Properties

Label 429.2.n.a.196.3
Level $429$
Weight $2$
Character 429.196
Analytic conductor $3.426$
Analytic rank $0$
Dimension $12$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} - 17 x^{3} + 14 x^{2} - 5 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 196.3
Root \(0.622685 + 1.91643i\) of defining polynomial
Character \(\chi\) \(=\) 429.196
Dual form 429.2.n.a.313.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.622685 - 1.91643i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.66692 - 1.21109i) q^{4} +(-0.155663 - 0.479080i) q^{5} +(0.622685 + 1.91643i) q^{6} +(2.43923 + 1.77220i) q^{7} +(-0.0985128 + 0.0715738i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.622685 - 1.91643i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.66692 - 1.21109i) q^{4} +(-0.155663 - 0.479080i) q^{5} +(0.622685 + 1.91643i) q^{6} +(2.43923 + 1.77220i) q^{7} +(-0.0985128 + 0.0715738i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.01505 q^{10} +(2.03498 - 2.61894i) q^{11} +2.06043 q^{12} +(0.309017 - 0.951057i) q^{13} +(4.91517 - 3.57108i) q^{14} +(0.407530 + 0.296088i) q^{15} +(-1.19759 - 3.68581i) q^{16} +(-0.836357 - 2.57404i) q^{17} +(-1.63021 - 1.18442i) q^{18} +(-1.38208 + 1.00414i) q^{19} +(-0.320732 + 0.987111i) q^{20} -3.01505 q^{21} +(-3.75187 - 5.53066i) q^{22} +1.83758 q^{23} +(0.0376286 - 0.115809i) q^{24} +(3.83980 - 2.78978i) q^{25} +(-1.63021 - 1.18442i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.91971 - 5.90825i) q^{28} +(-2.23832 - 1.62623i) q^{29} +(0.821193 - 0.596632i) q^{30} +(-3.02477 + 9.30929i) q^{31} -8.05284 q^{32} +(-0.106955 + 3.31490i) q^{33} -5.45375 q^{34} +(0.469330 - 1.44445i) q^{35} +(-1.66692 + 1.21109i) q^{36} +(-0.248313 - 0.180410i) q^{37} +(1.06376 + 3.27391i) q^{38} +(0.309017 + 0.951057i) q^{39} +(0.0496243 + 0.0360542i) q^{40} +(4.08914 - 2.97093i) q^{41} +(-1.87743 + 5.77813i) q^{42} -1.76211 q^{43} +(-6.56393 + 1.90104i) q^{44} -0.503735 q^{45} +(1.14423 - 3.52159i) q^{46} +(9.78758 - 7.11109i) q^{47} +(3.13534 + 2.27796i) q^{48} +(0.646010 + 1.98821i) q^{49} +(-2.95542 - 9.09585i) q^{50} +(2.18961 + 1.59085i) q^{51} +(-1.66692 + 1.21109i) q^{52} +(-3.19081 + 9.82031i) q^{53} +2.01505 q^{54} +(-1.57145 - 0.567246i) q^{55} -0.367138 q^{56} +(0.527907 - 1.62473i) q^{57} +(-4.51033 + 3.27695i) q^{58} +(-0.0976321 - 0.0709338i) q^{59} +(-0.320732 - 0.987111i) q^{60} +(4.54367 + 13.9840i) q^{61} +(15.9571 + 11.5935i) q^{62} +(2.43923 - 1.77220i) q^{63} +(-2.61920 + 8.06107i) q^{64} -0.503735 q^{65} +(6.28616 + 2.26911i) q^{66} -8.35118 q^{67} +(-1.72326 + 5.30363i) q^{68} +(-1.48663 + 1.08010i) q^{69} +(-2.47594 - 1.79888i) q^{70} +(3.61346 + 11.1211i) q^{71} +(0.0376286 + 0.115809i) q^{72} +(-4.71162 - 3.42319i) q^{73} +(-0.500364 + 0.363536i) q^{74} +(-1.46667 + 4.51395i) q^{75} +3.51992 q^{76} +(9.60507 - 2.78181i) q^{77} +2.01505 q^{78} +(2.54366 - 7.82859i) q^{79} +(-1.57938 + 1.14748i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.14733 - 9.68649i) q^{82} +(0.961299 + 2.95857i) q^{83} +(5.02586 + 3.65150i) q^{84} +(-1.10298 + 0.801364i) q^{85} +(-1.09724 + 3.37696i) q^{86} +2.76672 q^{87} +(-0.0130237 + 0.403651i) q^{88} -6.94532 q^{89} +(-0.313668 + 0.965371i) q^{90} +(2.43923 - 1.77220i) q^{91} +(-3.06310 - 2.22547i) q^{92} +(-3.02477 - 9.30929i) q^{93} +(-7.53331 - 23.1852i) q^{94} +(0.696200 + 0.505819i) q^{95} +(6.51489 - 4.73334i) q^{96} +(-4.98454 + 15.3408i) q^{97} +4.21253 q^{98} +(-1.86192 - 2.74468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.622685 1.91643i 0.440305 1.35512i −0.447247 0.894411i \(-0.647595\pi\)
0.887552 0.460708i \(-0.152405\pi\)
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −1.66692 1.21109i −0.833461 0.605545i
\(5\) −0.155663 0.479080i −0.0696144 0.214251i 0.910197 0.414176i \(-0.135930\pi\)
−0.979811 + 0.199925i \(0.935930\pi\)
\(6\) 0.622685 + 1.91643i 0.254210 + 0.782378i
\(7\) 2.43923 + 1.77220i 0.921941 + 0.669830i 0.944006 0.329927i \(-0.107024\pi\)
−0.0220652 + 0.999757i \(0.507024\pi\)
\(8\) −0.0985128 + 0.0715738i −0.0348296 + 0.0253051i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) −1.01505 −0.320987
\(11\) 2.03498 2.61894i 0.613569 0.789641i
\(12\) 2.06043 0.594795
\(13\) 0.309017 0.951057i 0.0857059 0.263776i
\(14\) 4.91517 3.57108i 1.31363 0.954411i
\(15\) 0.407530 + 0.296088i 0.105224 + 0.0764495i
\(16\) −1.19759 3.68581i −0.299398 0.921452i
\(17\) −0.836357 2.57404i −0.202846 0.624297i −0.999795 0.0202499i \(-0.993554\pi\)
0.796949 0.604047i \(-0.206446\pi\)
\(18\) −1.63021 1.18442i −0.384244 0.279170i
\(19\) −1.38208 + 1.00414i −0.317070 + 0.230365i −0.734924 0.678149i \(-0.762782\pi\)
0.417854 + 0.908514i \(0.362782\pi\)
\(20\) −0.320732 + 0.987111i −0.0717178 + 0.220725i
\(21\) −3.01505 −0.657938
\(22\) −3.75187 5.53066i −0.799900 1.17914i
\(23\) 1.83758 0.383162 0.191581 0.981477i \(-0.438639\pi\)
0.191581 + 0.981477i \(0.438639\pi\)
\(24\) 0.0376286 0.115809i 0.00768090 0.0236394i
\(25\) 3.83980 2.78978i 0.767960 0.557955i
\(26\) −1.63021 1.18442i −0.319711 0.232283i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) −1.91971 5.90825i −0.362790 1.11655i
\(29\) −2.23832 1.62623i −0.415646 0.301984i 0.360238 0.932860i \(-0.382696\pi\)
−0.775883 + 0.630876i \(0.782696\pi\)
\(30\) 0.821193 0.596632i 0.149929 0.108930i
\(31\) −3.02477 + 9.30929i −0.543265 + 1.67200i 0.181814 + 0.983333i \(0.441803\pi\)
−0.725079 + 0.688665i \(0.758197\pi\)
\(32\) −8.05284 −1.42356
\(33\) −0.106955 + 3.31490i −0.0186184 + 0.577050i
\(34\) −5.45375 −0.935311
\(35\) 0.469330 1.44445i 0.0793313 0.244157i
\(36\) −1.66692 + 1.21109i −0.277820 + 0.201848i
\(37\) −0.248313 0.180410i −0.0408224 0.0296592i 0.567187 0.823589i \(-0.308032\pi\)
−0.608009 + 0.793930i \(0.708032\pi\)
\(38\) 1.06376 + 3.27391i 0.172564 + 0.531099i
\(39\) 0.309017 + 0.951057i 0.0494823 + 0.152291i
\(40\) 0.0496243 + 0.0360542i 0.00784629 + 0.00570067i
\(41\) 4.08914 2.97093i 0.638616 0.463982i −0.220758 0.975329i \(-0.570853\pi\)
0.859375 + 0.511347i \(0.170853\pi\)
\(42\) −1.87743 + 5.77813i −0.289693 + 0.891584i
\(43\) −1.76211 −0.268720 −0.134360 0.990933i \(-0.542898\pi\)
−0.134360 + 0.990933i \(0.542898\pi\)
\(44\) −6.56393 + 1.90104i −0.989549 + 0.286592i
\(45\) −0.503735 −0.0750923
\(46\) 1.14423 3.52159i 0.168708 0.519230i
\(47\) 9.78758 7.11109i 1.42767 1.03726i 0.437220 0.899355i \(-0.355963\pi\)
0.990446 0.137905i \(-0.0440367\pi\)
\(48\) 3.13534 + 2.27796i 0.452547 + 0.328795i
\(49\) 0.646010 + 1.98821i 0.0922871 + 0.284030i
\(50\) −2.95542 9.09585i −0.417959 1.28635i
\(51\) 2.18961 + 1.59085i 0.306607 + 0.222763i
\(52\) −1.66692 + 1.21109i −0.231161 + 0.167948i
\(53\) −3.19081 + 9.82031i −0.438292 + 1.34892i 0.451383 + 0.892330i \(0.350931\pi\)
−0.889675 + 0.456594i \(0.849069\pi\)
\(54\) 2.01505 0.274214
\(55\) −1.57145 0.567246i −0.211895 0.0764874i
\(56\) −0.367138 −0.0490609
\(57\) 0.527907 1.62473i 0.0699229 0.215201i
\(58\) −4.51033 + 3.27695i −0.592235 + 0.430284i
\(59\) −0.0976321 0.0709338i −0.0127106 0.00923480i 0.581412 0.813609i \(-0.302501\pi\)
−0.594122 + 0.804375i \(0.702501\pi\)
\(60\) −0.320732 0.987111i −0.0414063 0.127435i
\(61\) 4.54367 + 13.9840i 0.581757 + 1.79046i 0.611920 + 0.790920i \(0.290397\pi\)
−0.0301626 + 0.999545i \(0.509603\pi\)
\(62\) 15.9571 + 11.5935i 2.02655 + 1.47238i
\(63\) 2.43923 1.77220i 0.307314 0.223277i
\(64\) −2.61920 + 8.06107i −0.327400 + 1.00763i
\(65\) −0.503735 −0.0624806
\(66\) 6.28616 + 2.26911i 0.773773 + 0.279308i
\(67\) −8.35118 −1.02026 −0.510129 0.860098i \(-0.670402\pi\)
