Properties

Label 418.2.f.g.115.3
Level $418$
Weight $2$
Character 418.115
Analytic conductor $3.338$
Analytic rank $0$
Dimension $16$
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] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
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("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), degree \(4\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} - 2960 x^{7} + 5348 x^{6} - 6872 x^{5} + 8232 x^{4} - 6344 x^{3} + 3984 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 115.3
Root \(0.956027 + 0.694595i\) of defining polynomial
Character \(\chi\) \(=\) 418.115
Dual form 418.2.f.g.229.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.956027 + 0.694595i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0364140 + 0.112071i) q^{5} +(0.365170 - 1.12388i) q^{6} +(1.41067 - 1.02491i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.495524 - 1.52507i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.956027 + 0.694595i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.0364140 + 0.112071i) q^{5} +(0.365170 - 1.12388i) q^{6} +(1.41067 - 1.02491i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.495524 - 1.52507i) q^{9} +0.117838 q^{10} +(3.18641 + 0.920226i) q^{11} -1.18171 q^{12} +(0.656165 + 2.01947i) q^{13} +(-1.41067 - 1.02491i) q^{14} +(-0.112657 + 0.0818499i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.672362 - 2.06932i) q^{17} +(-1.29730 + 0.942543i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.0364140 - 0.112071i) q^{20} +2.06054 q^{21} +(-0.109466 - 3.31482i) q^{22} +6.90496 q^{23} +(0.365170 + 1.12388i) q^{24} +(4.03385 + 2.93076i) q^{25} +(1.71786 - 1.24810i) q^{26} +(1.68108 - 5.17383i) q^{27} +(-0.538830 + 1.65835i) q^{28} +(-2.35143 + 1.70841i) q^{29} +(0.112657 + 0.0818499i) q^{30} +(-0.633297 - 1.94909i) q^{31} -1.00000 q^{32} +(2.40711 + 3.09302i) q^{33} -2.17581 q^{34} +(0.0634948 + 0.195417i) q^{35} +(1.29730 + 0.942543i) q^{36} +(1.65368 - 1.20147i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(-0.775400 + 2.38644i) q^{39} +(-0.0953332 + 0.0692636i) q^{40} +(-0.497734 - 0.361625i) q^{41} +(-0.636743 - 1.95969i) q^{42} -10.0414 q^{43} +(-3.11875 + 1.12844i) q^{44} +0.188960 q^{45} +(-2.13375 - 6.56701i) q^{46} +(4.93079 + 3.58243i) q^{47} +(0.956027 - 0.694595i) q^{48} +(-1.22357 + 3.76575i) q^{49} +(1.54079 - 4.74208i) q^{50} +(2.08013 - 1.51131i) q^{51} +(-1.71786 - 1.24810i) q^{52} +(-2.83556 - 8.72697i) q^{53} -5.44008 q^{54} +(-0.219161 + 0.323594i) q^{55} +1.74369 q^{56} +(-0.365170 - 1.12388i) q^{57} +(2.35143 + 1.70841i) q^{58} +(-4.54252 + 3.30034i) q^{59} +(0.0430310 - 0.132436i) q^{60} +(1.61691 - 4.97634i) q^{61} +(-1.65799 + 1.20460i) q^{62} +(-2.26209 - 1.64350i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.250217 q^{65} +(2.19780 - 3.24509i) q^{66} -13.9348 q^{67} +(0.672362 + 2.06932i) q^{68} +(6.60133 + 4.79615i) q^{69} +(0.166231 - 0.120774i) q^{70} +(-2.83485 + 8.72478i) q^{71} +(0.495524 - 1.52507i) q^{72} +(-10.8850 + 7.90844i) q^{73} +(-1.65368 - 1.20147i) q^{74} +(1.82078 + 5.60378i) q^{75} +1.00000 q^{76} +(5.43813 - 1.96766i) q^{77} +2.50925 q^{78} +(-1.69197 - 5.20734i) q^{79} +(0.0953332 + 0.0692636i) q^{80} +(1.30897 - 0.951023i) q^{81} +(-0.190117 + 0.585121i) q^{82} +(2.92563 - 9.00415i) q^{83} +(-1.66701 + 1.21116i) q^{84} +(0.207427 + 0.150705i) q^{85} +(3.10295 + 9.54991i) q^{86} -3.43468 q^{87} +(2.03696 + 2.61740i) q^{88} +4.79411 q^{89} +(-0.0583917 - 0.179711i) q^{90} +(2.99542 + 2.17630i) q^{91} +(-5.58623 + 4.05863i) q^{92} +(0.748377 - 2.30327i) q^{93} +(1.88339 - 5.79649i) q^{94} +(0.0953332 - 0.0692636i) q^{95} +(-0.956027 - 0.694595i) q^{96} +(3.45324 + 10.6280i) q^{97} +3.95955 q^{98} +(-0.175535 - 5.31548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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
\(3\) 0.956027 + 0.694595i 0.551963 + 0.401024i 0.828509 0.559976i \(-0.189190\pi\)
−0.276546 + 0.961001i \(0.589190\pi\)
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −0.0364140 + 0.112071i −0.0162849 + 0.0501196i −0.958869 0.283850i \(-0.908388\pi\)
0.942584 + 0.333970i \(0.108388\pi\)
\(6\) 0.365170 1.12388i 0.149080 0.458821i
\(7\) 1.41067 1.02491i 0.533185 0.387381i −0.288363 0.957521i \(-0.593111\pi\)
0.821548 + 0.570140i \(0.193111\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) −0.495524 1.52507i −0.165175 0.508356i
\(10\) 0.117838 0.0372638
\(11\) 3.18641 + 0.920226i 0.960738 + 0.277459i
\(12\) −1.18171 −0.341132
\(13\) 0.656165 + 2.01947i 0.181987 + 0.560100i 0.999883 0.0152662i \(-0.00485958\pi\)
−0.817896 + 0.575366i \(0.804860\pi\)
\(14\) −1.41067 1.02491i −0.377018 0.273920i
\(15\) −0.112657 + 0.0818499i −0.0290878 + 0.0211335i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.672362 2.06932i 0.163072 0.501883i −0.835817 0.549008i \(-0.815006\pi\)
0.998889 + 0.0471244i \(0.0150057\pi\)
\(18\) −1.29730 + 0.942543i −0.305776 + 0.222160i
\(19\) −0.809017 0.587785i −0.185601 0.134847i
\(20\) −0.0364140 0.112071i −0.00814243 0.0250598i
\(21\) 2.06054 0.449647
\(22\) −0.109466 3.31482i −0.0233383 0.706722i
\(23\) 6.90496 1.43978 0.719892 0.694086i \(-0.244191\pi\)
0.719892 + 0.694086i \(0.244191\pi\)
\(24\) 0.365170 + 1.12388i 0.0745400 + 0.229411i
\(25\) 4.03385 + 2.93076i 0.806770 + 0.586153i
\(26\) 1.71786 1.24810i 0.336901 0.244773i
\(27\) 1.68108 5.17383i 0.323524 0.995703i
\(28\) −0.538830 + 1.65835i −0.101829 + 0.313398i
\(29\) −2.35143 + 1.70841i −0.436649 + 0.317244i −0.784302 0.620379i \(-0.786979\pi\)
0.347653 + 0.937623i \(0.386979\pi\)
\(30\) 0.112657 + 0.0818499i 0.0205682 + 0.0149437i
\(31\) −0.633297 1.94909i −0.113744 0.350067i 0.877939 0.478772i \(-0.158918\pi\)
−0.991683 + 0.128705i \(0.958918\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.40711 + 3.09302i 0.419024 + 0.538426i
\(34\) −2.17581 −0.373148
\(35\) 0.0634948 + 0.195417i 0.0107326 + 0.0330315i
\(36\) 1.29730 + 0.942543i 0.216217 + 0.157091i
\(37\) 1.65368 1.20147i 0.271864 0.197521i −0.443497 0.896276i \(-0.646262\pi\)
0.715361 + 0.698755i \(0.246262\pi\)
\(38\) −0.309017 + 0.951057i −0.0501292 + 0.154282i
\(39\) −0.775400 + 2.38644i −0.124163 + 0.382136i
\(40\) −0.0953332 + 0.0692636i −0.0150735 + 0.0109515i
\(41\) −0.497734 0.361625i −0.0777330 0.0564763i 0.548240 0.836321i \(-0.315298\pi\)
−0.625973 + 0.779845i \(0.715298\pi\)
\(42\) −0.636743 1.95969i −0.0982516 0.302387i
\(43\) −10.0414 −1.53129 −0.765647 0.643261i \(-0.777581\pi\)
−0.765647 + 0.643261i \(0.777581\pi\)
\(44\) −3.11875 + 1.12844i −0.470170 + 0.170119i
\(45\) 0.188960 0.0281684
\(46\) −2.13375 6.56701i −0.314604 0.968253i
\(47\) 4.93079 + 3.58243i 0.719229 + 0.522551i 0.886138 0.463422i \(-0.153379\pi\)
−0.166909 + 0.985972i \(0.553379\pi\)
\(48\) 0.956027 0.694595i 0.137991 0.100256i
\(49\) −1.22357 + 3.76575i −0.174795 + 0.537965i
\(50\) 1.54079 4.74208i 0.217901 0.670631i
\(51\) 2.08013 1.51131i 0.291277 0.211625i
\(52\) −1.71786 1.24810i −0.238225 0.173080i
\(53\) −2.83556 8.72697i −0.389495 1.19874i −0.933167 0.359444i \(-0.882966\pi\)
0.543672 0.839298i \(-0.317034\pi\)
\(54\) −5.44008 −0.740302
\(55\) −0.219161 + 0.323594i −0.0295516 + 0.0436334i
\(56\) 1.74369 0.233010
\(57\) −0.365170 1.12388i −0.0483679 0.148861i
\(58\) 2.35143 + 1.70841i 0.308757 + 0.224325i
\(59\) −4.54252 + 3.30034i −0.591386 + 0.429667i −0.842811 0.538210i \(-0.819101\pi\)
0.251425 + 0.967877i \(0.419101\pi\)
\(60\) 0.0430310 0.132436i 0.00555528 0.0170974i
\(61\) 1.61691 4.97634i 0.207024 0.637154i −0.792600 0.609742i \(-0.791273\pi\)
0.999624 0.0274127i \(-0.00872683\pi\)
\(62\) −1.65799 + 1.20460i −0.210565 + 0.152985i
