Properties

Label 726.2.e.o.493.1
Level $726$
Weight $2$
Character 726.493
Analytic conductor $5.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [726,2,Mod(487,726)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(726, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("726.487");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\), degree \(4\), 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: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 493.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 726.493
Dual form 726.2.e.o.511.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-3.23607 - 2.35114i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.618034 + 1.90211i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-3.23607 - 2.35114i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -2.00000 q^{10} -1.00000 q^{12} +(1.85410 - 5.70634i) q^{13} +(3.23607 - 2.35114i) q^{14} +(1.61803 + 1.17557i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.618034 - 1.90211i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.23607 - 2.35114i) q^{19} +(0.618034 - 1.90211i) q^{20} -4.00000 q^{21} +4.00000 q^{23} +(0.309017 - 0.951057i) q^{24} +(0.809017 - 0.587785i) q^{25} +(4.85410 + 3.52671i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.23607 + 3.80423i) q^{28} +(4.85410 + 3.52671i) q^{29} +(-1.61803 + 1.17557i) q^{30} -1.00000 q^{32} +2.00000 q^{34} +(2.47214 - 7.60845i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-4.85410 - 3.52671i) q^{37} +(1.23607 + 3.80423i) q^{38} +(-1.85410 - 5.70634i) q^{39} +(1.61803 + 1.17557i) q^{40} +(-4.85410 + 3.52671i) q^{41} +(1.23607 - 3.80423i) q^{42} -4.00000 q^{43} +2.00000 q^{45} +(-1.23607 + 3.80423i) q^{46} +(9.70820 - 7.05342i) q^{47} +(0.809017 + 0.587785i) q^{48} +(2.78115 + 8.55951i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-1.61803 - 1.17557i) q^{51} +(-4.85410 + 3.52671i) q^{52} +(0.618034 - 1.90211i) q^{53} +1.00000 q^{54} -4.00000 q^{56} +(1.23607 - 3.80423i) q^{57} +(-4.85410 + 3.52671i) q^{58} +(-9.70820 - 7.05342i) q^{59} +(-0.618034 - 1.90211i) q^{60} +(4.32624 + 13.3148i) q^{61} +(-3.23607 + 2.35114i) q^{63} +(0.309017 - 0.951057i) q^{64} +12.0000 q^{65} +4.00000 q^{67} +(-0.618034 + 1.90211i) q^{68} +(3.23607 - 2.35114i) q^{69} +(6.47214 + 4.70228i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-4.85410 - 3.52671i) q^{73} +(4.85410 - 3.52671i) q^{74} +(0.309017 - 0.951057i) q^{75} -4.00000 q^{76} +6.00000 q^{78} +(1.23607 - 3.80423i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.85410 - 5.70634i) q^{82} +(-1.23607 - 3.80423i) q^{83} +(3.23607 + 2.35114i) q^{84} +(3.23607 - 2.35114i) q^{85} +(1.23607 - 3.80423i) q^{86} +6.00000 q^{87} +10.0000 q^{89} +(-0.618034 + 1.90211i) q^{90} +(-19.4164 + 14.1068i) q^{91} +(-3.23607 - 2.35114i) q^{92} +(3.70820 + 11.4127i) q^{94} +(6.47214 + 4.70228i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-4.32624 + 13.3148i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} - q^{9} - 8 q^{10} - 4 q^{12} - 6 q^{13} + 4 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} - 16 q^{21} + 16 q^{23} - q^{24} + q^{25} + 6 q^{26} + q^{27} - 4 q^{28} + 6 q^{29} - 2 q^{30} - 4 q^{32} + 8 q^{34} - 8 q^{35} - q^{36} - 6 q^{37} - 4 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} - 4 q^{42} - 16 q^{43} + 8 q^{45} + 4 q^{46} + 12 q^{47} + q^{48} - 9 q^{49} - q^{50} - 2 q^{51} - 6 q^{52} - 2 q^{53} + 4 q^{54} - 16 q^{56} - 4 q^{57} - 6 q^{58} - 12 q^{59} + 2 q^{60} - 14 q^{61} - 4 q^{63} - q^{64} + 48 q^{65} + 16 q^{67} + 2 q^{68} + 4 q^{69} + 8 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} + 6 q^{74} - q^{75} - 16 q^{76} + 24 q^{78} - 4 q^{79} - 2 q^{80} - q^{81} + 6 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{85} - 4 q^{86} + 24 q^{87} + 40 q^{89} + 2 q^{90} - 24 q^{91} - 4 q^{92} - 12 q^{94} + 8 q^{95} - q^{96} + 14 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.618034 + 1.90211i 0.276393 + 0.850651i 0.988847 + 0.148932i \(0.0475836\pi\)
−0.712454 + 0.701719i \(0.752416\pi\)
\(6\) 0.309017 + 0.951057i 0.126156 + 0.388267i
\(7\) −3.23607 2.35114i −1.22312 0.888648i −0.226764 0.973950i \(-0.572814\pi\)
−0.996355 + 0.0853021i \(0.972814\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) −2.00000 −0.632456
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) 1.85410 5.70634i 0.514235 1.58265i −0.270434 0.962739i \(-0.587167\pi\)
0.784669 0.619915i \(-0.212833\pi\)
\(14\) 3.23607 2.35114i 0.864876 0.628369i
\(15\) 1.61803 + 1.17557i 0.417775 + 0.303531i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.618034 1.90211i −0.149895 0.461330i 0.847713 0.530456i \(-0.177979\pi\)
−0.997608 + 0.0691254i \(0.977979\pi\)
\(18\) 0.809017 + 0.587785i 0.190687 + 0.138542i
\(19\) 3.23607 2.35114i 0.742405 0.539389i −0.151058 0.988525i \(-0.548268\pi\)
0.893463 + 0.449136i \(0.148268\pi\)
\(20\) 0.618034 1.90211i 0.138197 0.425325i
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0.309017 0.951057i 0.0630778 0.194134i
\(25\) 0.809017 0.587785i 0.161803 0.117557i
\(26\) 4.85410 + 3.52671i 0.951968 + 0.691645i
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) 1.23607 + 3.80423i 0.233595 + 0.718931i
\(29\) 4.85410 + 3.52671i 0.901384 + 0.654894i 0.938821 0.344405i \(-0.111919\pi\)
−0.0374370 + 0.999299i \(0.511919\pi\)
\(30\) −1.61803 + 1.17557i −0.295411 + 0.214629i
\(31\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.47214 7.60845i 0.417867 1.28606i
\(36\) −0.809017 + 0.587785i −0.134836 + 0.0979642i
\(37\) −4.85410 3.52671i −0.798009 0.579788i 0.112320 0.993672i \(-0.464172\pi\)
−0.910330 + 0.413884i \(0.864172\pi\)
\(38\) 1.23607 + 3.80423i 0.200517 + 0.617127i
\(39\) −1.85410 5.70634i −0.296894 0.913746i
\(40\) 1.61803 + 1.17557i 0.255834 + 0.185874i
\(41\) −4.85410 + 3.52671i −0.758083 + 0.550780i −0.898322 0.439338i \(-0.855213\pi\)
0.140238 + 0.990118i \(0.455213\pi\)
\(42\) 1.23607 3.80423i 0.190729 0.587005i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) −1.23607 + 3.80423i −0.182248 + 0.560903i
\(47\) 9.70820 7.05342i 1.41609 1.02885i 0.423685 0.905810i \(-0.360736\pi\)
0.992402 0.123038i \(-0.0392637\pi\)
\(48\) 0.809017 + 0.587785i 0.116772 + 0.0848395i
\(49\) 2.78115 + 8.55951i 0.397308 + 1.22279i
\(50\) 0.309017 + 0.951057i 0.0437016 + 0.134500i
\(51\) −1.61803 1.17557i −0.226570 0.164613i
\(52\) −4.85410 + 3.52671i −0.673143 + 0.489067i
\(53\) 0.618034 1.90211i 0.0848935 0.261275i −0.899595 0.436726i \(-0.856138\pi\)
0.984488 + 0.175450i \(0.0561381\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) 1.23607 3.80423i 0.163721 0.503882i
\(58\) −4.85410 + 3.52671i −0.637375 + 0.463080i
\(59\) −9.70820 7.05342i −1.26390 0.918277i −0.264958 0.964260i \(-0.585358\pi\)