−0.510129 + 0.860098i \(0.670402\pi\)
\(68\) −1.72326 + 5.30363i −0.208975 + 0.643160i
\(69\) −1.48663 + 1.08010i −0.178970 + 0.130029i
\(70\) −2.47594 1.79888i −0.295931 0.215007i
\(71\) 3.61346 + 11.1211i 0.428839 + 1.31983i 0.899270 + 0.437393i \(0.144098\pi\)
−0.470432 + 0.882436i \(0.655902\pi\)
\(72\) 0.0376286 + 0.115809i 0.00443457 + 0.0136482i
\(73\) −4.71162 3.42319i −0.551454 0.400654i 0.276868 0.960908i \(-0.410704\pi\)
−0.828321 + 0.560254i \(0.810704\pi\)
\(74\) −0.500364 + 0.363536i −0.0581661 + 0.0422602i
\(75\) −1.46667 + 4.51395i −0.169357 + 0.521226i
\(76\) 3.51992 0.403762
\(77\) 9.60507 2.78181i 1.09460 0.317016i
\(78\) 2.01505 0.228160
\(79\) 2.54366 7.82859i 0.286184 0.880785i −0.699857 0.714283i \(-0.746753\pi\)
0.986041 0.166502i \(-0.0532472\pi\)
\(80\) −1.57938 + 1.14748i −0.176580 + 0.128293i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −3.14733 9.68649i −0.347565 1.06969i
\(83\) 0.961299 + 2.95857i 0.105516 + 0.324746i 0.989851 0.142107i \(-0.0453878\pi\)
−0.884335 + 0.466853i \(0.845388\pi\)
\(84\) 5.02586 + 3.65150i 0.548366 + 0.398411i
\(85\) −1.10298 + 0.801364i −0.119635 + 0.0869202i
\(86\) −1.09724 + 3.37696i −0.118319 + 0.364147i
\(87\) 2.76672 0.296623
\(88\) −0.0130237 + 0.403651i −0.00138833 + 0.0430293i
\(89\) −6.94532 −0.736202 −0.368101 0.929786i \(-0.619992\pi\)
−0.368101 + 0.929786i \(0.619992\pi\)
\(90\) −0.313668 + 0.965371i −0.0330635 + 0.101759i
\(91\) 2.43923 1.77220i 0.255700 0.185777i
\(92\) −3.06310 2.22547i −0.319351 0.232022i
\(93\) −3.02477 9.30929i −0.313654 0.965329i
\(94\) −7.53331 23.1852i −0.777002 2.39137i
\(95\) 0.696200 + 0.505819i 0.0714286 + 0.0518959i
\(96\) 6.51489 4.73334i 0.664923 0.483095i
\(97\) −4.98454 + 15.3408i −0.506103 + 1.55762i 0.292806 + 0.956172i \(0.405411\pi\)
−0.798909 + 0.601453i \(0.794589\pi\)
\(98\) 4.21253 0.425529
\(99\) −1.86192 2.74468i −0.187130 0.275850i
\(100\) −9.77932 −0.977932
\(101\) −3.64428 + 11.2159i −0.362619 + 1.11603i 0.588839 + 0.808250i \(0.299585\pi\)
−0.951458 + 0.307777i \(0.900415\pi\)
\(102\) 4.41218 3.20564i 0.436871 0.317405i
\(103\) 2.19756 + 1.59662i 0.216532 + 0.157320i 0.690764 0.723080i \(-0.257274\pi\)
−0.474232 + 0.880400i \(0.657274\pi\)
\(104\) 0.0376286 + 0.115809i 0.00368978 + 0.0113560i
\(105\) 0.469330 + 1.44445i 0.0458020 + 0.140964i
\(106\) 16.8330 + 12.2299i 1.63497 + 1.18788i
\(107\) −1.04252 + 0.757434i −0.100784 + 0.0732239i −0.637036 0.770834i \(-0.719840\pi\)
0.536252 + 0.844058i \(0.319840\pi\)
\(108\) 0.636708 1.95958i 0.0612672 0.188561i
\(109\) −11.5355 −1.10490 −0.552448 0.833547i \(-0.686306\pi\)
−0.552448 + 0.833547i \(0.686306\pi\)
\(110\) −2.06561 + 2.65836i −0.196948 + 0.253465i
\(111\) 0.306932 0.0291327
\(112\) 3.61080 11.1129i 0.341189 1.05007i
\(113\) −1.81994 + 1.32227i −0.171206 + 0.124388i −0.670089 0.742281i \(-0.733744\pi\)
0.498883 + 0.866670i \(0.333744\pi\)
\(114\) −2.78496 2.02339i −0.260835 0.189508i
\(115\) −0.286042 0.880348i −0.0266736 0.0820929i
\(116\) 1.76159 + 5.42161i 0.163559 + 0.503384i
\(117\) −0.809017 0.587785i −0.0747936 0.0543408i
\(118\) −0.196734 + 0.142935i −0.0181108 + 0.0131583i
\(119\) 2.52166 7.76087i 0.231160 0.711438i
\(120\) −0.0613390 −0.00559946
\(121\) −2.71773 10.6590i −0.247067 0.968998i
\(122\) 29.6285 2.68244
\(123\) −1.56191 + 4.80707i −0.140833 + 0.433439i
\(124\) 16.3165 11.8546i 1.46526 1.06457i
\(125\) −3.97189 2.88575i −0.355256 0.258109i
\(126\) −1.87743 5.77813i −0.167254 0.514756i
\(127\) 3.95908 + 12.1848i 0.351311 + 1.08122i 0.958118 + 0.286375i \(0.0924503\pi\)
−0.606806 + 0.794850i \(0.707550\pi\)
\(128\) 0.787743 + 0.572329i 0.0696273 + 0.0505872i
\(129\) 1.42558 1.03574i 0.125515 0.0911922i
\(130\) −0.313668 + 0.965371i −0.0275105 + 0.0846686i
\(131\) 9.36428 0.818161 0.409081 0.912498i \(-0.365849\pi\)
0.409081 + 0.912498i \(0.365849\pi\)
\(132\) 4.19293 5.39615i 0.364947 0.469675i
\(133\) −5.15074 −0.446626
\(134\) −5.20015 + 16.0044i −0.449225 + 1.38257i
\(135\) 0.407530 0.296088i 0.0350746 0.0254832i
\(136\) 0.266626 + 0.193715i 0.0228630 + 0.0166109i
\(137\) −1.19962 3.69205i −0.102490 0.315433i 0.886643 0.462455i \(-0.153031\pi\)
−0.989133 + 0.147022i \(0.953031\pi\)
\(138\) 1.14423 + 3.52159i 0.0974036 + 0.299777i
\(139\) 12.1390 + 8.81952i 1.02962 + 0.748062i 0.968232 0.250053i \(-0.0804479\pi\)
0.0613862 + 0.998114i \(0.480448\pi\)
\(140\) −2.53170 + 1.83939i −0.213967 + 0.155456i
\(141\) −3.73852 + 11.5060i −0.314840 + 0.968979i
\(142\) 23.5628 1.97735
\(143\) −1.86192 2.74468i −0.155702 0.229521i
\(144\) −3.87549 −0.322957
\(145\) −0.430674 + 1.32548i −0.0357655 + 0.110075i
\(146\) −9.49416 + 6.89791i −0.785742 + 0.570875i
\(147\) −1.69128 1.22878i −0.139494 0.101348i
\(148\) 0.195426 + 0.601459i 0.0160639 + 0.0494397i
\(149\) −2.58972 7.97032i −0.212158 0.652954i −0.999343 0.0362380i \(-0.988463\pi\)
0.787185 0.616716i \(-0.211537\pi\)
\(150\) 7.73739 + 5.62154i 0.631755 + 0.458997i
\(151\) 11.6209 8.44310i 0.945697 0.687089i −0.00408790 0.999992i \(-0.501301\pi\)
0.949785 + 0.312902i \(0.101301\pi\)
\(152\) 0.0642824 0.197841i 0.00521399 0.0160470i
\(153\) −2.70651 −0.218808
\(154\) 0.649800 20.1396i 0.0523624 1.62290i
\(155\) 4.93074 0.396047
\(156\) 0.636708 1.95958i 0.0509774 0.156892i
\(157\) −9.75470 + 7.08721i −0.778510 + 0.565621i −0.904531 0.426407i \(-0.859779\pi\)
0.126021 + 0.992028i \(0.459779\pi\)
\(158\) −13.4190 9.74949i −1.06756 0.775628i
\(159\) −3.19081 9.82031i −0.253048 0.778802i
\(160\) 1.25353 + 3.85796i 0.0991000 + 0.304998i
\(161\) 4.48227 + 3.25656i 0.353253 + 0.256653i
\(162\) −1.63021 + 1.18442i −0.128081 + 0.0930566i
\(163\) 1.80659 5.56013i 0.141503 0.435503i −0.855041 0.518560i \(-0.826468\pi\)
0.996545 + 0.0830570i \(0.0264684\pi\)
\(164\) −10.4143 −0.813224
\(165\) 1.60475 0.464766i 0.124930 0.0361820i
\(166\) 6.26848 0.486528
\(167\) −3.27841 + 10.0899i −0.253691 + 0.780780i 0.740394 + 0.672173i \(0.234639\pi\)
−0.994085 + 0.108607i \(0.965361\pi\)
\(168\) 0.297021 0.215799i 0.0229157 0.0166492i
\(169\) −0.809017 0.587785i −0.0622321 0.0452143i
\(170\) 0.848945 + 2.61278i 0.0651111 + 0.200391i
\(171\) 0.527907 + 1.62473i 0.0403700 + 0.124246i
\(172\) 2.93731 + 2.13408i 0.223967 + 0.162722i
\(173\) −13.7117 + 9.96213i −1.04248 + 0.757407i −0.970768 0.240019i \(-0.922846\pi\)
−0.0717125 + 0.997425i \(0.522846\pi\)
\(174\) 1.72279 5.30221i 0.130605 0.401959i
\(175\) 14.3102 1.08175
\(176\) −12.0900 4.36411i −0.911318 0.328957i
\(177\) 0.120680 0.00907085
\(178\) −4.32475 + 13.3102i −0.324153 + 0.997642i
\(179\) 3.19073 2.31820i 0.238487 0.173271i −0.462122 0.886816i \(-0.652912\pi\)
0.700609 + 0.713546i \(0.252912\pi\)
\(180\) 0.839687 + 0.610068i 0.0625865 + 0.0454718i
\(181\) 0.104067 + 0.320284i 0.00773521 + 0.0238065i 0.954850 0.297090i \(-0.0960160\pi\)
−0.947114 + 0.320896i \(0.896016\pi\)
\(182\) −1.87743 5.77813i −0.139164 0.428303i
\(183\) −11.8955 8.64257i −0.879339 0.638877i
\(184\) −0.181025 + 0.131523i −0.0133454 + 0.00969597i
\(185\) −0.0477778 + 0.147045i −0.00351270 + 0.0108110i
\(186\) −19.7241 −1.44624
\(187\) −8.44324 3.04775i −0.617431 0.222873i
\(188\) −24.9273 −1.81801
\(189\) −0.931702 + 2.86748i −0.0677713 + 0.208579i
\(190\) 1.40288 1.01925i 0.101776 0.0739443i
\(191\) −19.7385 14.3409i −1.42823 1.03767i −0.990343 0.138637i \(-0.955728\pi\)
−0.437885 0.899031i \(-0.644272\pi\)
\(192\) −2.61920 8.06107i −0.189025 0.581758i
\(193\) 3.05016 + 9.38743i 0.219555 + 0.675722i 0.998799 + 0.0490007i \(0.0156037\pi\)
−0.779243 + 0.626722i \(0.784396\pi\)
\(194\) 26.2958 + 19.1050i 1.88793 + 1.37166i