\(63\) −2.26209 1.64350i −0.284996 0.207062i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −0.250217 −0.0310356
\(66\) 2.19780 3.24509i 0.270531 0.399443i
\(67\) −13.9348 −1.70241 −0.851205 0.524833i \(-0.824128\pi\)
−0.851205 + 0.524833i \(0.824128\pi\)
\(68\) 0.672362 + 2.06932i 0.0815359 + 0.250942i
\(69\) 6.60133 + 4.79615i 0.794707 + 0.577388i
\(70\) 0.166231 0.120774i 0.0198685 0.0144353i
\(71\) −2.83485 + 8.72478i −0.336435 + 1.03544i 0.629576 + 0.776939i \(0.283229\pi\)
−0.966011 + 0.258501i \(0.916771\pi\)
\(72\) 0.495524 1.52507i 0.0583981 0.179731i
\(73\) −10.8850 + 7.90844i −1.27400 + 0.925613i −0.999354 0.0359327i \(-0.988560\pi\)
−0.274643 + 0.961546i \(0.588560\pi\)
\(74\) −1.65368 1.20147i −0.192237 0.139668i
\(75\) 1.82078 + 5.60378i 0.210245 + 0.647069i
\(76\) 1.00000 0.114708
\(77\) 5.43813 1.96766i 0.619733 0.224235i
\(78\) 2.50925 0.284116
\(79\) −1.69197 5.20734i −0.190361 0.585871i 0.809638 0.586929i \(-0.199663\pi\)
−0.999999 + 0.00105787i \(0.999663\pi\)
\(80\) 0.0953332 + 0.0692636i 0.0106586 + 0.00774391i
\(81\) 1.30897 0.951023i 0.145441 0.105669i
\(82\) −0.190117 + 0.585121i −0.0209950 + 0.0646158i
\(83\) 2.92563 9.00415i 0.321129 0.988334i −0.652028 0.758195i \(-0.726082\pi\)
0.973158 0.230140i \(-0.0739183\pi\)
\(84\) −1.66701 + 1.21116i −0.181886 + 0.132148i
\(85\) 0.207427 + 0.150705i 0.0224986 + 0.0163462i
\(86\) 3.10295 + 9.54991i 0.334600 + 1.02979i
\(87\) −3.43468 −0.368236
\(88\) 2.03696 + 2.61740i 0.217141 + 0.279016i
\(89\) 4.79411 0.508174 0.254087 0.967181i \(-0.418225\pi\)
0.254087 + 0.967181i \(0.418225\pi\)
\(90\) −0.0583917 0.179711i −0.00615503 0.0189432i
\(91\) 2.99542 + 2.17630i 0.314005 + 0.228138i
\(92\) −5.58623 + 4.05863i −0.582405 + 0.423142i
\(93\) 0.748377 2.30327i 0.0776030 0.238838i
\(94\) 1.88339 5.79649i 0.194257 0.597862i
\(95\) 0.0953332 0.0692636i 0.00978098 0.00710630i
\(96\) −0.956027 0.694595i −0.0975741 0.0708918i
\(97\) 3.45324 + 10.6280i 0.350623 + 1.07911i 0.958504 + 0.285079i \(0.0920197\pi\)
−0.607881 + 0.794028i \(0.707980\pi\)
\(98\) 3.95955 0.399975
\(99\) −0.175535 5.31548i −0.0176419 0.534225i
\(100\) −4.98611 −0.498611
\(101\) 1.04855 + 3.22711i 0.104335 + 0.321109i 0.989574 0.144027i \(-0.0460053\pi\)
−0.885239 + 0.465136i \(0.846005\pi\)
\(102\) −2.08013 1.51131i −0.205964 0.149642i
\(103\) −14.3204 + 10.4044i −1.41103 + 1.02517i −0.417861 + 0.908511i \(0.637220\pi\)
−0.993171 + 0.116664i \(0.962780\pi\)
\(104\) −0.656165 + 2.01947i −0.0643423 + 0.198025i
\(105\) −0.0750327 + 0.230927i −0.00732244 + 0.0225362i
\(106\) −7.42361 + 5.39356i −0.721044 + 0.523869i
\(107\) 0.418265 + 0.303887i 0.0404352 + 0.0293779i 0.607819 0.794075i \(-0.292045\pi\)
−0.567384 + 0.823453i \(0.692045\pi\)
\(108\) 1.68108 + 5.17383i 0.161762 + 0.497852i
\(109\) −7.94333 −0.760833 −0.380417 0.924815i \(-0.624219\pi\)
−0.380417 + 0.924815i \(0.624219\pi\)
\(110\) 0.375481 + 0.108438i 0.0358007 + 0.0103392i
\(111\) 2.41550 0.229270
\(112\) −0.538830 1.65835i −0.0509146 0.156699i
\(113\) 13.0739 + 9.49874i 1.22989 + 0.893566i 0.996882 0.0789087i \(-0.0251436\pi\)
0.233007 + 0.972475i \(0.425144\pi\)
\(114\) −0.956027 + 0.694595i −0.0895402 + 0.0650547i
\(115\) −0.251438 + 0.773845i −0.0234467 + 0.0721614i
\(116\) 0.898165 2.76427i 0.0833925 0.256656i
\(117\) 2.75468 2.00139i 0.254670 0.185029i
\(118\) 4.54252 + 3.30034i 0.418173 + 0.303821i
\(119\) −1.17239 3.60825i −0.107473 0.330768i
\(120\) −0.139251 −0.0127118
\(121\) 9.30637 + 5.86443i 0.846033 + 0.533130i
\(122\) −5.23243 −0.473722
\(123\) −0.224665 0.691446i −0.0202573 0.0623456i
\(124\) 1.65799 + 1.20460i 0.148892 + 0.108177i
\(125\) −0.952008 + 0.691675i −0.0851502 + 0.0618653i
\(126\) −0.864040 + 2.65924i −0.0769748 + 0.236904i
\(127\) 0.859002 2.64374i 0.0762241 0.234594i −0.905683 0.423955i \(-0.860642\pi\)
0.981908 + 0.189361i \(0.0606416\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) −9.59983 6.97468i −0.845217 0.614086i
\(130\) 0.0773214 + 0.237971i 0.00678154 + 0.0208714i
\(131\) −10.0755 −0.880298 −0.440149 0.897925i \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(132\) −3.76542 1.08745i −0.327738 0.0946499i
\(133\) −1.74369 −0.151197
\(134\) 4.30610 + 13.2528i 0.371990 + 1.14487i
\(135\) 0.518621 + 0.376800i 0.0446358 + 0.0324298i
\(136\) 1.76027 1.27891i 0.150942 0.109666i
\(137\) −0.148894 + 0.458249i −0.0127209 + 0.0391509i −0.957215 0.289376i \(-0.906552\pi\)
0.944495 + 0.328527i \(0.106552\pi\)
\(138\) 2.52148 7.76033i 0.214643 0.660603i
\(139\) −16.0011 + 11.6255i −1.35720 + 0.986061i −0.358578 + 0.933500i \(0.616738\pi\)
−0.998618 + 0.0525610i \(0.983262\pi\)
\(140\) −0.166231 0.120774i −0.0140491 0.0102073i
\(141\) 2.22563 + 6.84979i 0.187432 + 0.576857i
\(142\) 9.17377 0.769846
\(143\) 0.232441 + 7.03867i 0.0194377 + 0.588603i
\(144\) −1.60355 −0.133629
\(145\) −0.105838 0.325737i −0.00878939 0.0270510i
\(146\) 10.8850 + 7.90844i 0.900852 + 0.654508i
\(147\) −3.78544 + 2.75028i −0.312218 + 0.226839i
\(148\) −0.631651 + 1.94402i −0.0519214 + 0.159798i
\(149\) 1.65901 5.10592i 0.135912 0.418293i −0.859819 0.510599i \(-0.829424\pi\)
0.995731 + 0.0923058i \(0.0294237\pi\)
\(150\) 4.76686 3.46333i 0.389213 0.282780i
\(151\) −16.8173 12.2185i −1.36857 0.994324i −0.997847 0.0655810i \(-0.979110\pi\)
−0.370723 0.928744i \(-0.620890\pi\)
\(152\) −0.309017 0.951057i −0.0250646 0.0771409i
\(153\) −3.48902 −0.282071
\(154\) −3.55183 4.56393i −0.286214 0.367772i
\(155\) 0.241497 0.0193975
\(156\) −0.775400 2.38644i −0.0620817 0.191068i
\(157\) −5.44933 3.95917i −0.434904 0.315976i 0.348703 0.937233i \(-0.386622\pi\)
−0.783607 + 0.621257i \(0.786622\pi\)
\(158\) −4.42963 + 3.21831i −0.352402 + 0.256035i
\(159\) 3.35083 10.3128i 0.265738 0.817858i
\(160\) 0.0364140 0.112071i 0.00287878 0.00885998i
\(161\) 9.74065 7.07700i 0.767671 0.557745i
\(162\) −1.30897 0.951023i −0.102842 0.0747194i
\(163\) 1.39938 + 4.30684i 0.109608 + 0.337338i 0.990784 0.135450i \(-0.0432479\pi\)
−0.881177 + 0.472787i \(0.843248\pi\)
\(164\) 0.615233 0.0480416
\(165\) −0.434290 + 0.157137i −0.0338095 + 0.0122331i
\(166\) −9.46753 −0.734823
\(167\) −1.53398 4.72111i −0.118703 0.365331i 0.873998 0.485929i \(-0.161519\pi\)
−0.992701 + 0.120598i \(0.961519\pi\)
\(168\) 1.66701 + 1.21116i 0.128613 + 0.0934428i
\(169\) 6.86952 4.99100i 0.528425 0.383923i
\(170\) 0.0792301 0.243845i 0.00607667 0.0187021i
\(171\) −0.495524 + 1.52507i −0.0378937 + 0.116625i
\(172\) 8.12364 5.90217i 0.619422 0.450036i
\(173\) −0.717302 0.521150i −0.0545355 0.0396223i 0.560184 0.828369i \(-0.310731\pi\)
−0.614719 + 0.788746i \(0.710731\pi\)
\(174\) 1.06137 + 3.26658i 0.0804626 + 0.247638i
\(175\) 8.69423 0.657222
\(176\) 1.85984 2.74609i 0.140191 0.206994i
\(177\) −6.63517 −0.498730
\(178\) −1.48146 4.55947i −0.111040 0.341746i
\(179\) 2.18727 + 1.58914i 0.163484 + 0.118778i 0.666519 0.745488i \(-0.267783\pi\)
−0.503035 + 0.864266i \(0.667783\pi\)
\(180\) −0.152872 + 0.111068i −0.0113944 + 0.00827850i
\(181\) 4.95861 15.2610i 0.368571 1.13434i −0.579144 0.815225i \(-0.696613\pi\)
0.947715 0.319118i \(-0.103387\pi\)
\(182\) 1.14415 3.52133i 0.0848099 0.261018i
\(183\) 5.00235 3.63442i 0.369784 0.268664i
\(184\) 5.58623 + 4.05863i 0.411822 + 0.299206i
\(185\) 0.0744328 + 0.229080i 0.00547240 + 0.0168423i
\(186\) −2.42180 −0.177575
\(187\) 4.04666 5.97496i 0.295921 0.436933i
\(188\) −6.09479 −0.444508
\(189\) −2.93128 9.02154i −0.213219 0.656221i
\(190\) −0.0953332 0.0692636i −0.00691620 0.00502491i
\(191\) 18.9608 13.7758i 1.37195 0.996783i 0.374373 0.927278i \(-0.377858\pi\)
0.997582 0.0695052i \(-0.0221420\pi\)
