356 + 0.0473467i
\(782\) 8.94427 + 15.4919i 0.319847 + 0.553990i
\(783\) 6.83282 0.244185
\(784\) 0 0
\(785\) 13.8885 0.495703
\(786\) −50.2492 87.0342i −1.79233 3.10441i
\(787\) −8.29180 + 14.3618i −0.295571 + 0.511943i −0.975117 0.221689i \(-0.928843\pi\)
0.679547 + 0.733632i \(0.262176\pi\)
\(788\) 3.00000 5.19615i 0.106871 0.185105i
\(789\) 0 0
\(790\) −40.0000 −1.42314
\(791\) 0 0
\(792\) 16.7082 0.593700
\(793\) −1.70820 2.95870i −0.0606601 0.105066i
\(794\) 0.124612 0.215834i 0.00442231 0.00765966i
\(795\) 27.4164 47.4866i 0.972360 1.68418i
\(796\) 30.2705 + 52.4301i 1.07291 + 1.85833i
\(797\) −2.94427 −0.104291 −0.0521457 0.998639i \(-0.516606\pi\)
−0.0521457 + 0.998639i \(0.516606\pi\)
\(798\) 0 0
\(799\) 8.94427 0.316426
\(800\) 3.35410 + 5.80948i 0.118585 + 0.205396i
\(801\) 7.47214 12.9421i 0.264015 0.457287i
\(802\) 5.65248 9.79038i 0.199596 0.345710i
\(803\) 2.61803 + 4.53457i 0.0923884 + 0.160021i
\(804\) −53.6656 −1.89264
\(805\) 0 0
\(806\) −20.0000 −0.704470
\(807\) 21.7082 + 37.5997i 0.764165 + 1.32357i
\(808\) 10.3262 17.8856i 0.363276 0.629212i
\(809\) −19.4721 + 33.7267i −0.684604 + 1.18577i 0.288957 + 0.957342i \(0.406691\pi\)
−0.973561 + 0.228427i \(0.926642\pi\)
\(810\) 54.5967 + 94.5643i 1.91833 + 3.32265i
\(811\) −18.8328 −0.661310 −0.330655 0.943752i \(-0.607270\pi\)
−0.330655 + 0.943752i \(0.607270\pi\)
\(812\) 0 0
\(813\) −4.94427 −0.173403
\(814\) −0.527864 0.914287i −0.0185016 0.0320458i
\(815\) −23.4164 + 40.5584i −0.820241 + 1.42070i
\(816\) 2.00000 3.46410i 0.0700140 0.121268i
\(817\) −9.88854 17.1275i −0.345956 0.599214i
\(818\) −69.5967 −2.43339
\(819\) 0 0
\(820\) 40.5836 1.41724
\(821\) 4.41641 + 7.64944i 0.154134 + 0.266967i 0.932743 0.360541i \(-0.117408\pi\)
−0.778610 + 0.627509i \(0.784075\pi\)
\(822\) −27.2361 + 47.1743i −0.949967 + 1.64539i
\(823\) 24.9443 43.2047i 0.869503 1.50602i 0.00699691 0.999976i \(-0.497773\pi\)
0.862506 0.506047i \(-0.168894\pi\)
\(824\) 6.38197 + 11.0539i 0.222326 + 0.385080i
\(825\) −3.23607 −0.112665
\(826\) 0 0
\(827\) 4.94427 0.171929 0.0859646 0.996298i \(-0.472603\pi\)
0.0859646 + 0.996298i \(0.472603\pi\)
\(828\) 72.5410 + 125.645i 2.52097 + 4.36646i
\(829\) −8.41641 + 14.5776i −0.292314 + 0.506303i −0.974356 0.225010i \(-0.927759\pi\)
0.682043 + 0.731312i \(0.261092\pi\)
\(830\) −34.4721 + 59.7075i −1.19655 + 2.07248i