−0.998942 + 0.0459824i \(0.985358\pi\)
\(60\) −0.618034 1.90211i −0.0797878 0.245562i
\(61\) 4.32624 + 13.3148i 0.553918 + 1.70478i 0.698784 + 0.715333i \(0.253725\pi\)
−0.144866 + 0.989451i \(0.546275\pi\)
\(62\) 0 0
\(63\) −3.23607 + 2.35114i −0.407706 + 0.296216i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −0.618034 + 1.90211i −0.0749476 + 0.230665i
\(69\) 3.23607 2.35114i 0.389577 0.283044i
\(70\) 6.47214 + 4.70228i 0.773568 + 0.562030i
\(71\) −3.70820 11.4127i −0.440083 1.35444i −0.887787 0.460254i \(-0.847758\pi\)
0.447704 0.894182i \(-0.352242\pi\)
\(72\) −0.309017 0.951057i −0.0364180 0.112083i
\(73\) −4.85410 3.52671i −0.568130 0.412770i 0.266296 0.963891i \(-0.414200\pi\)
−0.834425 + 0.551121i \(0.814200\pi\)
\(74\) 4.85410 3.52671i 0.564278 0.409972i
\(75\) 0.309017 0.951057i 0.0356822 0.109819i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 6.00000 0.679366
\(79\) 1.23607 3.80423i 0.139069 0.428009i −0.857132 0.515097i \(-0.827756\pi\)
0.996201 + 0.0870877i \(0.0277560\pi\)
\(80\) −1.61803 + 1.17557i −0.180902 + 0.131433i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −1.85410 5.70634i −0.204751 0.630160i
\(83\) −1.23607 3.80423i −0.135676 0.417568i 0.860018 0.510263i \(-0.170452\pi\)
−0.995695 + 0.0926948i \(0.970452\pi\)
\(84\) 3.23607 + 2.35114i 0.353084 + 0.256531i
\(85\) 3.23607 2.35114i 0.351001 0.255017i
\(86\) 1.23607 3.80423i 0.133289 0.410220i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −0.618034 + 1.90211i −0.0651465 + 0.200500i
\(91\) −19.4164 + 14.1068i −2.03539 + 1.47880i
\(92\) −3.23607 2.35114i −0.337383 0.245123i
\(93\) 0 0
\(94\) 3.70820 + 11.4127i 0.382472 + 1.17713i
\(95\) 6.47214 + 4.70228i 0.664027 + 0.482444i
\(96\) −0.809017 + 0.587785i −0.0825700 + 0.0599906i
\(97\) −4.32624 + 13.3148i −0.439263 + 1.35191i 0.449392 + 0.893335i \(0.351641\pi\)
−0.888654 + 0.458577i \(0.848359\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −4.32624 + 13.3148i −0.430477 + 1.32487i 0.467175 + 0.884165i \(0.345272\pi\)
−0.897651 + 0.440706i \(0.854728\pi\)
\(102\) 1.61803 1.17557i 0.160209 0.116399i
\(103\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(104\) −1.85410 5.70634i −0.181810 0.559553i
\(105\) −2.47214 7.60845i −0.241256 0.742509i
\(106\) 1.61803 + 1.17557i 0.157157 + 0.114182i
\(107\) 3.23607 2.35114i 0.312842 0.227293i −0.420273 0.907398i \(-0.638066\pi\)
0.733115 + 0.680104i \(0.238066\pi\)
\(108\) −0.309017 + 0.951057i −0.0297352 + 0.0915155i
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 1.23607 3.80423i 0.116797 0.359466i
\(113\) −1.61803 + 1.17557i −0.152212 + 0.110588i −0.661285 0.750135i \(-0.729988\pi\)
0.509073 + 0.860724i \(0.329988\pi\)
\(114\) 3.23607 + 2.35114i 0.303086 + 0.220205i
\(115\) 2.47214 + 7.60845i 0.230528 + 0.709492i
\(116\) −1.85410 5.70634i −0.172149 0.529820i
\(117\) −4.85410 3.52671i −0.448762 0.326045i
\(118\) 9.70820 7.05342i 0.893713 0.649320i
\(119\) −2.47214 + 7.60845i −0.226620 + 0.697466i
\(120\) 2.00000 0.182574
\(121\) 0 0
\(122\) −14.0000 −1.26750
\(123\) −1.85410 + 5.70634i −0.167179 + 0.514523i
\(124\) 0 0
\(125\) 9.70820 + 7.05342i 0.868328 + 0.630877i
\(126\) −1.23607 3.80423i −0.110118 0.338907i
\(127\) −3.70820 11.4127i −0.329050 1.01271i −0.969579 0.244778i \(-0.921285\pi\)
0.640529 0.767934i \(-0.278715\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) −3.23607 + 2.35114i −0.284920 + 0.207006i
\(130\) −3.70820 + 11.4127i −0.325231 + 1.00096i
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) −16.0000 −1.38738
\(134\) −1.23607 + 3.80423i −0.106780 + 0.328635i
\(135\) 1.61803 1.17557i 0.139258 0.101177i
\(136\) −1.61803 1.17557i −0.138745 0.100804i
\(137\) 0.618034 + 1.90211i 0.0528022 + 0.162508i 0.973980 0.226633i \(-0.0727718\pi\)
−0.921178 + 0.389141i \(0.872772\pi\)
\(138\) 1.23607 + 3.80423i 0.105221 + 0.323837i
\(139\) −3.23607 2.35114i −0.274480 0.199421i 0.442026 0.897002i \(-0.354260\pi\)
−0.716506 + 0.697581i \(0.754260\pi\)
\(140\) −6.47214 + 4.70228i −0.546995 + 0.397415i
\(141\) 3.70820 11.4127i 0.312287 0.961121i
\(142\) 12.0000 1.00702
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −3.70820 + 11.4127i −0.307950 + 0.947771i
\(146\) 4.85410 3.52671i 0.401728 0.291873i
\(147\) 7.28115 + 5.29007i 0.600539 + 0.436317i
\(148\) 1.85410 + 5.70634i 0.152406 + 0.469058i
\(149\) 3.09017 + 9.51057i 0.253157 + 0.779136i 0.994187 + 0.107665i \(0.0343373\pi\)
−0.741031 + 0.671471i \(0.765663\pi\)
\(150\) 0.809017 + 0.587785i 0.0660560 + 0.0479925i
\(151\) 3.23607 2.35114i 0.263347 0.191333i −0.448274 0.893896i \(-0.647961\pi\)
0.711622 + 0.702563i \(0.247961\pi\)
\(152\) 1.23607 3.80423i 0.100258 0.308563i
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) −1.85410 + 5.70634i −0.148447 + 0.456873i
\(157\) 8.09017 5.87785i 0.645666 0.469104i −0.216126 0.976365i \(-0.569342\pi\)
0.861792 + 0.507262i \(0.169342\pi\)
\(158\) 3.23607 + 2.35114i 0.257448 + 0.187047i
\(159\) −0.618034 1.90211i −0.0490133 0.150847i
\(160\) −0.618034 1.90211i −0.0488599 0.150375i
\(161\) −12.9443 9.40456i −1.02015 0.741183i
\(162\) 0.809017 0.587785i 0.0635624 0.0461808i
\(163\) −6.18034 + 19.0211i −0.484082 + 1.48985i 0.349225 + 0.937039i \(0.386445\pi\)
−0.833307 + 0.552811i \(0.813555\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(168\) −3.23607 + 2.35114i −0.249668 + 0.181394i
\(169\) −18.6074 13.5191i −1.43134 1.03993i
\(170\) 1.23607 + 3.80423i 0.0948021 + 0.291771i
\(171\) −1.23607 3.80423i −0.0945245 0.290916i
\(172\) 3.23607 + 2.35114i 0.246748 + 0.179273i
\(173\) −8.09017 + 5.87785i −0.615084 + 0.446885i −0.851201 0.524840i \(-0.824125\pi\)
0.236117 + 0.971725i \(0.424125\pi\)
\(174\) −1.85410 + 5.70634i −0.140559 + 0.432596i
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) −3.09017 + 9.51057i −0.231618 + 0.712847i
\(179\) −16.1803 + 11.7557i −1.20938 + 0.878663i −0.995174 0.0981269i \(-0.968715\pi\)
−0.214201 + 0.976790i \(0.568715\pi\)
\(180\) −1.61803 1.17557i −0.120601 0.0876219i
\(181\) −0.618034 1.90211i −0.0459381 0.141383i 0.925457 0.378854i \(-0.123682\pi\)
−0.971395 + 0.237471i \(0.923682\pi\)
\(182\) −7.41641 22.8254i −0.549741 1.69193i
\(183\) 11.3262 + 8.22899i 0.837260 + 0.608305i
\(184\) 3.23607 2.35114i 0.238566 0.173328i
\(185\) 3.70820 11.4127i 0.272633 0.839077i
\(186\) 0 0
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) −1.23607 + 3.80423i −0.0899107 + 0.276717i
\(190\) −6.47214 + 4.70228i −0.469538 + 0.341139i
\(191\) 9.70820 + 7.05342i 0.702461 + 0.510368i 0.880733 0.473614i \(-0.157051\pi\)
−0.178272 + 0.983981i \(0.557051\pi\)
\(192\) −0.309017 0.951057i −0.0223014 0.0686366i
\(193\) −3.09017 9.51057i −0.222435 0.684585i −0.998542 0.0539836i \(-0.982808\pi\)
