Properties

Label 429.2.n.a.235.2
Level $429$
Weight $2$
Character 429.235
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 235.2
Root \(0.275227 - 0.199964i\) of defining polynomial
Character \(\chi\) \(=\) 429.235
Dual form 429.2.n.a.157.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.275227 + 0.199964i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.582270 - 1.79204i) q^{4} +(3.18709 - 2.31555i) q^{5} +(0.275227 - 0.199964i) q^{6} +(-0.203890 - 0.627508i) q^{7} +(0.408342 - 1.25675i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.275227 + 0.199964i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.582270 - 1.79204i) q^{4} +(3.18709 - 2.31555i) q^{5} +(0.275227 - 0.199964i) q^{6} +(-0.203890 - 0.627508i) q^{7} +(0.408342 - 1.25675i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.34020 q^{10} +(-0.0920501 + 3.31535i) q^{11} -1.88426 q^{12} +(-0.809017 - 0.587785i) q^{13} +(0.0693631 - 0.213478i) q^{14} +(-1.21736 - 3.74665i) q^{15} +(-2.68511 + 1.95085i) q^{16} +(-0.812211 + 0.590106i) q^{17} +(-0.105127 - 0.323548i) q^{18} +(-1.57486 + 4.84691i) q^{19} +(-6.00532 - 4.36312i) q^{20} -0.659801 q^{21} +(-0.688284 + 0.894065i) q^{22} +3.10400 q^{23} +(-1.06905 - 0.776713i) q^{24} +(3.25065 - 10.0045i) q^{25} +(-0.105127 - 0.323548i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.00580 + 0.730758i) q^{28} +(-0.247787 - 0.762610i) q^{29} +(0.414144 - 1.27460i) q^{30} +(4.03228 + 2.92962i) q^{31} -3.77196 q^{32} +(3.12464 + 1.11204i) q^{33} -0.341542 q^{34} +(-2.10284 - 1.52781i) q^{35} +(-0.582270 + 1.79204i) q^{36} +(0.206975 + 0.637002i) q^{37} +(-1.40265 + 1.01908i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(-1.60865 - 4.95090i) q^{40} +(-0.545701 + 1.67949i) q^{41} +(-0.181595 - 0.131936i) q^{42} +11.9438 q^{43} +(5.99484 - 1.76547i) q^{44} -3.93946 q^{45} +(0.854303 + 0.620687i) q^{46} +(1.78728 - 5.50070i) q^{47} +(1.02562 + 3.15654i) q^{48} +(5.31092 - 3.85861i) q^{49} +(2.89520 - 2.10348i) q^{50} +(0.310237 + 0.954811i) q^{51} +(-0.582270 + 1.79204i) q^{52} +(-9.61976 - 6.98917i) q^{53} -0.340199 q^{54} +(7.38350 + 10.7794i) q^{55} -0.871876 q^{56} +(4.12303 + 2.99555i) q^{57} +(0.0842969 - 0.259439i) q^{58} +(-0.106583 - 0.328029i) q^{59} +(-6.00532 + 4.36312i) q^{60} +(-3.47620 + 2.52561i) q^{61} +(0.523972 + 1.61262i) q^{62} +(-0.203890 + 0.627508i) q^{63} +(4.33208 + 3.14744i) q^{64} -3.93946 q^{65} +(0.637615 + 0.930879i) q^{66} -2.12212 q^{67} +(1.53042 + 1.11192i) q^{68} +(0.959188 - 2.95208i) q^{69} +(-0.273253 - 0.840986i) q^{70} +(-7.84151 + 5.69719i) q^{71} +(-1.06905 + 0.776713i) q^{72} +(3.20186 + 9.85431i) q^{73} +(-0.0704125 + 0.216708i) q^{74} +(-8.51031 - 6.18310i) q^{75} +9.60285 q^{76} +(2.09918 - 0.618203i) q^{77} -0.340199 q^{78} +(5.15995 + 3.74892i) q^{79} +(-4.04039 + 12.4351i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.486030 + 0.353121i) q^{82} +(6.22609 - 4.52352i) q^{83} +(0.384182 + 1.18239i) q^{84} +(-1.22216 + 3.76144i) q^{85} +(3.28726 + 2.38834i) q^{86} -0.801856 q^{87} +(4.12897 + 1.46948i) q^{88} -4.75754 q^{89} +(-1.08424 - 0.787749i) q^{90} +(-0.203890 + 0.627508i) q^{91} +(-1.80736 - 5.56249i) q^{92} +(4.03228 - 2.92962i) q^{93} +(1.59185 - 1.15655i) q^{94} +(6.20408 + 19.0942i) q^{95} +(-1.16560 + 3.58735i) q^{96} +(7.33533 + 5.32943i) q^{97} +2.23329 q^{98} +(2.02318 - 2.62807i) 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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.275227 + 0.199964i 0.194615 + 0.141396i 0.680825 0.732446i \(-0.261621\pi\)
−0.486211 + 0.873842i \(0.661621\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) −0.582270 1.79204i −0.291135 0.896021i
\(5\) 3.18709 2.31555i 1.42531 1.03555i 0.434443 0.900700i \(-0.356945\pi\)
0.990866 0.134848i \(-0.0430546\pi\)
\(6\) 0.275227 0.199964i 0.112361 0.0816349i
\(7\) −0.203890 0.627508i −0.0770631 0.237176i 0.905103 0.425193i \(-0.139794\pi\)
−0.982166 + 0.188017i \(0.939794\pi\)
\(8\) 0.408342 1.25675i 0.144371 0.444327i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 1.34020 0.423808
\(11\) −0.0920501 + 3.31535i −0.0277541 + 0.999615i
\(12\) −1.88426 −0.543940
\(13\) −0.809017 0.587785i −0.224381 0.163022i
\(14\) 0.0693631 0.213478i 0.0185381 0.0570543i
\(15\) −1.21736 3.74665i −0.314321 0.967380i
\(16\) −2.68511 + 1.95085i −0.671278 + 0.487712i
\(17\) −0.812211 + 0.590106i −0.196990 + 0.143122i −0.681908 0.731438i \(-0.738850\pi\)
0.484918 + 0.874560i \(0.338850\pi\)
\(18\) −0.105127 0.323548i −0.0247787 0.0762611i
\(19\) −1.57486 + 4.84691i −0.361297 + 1.11196i 0.590971 + 0.806693i \(0.298745\pi\)
−0.952268 + 0.305264i \(0.901255\pi\)
\(20\) −6.00532 4.36312i −1.34283 0.975623i
\(21\) −0.659801 −0.143980
\(22\) −0.688284 + 0.894065i −0.146743 + 0.190615i
\(23\) 3.10400 0.647228 0.323614 0.946189i \(-0.395102\pi\)
0.323614 + 0.946189i \(0.395102\pi\)
\(24\) −1.06905 0.776713i −0.218220 0.158546i
\(25\) 3.25065 10.0045i 0.650130 2.00089i
\(26\) −0.105127 0.323548i −0.0206171 0.0634531i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −1.00580 + 0.730758i −0.190079 + 0.138100i
\(29\) −0.247787 0.762610i −0.0460129 0.141613i 0.925411 0.378966i \(-0.123720\pi\)
−0.971424 + 0.237353i \(0.923720\pi\)
\(30\) 0.414144 1.27460i 0.0756120 0.232710i
\(31\) 4.03228 + 2.92962i 0.724218 + 0.526176i 0.887729 0.460366i \(-0.152282\pi\)
−0.163511 + 0.986542i \(0.552282\pi\)
\(32\) −3.77196 −0.666795
\(33\) 3.12464 + 1.11204i 0.543930 + 0.193582i
\(34\) −0.341542 −0.0585740
\(35\) −2.10284 1.52781i −0.355445 0.258246i
\(36\) −0.582270 + 1.79204i −0.0970450 + 0.298674i
\(37\) 0.206975 + 0.637002i 0.0340264 + 0.104723i 0.966627 0.256187i \(-0.0824663\pi\)
−0.932601 + 0.360910i \(0.882466\pi\)
\(38\) −1.40265 + 1.01908i −0.227540 + 0.165317i
\(39\) −0.809017 + 0.587785i −0.129546 + 0.0941210i
\(40\) −1.60865 4.95090i −0.254349 0.782806i
\(41\) −0.545701 + 1.67949i −0.0852241 + 0.262293i −0.984583 0.174918i \(-0.944034\pi\)
0.899359 + 0.437211i \(0.144034\pi\)
\(42\) −0.181595 0.131936i −0.0280207 0.0203582i
\(43\) 11.9438 1.82142 0.910709 0.413049i \(-0.135536\pi\)
0.910709 + 0.413049i \(0.135536\pi\)
\(44\) 5.99484 1.76547i 0.903756 0.266154i
\(45\) −3.93946 −0.587260
\(46\) 0.854303 + 0.620687i 0.125960 + 0.0915153i
\(47\) 1.78728 5.50070i 0.260702 0.802359i −0.731950 0.681358i \(-0.761390\pi\)
0.992652 0.121001i \(-0.0386104\pi\)
\(48\) 1.02562 + 3.15654i 0.148036 + 0.455607i
\(49\) 5.31092 3.85861i 0.758703 0.551230i
\(50\) 2.89520 2.10348i 0.409443 0.297478i
\(51\) 0.310237 + 0.954811i 0.0434419 + 0.133700i
\(52\) −0.582270 + 1.79204i −0.0807463 + 0.248512i
\(53\) −9.61976 6.98917i −1.32138 0.960036i −0.999914 0.0131136i \(-0.995826\pi\)
−0.321462 0.946922i \(-0.604174\pi\)
\(54\) −0.340199 −0.0462952
\(55\) 7.38350 + 10.7794i 0.995590 + 1.45350i
\(56\) −0.871876 −0.116509
\(57\) 4.12303 + 2.99555i 0.546108 + 0.396771i
\(58\) 0.0842969 0.259439i 0.0110687 0.0340660i
\(59\) −0.106583 0.328029i −0.0138759 0.0427057i 0.943879 0.330292i \(-0.107147\pi\)
−0.957755 + 0.287586i \(0.907147\pi\)
\(60\) −6.00532 + 4.36312i −0.775283 + 0.563276i
\(61\) −3.47620 + 2.52561i −0.445082 + 0.323371i −0.787651 0.616122i \(-0.788703\pi\)
0.342569 + 0.939493i \(0.388703\pi\)
\(62\) 0.523972 + 1.61262i 0.0665445 + 0.204803i
\(63\) −0.203890 + 0.627508i −0.0256877 + 0.0790586i
\(64\) 4.33208 + 3.14744i 0.541510 + 0.393430i
\(65\) −3.93946 −0.488629
\(66\) 0.637615 + 0.930879i 0.0784850 + 0.114583i
\(67\) −2.12212 −0.259259 −0.129629 0.991563i \(-0.541379\pi\)
−0.129629 + 0.991563i \(0.541379\pi\)