\(192\) −0.365170 + 1.12388i −0.0263539 + 0.0811089i
\(193\) 2.56418 7.89174i 0.184574 0.568060i −0.815367 0.578944i \(-0.803465\pi\)
0.999941 + 0.0108849i \(0.00346483\pi\)
\(194\) 9.04069 6.56845i 0.649084 0.471587i
\(195\) −0.239215 0.173800i −0.0171305 0.0124460i
\(196\) −1.22357 3.76575i −0.0873977 0.268982i
\(197\) 25.7155 1.83215 0.916077 0.401003i \(-0.131338\pi\)
0.916077 + 0.401003i \(0.131338\pi\)
\(198\) −5.00107 + 1.80952i −0.355411 + 0.128597i
\(199\) 7.28088 0.516128 0.258064 0.966128i \(-0.416915\pi\)
0.258064 + 0.966128i \(0.416915\pi\)
\(200\) 1.54079 + 4.74208i 0.108951 + 0.335315i
\(201\) −13.3221 9.67905i −0.939667 0.682708i
\(202\) 2.74514 1.99446i 0.193148 0.140330i
\(203\) −1.56612 + 4.82002i −0.109920 + 0.338299i
\(204\) −0.794541 + 2.44534i −0.0556290 + 0.171208i
\(205\) 0.0586521 0.0426133i 0.00409644 0.00297624i
\(206\) 14.3204 + 10.4044i 0.997751 + 0.724908i
\(207\) −3.42158 10.5305i −0.237816 0.731922i
\(208\) 2.12340 0.147231
\(209\) −2.03696 2.61740i −0.140900 0.181049i
\(210\) 0.242811 0.0167555
\(211\) 3.03706 + 9.34710i 0.209080 + 0.643481i 0.999521 + 0.0309432i \(0.00985111\pi\)
−0.790442 + 0.612537i \(0.790149\pi\)
\(212\) 7.42361 + 5.39356i 0.509855 + 0.370432i
\(213\) −8.77038 + 6.37205i −0.600936 + 0.436606i
\(214\) 0.159763 0.491699i 0.0109212 0.0336119i
\(215\) 0.365647 1.12535i 0.0249369 0.0767479i
\(216\) 4.40112 3.19760i 0.299458 0.217569i
\(217\) −2.89102 2.10045i −0.196256 0.142588i
\(218\) 2.45462 + 7.55456i 0.166248 + 0.511659i
\(219\) −15.8996 −1.07439
\(220\) −0.0128993 0.390613i −0.000869674 0.0263351i
\(221\) 4.62011 0.310782
\(222\) −0.746432 2.29728i −0.0500972 0.154183i
\(223\) −1.21763 0.884658i −0.0815383 0.0592411i 0.546269 0.837610i \(-0.316048\pi\)
−0.627808 + 0.778369i \(0.716048\pi\)
\(224\) −1.41067 + 1.02491i −0.0942546 + 0.0684800i
\(225\) 2.47074 7.60416i 0.164716 0.506944i
\(226\) 4.99378 15.3693i 0.332182 1.02235i
\(227\) −0.204927 + 0.148888i −0.0136015 + 0.00988206i −0.594565 0.804047i \(-0.702676\pi\)
0.580964 + 0.813929i \(0.302676\pi\)
\(228\) 0.956027 + 0.694595i 0.0633145 + 0.0460006i
\(229\) −2.70334 8.32002i −0.178642 0.549803i 0.821139 0.570728i \(-0.193339\pi\)
−0.999781 + 0.0209252i \(0.993339\pi\)
\(230\) 0.813669 0.0536518
\(231\) 6.56573 + 1.89617i 0.431993 + 0.124759i
\(232\) −2.90652 −0.190823
\(233\) 3.81895 + 11.7535i 0.250188 + 0.769998i 0.994740 + 0.102434i \(0.0326631\pi\)
−0.744552 + 0.667564i \(0.767337\pi\)
\(234\) −2.75468 2.00139i −0.180079 0.130835i
\(235\) −0.581036 + 0.422147i −0.0379026 + 0.0275378i
\(236\) 1.73509 5.34006i 0.112945 0.347608i
\(237\) 1.99942 6.15359i 0.129876 0.399718i
\(238\) −3.06936 + 2.23002i −0.198957 + 0.144551i
\(239\) −15.5530 11.2999i −1.00604 0.730929i −0.0426635 0.999089i \(-0.513584\pi\)
−0.963374 + 0.268160i \(0.913584\pi\)
\(240\) 0.0430310 + 0.132436i 0.00277764 + 0.00854870i
\(241\) 19.1933 1.23635 0.618176 0.786040i \(-0.287872\pi\)
0.618176 + 0.786040i \(0.287872\pi\)
\(242\) 2.70158 10.6631i 0.173664 0.685449i
\(243\) −14.4083 −0.924290
\(244\) 1.61691 + 4.97634i 0.103512 + 0.318577i
\(245\) −0.377477 0.274253i −0.0241161 0.0175214i
\(246\) −0.588179 + 0.427337i −0.0375010 + 0.0272460i
\(247\) 0.656165 2.01947i 0.0417508 0.128496i
\(248\) 0.633297 1.94909i 0.0402144 0.123767i
\(249\) 9.05122 6.57609i 0.573598 0.416743i
\(250\) 0.952008 + 0.691675i 0.0602103 + 0.0437453i
\(251\) −2.70895 8.33729i −0.170987 0.526245i 0.828440 0.560078i \(-0.189229\pi\)
−0.999428 + 0.0338325i \(0.989229\pi\)
\(252\) 2.79609 0.176137
\(253\) 22.0020 + 6.35413i 1.38325 + 0.399481i
\(254\) −2.77979 −0.174419
\(255\) 0.0936273 + 0.288155i 0.00586317 + 0.0180450i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −20.4386 + 14.8495i −1.27493 + 0.926288i −0.999387 0.0350021i \(-0.988856\pi\)
−0.275539 + 0.961290i \(0.588856\pi\)
\(258\) −3.66681 + 11.2853i −0.228285 + 0.702590i
\(259\) 1.10140 3.38977i 0.0684379 0.210630i
\(260\) 0.202430 0.147074i 0.0125542 0.00912115i
\(261\) 3.77063 + 2.73952i 0.233396 + 0.169572i
\(262\) 3.11349 + 9.58235i 0.192352 + 0.591999i
\(263\) −19.1737 −1.18230 −0.591149 0.806562i \(-0.701326\pi\)
−0.591149 + 0.806562i \(0.701326\pi\)
\(264\) 0.129358 + 3.91717i 0.00796144 + 0.241085i
\(265\) 1.08129 0.0664234
\(266\) 0.538830 + 1.65835i 0.0330378 + 0.101680i
\(267\) 4.58330 + 3.32996i 0.280493 + 0.203790i
\(268\) 11.2735 8.19069i 0.688639 0.500326i
\(269\) 2.55591 7.86628i 0.155836 0.479615i −0.842408 0.538840i \(-0.818863\pi\)
0.998245 + 0.0592245i \(0.0188628\pi\)
\(270\) 0.198095 0.609675i 0.0120557 0.0371036i
\(271\) 7.35162 5.34126i 0.446579 0.324459i −0.341665 0.939822i \(-0.610991\pi\)
0.788244 + 0.615363i \(0.210991\pi\)
\(272\) −1.76027 1.27891i −0.106732 0.0775453i
\(273\) 1.35206 + 4.16120i 0.0818302 + 0.251847i
\(274\) 0.481832 0.0291085
\(275\) 10.1565 + 13.0507i 0.612461 + 0.786984i
\(276\) −8.15970 −0.491156
\(277\) −1.41257 4.34743i −0.0848729 0.261212i 0.899610 0.436695i \(-0.143851\pi\)
−0.984482 + 0.175483i \(0.943851\pi\)
\(278\) 16.0011 + 11.6255i 0.959683 + 0.697250i
\(279\) −2.65868 + 1.93164i −0.159171 + 0.115644i
\(280\) −0.0634948 + 0.195417i −0.00379454 + 0.0116784i
\(281\) −0.380386 + 1.17071i −0.0226920 + 0.0698386i −0.961761 0.273889i \(-0.911690\pi\)
0.939069 + 0.343728i \(0.111690\pi\)
\(282\) 5.82678 4.23341i 0.346980 0.252096i
\(283\) −21.3806 15.5339i −1.27095 0.923397i −0.271708 0.962380i \(-0.587588\pi\)
−0.999240 + 0.0389825i \(0.987588\pi\)
\(284\) −2.83485 8.72478i −0.168218 0.517720i
\(285\) 0.139251 0.00824854
\(286\) 6.62234 2.39613i 0.391587 0.141686i
\(287\) −1.07277 −0.0633239
\(288\) 0.495524 + 1.52507i 0.0291990 + 0.0898654i
\(289\) 9.92328 + 7.20969i 0.583722 + 0.424099i
\(290\) −0.277088 + 0.201316i −0.0162712 + 0.0118217i
\(291\) −4.08074 + 12.5592i −0.239217 + 0.736235i
\(292\) 4.15772 12.7961i 0.243312 0.748837i
\(293\) −5.10406 + 3.70832i −0.298183 + 0.216642i −0.726809 0.686839i \(-0.758998\pi\)
0.428627 + 0.903482i \(0.358998\pi\)
\(294\) 3.78544 + 2.75028i 0.220771 + 0.160400i
\(295\) −0.204460 0.629264i −0.0119041 0.0366371i
\(296\) 2.04407 0.118809
\(297\) 10.1177 14.9389i 0.587088 0.866845i
\(298\) −5.36868 −0.310999
\(299\) 4.53080 + 13.9444i 0.262023 + 0.806423i
\(300\) −4.76686 3.46333i −0.275215 0.199955i
\(301\) −14.1651 + 10.2915i −0.816463 + 0.593195i
\(302\) −6.42363 + 19.7699i −0.369638 + 1.13763i
\(303\) −1.23909 + 3.81352i −0.0711838 + 0.219081i
\(304\) −0.809017 + 0.587785i −0.0464003 + 0.0337118i
\(305\) 0.498824 + 0.362417i 0.0285626 + 0.0207519i
\(306\) 1.07817 + 3.31826i 0.0616347 + 0.189692i
\(307\) −18.2913 −1.04394 −0.521971 0.852963i \(-0.674803\pi\)
−0.521971 + 0.852963i \(0.674803\pi\)
\(308\) −3.24298 + 4.78832i −0.184786 + 0.272840i
\(309\) −20.9175 −1.18996
\(310\) −0.0746267 0.229677i −0.00423851 0.0130448i
\(311\) 23.3956 + 16.9979i 1.32665 + 0.963864i 0.999824 + 0.0187781i \(0.00597761\pi\)
0.326822 + 0.945086i \(0.394022\pi\)
\(312\) −2.03002 + 1.47490i −0.114927 + 0.0834997i
\(313\) 5.65605 17.4075i 0.319699 0.983932i −0.654078 0.756427i \(-0.726943\pi\)
0.973777 0.227505i \(-0.0730567\pi\)
\(314\) −2.08146 + 6.40607i −0.117463 + 0.361515i
\(315\) 0.266560 0.193668i 0.0150190 0.0109119i
\(316\) 4.42963 + 3.21831i 0.249186 + 0.181044i
\(317\) 6.96560 + 21.4379i 0.391227 + 1.20407i 0.931861 + 0.362816i \(0.118184\pi\)
−0.540634 + 0.841258i \(0.681816\pi\)
\(318\) −10.8435 −0.608074
\(319\) −9.06472 + 3.27985i −0.507527 + 0.183636i
\(320\) −0.117838 −0.00658736
\(321\) 0.188794 + 0.581049i 0.0105375 + 0.0324310i
\(322\) −9.74065 7.07700i −0.542825 0.394386i
\(323\) −1.76027 + 1.27891i −0.0979439 + 0.0711604i
\(324\) −0.499982 + 1.53879i −0.0277768 + 0.0854882i