0.776107 0.630602i \(-0.217192\pi\)
\(194\) −11.3262 8.22899i −0.813176 0.590807i
\(195\) 9.70820 7.05342i 0.695219 0.505106i
\(196\) 2.78115 8.55951i 0.198654 0.611393i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0.309017 0.951057i 0.0218508 0.0672499i
\(201\) 3.23607 2.35114i 0.228255 0.165837i
\(202\) −11.3262 8.22899i −0.796911 0.578990i
\(203\) −7.41641 22.8254i −0.520530 1.60203i
\(204\) 0.618034 + 1.90211i 0.0432710 + 0.133175i
\(205\) −9.70820 7.05342i −0.678050 0.492632i
\(206\) 0 0
\(207\) 1.23607 3.80423i 0.0859127 0.264412i
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 8.00000 0.552052
\(211\) 1.23607 3.80423i 0.0850944 0.261894i −0.899451 0.437021i \(-0.856034\pi\)
0.984546 + 0.175127i \(0.0560336\pi\)
\(212\) −1.61803 + 1.17557i −0.111127 + 0.0807385i
\(213\) −9.70820 7.05342i −0.665195 0.483293i
\(214\) 1.23607 + 3.80423i 0.0844959 + 0.260052i
\(215\) −2.47214 7.60845i −0.168598 0.518892i
\(216\) −0.809017 0.587785i −0.0550466 0.0399937i
\(217\) 0 0
\(218\) −1.85410 + 5.70634i −0.125576 + 0.386482i
\(219\) −6.00000 −0.405442
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 1.85410 5.70634i 0.124439 0.382984i
\(223\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(224\) 3.23607 + 2.35114i 0.216219 + 0.157092i
\(225\) −0.309017 0.951057i −0.0206011 0.0634038i
\(226\) −0.618034 1.90211i −0.0411110 0.126527i
\(227\) 9.70820 + 7.05342i 0.644356 + 0.468152i 0.861344 0.508022i \(-0.169623\pi\)
−0.216988 + 0.976174i \(0.569623\pi\)
\(228\) −3.23607 + 2.35114i −0.214314 + 0.155708i
\(229\) 4.32624 13.3148i 0.285886 0.879866i −0.700246 0.713902i \(-0.746926\pi\)
0.986132 0.165964i \(-0.0530737\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −3.09017 + 9.51057i −0.202444 + 0.623058i 0.797365 + 0.603497i \(0.206227\pi\)
−0.999809 + 0.0195604i \(0.993773\pi\)
\(234\) 4.85410 3.52671i 0.317323 0.230548i
\(235\) 19.4164 + 14.1068i 1.26659 + 0.920229i
\(236\) 3.70820 + 11.4127i 0.241384 + 0.742902i
\(237\) −1.23607 3.80423i −0.0802912 0.247111i
\(238\) −6.47214 4.70228i −0.419526 0.304804i
\(239\) 6.47214 4.70228i 0.418648 0.304165i −0.358446 0.933551i \(-0.616693\pi\)
0.777093 + 0.629385i \(0.216693\pi\)
\(240\) −0.618034 + 1.90211i −0.0398939 + 0.122781i
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 4.32624 13.3148i 0.276959 0.852392i
\(245\) −14.5623 + 10.5801i −0.930352 + 0.675940i
\(246\) −4.85410 3.52671i −0.309486 0.224855i
\(247\) −7.41641 22.8254i −0.471895 1.45234i
\(248\) 0 0
\(249\) −3.23607 2.35114i −0.205077 0.148998i
\(250\) −9.70820 + 7.05342i −0.614001 + 0.446098i
\(251\) −1.23607 + 3.80423i −0.0780199 + 0.240121i −0.982458 0.186485i \(-0.940291\pi\)
0.904438 + 0.426605i \(0.140291\pi\)
\(252\) 4.00000 0.251976
\(253\) 0 0
\(254\) 12.0000 0.752947
\(255\) 1.23607 3.80423i 0.0774056 0.238230i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −1.61803 1.17557i −0.100930 0.0733301i 0.536175 0.844107i \(-0.319869\pi\)
−0.637106 + 0.770776i \(0.719869\pi\)
\(258\) −1.23607 3.80423i −0.0769542 0.236841i
\(259\) 7.41641 + 22.8254i 0.460833 + 1.41830i
\(260\) −9.70820 7.05342i −0.602077 0.437435i
\(261\) 4.85410 3.52671i 0.300461 0.218298i
\(262\) 1.23607 3.80423i 0.0763645 0.235026i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 4.94427 15.2169i 0.303153 0.933008i
\(267\) 8.09017 5.87785i 0.495110 0.359719i
\(268\) −3.23607 2.35114i −0.197674 0.143619i
\(269\) 8.03444 + 24.7275i 0.489869 + 1.50766i 0.824804 + 0.565419i \(0.191286\pi\)
−0.334935 + 0.942241i \(0.608714\pi\)
\(270\) 0.618034 + 1.90211i 0.0376124 + 0.115759i
\(271\) 16.1803 + 11.7557i 0.982886 + 0.714108i 0.958352 0.285591i \(-0.0921898\pi\)
0.0245340 + 0.999699i \(0.492190\pi\)
\(272\) 1.61803 1.17557i 0.0981077 0.0712794i
\(273\) −7.41641 + 22.8254i −0.448861 + 1.38145i
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) −8.03444 + 24.7275i −0.482743 + 1.48573i 0.352481 + 0.935819i \(0.385338\pi\)
−0.835224 + 0.549911i \(0.814662\pi\)
\(278\) 3.23607 2.35114i 0.194086 0.141012i
\(279\) 0 0
\(280\) −2.47214 7.60845i −0.147738 0.454692i
\(281\) 6.79837 + 20.9232i 0.405557 + 1.24818i 0.920429 + 0.390909i \(0.127839\pi\)
−0.514872 + 0.857267i \(0.672161\pi\)
\(282\) 9.70820 + 7.05342i 0.578115 + 0.420025i
\(283\) 3.23607 2.35114i 0.192364 0.139761i −0.487434 0.873160i \(-0.662067\pi\)
0.679799 + 0.733399i \(0.262067\pi\)
\(284\) −3.70820 + 11.4127i −0.220041 + 0.677218i
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) −0.309017 + 0.951057i −0.0182090 + 0.0560415i
\(289\) 10.5172 7.64121i 0.618660 0.449483i
\(290\) −9.70820 7.05342i −0.570085 0.414191i
\(291\) 4.32624 + 13.3148i 0.253609 + 0.780527i
\(292\) 1.85410 + 5.70634i 0.108503 + 0.333938i
\(293\) 17.7984 + 12.9313i 1.03979 + 0.755453i 0.970245 0.242125i \(-0.0778446\pi\)
0.0695472 + 0.997579i \(0.477845\pi\)
\(294\) −7.28115 + 5.29007i −0.424645 + 0.308523i
\(295\) 7.41641 22.8254i 0.431800 1.32894i
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 7.41641 22.8254i 0.428902 1.32002i
\(300\) −0.809017 + 0.587785i −0.0467086 + 0.0339358i
\(301\) 12.9443 + 9.40456i 0.746095 + 0.542070i
\(302\) 1.23607 + 3.80423i 0.0711277 + 0.218909i
\(303\) 4.32624 + 13.3148i 0.248536 + 0.764915i
\(304\) 3.23607 + 2.35114i 0.185601 + 0.134847i
\(305\) −22.6525 + 16.4580i −1.29708 + 0.942382i
\(306\) 0.618034 1.90211i 0.0353307 0.108737i
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.23607 + 2.35114i −0.183501 + 0.133321i −0.675743 0.737137i \(-0.736177\pi\)
0.492243 + 0.870458i \(0.336177\pi\)
\(312\) −4.85410 3.52671i −0.274809 0.199661i
\(313\) 8.03444 + 24.7275i 0.454134 + 1.39768i 0.872149 + 0.489240i \(0.162726\pi\)
−0.418016 + 0.908440i \(0.637274\pi\)
\(314\) 3.09017 + 9.51057i 0.174388 + 0.536712i
\(315\) −6.47214 4.70228i −0.364664 0.264944i
\(316\) −3.23607 + 2.35114i −0.182043 + 0.132262i
\(317\) 5.56231 17.1190i 0.312410 0.961500i −0.664397 0.747380i \(-0.731312\pi\)
0.976807 0.214120i \(-0.0686884\pi\)
\(318\) 2.00000 0.112154
\(319\) 0 0
\(320\) 2.00000 0.111803
\(321\) 1.23607 3.80423i 0.0689906 0.212331i
\(322\) 12.9443 9.40456i 0.721356 0.524096i
\(323\) −6.47214 4.70228i −0.360119 0.261642i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) −1.85410 5.70634i −0.102847 0.316531i
\(326\) −16.1803 11.7557i −0.896146 0.651088i
\(327\) 4.85410 3.52671i 0.268432 0.195028i
\(328\) −1.85410 + 5.70634i −0.102376 + 0.315080i
\(329\) −48.0000 −2.64633
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −1.23607 + 3.80423i −0.0678380 + 0.208784i
\(333\) −4.85410 + 3.52671i −0.266003 + 0.193263i
\(334\) 0 0
\(335\) 2.47214 + 7.60845i 0.135067 + 0.415694i
\(336\) −1.23607 3.80423i −0.0674330 0.207538i