\(68\) 1.53042 + 1.11192i 0.185591 + 0.134840i
\(69\) 0.959188 2.95208i 0.115473 0.355388i
\(70\) −0.273253 0.840986i −0.0326600 0.100517i
\(71\) −7.84151 + 5.69719i −0.930616 + 0.676132i −0.946144 0.323747i \(-0.895057\pi\)
0.0155275 + 0.999879i \(0.495057\pi\)
\(72\) −1.06905 + 0.776713i −0.125989 + 0.0915365i
\(73\) 3.20186 + 9.85431i 0.374749 + 1.15336i 0.943648 + 0.330952i \(0.107370\pi\)
−0.568898 + 0.822408i \(0.692630\pi\)
\(74\) −0.0704125 + 0.216708i −0.00818529 + 0.0251917i
\(75\) −8.51031 6.18310i −0.982686 0.713963i
\(76\) 9.60285 1.10152
\(77\) 2.09918 0.618203i 0.239223 0.0704508i
\(78\) −0.340199 −0.0385199
\(79\) 5.15995 + 3.74892i 0.580540 + 0.421787i 0.838919 0.544257i \(-0.183188\pi\)
−0.258379 + 0.966044i \(0.583188\pi\)
\(80\) −4.04039 + 12.4351i −0.451730 + 1.39028i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −0.486030 + 0.353121i −0.0536730 + 0.0389957i
\(83\) 6.22609 4.52352i 0.683403 0.496521i −0.191082 0.981574i \(-0.561200\pi\)
0.874485 + 0.485053i \(0.161200\pi\)
\(84\) 0.384182 + 1.18239i 0.0419177 + 0.129009i
\(85\) −1.22216 + 3.76144i −0.132562 + 0.407985i
\(86\) 3.28726 + 2.38834i 0.354475 + 0.257541i
\(87\) −0.801856 −0.0859680
\(88\) 4.12897 + 1.46948i 0.440149 + 0.156647i
\(89\) −4.75754 −0.504299 −0.252149 0.967688i \(-0.581137\pi\)
−0.252149 + 0.967688i \(0.581137\pi\)
\(90\) −1.08424 0.787749i −0.114289 0.0830361i
\(91\) −0.203890 + 0.627508i −0.0213735 + 0.0657807i
\(92\) −1.80736 5.56249i −0.188431 0.579930i
\(93\) 4.03228 2.92962i 0.418128 0.303788i
\(94\) 1.59185 1.15655i 0.164187 0.119289i
\(95\) 6.20408 + 19.0942i 0.636525 + 1.95902i
\(96\) −1.16560 + 3.58735i −0.118964 + 0.366132i
\(97\) 7.33533 + 5.32943i 0.744790 + 0.541122i 0.894208 0.447653i \(-0.147740\pi\)
−0.149418 + 0.988774i \(0.547740\pi\)
\(98\) 2.23329 0.225596
\(99\) 2.02318 2.62807i 0.203337 0.264131i
\(100\) −19.8212 −1.98212
\(101\) −15.2148 11.0542i −1.51393 1.09994i −0.964394 0.264469i \(-0.914803\pi\)
−0.549539 0.835468i \(-0.685197\pi\)
\(102\) −0.105542 + 0.324826i −0.0104502 + 0.0321625i
\(103\) −5.91976 18.2192i −0.583292 1.79519i −0.606025 0.795446i \(-0.707237\pi\)
0.0227335 0.999742i \(-0.492763\pi\)
\(104\) −1.06905 + 0.776713i −0.104829 + 0.0761630i
\(105\) −2.10284 + 1.52781i −0.205217 + 0.149099i
\(106\) −1.25003 3.84721i −0.121414 0.373674i
\(107\) −6.13770 + 18.8899i −0.593354 + 1.82616i −0.0305990 + 0.999532i \(0.509741\pi\)
−0.562755 + 0.826624i \(0.690259\pi\)
\(108\) 1.52440 + 1.10754i 0.146686 + 0.106573i
\(109\) −2.61734 −0.250696 −0.125348 0.992113i \(-0.540005\pi\)
−0.125348 + 0.992113i \(0.540005\pi\)
\(110\) −0.123365 + 4.44322i −0.0117624 + 0.423645i
\(111\) 0.669784 0.0635731
\(112\) 1.77164 + 1.28717i 0.167404 + 0.121626i
\(113\) −2.94569 + 9.06589i −0.277107 + 0.852847i 0.711547 + 0.702638i \(0.247995\pi\)
−0.988654 + 0.150209i \(0.952005\pi\)
\(114\) 0.535764 + 1.64891i 0.0501789 + 0.154435i
\(115\) 9.89271 7.18747i 0.922500 0.670235i
\(116\) −1.22235 + 0.888090i −0.113492 + 0.0824571i
\(117\) 0.309017 + 0.951057i 0.0285686 + 0.0879252i
\(118\) 0.0362594 0.111595i 0.00333795 0.0102732i
\(119\) 0.535898 + 0.389352i 0.0491257 + 0.0356919i
\(120\) −5.20569 −0.475212
\(121\) −10.9831 0.610356i −0.998459 0.0554869i
\(122\) −1.46177 −0.132343
\(123\) 1.42866 + 1.03798i 0.128818 + 0.0935919i
\(124\) 2.90213 8.93184i 0.260619 0.802103i
\(125\) −6.71899 20.6789i −0.600965 1.84958i
\(126\) −0.181595 + 0.131936i −0.0161778 + 0.0117538i
\(127\) −6.13021 + 4.45386i −0.543968 + 0.395216i −0.825557 0.564319i \(-0.809139\pi\)
0.281589 + 0.959535i \(0.409139\pi\)
\(128\) 2.89413 + 8.90721i 0.255807 + 0.787294i
\(129\) 3.69085 11.3593i 0.324961 1.00013i
\(130\) −1.08424 0.787749i −0.0950945 0.0690902i
\(131\) 19.9723 1.74499 0.872496 0.488622i \(-0.162500\pi\)
0.872496 + 0.488622i \(0.162500\pi\)
\(132\) 0.173447 6.24699i 0.0150966 0.543731i
\(133\) 3.36257 0.291572
\(134\) −0.584065 0.424348i −0.0504555 0.0366581i
\(135\) −1.21736 + 3.74665i −0.104774 + 0.322460i
\(136\) 0.409954 + 1.26171i 0.0351533 + 0.108191i
\(137\) 9.58097 6.96098i 0.818557 0.594717i −0.0977417 0.995212i \(-0.531162\pi\)
0.916299 + 0.400495i \(0.131162\pi\)
\(138\) 0.854303 0.620687i 0.0727231 0.0528364i
\(139\) 0.728026 + 2.24063i 0.0617503 + 0.190048i 0.977173 0.212447i \(-0.0681432\pi\)
−0.915422 + 0.402495i \(0.868143\pi\)
\(140\) −1.51347 + 4.65798i −0.127912 + 0.393671i
\(141\) −4.67917 3.39962i −0.394057 0.286299i
\(142\) −3.29743 −0.276714
\(143\) 2.02318 2.62807i 0.169187 0.219770i
\(144\) 3.31898 0.276582
\(145\) −2.55558 1.85674i −0.212230 0.154194i
\(146\) −1.08927 + 3.35243i −0.0901485 + 0.277449i
\(147\) −2.02859 6.24337i −0.167315 0.514944i
\(148\) 1.02102 0.741815i 0.0839273 0.0609768i
\(149\) 13.1351 9.54324i 1.07607 0.781813i 0.0990791 0.995080i \(-0.468410\pi\)
0.976994 + 0.213267i \(0.0684103\pi\)
\(150\) −1.10587 3.40351i −0.0902937 0.277895i
\(151\) −2.52549 + 7.77264i −0.205521 + 0.632529i 0.794171 + 0.607695i \(0.207906\pi\)
−0.999692 + 0.0248338i \(0.992094\pi\)
\(152\) 5.44826 + 3.95839i 0.441912 + 0.321068i
\(153\) 1.00395 0.0811644
\(154\) 0.701367 + 0.249613i 0.0565178 + 0.0201144i
\(155\) 19.6349 1.57711
\(156\) 1.52440 + 1.10754i 0.122050 + 0.0886744i
\(157\) −7.61129 + 23.4251i −0.607447 + 1.86953i −0.128444 + 0.991717i \(0.540998\pi\)
−0.479003 + 0.877813i \(0.659002\pi\)
\(158\) 0.670507 + 2.06361i 0.0533426 + 0.164172i
\(159\) −9.61976 + 6.98917i −0.762897 + 0.554277i
\(160\) −12.0216 + 8.73418i −0.950388 + 0.690497i
\(161\) −0.632873 1.94778i −0.0498774 0.153507i
\(162\) −0.105127 + 0.323548i −0.00825958 + 0.0254204i
\(163\) 17.5727 + 12.7673i 1.37640 + 1.00001i 0.997206 + 0.0746980i \(0.0237993\pi\)
0.379196 + 0.925317i \(0.376201\pi\)
\(164\) 3.32747 0.259832
\(165\) 12.5335 3.69109i 0.975731 0.287351i
\(166\) 2.61813 0.203206
\(167\) −13.5302 9.83028i −1.04700 0.760690i −0.0753602 0.997156i \(-0.524011\pi\)
−0.971640 + 0.236466i \(0.924011\pi\)
\(168\) −0.269425 + 0.829203i −0.0207866 + 0.0639744i
\(169\) 0.309017 + 0.951057i 0.0237705 + 0.0731582i
\(170\) −1.08852 + 0.790859i −0.0834860 + 0.0606561i
\(171\) 4.12303 2.99555i 0.315296 0.229076i
\(172\) −6.95454 21.4039i −0.530278 1.63203i
\(173\) −2.95988 + 9.10959i −0.225036 + 0.692589i 0.773252 + 0.634099i \(0.218629\pi\)
−0.998288 + 0.0584904i \(0.981371\pi\)
\(174\) −0.220692 0.160342i −0.0167306 0.0121555i
\(175\) −6.94066 −0.524664
\(176\) −6.22058 9.08166i −0.468894 0.684556i
\(177\) −0.344910 −0.0259250
\(178\) −1.30940 0.951337i −0.0981439 0.0713057i
\(179\) −0.259669 + 0.799178i −0.0194086 + 0.0597334i −0.960292 0.278998i \(-0.909998\pi\)
0.940883 + 0.338731i \(0.109998\pi\)
\(180\) 2.29383 + 7.05967i 0.170972 + 0.526197i
\(181\) 2.63862 1.91707i 0.196127 0.142495i −0.485387 0.874299i \(-0.661321\pi\)
0.681515 + 0.731804i \(0.261321\pi\)
\(182\) −0.181595 + 0.131936i −0.0134607 + 0.00977978i
\(183\) 1.32779 + 4.08652i 0.0981530 + 0.302084i
\(184\) 1.26749 3.90094i 0.0934408 0.287581i
\(185\) 2.13466 + 1.55092i 0.156943 + 0.114026i
\(186\) 1.69561 0.124328
\(187\) −1.88164 2.74708i −0.137599 0.200886i
\(188\) −10.8982 −0.794830
\(189\) 0.533790 + 0.387821i 0.0388275 + 0.0282099i
\(190\) −2.11062 + 6.49582i −0.153120 + 0.471256i
\(191\) 1.18850 + 3.65781i 0.0859965 + 0.264670i 0.984803 0.173676i \(-0.0555645\pi\)
−0.898806 + 0.438346i \(0.855565\pi\)
\(192\) 4.33208 3.14744i 0.312641 0.227147i
\(193\) 17.0295 12.3727i 1.22581 0.890603i 0.229241 0.973370i \(-0.426376\pi\)
0.996569 + 0.0827667i \(0.0263756\pi\)
\(194\) 0.953185 + 2.93360i 0.0684347 + 0.210620i