\(325\) −3.27171 + 10.0693i −0.181482 + 0.558544i
\(326\) 3.66362 2.66177i 0.202909 0.147422i
\(327\) −7.59404 5.51739i −0.419951 0.305113i
\(328\) −0.190117 0.585121i −0.0104975 0.0323079i
\(329\) 10.6274 0.585908
\(330\) 0.283650 + 0.364477i 0.0156144 + 0.0200638i
\(331\) 8.07958 0.444094 0.222047 0.975036i \(-0.428726\pi\)
0.222047 + 0.975036i \(0.428726\pi\)
\(332\) 2.92563 + 9.00415i 0.160565 + 0.494167i
\(333\) −2.65177 1.92662i −0.145316 0.105578i
\(334\) −4.01602 + 2.91781i −0.219747 + 0.159655i
\(335\) 0.507423 1.56169i 0.0277235 0.0853242i
\(336\) 0.636743 1.95969i 0.0347372 0.106910i
\(337\) −25.5610 + 18.5711i −1.39239 + 1.01163i −0.396796 + 0.917907i \(0.629878\pi\)
−0.995598 + 0.0937270i \(0.970122\pi\)
\(338\) −6.86952 4.99100i −0.373653 0.271475i
\(339\) 5.90123 + 18.1621i 0.320511 + 0.986431i
\(340\) −0.256394 −0.0139049
\(341\) −0.224340 6.79336i −0.0121487 0.367881i
\(342\) 1.60355 0.0867101
\(343\) 5.90533 + 18.1747i 0.318858 + 0.981343i
\(344\) −8.12364 5.90217i −0.437997 0.318224i
\(345\) −0.777890 + 0.565170i −0.0418802 + 0.0304277i
\(346\) −0.273985 + 0.843239i −0.0147295 + 0.0453328i
\(347\) −8.38797 + 25.8155i −0.450290 + 1.38585i 0.426287 + 0.904588i \(0.359821\pi\)
−0.876577 + 0.481262i \(0.840179\pi\)
\(348\) 2.77872 2.01885i 0.148955 0.108222i
\(349\) 7.66322 + 5.56766i 0.410203 + 0.298030i 0.773684 0.633572i \(-0.218412\pi\)
−0.363481 + 0.931602i \(0.618412\pi\)
\(350\) −2.68667 8.26871i −0.143608 0.441981i
\(351\) 11.5514 0.616571
\(352\) −3.18641 0.920226i −0.169836 0.0490482i
\(353\) 12.0966 0.643837 0.321918 0.946767i \(-0.395672\pi\)
0.321918 + 0.946767i \(0.395672\pi\)
\(354\) 2.05038 + 6.31043i 0.108977 + 0.335395i
\(355\) −0.874565 0.635409i −0.0464171 0.0337240i
\(356\) −3.87851 + 2.81790i −0.205561 + 0.149349i
\(357\) 1.38543 4.26392i 0.0733248 0.225671i
\(358\) 0.835462 2.57129i 0.0441556 0.135897i
\(359\) 6.46948 4.70036i 0.341446 0.248075i −0.403825 0.914836i \(-0.632320\pi\)
0.745272 + 0.666761i \(0.232320\pi\)
\(360\) 0.152872 + 0.111068i 0.00805704 + 0.00585378i
\(361\) 0.309017 + 0.951057i 0.0162641 + 0.0500556i
\(362\) −16.0464 −0.843380
\(363\) 4.82374 + 12.0707i 0.253181 + 0.633548i
\(364\) −3.70254 −0.194066
\(365\) −0.489938 1.50787i −0.0256445 0.0789258i
\(366\) −5.00235 3.63442i −0.261477 0.189974i
\(367\) −1.05669 + 0.767732i −0.0551589 + 0.0400753i −0.615023 0.788509i \(-0.710853\pi\)
0.559864 + 0.828584i \(0.310853\pi\)
\(368\) 2.13375 6.56701i 0.111229 0.342329i
\(369\) −0.304863 + 0.938271i −0.0158705 + 0.0488444i
\(370\) 0.194867 0.141580i 0.0101307 0.00736037i
\(371\) −12.9445 9.40470i −0.672043 0.488268i
\(372\) 0.748377 + 2.30327i 0.0388015 + 0.119419i
\(373\) 11.9113 0.616744 0.308372 0.951266i \(-0.400216\pi\)
0.308372 + 0.951266i \(0.400216\pi\)
\(374\) −6.93302 2.00224i −0.358498 0.103533i
\(375\) −1.39058 −0.0718092
\(376\) 1.88339 + 5.79649i 0.0971286 + 0.298931i
\(377\) −4.99301 3.62763i −0.257153 0.186833i
\(378\) −7.67418 + 5.57562i −0.394717 + 0.286779i
\(379\) −4.83050 + 14.8668i −0.248126 + 0.763654i 0.746980 + 0.664846i \(0.231503\pi\)
−0.995107 + 0.0988079i \(0.968497\pi\)
\(380\) −0.0364140 + 0.112071i −0.00186800 + 0.00574912i
\(381\) 2.65755 1.93083i 0.136151 0.0989192i
\(382\) −18.9608 13.7758i −0.970118 0.704832i
\(383\) −3.81548 11.7428i −0.194962 0.600031i −0.999977 0.00677661i \(-0.997843\pi\)
0.805015 0.593254i \(-0.202157\pi\)
\(384\) 1.18171 0.0603041
\(385\) 0.0224924 + 0.681107i 0.00114632 + 0.0347124i
\(386\) −8.29786 −0.422350
\(387\) 4.97574 + 15.3138i 0.252931 + 0.778442i
\(388\) −9.04069 6.56845i −0.458971 0.333462i
\(389\) 12.2598 8.90730i 0.621599 0.451618i −0.231881 0.972744i \(-0.574488\pi\)
0.853480 + 0.521126i \(0.174488\pi\)
\(390\) −0.0913719 + 0.281214i −0.00462679 + 0.0142398i
\(391\) 4.64264 14.2886i 0.234788 0.722604i
\(392\) −3.20334 + 2.32736i −0.161793 + 0.117550i
\(393\) −9.63243 6.99837i −0.485892 0.353021i
\(394\) −7.94653 24.4569i −0.400340 1.23212i
\(395\) 0.645202 0.0324637
\(396\) 3.26637 + 4.19713i 0.164141 + 0.210914i
\(397\) −1.08003 −0.0542050 −0.0271025 0.999633i \(-0.508628\pi\)
−0.0271025 + 0.999633i \(0.508628\pi\)
\(398\) −2.24992 6.92453i −0.112778 0.347095i
\(399\) −1.66701 1.21116i −0.0834551 0.0606337i
\(400\) 4.03385 2.93076i 0.201693 0.146538i
\(401\) 7.06012 21.7288i 0.352566 1.08509i −0.604842 0.796346i \(-0.706764\pi\)
0.957408 0.288740i \(-0.0932363\pi\)
\(402\) −5.08858 + 15.6610i −0.253795 + 0.781102i
\(403\) 3.52058 2.55785i 0.175372 0.127415i
\(404\) −2.74514 1.99446i −0.136576 0.0992282i
\(405\) 0.0589171 + 0.181328i 0.00292761 + 0.00901027i
\(406\) 5.06807 0.251524
\(407\) 6.37494 2.30661i 0.315994 0.114335i
\(408\) 2.57119 0.127293
\(409\) 5.09464 + 15.6797i 0.251914 + 0.775311i 0.994422 + 0.105474i \(0.0336359\pi\)
−0.742508 + 0.669837i \(0.766364\pi\)
\(410\) −0.0586521 0.0426133i −0.00289662 0.00210452i
\(411\) −0.460644 + 0.334678i −0.0227219 + 0.0165084i
\(412\) 5.46991 16.8347i 0.269483 0.829384i
\(413\) −3.02546 + 9.31140i −0.148873 + 0.458184i
\(414\) −8.95780 + 6.50822i −0.440252 + 0.319862i
\(415\) 0.902570 + 0.655755i 0.0443054 + 0.0321898i
\(416\) −0.656165 2.01947i −0.0321711 0.0990126i
\(417\) −23.3725 −1.14456
\(418\) −1.85984 + 2.74609i −0.0909678 + 0.134315i
\(419\) 4.02294 0.196534 0.0982668 0.995160i \(-0.468670\pi\)
0.0982668 + 0.995160i \(0.468670\pi\)
\(420\) −0.0750327 0.230927i −0.00366122 0.0112681i
\(421\) 7.52733 + 5.46893i 0.366860 + 0.266539i 0.755908 0.654678i \(-0.227196\pi\)
−0.389048 + 0.921218i \(0.627196\pi\)
\(422\) 7.95111 5.77682i 0.387054 0.281211i
\(423\) 3.02011 9.29496i 0.146843 0.451936i
\(424\) 2.83556 8.72697i 0.137707 0.423819i
\(425\) 8.77689 6.37679i 0.425742 0.309320i
\(426\) 8.77038 + 6.37205i 0.424926 + 0.308727i
\(427\) −2.81939 8.67718i −0.136440 0.419918i
\(428\) −0.517003 −0.0249903
\(429\) −4.66680 + 6.89061i −0.225315 + 0.332682i
\(430\) −1.18326 −0.0570618
\(431\) −0.789653 2.43030i −0.0380362 0.117064i 0.930236 0.366963i \(-0.119602\pi\)
−0.968272 + 0.249899i \(0.919602\pi\)
\(432\) −4.40112 3.19760i −0.211749 0.153845i
\(433\) −31.1684 + 22.6452i −1.49786 + 1.08826i −0.526636 + 0.850091i \(0.676547\pi\)
−0.971224 + 0.238168i \(0.923453\pi\)
\(434\) −1.10427 + 3.39860i −0.0530068 + 0.163138i
\(435\) 0.125071 0.384928i 0.00599668 0.0184559i
\(436\) 6.42629 4.66897i 0.307763 0.223603i
\(437\) −5.58623 4.05863i −0.267226 0.194151i
\(438\) 4.91323 + 15.1214i 0.234763 + 0.722527i
\(439\) 34.2110 1.63280 0.816401 0.577485i \(-0.195966\pi\)
0.816401 + 0.577485i \(0.195966\pi\)
\(440\) −0.367509 + 0.132974i −0.0175203 + 0.00633928i
\(441\) 6.34933 0.302349
\(442\) −1.42769 4.39398i −0.0679083 0.209000i
\(443\) −22.9403 16.6671i −1.08992 0.791876i −0.110538 0.993872i \(-0.535257\pi\)
−0.979386 + 0.201996i \(0.935257\pi\)
\(444\) −1.95418 + 1.41980i −0.0927415 + 0.0673806i
\(445\) −0.174573 + 0.537280i −0.00827554 + 0.0254695i
\(446\) −0.465092 + 1.43141i −0.0220228 + 0.0677791i
\(447\) 5.13260 3.72905i 0.242764 0.176378i
\(448\) 1.41067 + 1.02491i 0.0666481 + 0.0484227i
\(449\) 6.09749 + 18.7661i 0.287758 + 0.885629i 0.985558 + 0.169336i \(0.0541625\pi\)
−0.697800 + 0.716293i \(0.745838\pi\)
\(450\) −7.99548 −0.376911
\(451\) −1.25321 1.61031i −0.0590111 0.0758266i
\(452\) −16.1602 −0.760113
\(453\) −7.59089 23.3624i −0.356651 1.09766i
\(454\) 0.204927 + 0.148888i 0.00961771 + 0.00698767i
\(455\) −0.352975 + 0.256451i −0.0165477 + 0.0120226i
\(456\) 0.365170 1.12388i 0.0171007 0.0526304i
\(457\) 2.69412 8.29164i 0.126025 0.387866i −0.868061 0.496457i \(-0.834634\pi\)
0.994087 + 0.108591i \(0.0346339\pi\)