\(337\) 14.5623 + 10.5801i 0.793259 + 0.576337i 0.908929 0.416951i \(-0.136901\pi\)
−0.115670 + 0.993288i \(0.536901\pi\)
\(338\) 18.6074 13.5191i 1.01211 0.735340i
\(339\) −0.618034 + 1.90211i −0.0335670 + 0.103309i
\(340\) −4.00000 −0.216930
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 2.47214 7.60845i 0.133483 0.410818i
\(344\) −3.23607 + 2.35114i −0.174477 + 0.126765i
\(345\) 6.47214 + 4.70228i 0.348448 + 0.253162i
\(346\) −3.09017 9.51057i −0.166129 0.511291i
\(347\) 1.23607 + 3.80423i 0.0663556 + 0.204222i 0.978737 0.205120i \(-0.0657585\pi\)
−0.912381 + 0.409342i \(0.865758\pi\)
\(348\) −4.85410 3.52671i −0.260207 0.189052i
\(349\) −4.85410 + 3.52671i −0.259834 + 0.188781i −0.710074 0.704127i \(-0.751338\pi\)
0.450240 + 0.892908i \(0.351338\pi\)
\(350\) 1.23607 3.80423i 0.0660706 0.203344i
\(351\) −6.00000 −0.320256
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 3.70820 11.4127i 0.197089 0.606577i
\(355\) 19.4164 14.1068i 1.03052 0.748714i
\(356\) −8.09017 5.87785i −0.428778 0.311526i
\(357\) 2.47214 + 7.60845i 0.130839 + 0.402682i
\(358\) −6.18034 19.0211i −0.326641 1.00530i
\(359\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) 1.61803 1.17557i 0.0852779 0.0619580i
\(361\) −0.927051 + 2.85317i −0.0487922 + 0.150167i
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 24.0000 1.25794
\(365\) 3.70820 11.4127i 0.194096 0.597367i
\(366\) −11.3262 + 8.22899i −0.592032 + 0.430136i
\(367\) 12.9443 + 9.40456i 0.675685 + 0.490914i 0.871924 0.489642i \(-0.162873\pi\)
−0.196238 + 0.980556i \(0.562873\pi\)
\(368\) 1.23607 + 3.80423i 0.0644345 + 0.198309i
\(369\) 1.85410 + 5.70634i 0.0965207 + 0.297060i
\(370\) 9.70820 + 7.05342i 0.504705 + 0.366690i
\(371\) −6.47214 + 4.70228i −0.336017 + 0.244130i
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 12.0000 0.619677
\(376\) 3.70820 11.4127i 0.191236 0.588564i
\(377\) 29.1246 21.1603i 1.49999 1.08981i
\(378\) −3.23607 2.35114i −0.166445 0.120930i
\(379\) −8.65248 26.6296i −0.444448 1.36787i −0.883088 0.469207i \(-0.844540\pi\)
0.438640 0.898663i \(-0.355460\pi\)
\(380\) −2.47214 7.60845i −0.126818 0.390305i
\(381\) −9.70820 7.05342i −0.497366 0.361358i
\(382\) −9.70820 + 7.05342i −0.496715 + 0.360885i
\(383\) −1.23607 + 3.80423i −0.0631601 + 0.194387i −0.977657 0.210206i \(-0.932587\pi\)
0.914497 + 0.404593i \(0.132587\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −1.23607 + 3.80423i −0.0628329 + 0.193380i
\(388\) 11.3262 8.22899i 0.575003 0.417764i
\(389\) 24.2705 + 17.6336i 1.23056 + 0.894057i 0.996932 0.0782684i \(-0.0249391\pi\)
0.233631 + 0.972325i \(0.424939\pi\)
\(390\) 3.70820 + 11.4127i 0.187772 + 0.577903i
\(391\) −2.47214 7.60845i −0.125021 0.384776i
\(392\) 7.28115 + 5.29007i 0.367754 + 0.267189i
\(393\) −3.23607 + 2.35114i −0.163238 + 0.118599i
\(394\) −0.618034 + 1.90211i −0.0311361 + 0.0958271i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 4.94427 15.2169i 0.247834 0.762754i
\(399\) −12.9443 + 9.40456i −0.648024 + 0.470817i
\(400\) 0.809017 + 0.587785i 0.0404508 + 0.0293893i
\(401\) −11.7426 36.1401i −0.586400 1.80475i −0.593575 0.804779i \(-0.702284\pi\)
0.00717537 0.999974i \(-0.497716\pi\)
\(402\) 1.23607 + 3.80423i 0.0616495 + 0.189738i
\(403\) 0 0
\(404\) 11.3262 8.22899i 0.563501 0.409408i
\(405\) 0.618034 1.90211i 0.0307104 0.0945168i
\(406\) 24.0000 1.19110
\(407\) 0 0
\(408\) −2.00000 −0.0990148
\(409\) 4.32624 13.3148i 0.213919 0.658374i −0.785310 0.619103i \(-0.787496\pi\)
0.999229 0.0392712i \(-0.0125036\pi\)
\(410\) 9.70820 7.05342i 0.479454 0.348344i
\(411\) 1.61803 + 1.17557i 0.0798117 + 0.0579866i
\(412\) 0 0
\(413\) 14.8328 + 45.6507i 0.729875 + 2.24632i
\(414\) 3.23607 + 2.35114i 0.159044 + 0.115552i
\(415\) 6.47214 4.70228i 0.317705 0.230826i
\(416\) −1.85410 + 5.70634i −0.0909048 + 0.279776i
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −2.47214 + 7.60845i −0.120628 + 0.371254i
\(421\) 8.09017 5.87785i 0.394291 0.286469i −0.372921 0.927863i \(-0.621644\pi\)
0.767211 + 0.641394i \(0.221644\pi\)
\(422\) 3.23607 + 2.35114i 0.157529 + 0.114452i
\(423\) −3.70820 11.4127i −0.180299 0.554903i
\(424\) −0.618034 1.90211i −0.0300144 0.0923748i
\(425\) −1.61803 1.17557i −0.0784862 0.0570235i
\(426\) 9.70820 7.05342i 0.470364 0.341739i
\(427\) 17.3050 53.2592i 0.837445 2.57739i
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(432\) 0.809017 0.587785i 0.0389238 0.0282798i
\(433\) −1.61803 1.17557i −0.0777578 0.0564943i 0.548227 0.836329i \(-0.315303\pi\)
−0.625985 + 0.779835i \(0.715303\pi\)
\(434\) 0 0
\(435\) 3.70820 + 11.4127i 0.177795 + 0.547196i
\(436\) −4.85410 3.52671i −0.232469 0.168899i
\(437\) 12.9443 9.40456i 0.619208 0.449881i
\(438\) 1.85410 5.70634i 0.0885924 0.272659i
\(439\) −4.00000 −0.190910 −0.0954548 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 3.70820 11.4127i 0.176381 0.542846i
\(443\) −22.6525 + 16.4580i −1.07625 + 0.781943i −0.977026 0.213122i \(-0.931637\pi\)
−0.0992261 + 0.995065i \(0.531637\pi\)
\(444\) 4.85410 + 3.52671i 0.230365 + 0.167370i
\(445\) 6.18034 + 19.0211i 0.292976 + 0.901688i
\(446\) 0 0
\(447\) 8.09017 + 5.87785i 0.382652 + 0.278013i
\(448\) −3.23607 + 2.35114i −0.152890 + 0.111081i
\(449\) −6.79837 + 20.9232i −0.320835 + 0.987429i 0.652451 + 0.757831i \(0.273741\pi\)
−0.973286 + 0.229598i \(0.926259\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) 1.23607 3.80423i 0.0580755 0.178738i
\(454\) −9.70820 + 7.05342i −0.455629 + 0.331034i
\(455\) −38.8328 28.2137i −1.82051 1.32268i
\(456\) −1.23607 3.80423i −0.0578842 0.178149i
\(457\) −10.5066 32.3359i −0.491477 1.51261i −0.822376 0.568944i \(-0.807352\pi\)
0.330899 0.943666i \(-0.392648\pi\)
\(458\) 11.3262 + 8.22899i 0.529240 + 0.384516i
\(459\) −1.61803 + 1.17557i −0.0755234 + 0.0548709i
\(460\) 2.47214 7.60845i 0.115264 0.354746i
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −1.85410 + 5.70634i −0.0860745 + 0.264910i
\(465\) 0 0
\(466\) −8.09017 5.87785i −0.374770 0.272286i
\(467\) 3.70820 + 11.4127i 0.171595 + 0.528116i 0.999462 0.0328096i \(-0.0104455\pi\)
−0.827866 + 0.560925i \(0.810445\pi\)
\(468\) 1.85410 + 5.70634i 0.0857059 + 0.263776i
\(469\) −12.9443 9.40456i −0.597711 0.434262i
\(470\) −19.4164 + 14.1068i −0.895612 + 0.650700i
\(471\) 3.09017 9.51057i 0.142388 0.438224i
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) 4.00000 0.183726
\(475\) 1.23607 3.80423i 0.0567147 0.174550i
\(476\) 6.47214 4.70228i 0.296650 0.215529i
\(477\) −1.61803 1.17557i −0.0740847 0.0538257i
\(478\) 2.47214 + 7.60845i 0.113073 + 0.348003i
\(479\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(480\) −1.61803 1.17557i −0.0738528 0.0536572i
\(481\) −29.1246 + 21.1603i −1.32797 + 0.964825i
\(482\) 3.09017 9.51057i 0.140753 0.433194i