\(195\) −1.21736 + 3.74665i −0.0871769 + 0.268303i
\(196\) −10.0072 7.27065i −0.714799 0.519332i
\(197\) −10.2644 −0.731305 −0.365653 0.930751i \(-0.619154\pi\)
−0.365653 + 0.930751i \(0.619154\pi\)
\(198\) 1.08235 0.318751i 0.0769194 0.0226526i
\(199\) −9.31129 −0.660060 −0.330030 0.943970i \(-0.607059\pi\)
−0.330030 + 0.943970i \(0.607059\pi\)
\(200\) −11.2457 8.17049i −0.795192 0.577741i
\(201\) −0.655772 + 2.01826i −0.0462546 + 0.142357i
\(202\) −1.97708 6.08484i −0.139107 0.428128i
\(203\) −0.428023 + 0.310977i −0.0300413 + 0.0218263i
\(204\) 1.53042 1.11192i 0.107151 0.0778496i
\(205\) 2.14976 + 6.61629i 0.150146 + 0.462102i
\(206\) 2.01390 6.19814i 0.140315 0.431845i
\(207\) −2.51119 1.82448i −0.174539 0.126810i
\(208\) 3.31898 0.230130
\(209\) −15.9242 5.66735i −1.10150 0.392019i
\(210\) −0.884265 −0.0610201
\(211\) −10.1240 7.35554i −0.696967 0.506376i 0.181976 0.983303i \(-0.441751\pi\)
−0.878943 + 0.476927i \(0.841751\pi\)
\(212\) −6.92359 + 21.3086i −0.475514 + 1.46348i
\(213\) 2.99519 + 9.21825i 0.205227 + 0.631624i
\(214\) −5.46656 + 3.97169i −0.373686 + 0.271499i
\(215\) 38.0660 27.6566i 2.59608 1.88616i
\(216\) 0.408342 + 1.25675i 0.0277842 + 0.0855108i
\(217\) 1.01622 3.12761i 0.0689856 0.212316i
\(218\) −0.720363 0.523374i −0.0487891 0.0354474i
\(219\) 10.3614 0.700161
\(220\) 15.0180 19.5081i 1.01252 1.31523i
\(221\) 1.00395 0.0675328
\(222\) 0.184342 + 0.133933i 0.0123723 + 0.00898897i
\(223\) −1.55273 + 4.77881i −0.103978 + 0.320013i −0.989489 0.144606i \(-0.953809\pi\)
0.885511 + 0.464619i \(0.153809\pi\)
\(224\) 0.769064 + 2.36694i 0.0513852 + 0.158148i
\(225\) −8.51031 + 6.18310i −0.567354 + 0.412207i
\(226\) −2.62358 + 1.90614i −0.174518 + 0.126795i
\(227\) −1.40258 4.31670i −0.0930925 0.286509i 0.893659 0.448746i \(-0.148129\pi\)
−0.986752 + 0.162237i \(0.948129\pi\)
\(228\) 2.96744 9.13286i 0.196524 0.604838i
\(229\) 2.54757 + 1.85092i 0.168348 + 0.122312i 0.668769 0.743470i \(-0.266821\pi\)
−0.500421 + 0.865782i \(0.666821\pi\)
\(230\) 4.15997 0.274300
\(231\) 0.0607347 2.18747i 0.00399605 0.143925i
\(232\) −1.05959 −0.0695655
\(233\) 1.46099 + 1.06147i 0.0957130 + 0.0695395i 0.634612 0.772831i \(-0.281160\pi\)
−0.538899 + 0.842370i \(0.681160\pi\)
\(234\) −0.105127 + 0.323548i −0.00687238 + 0.0211510i
\(235\) −7.04093 21.6698i −0.459300 1.41358i
\(236\) −0.525781 + 0.382002i −0.0342254 + 0.0248662i
\(237\) 5.15995 3.74892i 0.335175 0.243519i
\(238\) 0.0696369 + 0.214320i 0.00451389 + 0.0138923i
\(239\) 4.35768 13.4116i 0.281875 0.867522i −0.705443 0.708767i \(-0.749252\pi\)
0.987318 0.158756i \(-0.0507482\pi\)
\(240\) 10.5779 + 7.68529i 0.682800 + 0.496083i
\(241\) −8.19384 −0.527811 −0.263906 0.964548i \(-0.585011\pi\)
−0.263906 + 0.964548i \(0.585011\pi\)
\(242\) −2.90078 2.36420i −0.186469 0.151977i
\(243\) 1.00000 0.0641500
\(244\) 6.55008 + 4.75891i 0.419326 + 0.304658i
\(245\) 7.99155 24.5955i 0.510561 1.57135i
\(246\) 0.185647 + 0.571362i 0.0118364 + 0.0364287i
\(247\) 4.12303 2.99555i 0.262342 0.190602i
\(248\) 5.32834 3.87127i 0.338350 0.245826i
\(249\) −2.37816 7.31921i −0.150710 0.463836i
\(250\) 2.28579 7.03495i 0.144566 0.444929i
\(251\) −3.99311 2.90116i −0.252043 0.183120i 0.454589 0.890701i \(-0.349786\pi\)
−0.706632 + 0.707582i \(0.749786\pi\)
\(252\) 1.24324 0.0783168
\(253\) −0.285723 + 10.2908i −0.0179633 + 0.646979i
\(254\) −2.57781 −0.161746
\(255\) 3.19967 + 2.32470i 0.200371 + 0.145578i
\(256\) 2.32484 7.15511i 0.145302 0.447195i
\(257\) −3.08169 9.48446i −0.192230 0.591624i −0.999998 0.00212277i \(-0.999324\pi\)
0.807767 0.589501i \(-0.200676\pi\)
\(258\) 3.28726 2.38834i 0.204656 0.148691i
\(259\) 0.357524 0.259757i 0.0222155 0.0161405i
\(260\) 2.29383 + 7.05967i 0.142257 + 0.437822i
\(261\) −0.247787 + 0.762610i −0.0153376 + 0.0472044i
\(262\) 5.49692 + 3.99375i 0.339601 + 0.246735i
\(263\) −20.3964 −1.25769 −0.628847 0.777529i \(-0.716473\pi\)
−0.628847 + 0.777529i \(0.716473\pi\)
\(264\) 2.67348 3.47279i 0.164541 0.213735i
\(265\) −46.8428 −2.87753
\(266\) 0.925469 + 0.672393i 0.0567442 + 0.0412270i
\(267\) −1.47016 + 4.52469i −0.0899725 + 0.276907i
\(268\) 1.23565 + 3.80293i 0.0754792 + 0.232301i
\(269\) 11.7201 8.51518i 0.714590 0.519180i −0.170061 0.985433i \(-0.554397\pi\)
0.884651 + 0.466254i \(0.154397\pi\)
\(270\) −1.08424 + 0.787749i −0.0659850 + 0.0479409i
\(271\) −6.73152 20.7175i −0.408911 1.25850i −0.917585 0.397539i \(-0.869864\pi\)
0.508675 0.860959i \(-0.330136\pi\)
\(272\) 1.02967 3.16900i 0.0624330 0.192149i
\(273\) 0.533790 + 0.387821i 0.0323065 + 0.0234720i
\(274\) 4.02888 0.243394
\(275\) 32.8691 + 11.6979i 1.98208 + 0.705412i
\(276\) −5.84875 −0.352053
\(277\) −10.5400 7.65777i −0.633288 0.460111i 0.224250 0.974532i \(-0.428007\pi\)
−0.857538 + 0.514421i \(0.828007\pi\)
\(278\) −0.247674 + 0.762261i −0.0148545 + 0.0457174i
\(279\) −1.54019 4.74023i −0.0922089 0.283790i
\(280\) −2.77875 + 2.01888i −0.166062 + 0.120651i
\(281\) −24.2018 + 17.5836i −1.44376 + 1.04895i −0.456519 + 0.889714i \(0.650904\pi\)
−0.987240 + 0.159239i \(0.949096\pi\)
\(282\) −0.608032 1.87133i −0.0362078 0.111436i
\(283\) −5.92466 + 18.2342i −0.352184 + 1.08391i 0.605440 + 0.795891i \(0.292997\pi\)
−0.957624 + 0.288021i \(0.907003\pi\)
\(284\) 14.7755 + 10.7350i 0.876764 + 0.637006i
\(285\) 20.0768 1.18925
\(286\) 1.08235 0.318751i 0.0640008 0.0188481i
\(287\) 1.16516 0.0687772
\(288\) 3.05158 + 2.21710i 0.179816 + 0.130644i
\(289\) −4.94183 + 15.2094i −0.290696 + 0.894669i
\(290\) −0.332084 1.02205i −0.0195006 0.0600168i
\(291\) 7.33533 5.32943i 0.430005 0.312417i
\(292\) 15.7950 11.4757i 0.924332 0.671566i
\(293\) −3.67687 11.3162i −0.214805 0.661101i −0.999167 0.0407987i \(-0.987010\pi\)
0.784362 0.620303i \(-0.212990\pi\)
\(294\) 0.690125 2.12399i 0.0402489 0.123873i
\(295\) −1.09926 0.798657i −0.0640013 0.0464996i
\(296\) 0.885068 0.0514435
\(297\) −1.87424 2.73628i −0.108755 0.158775i
\(298\) 5.52345 0.319965
\(299\) −2.51119 1.82448i −0.145226 0.105513i
\(300\) −6.12508 + 18.8511i −0.353632 + 1.08837i
\(301\) −2.43523 7.49485i −0.140364 0.431996i
\(302\) −2.24933 + 1.63423i −0.129434 + 0.0940396i
\(303\) −15.2148 + 11.0542i −0.874070 + 0.635049i
\(304\) −5.22692 16.0868i −0.299784 0.922641i
\(305\) −5.23077 + 16.0987i −0.299513 + 0.921806i
\(306\) 0.276313 + 0.200753i 0.0157958 + 0.0114763i
\(307\) 24.3043 1.38712 0.693560 0.720398i \(-0.256041\pi\)
0.693560 + 0.720398i \(0.256041\pi\)
\(308\) −2.33013 3.40185i −0.132772 0.193838i
\(309\) −19.1568 −1.08979
\(310\) 5.40405 + 3.92628i 0.306930 + 0.222997i
\(311\) −4.53712 + 13.9638i −0.257276 + 0.791815i 0.736096 + 0.676877i \(0.236667\pi\)
−0.993373 + 0.114938i \(0.963333\pi\)
\(312\) 0.408342 + 1.25675i 0.0231178 + 0.0711493i
\(313\) −5.90356 + 4.28919i −0.333689 + 0.242439i −0.741994 0.670406i \(-0.766120\pi\)
0.408305 + 0.912845i \(0.366120\pi\)
\(314\) −6.77901 + 4.92524i −0.382562 + 0.277947i
\(315\) 0.803215 + 2.47204i 0.0452560 + 0.139284i
\(316\) 3.71375 11.4297i 0.208914 0.642973i
\(317\) 4.48152 + 3.25601i 0.251707 + 0.182876i 0.706483 0.707730i \(-0.250281\pi\)
−0.454776 + 0.890606i \(0.650281\pi\)
\(318\) −4.04520 −0.226843
\(319\) 2.55113 0.751302i 0.142836 0.0420648i
\(320\) 21.0948 1.17924
\(321\) 16.0687 + 11.6746i 0.896868 + 0.651613i
\(322\) 0.215303 0.662634i 0.0119984 0.0369271i
\(323\) −1.58107 4.86604i −0.0879732 0.270754i
\(324\) 1.52440 1.10754i 0.0846890 0.0615302i
\(325\) −8.51031 + 6.18310i −0.472067 + 0.342977i
\(326\) 2.28348 + 7.02782i 0.126470 + 0.389235i
\(327\) −0.808804 + 2.48924i −0.0447270 + 0.137655i
\(328\) 1.88787 + 1.37162i 0.104240 + 0.0757348i