\(458\) −7.07743 + 5.14206i −0.330707 + 0.240273i
\(459\) −9.57600 6.95737i −0.446969 0.324742i
\(460\) −0.251438 0.773845i −0.0117233 0.0360807i
\(461\) 10.8220 0.504033 0.252016 0.967723i \(-0.418906\pi\)
0.252016 + 0.967723i \(0.418906\pi\)
\(462\) −0.225560 6.83032i −0.0104940 0.317775i
\(463\) 38.6978 1.79844 0.899220 0.437496i \(-0.144135\pi\)
0.899220 + 0.437496i \(0.144135\pi\)
\(464\) 0.898165 + 2.76427i 0.0416963 + 0.128328i
\(465\) 0.230878 + 0.167743i 0.0107067 + 0.00777887i
\(466\) 9.99814 7.26407i 0.463155 0.336502i
\(467\) 2.02104 6.22011i 0.0935224 0.287832i −0.893343 0.449375i \(-0.851647\pi\)
0.986866 + 0.161542i \(0.0516469\pi\)
\(468\) −1.05219 + 3.23832i −0.0486377 + 0.149691i
\(469\) −19.6575 + 14.2820i −0.907699 + 0.659482i
\(470\) 0.581036 + 0.422147i 0.0268012 + 0.0194722i
\(471\) −2.45969 7.57015i −0.113337 0.348814i
\(472\) −5.61487 −0.258445
\(473\) −31.9959 9.24033i −1.47117 0.424871i
\(474\) −6.47027 −0.297189
\(475\) −1.54079 4.74208i −0.0706965 0.217581i
\(476\) 3.06936 + 2.23002i 0.140684 + 0.102213i
\(477\) −11.9041 + 8.64885i −0.545052 + 0.396004i
\(478\) −5.94071 + 18.2836i −0.271722 + 0.836273i
\(479\) −10.2111 + 31.4264i −0.466556 + 1.43591i 0.390459 + 0.920620i \(0.372316\pi\)
−0.857015 + 0.515291i \(0.827684\pi\)
\(480\) 0.112657 0.0818499i 0.00514205 0.00373592i
\(481\) 3.51143 + 2.55120i 0.160107 + 0.116325i
\(482\) −5.93107 18.2539i −0.270153 0.831444i
\(483\) 14.2280 0.647395
\(484\) −10.9760 + 0.725723i −0.498911 + 0.0329874i
\(485\) −1.31683 −0.0597943
\(486\) 4.45240 + 13.7031i 0.201965 + 0.621584i
\(487\) −5.17764 3.76178i −0.234621 0.170462i 0.464262 0.885698i \(-0.346320\pi\)
−0.698884 + 0.715235i \(0.746320\pi\)
\(488\) 4.23312 3.07554i 0.191625 0.139223i
\(489\) −1.65366 + 5.08946i −0.0747813 + 0.230153i
\(490\) −0.144183 + 0.443750i −0.00651353 + 0.0200466i
\(491\) 23.9935 17.4323i 1.08281 0.786708i 0.104639 0.994510i \(-0.466631\pi\)
0.978171 + 0.207803i \(0.0666312\pi\)
\(492\) 0.588179 + 0.427337i 0.0265172 + 0.0192659i
\(493\) 1.95424 + 6.01452i 0.0880144 + 0.270880i
\(494\) −2.12340 −0.0955361
\(495\) 0.602102 + 0.173886i 0.0270625 + 0.00781558i
\(496\) −2.04939 −0.0920204
\(497\) 4.94310 + 15.2133i 0.221728 + 0.682410i
\(498\) −9.05122 6.57609i −0.405595 0.294682i
\(499\) 8.39708 6.10083i 0.375905 0.273111i −0.383750 0.923437i \(-0.625368\pi\)
0.759655 + 0.650326i \(0.225368\pi\)
\(500\) 0.363635 1.11915i 0.0162622 0.0500500i
\(501\) 1.81273 5.57901i 0.0809868 0.249252i
\(502\) −7.09212 + 5.15273i −0.316537 + 0.229978i
\(503\) −4.30292 3.12625i −0.191858 0.139393i 0.487710 0.873006i \(-0.337832\pi\)
−0.679567 + 0.733613i \(0.737832\pi\)
\(504\) −0.864040 2.65924i −0.0384874 0.118452i
\(505\) −0.399847 −0.0177930
\(506\) −0.755862 22.8887i −0.0336021 1.01753i
\(507\) 10.0342 0.445633
\(508\) 0.859002 + 2.64374i 0.0381120 + 0.117297i
\(509\) −17.5568 12.7558i −0.778193 0.565391i 0.126243 0.991999i \(-0.459708\pi\)
−0.904436 + 0.426609i \(0.859708\pi\)
\(510\) 0.245120 0.178090i 0.0108541 0.00788595i
\(511\) −7.24976 + 22.3125i −0.320711 + 0.987046i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) −4.40112 + 3.19760i −0.194314 + 0.141178i
\(514\) 20.4386 + 14.8495i 0.901509 + 0.654984i
\(515\) −0.644565 1.98377i −0.0284029 0.0874153i
\(516\) 11.8660 0.522373
\(517\) 12.4148 + 15.9525i 0.546004 + 0.701590i
\(518\) −3.56422 −0.156603
\(519\) −0.323772 0.996468i −0.0142120 0.0437401i
\(520\) −0.202430 0.147074i −0.00887715 0.00644962i
\(521\) −12.6096 + 9.16142i −0.552437 + 0.401369i −0.828683 0.559718i \(-0.810910\pi\)
0.276246 + 0.961087i \(0.410910\pi\)
\(522\) 1.44025 4.43264i 0.0630381 0.194011i
\(523\) −1.07576 + 3.31086i −0.0470399 + 0.144774i −0.971818 0.235734i \(-0.924251\pi\)
0.924778 + 0.380508i \(0.124251\pi\)
\(524\) 8.15123 5.92222i 0.356088 0.258713i
\(525\) 8.31192 + 6.03897i 0.362762 + 0.263562i
\(526\) 5.92499 + 18.2352i 0.258342 + 0.795094i
\(527\) −4.45909 −0.194241
\(528\) 3.68548 1.33350i 0.160390 0.0580331i
\(529\) 24.6785 1.07298
\(530\) −0.334138 1.02837i −0.0145140 0.0446696i
\(531\) 7.28417 + 5.29226i 0.316106 + 0.229664i
\(532\) 1.41067 1.02491i 0.0611605 0.0444357i
\(533\) 0.403694 1.24244i 0.0174859 0.0538162i
\(534\) 1.75066 5.38799i 0.0757586 0.233161i
\(535\) −0.0492876 + 0.0358095i −0.00213089 + 0.00154818i
\(536\) −11.2735 8.19069i −0.486942 0.353784i
\(537\) 0.987278 + 3.03853i 0.0426042 + 0.131122i
\(538\) −8.27109 −0.356592
\(539\) −7.36413 + 10.8733i −0.317196 + 0.468345i
\(540\) −0.641050 −0.0275864
\(541\) −0.649898 2.00018i −0.0279413 0.0859945i 0.936113 0.351698i \(-0.114396\pi\)
−0.964055 + 0.265704i \(0.914396\pi\)
\(542\) −7.35162 5.34126i −0.315779 0.229427i
\(543\) 15.3408 11.1457i 0.658337 0.478309i
\(544\) −0.672362 + 2.06932i −0.0288273 + 0.0887213i
\(545\) 0.289249 0.890216i 0.0123901 0.0381327i
\(546\) 3.53973 2.57176i 0.151486 0.110061i
\(547\) −8.19322 5.95272i −0.350317 0.254520i 0.398685 0.917088i \(-0.369467\pi\)
−0.749002 + 0.662568i \(0.769467\pi\)
\(548\) −0.148894 0.458249i −0.00636045 0.0195754i
\(549\) −8.39046 −0.358096
\(550\) 9.27338 13.6923i 0.395418 0.583842i
\(551\) 2.90652 0.123822
\(552\) 2.52148 + 7.76033i 0.107322 + 0.330302i
\(553\) −7.72389 5.61173i −0.328453 0.238635i
\(554\) −3.69815 + 2.68686i −0.157119 + 0.114154i
\(555\) −0.0879583 + 0.270708i −0.00373362 + 0.0114909i
\(556\) 6.11188 18.8104i 0.259201 0.797740i
\(557\) −0.494297 + 0.359127i −0.0209440 + 0.0152167i −0.598208 0.801341i \(-0.704120\pi\)
0.577264 + 0.816558i \(0.304120\pi\)
\(558\) 2.65868 + 1.93164i 0.112551 + 0.0817729i
\(559\) −6.58880 20.2782i −0.278676 0.857678i
\(560\) 0.205473 0.00868284
\(561\) 8.01890 2.90144i 0.338558 0.122499i
\(562\) 1.23096 0.0519248
\(563\) −8.51870 26.2179i −0.359020 1.10495i −0.953642 0.300945i \(-0.902698\pi\)
0.594621 0.804006i \(-0.297302\pi\)
\(564\) −5.82678 4.23341i −0.245352 0.178259i
\(565\) −1.54061 + 1.11932i −0.0648138 + 0.0470900i
\(566\) −8.16668 + 25.1345i −0.343271 + 1.05648i
\(567\) 0.871814 2.68317i 0.0366127 0.112682i
\(568\) −7.42174 + 5.39221i −0.311409 + 0.226252i
\(569\) −17.3837 12.6300i −0.728765 0.529478i 0.160408 0.987051i \(-0.448719\pi\)
−0.889172 + 0.457572i \(0.848719\pi\)
\(570\) −0.0430310 0.132436i −0.00180237 0.00554713i
\(571\) 29.1419 1.21955 0.609775 0.792575i \(-0.291260\pi\)
0.609775 + 0.792575i \(0.291260\pi\)
\(572\) −4.32527 5.55778i −0.180849 0.232382i
\(573\) 27.6956 1.15700
\(574\) 0.331506 + 1.02027i 0.0138368 + 0.0425852i
\(575\) 27.8536 + 20.2368i 1.16157 + 0.843933i
\(576\) 1.29730 0.942543i 0.0540541 0.0392726i
\(577\) −11.1128 + 34.2016i −0.462631 + 1.42383i 0.399306 + 0.916818i \(0.369251\pi\)
−0.861938 + 0.507014i \(0.830749\pi\)
\(578\) 3.79036 11.6655i 0.157658 0.485222i
\(579\) 7.93298 5.76365i 0.329684 0.239529i
\(580\) 0.277088 + 0.201316i 0.0115055 + 0.00835920i
\(581\) −5.10138 15.7004i −0.211641 0.651364i
\(582\) 13.2056 0.547388
\(583\) −1.00447 30.4170i −0.0416010 1.25974i
\(584\) −13.4547 −0.556757
\(585\) 0.123989 + 0.381598i 0.00512630 + 0.0157771i
\(586\) 5.10406 + 3.70832i 0.210847 + 0.153189i
\(587\) −32.1187 + 23.3356i −1.32568 + 0.963162i −0.325836 + 0.945426i \(0.605646\pi\)
−0.999843 + 0.0177358i \(0.994354\pi\)
\(588\) 1.44591 4.45005i 0.0596283 0.183517i
\(589\) −0.633297 + 1.94909i −0.0260946 + 0.0803108i
\(590\) −0.535284 + 0.388906i −0.0220373 + 0.0160110i
\(591\) 24.5847 + 17.8618i 1.01128 + 0.734738i
\(592\) −0.631651 1.94402i −0.0259607 0.0798989i
\(593\) −16.7269 −0.686892 −0.343446 0.939172i \(-0.611594\pi\)
−0.343446 + 0.939172i \(0.611594\pi\)
\(594\) −17.3343 5.00611i −0.711236 0.205403i
\(595\) 0.447071 0.0183281