\(195\) 0.407530 0.296088i 0.0291838 0.0212033i
\(196\) 1.33106 4.09657i 0.0950755 0.292612i
\(197\) −5.60798 −0.399552 −0.199776 0.979842i \(-0.564021\pi\)
−0.199776 + 0.979842i \(0.564021\pi\)
\(198\) −6.41936 + 1.85917i −0.456204 + 0.132125i
\(199\) −20.9810 −1.48730 −0.743650 0.668569i \(-0.766907\pi\)
−0.743650 + 0.668569i \(0.766907\pi\)
\(200\) −0.178595 + 0.549658i −0.0126285 + 0.0388667i
\(201\) 6.75625 4.90870i 0.476549 0.346233i
\(202\) 19.2253 + 13.9680i 1.35269 + 0.982785i
\(203\) −2.57775 7.93351i −0.180923 0.556823i
\(204\) −1.72326 5.30363i −0.120652 0.371329i
\(205\) −2.05984 1.49656i −0.143866 0.104524i
\(206\) 4.42820 3.21728i 0.308527 0.224158i
\(207\) 0.567843 1.74764i 0.0394678 0.121470i
\(208\) −3.87549 −0.268717
\(209\) −0.182715 + 5.66298i −0.0126387 + 0.391717i
\(210\) 3.06043 0.211190
\(211\) 4.64799 14.3051i 0.319981 0.984801i −0.653674 0.756776i \(-0.726773\pi\)
0.973655 0.228025i \(-0.0732267\pi\)
\(212\) 17.2121 12.5053i 1.18213 0.858870i
\(213\) −9.46016 6.87321i −0.648199 0.470944i
\(214\) 0.802406 + 2.46955i 0.0548514 + 0.168815i
\(215\) 0.274295 + 0.844193i 0.0187068 + 0.0575735i
\(216\) −0.0985128 0.0715738i −0.00670295 0.00486998i
\(217\) −23.8761 + 17.3470i −1.62081 + 1.17759i
\(218\) −7.18296 + 22.1069i −0.486491 + 1.49727i
\(219\) 5.82388 0.393542
\(220\) 1.93251 + 2.84873i 0.130290 + 0.192061i
\(221\) −2.70651 −0.182060
\(222\) 0.191122 0.588213i 0.0128273 0.0394783i
\(223\) −15.2695 + 11.0940i −1.02252 + 0.742906i −0.966799 0.255540i \(-0.917747\pi\)
−0.0557245 + 0.998446i \(0.517747\pi\)
\(224\) −19.6427 14.2713i −1.31243 0.953539i
\(225\) −1.46667 4.51395i −0.0977782 0.300930i
\(226\) 1.40078 + 4.31115i 0.0931783 + 0.286773i
\(227\) −14.9614 10.8701i −0.993024 0.721474i −0.0324430 0.999474i \(-0.510329\pi\)
−0.960581 + 0.277999i \(0.910329\pi\)
\(228\) −2.84767 + 2.06896i −0.188592 + 0.137020i
\(229\) 3.20872 9.87541i 0.212038 0.652586i −0.787313 0.616554i \(-0.788528\pi\)
0.999351 0.0360318i \(-0.0114718\pi\)
\(230\) −1.86524 −0.122990
\(231\) −6.13556 + 7.89625i −0.403690 + 0.519535i
\(232\) 0.336899 0.0221185
\(233\) −3.12152 + 9.60704i −0.204497 + 0.629378i 0.795236 + 0.606300i \(0.207347\pi\)
−0.999734 + 0.0230784i \(0.992653\pi\)
\(234\) −1.63021 + 1.18442i −0.106570 + 0.0774278i
\(235\) −4.93034 3.58210i −0.321620 0.233671i
\(236\) 0.0768378 + 0.236482i 0.00500172 + 0.0153937i
\(237\) 2.54366 + 7.82859i 0.165229 + 0.508521i
\(238\) −13.3029 9.66515i −0.862302 0.626499i
\(239\) 22.8318 16.5882i 1.47686 1.07300i 0.498314 0.866997i \(-0.333953\pi\)
0.978550 0.206008i \(-0.0660472\pi\)
\(240\) 0.603269 1.85667i 0.0389408 0.119848i
\(241\) 20.2592 1.30501 0.652504 0.757785i \(-0.273719\pi\)
0.652504 + 0.757785i \(0.273719\pi\)
\(242\) −22.1195 1.42885i −1.42189 0.0918498i
\(243\) 1.00000 0.0641500
\(244\) 9.36191 28.8130i 0.599335 1.84456i
\(245\) 0.851954 0.618981i 0.0544293 0.0395452i
\(246\) 8.23982 + 5.98658i 0.525352 + 0.381691i
\(247\) 0.527907 + 1.62473i 0.0335899 + 0.103379i
\(248\) −0.368322 1.13358i −0.0233885 0.0719824i
\(249\) −2.51671 1.82850i −0.159490 0.115876i
\(250\) −8.00356 + 5.81492i −0.506189 + 0.367768i
\(251\) −3.72780 + 11.4730i −0.235297 + 0.724169i 0.761785 + 0.647830i \(0.224323\pi\)
−0.997082 + 0.0763392i \(0.975677\pi\)
\(252\) −6.21230 −0.391338
\(253\) 3.73943 4.81252i 0.235096 0.302560i
\(254\) 25.8165 1.61987
\(255\) 0.421302 1.29663i 0.0263830 0.0811984i
\(256\) −12.1270 + 8.81076i −0.757936 + 0.550673i
\(257\) −16.4322 11.9387i −1.02501 0.744717i −0.0577100 0.998333i \(-0.518380\pi\)
−0.967305 + 0.253617i \(0.918380\pi\)
\(258\) −1.09724 3.37696i −0.0683113 0.210240i
\(259\) −0.285969 0.880123i −0.0177693 0.0546882i
\(260\) 0.839687 + 0.610068i 0.0520751 + 0.0378348i
\(261\) −2.23832 + 1.62623i −0.138549 + 0.100661i
\(262\) 5.83100 17.9460i 0.360240 1.10871i
\(263\) 26.5877 1.63947 0.819734 0.572745i \(-0.194121\pi\)
0.819734 + 0.572745i \(0.194121\pi\)
\(264\) −0.226723 0.334215i −0.0139539 0.0205695i
\(265\) 5.20141 0.319520
\(266\) −3.20729 + 9.87101i −0.196651 + 0.605231i
\(267\) 5.61888 4.08236i 0.343870 0.249836i
\(268\) 13.9208 + 10.1140i 0.850346 + 0.617813i
\(269\) −6.94122 21.3629i −0.423214 1.30252i −0.904695 0.426061i \(-0.859901\pi\)
0.481481 0.876457i \(-0.340099\pi\)
\(270\) −0.313668 0.965371i −0.0190892 0.0587506i
\(271\) 14.6456 + 10.6407i 0.889660 + 0.646376i 0.935789 0.352560i \(-0.114689\pi\)
−0.0461295 + 0.998935i \(0.514689\pi\)
\(272\) −8.48582 + 6.16531i −0.514528 + 0.373827i
\(273\) −0.931702 + 2.86748i −0.0563892 + 0.173548i
\(274\) −7.82253 −0.472576
\(275\) 0.507633 15.7333i 0.0306114 0.948757i
\(276\) 3.78620 0.227903
\(277\) −7.20212 + 22.1658i −0.432733 + 1.33182i 0.462658 + 0.886537i \(0.346896\pi\)
−0.895392 + 0.445279i \(0.853104\pi\)
\(278\) 24.4607 17.7718i 1.46706 1.06588i
\(279\) 7.91896 + 5.75346i 0.474096 + 0.344451i
\(280\) 0.0571497 + 0.175889i 0.00341535 + 0.0105114i
\(281\) 0.525419 + 1.61707i 0.0313439 + 0.0964665i 0.965505 0.260386i \(-0.0838498\pi\)
−0.934161 + 0.356853i \(0.883850\pi\)
\(282\) 19.7225 + 14.3292i 1.17446 + 0.853292i
\(283\) 7.94001 5.76876i 0.471985 0.342917i −0.326230 0.945291i \(-0.605778\pi\)
0.798214 + 0.602374i \(0.205778\pi\)
\(284\) 7.44528 22.9142i 0.441796 1.35971i
\(285\) −0.860551 −0.0509746
\(286\) −6.41936 + 1.85917i −0.379585 + 0.109935i
\(287\) 15.2394 0.899555
\(288\) −2.48847 + 7.65871i −0.146634 + 0.451294i
\(289\) 7.82708 5.68671i 0.460417 0.334512i
\(290\) 2.27201 + 1.65071i 0.133417 + 0.0969331i
\(291\) −4.98454 15.3408i −0.292199 0.899295i
\(292\) 3.70811 + 11.4124i 0.217001 + 0.667860i
\(293\) −9.50684 6.90712i −0.555396 0.403519i 0.274375 0.961623i \(-0.411529\pi\)
−0.829771 + 0.558104i \(0.811529\pi\)
\(294\) −3.40801 + 2.47606i −0.198759 + 0.144407i
\(295\) −0.0187853 + 0.0578153i −0.00109372 + 0.00336614i
\(296\) 0.0373747 0.00217236
\(297\) 3.11961 + 1.12608i 0.181018 + 0.0653418i
\(298\) −16.8871 −0.978245
\(299\) 0.567843 1.74764i 0.0328392 0.101069i
\(300\) 7.91163 5.74814i 0.456778 0.331869i
\(301\) −4.29819 3.12282i −0.247744 0.179996i
\(302\) −8.94440 27.5280i −0.514693 1.58406i
\(303\) −3.64428 11.2159i −0.209358 0.644339i
\(304\) 5.35623 + 3.89153i 0.307201 + 0.223194i
\(305\) 5.99217 4.35356i 0.343110 0.249284i
\(306\) −1.68530 + 5.18683i −0.0963423 + 0.296511i
\(307\) 3.60579 0.205793 0.102897 0.994692i \(-0.467189\pi\)
0.102897 + 0.994692i \(0.467189\pi\)
\(308\) −19.3799 6.99555i −1.10427 0.398608i
\(309\) −2.71634 −0.154527
\(310\) 3.07030 9.44940i 0.174381 0.536690i
\(311\) 15.6556 11.3744i 0.887746 0.644985i −0.0475434 0.998869i \(-0.515139\pi\)
0.935289 + 0.353884i \(0.115139\pi\)
\(312\) −0.0985128 0.0715738i −0.00557719 0.00405207i
\(313\) 5.55059 + 17.0830i 0.313738 + 0.965586i 0.976271 + 0.216553i \(0.0694814\pi\)
−0.662533 + 0.749033i \(0.730519\pi\)
\(314\) 7.50801 + 23.1073i 0.423701 + 1.30402i
\(315\) −1.22872 0.892720i −0.0692307 0.0502991i
\(316\) −13.7212 + 9.96905i −0.771879 + 0.560803i
\(317\) 0.538117 1.65616i 0.0302237 0.0930189i −0.934807 0.355157i \(-0.884427\pi\)
0.965030 + 0.262138i \(0.0844275\pi\)
\(318\) −20.8068 −1.16679
\(319\) −8.81395 + 2.55268i −0.493486 + 0.142923i
\(320\) 4.26961 0.238678
\(321\) 0.398206 1.22555i 0.0222257 0.0684037i
\(322\) 9.03201 6.56214i 0.503334 0.365694i
\(323\) 3.74061 + 2.71771i 0.208133 + 0.151217i
\(324\) 0.636708 + 1.95958i 0.0353727 + 0.108866i
\(325\) −1.46667 4.51395i −0.0813563 0.250389i
\(326\) −9.53064 6.92441i −0.527853 0.383508i
\(327\) 9.33238 6.78037i 0.516082 0.374955i
\(328\) −0.190192 + 0.585350i −0.0105016 + 0.0323206i