\(483\) −16.0000 −0.728025
\(484\) 0 0
\(485\) −28.0000 −1.27141
\(486\) 0.309017 0.951057i 0.0140173 0.0431408i
\(487\) 12.9443 9.40456i 0.586561 0.426161i −0.254523 0.967067i \(-0.581918\pi\)
0.841083 + 0.540905i \(0.181918\pi\)
\(488\) 11.3262 + 8.22899i 0.512715 + 0.372509i
\(489\) 6.18034 + 19.0211i 0.279485 + 0.860165i
\(490\) −5.56231 17.1190i −0.251279 0.773358i
\(491\) −22.6525 16.4580i −1.02229 0.742739i −0.0555405 0.998456i \(-0.517688\pi\)
−0.966751 + 0.255718i \(0.917688\pi\)
\(492\) 4.85410 3.52671i 0.218840 0.158996i
\(493\) 3.70820 11.4127i 0.167009 0.514001i
\(494\) 24.0000 1.07981
\(495\) 0 0
\(496\) 0 0
\(497\) −14.8328 + 45.6507i −0.665343 + 2.04771i
\(498\) 3.23607 2.35114i 0.145012 0.105357i
\(499\) 3.23607 + 2.35114i 0.144866 + 0.105252i 0.657858 0.753142i \(-0.271463\pi\)
−0.512992 + 0.858394i \(0.671463\pi\)
\(500\) −3.70820 11.4127i −0.165836 0.510390i
\(501\) 0 0
\(502\) −3.23607 2.35114i −0.144433 0.104937i
\(503\) 25.8885 18.8091i 1.15431 0.838658i 0.165265 0.986249i \(-0.447152\pi\)
0.989048 + 0.147592i \(0.0471521\pi\)
\(504\) −1.23607 + 3.80423i −0.0550588 + 0.169454i
\(505\) −28.0000 −1.24598
\(506\) 0 0
\(507\) −23.0000 −1.02147
\(508\) −3.70820 + 11.4127i −0.164525 + 0.506356i
\(509\) 17.7984 12.9313i 0.788899 0.573169i −0.118737 0.992926i \(-0.537885\pi\)
0.907637 + 0.419757i \(0.137885\pi\)
\(510\) 3.23607 + 2.35114i 0.143295 + 0.104110i
\(511\) 7.41641 + 22.8254i 0.328083 + 1.00973i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −3.23607 2.35114i −0.142876 0.103805i
\(514\) 1.61803 1.17557i 0.0713684 0.0518522i
\(515\) 0 0
\(516\) 4.00000 0.176090
\(517\) 0 0
\(518\) −24.0000 −1.05450
\(519\) −3.09017 + 9.51057i −0.135643 + 0.417467i
\(520\) 9.70820 7.05342i 0.425733 0.309313i
\(521\) −14.5623 10.5801i −0.637986 0.463524i 0.221172 0.975235i \(-0.429012\pi\)
−0.859158 + 0.511711i \(0.829012\pi\)
\(522\) 1.85410 + 5.70634i 0.0811518 + 0.249760i
\(523\) −6.18034 19.0211i −0.270247 0.831736i −0.990438 0.137960i \(-0.955946\pi\)
0.720190 0.693776i \(-0.244054\pi\)
\(524\) 3.23607 + 2.35114i 0.141368 + 0.102710i
\(525\) −3.23607 + 2.35114i −0.141234 + 0.102612i
\(526\) −7.41641 + 22.8254i −0.323371 + 0.995233i
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −1.23607 + 3.80423i −0.0536914 + 0.165245i
\(531\) −9.70820 + 7.05342i −0.421300 + 0.306092i
\(532\) 12.9443 + 9.40456i 0.561205 + 0.407740i
\(533\) 11.1246 + 34.2380i 0.481860 + 1.48301i
\(534\) 3.09017 + 9.51057i 0.133725 + 0.411562i
\(535\) 6.47214 + 4.70228i 0.279815 + 0.203297i
\(536\) 3.23607 2.35114i 0.139777 0.101554i
\(537\) −6.18034 + 19.0211i −0.266701 + 0.820822i
\(538\) −26.0000 −1.12094
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) 11.7426 36.1401i 0.504856 1.55379i −0.296157 0.955139i \(-0.595705\pi\)
0.801013 0.598647i \(-0.204295\pi\)
\(542\) −16.1803 + 11.7557i −0.695005 + 0.504951i
\(543\) −1.61803 1.17557i −0.0694365 0.0504486i
\(544\) 0.618034 + 1.90211i 0.0264980 + 0.0815524i
\(545\) 3.70820 + 11.4127i 0.158842 + 0.488865i
\(546\) −19.4164 14.1068i −0.830946 0.603717i
\(547\) −22.6525 + 16.4580i −0.968550 + 0.703693i −0.955121 0.296217i \(-0.904275\pi\)
−0.0134293 + 0.999910i \(0.504275\pi\)
\(548\) 0.618034 1.90211i 0.0264011 0.0812542i
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 1.23607 3.80423i 0.0526105 0.161919i
\(553\) −12.9443 + 9.40456i −0.550446 + 0.399923i
\(554\) −21.0344 15.2824i −0.893668 0.649288i
\(555\) −3.70820 11.4127i −0.157404 0.484441i
\(556\) 1.23607 + 3.80423i 0.0524210 + 0.161335i
\(557\) 24.2705 + 17.6336i 1.02837 + 0.747158i 0.967983 0.251017i \(-0.0807650\pi\)
0.0603918 + 0.998175i \(0.480765\pi\)
\(558\) 0 0
\(559\) −7.41641 + 22.8254i −0.313681 + 0.965410i
\(560\) 8.00000 0.338062
\(561\) 0 0
\(562\) −22.0000 −0.928014
\(563\) 6.18034 19.0211i 0.260470 0.801645i −0.732232 0.681055i \(-0.761521\pi\)
0.992702 0.120590i \(-0.0384786\pi\)
\(564\) −9.70820 + 7.05342i −0.408789 + 0.297003i
\(565\) −3.23607 2.35114i −0.136142 0.0989132i
\(566\) 1.23607 + 3.80423i 0.0519558 + 0.159904i
\(567\) 1.23607 + 3.80423i 0.0519100 + 0.159762i
\(568\) −9.70820 7.05342i −0.407347 0.295955i
\(569\) 8.09017 5.87785i 0.339158 0.246412i −0.405149 0.914251i \(-0.632780\pi\)
0.744306 + 0.667838i \(0.232780\pi\)
\(570\) −2.47214 + 7.60845i −0.103546 + 0.318683i
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) −7.41641 + 22.8254i −0.309555 + 0.952712i
\(575\) 3.23607 2.35114i 0.134953 0.0980494i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) −14.2148 43.7486i −0.591769 1.82128i −0.570193 0.821511i \(-0.693132\pi\)
−0.0215762 0.999767i \(-0.506868\pi\)
\(578\) 4.01722 + 12.3637i 0.167094 + 0.514264i
\(579\) −8.09017 5.87785i −0.336216 0.244275i
\(580\) 9.70820 7.05342i 0.403111 0.292877i
\(581\) −4.94427 + 15.2169i −0.205123 + 0.631304i
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 3.70820 11.4127i 0.153315 0.471856i
\(586\) −17.7984 + 12.9313i −0.735244 + 0.534186i
\(587\) 29.1246 + 21.1603i 1.20210 + 0.873378i 0.994490 0.104834i \(-0.0334310\pi\)
0.207612 + 0.978211i \(0.433431\pi\)
\(588\) −2.78115 8.55951i −0.114693 0.352988i
\(589\) 0 0
\(590\) 19.4164 + 14.1068i 0.799361 + 0.580770i
\(591\) 1.61803 1.17557i 0.0665570 0.0483565i
\(592\) 1.85410 5.70634i 0.0762031 0.234529i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 3.09017 9.51057i 0.126578 0.389568i
\(597\) −12.9443 + 9.40456i −0.529774 + 0.384903i
\(598\) 19.4164 + 14.1068i 0.793996 + 0.576872i
\(599\) 11.1246 + 34.2380i 0.454539 + 1.39893i 0.871675 + 0.490084i \(0.163034\pi\)
−0.417136 + 0.908844i \(0.636966\pi\)
\(600\) −0.309017 0.951057i −0.0126156 0.0388267i
\(601\) 8.09017 + 5.87785i 0.330005 + 0.239763i 0.740433 0.672130i \(-0.234621\pi\)
−0.410428 + 0.911893i \(0.634621\pi\)
\(602\) −12.9443 + 9.40456i −0.527569 + 0.383301i
\(603\) 1.23607 3.80423i 0.0503366 0.154920i
\(604\) −4.00000 −0.162758
\(605\) 0 0
\(606\) −14.0000 −0.568711
\(607\) −8.65248 + 26.6296i −0.351193 + 1.08086i 0.606991 + 0.794709i \(0.292376\pi\)
−0.958184 + 0.286153i \(0.907624\pi\)
\(608\) −3.23607 + 2.35114i −0.131240 + 0.0953514i
\(609\) −19.4164 14.1068i −0.786793 0.571638i
\(610\) −8.65248 26.6296i −0.350329 1.07820i
\(611\) −22.2492 68.4761i −0.900107 2.77025i
\(612\) 1.61803 + 1.17557i 0.0654051 + 0.0475196i
\(613\) −4.85410 + 3.52671i −0.196055 + 0.142443i −0.681482 0.731835i \(-0.738664\pi\)
0.485427 + 0.874277i \(0.338664\pi\)
\(614\) 1.23607 3.80423i 0.0498836 0.153526i
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) 3.23607 2.35114i 0.130069 0.0945003i −0.520849 0.853649i \(-0.674384\pi\)
0.650917 + 0.759149i \(0.274384\pi\)
\(620\) 0 0
\(621\) −1.23607 3.80423i −0.0496017 0.152658i
\(622\) −1.23607 3.80423i −0.0495618 0.152536i