\(596\) 1.65901 + 5.10592i 0.0679558 + 0.209146i
\(597\) 6.96072 + 5.05726i 0.284883 + 0.206980i
\(598\) 11.8618 8.61808i 0.485064 0.352420i
\(599\) 13.4287 41.3293i 0.548682 1.68867i −0.163388 0.986562i \(-0.552242\pi\)
0.712070 0.702108i \(-0.247758\pi\)
\(600\) −1.82078 + 5.60378i −0.0743330 + 0.228773i
\(601\) 4.87881 3.54467i 0.199011 0.144590i −0.483817 0.875169i \(-0.660750\pi\)
0.682828 + 0.730579i \(0.260750\pi\)
\(602\) 14.1651 + 10.2915i 0.577326 + 0.419452i
\(603\) 6.90504 + 21.2515i 0.281195 + 0.865430i
\(604\) 20.7873 0.845823
\(605\) −0.996114 + 0.829426i −0.0404978 + 0.0337209i
\(606\) 4.00977 0.162886
\(607\) 13.4942 + 41.5307i 0.547711 + 1.68568i 0.714456 + 0.699680i \(0.246674\pi\)
−0.166745 + 0.986000i \(0.553326\pi\)
\(608\) 0.809017 + 0.587785i 0.0328100 + 0.0238378i
\(609\) −4.84521 + 3.52025i −0.196338 + 0.142648i
\(610\) 0.190534 0.586403i 0.00771449 0.0237428i
\(611\) −3.99919 + 12.3082i −0.161790 + 0.497938i
\(612\) 2.82268 2.05079i 0.114100 0.0828985i
\(613\) 17.8057 + 12.9366i 0.719166 + 0.522505i 0.886118 0.463461i \(-0.153392\pi\)
−0.166952 + 0.985965i \(0.553392\pi\)
\(614\) 5.65233 + 17.3961i 0.228110 + 0.702049i
\(615\) 0.0856720 0.00345463
\(616\) 5.55610 + 1.60459i 0.223862 + 0.0646507i
\(617\) 2.73799 0.110227 0.0551137 0.998480i \(-0.482448\pi\)
0.0551137 + 0.998480i \(0.482448\pi\)
\(618\) 6.46388 + 19.8938i 0.260015 + 0.800245i
\(619\) −17.2900 12.5619i −0.694942 0.504905i 0.183339 0.983050i \(-0.441309\pi\)
−0.878281 + 0.478145i \(0.841309\pi\)
\(620\) −0.195375 + 0.141948i −0.00784646 + 0.00570078i
\(621\) 11.6078 35.7251i 0.465804 1.43360i
\(622\) 8.93634 27.5032i 0.358315 1.10278i
\(623\) 6.76292 4.91355i 0.270951 0.196857i
\(624\) 2.03002 + 1.47490i 0.0812660 + 0.0590432i
\(625\) 7.66112 + 23.5785i 0.306445 + 0.943140i
\(626\) −18.3034 −0.731549
\(627\) −0.129358 3.91717i −0.00516607 0.156437i
\(628\) 6.73574 0.268785
\(629\) −1.37435 4.22983i −0.0547991 0.168654i
\(630\) −0.266560 0.193668i −0.0106200 0.00771590i
\(631\) 26.0784 18.9470i 1.03816 0.754270i 0.0682371 0.997669i \(-0.478263\pi\)
0.969926 + 0.243399i \(0.0782626\pi\)
\(632\) 1.69197 5.20734i 0.0673028 0.207137i
\(633\) −3.58893 + 11.0456i −0.142647 + 0.439023i
\(634\) 18.2362 13.2494i 0.724251 0.526199i
\(635\) 0.265006 + 0.192538i 0.0105164 + 0.00764065i
\(636\) 3.35083 + 10.3128i 0.132869 + 0.408929i
\(637\) −8.40769 −0.333125
\(638\) 5.92047 + 7.60754i 0.234394 + 0.301185i
\(639\) 14.7106 0.581943
\(640\) 0.0364140 + 0.112071i 0.00143939 + 0.00442999i
\(641\) −20.7925 15.1067i −0.821255 0.596677i 0.0958166 0.995399i \(-0.469454\pi\)
−0.917072 + 0.398722i \(0.869454\pi\)
\(642\) 0.494269 0.359108i 0.0195073 0.0141729i
\(643\) −2.05507 + 6.32486i −0.0810442 + 0.249428i −0.983366 0.181634i \(-0.941861\pi\)
0.902322 + 0.431063i \(0.141861\pi\)
\(644\) −3.72060 + 11.4508i −0.146612 + 0.451226i
\(645\) 1.13123 0.821885i 0.0445420 0.0323617i
\(646\) 1.76027 + 1.27891i 0.0692568 + 0.0503180i
\(647\) −9.34865 28.7722i −0.367533 1.13115i −0.948380 0.317138i \(-0.897278\pi\)
0.580846 0.814013i \(-0.302722\pi\)
\(648\) 1.61798 0.0635602
\(649\) −17.5114 + 6.33606i −0.687382 + 0.248712i
\(650\) 10.5875 0.415276
\(651\) −1.30494 4.01618i −0.0511445 0.157407i
\(652\) −3.66362 2.66177i −0.143478 0.104243i
\(653\) −12.9982 + 9.44375i −0.508659 + 0.369562i −0.812315 0.583219i \(-0.801793\pi\)
0.303656 + 0.952782i \(0.401793\pi\)
\(654\) −2.90067 + 8.92733i −0.113425 + 0.349086i
\(655\) 0.366889 1.12917i 0.0143355 0.0441202i
\(656\) −0.497734 + 0.361625i −0.0194332 + 0.0141191i
\(657\) 17.4547 + 12.6816i 0.680973 + 0.494756i
\(658\) −3.28405 10.1073i −0.128026 0.394022i
\(659\) −8.59809 −0.334934 −0.167467 0.985878i \(-0.553559\pi\)
−0.167467 + 0.985878i \(0.553559\pi\)
\(660\) 0.258985 0.382396i 0.0100810 0.0148848i
\(661\) −24.7734 −0.963573 −0.481787 0.876289i \(-0.660012\pi\)
−0.481787 + 0.876289i \(0.660012\pi\)
\(662\) −2.49673 7.68414i −0.0970381 0.298652i
\(663\) 4.41695 + 3.20910i 0.171540 + 0.124631i
\(664\) 7.65939 5.56487i 0.297242 0.215959i
\(665\) 0.0634948 0.195417i 0.00246222 0.00757794i
\(666\) −1.01288 + 3.11734i −0.0392485 + 0.120794i
\(667\) −16.2365 + 11.7965i −0.628680 + 0.456763i
\(668\) 4.01602 + 2.91781i 0.155384 + 0.112893i
\(669\) −0.549606 1.69151i −0.0212490 0.0653977i
\(670\) −1.64206 −0.0634382
\(671\) 9.73148 14.3687i 0.375680 0.554698i
\(672\) −2.06054 −0.0794872
\(673\) −12.1070 37.2614i −0.466689 1.43632i −0.856846 0.515572i \(-0.827579\pi\)
0.390157 0.920748i \(-0.372421\pi\)
\(674\) 25.5610 + 18.5711i 0.984571 + 0.715333i
\(675\) 21.9445 15.9436i 0.844644 0.613670i
\(676\) −2.62392 + 8.07560i −0.100920 + 0.310600i
\(677\) 5.29532 16.2973i 0.203516 0.626356i −0.796256 0.604960i \(-0.793189\pi\)
0.999771 0.0213960i \(-0.00681109\pi\)
\(678\) 15.4496 11.2248i 0.593339 0.431086i
\(679\) 15.7641 + 11.4533i 0.604973 + 0.439538i
\(680\) 0.0792301 + 0.243845i 0.00303833 + 0.00935103i
\(681\) −0.299333 −0.0114705
\(682\) −6.39155 + 2.31262i −0.244745 + 0.0885550i
\(683\) 45.1219 1.72654 0.863271 0.504740i \(-0.168412\pi\)
0.863271 + 0.504740i \(0.168412\pi\)
\(684\) −0.495524 1.52507i −0.0189468 0.0583124i
\(685\) −0.0459346 0.0333734i −0.00175507 0.00127513i
\(686\) 15.4604 11.2326i 0.590279 0.428863i
\(687\) 3.19458 9.83189i 0.121881 0.375110i
\(688\) −3.10295 + 9.54991i −0.118299 + 0.364087i
\(689\) 15.7632 11.4527i 0.600532 0.436312i
\(690\) 0.777890 + 0.565170i 0.0296138 + 0.0215157i
\(691\) −2.25598 6.94318i −0.0858214 0.264131i 0.898932 0.438089i \(-0.144344\pi\)
−0.984753 + 0.173958i \(0.944344\pi\)
\(692\) 0.886634 0.0337048
\(693\) −5.69553 7.31850i −0.216355 0.278007i
\(694\) 27.1440 1.03037
\(695\) −0.720214 2.21659i −0.0273193 0.0840800i
\(696\) −2.77872 2.01885i −0.105327 0.0765245i
\(697\) −1.08297 + 0.786827i −0.0410206 + 0.0298032i
\(698\) 2.92709 9.00866i 0.110792 0.340983i
\(699\) −4.51291 + 13.8893i −0.170694 + 0.525342i
\(700\) −7.03378 + 5.11034i −0.265852 + 0.193153i
\(701\) 23.4387 + 17.0292i 0.885268 + 0.643185i 0.934640 0.355596i \(-0.115722\pi\)
−0.0493722 + 0.998780i \(0.515722\pi\)
\(702\) −3.56959 10.9861i −0.134726 0.414643i
\(703\) −2.04407 −0.0770934
\(704\) 0.109466 + 3.31482i 0.00412567 + 0.124932i
\(705\) −0.848707 −0.0319642
\(706\) −3.73805 11.5045i −0.140683 0.432979i
\(707\) 4.78667 + 3.47772i 0.180021 + 0.130793i
\(708\) 5.36797 3.90006i 0.201741 0.146573i
\(709\) 10.3751 31.9313i 0.389645 1.19920i −0.543409 0.839468i \(-0.682867\pi\)
0.933054 0.359736i \(-0.117133\pi\)
\(710\) −0.334054 + 1.02811i −0.0125368 + 0.0385844i
\(711\) −7.10313 + 5.16072i −0.266388 + 0.193542i
\(712\) 3.87851 + 2.81790i 0.145353 + 0.105605i
\(713\) −4.37289 13.4584i −0.163766 0.504020i
\(714\) −4.48335 −0.167785
\(715\) −0.797294 0.230257i −0.0298171 0.00861111i
\(716\) −2.70361 −0.101039
\(717\) −7.02022 21.6060i −0.262175 0.806891i
\(718\) −6.46948 4.70036i −0.241439 0.175416i
\(719\) −8.70969 + 6.32796i −0.324817 + 0.235993i −0.738228 0.674551i \(-0.764337\pi\)
0.413411 + 0.910544i \(0.364337\pi\)
\(720\) 0.0583917 0.179711i 0.00217613 0.00669745i
\(721\) −9.53782 + 29.3544i −0.355207 + 1.09322i
\(722\) 0.809017 0.587785i 0.0301085 0.0218751i
\(723\) 18.3494 + 13.3316i 0.682420 + 0.495807i
\(724\) 4.95861 + 15.2610i 0.184285 + 0.567172i
\(725\) −14.4923 −0.538229
\(726\) 9.98931 8.31770i 0.370738 0.308699i
\(727\) −6.94503 −0.257577 −0.128788 0.991672i \(-0.541109\pi\)
−0.128788 + 0.991672i \(0.541109\pi\)
\(728\) 1.14415 + 3.52133i 0.0424049 + 0.130509i
\(729\) −17.7016 12.8610i −0.655615 0.476332i
\(730\) −1.28268 + 0.931918i −0.0474739 + 0.0344918i
\(731\) −6.75144 + 20.7788i −0.249711 + 0.768531i