\(329\) 36.4764 2.01101
\(330\) 0.108564 3.36479i 0.00597627 0.185226i
\(331\) 5.50106 0.302365 0.151183 0.988506i \(-0.451692\pi\)
0.151183 + 0.988506i \(0.451692\pi\)
\(332\) 1.98069 6.09593i 0.108704 0.334558i
\(333\) −0.248313 + 0.180410i −0.0136075 + 0.00988641i
\(334\) 17.2952 + 12.5657i 0.946349 + 0.687563i
\(335\) 1.29997 + 4.00088i 0.0710247 + 0.218592i
\(336\) 3.61080 + 11.1129i 0.196985 + 0.606259i
\(337\) −3.51773 2.55578i −0.191623 0.139222i 0.487837 0.872935i \(-0.337786\pi\)
−0.679460 + 0.733712i \(0.737786\pi\)
\(338\) −1.63021 + 1.18442i −0.0886718 + 0.0644238i
\(339\) 0.695157 2.13947i 0.0377557 0.116200i
\(340\) 2.80911 0.152345
\(341\) 18.2252 + 26.8659i 0.986948 + 1.45487i
\(342\) 3.44240 0.186143
\(343\) 4.57416 14.0778i 0.246982 0.760131i
\(344\) 0.173591 0.126121i 0.00935939 0.00679999i
\(345\) 0.748869 + 0.544085i 0.0403177 + 0.0292925i
\(346\) 10.5536 + 32.4807i 0.567367 + 1.74617i
\(347\) −4.20501 12.9417i −0.225737 0.694747i −0.998216 0.0597064i \(-0.980984\pi\)
0.772479 0.635040i \(-0.219016\pi\)
\(348\) −4.61190 3.35074i −0.247224 0.179619i
\(349\) 19.1999 13.9495i 1.02775 0.746701i 0.0598894 0.998205i \(-0.480925\pi\)
0.967856 + 0.251504i \(0.0809252\pi\)
\(350\) 8.91074 27.4244i 0.476299 1.46590i
\(351\) 1.00000 0.0533761
\(352\) −16.3874 + 21.0899i −0.873449 + 1.12410i
\(353\) 7.35753 0.391602 0.195801 0.980644i \(-0.437269\pi\)
0.195801 + 0.980644i \(0.437269\pi\)
\(354\) 0.0751455 0.231274i 0.00399394 0.0122921i
\(355\) 4.76541 3.46227i 0.252922 0.183758i
\(356\) 11.5773 + 8.41141i 0.613596 + 0.445804i
\(357\) 2.52166 + 7.76087i 0.133460 + 0.410749i
\(358\) −2.45585 7.55832i −0.129796 0.399470i
\(359\) −15.0097 10.9052i −0.792179 0.575552i 0.116430 0.993199i \(-0.462855\pi\)
−0.908609 + 0.417647i \(0.862855\pi\)
\(360\) 0.0496243 0.0360542i 0.00261543 0.00190022i
\(361\) −4.96948 + 15.2945i −0.261551 + 0.804973i
\(362\) 0.678601 0.0356665
\(363\) 8.46389 + 7.02585i 0.444239 + 0.368762i
\(364\) −6.21230 −0.325613
\(365\) −0.906561 + 2.79011i −0.0474516 + 0.146041i
\(366\) −23.9700 + 17.4152i −1.25293 + 0.910308i
\(367\) 20.3776 + 14.8052i 1.06370 + 0.772826i 0.974770 0.223212i \(-0.0716541\pi\)
0.0889336 + 0.996038i \(0.471654\pi\)
\(368\) −2.20067 6.77297i −0.114718 0.353065i
\(369\) −1.56191 4.80707i −0.0813099 0.250246i
\(370\) 0.252051 + 0.183125i 0.0131035 + 0.00952024i
\(371\) −25.1867 + 18.2992i −1.30763 + 0.950048i
\(372\) −6.23233 + 19.1811i −0.323131 + 0.994496i
\(373\) 4.76978 0.246970 0.123485 0.992346i \(-0.460593\pi\)
0.123485 + 0.992346i \(0.460593\pi\)
\(374\) −11.0983 + 14.2831i −0.573878 + 0.738560i
\(375\) 4.90952 0.253527
\(376\) −0.455235 + 1.40107i −0.0234769 + 0.0722546i
\(377\) −2.23832 + 1.62623i −0.115279 + 0.0837553i
\(378\) 4.91517 + 3.57108i 0.252809 + 0.183676i
\(379\) 5.11951 + 15.7562i 0.262972 + 0.809344i 0.992154 + 0.125024i \(0.0399008\pi\)
−0.729182 + 0.684320i \(0.760099\pi\)
\(380\) −0.547919 1.68632i −0.0281077 0.0865065i
\(381\) −10.3650 7.53061i −0.531015 0.385805i
\(382\) −39.7741 + 28.8976i −2.03502 + 1.47853i
\(383\) 9.81799 30.2167i 0.501676 1.54400i −0.304612 0.952477i \(-0.598527\pi\)
0.806288 0.591523i \(-0.201473\pi\)
\(384\) −0.973704 −0.0496891
\(385\) −2.82786 4.16857i −0.144121 0.212450i
\(386\) 19.8896 1.01236
\(387\) −0.544523 + 1.67587i −0.0276797 + 0.0851892i
\(388\) 26.8880 19.5352i 1.36503 0.991752i
\(389\) −2.39682 1.74139i −0.121524 0.0882920i 0.525363 0.850878i \(-0.323929\pi\)
−0.646887 + 0.762586i \(0.723929\pi\)
\(390\) −0.313668 0.965371i −0.0158832 0.0488834i
\(391\) −1.53687 4.73001i −0.0777230 0.239207i
\(392\) −0.205944 0.149627i −0.0104018 0.00755731i
\(393\) −7.57586 + 5.50419i −0.382152 + 0.277650i
\(394\) −3.49201 + 10.7473i −0.175925 + 0.541441i
\(395\) −4.14647 −0.208632
\(396\) −0.220372 + 6.83012i −0.0110741 + 0.343226i
\(397\) 23.2897 1.16888 0.584438 0.811439i \(-0.301315\pi\)
0.584438 + 0.811439i \(0.301315\pi\)
\(398\) −13.0645 + 40.2085i −0.654865 + 2.01547i
\(399\) 4.16703 3.02753i 0.208613 0.151566i
\(400\) −14.8811 10.8117i −0.744055 0.540587i
\(401\) −0.0508412 0.156473i −0.00253889 0.00781390i 0.949779 0.312921i \(-0.101308\pi\)
−0.952318 + 0.305107i \(0.901308\pi\)
\(402\) −5.20015 16.0044i −0.259360 0.798228i
\(403\) 7.91896 + 5.75346i 0.394471 + 0.286600i
\(404\) 19.6582 14.2826i 0.978034 0.710584i
\(405\) −0.155663 + 0.479080i −0.00773493 + 0.0238057i
\(406\) −16.8091 −0.834223
\(407\) −0.977796 + 0.283188i −0.0484675 + 0.0140371i
\(408\) −0.329568 −0.0163160
\(409\) 6.36359 19.5851i 0.314659 0.968422i −0.661235 0.750179i \(-0.729967\pi\)
0.975894 0.218243i \(-0.0700325\pi\)
\(410\) −4.15068 + 3.01565i −0.204988 + 0.148932i
\(411\) 3.14065 + 2.28181i 0.154917 + 0.112554i
\(412\) −1.72951 5.32289i −0.0852070 0.262240i
\(413\) −0.112438 0.346048i −0.00553270 0.0170279i
\(414\) −2.99564 2.17646i −0.147228 0.106967i
\(415\) 1.26776 0.921079i 0.0622317 0.0452140i
\(416\) −2.48847 + 7.65871i −0.122007 + 0.375499i
\(417\) −15.0047 −0.734781
\(418\) 10.7389 + 3.87641i 0.525258 + 0.189602i
\(419\) −17.6844 −0.863940 −0.431970 0.901888i \(-0.642181\pi\)
−0.431970 + 0.901888i \(0.642181\pi\)
\(420\) 0.967022 2.97619i 0.0471859 0.145223i
\(421\) 12.1495 8.82716i 0.592132 0.430209i −0.250945 0.968001i \(-0.580741\pi\)
0.843078 + 0.537792i \(0.180741\pi\)
\(422\) −24.5204 17.8151i −1.19363 0.867225i
\(423\) −3.73852 11.5060i −0.181773 0.559440i
\(424\) −0.388541 1.19581i −0.0188692 0.0580735i
\(425\) −10.3924 7.55056i −0.504108 0.366256i
\(426\) −19.0627 + 13.8499i −0.923591 + 0.671028i
\(427\) −13.6994 + 42.1624i −0.662960 + 2.04038i
\(428\) 2.65512 0.128340
\(429\) 3.11961 + 1.12608i 0.150616 + 0.0543677i
\(430\) 1.78863 0.0862556
\(431\) 2.54742 7.84014i 0.122705 0.377646i −0.870771 0.491688i \(-0.836380\pi\)
0.993476 + 0.114042i \(0.0363799\pi\)
\(432\) 3.13534 2.27796i 0.150849 0.109598i
\(433\) 14.2108 + 10.3248i 0.682928 + 0.496176i 0.874328 0.485336i \(-0.161303\pi\)
−0.191400 + 0.981512i \(0.561303\pi\)
\(434\) 18.3769 + 56.5584i 0.882122 + 2.71489i
\(435\) −0.430674 1.32548i −0.0206492 0.0635518i
\(436\) 19.2287 + 13.9705i 0.920889 + 0.669065i
\(437\) −2.53968 + 1.84518i −0.121489 + 0.0882671i
\(438\) 3.62645 11.1611i 0.173278 0.533296i
\(439\) 35.0774 1.67415 0.837075 0.547087i \(-0.184264\pi\)
0.837075 + 0.547087i \(0.184264\pi\)
\(440\) 0.195408 0.0565939i 0.00931572 0.00269801i
\(441\) 2.09053 0.0995491
\(442\) −1.68530 + 5.18683i −0.0801617 + 0.246712i
\(443\) −29.4534 + 21.3991i −1.39937 + 1.01670i −0.404609 + 0.914490i \(0.632592\pi\)
−0.994763 + 0.102213i \(0.967408\pi\)
\(444\) −0.511632 0.371722i −0.0242810 0.0176412i
\(445\) 1.08113 + 3.32736i 0.0512503 + 0.157732i
\(446\) 11.7527 + 36.1710i 0.556505 + 1.71275i
\(447\) 6.77996 + 4.92593i 0.320681 + 0.232989i
\(448\) −20.6747 + 15.0210i −0.976787 + 0.709677i
\(449\) 6.65709 20.4884i 0.314168 0.966908i −0.661928 0.749567i \(-0.730262\pi\)
0.976096 0.217341i \(-0.0697384\pi\)
\(450\) −9.56394 −0.450848
\(451\) 0.540597 16.7550i 0.0254557 0.788963i
\(452\) 4.63509 0.218016
\(453\) −4.43880 + 13.6612i −0.208553 + 0.641860i
\(454\) −30.1480 + 21.9038i −1.41492 + 1.02800i
\(455\) −1.22872 0.892720i −0.0576034 0.0418513i
\(456\) 0.0642824 + 0.197841i 0.00301030 + 0.00926475i
\(457\) −6.15430 18.9410i −0.287886 0.886023i −0.985519 0.169567i \(-0.945763\pi\)
0.697633 0.716456i \(-0.254237\pi\)
\(458\) −16.9275 12.2985i −0.790970 0.574673i
\(459\) 2.18961 1.59085i 0.102202 0.0742543i
\(460\) −0.589370 + 1.81389i −0.0274795 + 0.0845733i
\(461\) −17.9949 −0.838105 −0.419052 0.907962i \(-0.637638\pi\)