\(831\) 25.7082 + 44.5279i 0.891808 + 1.54466i
\(832\) −16.0689 −0.557088
\(833\) 0 0
\(834\) 75.7771 2.62395
\(835\) −12.9443 22.4201i −0.447955 0.775881i
\(836\) 3.70820 6.42280i 0.128251 0.222137i
\(837\) 52.3607 90.6914i 1.80985 3.13475i
\(838\) 7.43769 + 12.8825i 0.256931 + 0.445017i
\(839\) 14.0689 0.485712 0.242856 0.970062i \(-0.421916\pi\)
0.242856 + 0.970062i \(0.421916\pi\)
\(840\) 0 0
\(841\) −28.7771 −0.992313
\(842\) −25.0000 43.3013i −0.861557 1.49226i
\(843\) −20.1803 + 34.9534i −0.695048 + 1.20386i
\(844\) −32.8328 + 56.8681i −1.13015 + 1.95748i
\(845\) 11.4721 + 19.8703i 0.394653 + 0.683560i
\(846\) 120.902 4.15669
\(847\) 0 0
\(848\) −8.47214 −0.290934
\(849\) 9.52786 + 16.5027i 0.326995 + 0.566373i
\(850\) 1.38197 2.39364i 0.0474010 0.0821010i
\(851\) 1.52786 2.64634i 0.0523745 0.0907153i
\(852\) −7.41641 12.8456i −0.254082 0.440083i
\(853\) −0.652476 −0.0223403 −0.0111702 0.999938i \(-0.503556\pi\)
−0.0111702 + 0.999938i \(0.503556\pi\)
\(854\) 0 0
\(855\) 36.9443 1.26347
\(856\) −4.47214 7.74597i −0.152854 0.264752i
\(857\) 5.38197 9.32184i 0.183844 0.318428i −0.759342 0.650692i \(-0.774479\pi\)
0.943187 + 0.332264i \(0.107812\pi\)
\(858\) 4.47214 7.74597i 0.152676 0.264443i
\(859\) 20.2705 + 35.1096i 0.691621 + 1.19792i 0.971307 + 0.237831i \(0.0764364\pi\)
−0.279686 + 0.960092i \(0.590230\pi\)
\(860\) 48.0000 1.63679
\(861\) 0 0
\(862\) −26.8328 −0.913929
\(863\) 10.4721 + 18.1383i 0.356476 + 0.617434i 0.987369 0.158435i \(-0.0506449\pi\)
−0.630894 + 0.775869i \(0.717312\pi\)
\(864\) 48.5410 84.0755i 1.65140 2.86031i
\(865\) −17.2361 + 29.8537i −0.586044 + 1.01506i
\(866\) −0.527864 0.914287i −0.0179376 0.0310687i
\(867\) 50.0689 1.70043
\(868\) 0 0
\(869\) −8.94427 −0.303414
\(870\) 3.41641 + 5.91739i 0.115827 + 0.200618i
\(871\) −3.41641 + 5.91739i −0.115761 + 0.200503i
\(872\) 5.00000 8.66025i 0.169321 0.293273i
\(873\) −35.1803 60.9341i −1.19067 2.06231i
\(874\) 35.7771 1.21018
\(875\) 0 0
\(876\) −50.8328 −1.71748
\(877\) −20.7082 35.8677i −0.699266 1.21116i −0.968721 0.248152i \(-0.920177\pi\)
0.269455 0.963013i \(-0.413157\pi\)
\(878\) −1.70820 + 2.95870i −0.0576491 + 0.0998512i
\(879\) −24.4721 + 42.3870i −0.825425 + 1.42968i
\(880\) −1.00000 1.73205i −0.0337100 0.0583874i
\(881\) −29.4164 −0.991064 −0.495532 0.868590i \(-0.665027\pi\)
−0.495532 + 0.868590i \(0.665027\pi\)
\(882\) 0 0