\(732\) −1.91073 + 5.88061i −0.0706225 + 0.217354i
\(733\) −23.8218 + 17.3075i −0.879878 + 0.639268i −0.933219 0.359308i \(-0.883013\pi\)
0.0533415 + 0.998576i \(0.483013\pi\)
\(734\) 1.05669 + 0.767732i 0.0390032 + 0.0283375i
\(735\) −0.170383 0.524386i −0.00628469 0.0193423i
\(736\) −6.90496 −0.254520
\(737\) −44.4020 12.8232i −1.63557 0.472348i
\(738\) 0.986557 0.0363157
\(739\) −13.0387 40.1289i −0.479635 1.47617i −0.839603 0.543201i \(-0.817212\pi\)
0.359967 0.932965i \(-0.382788\pi\)
\(740\) −0.194867 0.141580i −0.00716347 0.00520457i
\(741\) 2.03002 1.47490i 0.0745748 0.0541818i
\(742\) −4.94434 + 15.2171i −0.181513 + 0.558638i
\(743\) 9.82253 30.2306i 0.360354 1.10905i −0.592486 0.805581i \(-0.701853\pi\)
0.952840 0.303474i \(-0.0981465\pi\)
\(744\) 1.95928 1.42350i 0.0718305 0.0521879i
\(745\) 0.511813 + 0.371854i 0.0187514 + 0.0136237i
\(746\) −3.68080 11.3283i −0.134764 0.414759i
\(747\) −15.1817 −0.555468
\(748\) 0.238178 + 7.21241i 0.00870866 + 0.263712i
\(749\) 0.901493 0.0329398
\(750\) 0.429713 + 1.32252i 0.0156909 + 0.0482916i
\(751\) −10.2131 7.42024i −0.372681 0.270768i 0.385641 0.922649i \(-0.373980\pi\)
−0.758322 + 0.651881i \(0.773980\pi\)
\(752\) 4.93079 3.58243i 0.179807 0.130638i
\(753\) 3.20121 9.85230i 0.116658 0.359038i
\(754\) −1.90716 + 5.86963i −0.0694546 + 0.213759i
\(755\) 1.98172 1.43980i 0.0721222 0.0523998i
\(756\) 7.67418 + 5.57562i 0.279107 + 0.202783i
\(757\) −4.62211 14.2254i −0.167994 0.517031i 0.831251 0.555898i \(-0.187625\pi\)
−0.999244 + 0.0388664i \(0.987625\pi\)
\(758\) 15.6318 0.567774
\(759\) 16.6210 + 21.3572i 0.603303 + 0.775217i
\(760\) 0.117838 0.00427445
\(761\) −15.6462 48.1539i −0.567173 1.74558i −0.661405 0.750029i \(-0.730039\pi\)
0.0942319 0.995550i \(-0.469961\pi\)
\(762\) −2.65755 1.93083i −0.0962730 0.0699464i
\(763\) −11.2054 + 8.14124i −0.405665 + 0.294733i
\(764\) −7.24238 + 22.2897i −0.262020 + 0.806415i
\(765\) 0.127049 0.391018i 0.00459348 0.0141373i
\(766\) −9.98905 + 7.25747i −0.360919 + 0.262223i
\(767\) −9.64557 7.00792i −0.348282 0.253041i
\(768\) −0.365170 1.12388i −0.0131769 0.0405544i
\(769\) 29.6272 1.06839 0.534193 0.845363i \(-0.320616\pi\)
0.534193 + 0.845363i \(0.320616\pi\)
\(770\) 0.640821 0.231865i 0.0230936 0.00835584i
\(771\) −29.8543 −1.07518
\(772\) 2.56418 + 7.89174i 0.0922869 + 0.284030i
\(773\) −2.56970 1.86699i −0.0924255 0.0671511i 0.540613 0.841272i \(-0.318192\pi\)
−0.633038 + 0.774120i \(0.718192\pi\)
\(774\) 13.0267 9.46442i 0.468234 0.340192i
\(775\) 3.15769 9.71838i 0.113428 0.349094i
\(776\) −3.45324 + 10.6280i −0.123964 + 0.381522i
\(777\) 3.40749 2.47569i 0.122243 0.0888147i
\(778\) −12.2598 8.90730i −0.439537 0.319342i
\(779\) 0.190117 + 0.585121i 0.00681166 + 0.0209641i
\(780\) 0.295686 0.0105872
\(781\) −17.0618 + 25.1920i −0.610518 + 0.901440i
\(782\) −15.0239 −0.537253
\(783\) 4.88609 + 15.0378i 0.174615 + 0.537409i
\(784\) 3.20334 + 2.32736i 0.114405 + 0.0831202i
\(785\) 0.642140 0.466542i 0.0229190 0.0166516i
\(786\) −3.67926 + 11.3236i −0.131235 + 0.403899i
\(787\) −7.93976 + 24.4361i −0.283022 + 0.871052i 0.703963 + 0.710237i \(0.251412\pi\)
−0.986985 + 0.160815i \(0.948588\pi\)
\(788\) −20.8043 + 15.1152i −0.741122 + 0.538456i
\(789\) −18.3305 13.3179i −0.652585 0.474130i
\(790\) −0.199379 0.613624i −0.00709357 0.0218318i
\(791\) 28.1784 1.00191
\(792\) 2.98235 4.40349i 0.105973 0.156471i
\(793\) 11.1105 0.394546
\(794\) 0.333746 + 1.02717i 0.0118442 + 0.0364528i
\(795\) 1.03375 + 0.751061i 0.0366632 + 0.0266374i
\(796\) −5.89035 + 4.27959i −0.208778 + 0.151686i
\(797\) −10.3187 + 31.7577i −0.365508 + 1.12492i 0.584155 + 0.811642i \(0.301426\pi\)
−0.949663 + 0.313274i \(0.898574\pi\)
\(798\) −0.636743 + 1.95969i −0.0225405 + 0.0693724i
\(799\) 10.7285 7.79468i 0.379545 0.275756i
\(800\) −4.03385 2.93076i −0.142618 0.103618i
\(801\) −2.37560 7.31133i −0.0839375 0.258333i
\(802\) −22.8470 −0.806757
\(803\) −41.9617 + 15.1828i −1.48080 + 0.535790i
\(804\) 16.4670 0.580746
\(805\) 0.438429 + 1.34935i 0.0154526 + 0.0475582i
\(806\) −3.52058 2.55785i −0.124007 0.0900963i
\(807\) 7.90739 5.74506i 0.278353 0.202236i
\(808\) −1.04855 + 3.22711i −0.0368879 + 0.113529i
\(809\) 5.98968 18.4343i 0.210586 0.648116i −0.788852 0.614583i \(-0.789324\pi\)
0.999438 0.0335329i \(-0.0106759\pi\)
\(810\) 0.154247 0.112067i 0.00541969 0.00393763i
\(811\) 38.9301 + 28.2844i 1.36702 + 0.993200i 0.997963 + 0.0637935i \(0.0203199\pi\)
0.369059 + 0.929406i \(0.379680\pi\)
\(812\) −1.56612 4.82002i −0.0549600 0.169150i
\(813\) 10.7384 0.376611
\(814\) −4.16369 5.35014i −0.145937 0.187522i
\(815\) −0.533629 −0.0186922
\(816\) −0.794541 2.44534i −0.0278145 0.0856042i
\(817\) 8.12364 + 5.90217i 0.284210 + 0.206491i
\(818\) 13.3379 9.69058i 0.466350 0.338823i
\(819\) 1.83470 5.64662i 0.0641096 0.197309i
\(820\) −0.0224031 + 0.0689497i −0.000782351 + 0.00240783i
\(821\) −20.8040 + 15.1150i −0.726063 + 0.527516i −0.888316 0.459233i \(-0.848124\pi\)
0.162252 + 0.986749i \(0.448124\pi\)
\(822\) 0.460644 + 0.334678i 0.0160668 + 0.0116732i
\(823\) −11.5079 35.4176i −0.401139 1.23458i −0.924076 0.382208i \(-0.875164\pi\)
0.522937 0.852371i \(-0.324836\pi\)
\(824\) −17.7010 −0.616644
\(825\) 0.644994 + 19.5315i 0.0224558 + 0.679998i
\(826\) 9.79059 0.340658
\(827\) 6.97834 + 21.4771i 0.242661 + 0.746833i 0.996012 + 0.0892150i \(0.0284358\pi\)
−0.753352 + 0.657618i \(0.771564\pi\)
\(828\) 8.95780 + 6.50822i 0.311305 + 0.226176i
\(829\) −27.7912 + 20.1915i −0.965229 + 0.701280i −0.954359 0.298661i \(-0.903460\pi\)
−0.0108696 + 0.999941i \(0.503460\pi\)
\(830\) 0.344751 1.06103i 0.0119665 0.0368290i
\(831\) 1.66925 5.13743i 0.0579057 0.178215i
\(832\) −1.71786 + 1.24810i −0.0595562 + 0.0432701i
\(833\) 6.96987 + 5.06390i 0.241492 + 0.175454i
\(834\) 7.22250 + 22.2286i 0.250095 + 0.769712i
\(835\) 0.584958 0.0202433
\(836\) 3.18641 + 0.920226i 0.110204 + 0.0318267i
\(837\) −11.1489 −0.385361
\(838\) −1.24316 3.82604i −0.0429441 0.132169i
\(839\) −2.47258 1.79643i −0.0853630 0.0620198i 0.544285 0.838900i \(-0.316801\pi\)
−0.629648 + 0.776880i \(0.716801\pi\)
\(840\) −0.196438 + 0.142721i −0.00677776 + 0.00492433i
\(841\) −6.35096 + 19.5462i −0.218999 + 0.674008i
\(842\) 2.87519 8.84891i 0.0990854 0.304954i
\(843\) −1.17683 + 0.855016i −0.0405321 + 0.0294483i
\(844\) −7.95111 5.77682i −0.273689 0.198846i
\(845\) 0.309199 + 0.951616i 0.0106368 + 0.0327366i
\(846\) −9.77330 −0.336013
\(847\) 19.1388 1.26543i 0.657617 0.0434809i
\(848\) −9.17608 −0.315108
\(849\) −9.65069 29.7018i −0.331211 1.01936i
\(850\) −8.77689 6.37679i −0.301045 0.218722i
\(851\) 11.4186 8.29612i 0.391426 0.284387i
\(852\) 3.34999 10.3102i 0.114769 0.353222i
\(853\) −1.01187 + 3.11423i −0.0346459 + 0.106629i −0.966884 0.255217i \(-0.917853\pi\)
0.932238 + 0.361846i \(0.117853\pi\)
\(854\) −7.38125 + 5.36279i −0.252581 + 0.183511i
\(855\) −0.152872 0.111068i −0.00522810 0.00379844i
\(856\) 0.159763 + 0.491699i 0.00546058 + 0.0168059i
\(857\) −6.04478 −0.206486 −0.103243 0.994656i \(-0.532922\pi\)
−0.103243 + 0.994656i \(0.532922\pi\)
\(858\) 7.99548 + 2.30908i 0.272961 + 0.0788305i
\(859\) 1.52525 0.0520409 0.0260204 0.999661i \(-0.491717\pi\)
0.0260204 + 0.999661i \(0.491717\pi\)
\(860\) 0.365647 + 1.12535i 0.0124685 + 0.0383740i
\(861\) −1.02560 0.745143i −0.0349524 0.0253944i
\(862\) −2.06734 + 1.50201i −0.0704138 + 0.0511586i
\(863\) −11.2931 + 34.7567i −0.384423 + 1.18313i 0.552475 + 0.833529i \(0.313683\pi\)
−0.936898 + 0.349602i \(0.886317\pi\)
\(864\) −1.68108 + 5.17383i −0.0571914 + 0.176017i
\(865\) 0.0845257 0.0614115i 0.00287396 0.00208805i
\(866\) 31.1684 + 22.6452i 1.05915 + 0.769515i