\(329\) −3.81614 −0.210391
\(330\) 4.18764 + 1.49036i 0.230522 + 0.0820416i
\(331\) −26.0563 −1.43218 −0.716091 0.698007i \(-0.754071\pi\)
−0.716091 + 0.698007i \(0.754071\pi\)
\(332\) −11.7316 8.52351i −0.643856 0.467789i
\(333\) 0.206975 0.637002i 0.0113421 0.0349075i
\(334\) −1.75818 5.41111i −0.0962031 0.296083i
\(335\) −6.76339 + 4.91389i −0.369524 + 0.268475i
\(336\) 1.77164 1.28717i 0.0966509 0.0702210i
\(337\) −4.31503 13.2803i −0.235055 0.723424i −0.997114 0.0759172i \(-0.975812\pi\)
0.762059 0.647507i \(-0.224188\pi\)
\(338\) −0.105127 + 0.323548i −0.00571817 + 0.0175987i
\(339\) 7.71191 + 5.60303i 0.418853 + 0.304315i
\(340\) 7.45228 0.404157
\(341\) −10.0839 + 13.0987i −0.546073 + 0.709336i
\(342\) 1.73377 0.0937515
\(343\) −7.24069 5.26067i −0.390960 0.284049i
\(344\) 4.87717 15.0104i 0.262959 0.809306i
\(345\) −3.77868 11.6296i −0.203437 0.626115i
\(346\) −2.63623 + 1.91533i −0.141724 + 0.102969i
\(347\) −20.2001 + 14.6763i −1.08440 + 0.787863i −0.978445 0.206508i \(-0.933790\pi\)
−0.105955 + 0.994371i \(0.533790\pi\)
\(348\) 0.466896 + 1.43696i 0.0250283 + 0.0770291i
\(349\) −9.31548 + 28.6701i −0.498646 + 1.53468i 0.312550 + 0.949901i \(0.398817\pi\)
−0.811196 + 0.584774i \(0.801183\pi\)
\(350\) −1.91025 1.38788i −0.102107 0.0741854i
\(351\) 1.00000 0.0533761
\(352\) 0.347209 12.5054i 0.0185063 0.666538i
\(353\) 26.6798 1.42002 0.710011 0.704191i \(-0.248690\pi\)
0.710011 + 0.704191i \(0.248690\pi\)
\(354\) −0.0949284 0.0689695i −0.00504539 0.00366569i
\(355\) −11.7994 + 36.3149i −0.626248 + 1.92739i
\(356\) 2.77017 + 8.52572i 0.146819 + 0.451862i
\(357\) 0.535898 0.389352i 0.0283627 0.0206067i
\(358\) −0.231275 + 0.168031i −0.0122232 + 0.00888071i
\(359\) 4.51067 + 13.8824i 0.238064 + 0.732686i 0.996700 + 0.0811716i \(0.0258662\pi\)
−0.758636 + 0.651515i \(0.774134\pi\)
\(360\) −1.60865 + 4.95090i −0.0847831 + 0.260935i
\(361\) −5.64102 4.09844i −0.296896 0.215707i
\(362\) 1.10957 0.0583175
\(363\) −3.97443 + 10.2569i −0.208604 + 0.538347i
\(364\) 1.24324 0.0651635
\(365\) 33.0228 + 23.9925i 1.72849 + 1.25582i
\(366\) −0.451713 + 1.39023i −0.0236114 + 0.0726684i
\(367\) 6.78242 + 20.8741i 0.354039 + 1.08962i 0.956564 + 0.291521i \(0.0941614\pi\)
−0.602525 + 0.798100i \(0.705839\pi\)
\(368\) −8.33458 + 6.05543i −0.434470 + 0.315661i
\(369\) 1.42866 1.03798i 0.0743732 0.0540353i
\(370\) 0.277387 + 0.853710i 0.0144207 + 0.0443823i
\(371\) −2.42439 + 7.46150i −0.125868 + 0.387382i
\(372\) −7.59788 5.52018i −0.393932 0.286208i
\(373\) 8.28362 0.428909 0.214455 0.976734i \(-0.431203\pi\)
0.214455 + 0.976734i \(0.431203\pi\)
\(374\) 0.0314390 1.13233i 0.00162567 0.0585514i
\(375\) −21.7431 −1.12281
\(376\) −6.18316 4.49233i −0.318872 0.231674i
\(377\) −0.247787 + 0.762610i −0.0127617 + 0.0392764i
\(378\) 0.0693631 + 0.213478i 0.00356765 + 0.0109801i
\(379\) −15.9486 + 11.5873i −0.819222 + 0.595200i −0.916490 0.400058i \(-0.868990\pi\)
0.0972673 + 0.995258i \(0.468990\pi\)
\(380\) 30.6051 22.2359i 1.57001 1.14068i
\(381\) 2.34153 + 7.20649i 0.119960 + 0.369200i
\(382\) −0.404325 + 1.24438i −0.0206871 + 0.0636682i
\(383\) 7.88111 + 5.72596i 0.402706 + 0.292583i 0.770642 0.637268i \(-0.219936\pi\)
−0.367936 + 0.929851i \(0.619936\pi\)
\(384\) 9.36560 0.477936
\(385\) 5.25877 6.83102i 0.268012 0.348141i
\(386\) 7.16106 0.364488
\(387\) −9.66277 7.02041i −0.491186 0.356868i
\(388\) 5.27942 16.2484i 0.268022 0.824887i
\(389\) −5.07773 15.6276i −0.257451 0.792353i −0.993337 0.115247i \(-0.963234\pi\)
0.735886 0.677106i \(-0.236766\pi\)
\(390\) −1.08424 + 0.787749i −0.0549028 + 0.0398892i
\(391\) −2.52110 + 1.83169i −0.127497 + 0.0926323i
\(392\) −2.68063 8.25012i −0.135392 0.416694i
\(393\) 6.17179 18.9948i 0.311326 0.958162i
\(394\) −2.82503 2.05250i −0.142323 0.103404i
\(395\) 25.1260 1.26423
\(396\) −5.88764 2.09538i −0.295865 0.105297i
\(397\) 18.1880 0.912832 0.456416 0.889767i \(-0.349133\pi\)
0.456416 + 0.889767i \(0.349133\pi\)
\(398\) −2.56272 1.86192i −0.128457 0.0933298i
\(399\) 1.03909 3.19799i 0.0520196 0.160100i
\(400\) 10.7888 + 33.2047i 0.539442 + 1.66023i
\(401\) −0.433267 + 0.314787i −0.0216363 + 0.0157197i −0.598551 0.801085i \(-0.704257\pi\)
0.576915 + 0.816805i \(0.304257\pi\)
\(402\) −0.584065 + 0.424348i −0.0291305 + 0.0211646i
\(403\) −1.54019 4.74023i −0.0767225 0.236128i
\(404\) −10.9505 + 33.7022i −0.544808 + 1.67675i
\(405\) 3.18709 + 2.31555i 0.158368 + 0.115061i
\(406\) −0.179987 −0.00893263
\(407\) −2.13094 + 0.627557i −0.105627 + 0.0311068i
\(408\) 1.32664 0.0656784
\(409\) −14.8912 10.8191i −0.736325 0.534971i 0.155233 0.987878i \(-0.450387\pi\)
−0.891558 + 0.452907i \(0.850387\pi\)
\(410\) −0.731348 + 2.25086i −0.0361187 + 0.111162i
\(411\) −3.65960 11.2631i −0.180515 0.555568i
\(412\) −29.2026 + 21.2169i −1.43871 + 1.04528i
\(413\) −0.184110 + 0.133763i −0.00905944 + 0.00658207i
\(414\) −0.326315 1.00429i −0.0160375 0.0493583i
\(415\) 9.36864 28.8337i 0.459889 1.41539i
\(416\) 3.05158 + 2.21710i 0.149616 + 0.108702i
\(417\) 2.35594 0.115371
\(418\) −3.24950 4.74407i −0.158938 0.232040i
\(419\) −29.9674 −1.46400 −0.732001 0.681304i \(-0.761413\pi\)
−0.732001 + 0.681304i \(0.761413\pi\)
\(420\) 3.96231 + 2.87879i 0.193341 + 0.140471i
\(421\) 10.3326 31.8004i 0.503579 1.54986i −0.299567 0.954075i \(-0.596842\pi\)
0.803146 0.595782i \(-0.203158\pi\)
\(422\) −1.31556 4.04888i −0.0640405 0.197096i
\(423\) −4.67917 + 3.39962i −0.227509 + 0.165295i
\(424\) −12.7118 + 9.23564i −0.617338 + 0.448523i
\(425\) 3.26348 + 10.0440i 0.158302 + 0.487204i
\(426\) −1.01896 + 3.13604i −0.0493688 + 0.151942i
\(427\) 2.29360 + 1.66640i 0.110995 + 0.0806426i
\(428\) 37.4253 1.80902
\(429\) −1.87424 2.73628i −0.0904893 0.132109i
\(430\) 16.0071 0.771932
\(431\) −20.7326 15.0631i −0.998652 0.725563i −0.0368535 0.999321i \(-0.511733\pi\)
−0.961799 + 0.273757i \(0.911733\pi\)
\(432\) 1.02562 3.15654i 0.0493453 0.151869i
\(433\) −2.13509 6.57112i −0.102606 0.315788i 0.886555 0.462623i \(-0.153091\pi\)
−0.989161 + 0.146835i \(0.953091\pi\)
\(434\) 0.905100 0.657593i 0.0434462 0.0315655i
\(435\) −2.55558 + 1.85674i −0.122531 + 0.0890239i
\(436\) 1.52400 + 4.69039i 0.0729864 + 0.224629i
\(437\) −4.88835 + 15.0448i −0.233841 + 0.719690i
\(438\) 2.85174 + 2.07191i 0.136262 + 0.0989998i
\(439\) 26.9412 1.28583 0.642916 0.765936i \(-0.277724\pi\)
0.642916 + 0.765936i \(0.277724\pi\)
\(440\) 16.5620 4.87749i 0.789564 0.232525i
\(441\) −6.56466 −0.312603
\(442\) 0.276313 + 0.200753i 0.0131429 + 0.00954886i
\(443\) 3.95952 12.1862i 0.188123 0.578982i −0.811866 0.583844i \(-0.801548\pi\)
0.999988 + 0.00486252i \(0.00154779\pi\)
\(444\) −0.389995 1.20028i −0.0185083 0.0569628i
\(445\) −15.1627 + 11.0164i −0.718781 + 0.522225i
\(446\) −1.38294 + 1.00477i −0.0654842 + 0.0475770i
\(447\) −5.01718 15.4413i −0.237304 0.730348i
\(448\) 1.09178 3.36015i 0.0515817 0.158752i
\(449\) −15.5283 11.2819i −0.732824 0.532428i 0.157631 0.987498i \(-0.449614\pi\)
−0.890456 + 0.455070i \(0.849614\pi\)
\(450\) −3.57866 −0.168700
\(451\) −5.51787 1.96378i −0.259827 0.0924710i
\(452\) 17.9616 0.844845
\(453\) 6.61181 + 4.80376i 0.310650 + 0.225700i
\(454\) 0.477156 1.46854i 0.0223940 0.0689218i
\(455\) 0.803215 + 2.47204i 0.0376553 + 0.115891i
\(456\) 5.44826 3.95839i 0.255138 0.185369i
\(457\) 1.34891 0.980037i 0.0630991 0.0458442i −0.555789 0.831324i \(-0.687584\pi\)
0.618888 + 0.785479i \(0.287584\pi\)
\(458\) 0.331043 + 1.01885i 0.0154686 + 0.0476075i
\(459\) 0.310237 0.954811i 0.0144806 0.0445668i
\(460\) −18.6405 13.5431i −0.869117 0.631450i