\(883\) 8.94427 0.300999 0.150499 0.988610i \(-0.451912\pi\)
0.150499 + 0.988610i \(0.451912\pi\)
\(884\) 2.29180 + 3.96951i 0.0770814 + 0.133509i
\(885\) −10.4721 + 18.1383i −0.352017 + 0.609711i
\(886\) −7.88854 + 13.6634i −0.265021 + 0.459030i
\(887\) 20.1803 + 34.9534i 0.677589 + 1.17362i 0.975705 + 0.219090i \(0.0703087\pi\)
−0.298115 + 0.954530i \(0.596358\pi\)
\(888\) 3.41641 0.114647
\(889\) 0 0
\(890\) 8.94427 0.299813
\(891\) 12.2082 + 21.1452i 0.408990 + 0.708392i
\(892\) 18.2705 31.6455i 0.611742 1.05957i
\(893\) 8.94427 15.4919i 0.299309 0.518418i
\(894\) −50.6525 87.7327i −1.69407 2.93422i
\(895\) 17.8885 0.597948
\(896\) 0 0
\(897\) 25.8885 0.864393
\(898\) −21.8328 37.8155i −0.728570 1.26192i
\(899\) 1.70820 2.95870i 0.0569718 0.0986780i
\(900\) 11.2082 19.4132i 0.373607 0.647106i
\(901\) 5.23607 + 9.06914i 0.174439 + 0.302137i
\(902\) 15.1246 0.503594
\(903\) 0 0
\(904\) −4.47214 −0.148741
\(905\) 1.41641 + 2.45329i 0.0470830 + 0.0815501i
\(906\) 32.3607 56.0503i 1.07511 1.86215i
\(907\) −6.76393 + 11.7155i −0.224593 + 0.389006i −0.956197 0.292723i \(-0.905438\pi\)
0.731604 + 0.681729i \(0.238772\pi\)
\(908\) −44.8328 77.6527i −1.48783 2.57700i
\(909\) 69.0132 2.28902
\(910\) 0 0
\(911\) 33.5279 1.11083 0.555414 0.831574i \(-0.312560\pi\)
0.555414 + 0.831574i \(0.312560\pi\)
\(912\) −4.00000 6.92820i −0.132453 0.229416i
\(913\) −7.70820 + 13.3510i −0.255104 + 0.441854i
\(914\) 27.7639 48.0885i 0.918349 1.59063i
\(915\) 8.94427 + 15.4919i 0.295689 + 0.512148i
\(916\) −13.4164 −0.443291
\(917\) 0 0
\(918\) −40.0000 −1.32020
\(919\) −3.05573 5.29268i −0.100799 0.174589i 0.811215 0.584748i \(-0.198807\pi\)
−0.912014 + 0.410159i \(0.865473\pi\)
\(920\) −14.4721 + 25.0665i −0.477132 + 0.826417i
\(921\) −14.4721 + 25.0665i −0.476873 + 0.825968i
\(922\) −11.3820 19.7141i −0.374845 0.649251i
\(923\) −1.88854 −0.0621622
\(924\) 0 0
\(925\) −0.472136 −0.0155237
\(926\) −16.1803 28.0252i −0.531719 0.920964i
\(927\) −21.3262 + 36.9381i −0.700446 + 1.21321i
\(928\) 1.58359 2.74286i 0.0519840 0.0900389i
\(929\) 14.1246 + 24.4645i 0.463413 + 0.802656i 0.999128 0.0417432i \(-0.0132911\pi\)
−0.535715 + 0.844399i \(0.679958\pi\)
\(930\) 104.721 3.43395
\(931\) 0 0
\(932\) −52.2492 −1.71148
\(933\) 35.1246 + 60.8376i 1.14993 + 1.99173i
\(934\) 38.0902 65.9741i 1.24635 2.15874i
\(935\) −1.23607 + 2.14093i −0.0404237 + 0.0700160i