\(867\) 4.47912 + 13.7853i 0.152119 + 0.468174i
\(868\) 3.57350 0.121293
\(869\) −0.599364 18.1497i −0.0203320 0.615686i
\(870\) −0.404737 −0.0137219
\(871\) −9.14355 28.1409i −0.309817 0.953520i
\(872\) −6.42629 4.66897i −0.217622 0.158111i
\(873\) 14.4972 10.5328i 0.490656 0.356482i
\(874\) −2.13375 + 6.56701i −0.0721752 + 0.222132i
\(875\) −0.634066 + 1.95145i −0.0214353 + 0.0659712i
\(876\) 12.8630 9.34553i 0.434601 0.315756i
\(877\) 6.61954 + 4.80938i 0.223526 + 0.162401i 0.693912 0.720059i \(-0.255885\pi\)
−0.470386 + 0.882461i \(0.655885\pi\)
\(878\) −10.5718 32.5366i −0.356780 1.09806i
\(879\) −7.45540 −0.251465
\(880\) 0.240032 + 0.308430i 0.00809148 + 0.0103972i
\(881\) −23.0229 −0.775662 −0.387831 0.921731i \(-0.626776\pi\)
−0.387831 + 0.921731i \(0.626776\pi\)
\(882\) −1.96205 6.03858i −0.0660657 0.203329i
\(883\) −43.6925 31.7445i −1.47037 1.06829i −0.980506 0.196489i \(-0.937046\pi\)
−0.489865 0.871798i \(-0.662954\pi\)
\(884\) −3.73774 + 2.71563i −0.125714 + 0.0913365i
\(885\) 0.241614 0.743610i 0.00812175 0.0249962i
\(886\) −8.76240 + 26.9679i −0.294378 + 0.906004i
\(887\) −25.5025 + 18.5286i −0.856289 + 0.622130i −0.926873 0.375375i \(-0.877514\pi\)
0.0705838 + 0.997506i \(0.477514\pi\)
\(888\) 1.95418 + 1.41980i 0.0655781 + 0.0476453i
\(889\) −1.49783 4.60985i −0.0502357 0.154609i
\(890\) 0.564929 0.0189365
\(891\) 5.04607 1.82580i 0.169050 0.0611665i
\(892\) 1.50507 0.0503935
\(893\) −1.88339 5.79649i −0.0630253 0.193972i
\(894\) −5.13260 3.72905i −0.171660 0.124718i
\(895\) −0.257744 + 0.187262i −0.00861544 + 0.00625948i
\(896\) 0.538830 1.65835i 0.0180010 0.0554015i
\(897\) −5.35411 + 16.4782i −0.178768 + 0.550193i
\(898\) 15.9634 11.5981i 0.532707 0.387034i
\(899\) 4.81899 + 3.50120i 0.160722 + 0.116772i
\(900\) 2.47074 + 7.60416i 0.0823580 + 0.253472i
\(901\) −19.9654 −0.665144
\(902\) −1.14424 + 1.68948i −0.0380989 + 0.0562536i
\(903\) −20.6907 −0.688543
\(904\) 4.99378 + 15.3693i 0.166091 + 0.511175i
\(905\) 1.52975 + 1.11143i 0.0508508 + 0.0369452i
\(906\) −19.8732 + 14.4387i −0.660244 + 0.479695i
\(907\) 0.596394 1.83551i 0.0198029 0.0609472i −0.940667 0.339332i \(-0.889799\pi\)
0.960470 + 0.278385i \(0.0897990\pi\)
\(908\) 0.0782752 0.240906i 0.00259765 0.00799476i
\(909\) 4.40197 3.19822i 0.146004 0.106078i
\(910\) 0.352975 + 0.256451i 0.0117010 + 0.00850128i
\(911\) 0.124252 + 0.382407i 0.00411664 + 0.0126697i 0.953094 0.302675i \(-0.0978798\pi\)
−0.948977 + 0.315345i \(0.897880\pi\)
\(912\) −1.18171 −0.0391305
\(913\) 17.6081 25.9987i 0.582743 0.860430i
\(914\) −8.71834 −0.288377
\(915\) 0.225157 + 0.692961i 0.00744345 + 0.0229086i
\(916\) 7.07743 + 5.14206i 0.233845 + 0.169898i
\(917\) −14.2132 + 10.3265i −0.469362 + 0.341011i
\(918\) −3.65771 + 11.2573i −0.120722 + 0.371545i
\(919\) −11.9961 + 36.9202i −0.395714 + 1.21788i 0.532689 + 0.846311i \(0.321181\pi\)
−0.928404 + 0.371573i \(0.878819\pi\)
\(920\) −0.658272 + 0.478263i −0.0217026 + 0.0157679i
\(921\) −17.4870 12.7051i −0.576217 0.418646i
\(922\) −3.34419 10.2924i −0.110135 0.338961i
\(923\) −19.4795 −0.641177
\(924\) −6.42632 + 2.32521i −0.211411 + 0.0764937i
\(925\) 10.1920 0.335109
\(926\) −11.9583 36.8038i −0.392974 1.20945i
\(927\) 22.9635 + 16.6840i 0.754220 + 0.547973i
\(928\) 2.35143 1.70841i 0.0771893 0.0560813i
\(929\) −1.80186 + 5.54554i −0.0591170 + 0.181943i −0.976254 0.216628i \(-0.930494\pi\)
0.917137 + 0.398572i \(0.130494\pi\)
\(930\) 0.0881875 0.271413i 0.00289178 0.00889999i
\(931\) 3.20334 2.32736i 0.104985 0.0762763i
\(932\) −9.99814 7.26407i −0.327500 0.237943i
\(933\) 10.5602 + 32.5010i 0.345726 + 1.06403i
\(934\) −6.54021 −0.214002
\(935\) 0.522264 + 0.671086i 0.0170799 + 0.0219468i
\(936\) 3.40497 0.111295
\(937\) 4.24996 + 13.0800i 0.138840 + 0.427306i 0.996168 0.0874656i \(-0.0278768\pi\)
−0.857327 + 0.514771i \(0.827877\pi\)
\(938\) 19.6575 + 14.2820i 0.641840 + 0.466324i
\(939\) 17.4985 12.7134i 0.571042 0.414887i
\(940\) 0.221936 0.683048i 0.00723875 0.0222786i
\(941\) −12.8489 + 39.5449i −0.418863 + 1.28913i 0.489887 + 0.871786i \(0.337038\pi\)
−0.908750 + 0.417341i \(0.862962\pi\)
\(942\) −6.43955 + 4.67861i −0.209812 + 0.152437i
\(943\) −3.43683 2.49701i −0.111919 0.0813137i
\(944\) 1.73509 + 5.34006i 0.0564724 + 0.173804i
\(945\) 1.11779 0.0363618
\(946\) 1.09919 + 33.2853i 0.0357379 + 1.08220i
\(947\) 14.7404 0.478999 0.239500 0.970896i \(-0.423017\pi\)
0.239500 + 0.970896i \(0.423017\pi\)
\(948\) 1.99942 + 6.15359i 0.0649382 + 0.199859i
\(949\) −23.1132 16.7928i −0.750288 0.545116i
\(950\) −4.03385 + 2.93076i −0.130875 + 0.0950866i
\(951\) −8.23136 + 25.3335i −0.266920 + 0.821495i
\(952\) 1.17239 3.60825i 0.0379974 0.116944i
\(953\) 24.6250 17.8911i 0.797683 0.579551i −0.112550 0.993646i \(-0.535902\pi\)
0.910233 + 0.414095i \(0.135902\pi\)
\(954\) 11.9041 + 8.64885i 0.385410 + 0.280017i
\(955\) 0.853430 + 2.62659i 0.0276163 + 0.0849943i
\(956\) 19.2245 0.621766
\(957\) −10.9443 3.16068i −0.353779 0.102170i
\(958\) 33.0437 1.06759
\(959\) 0.259625 + 0.799044i 0.00838374 + 0.0258025i
\(960\) −0.112657 0.0818499i −0.00363598 0.00264169i
\(961\) 21.6816 15.7526i 0.699408 0.508150i
\(962\) 1.34125 4.12793i 0.0432435 0.133090i
\(963\) 0.256188 0.788465i 0.00825553 0.0254079i
\(964\) −15.5277 + 11.2816i −0.500115 + 0.363355i
\(965\) 0.791062 + 0.574740i 0.0254652 + 0.0185015i
\(966\) −4.39668 13.5316i −0.141461 0.435372i
\(967\) 9.20321 0.295955 0.147978 0.988991i \(-0.452724\pi\)
0.147978 + 0.988991i \(0.452724\pi\)
\(968\) 4.08198 + 10.2146i 0.131200 + 0.328309i
\(969\) −2.57119 −0.0825984
\(970\) 0.406924 + 1.25238i 0.0130655 + 0.0402116i
\(971\) −9.93200 7.21602i −0.318733 0.231573i 0.416902 0.908952i \(-0.363116\pi\)
−0.735635 + 0.677378i \(0.763116\pi\)
\(972\) 11.6565 8.46896i 0.373883 0.271642i
\(973\) −10.6572 + 32.7995i −0.341655 + 1.05150i
\(974\) −1.97768 + 6.08668i −0.0633691 + 0.195030i
\(975\) −10.1219 + 7.35401i −0.324161 + 0.235517i
\(976\) −4.23312 3.07554i −0.135499 0.0984458i
\(977\) −7.56956 23.2967i −0.242172 0.745328i −0.996089 0.0883583i \(-0.971838\pi\)
0.753917 0.656970i \(-0.228162\pi\)
\(978\) 5.35137 0.171118
\(979\) 15.2760 + 4.41166i 0.488222 + 0.140997i
\(980\) 0.466587 0.0149046
\(981\) 3.93611 + 12.1141i 0.125670 + 0.386774i
\(982\) −23.9935 17.4323i −0.765662 0.556286i
\(983\) 27.0287 19.6375i 0.862082 0.626339i −0.0663685 0.997795i \(-0.521141\pi\)
0.928451 + 0.371456i \(0.121141\pi\)
\(984\) 0.224665 0.691446i 0.00716204 0.0220425i
\(985\) −0.936406 + 2.88196i −0.0298364 + 0.0918269i
\(986\) 5.11626 3.71718i 0.162935 0.118379i
\(987\) 10.1601 + 7.38174i 0.323399 + 0.234963i
\(988\) 0.656165 + 2.01947i 0.0208754 + 0.0642479i
\(989\) −69.3353 −2.20473
\(990\) −0.0206847 0.626367i −0.000657404 0.0199072i
\(991\) −18.4683 −0.586664 −0.293332 0.956011i \(-0.594764\pi\)
−0.293332 + 0.956011i \(0.594764\pi\)
\(992\) 0.633297 + 1.94909i 0.0201072 + 0.0618836i
\(993\) 7.72430 + 5.61203i 0.245123 + 0.178092i
\(994\) 12.9412 9.40233i 0.410470 0.298224i
\(995\) −0.265126 + 0.815975i −0.00840507 + 0.0258681i
\(996\) −3.45726 + 10.6403i −0.109547 + 0.337152i
\(997\) −30.1618 + 21.9138i −0.955234 + 0.694018i −0.952039 0.305977i \(-0.901017\pi\)
−0.00319484 + 0.999995i \(0.501017\pi\)
\(998\) −8.39708 6.10083i −0.265805 0.193118i
\(999\) −3.43624 10.5756i −0.108718 0.334599i
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 418.2.f.g.115.3 16
11.3 even 5 4598.2.a.bw.1.4 8
11.8 odd 10 4598.2.a.bz.1.4 8
11.9 even 5 inner 418.2.f.g.229.3 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.g.115.3 16 1.1 even 1 trivial
418.2.f.g.229.3 yes 16 11.9 even 5 inner
4598.2.a.bw.1.4 8 11.3 even 5
4598.2.a.bz.1.4 8 11.8 odd 10