\(461\) −18.7395 −0.872787 −0.436394 0.899756i \(-0.643745\pi\)
−0.436394 + 0.899756i \(0.643745\pi\)
\(462\) 0.454131 0.589905i 0.0211281 0.0274449i
\(463\) 11.4490 0.532080 0.266040 0.963962i \(-0.414285\pi\)
0.266040 + 0.963962i \(0.414285\pi\)
\(464\) 2.15307 + 1.56430i 0.0999539 + 0.0726208i
\(465\) 6.06752 18.6739i 0.281375 0.865982i
\(466\) 0.189848 + 0.584293i 0.00879455 + 0.0270668i
\(467\) −11.1486 + 8.09994i −0.515896 + 0.374820i −0.815056 0.579383i \(-0.803294\pi\)
0.299160 + 0.954203i \(0.403294\pi\)
\(468\) 1.52440 1.10754i 0.0704655 0.0511962i
\(469\) 0.432679 + 1.33165i 0.0199793 + 0.0614899i
\(470\) 2.39532 7.37203i 0.110488 0.340046i
\(471\) 19.9266 + 14.4775i 0.918170 + 0.667090i
\(472\) −0.455772 −0.0209786
\(473\) −1.09943 + 39.5980i −0.0505519 + 1.82072i
\(474\) 2.16981 0.0996625
\(475\) 43.3714 + 31.5112i 1.99002 + 1.44583i
\(476\) 0.385699 1.18706i 0.0176785 0.0544088i
\(477\) 3.67442 + 11.3087i 0.168240 + 0.517790i
\(478\) 3.88118 2.81984i 0.177521 0.128977i
\(479\) −12.3069 + 8.94147i −0.562315 + 0.408546i −0.832306 0.554317i \(-0.812980\pi\)
0.269990 + 0.962863i \(0.412980\pi\)
\(480\) 4.59183 + 14.1322i 0.209587 + 0.645044i
\(481\) 0.206975 0.637002i 0.00943723 0.0290448i
\(482\) −2.25516 1.63847i −0.102720 0.0746303i
\(483\) −2.04802 −0.0931881
\(484\) 5.30132 + 20.0375i 0.240969 + 0.910795i
\(485\) 35.7189 1.62191
\(486\) 0.275227 + 0.199964i 0.0124845 + 0.00907055i
\(487\) −6.43804 + 19.8143i −0.291736 + 0.897870i 0.692563 + 0.721358i \(0.256482\pi\)
−0.984298 + 0.176512i \(0.943518\pi\)
\(488\) 1.75457 + 5.40002i 0.0794257 + 0.244447i
\(489\) 17.5727 12.7673i 0.794666 0.577359i
\(490\) 7.11769 5.17131i 0.321545 0.233616i
\(491\) 9.26355 + 28.5103i 0.418058 + 1.28665i 0.909487 + 0.415732i \(0.136475\pi\)
−0.491429 + 0.870918i \(0.663525\pi\)
\(492\) 1.02824 3.16461i 0.0463568 0.142672i
\(493\) 0.651276 + 0.473180i 0.0293320 + 0.0213109i
\(494\) 1.73377 0.0780060
\(495\) 0.362627 13.0607i 0.0162989 0.587033i
\(496\) −16.5424 −0.742774
\(497\) 5.17384 + 3.75901i 0.232078 + 0.168615i
\(498\) 0.809046 2.48999i 0.0362542 0.111579i
\(499\) 7.49341 + 23.0624i 0.335451 + 1.03241i 0.966499 + 0.256669i \(0.0826251\pi\)
−0.631048 + 0.775744i \(0.717375\pi\)
\(500\) −33.1453 + 24.0814i −1.48230 + 1.07695i
\(501\) −13.5302 + 9.83028i −0.604486 + 0.439185i
\(502\) −0.518882 1.59696i −0.0231588 0.0712756i
\(503\) −9.17099 + 28.2254i −0.408914 + 1.25851i 0.508668 + 0.860963i \(0.330138\pi\)
−0.917582 + 0.397546i \(0.869862\pi\)
\(504\) 0.705363 + 0.512476i 0.0314193 + 0.0228275i
\(505\) −74.0877 −3.29686
\(506\) −2.13643 + 2.77518i −0.0949760 + 0.123372i
\(507\) 1.00000 0.0444116
\(508\) 11.5509 + 8.39224i 0.512490 + 0.372346i
\(509\) 9.22302 28.3855i 0.408803 1.25817i −0.508875 0.860841i \(-0.669938\pi\)
0.917678 0.397326i \(-0.130062\pi\)
\(510\) 0.415779 + 1.27964i 0.0184110 + 0.0566633i
\(511\) 5.53083 4.01839i 0.244670 0.177763i
\(512\) 17.2245 12.5143i 0.761222 0.553060i
\(513\) −1.57486 4.84691i −0.0695316 0.213996i
\(514\) 1.04839 3.22660i 0.0462423 0.142319i
\(515\) −61.0543 44.3585i −2.69037 1.95467i
\(516\) −22.5053 −0.990743
\(517\) 18.0722 + 6.43181i 0.794814 + 0.282871i
\(518\) 0.150342 0.00660565
\(519\) 7.74908 + 5.63003i 0.340147 + 0.247131i
\(520\) −1.60865 + 4.95090i −0.0705438 + 0.217111i
\(521\) −6.36929 19.6027i −0.279044 0.858808i −0.988121 0.153678i \(-0.950888\pi\)
0.709077 0.705131i \(-0.249112\pi\)
\(522\) −0.220692 + 0.160342i −0.00965943 + 0.00701799i
\(523\) 30.1568 21.9102i 1.31867 0.958067i 0.318718 0.947850i \(-0.396748\pi\)
0.999948 0.0102173i \(-0.00325232\pi\)
\(524\) −11.6293 35.7913i −0.508028 1.56355i
\(525\) −2.14478 + 6.60096i −0.0936059 + 0.288089i
\(526\) −5.61362 4.07853i −0.244766 0.177833i
\(527\) −5.00385 −0.217971
\(528\) −10.5594 + 3.10973i −0.459540 + 0.135334i
\(529\) −13.3652 −0.581096
\(530\) −12.8924 9.36688i −0.560010 0.406871i
\(531\) −0.106583 + 0.328029i −0.00462531 + 0.0142352i
\(532\) −1.95792 6.02587i −0.0848867 0.261255i
\(533\) 1.42866 1.03798i 0.0618823 0.0449601i
\(534\) −1.30940 + 0.951337i −0.0566634 + 0.0411684i
\(535\) 24.1792 + 74.4159i 1.04536 + 3.21728i
\(536\) −0.866552 + 2.66697i −0.0374293 + 0.115196i
\(537\) 0.679822 + 0.493919i 0.0293365 + 0.0213142i
\(538\) 4.92843 0.212479
\(539\) 12.3038 + 17.9627i 0.529961 + 0.773710i
\(540\) 7.42298 0.319434
\(541\) 11.0229 + 8.00863i 0.473913 + 0.344318i 0.798964 0.601378i \(-0.205382\pi\)
−0.325051 + 0.945696i \(0.605382\pi\)
\(542\) 2.29006 7.04807i 0.0983663 0.302740i
\(543\) −1.00787 3.10189i −0.0432516 0.133115i
\(544\) 3.06363 2.22585i 0.131352 0.0954327i
\(545\) −8.34171 + 6.06060i −0.357319 + 0.259608i
\(546\) 0.0693631 + 0.213478i 0.00296847 + 0.00913600i
\(547\) 5.04386 15.5234i 0.215660 0.663732i −0.783446 0.621459i \(-0.786540\pi\)
0.999106 0.0422730i \(-0.0134599\pi\)
\(548\) −18.0531 13.1163i −0.771189 0.560302i
\(549\) 4.29682 0.183384
\(550\) 6.70728 + 9.79221i 0.285999 + 0.417541i
\(551\) 4.08653 0.174092
\(552\) −3.31834 2.41091i −0.141238 0.102615i
\(553\) 1.30042 4.00228i 0.0552994 0.170194i
\(554\) −1.36962 4.21524i −0.0581894 0.179089i
\(555\) 2.13466 1.55092i 0.0906113 0.0658329i
\(556\) 3.59140 2.60931i 0.152309 0.110659i
\(557\) −5.34308 16.4443i −0.226394 0.696768i −0.998147 0.0608464i \(-0.980620\pi\)
0.771753 0.635922i \(-0.219380\pi\)
\(558\) 0.523972 1.61262i 0.0221815 0.0682677i
\(559\) −9.66277 7.02041i −0.408691 0.296932i
\(560\) 8.62689 0.364553
\(561\) −3.19409 + 0.940653i −0.134854 + 0.0397144i
\(562\) −10.1771 −0.429294
\(563\) 0.465126 + 0.337934i 0.0196027 + 0.0142422i 0.597543 0.801837i \(-0.296144\pi\)
−0.577941 + 0.816079i \(0.696144\pi\)
\(564\) −3.36772 + 10.3648i −0.141806 + 0.436435i
\(565\) 11.6044 + 35.7147i 0.488201 + 1.50253i
\(566\) −5.27681 + 3.83383i −0.221801 + 0.161148i
\(567\) 0.533790 0.387821i 0.0224171 0.0162870i
\(568\) 3.95791 + 12.1812i 0.166070 + 0.511112i
\(569\) 11.8375 36.4320i 0.496253 1.52731i −0.318742 0.947841i \(-0.603260\pi\)
0.814995 0.579468i \(-0.196740\pi\)
\(570\) 5.52567 + 4.01464i 0.231445 + 0.168155i
\(571\) −20.0309 −0.838267 −0.419133 0.907925i \(-0.637666\pi\)
−0.419133 + 0.907925i \(0.637666\pi\)
\(572\) −5.88764 2.09538i −0.246175 0.0876124i
\(573\) 3.84605 0.160671
\(574\) 0.320683 + 0.232990i 0.0133850 + 0.00972480i
\(575\) 10.0900 31.0538i 0.420782 1.29503i
\(576\) −1.65471 5.09267i −0.0689462 0.212195i
\(577\) 23.0579 16.7525i 0.959911 0.697416i 0.00678098 0.999977i \(-0.497842\pi\)
0.953130 + 0.302561i \(0.0978415\pi\)
\(578\) −4.40145 + 3.19784i −0.183076 + 0.133013i
\(579\) −6.50469 20.0194i −0.270326 0.831977i
\(580\) −1.83932 + 5.66084i −0.0763735 + 0.235054i
\(581\) −4.10798 2.98462i −0.170428 0.123823i
\(582\) 3.08457 0.127860
\(583\) 24.0570 31.2495i 0.996340 1.29422i
\(584\) 13.6918 0.566572
\(585\) 3.18709 + 2.31555i 0.131770 + 0.0957364i
\(586\) 1.25087 3.84977i 0.0516728 0.159033i
\(587\) −5.76814 17.7525i −0.238076 0.732724i −0.996698 0.0811929i \(-0.974127\pi\)
0.758622 0.651531i \(-0.225873\pi\)
\(588\) −10.0072 + 7.27065i −0.412689 + 0.299836i
\(589\) −20.5499 + 14.9303i −0.846742 + 0.615194i
\(590\) −0.142842 0.439624i −0.00588073 0.0180990i
\(591\) −3.17186 + 9.76199i −0.130473 + 0.401554i
\(592\) −1.79845 1.30665i −0.0739157 0.0537029i
\(593\) 29.4986 1.21136 0.605681 0.795708i \(-0.292901\pi\)
0.605681 + 0.795708i \(0.292901\pi\)
\(594\) 0.0313153 1.12788i 0.00128488 0.0462774i
\(595\) 2.60952 0.106980
\(596\) −24.7501 17.9820i −1.01380 0.736571i
\(597\) −2.87735 + 8.85557i −0.117762 + 0.362434i
\(598\) −0.326315 1.00429i −0.0133440 0.0410686i