\(936\) 10.3262 + 17.8856i 0.337524 + 0.584608i
\(937\) −20.6525 −0.674687 −0.337343 0.941382i \(-0.609528\pi\)
−0.337343 + 0.941382i \(0.609528\pi\)
\(938\) 0 0
\(939\) −9.52786 −0.310930
\(940\) 21.7082 + 37.5997i 0.708044 + 1.22637i
\(941\) −20.7984 + 36.0238i −0.678008 + 1.17434i 0.297572 + 0.954699i \(0.403823\pi\)
−0.975580 + 0.219644i \(0.929510\pi\)
\(942\) −25.1246 + 43.5171i −0.818604 + 1.41786i
\(943\) 21.8885 + 37.9121i 0.712789 + 1.23459i
\(944\) 3.23607 0.105325
\(945\) 0 0
\(946\) 17.8885 0.581607
\(947\) 29.4164 + 50.9507i 0.955905 + 1.65568i 0.732284 + 0.681000i \(0.238454\pi\)
0.223621 + 0.974676i \(0.428212\pi\)
\(948\) 43.4164 75.1994i 1.41010 2.44236i
\(949\) −3.23607 + 5.60503i −0.105047 + 0.181947i
\(950\) −2.76393 4.78727i −0.0896738 0.155320i
\(951\) −45.3050 −1.46911
\(952\) 0 0
\(953\) 5.05573 0.163771 0.0818855 0.996642i \(-0.473906\pi\)
0.0818855 + 0.996642i \(0.473906\pi\)
\(954\) 70.7771 + 122.590i 2.29149 + 3.96898i
\(955\) 20.9443 36.2765i 0.677741 1.17388i
\(956\) −38.8328 + 67.2604i −1.25594 + 2.17536i
\(957\) 0.763932 + 1.32317i 0.0246944 + 0.0427720i
\(958\) 50.2492 1.62348
\(959\) 0 0
\(960\) 84.1378 2.71553
\(961\) −10.6803 18.4989i −0.344527 0.596738i
\(962\) 0.652476 1.13012i 0.0210367 0.0364366i
\(963\) 14.9443 25.8842i 0.481572 0.834108i
\(964\) 40.6869 + 70.4718i 1.31044 + 2.26974i
\(965\) −47.7771 −1.53800
\(966\) 0 0
\(967\) 21.8885 0.703888 0.351944 0.936021i \(-0.385521\pi\)
0.351944 + 0.936021i \(0.385521\pi\)
\(968\) 1.11803 + 1.93649i 0.0359350 + 0.0622412i
\(969\) −4.94427 + 8.56373i −0.158833 + 0.275107i
\(970\) 21.0557 36.4696i 0.676059 1.17097i
\(971\) −14.5623 25.2227i −0.467327 0.809433i 0.531977 0.846759i \(-0.321449\pi\)
−0.999303 + 0.0373256i \(0.988116\pi\)
\(972\) −106.790 −3.42530
\(973\) 0 0
\(974\) −18.6950 −0.599028
\(975\) −2.00000 3.46410i −0.0640513 0.110940i
\(976\) 1.38197 2.39364i 0.0442357 0.0766184i
\(977\) −2.52786 + 4.37839i −0.0808735 + 0.140077i −0.903625 0.428324i \(-0.859104\pi\)
0.822752 + 0.568401i \(0.192438\pi\)
\(978\) −84.7214 146.742i −2.70909 4.69228i
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) 33.4164 1.06690
\(982\) 0 0
\(983\) 22.0902 38.2613i 0.704567 1.22035i −0.262281 0.964992i \(-0.584475\pi\)
0.966848 0.255354i \(-0.0821921\pi\)
\(984\) −24.4721 + 42.3870i −0.780143 + 1.35125i