−0.419052 + 0.907962i \(0.637638\pi\)
\(462\) 11.3121 + 16.6752i 0.526285 + 0.775802i
\(463\) −9.00266 −0.418389 −0.209194 0.977874i \(-0.567084\pi\)
−0.209194 + 0.977874i \(0.567084\pi\)
\(464\) −3.31340 + 10.1976i −0.153821 + 0.473411i
\(465\) −3.98905 + 2.89822i −0.184988 + 0.134402i
\(466\) 16.4675 + 11.9643i 0.762841 + 0.554236i
\(467\) −10.9024 33.5541i −0.504502 1.55270i −0.801606 0.597852i \(-0.796021\pi\)
0.297104 0.954845i \(-0.403979\pi\)
\(468\) 0.636708 + 1.95958i 0.0294318 + 0.0905818i
\(469\) −20.3704 14.8000i −0.940619 0.683399i
\(470\) −9.93489 + 7.21812i −0.458262 + 0.332947i
\(471\) 3.72596 11.4673i 0.171683 0.528387i
\(472\) 0.0146950 0.000676393
\(473\) −3.58586 + 4.61488i −0.164878 + 0.212192i
\(474\) 16.5868 0.761858
\(475\) −2.50558 + 7.71138i −0.114964 + 0.353822i
\(476\) −13.6025 + 9.88281i −0.623471 + 0.452978i
\(477\) 8.35366 + 6.06929i 0.382488 + 0.277894i
\(478\) −17.5732 54.0847i −0.803778 2.47377i
\(479\) 4.74905 + 14.6161i 0.216990 + 0.667826i 0.999006 + 0.0445680i \(0.0141911\pi\)
−0.782017 + 0.623258i \(0.785809\pi\)
\(480\) −3.28177 2.38435i −0.149792 0.108830i
\(481\) −0.248313 + 0.180410i −0.0113221 + 0.00822599i
\(482\) 12.6151 38.8252i 0.574601 1.76844i
\(483\) −5.54040 −0.252097
\(484\) −8.37874 + 21.0591i −0.380852 + 0.957233i
\(485\) 8.12539 0.368955
\(486\) 0.622685 1.91643i 0.0282456 0.0869309i
\(487\) −27.3538 + 19.8737i −1.23952 + 0.900564i −0.997566 0.0697235i \(-0.977788\pi\)
−0.241954 + 0.970288i \(0.577788\pi\)
\(488\) −1.44850 1.05239i −0.0655703 0.0476396i
\(489\) 1.80659 + 5.56013i 0.0816970 + 0.251438i
\(490\) −0.655733 2.01814i −0.0296230 0.0911701i
\(491\) 16.9393 + 12.3072i 0.764462 + 0.555414i 0.900276 0.435320i \(-0.143365\pi\)
−0.135814 + 0.990734i \(0.543365\pi\)
\(492\) 8.42538 6.12140i 0.379846 0.275974i
\(493\) −2.31396 + 7.12165i −0.104216 + 0.320743i
\(494\) 3.44240 0.154881
\(495\) −1.02509 + 1.31925i −0.0460743 + 0.0592960i
\(496\) 37.9347 1.70332
\(497\) −10.8948 + 33.5306i −0.488697 + 1.50405i
\(498\) −5.07131 + 3.68452i −0.227251 + 0.165107i
\(499\) 1.70160 + 1.23628i 0.0761741 + 0.0553437i 0.625221 0.780448i \(-0.285009\pi\)
−0.549046 + 0.835792i \(0.685009\pi\)
\(500\) 3.12593 + 9.62063i 0.139796 + 0.430248i
\(501\) −3.27841 10.0899i −0.146469 0.450784i
\(502\) 19.6659 + 14.2881i 0.877732 + 0.637710i
\(503\) −16.9728 + 12.3315i −0.756781 + 0.549834i −0.897921 0.440156i \(-0.854923\pi\)
0.141140 + 0.989990i \(0.454923\pi\)
\(504\) −0.113452 + 0.349169i −0.00505355 + 0.0155532i
\(505\) 5.94061 0.264354
\(506\) −6.89435 10.1630i −0.306491 0.451802i
\(507\) 1.00000 0.0444116
\(508\) 8.15740 25.1059i 0.361926 1.11389i
\(509\) −33.8976 + 24.6280i −1.50248 + 1.09162i −0.533106 + 0.846049i \(0.678975\pi\)
−0.969379 + 0.245570i \(0.921025\pi\)
\(510\) −2.22257 1.61479i −0.0984169 0.0715041i
\(511\) −5.42612 16.6999i −0.240038 0.738760i
\(512\) 9.93568 + 30.5789i 0.439099 + 1.35141i
\(513\) −1.38208 1.00414i −0.0610202 0.0443338i
\(514\) −33.1118 + 24.0571i −1.46050 + 1.06111i
\(515\) 0.422832 1.30134i 0.0186322 0.0573440i
\(516\) −3.63071 −0.159833
\(517\) 1.29395 40.1040i 0.0569078 1.76377i
\(518\) −1.86476 −0.0819328
\(519\) 5.23740 16.1191i 0.229896 0.707548i
\(520\) 0.0496243 0.0360542i 0.00217617 0.00158108i
\(521\) 29.5259 + 21.4518i 1.29355 + 0.939820i 0.999871 0.0160836i \(-0.00511978\pi\)
0.293681 + 0.955904i \(0.405120\pi\)
\(522\) 1.72279 + 5.30221i 0.0754046 + 0.232071i
\(523\) 1.44454 + 4.44584i 0.0631654 + 0.194403i 0.977659 0.210197i \(-0.0674106\pi\)
−0.914494 + 0.404600i \(0.867411\pi\)
\(524\) −15.6095 11.3410i −0.681906 0.495434i
\(525\) −11.5772 + 8.41132i −0.505270 + 0.367100i
\(526\) 16.5558 50.9534i 0.721865 2.22167i
\(527\) 26.4923 1.15402
\(528\) 12.3462 3.57568i 0.537298 0.155612i
\(529\) −19.6233 −0.853187
\(530\) 3.23884 9.96812i 0.140686 0.432987i
\(531\) −0.0976321 + 0.0709338i −0.00423687 + 0.00307827i
\(532\) 8.58588 + 6.23801i 0.372245 + 0.270452i
\(533\) −1.56191 4.80707i −0.0676539 0.208217i
\(534\) −4.32475 13.3102i −0.187150 0.575989i
\(535\) 0.525152 + 0.381546i 0.0227043 + 0.0164957i
\(536\) 0.822698 0.597725i 0.0355352 0.0258178i
\(537\) −1.21875 + 3.75093i −0.0525930 + 0.161865i
\(538\) −45.2626 −1.95141
\(539\) 6.52163 + 2.35411i 0.280907 + 0.101399i
\(540\) −1.03791 −0.0446645
\(541\) 4.65545 14.3280i 0.200153 0.616009i −0.799724 0.600367i \(-0.795021\pi\)
0.999878 0.0156413i \(-0.00497897\pi\)
\(542\) 29.5117 21.4415i 1.26764 0.920992i
\(543\) −0.272450 0.197946i −0.0116919 0.00849469i
\(544\) 6.73506 + 20.7284i 0.288763 + 0.888722i
\(545\) 1.79564 + 5.52641i 0.0769167 + 0.236725i
\(546\) 4.91517 + 3.57108i 0.210350 + 0.152828i
\(547\) −19.7950 + 14.3819i −0.846371 + 0.614925i −0.924143 0.382046i \(-0.875219\pi\)
0.0777718 + 0.996971i \(0.475219\pi\)
\(548\) −2.47173 + 7.60721i −0.105587 + 0.324964i
\(549\) 14.7036 0.627535
\(550\) −29.8357 10.7698i −1.27220 0.459224i
\(551\) 4.72650 0.201355
\(552\) 0.0691455 0.212808i 0.00294303 0.00905770i
\(553\) 20.0784 14.5878i 0.853821 0.620337i
\(554\) 37.9946 + 27.6047i 1.61423 + 1.17281i
\(555\) −0.0477778 0.147045i −0.00202806 0.00624171i
\(556\) −9.55358 29.4029i −0.405162 1.24696i
\(557\) −1.66821 1.21203i −0.0706844 0.0513552i 0.551882 0.833922i \(-0.313910\pi\)
−0.622566 + 0.782567i \(0.713910\pi\)
\(558\) 15.9571 11.5935i 0.675518 0.490793i
\(559\) −0.544523 + 1.67587i −0.0230309 + 0.0708817i
\(560\) −5.88604 −0.248730
\(561\) 8.62215 2.49714i 0.364027 0.105429i
\(562\) 3.42617 0.144524
\(563\) 2.08233 6.40875i 0.0877597 0.270096i −0.897540 0.440934i \(-0.854647\pi\)
0.985299 + 0.170837i \(0.0546473\pi\)
\(564\) 20.1666 14.6519i 0.849168 0.616956i
\(565\) 0.916769 + 0.666072i 0.0385688 + 0.0280219i
\(566\) −6.11128 18.8086i −0.256876 0.790583i
\(567\) −0.931702 2.86748i −0.0391278 0.120423i
\(568\) −1.15195 0.836941i −0.0483347 0.0351172i
\(569\) 15.3660 11.1641i 0.644178 0.468023i −0.217105 0.976148i \(-0.569661\pi\)
0.861283 + 0.508125i \(0.169661\pi\)
\(570\) −0.535852 + 1.64918i −0.0224444 + 0.0690767i
\(571\) 25.5853 1.07071 0.535357 0.844626i \(-0.320177\pi\)
0.535357 + 0.844626i \(0.320177\pi\)
\(572\) −0.220372 + 6.83012i −0.00921423 + 0.285582i
\(573\) 24.3981 1.01925
\(574\) 9.48937 29.2053i 0.396079 1.21900i
\(575\) 7.05593 5.12644i 0.294253 0.213787i
\(576\) 6.85716 + 4.98202i 0.285715 + 0.207584i
\(577\) −3.31312 10.1967i −0.137927 0.424496i 0.858107 0.513471i \(-0.171641\pi\)
−0.996034 + 0.0889753i \(0.971641\pi\)
\(578\) −6.02436 18.5411i −0.250580 0.771207i
\(579\) −7.98543 5.80175i −0.331863 0.241113i
\(580\) 2.32317 1.68788i 0.0964645 0.0700856i
\(581\) −2.89837 + 8.92025i −0.120244 + 0.370074i
\(582\) −32.5034 −1.34731
\(583\) 19.2256 + 28.3407i 0.796244 + 1.17375i
\(584\) 0.709166 0.0293455
\(585\) −0.155663 + 0.479080i −0.00643585 + 0.0198075i
\(586\) −19.1568 + 13.9182i −0.791359 + 0.574956i
\(587\) −3.19934 2.32446i −0.132051 0.0959407i 0.519799 0.854289i \(-0.326007\pi\)
−0.651850 + 0.758348i \(0.726007\pi\)
\(588\) 1.33106 + 4.09657i 0.0548919 + 0.168940i
\(589\) −5.16735 15.9035i −0.212917 0.655290i
\(590\) 0.0991015 + 0.0720015i 0.00407994 + 0.00296425i
\(591\) 4.53695 3.29629i 0.186625 0.135591i
\(592\) −0.367579 + 1.13129i −0.0151074 + 0.0464959i
\(593\) −1.31718 −0.0540902 −0.0270451 0.999634i \(-0.508610\pi\)
−0.0270451 + 0.999634i \(0.508610\pi\)
\(594\) 4.10058 5.27730i 0.168249 0.216530i
\(595\) −4.11061 −0.168518
\(596\) −5.33593 + 16.4223i −0.218568 + 0.672683i
\(597\) 16.9739 12.3323i 0.694697 0.504727i
\(598\) −2.99564 2.17646i −0.122501 0.0890021i