\(599\) 9.53109 6.92474i 0.389430 0.282937i −0.375792 0.926704i \(-0.622629\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(600\) −11.2457 + 8.17049i −0.459104 + 0.333559i
\(601\) −14.4309 44.4138i −0.588650 1.81168i −0.584092 0.811687i \(-0.698549\pi\)
−0.00455763 0.999990i \(-0.501451\pi\)
\(602\) 0.828461 2.54974i 0.0337656 0.103920i
\(603\) 1.71683 + 1.24735i 0.0699149 + 0.0507961i
\(604\) 15.3994 0.626594
\(605\) −36.4173 + 23.4866i −1.48057 + 0.954866i
\(606\) −6.39798 −0.259900
\(607\) 3.41290 + 2.47962i 0.138525 + 0.100645i 0.654890 0.755724i \(-0.272715\pi\)
−0.516364 + 0.856369i \(0.672715\pi\)
\(608\) 5.94029 18.2823i 0.240911 0.741447i
\(609\) 0.163490 + 0.503171i 0.00662496 + 0.0203895i
\(610\) −4.65880 + 3.38481i −0.188629 + 0.137047i
\(611\) −4.67917 + 3.39962i −0.189299 + 0.137534i
\(612\) −0.584568 1.79912i −0.0236298 0.0727250i
\(613\) 9.91019 30.5004i 0.400269 1.23190i −0.524513 0.851402i \(-0.675753\pi\)
0.924782 0.380498i \(-0.124247\pi\)
\(614\) 6.68920 + 4.85999i 0.269954 + 0.196133i
\(615\) 6.95678 0.280525
\(616\) 0.0802562 2.89057i 0.00323362 0.116464i
\(617\) −15.7235 −0.633006 −0.316503 0.948591i \(-0.602509\pi\)
−0.316503 + 0.948591i \(0.602509\pi\)
\(618\) −5.27245 3.83066i −0.212089 0.154092i
\(619\) −11.4230 + 35.1565i −0.459131 + 1.41306i 0.407085 + 0.913390i \(0.366545\pi\)
−0.866216 + 0.499670i \(0.833455\pi\)
\(620\) −11.4328 35.1866i −0.459153 1.41313i
\(621\) −2.51119 + 1.82448i −0.100770 + 0.0732140i
\(622\) −4.04099 + 2.93595i −0.162029 + 0.117721i
\(623\) 0.970015 + 2.98540i 0.0388628 + 0.119607i
\(624\) 1.02562 3.15654i 0.0410577 0.126363i
\(625\) −26.7457 19.4319i −1.06983 0.777275i
\(626\) −2.48250 −0.0992207
\(627\) −10.3108 + 13.3935i −0.411775 + 0.534886i
\(628\) 46.4107 1.85199
\(629\) −0.544006 0.395243i −0.0216909 0.0157594i
\(630\) −0.273253 + 0.840986i −0.0108867 + 0.0335057i
\(631\) −9.64700 29.6904i −0.384041 1.18196i −0.937174 0.348863i \(-0.886568\pi\)
0.553133 0.833093i \(-0.313432\pi\)
\(632\) 6.81847 4.95391i 0.271224 0.197056i
\(633\) −10.1240 + 7.35554i −0.402394 + 0.292356i
\(634\) 0.582348 + 1.79228i 0.0231280 + 0.0711807i
\(635\) −9.22436 + 28.3897i −0.366057 + 1.12661i
\(636\) 18.1262 + 13.1694i 0.718750 + 0.522202i
\(637\) −6.56466 −0.260101
\(638\) 0.852371 + 0.303355i 0.0337457 + 0.0120099i
\(639\) 9.69264 0.383435
\(640\) 29.8490 + 21.6866i 1.17988 + 0.857236i
\(641\) 11.2858 34.7342i 0.445763 1.37192i −0.435882 0.900004i \(-0.643563\pi\)
0.881645 0.471914i \(-0.156437\pi\)
\(642\) 2.08804 + 6.42632i 0.0824083 + 0.253627i
\(643\) 29.4235 21.3774i 1.16035 0.843043i 0.170527 0.985353i \(-0.445453\pi\)
0.989822 + 0.142310i \(0.0454529\pi\)
\(644\) −3.12201 + 2.26827i −0.123024 + 0.0893824i
\(645\) −14.5399 44.7493i −0.572509 1.76200i
\(646\) 0.537879 1.65542i 0.0211626 0.0651317i
\(647\) 6.77898 + 4.92521i 0.266509 + 0.193630i 0.713012 0.701152i \(-0.247331\pi\)
−0.446503 + 0.894782i \(0.647331\pi\)
\(648\) 1.32142 0.0519104
\(649\) 1.09734 0.323165i 0.0430744 0.0126853i
\(650\) −3.57866 −0.140367
\(651\) −2.66050 1.93297i −0.104273 0.0757590i
\(652\) 12.6475 38.9251i 0.495315 1.52442i
\(653\) 0.126996 + 0.390853i 0.00496973 + 0.0152952i 0.953511 0.301359i \(-0.0974404\pi\)
−0.948541 + 0.316655i \(0.897440\pi\)
\(654\) −0.720363 + 0.523374i −0.0281684 + 0.0204656i
\(655\) 63.6536 46.2470i 2.48715 1.80702i
\(656\) −1.81117 5.57421i −0.0707144 0.217636i
\(657\) 3.20186 9.85431i 0.124916 0.384453i
\(658\) −1.05030 0.763090i −0.0409451 0.0297484i
\(659\) −47.2816 −1.84183 −0.920915 0.389764i \(-0.872557\pi\)
−0.920915 + 0.389764i \(0.872557\pi\)
\(660\) −13.9125 20.3113i −0.541542 0.790618i
\(661\) 17.5534 0.682749 0.341375 0.939927i \(-0.389108\pi\)
0.341375 + 0.939927i \(0.389108\pi\)
\(662\) −7.17138 5.21032i −0.278724 0.202505i
\(663\) 0.310237 0.954811i 0.0120486 0.0370818i
\(664\) −3.14255 9.67177i −0.121955 0.375338i
\(665\) 10.7168 7.78622i 0.415580 0.301936i
\(666\) 0.184342 0.133933i 0.00714312 0.00518978i
\(667\) −0.769130 2.36714i −0.0297808 0.0916560i
\(668\) −9.73804 + 29.9706i −0.376776 + 1.15960i
\(669\) 4.06510 + 2.95346i 0.157166 + 0.114188i
\(670\) −2.84407 −0.109876
\(671\) −8.05328 11.7573i −0.310893 0.453885i
\(672\) 2.48874 0.0960053
\(673\) 2.76098 + 2.00597i 0.106428 + 0.0773246i 0.639726 0.768603i \(-0.279048\pi\)
−0.533298 + 0.845927i \(0.679048\pi\)
\(674\) 1.46797 4.51795i 0.0565441 0.174025i
\(675\) 3.25065 + 10.0045i 0.125118 + 0.385072i
\(676\) 1.52440 1.10754i 0.0586309 0.0425978i
\(677\) −27.7761 + 20.1805i −1.06752 + 0.775601i −0.975465 0.220153i \(-0.929344\pi\)
−0.0920579 + 0.995754i \(0.529344\pi\)
\(678\) 1.00212 + 3.08421i 0.0384862 + 0.118448i
\(679\) 1.84866 5.68960i 0.0709451 0.218347i
\(680\) 4.22812 + 3.07191i 0.162141 + 0.117802i
\(681\) −4.53884 −0.173929
\(682\) −5.39463 + 1.58871i −0.206571 + 0.0608348i
\(683\) 2.04683 0.0783199 0.0391599 0.999233i \(-0.487532\pi\)
0.0391599 + 0.999233i \(0.487532\pi\)
\(684\) −7.76887 5.64442i −0.297050 0.215820i
\(685\) 14.4168 44.3705i 0.550839 1.69531i
\(686\) −0.940887 2.89575i −0.0359232 0.110560i
\(687\) 2.54757 1.85092i 0.0971960 0.0706170i
\(688\) −32.0706 + 23.3006i −1.22268 + 0.888328i
\(689\) 3.67442 + 11.3087i 0.139984 + 0.430828i
\(690\) 1.28550 3.95637i 0.0489382 0.150616i
\(691\) 33.7843 + 24.5457i 1.28521 + 0.933763i 0.999697 0.0246107i \(-0.00783461\pi\)
0.285517 + 0.958374i \(0.407835\pi\)
\(692\) 18.0482 0.686090
\(693\) −2.06164 0.733727i −0.0783152 0.0278720i
\(694\) −8.49434 −0.322441
\(695\) 7.50859 + 5.45531i 0.284817 + 0.206932i
\(696\) −0.327431 + 1.00773i −0.0124113 + 0.0381979i
\(697\) −0.547855 1.68612i −0.0207515 0.0638665i
\(698\) −8.29686 + 6.02802i −0.314041 + 0.228164i
\(699\) 1.46099 1.06147i 0.0552599 0.0401487i
\(700\) 4.04134 + 12.4380i 0.152748 + 0.470110i
\(701\) 12.7891 39.3607i 0.483036 1.48663i −0.351768 0.936087i \(-0.614420\pi\)
0.834805 0.550546i \(-0.185580\pi\)
\(702\) 0.275227 + 0.199964i 0.0103878 + 0.00754715i
\(703\) −3.41345 −0.128741
\(704\) −10.8336 + 14.0726i −0.408308 + 0.530382i
\(705\) −22.7849 −0.858130
\(706\) 7.34299 + 5.33500i 0.276357 + 0.200785i
\(707\) −3.83447 + 11.8013i −0.144210 + 0.443833i
\(708\) 0.200831 + 0.618093i 0.00754768 + 0.0232294i
\(709\) −21.1535 + 15.3689i −0.794437 + 0.577192i −0.909277 0.416192i \(-0.863365\pi\)
0.114840 + 0.993384i \(0.463365\pi\)
\(710\) −10.5092 + 7.63537i −0.394403 + 0.286550i
\(711\) −1.97093 6.06588i −0.0739155 0.227488i
\(712\) −1.94271 + 5.97903i −0.0728060 + 0.224074i
\(713\) 12.5162 + 9.09353i 0.468734 + 0.340556i
\(714\) 0.225350 0.00843350
\(715\) 0.362627 13.0607i 0.0135615 0.488441i
\(716\) 1.58336 0.0591729
\(717\) −11.4086 8.28881i −0.426061 0.309551i
\(718\) −1.53453 + 4.72279i −0.0572680 + 0.176253i
\(719\) −4.91562 15.1287i −0.183322 0.564206i 0.816594 0.577213i \(-0.195860\pi\)
−0.999915 + 0.0130068i \(0.995860\pi\)
\(720\) 10.5779 7.68529i 0.394215 0.286414i
\(721\) −10.2257 + 7.42940i −0.380825 + 0.276685i
\(722\) −0.733019 2.25600i −0.0272801 0.0839596i
\(723\) −2.53203 + 7.79280i −0.0941674 + 0.289817i
\(724\) −4.97187 3.61227i −0.184778 0.134249i
\(725\) −8.43498 −0.313267
\(726\) −3.14488 + 2.02823i −0.116717 + 0.0752746i
\(727\) −14.9983 −0.556256 −0.278128 0.960544i \(-0.589714\pi\)
−0.278128 + 0.960544i \(0.589714\pi\)
\(728\) 0.705363 + 0.512476i 0.0261425 + 0.0189936i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 4.29113 + 13.2067i 0.158822 + 0.488803i
\(731\) −9.70091 + 7.04813i −0.358801 + 0.260684i
\(732\) 6.55008 4.75891i 0.242098 0.175894i