\(623\) −32.3607 23.5114i −1.29650 0.941965i
\(624\) 4.85410 3.52671i 0.194320 0.141181i
\(625\) −5.87132 + 18.0701i −0.234853 + 0.722803i
\(626\) −26.0000 −1.03917
\(627\) 0 0
\(628\) −10.0000 −0.399043
\(629\) −3.70820 + 11.4127i −0.147856 + 0.455053i
\(630\) 6.47214 4.70228i 0.257856 0.187343i
\(631\) 6.47214 + 4.70228i 0.257652 + 0.187195i 0.709111 0.705097i \(-0.249096\pi\)
−0.451459 + 0.892292i \(0.649096\pi\)
\(632\) −1.23607 3.80423i −0.0491681 0.151324i
\(633\) −1.23607 3.80423i −0.0491293 0.151204i
\(634\) 14.5623 + 10.5801i 0.578343 + 0.420191i
\(635\) 19.4164 14.1068i 0.770517 0.559813i
\(636\) −0.618034 + 1.90211i −0.0245066 + 0.0754237i
\(637\) 54.0000 2.13956
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) −0.618034 + 1.90211i −0.0244299 + 0.0751876i
\(641\) −33.9787 + 24.6870i −1.34208 + 0.975077i −0.342714 + 0.939440i \(0.611346\pi\)
−0.999365 + 0.0356372i \(0.988654\pi\)
\(642\) 3.23607 + 2.35114i 0.127717 + 0.0927921i
\(643\) −8.65248 26.6296i −0.341220 1.05017i −0.963576 0.267434i \(-0.913824\pi\)
0.622356 0.782734i \(-0.286176\pi\)
\(644\) 4.94427 + 15.2169i 0.194832 + 0.599630i
\(645\) −6.47214 4.70228i −0.254840 0.185152i
\(646\) 6.47214 4.70228i 0.254643 0.185009i
\(647\) −8.65248 + 26.6296i −0.340164 + 1.04692i 0.623958 + 0.781458i \(0.285524\pi\)
−0.964122 + 0.265459i \(0.914476\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 16.1803 11.7557i 0.633671 0.460389i
\(653\) −14.5623 10.5801i −0.569867 0.414033i 0.265190 0.964196i \(-0.414565\pi\)
−0.835057 + 0.550164i \(0.814565\pi\)
\(654\) 1.85410 + 5.70634i 0.0725011 + 0.223136i
\(655\) −2.47214 7.60845i −0.0965943 0.297287i
\(656\) −4.85410 3.52671i −0.189521 0.137695i
\(657\) −4.85410 + 3.52671i −0.189377 + 0.137590i
\(658\) 14.8328 45.6507i 0.578243 1.77965i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) −6.18034 + 19.0211i −0.240206 + 0.739277i
\(663\) −9.70820 + 7.05342i −0.377035 + 0.273932i
\(664\) −3.23607 2.35114i −0.125584 0.0912420i
\(665\) −9.88854 30.4338i −0.383461 1.18017i
\(666\) −1.85410 5.70634i −0.0718450 0.221116i
\(667\) 19.4164 + 14.1068i 0.751806 + 0.546219i
\(668\) 0 0
\(669\) 0 0
\(670\) −8.00000 −0.309067
\(671\) 0 0
\(672\) 4.00000 0.154303
\(673\) −8.03444 + 24.7275i −0.309705 + 0.953174i 0.668174 + 0.744005i \(0.267076\pi\)
−0.977879 + 0.209169i \(0.932924\pi\)
\(674\) −14.5623 + 10.5801i −0.560919 + 0.407532i
\(675\) −0.809017 0.587785i −0.0311391 0.0226239i
\(676\) 7.10739 + 21.8743i 0.273361 + 0.841319i
\(677\) −14.2148 43.7486i −0.546318 1.68140i −0.717834 0.696214i \(-0.754866\pi\)
0.171516 0.985181i \(-0.445134\pi\)
\(678\) −1.61803 1.17557i −0.0621402 0.0451475i
\(679\) 45.3050 32.9160i 1.73864 1.26320i
\(680\) 1.23607 3.80423i 0.0474010 0.145885i
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −1.23607 + 3.80423i −0.0472622 + 0.145458i
\(685\) −3.23607 + 2.35114i −0.123644 + 0.0898325i
\(686\) 6.47214 + 4.70228i 0.247107 + 0.179534i
\(687\) −4.32624 13.3148i −0.165056 0.507991i
\(688\) −1.23607 3.80423i −0.0471246 0.145035i
\(689\) −9.70820 7.05342i −0.369853 0.268714i
\(690\) −6.47214 + 4.70228i −0.246390 + 0.179013i
\(691\) −3.70820 + 11.4127i −0.141067 + 0.434159i −0.996484 0.0837803i \(-0.973301\pi\)
0.855418 + 0.517939i \(0.173301\pi\)
\(692\) 10.0000 0.380143
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 2.47214 7.60845i 0.0937735 0.288605i
\(696\) 4.85410 3.52671i 0.183994 0.133680i
\(697\) 9.70820 + 7.05342i 0.367724 + 0.267167i
\(698\) −1.85410 5.70634i −0.0701788 0.215988i
\(699\) 3.09017 + 9.51057i 0.116881 + 0.359723i
\(700\) 3.23607 + 2.35114i 0.122312 + 0.0888648i
\(701\) 24.2705 17.6336i 0.916685 0.666010i −0.0260120 0.999662i \(-0.508281\pi\)
0.942697 + 0.333651i \(0.108281\pi\)
\(702\) 1.85410 5.70634i 0.0699786 0.215372i
\(703\) −24.0000 −0.905177
\(704\) 0 0
\(705\) 24.0000 0.903892
\(706\) −5.56231 + 17.1190i −0.209340 + 0.644283i
\(707\) 45.3050 32.9160i 1.70387 1.23793i
\(708\) 9.70820 + 7.05342i 0.364857 + 0.265084i
\(709\) −5.56231 17.1190i −0.208897 0.642918i −0.999531 0.0306292i \(-0.990249\pi\)
0.790634 0.612289i \(-0.209751\pi\)
\(710\) 7.41641 + 22.8254i 0.278333 + 0.856620i
\(711\) −3.23607 2.35114i −0.121362 0.0881747i
\(712\) 8.09017 5.87785i 0.303192 0.220282i
\(713\) 0 0
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 20.0000 0.747435
\(717\) 2.47214 7.60845i 0.0923236 0.284143i
\(718\) 0 0
\(719\) −9.70820 7.05342i −0.362055 0.263048i 0.391854 0.920028i \(-0.371834\pi\)
−0.753909 + 0.656979i \(0.771834\pi\)
\(720\) 0.618034 + 1.90211i 0.0230328 + 0.0708876i
\(721\) 0 0
\(722\) −2.42705 1.76336i −0.0903255 0.0656253i
\(723\) −8.09017 + 5.87785i −0.300877 + 0.218600i
\(724\) −0.618034 + 1.90211i −0.0229691 + 0.0706915i
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) −7.41641 + 22.8254i −0.274870 + 0.845964i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 9.70820 + 7.05342i 0.359317 + 0.261059i
\(731\) 2.47214 + 7.60845i 0.0914353 + 0.281409i
\(732\) −4.32624 13.3148i −0.159902 0.492129i
\(733\) −17.7984 12.9313i −0.657398 0.477628i 0.208385 0.978047i \(-0.433179\pi\)
−0.865783 + 0.500419i \(0.833179\pi\)
\(734\) −12.9443 + 9.40456i −0.477782 + 0.347129i
\(735\) −5.56231 + 17.1190i −0.205169 + 0.631444i
\(736\) −4.00000 −0.147442
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) −13.5967 + 41.8465i −0.500164 + 1.53935i 0.308586 + 0.951196i \(0.400144\pi\)
−0.808751 + 0.588152i \(0.799856\pi\)
\(740\) −9.70820 + 7.05342i −0.356881 + 0.259289i
\(741\) −19.4164 14.1068i −0.713280 0.518228i
\(742\) −2.47214 7.60845i −0.0907550 0.279315i
\(743\) 9.88854 + 30.4338i 0.362775 + 1.11651i 0.951362 + 0.308074i \(0.0996845\pi\)
−0.588587 + 0.808434i \(0.700316\pi\)
\(744\) 0 0
\(745\) −16.1803 + 11.7557i −0.592802 + 0.430696i
\(746\) −4.32624 + 13.3148i −0.158395 + 0.487489i
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) −3.70820 + 11.4127i −0.135404 + 0.416732i
\(751\) −25.8885 + 18.8091i −0.944686 + 0.686355i −0.949544 0.313633i \(-0.898454\pi\)
0.00485778 + 0.999988i \(0.498454\pi\)
\(752\) 9.70820 + 7.05342i 0.354022 + 0.257212i
\(753\) 1.23607 + 3.80423i 0.0450448 + 0.138634i
\(754\) 11.1246 + 34.2380i 0.405134 + 1.24688i
\(755\) 6.47214 + 4.70228i 0.235545 + 0.171134i
\(756\) 3.23607 2.35114i 0.117695 0.0855102i
\(757\) 11.7426 36.1401i 0.426794 1.31354i −0.474473 0.880270i \(-0.657361\pi\)
0.901266 0.433266i \(-0.142639\pi\)
\(758\) 28.0000 1.01701
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) −12.9787 + 39.9444i −0.470478 + 1.44798i 0.381482 + 0.924376i \(0.375414\pi\)
−0.851960 + 0.523606i \(0.824586\pi\)
\(762\) 9.70820 7.05342i 0.351691 0.255519i
\(763\) −19.4164 14.1068i −0.702921 0.510702i
\(764\) −3.70820 11.4127i −0.134158 0.412896i