\(599\) 5.09417 + 15.6782i 0.208142 + 0.640595i 0.999570 + 0.0293324i \(0.00933812\pi\)
−0.791428 + 0.611263i \(0.790662\pi\)
\(600\) −0.178595 0.549658i −0.00729109 0.0224397i
\(601\) −7.76270 5.63993i −0.316647 0.230058i 0.418096 0.908403i \(-0.362697\pi\)
−0.734743 + 0.678345i \(0.762697\pi\)
\(602\) −8.66108 + 6.29264i −0.352999 + 0.256469i
\(603\) −2.58066 + 7.94244i −0.105092 + 0.323441i
\(604\) −29.5965 −1.20427
\(605\) −4.68346 + 2.96122i −0.190410 + 0.120391i
\(606\) −23.7638 −0.965337
\(607\) 3.10034 9.54185i 0.125839 0.387292i −0.868214 0.496190i \(-0.834732\pi\)
0.994053 + 0.108898i \(0.0347321\pi\)
\(608\) 11.1297 8.08617i 0.451367 0.327937i
\(609\) 6.74865 + 4.90318i 0.273469 + 0.198687i
\(610\) −4.61206 14.1944i −0.186737 0.574716i
\(611\) −3.73852 11.5060i −0.151244 0.465482i
\(612\) 4.51154 + 3.27783i 0.182368 + 0.132498i
\(613\) 16.3499 11.8789i 0.660365 0.479783i −0.206421 0.978463i \(-0.566182\pi\)
0.866786 + 0.498680i \(0.166182\pi\)
\(614\) 2.24527 6.91023i 0.0906117 0.278874i
\(615\) 2.54610 0.102669
\(616\) −0.747118 + 0.961515i −0.0301023 + 0.0387405i
\(617\) −45.4642 −1.83032 −0.915161 0.403089i \(-0.867937\pi\)
−0.915161 + 0.403089i \(0.867937\pi\)
\(618\) −1.69142 + 5.20566i −0.0680390 + 0.209402i
\(619\) 23.9148 17.3751i 0.961218 0.698366i 0.00778499 0.999970i \(-0.497522\pi\)
0.953433 + 0.301604i \(0.0975219\pi\)
\(620\) −8.21916 5.97157i −0.330089 0.239824i
\(621\) 0.567843 + 1.74764i 0.0227868 + 0.0701305i
\(622\) −12.0498 37.0855i −0.483153 1.48699i
\(623\) −16.9412 12.3085i −0.678735 0.493130i
\(624\) 3.13534 2.27796i 0.125514 0.0911912i
\(625\) 6.56913 20.2177i 0.262765 0.808708i
\(626\) 36.1945 1.44662
\(627\) −3.18080 4.68885i −0.127029 0.187254i
\(628\) 24.8436 0.991367
\(629\) −0.256705 + 0.790056i −0.0102355 + 0.0315016i
\(630\) −2.47594 + 1.79888i −0.0986438 + 0.0716689i
\(631\) 7.94507 + 5.77243i 0.316288 + 0.229797i 0.734590 0.678511i \(-0.237375\pi\)
−0.418302 + 0.908308i \(0.637375\pi\)
\(632\) 0.309738 + 0.953276i 0.0123207 + 0.0379193i
\(633\) 4.64799 + 14.3051i 0.184741 + 0.568575i
\(634\) −2.83882 2.06253i −0.112744 0.0819134i
\(635\) 5.22121 3.79343i 0.207197 0.150538i
\(636\) −6.57445 + 20.2341i −0.260694 + 0.802333i
\(637\) 2.09053 0.0828299
\(638\) −0.596279 + 18.4808i −0.0236069 + 0.731662i
\(639\) 11.6934 0.462584
\(640\) 0.151569 0.466482i 0.00599130 0.0184393i
\(641\) 3.00141 2.18065i 0.118548 0.0861305i −0.526931 0.849908i \(-0.676657\pi\)
0.645480 + 0.763777i \(0.276657\pi\)
\(642\) −2.10073 1.52627i −0.0829091 0.0602370i
\(643\) −11.8025 36.3245i −0.465446 1.43250i −0.858420 0.512947i \(-0.828554\pi\)
0.392974 0.919550i \(-0.371446\pi\)
\(644\) −3.52761 10.8569i −0.139007 0.427821i
\(645\) −0.718114 0.521740i −0.0282757 0.0205435i
\(646\) 7.53751 5.47632i 0.296559 0.215463i
\(647\) −1.51425 + 4.66038i −0.0595312 + 0.183218i −0.976400 0.215971i \(-0.930708\pi\)
0.916869 + 0.399189i \(0.130708\pi\)
\(648\) 0.121769 0.00478352
\(649\) −0.384451 + 0.111344i −0.0150910 + 0.00437064i
\(650\) −9.56394 −0.375128
\(651\) 9.11984 28.0680i 0.357435 1.10007i
\(652\) −9.74527 + 7.08035i −0.381654 + 0.277288i
\(653\) 14.5884 + 10.5991i 0.570887 + 0.414773i 0.835427 0.549601i \(-0.185220\pi\)
−0.264541 + 0.964375i \(0.585220\pi\)
\(654\) −7.18296 22.1069i −0.280876 0.864447i
\(655\) −1.45767 4.48624i −0.0569558 0.175292i
\(656\) −15.8474 11.5138i −0.618738 0.449539i
\(657\) −4.71162 + 3.42319i −0.183818 + 0.133551i
\(658\) 22.7133 69.9044i 0.885457 2.72516i
\(659\) −14.1253 −0.550243 −0.275121 0.961409i \(-0.588718\pi\)
−0.275121 + 0.961409i \(0.588718\pi\)
\(660\) −3.23787 1.16877i −0.126034 0.0454943i
\(661\) −49.7686 −1.93578 −0.967888 0.251383i \(-0.919115\pi\)
−0.967888 + 0.251383i \(0.919115\pi\)
\(662\) 3.42543 10.5424i 0.133133 0.409741i
\(663\) 2.18961 1.59085i 0.0850375 0.0617833i
\(664\) −0.306457 0.222654i −0.0118928 0.00864064i
\(665\) 0.801777 + 2.46762i 0.0310916 + 0.0956900i
\(666\) 0.191122 + 0.588213i 0.00740583 + 0.0227928i
\(667\) −4.11309 2.98834i −0.159260 0.115709i
\(668\) 17.6846 12.8486i 0.684239 0.497129i
\(669\) 5.83244 17.9504i 0.225495 0.694003i
\(670\) 8.47687 0.327490
\(671\) 45.8695 + 16.5575i 1.77077 + 0.639194i
\(672\) 24.2797 0.936611
\(673\) −1.89380 + 5.82853i −0.0730008 + 0.224673i −0.980899 0.194517i \(-0.937686\pi\)
0.907898 + 0.419190i \(0.137686\pi\)
\(674\) −7.08841 + 5.15003i −0.273035 + 0.198372i
\(675\) 3.83980 + 2.78978i 0.147794 + 0.107379i
\(676\) 0.636708 + 1.95958i 0.0244888 + 0.0753687i
\(677\) −2.03380 6.25941i −0.0781654 0.240569i 0.904337 0.426820i \(-0.140366\pi\)
−0.982502 + 0.186251i \(0.940366\pi\)
\(678\) −3.66728 2.66444i −0.140841 0.102327i
\(679\) −39.3455 + 28.5861i −1.50994 + 1.09704i
\(680\) 0.0513014 0.157889i 0.00196732 0.00605478i
\(681\) 18.4933 0.708666
\(682\) 62.8351 18.1982i 2.40608 0.696846i
\(683\) −34.3084 −1.31277 −0.656387 0.754425i \(-0.727916\pi\)
−0.656387 + 0.754425i \(0.727916\pi\)
\(684\) 1.08771 3.34764i 0.0415898 0.128000i
\(685\) −1.58205 + 1.14943i −0.0604471 + 0.0439174i
\(686\) −24.1309 17.5321i −0.921320 0.669379i
\(687\) 3.20872 + 9.87541i 0.122420 + 0.376771i
\(688\) 2.11029 + 6.49481i 0.0804541 + 0.247612i
\(689\) 8.35366 + 6.06929i 0.318249 + 0.231221i
\(690\) 1.50901 1.09636i 0.0574470 0.0417377i
\(691\) −9.87018 + 30.3773i −0.375479 + 1.15561i 0.567675 + 0.823252i \(0.307843\pi\)
−0.943155 + 0.332354i \(0.892157\pi\)
\(692\) 34.9214 1.32751
\(693\) 0.322473 9.99459i 0.0122498 0.379663i
\(694\) −27.4202 −1.04086
\(695\) 2.33566 7.18843i 0.0885968 0.272673i
\(696\) −0.272557 + 0.198024i −0.0103312 + 0.00750609i
\(697\) −11.0673 8.04086i −0.419204 0.304569i
\(698\) −14.7778 45.4813i −0.559347 1.72149i
\(699\) −3.12152 9.60704i −0.118067 0.363372i
\(700\) −23.8540 17.3309i −0.901596 0.655048i
\(701\) 28.5661 20.7545i 1.07893 0.783887i 0.101433 0.994842i \(-0.467657\pi\)
0.977496 + 0.210955i \(0.0676573\pi\)
\(702\) 0.622685 1.91643i 0.0235017 0.0723309i
\(703\) 0.524345 0.0197760
\(704\) 15.7815 + 23.2636i 0.594787 + 0.876781i
\(705\) 6.09424 0.229522
\(706\) 4.58142 14.1002i 0.172424 0.530667i
\(707\) −28.7661 + 20.8998i −1.08186 + 0.786019i
\(708\) −0.201164 0.146154i −0.00756021 0.00549281i
\(709\) −16.3320 50.2647i −0.613360 1.88773i −0.423422 0.905933i \(-0.639171\pi\)
−0.189939 0.981796i \(-0.560829\pi\)
\(710\) −3.66784 11.2885i −0.137652 0.423648i
\(711\) −6.65940 4.83833i −0.249747 0.181452i
\(712\) 0.684203 0.497103i 0.0256416 0.0186297i
\(713\) −5.55826 + 17.1066i −0.208158 + 0.640646i
\(714\) 16.4433 0.615377
\(715\) −1.02509 + 1.31925i −0.0383361 + 0.0493373i
\(716\) −8.12626 −0.303693
\(717\) −8.72096 + 26.8403i −0.325690 + 1.00237i
\(718\) −30.2452 + 21.9744i −1.12874 + 0.820079i
\(719\) 20.7156 + 15.0508i 0.772562 + 0.561299i 0.902737 0.430192i \(-0.141554\pi\)
−0.130176 + 0.991491i \(0.541554\pi\)
\(720\) 0.603269 + 1.85667i 0.0224825 + 0.0691940i
\(721\) 2.53082 + 7.78905i 0.0942525 + 0.290080i
\(722\) 26.2163 + 19.0473i 0.975671 + 0.708867i
\(723\) −16.3900 + 11.9080i −0.609551 + 0.442865i
\(724\) 0.214422 0.659922i 0.00796892 0.0245258i
\(725\) −13.1315 −0.487693
\(726\) 18.7349 11.8455i 0.695316 0.439629i
\(727\) −0.251233 −0.00931771 −0.00465886 0.999989i \(-0.501483\pi\)
−0.00465886 + 0.999989i \(0.501483\pi\)
\(728\) −0.113452 + 0.349169i −0.00420481 + 0.0129411i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 4.78254 + 3.47472i 0.177010 + 0.128605i
\(731\) 1.47376 + 4.53575i 0.0545088 + 0.167761i
\(732\) 9.36191 + 28.8130i 0.346026 + 1.06496i