\(733\) 3.00726 + 9.25541i 0.111076 + 0.341856i 0.991108 0.133057i \(-0.0424794\pi\)
−0.880033 + 0.474913i \(0.842479\pi\)
\(734\) −2.30737 + 7.10136i −0.0851666 + 0.262116i
\(735\) −20.9222 15.2008i −0.771725 0.560691i
\(736\) −11.7081 −0.431568
\(737\) 0.195342 7.03557i 0.00719550 0.259159i
\(738\) 0.600766 0.0221145
\(739\) 4.76042 + 3.45865i 0.175115 + 0.127228i 0.671890 0.740651i \(-0.265483\pi\)
−0.496775 + 0.867879i \(0.665483\pi\)
\(740\) 1.53637 4.72846i 0.0564780 0.173821i
\(741\) −1.57486 4.84691i −0.0578538 0.178056i
\(742\) −2.15929 + 1.56881i −0.0792699 + 0.0575930i
\(743\) −15.4545 + 11.2284i −0.566971 + 0.411929i −0.834004 0.551759i \(-0.813957\pi\)
0.267033 + 0.963688i \(0.413957\pi\)
\(744\) −2.03525 6.26384i −0.0746157 0.229644i
\(745\) 19.7650 60.8303i 0.724132 2.22865i
\(746\) 2.27987 + 1.65642i 0.0834721 + 0.0606460i
\(747\) −7.69588 −0.281577
\(748\) −3.82726 + 4.97152i −0.139939 + 0.181777i
\(749\) 13.1050 0.478846
\(750\) −5.98429 4.34784i −0.218515 0.158761i
\(751\) −9.54262 + 29.3692i −0.348215 + 1.07170i 0.611625 + 0.791148i \(0.290516\pi\)
−0.959840 + 0.280548i \(0.909484\pi\)
\(752\) 5.93197 + 18.2567i 0.216317 + 0.665754i
\(753\) −3.99311 + 2.90116i −0.145517 + 0.105724i
\(754\) −0.220692 + 0.160342i −0.00803713 + 0.00583932i
\(755\) 9.94904 + 30.6200i 0.362083 + 1.11438i
\(756\) 0.384182 1.18239i 0.0139726 0.0430032i
\(757\) 2.86630 + 2.08249i 0.104178 + 0.0756895i 0.638654 0.769494i \(-0.279491\pi\)
−0.534477 + 0.845183i \(0.679491\pi\)
\(758\) −6.70651 −0.243591
\(759\) 9.69886 + 3.45178i 0.352046 + 0.125292i
\(760\) 26.5300 0.962342
\(761\) 36.8615 + 26.7814i 1.33623 + 0.970826i 0.999574 + 0.0291972i \(0.00929509\pi\)
0.336653 + 0.941629i \(0.390705\pi\)
\(762\) −0.796586 + 2.45164i −0.0288573 + 0.0888136i
\(763\) 0.533650 + 1.64240i 0.0193194 + 0.0594590i
\(764\) 5.86293 4.25967i 0.212113 0.154109i
\(765\) 3.19967 2.32470i 0.115684 0.0840496i
\(766\) 1.02411 + 3.15188i 0.0370025 + 0.113882i
\(767\) −0.106583 + 0.328029i −0.00384849 + 0.0118444i
\(768\) −6.08650 4.42210i −0.219628 0.159569i
\(769\) 27.0550 0.975629 0.487815 0.872947i \(-0.337794\pi\)
0.487815 + 0.872947i \(0.337794\pi\)
\(770\) 2.81331 0.828515i 0.101385 0.0298576i
\(771\) −9.97255 −0.359152
\(772\) −32.0881 23.3134i −1.15488 0.839066i
\(773\) 8.51708 26.2129i 0.306338 0.942811i −0.672837 0.739791i \(-0.734924\pi\)
0.979175 0.203020i \(-0.0650757\pi\)
\(774\) −1.25562 3.86441i −0.0451324 0.138903i
\(775\) 42.4168 30.8176i 1.52366 1.10700i
\(776\) 9.69307 7.04243i 0.347961 0.252809i
\(777\) −0.136562 0.420295i −0.00489914 0.0150780i
\(778\) 1.72744 5.31651i 0.0619316 0.190606i
\(779\) −7.28095 5.28992i −0.260867 0.189531i
\(780\) 7.42298 0.265785
\(781\) −18.1664 26.5218i −0.650043 0.949023i
\(782\) −1.06014 −0.0379107
\(783\) 0.648715 + 0.471319i 0.0231832 + 0.0168436i
\(784\) −6.73286 + 20.7216i −0.240459 + 0.740058i
\(785\) 29.9843 + 92.2823i 1.07019 + 3.29370i
\(786\) 5.49692 3.99375i 0.196069 0.142452i
\(787\) 28.6431 20.8105i 1.02102 0.741813i 0.0545264 0.998512i \(-0.482635\pi\)
0.966491 + 0.256700i \(0.0826351\pi\)
\(788\) 5.97663 + 18.3942i 0.212908 + 0.655265i
\(789\) −6.30282 + 19.3981i −0.224386 + 0.690590i
\(790\) 6.91536 + 5.02430i 0.246037 + 0.178757i
\(791\) 6.28952 0.223629
\(792\) −2.47667 3.61578i −0.0880045 0.128481i
\(793\) 4.29682 0.152584
\(794\) 5.00583 + 3.63695i 0.177650 + 0.129071i
\(795\) −14.4752 + 44.5502i −0.513384 + 1.58003i
\(796\) 5.42169 + 16.6862i 0.192167 + 0.591428i
\(797\) 25.9464 18.8512i 0.919070 0.667743i −0.0242225 0.999707i \(-0.507711\pi\)
0.943292 + 0.331963i \(0.107711\pi\)
\(798\) 0.925469 0.672393i 0.0327613 0.0238024i
\(799\) 1.79434 + 5.52241i 0.0634792 + 0.195369i
\(800\) −12.2613 + 37.7364i −0.433503 + 1.33418i
\(801\) 3.84893 + 2.79641i 0.135995 + 0.0988064i
\(802\) −0.182193 −0.00643345
\(803\) −32.9652 + 9.70818i −1.16332 + 0.342594i
\(804\) 3.99864 0.141021
\(805\) −6.52722 4.74230i −0.230054 0.167144i
\(806\) 0.523972 1.61262i 0.0184561 0.0568021i
\(807\) −4.47670 13.7779i −0.157587 0.485003i
\(808\) −20.1052 + 14.6073i −0.707300 + 0.513883i
\(809\) −2.90853 + 2.11317i −0.102259 + 0.0742952i −0.637740 0.770252i \(-0.720130\pi\)
0.535481 + 0.844547i \(0.320130\pi\)
\(810\) 0.414144 + 1.27460i 0.0145515 + 0.0447851i
\(811\) 2.38932 7.35357i 0.0839004 0.258219i −0.900302 0.435266i \(-0.856654\pi\)
0.984202 + 0.177047i \(0.0566544\pi\)
\(812\) 0.806508 + 0.585962i 0.0283029 + 0.0205633i
\(813\) −21.7837 −0.763986
\(814\) −0.711979 0.253390i −0.0249549 0.00888131i
\(815\) 85.5693 2.99736
\(816\) −2.69571 1.95855i −0.0943689 0.0685630i
\(817\) −18.8098 + 57.8907i −0.658072 + 2.02534i
\(818\) −1.93503 5.95542i −0.0676569 0.208226i
\(819\) 0.533790 0.387821i 0.0186521 0.0135516i
\(820\) 10.6049 7.70494i 0.370340 0.269068i
\(821\) −7.94062 24.4387i −0.277130 0.852918i −0.988648 0.150250i \(-0.951992\pi\)
0.711518 0.702668i \(-0.248008\pi\)
\(822\) 1.24499 3.83169i 0.0434241 0.133646i
\(823\) −11.5438 8.38708i −0.402392 0.292355i 0.368122 0.929777i \(-0.380001\pi\)
−0.770515 + 0.637422i \(0.780001\pi\)
\(824\) −25.3142 −0.881861
\(825\) 21.2825 27.6455i 0.740962 0.962492i
\(826\) −0.0774197 −0.00269378
\(827\) −3.82042 2.77570i −0.132849 0.0965205i 0.519376 0.854546i \(-0.326164\pi\)
−0.652225 + 0.758025i \(0.726164\pi\)
\(828\) −1.80736 + 5.56249i −0.0628102 + 0.193310i
\(829\) 13.8510 + 42.6289i 0.481064 + 1.48056i 0.837601 + 0.546283i \(0.183958\pi\)
−0.356536 + 0.934281i \(0.616042\pi\)
\(830\) 8.34420 6.06242i 0.289632 0.210430i
\(831\) −10.5400 + 7.65777i −0.365629 + 0.265645i
\(832\) −1.65471 5.09267i −0.0573667 0.176557i
\(833\) −2.03660 + 6.26801i −0.0705640 + 0.217174i
\(834\) 0.648418 + 0.471103i 0.0224529 + 0.0163130i
\(835\) −65.8845 −2.28003
\(836\) −0.883943 + 31.8368i −0.0305718 + 1.10110i
\(837\) −4.98417 −0.172278
\(838\) −8.24782 5.99239i −0.284916 0.207004i
\(839\) 1.59373 4.90500i 0.0550217 0.169339i −0.919769 0.392460i \(-0.871624\pi\)
0.974791 + 0.223120i \(0.0716243\pi\)
\(840\) 1.06139 + 3.26661i 0.0366213 + 0.112709i
\(841\) 22.9413 16.6678i 0.791080 0.574753i
\(842\) 9.20274 6.68618i 0.317147 0.230421i
\(843\) 9.24427 + 28.4509i 0.318390 + 0.979902i
\(844\) −7.28652 + 22.4256i −0.250812 + 0.771921i
\(845\) 3.18709 + 2.31555i 0.109639 + 0.0796575i
\(846\) −1.96763 −0.0676486
\(847\) 1.85633 + 7.01640i 0.0637842 + 0.241086i
\(848\) 39.4650 1.35523
\(849\) 15.5110 + 11.2694i 0.532335 + 0.386764i
\(850\) −1.11023 + 3.41695i −0.0380807 + 0.117200i
\(851\) 0.642448 + 1.97725i 0.0220229 + 0.0677794i
\(852\) 14.7755 10.7350i 0.506200 0.367776i
\(853\) 15.3270 11.1357i 0.524788 0.381281i −0.293617 0.955923i \(-0.594859\pi\)
0.818405 + 0.574643i \(0.194859\pi\)
\(854\) 0.298040 + 0.917274i 0.0101987 + 0.0313885i
\(855\) 6.20408 19.0942i 0.212175 0.653007i
\(856\) 21.2336 + 15.4271i 0.725748 + 0.527287i
\(857\) −34.9448 −1.19369 −0.596846 0.802356i \(-0.703580\pi\)
−0.596846 + 0.802356i \(0.703580\pi\)
\(858\) 0.0313153 1.12788i 0.00106909 0.0385051i
\(859\) −43.3058 −1.47757 −0.738787 0.673938i \(-0.764601\pi\)
−0.738787 + 0.673938i \(0.764601\pi\)
\(860\) −71.7265 52.1124i −2.44585 1.77702i
\(861\) 0.360054 1.10813i 0.0122706 0.0377650i
\(862\) −2.69408 8.29153i −0.0917608 0.282411i
\(863\) 23.6969 17.2168i 0.806653 0.586068i −0.106205 0.994344i \(-0.533870\pi\)
0.912858 + 0.408276i \(0.133870\pi\)
\(864\) 3.05158 2.21710i 0.103817 0.0754274i
\(865\) 11.6603 + 35.8868i 0.396463 + 1.22019i
\(866\) 0.726354 2.23549i 0.0246825 0.0759650i
\(867\) 12.9379 + 9.39991i 0.439393 + 0.319238i
\(868\) −6.19652 −0.210324