\(985\) 2.00000 + 3.46410i 0.0637253 + 0.110375i
\(986\) −1.30495 −0.0415581
\(987\) 0 0
\(988\) 9.16718 0.291647
\(989\) 25.8885 + 44.8403i 0.823208 + 1.42584i
\(990\) −16.7082 + 28.9395i −0.531022 + 0.919756i
\(991\) 13.1246 22.7325i 0.416917 0.722121i −0.578711 0.815533i \(-0.696444\pi\)
0.995628 + 0.0934115i \(0.0297772\pi\)
\(992\) −24.2705 42.0378i −0.770589 1.33470i
\(993\) −70.8328 −2.24781
\(994\) 0 0
\(995\) −40.3607 −1.27952
\(996\) −74.8328 129.614i −2.37117 4.10698i
\(997\) 16.3262 28.2779i 0.517057 0.895569i −0.482747 0.875760i \(-0.660361\pi\)
0.999804 0.0198092i \(-0.00630587\pi\)
\(998\) 11.7082 20.2792i 0.370617 0.641927i
\(999\) 3.41641 + 5.91739i 0.108090 + 0.187218i
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 539.2.e.j.67.2 4
7.2 even 3 inner 539.2.e.j.177.2 4
7.3 odd 6 77.2.a.d.1.1 2
7.4 even 3 539.2.a.f.1.1 2
7.5 odd 6 539.2.e.i.177.2 4
7.6 odd 2 539.2.e.i.67.2 4
21.11 odd 6 4851.2.a.y.1.2 2
21.17 even 6 693.2.a.h.1.2 2
28.3 even 6 1232.2.a.m.1.1 2
28.11 odd 6 8624.2.a.ce.1.2 2
35.3 even 12 1925.2.b.h.1849.4 4
35.17 even 12 1925.2.b.h.1849.1 4
35.24 odd 6 1925.2.a.r.1.2 2
56.3 even 6 4928.2.a.bv.1.2 2
56.45 odd 6 4928.2.a.bm.1.1 2
77.3 odd 30 847.2.f.a.372.1 4
77.10 even 6 847.2.a.f.1.2 2
77.17 even 30 847.2.f.b.729.1 4
77.24 even 30 847.2.f.b.323.1 4
77.31 odd 30 847.2.f.n.323.1 4
77.32 odd 6 5929.2.a.m.1.2 2
77.38 odd 30 847.2.f.n.729.1 4
77.52 even 30 847.2.f.m.372.1 4
77.59 odd 30 847.2.f.a.148.1 4
77.73 even 30 847.2.f.m.148.1 4
231.164 odd 6 7623.2.a.bl.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.d.1.1 2 7.3 odd 6
539.2.a.f.1.1 2 7.4 even 3
539.2.e.i.67.2 4 7.6 odd 2
539.2.e.i.177.2 4 7.5 odd 6
539.2.e.j.67.2 4 1.1 even 1 trivial
539.2.e.j.177.2 4 7.2 even 3 inner
693.2.a.h.1.2 2 21.17 even 6
847.2.a.f.1.2 2 77.10 even 6
847.2.f.a.148.1 4 77.59 odd 30
847.2.f.a.372.1 4 77.3 odd 30
847.2.f.b.323.1 4 77.24 even 30
847.2.f.b.729.1 4 77.17 even 30
847.2.f.m.148.1 4 77.73 even 30
847.2.f.m.372.1 4 77.52 even 30
847.2.f.n.323.1 4 77.31 odd 30
847.2.f.n.729.1 4 77.38 odd 30
1232.2.a.m.1.1 2 28.3 even 6
1925.2.a.r.1.2 2 35.24 odd 6
1925.2.b.h.1849.1 4 35.17 even 12
1925.2.b.h.1849.4 4 35.3 even 12
4851.2.a.y.1.2 2 21.11 odd 6
4928.2.a.bm.1.1 2 56.45 odd 6
4928.2.a.bv.1.2 2 56.3 even 6
5929.2.a.m.1.2 2 77.32 odd 6
7623.2.a.bl.1.1 2 231.164 odd 6
8624.2.a.ce.1.2 2 28.11 odd 6