\(765\) −1.23607 3.80423i −0.0446901 0.137542i
\(766\) −3.23607 2.35114i −0.116924 0.0849502i
\(767\) −58.2492 + 42.3205i −2.10326 + 1.52811i
\(768\) −0.309017 + 0.951057i −0.0111507 + 0.0343183i
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) −2.00000 −0.0720282
\(772\) −3.09017 + 9.51057i −0.111218 + 0.342293i
\(773\) −14.5623 + 10.5801i −0.523770 + 0.380541i −0.818022 0.575187i \(-0.804929\pi\)
0.294252 + 0.955728i \(0.404929\pi\)
\(774\) −3.23607 2.35114i −0.116318 0.0845100i
\(775\) 0 0
\(776\) 4.32624 + 13.3148i 0.155303 + 0.477973i
\(777\) 19.4164 + 14.1068i 0.696560 + 0.506080i
\(778\) −24.2705 + 17.6336i −0.870140 + 0.632194i
\(779\) −7.41641 + 22.8254i −0.265720 + 0.817803i
\(780\) −12.0000 −0.429669
\(781\) 0 0
\(782\) 8.00000 0.286079
\(783\) 1.85410 5.70634i 0.0662602 0.203928i
\(784\) −7.28115 + 5.29007i −0.260041 + 0.188931i
\(785\) 16.1803 + 11.7557i 0.577501 + 0.419579i
\(786\) −1.23607 3.80423i −0.0440891 0.135692i
\(787\) 6.18034 + 19.0211i 0.220305 + 0.678030i 0.998734 + 0.0502974i \(0.0160169\pi\)
−0.778429 + 0.627733i \(0.783983\pi\)
\(788\) −1.61803 1.17557i −0.0576401 0.0418780i
\(789\) 19.4164 14.1068i 0.691242 0.502217i
\(790\) −2.47214 + 7.60845i −0.0879547 + 0.270697i
\(791\) 8.00000 0.284447
\(792\) 0 0
\(793\) 84.0000 2.98293
\(794\) −6.79837 + 20.9232i −0.241265 + 0.742538i
\(795\) 3.23607 2.35114i 0.114772 0.0833864i
\(796\) 12.9443 + 9.40456i 0.458798 + 0.333336i
\(797\) −16.6869 51.3571i −0.591081 1.81916i −0.573340 0.819317i \(-0.694353\pi\)
−0.0177409 0.999843i \(-0.505647\pi\)
\(798\) −4.94427 15.2169i −0.175025 0.538673i
\(799\) −19.4164 14.1068i −0.686903 0.499064i
\(800\) −0.809017 + 0.587785i −0.0286031 + 0.0207813i
\(801\) 3.09017 9.51057i 0.109186 0.336039i
\(802\) 38.0000 1.34183
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 9.88854 30.4338i 0.348525 1.07265i
\(806\) 0 0
\(807\) 21.0344 + 15.2824i 0.740447 + 0.537967i
\(808\) 4.32624 + 13.3148i 0.152197 + 0.468413i
\(809\) −3.09017 9.51057i −0.108645 0.334374i 0.881924 0.471392i \(-0.156248\pi\)
−0.990569 + 0.137018i \(0.956248\pi\)
\(810\) 1.61803 + 1.17557i 0.0568519 + 0.0413053i
\(811\) −22.6525 + 16.4580i −0.795436 + 0.577918i −0.909572 0.415547i \(-0.863590\pi\)
0.114136 + 0.993465i \(0.463590\pi\)
\(812\) −7.41641 + 22.8254i −0.260265 + 0.801013i
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) −40.0000 −1.40114
\(816\) 0.618034 1.90211i 0.0216355 0.0665873i
\(817\) −12.9443 + 9.40456i −0.452863 + 0.329024i
\(818\) 11.3262 + 8.22899i 0.396013 + 0.287720i
\(819\) 7.41641 + 22.8254i 0.259150 + 0.797582i
\(820\) 3.70820 + 11.4127i 0.129496 + 0.398548i
\(821\) −1.61803 1.17557i −0.0564698 0.0410277i 0.559192 0.829038i \(-0.311111\pi\)
−0.615662 + 0.788010i \(0.711111\pi\)
\(822\) −1.61803 + 1.17557i −0.0564354 + 0.0410027i
\(823\) −12.3607 + 38.0423i −0.430866 + 1.32607i 0.466398 + 0.884575i \(0.345552\pi\)
−0.897264 + 0.441495i \(0.854448\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −48.0000 −1.67013
\(827\) 16.0689 49.4549i 0.558770 1.71972i −0.127004 0.991902i \(-0.540536\pi\)
0.685774 0.727815i \(-0.259464\pi\)
\(828\) −3.23607 + 2.35114i −0.112461 + 0.0817078i
\(829\) −37.2148 27.0381i −1.29252 0.939073i −0.292670 0.956214i \(-0.594544\pi\)
−0.999853 + 0.0171408i \(0.994544\pi\)
\(830\) 2.47214 + 7.60845i 0.0858091 + 0.264093i
\(831\) 8.03444 + 24.7275i 0.278712 + 0.857786i
\(832\) −4.85410 3.52671i −0.168286 0.122267i
\(833\) 14.5623 10.5801i 0.504554 0.366580i
\(834\) 1.23607 3.80423i 0.0428015 0.131730i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 3.70820 11.4127i 0.128098 0.394244i
\(839\) −9.70820 + 7.05342i −0.335164 + 0.243511i −0.742619 0.669714i \(-0.766417\pi\)
0.407454 + 0.913226i \(0.366417\pi\)
\(840\) −6.47214 4.70228i −0.223310 0.162244i
\(841\) 2.16312 + 6.65740i 0.0745903 + 0.229565i
\(842\) 3.09017 + 9.51057i 0.106494 + 0.327756i
\(843\) 17.7984 + 12.9313i 0.613009 + 0.445377i
\(844\) −3.23607 + 2.35114i −0.111390 + 0.0809296i
\(845\) 14.2148 43.7486i 0.489003 1.50500i
\(846\) 12.0000 0.412568
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) 1.23607 3.80423i 0.0424217 0.130561i
\(850\) 1.61803 1.17557i 0.0554981 0.0403217i
\(851\) −19.4164 14.1068i −0.665586 0.483576i
\(852\) 3.70820 + 11.4127i 0.127041 + 0.390992i
\(853\) 1.85410 + 5.70634i 0.0634832 + 0.195381i 0.977768 0.209692i \(-0.0672461\pi\)
−0.914284 + 0.405073i \(0.867246\pi\)
\(854\) 45.3050 + 32.9160i 1.55030 + 1.12636i
\(855\) 6.47214 4.70228i 0.221342 0.160815i
\(856\) 1.23607 3.80423i 0.0422479 0.130026i
\(857\) −26.0000 −0.888143 −0.444072 0.895991i \(-0.646466\pi\)
−0.444072 + 0.895991i \(0.646466\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) −2.47214 + 7.60845i −0.0842991 + 0.259446i
\(861\) 19.4164 14.1068i 0.661709 0.480760i
\(862\) 0 0
\(863\) 6.18034 + 19.0211i 0.210381 + 0.647487i 0.999449 + 0.0331811i \(0.0105638\pi\)
−0.789068 + 0.614306i \(0.789436\pi\)
\(864\) 0.309017 + 0.951057i 0.0105130 + 0.0323556i
\(865\) −16.1803 11.7557i −0.550148 0.399706i
\(866\) 1.61803 1.17557i 0.0549830 0.0399475i
\(867\) 4.01722 12.3637i 0.136432 0.419894i
\(868\) 0 0
\(869\) 0 0
\(870\) −12.0000 −0.406838
\(871\) 7.41641 22.8254i 0.251295 0.773408i
\(872\) 4.85410 3.52671i 0.164381 0.119430i
\(873\) 11.3262 + 8.22899i 0.383335 + 0.278509i
\(874\) 4.94427 + 15.2169i 0.167242 + 0.514719i
\(875\) −14.8328 45.6507i −0.501441 1.54328i
\(876\) 4.85410 + 3.52671i 0.164005 + 0.119157i
\(877\) 33.9787 24.6870i 1.14738 0.833620i 0.159249 0.987238i \(-0.449093\pi\)
0.988130 + 0.153618i \(0.0490926\pi\)
\(878\) 1.23607 3.80423i 0.0417153 0.128386i
\(879\) 22.0000 0.742042
\(880\) 0 0
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) −2.78115 + 8.55951i −0.0936463 + 0.288214i
\(883\) −3.23607 + 2.35114i −0.108902 + 0.0791222i −0.640904 0.767621i \(-0.721440\pi\)
0.532001 + 0.846744i \(0.321440\pi\)
\(884\) 9.70820 + 7.05342i 0.326522 + 0.237232i
\(885\) −7.41641 22.8254i −0.249300 0.767266i
\(886\) −8.65248 26.6296i −0.290686 0.894638i
\(887\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(888\) −4.85410 + 3.52671i −0.162893 + 0.118349i
\(889\) −14.8328 + 45.6507i −0.497477 + 1.53108i
\(890\) −20.0000 −0.670402
\(891\) 0 0
\(892\) 0 0
\(893\) 14.8328 45.6507i 0.496361 1.52764i
\(894\) −8.09017 + 5.87785i −0.270576 + 0.196585i
\(895\) −32.3607 23.5114i −1.08170 0.785900i
\(896\) −1.23607 3.80423i −0.0412941 0.127090i
\(897\) −7.41641 22.8254i −0.247627 0.762116i
\(898\) −17.7984 12.9313i −0.593939 0.431522i
\(899\) 0 0
\(900\) −0.309017 + 0.951057i −0.0103006 + 0.0317019i
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) −0.618034 + 1.90211i −0.0205555 + 0.0632633i