\(733\) −8.96150 6.51091i −0.331001 0.240486i 0.409855 0.912151i \(-0.365579\pi\)
−0.740855 + 0.671665i \(0.765579\pi\)
\(734\) 41.0620 29.8333i 1.51562 1.10117i
\(735\) −0.325417 + 1.00153i −0.0120032 + 0.0369421i
\(736\) −14.7977 −0.545452
\(737\) −16.9945 + 21.8713i −0.625999 + 0.805638i
\(738\) −10.1850 −0.374914
\(739\) −6.79912 + 20.9255i −0.250110 + 0.769758i 0.744644 + 0.667461i \(0.232619\pi\)
−0.994754 + 0.102297i \(0.967381\pi\)
\(740\) 0.257727 0.187249i 0.00947422 0.00688343i
\(741\) −1.38208 1.00414i −0.0507719 0.0368879i
\(742\) 19.3857 + 59.6631i 0.711672 + 2.19030i
\(743\) 11.4320 + 35.1841i 0.419400 + 1.29078i 0.908256 + 0.418416i \(0.137415\pi\)
−0.488856 + 0.872365i \(0.662585\pi\)
\(744\) 0.964280 + 0.700591i 0.0353522 + 0.0256849i
\(745\) −3.41530 + 2.48136i −0.125127 + 0.0909101i
\(746\) 2.97007 9.14094i 0.108742 0.334673i
\(747\) 3.11083 0.113819
\(748\) 10.3831 + 15.3059i 0.379645 + 0.559639i
\(749\) −3.88526 −0.141964
\(750\) 3.05709 9.40874i 0.111629 0.343559i
\(751\) 4.47236 3.24936i 0.163199 0.118571i −0.503188 0.864177i \(-0.667840\pi\)
0.666387 + 0.745606i \(0.267840\pi\)
\(752\) −37.9317 27.5590i −1.38323 1.00497i
\(753\) −3.72780 11.4730i −0.135849 0.418099i
\(754\) 1.72279 + 5.30221i 0.0627404 + 0.193095i
\(755\) −5.85386 4.25308i −0.213044 0.154785i
\(756\) 5.02586 3.65150i 0.182789 0.132804i
\(757\) −10.5945 + 32.6065i −0.385063 + 1.18510i 0.551371 + 0.834260i \(0.314105\pi\)
−0.936434 + 0.350843i \(0.885895\pi\)
\(758\) 33.3835 1.21254
\(759\) −0.196538 + 6.09139i −0.00713386 + 0.221104i
\(760\) −0.104788 −0.00380106
\(761\) −15.2850 + 47.0425i −0.554082 + 1.70529i 0.144275 + 0.989538i \(0.453915\pi\)
−0.698356 + 0.715750i \(0.746085\pi\)
\(762\) −20.8860 + 15.1746i −0.756620 + 0.549716i
\(763\) −28.1376 20.4432i −1.01865 0.740092i
\(764\) 15.5345 + 47.8102i 0.562018 + 1.72971i
\(765\) 0.421302 + 1.29663i 0.0152322 + 0.0468799i
\(766\) −51.7945 37.6309i −1.87141 1.35966i
\(767\) −0.0976321 + 0.0709338i −0.00352529 + 0.00256127i
\(768\) 4.63209 14.2561i 0.167146 0.514423i
\(769\) −27.9826 −1.00908 −0.504540 0.863388i \(-0.668338\pi\)
−0.504540 + 0.863388i \(0.668338\pi\)
\(770\) −9.74963 + 2.82368i −0.351352 + 0.101758i
\(771\) 20.3114 0.731496
\(772\) 6.28464 19.3421i 0.226189 0.696139i
\(773\) 3.87115 2.81255i 0.139236 0.101161i −0.515987 0.856596i \(-0.672575\pi\)
0.655223 + 0.755436i \(0.272575\pi\)
\(774\) 2.87261 + 2.08708i 0.103254 + 0.0750184i
\(775\) 14.3563 + 44.1842i 0.515695 + 1.58714i
\(776\) −0.606960 1.86803i −0.0217886 0.0670584i
\(777\) 0.748677 + 0.543946i 0.0268586 + 0.0195139i
\(778\) −4.82971 + 3.50899i −0.173154 + 0.125803i
\(779\) −2.66828 + 8.21212i −0.0956011 + 0.294230i
\(780\) −1.03791 −0.0371631
\(781\) 36.4788 + 13.1677i 1.30531 + 0.471178i
\(782\) −10.0217 −0.358375
\(783\) 0.854962 2.63130i 0.0305539 0.0940351i
\(784\) 6.55452 4.76214i 0.234090 0.170076i
\(785\) 4.91378 + 3.57007i 0.175380 + 0.127421i
\(786\) 5.83100 + 17.9460i 0.207985 + 0.640111i
\(787\) −7.86019 24.1912i −0.280185 0.862322i −0.987801 0.155724i \(-0.950229\pi\)
0.707615 0.706598i \(-0.249771\pi\)
\(788\) 9.34807 + 6.79177i 0.333011 + 0.241947i
\(789\) −21.5099 + 15.6279i −0.765773 + 0.556366i
\(790\) −2.58195 + 7.94642i −0.0918615 + 0.282721i
\(791\) −6.78258 −0.241161
\(792\) 0.379870 + 0.137121i 0.0134981 + 0.00487239i
\(793\) 14.7036 0.522141
\(794\) 14.5021 44.6330i 0.514661 1.58396i
\(795\) −4.20803 + 3.05731i −0.149243 + 0.108432i
\(796\) 34.9736 + 25.4098i 1.23961 + 0.900627i
\(797\) 9.60827 + 29.5712i 0.340342 + 1.04747i 0.964030 + 0.265793i \(0.0856337\pi\)
−0.623688 + 0.781674i \(0.714366\pi\)
\(798\) −3.20729 9.87101i −0.113537 0.349430i
\(799\) −26.4902 19.2462i −0.937155 0.680883i
\(800\) −30.9213 + 22.4656i −1.09323 + 0.794280i
\(801\) −2.14622 + 6.60539i −0.0758330 + 0.233390i
\(802\) −0.331527 −0.0117066
\(803\) −18.5532 + 5.37335i −0.654728 + 0.189621i
\(804\) −17.2070 −0.606845
\(805\) 0.862432 2.65429i 0.0303967 0.0935515i
\(806\) 15.9571 11.5935i 0.562065 0.408364i
\(807\) 18.1723 + 13.2030i 0.639697 + 0.464767i
\(808\) −0.443759 1.36575i −0.0156114 0.0480469i
\(809\) 11.1056 + 34.1796i 0.390454 + 1.20169i 0.932446 + 0.361309i \(0.117670\pi\)
−0.541993 + 0.840383i \(0.682330\pi\)
\(810\) 0.821193 + 0.596632i 0.0288538 + 0.0209635i
\(811\) 33.5233 24.3561i 1.17716 0.855258i 0.185313 0.982680i \(-0.440670\pi\)
0.991849 + 0.127422i \(0.0406702\pi\)
\(812\) −5.31128 + 16.3464i −0.186389 + 0.573648i
\(813\) −18.1030 −0.634901
\(814\) −0.0661497 + 2.05021i −0.00231854 + 0.0718599i
\(815\) −2.94497 −0.103158
\(816\) 3.24129 9.97568i 0.113468 0.349219i
\(817\) 2.43538 1.76940i 0.0852031 0.0619036i
\(818\) −33.5709 24.3907i −1.17378 0.852801i
\(819\) −0.931702 2.86748i −0.0325563 0.100198i
\(820\) 1.62112 + 4.98931i 0.0566121 + 0.174234i
\(821\) −38.1166 27.6933i −1.33028 0.966503i −0.999742 0.0227091i \(-0.992771\pi\)
−0.330535 0.943794i \(-0.607229\pi\)
\(822\) 6.32856 4.59797i 0.220734 0.160373i
\(823\) −1.67351 + 5.15053i −0.0583349 + 0.179536i −0.975978 0.217869i \(-0.930089\pi\)
0.917643 + 0.397406i \(0.130089\pi\)
\(824\) −0.330765 −0.0115227
\(825\) 8.83715 + 13.0269i 0.307670 + 0.453539i
\(826\) −0.733188 −0.0255109
\(827\) −1.40736 + 4.33142i −0.0489388 + 0.150618i −0.972540 0.232738i \(-0.925232\pi\)
0.923601 + 0.383356i \(0.125232\pi\)
\(828\) −3.06310 + 2.22547i −0.106450 + 0.0773406i
\(829\) 0.265751 + 0.193080i 0.00922993 + 0.00670594i 0.592391 0.805651i \(-0.298184\pi\)
−0.583161 + 0.812357i \(0.698184\pi\)
\(830\) −0.975767 3.00310i −0.0338694 0.104239i
\(831\) −7.20212 22.1658i −0.249839 0.768924i
\(832\) 6.85716 + 4.98202i 0.237729 + 0.172720i
\(833\) 4.57745 3.32571i 0.158599 0.115229i
\(834\) −9.34317 + 28.7553i −0.323528 + 0.995716i
\(835\) 5.34420 0.184944
\(836\) 7.16295 9.21847i 0.247736 0.318827i
\(837\) −9.78837 −0.338336
\(838\) −11.0118 + 33.8909i −0.380397 + 1.17074i
\(839\) −14.8942 + 10.8212i −0.514204 + 0.373591i −0.814416 0.580282i \(-0.802942\pi\)
0.300212 + 0.953872i \(0.402942\pi\)
\(840\) −0.149620 0.108705i −0.00516238 0.00375069i
\(841\) −6.59606 20.3006i −0.227450 0.700020i
\(842\) −9.35127 28.7802i −0.322266 0.991833i
\(843\) −1.37556 0.999406i −0.0473770 0.0344214i
\(844\) −25.0726 + 18.2163i −0.863033 + 0.627030i
\(845\) −0.155663 + 0.479080i −0.00535495 + 0.0164809i
\(846\) −24.3783 −0.838144
\(847\) 12.2607 30.8161i 0.421283 1.05885i
\(848\) 40.0171 1.37419
\(849\) −3.03282 + 9.33405i −0.104086 + 0.320344i
\(850\) −20.9413 + 15.2148i −0.718281 + 0.521862i
\(851\) −0.456295 0.331518i −0.0156416 0.0113643i
\(852\) 7.44528 + 22.9142i 0.255071 + 0.785028i
\(853\) −8.26753 25.4448i −0.283075 0.871215i −0.986969 0.160910i \(-0.948557\pi\)
0.703894 0.710305i \(-0.251443\pi\)
\(854\) 72.2708 + 52.5078i 2.47305 + 1.79678i
\(855\) 0.696200 0.505819i 0.0238095 0.0172986i
\(856\) 0.0484890 0.149234i 0.00165732 0.00510071i
\(857\) 13.4817 0.460525 0.230263 0.973129i \(-0.426042\pi\)
0.230263 + 0.973129i \(0.426042\pi\)
\(858\) 4.10058 5.27730i 0.139992 0.180164i
\(859\) −45.3445 −1.54713 −0.773566 0.633715i \(-0.781529\pi\)
−0.773566 + 0.633715i \(0.781529\pi\)
\(860\) 0.565166 1.73940i 0.0192720 0.0593131i
\(861\) −12.3290 + 8.95752i −0.420170 + 0.305271i
\(862\) −13.4388 9.76388i −0.457728 0.332559i
\(863\) −7.33942 22.5884i −0.249837 0.768918i −0.994803 0.101816i \(-0.967535\pi\)
0.744966 0.667102i \(-0.232465\pi\)
\(864\) −2.48847 7.65871i −0.0846593 0.260555i
\(865\) 6.90705 + 5.01827i 0.234847 + 0.170626i
\(866\) 28.6355 20.8049i 0.973074 0.706980i
\(867\) −2.98968 + 9.20129i −0.101535 + 0.312492i