\(869\) −12.9040 + 16.7619i −0.437737 + 0.568610i
\(870\) −1.07465 −0.0364339
\(871\) 1.71683 + 1.24735i 0.0581727 + 0.0422649i
\(872\) −1.06877 + 3.28934i −0.0361932 + 0.111391i
\(873\) −2.80185 8.62320i −0.0948282 0.291851i
\(874\) −4.35382 + 3.16323i −0.147270 + 0.106998i
\(875\) −11.6063 + 8.43244i −0.392363 + 0.285069i
\(876\) −6.03315 18.5681i −0.203841 0.627359i
\(877\) −3.16523 + 9.74156i −0.106882 + 0.328949i −0.990168 0.139886i \(-0.955326\pi\)
0.883286 + 0.468835i \(0.155326\pi\)
\(878\) 7.41493 + 5.38726i 0.250242 + 0.181811i
\(879\) −11.8986 −0.401330
\(880\) −40.8546 14.5400i −1.37721 0.490142i
\(881\) −40.9069 −1.37819 −0.689094 0.724672i \(-0.741991\pi\)
−0.689094 + 0.724672i \(0.741991\pi\)
\(882\) −1.80677 1.31270i −0.0608371 0.0442008i
\(883\) −9.59469 + 29.5294i −0.322887 + 0.993744i 0.649498 + 0.760363i \(0.274979\pi\)
−0.972385 + 0.233381i \(0.925021\pi\)
\(884\) −0.584568 1.79912i −0.0196612 0.0605108i
\(885\) −1.09926 + 0.798657i −0.0369511 + 0.0268466i
\(886\) 3.52656 2.56219i 0.118477 0.0860786i
\(887\) 1.62682 + 5.00683i 0.0546232 + 0.168113i 0.974646 0.223751i \(-0.0718303\pi\)
−0.920023 + 0.391864i \(0.871830\pi\)
\(888\) 0.273501 0.841749i 0.00917809 0.0282473i
\(889\) 4.04472 + 2.93866i 0.135655 + 0.0985595i
\(890\) −6.37606 −0.213726
\(891\) −3.18153 + 0.936954i −0.106585 + 0.0313891i
\(892\) 9.46793 0.317010
\(893\) 23.8467 + 17.3256i 0.797998 + 0.579779i
\(894\) 1.70684 5.25311i 0.0570852 0.175690i
\(895\) 1.02295 + 3.14833i 0.0341936 + 0.105237i
\(896\) 4.99927 3.63218i 0.167014 0.121343i
\(897\) −2.51119 + 1.82448i −0.0838461 + 0.0609177i
\(898\) −2.01781 6.21019i −0.0673353 0.207237i
\(899\) 1.23501 3.80098i 0.0411900 0.126770i
\(900\) 16.0357 + 11.6506i 0.534522 + 0.388353i
\(901\) 11.9376 0.397700
\(902\) −1.12598 1.64386i −0.0374910 0.0547346i
\(903\) −7.88056 −0.262248
\(904\) 10.1907 + 7.40397i 0.338937 + 0.246252i
\(905\) 3.97044 12.2198i 0.131982 0.406199i
\(906\) 0.859167 + 2.64425i 0.0285439 + 0.0878492i
\(907\) 18.1418 13.1808i 0.602387 0.437660i −0.244338 0.969690i \(-0.578571\pi\)
0.846725 + 0.532030i \(0.178571\pi\)
\(908\) −6.91902 + 5.02696i −0.229616 + 0.166826i
\(909\) 5.81155 + 17.8861i 0.192757 + 0.593245i
\(910\) −0.273253 + 0.840986i −0.00905824 + 0.0278784i
\(911\) −20.5237 14.9114i −0.679982 0.494036i 0.193370 0.981126i \(-0.438058\pi\)
−0.873352 + 0.487090i \(0.838058\pi\)
\(912\) −16.9147 −0.560100
\(913\) 14.4239 + 21.0581i 0.477363 + 0.696920i
\(914\) 0.567227 0.0187622
\(915\) 13.6943 + 9.94952i 0.452721 + 0.328921i
\(916\) 1.83355 5.64310i 0.0605823 0.186453i
\(917\) −4.07216 12.5328i −0.134474 0.413870i
\(918\) 0.276313 0.200753i 0.00911970 0.00662585i
\(919\) 23.1138 16.7932i 0.762455 0.553956i −0.137207 0.990542i \(-0.543813\pi\)
0.899662 + 0.436586i \(0.143813\pi\)
\(920\) −4.99323 15.3676i −0.164622 0.506654i
\(921\) 7.51045 23.1148i 0.247478 0.761658i
\(922\) −5.15762 3.74723i −0.169857 0.123409i
\(923\) 9.69264 0.319037
\(924\) −3.95540 + 1.16486i −0.130123 + 0.0383210i
\(925\) 7.04567 0.231660
\(926\) 3.15107 + 2.28939i 0.103551 + 0.0752340i
\(927\) −5.91976 + 18.2192i −0.194431 + 0.598396i
\(928\) 0.934643 + 2.87653i 0.0306811 + 0.0944269i
\(929\) 41.7745 30.3510i 1.37058 0.995783i 0.372886 0.927877i \(-0.378368\pi\)
0.997692 0.0679061i \(-0.0216318\pi\)
\(930\) 5.40405 3.92628i 0.177206 0.128748i
\(931\) 10.3384 + 31.8183i 0.338827 + 1.04280i
\(932\) 1.05151 3.23623i 0.0344435 0.106006i
\(933\) 11.8783 + 8.63011i 0.388879 + 0.282537i
\(934\) −4.68809 −0.153399
\(935\) −12.3580 4.39814i −0.404149 0.143835i
\(936\) 1.32142 0.0431921
\(937\) 0.162230 + 0.117867i 0.00529983 + 0.00385055i 0.590432 0.807087i \(-0.298957\pi\)
−0.585132 + 0.810938i \(0.698957\pi\)
\(938\) −0.147197 + 0.453026i −0.00480615 + 0.0147918i
\(939\) 2.25496 + 6.94005i 0.0735878 + 0.226480i
\(940\) −34.7334 + 25.2353i −1.13288 + 0.823084i
\(941\) 0.626931 0.455492i 0.0204374 0.0148486i −0.577520 0.816377i \(-0.695979\pi\)
0.597957 + 0.801528i \(0.295979\pi\)
\(942\) 2.58935 + 7.96921i 0.0843657 + 0.259651i
\(943\) −1.69385 + 5.21314i −0.0551594 + 0.169763i
\(944\) 0.926122 + 0.672867i 0.0301427 + 0.0219000i
\(945\) 2.59926 0.0845539
\(946\) −8.22076 + 10.6786i −0.267280 + 0.347190i
\(947\) −4.68762 −0.152327 −0.0761637 0.997095i \(-0.524267\pi\)
−0.0761637 + 0.997095i \(0.524267\pi\)
\(948\) −9.72271 7.06396i −0.315779 0.229427i
\(949\) 3.20186 9.85431i 0.103937 0.319884i
\(950\) 5.63587 + 17.3454i 0.182852 + 0.562760i
\(951\) 4.48152 3.25601i 0.145323 0.105583i
\(952\) 0.708147 0.514499i 0.0229512 0.0166750i
\(953\) −4.15847 12.7984i −0.134706 0.414582i 0.860838 0.508879i \(-0.169940\pi\)
−0.995544 + 0.0942965i \(0.969940\pi\)
\(954\) −1.25003 + 3.84721i −0.0404714 + 0.124558i
\(955\) 12.2577 + 8.90574i 0.396650 + 0.288183i
\(956\) −26.5715 −0.859382
\(957\) 0.0738109 2.65843i 0.00238597 0.0859348i
\(958\) −5.17515 −0.167202
\(959\) −6.32153 4.59286i −0.204133 0.148311i
\(960\) 6.51865 20.0623i 0.210389 0.647510i
\(961\) −1.90294 5.85666i −0.0613853 0.188924i
\(962\) 0.184342 0.133933i 0.00594344 0.00431816i
\(963\) 16.0687 11.6746i 0.517807 0.376209i
\(964\) 4.77102 + 14.6837i 0.153664 + 0.472930i
\(965\) 25.6249 78.8654i 0.824896 2.53877i
\(966\) −0.563670 0.409530i −0.0181358 0.0131764i
\(967\) −21.8025 −0.701120 −0.350560 0.936540i \(-0.614009\pi\)
−0.350560 + 0.936540i \(0.614009\pi\)
\(968\) −5.25191 + 13.5537i −0.168803 + 0.435632i
\(969\) −5.11646 −0.164364
\(970\) 9.83080 + 7.14250i 0.315648 + 0.229332i
\(971\) −8.74469 + 26.9134i −0.280630 + 0.863692i 0.707044 + 0.707170i \(0.250028\pi\)
−0.987674 + 0.156522i \(0.949972\pi\)
\(972\) −0.582270 1.79204i −0.0186763 0.0574798i
\(973\) 1.25758 0.913684i 0.0403161 0.0292914i
\(974\) −5.73406 + 4.16604i −0.183731 + 0.133488i
\(975\) 3.25065 + 10.0045i 0.104104 + 0.320399i
\(976\) 4.40691 13.5631i 0.141062 0.434144i
\(977\) 38.5788 + 28.0292i 1.23425 + 0.896732i 0.997201 0.0747664i \(-0.0238211\pi\)
0.237045 + 0.971499i \(0.423821\pi\)
\(978\) 7.38949 0.236290
\(979\) 0.437932 15.7729i 0.0139964 0.504104i
\(980\) −48.7294 −1.55660
\(981\) 2.11748 + 1.53844i 0.0676058 + 0.0491185i
\(982\) −3.15145 + 9.69916i −0.100567 + 0.309513i
\(983\) 7.01481 + 21.5894i 0.223738 + 0.688594i 0.998417 + 0.0562399i \(0.0179112\pi\)
−0.774680 + 0.632354i \(0.782089\pi\)
\(984\) 1.88787 1.37162i 0.0601830 0.0437255i
\(985\) −32.7134 + 23.7677i −1.04234 + 0.757301i
\(986\) 0.0846297 + 0.260463i 0.00269516 + 0.00829484i
\(987\) −1.17925 + 3.62937i −0.0375360 + 0.115524i
\(988\) −7.76887 5.64442i −0.247161 0.179573i
\(989\) 37.0736 1.17887
\(990\) 2.71147 3.52213i 0.0861761 0.111941i
\(991\) −5.00165 −0.158883 −0.0794413 0.996840i \(-0.525314\pi\)
−0.0794413 + 0.996840i \(0.525314\pi\)
\(992\) −15.2096 11.0504i −0.482905 0.350851i
\(993\) −8.05183 + 24.7810i −0.255517 + 0.786401i
\(994\) 0.672311 + 2.06916i 0.0213244 + 0.0656298i
\(995\) −29.6759 + 21.5608i −0.940789 + 0.683524i
\(996\) −11.7316 + 8.52351i −0.371730 + 0.270078i
\(997\) 12.6302 + 38.8719i 0.400004 + 1.23108i 0.924996 + 0.379978i \(0.124068\pi\)
−0.524992 + 0.851107i \(0.675932\pi\)
\(998\) −2.54925 + 7.84579i −0.0806951 + 0.248354i
\(999\) −0.541867 0.393689i −0.0171439 0.0124558i
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.235.2 yes 12
11.3 even 5 inner 429.2.n.a.157.2 12
11.5 even 5 4719.2.a.bg.1.3 6
11.6 odd 10 4719.2.a.bh.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.a.157.2 12 11.3 even 5 inner
429.2.n.a.235.2 yes 12 1.1 even 1 trivial
4719.2.a.bg.1.3 6 11.5 even 5
4719.2.a.bh.1.4 6 11.6 odd 10