\(905\) 3.23607 2.35114i 0.107571 0.0781546i
\(906\) 3.23607 + 2.35114i 0.107511 + 0.0781114i
\(907\) 8.65248 + 26.6296i 0.287301 + 0.884221i 0.985700 + 0.168512i \(0.0538962\pi\)
−0.698399 + 0.715709i \(0.746104\pi\)
\(908\) −3.70820 11.4127i −0.123061 0.378743i
\(909\) 11.3262 + 8.22899i 0.375668 + 0.272938i
\(910\) 38.8328 28.2137i 1.28730 0.935275i
\(911\) 3.70820 11.4127i 0.122858 0.378119i −0.870647 0.491909i \(-0.836299\pi\)
0.993505 + 0.113790i \(0.0362992\pi\)
\(912\) 4.00000 0.132453
\(913\) 0 0
\(914\) 34.0000 1.12462
\(915\) −8.65248 + 26.6296i −0.286042 + 0.880347i
\(916\) −11.3262 + 8.22899i −0.374229 + 0.271894i
\(917\) 12.9443 + 9.40456i 0.427458 + 0.310566i
\(918\) −0.618034 1.90211i −0.0203982 0.0627791i
\(919\) 1.23607 + 3.80423i 0.0407741 + 0.125490i 0.969372 0.245599i \(-0.0789846\pi\)
−0.928597 + 0.371089i \(0.878985\pi\)
\(920\) 6.47214 + 4.70228i 0.213380 + 0.155030i
\(921\) −3.23607 + 2.35114i −0.106632 + 0.0774727i
\(922\) 4.32624 13.3148i 0.142477 0.438499i
\(923\) −72.0000 −2.36991
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 7.41641 22.8254i 0.243718 0.750088i
\(927\) 0 0
\(928\) −4.85410 3.52671i −0.159344 0.115770i
\(929\) 12.9787 + 39.9444i 0.425818 + 1.31053i 0.902209 + 0.431299i \(0.141945\pi\)
−0.476391 + 0.879233i \(0.658055\pi\)
\(930\) 0 0
\(931\) 29.1246 + 21.1603i 0.954521 + 0.693500i
\(932\) 8.09017 5.87785i 0.265002 0.192535i
\(933\) −1.23607 + 3.80423i −0.0404670 + 0.124545i
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) 11.7426 36.1401i 0.383616 1.18065i −0.553864 0.832607i \(-0.686847\pi\)
0.937480 0.348040i \(-0.113153\pi\)
\(938\) 12.9443 9.40456i 0.422645 0.307070i
\(939\) 21.0344 + 15.2824i 0.686433 + 0.498723i
\(940\) −7.41641 22.8254i −0.241897 0.744481i
\(941\) 12.9787 + 39.9444i 0.423094 + 1.30215i 0.904808 + 0.425821i \(0.140015\pi\)
−0.481714 + 0.876329i \(0.659985\pi\)
\(942\) 8.09017 + 5.87785i 0.263592 + 0.191511i
\(943\) −19.4164 + 14.1068i −0.632285 + 0.459382i
\(944\) 3.70820 11.4127i 0.120692 0.371451i
\(945\) −8.00000 −0.260240
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) −1.23607 + 3.80423i −0.0401456 + 0.123556i
\(949\) −29.1246 + 21.1603i −0.945425 + 0.686891i
\(950\) 3.23607 + 2.35114i 0.104992 + 0.0762811i
\(951\) −5.56231 17.1190i −0.180370 0.555122i
\(952\) 2.47214 + 7.60845i 0.0801224 + 0.246591i
\(953\) −4.85410 3.52671i −0.157240 0.114241i 0.506383 0.862309i \(-0.330982\pi\)
−0.663623 + 0.748067i \(0.730982\pi\)
\(954\) 1.61803 1.17557i 0.0523858 0.0380605i
\(955\) −7.41641 + 22.8254i −0.239989 + 0.738611i
\(956\) −8.00000 −0.258738
\(957\) 0 0
\(958\) 0 0
\(959\) 2.47214 7.60845i 0.0798294 0.245690i
\(960\) 1.61803 1.17557i 0.0522218 0.0379414i
\(961\) 25.0795 + 18.2213i 0.809017 + 0.587785i
\(962\) −11.1246 34.2380i −0.358672 1.10388i
\(963\) −1.23607 3.80423i −0.0398317 0.122589i
\(964\) 8.09017 + 5.87785i 0.260567 + 0.189313i
\(965\) 16.1803 11.7557i 0.520864 0.378430i
\(966\) 4.94427 15.2169i 0.159079 0.489596i
\(967\) 44.0000 1.41494 0.707472 0.706741i \(-0.249835\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(968\) 0 0
\(969\) −8.00000 −0.256997
\(970\) 8.65248 26.6296i 0.277814 0.855024i
\(971\) −9.70820 + 7.05342i −0.311551 + 0.226355i −0.732562 0.680701i \(-0.761675\pi\)
0.421011 + 0.907056i \(0.361675\pi\)
\(972\) 0.809017 + 0.587785i 0.0259492 + 0.0188532i
\(973\) 4.94427 + 15.2169i 0.158506 + 0.487832i
\(974\) 4.94427 + 15.2169i 0.158425 + 0.487581i
\(975\) −4.85410 3.52671i −0.155456 0.112945i
\(976\) −11.3262 + 8.22899i −0.362544 + 0.263404i
\(977\) 8.03444 24.7275i 0.257045 0.791102i −0.736375 0.676573i \(-0.763464\pi\)
0.993420 0.114529i \(-0.0365358\pi\)
\(978\) −20.0000 −0.639529
\(979\) 0 0
\(980\) 18.0000 0.574989
\(981\) 1.85410 5.70634i 0.0591969 0.182189i
\(982\) 22.6525 16.4580i 0.722870 0.525195i
\(983\) −29.1246 21.1603i −0.928931 0.674908i 0.0168000 0.999859i \(-0.494652\pi\)
−0.945731 + 0.324951i \(0.894652\pi\)
\(984\) 1.85410 + 5.70634i 0.0591066 + 0.181911i
\(985\) 1.23607 + 3.80423i 0.0393844 + 0.121213i
\(986\) 9.70820 + 7.05342i 0.309172 + 0.224627i
\(987\) −38.8328 + 28.2137i −1.23606 + 0.898052i
\(988\) −7.41641 + 22.8254i −0.235947 + 0.726171i
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 0 0
\(993\) 16.1803 11.7557i 0.513468 0.373056i
\(994\) −38.8328 28.2137i −1.23170 0.894884i
\(995\) −9.88854 30.4338i −0.313488 0.964817i
\(996\) 1.23607 + 3.80423i 0.0391663 + 0.120542i
\(997\) −11.3262 8.22899i −0.358706 0.260615i 0.393806 0.919193i \(-0.371158\pi\)
−0.752512 + 0.658579i \(0.771158\pi\)
\(998\) −3.23607 + 2.35114i −0.102436 + 0.0744241i
\(999\) −1.85410 + 5.70634i −0.0586612 + 0.180541i
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 726.2.e.o.493.1 4
11.2 odd 10 726.2.e.g.487.1 4
11.3 even 5 inner 726.2.e.o.565.1 4
11.4 even 5 726.2.a.c.1.1 1
11.5 even 5 inner 726.2.e.o.511.1 4
11.6 odd 10 726.2.e.g.511.1 4
11.7 odd 10 66.2.a.b.1.1 1
11.8 odd 10 726.2.e.g.565.1 4
11.9 even 5 inner 726.2.e.o.487.1 4
11.10 odd 2 726.2.e.g.493.1 4
33.26 odd 10 2178.2.a.g.1.1 1
33.29 even 10 198.2.a.a.1.1 1
44.7 even 10 528.2.a.j.1.1 1
44.15 odd 10 5808.2.a.bc.1.1 1
55.7 even 20 1650.2.c.e.199.2 2
55.18 even 20 1650.2.c.e.199.1 2
55.29 odd 10 1650.2.a.k.1.1 1
77.62 even 10 3234.2.a.t.1.1 1
88.29 odd 10 2112.2.a.r.1.1 1
88.51 even 10 2112.2.a.e.1.1 1
99.7 odd 30 1782.2.e.e.595.1 2
99.29 even 30 1782.2.e.v.595.1 2
99.40 odd 30 1782.2.e.e.1189.1 2
99.95 even 30 1782.2.e.v.1189.1 2
132.95 odd 10 1584.2.a.f.1.1 1
165.29 even 10 4950.2.a.bu.1.1 1
165.62 odd 20 4950.2.c.p.199.1 2
165.128 odd 20 4950.2.c.p.199.2 2
231.62 odd 10 9702.2.a.x.1.1 1
264.29 even 10 6336.2.a.bw.1.1 1
264.227 odd 10 6336.2.a.cj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
66.2.a.b.1.1 1 11.7 odd 10
198.2.a.a.1.1 1 33.29 even 10
528.2.a.j.1.1 1 44.7 even 10
726.2.a.c.1.1 1 11.4 even 5
726.2.e.g.487.1 4 11.2 odd 10
726.2.e.g.493.1 4 11.10 odd 2
726.2.e.g.511.1 4 11.6 odd 10
726.2.e.g.565.1 4 11.8 odd 10
726.2.e.o.487.1 4 11.9 even 5 inner
726.2.e.o.493.1 4 1.1 even 1 trivial
726.2.e.o.511.1 4 11.5 even 5 inner
726.2.e.o.565.1 4 11.3 even 5 inner
1584.2.a.f.1.1 1 132.95 odd 10
1650.2.a.k.1.1 1 55.29 odd 10
1650.2.c.e.199.1 2 55.18 even 20
1650.2.c.e.199.2 2 55.7 even 20
1782.2.e.e.595.1 2 99.7 odd 30
1782.2.e.e.1189.1 2 99.40 odd 30
1782.2.e.v.595.1 2 99.29 even 30
1782.2.e.v.1189.1 2 99.95 even 30
2112.2.a.e.1.1 1 88.51 even 10
2112.2.a.r.1.1 1 88.29 odd 10
2178.2.a.g.1.1 1 33.26 odd 10
3234.2.a.t.1.1 1 77.62 even 10
4950.2.a.bu.1.1 1 165.29 even 10
4950.2.c.p.199.1 2 165.62 odd 20
4950.2.c.p.199.2 2 165.128 odd 20
5808.2.a.bc.1.1 1 44.15 odd 10
6336.2.a.bw.1.1 1 264.29 even 10
6336.2.a.cj.1.1 1 264.227 odd 10
9702.2.a.x.1.1 1 231.62 odd 10