\(868\) 60.8083 2.06397
\(869\) −15.3263 22.5927i −0.519910 0.766405i
\(870\) −2.80836 −0.0952122
\(871\) −2.58066 + 7.94244i −0.0874422 + 0.269119i
\(872\) 1.13639 0.825636i 0.0384831 0.0279596i
\(873\) 13.0497 + 9.48115i 0.441665 + 0.320888i
\(874\) 1.95474 + 6.01608i 0.0661201 + 0.203497i
\(875\) −4.57421 14.0780i −0.154637 0.475923i
\(876\) −9.70796 7.05325i −0.328002 0.238307i
\(877\) 44.9065 32.6265i 1.51638 1.10172i 0.553141 0.833088i \(-0.313429\pi\)
0.963243 0.268630i \(-0.0865708\pi\)
\(878\) 21.8421 67.2232i 0.737137 2.26867i
\(879\) 11.7511 0.396355
\(880\) −0.208799 + 6.47141i −0.00703860 + 0.218151i
\(881\) −17.3766 −0.585432 −0.292716 0.956199i \(-0.594559\pi\)
−0.292716 + 0.956199i \(0.594559\pi\)
\(882\) 1.30174 4.00635i 0.0438319 0.134901i
\(883\) −41.2893 + 29.9984i −1.38949 + 1.00953i −0.393574 + 0.919293i \(0.628762\pi\)
−0.995921 + 0.0902344i \(0.971238\pi\)
\(884\) 4.51154 + 3.27783i 0.151740 + 0.110245i
\(885\) −0.0187853 0.0578153i −0.000631462 0.00194344i
\(886\) 22.6697 + 69.7701i 0.761603 + 2.34397i
\(887\) −10.6419 7.73183i −0.357322 0.259609i 0.394612 0.918848i \(-0.370879\pi\)
−0.751934 + 0.659238i \(0.770879\pi\)
\(888\) −0.0302368 + 0.0219683i −0.00101468 + 0.000737207i
\(889\) −11.9368 + 36.7377i −0.400348 + 1.23214i
\(890\) 7.04985 0.236312
\(891\) −3.18571 + 0.922641i −0.106725 + 0.0309096i
\(892\) 38.8889 1.30210
\(893\) −6.38667 + 19.6562i −0.213722 + 0.657768i
\(894\) 13.6620 9.92600i 0.456925 0.331975i
\(895\) −1.60728 1.16776i −0.0537255 0.0390339i
\(896\) 0.907202 + 2.79208i 0.0303075 + 0.0932768i
\(897\) 0.567843 + 1.74764i 0.0189597 + 0.0583521i
\(898\) −35.1193 25.5157i −1.17195 0.851469i
\(899\) 21.9095 15.9182i 0.730723 0.530901i
\(900\) −3.02198 + 9.30068i −0.100733 + 0.310023i
\(901\) 27.9466 0.931035
\(902\) −31.7731 11.4691i −1.05793 0.381879i
\(903\) 5.31286 0.176801
\(904\) 0.0846483 0.260521i 0.00281536 0.00866479i
\(905\) 0.137242 0.0997124i 0.00456209 0.00331455i
\(906\) 23.4168 + 17.0133i 0.777970 + 0.565228i
\(907\) 4.63498 + 14.2650i 0.153902 + 0.473662i 0.998048 0.0624515i \(-0.0198919\pi\)
−0.844146 + 0.536114i \(0.819892\pi\)
\(908\) 11.7748 + 36.2393i 0.390762 + 1.20264i
\(909\) 9.54085 + 6.93183i 0.316450 + 0.229914i
\(910\) −2.47594 + 1.79888i −0.0820766 + 0.0596321i
\(911\) 8.77559 27.0085i 0.290748 0.894831i −0.693868 0.720102i \(-0.744095\pi\)
0.984617 0.174729i \(-0.0559050\pi\)
\(912\) −6.62066 −0.219232
\(913\) 9.70456 + 3.50304i 0.321174 + 0.115934i
\(914\) −40.1312 −1.32742
\(915\) −2.28880 + 7.04421i −0.0756655 + 0.232874i
\(916\) −17.3087 + 12.5755i −0.571896 + 0.415506i
\(917\) 22.8416 + 16.5954i 0.754297 + 0.548029i
\(918\) −1.68530 5.18683i −0.0556233 0.171191i
\(919\) 3.87049 + 11.9121i 0.127676 + 0.392945i 0.994379 0.105879i \(-0.0337655\pi\)
−0.866703 + 0.498824i \(0.833766\pi\)
\(920\) 0.0911887 + 0.0662524i 0.00300640 + 0.00218428i
\(921\) −2.91714 + 2.11943i −0.0961231 + 0.0698375i
\(922\) −11.2051 + 34.4859i −0.369021 + 1.13573i
\(923\) 11.6934 0.384893
\(924\) 19.7906 5.73172i 0.651062 0.188560i
\(925\) −1.45678 −0.0478985
\(926\) −5.60582 + 17.2529i −0.184219 + 0.566967i
\(927\) 2.19756 1.59662i 0.0721774 0.0524400i
\(928\) 18.0248 + 13.0958i 0.591694 + 0.429891i
\(929\) 13.1996 + 40.6242i 0.433065 + 1.33284i 0.895057 + 0.445952i \(0.147135\pi\)
−0.461992 + 0.886884i \(0.652865\pi\)
\(930\) 3.07030 + 9.44940i 0.100679 + 0.309858i
\(931\) −2.88928 2.09918i −0.0946922 0.0687979i
\(932\) 16.8383 12.2338i 0.551557 0.400730i
\(933\) −5.97990 + 18.4042i −0.195773 + 0.602527i
\(934\) −71.0927 −2.32622
\(935\) −0.145818 + 4.51941i −0.00476875 + 0.147800i
\(936\) 0.121769 0.00398013
\(937\) −13.5892 + 41.8232i −0.443939 + 1.36630i 0.439704 + 0.898143i \(0.355083\pi\)
−0.883643 + 0.468161i \(0.844917\pi\)
\(938\) −41.0474 + 29.8227i −1.34025 + 0.973746i
\(939\) −14.5316 10.5578i −0.474222 0.344542i
\(940\) 3.88025 + 11.9422i 0.126560 + 0.389511i
\(941\) −13.9940 43.0692i −0.456193 1.40402i −0.869729 0.493529i \(-0.835707\pi\)
0.413536 0.910488i \(-0.364293\pi\)
\(942\) −19.6562 14.2811i −0.640434 0.465303i
\(943\) 7.51412 5.45933i 0.244693 0.177780i
\(944\) −0.144525 + 0.444803i −0.00470390 + 0.0144771i
\(945\) 1.51879 0.0494061
\(946\) 6.61121 + 9.74565i 0.214949 + 0.316858i
\(947\) −5.38326 −0.174932 −0.0874662 0.996167i \(-0.527877\pi\)
−0.0874662 + 0.996167i \(0.527877\pi\)
\(948\) 5.24104 16.1303i 0.170221 0.523886i
\(949\) −4.71162 + 3.42319i −0.152946 + 0.111122i
\(950\) 13.2181 + 9.60351i 0.428852 + 0.311579i
\(951\) 0.538117 + 1.65616i 0.0174497 + 0.0537045i
\(952\) 0.307059 + 0.945030i 0.00995184 + 0.0306286i
\(953\) −28.3584 20.6036i −0.918617 0.667415i 0.0245622 0.999698i \(-0.492181\pi\)
−0.943179 + 0.332284i \(0.892181\pi\)
\(954\) 16.8330 12.2299i 0.544990 0.395958i
\(955\) −3.79788 + 11.6887i −0.122896 + 0.378236i
\(956\) −58.1486 −1.88066
\(957\) 5.63020 7.24587i 0.181999 0.234226i
\(958\) 30.9678 1.00052
\(959\) 3.61691 11.1317i 0.116796 0.359462i
\(960\) −3.45419 + 2.50961i −0.111483 + 0.0809974i
\(961\) −52.4342 38.0956i −1.69142 1.22889i
\(962\) 0.191122 + 0.588213i 0.00616202 + 0.0189647i
\(963\) 0.398206 + 1.22555i 0.0128320 + 0.0394929i
\(964\) −33.7705 24.5357i −1.08767 0.790241i
\(965\) 4.02254 2.92254i 0.129490 0.0940800i
\(966\) −3.44992 + 10.6178i −0.110999 + 0.341621i
\(967\) −38.3000 −1.23164 −0.615822 0.787885i \(-0.711176\pi\)
−0.615822 + 0.787885i \(0.711176\pi\)
\(968\) 1.03064 + 0.855528i 0.0331259 + 0.0274977i
\(969\) −4.62364 −0.148533
\(970\) 5.05956 15.5717i 0.162453 0.499978i
\(971\) 18.6535 13.5525i 0.598619 0.434922i −0.246770 0.969074i \(-0.579369\pi\)
0.845388 + 0.534152i \(0.179369\pi\)
\(972\) −1.66692 1.21109i −0.0534666 0.0388457i
\(973\) 13.9799 + 43.0256i 0.448174 + 1.37934i
\(974\) 21.0537 + 64.7967i 0.674605 + 2.07622i
\(975\) 3.83980 + 2.78978i 0.122972 + 0.0893444i
\(976\) 46.1008 33.4942i 1.47565 1.07212i
\(977\) 12.4301 38.2560i 0.397675 1.22392i −0.529183 0.848508i \(-0.677502\pi\)
0.926858 0.375411i \(-0.122498\pi\)
\(978\) 11.7805 0.376699
\(979\) −14.1336 + 18.1894i −0.451711 + 0.581336i
\(980\) −2.16978 −0.0693112
\(981\) −3.56465 + 10.9709i −0.113811 + 0.350273i
\(982\) 34.1336 24.7995i 1.08925 0.791385i
\(983\) −46.5183 33.7975i −1.48370 1.07797i −0.976340 0.216239i \(-0.930621\pi\)
−0.507362 0.861733i \(-0.669379\pi\)
\(984\) −0.190192 0.585350i −0.00606309 0.0186603i
\(985\) 0.872953 + 2.68667i 0.0278146 + 0.0856045i
\(986\) 12.2072 + 8.86908i 0.388758 + 0.282449i
\(987\) −29.5100 + 21.4403i −0.939315 + 0.682452i
\(988\) 1.08771 3.34764i 0.0346048 0.106503i
\(989\) −3.23802 −0.102963
\(990\) 1.88994 + 2.78599i 0.0600664 + 0.0885444i
\(991\) 35.8103 1.13755 0.568777 0.822492i \(-0.307417\pi\)
0.568777 + 0.822492i \(0.307417\pi\)
\(992\) 24.3580 74.9663i 0.773368 2.38018i
\(993\) −4.45045 + 3.23344i −0.141231 + 0.102610i
\(994\) 57.4750 + 41.7580i 1.82300 + 1.32448i
\(995\) 3.26595 + 10.0516i 0.103538 + 0.318656i
\(996\) 1.98069 + 6.09593i 0.0627605 + 0.193157i
\(997\) 18.0174 + 13.0904i 0.570618 + 0.414578i 0.835330 0.549749i \(-0.185277\pi\)
−0.264712 + 0.964328i \(0.585277\pi\)
\(998\) 3.42881 2.49118i 0.108537 0.0788568i
\(999\) 0.0948472 0.291910i 0.00300083 0.00923562i
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 429.2.n.a.196.3 12
11.4 even 5 4719.2.a.bg.1.6 6
11.5 even 5 inner 429.2.n.a.313.3 yes 12
11.7 odd 10 4719.2.a.bh.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.a.196.3 12 1.1 even 1 trivial
429.2.n.a.313.3 yes 12 11.5 even 5 inner
4719.2.a.bg.1.6 6 11.4 even 5
4719.2.a.bh.1.1 6 11.7 odd 10