Properties

Label 187.2.m.a.10.15
Level $187$
Weight $2$
Character 187.10
Analytic conductor $1.493$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [187,2,Mod(10,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.m (of order \(16\), degree \(8\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 10.15
Character \(\chi\) \(=\) 187.10
Dual form 187.2.m.a.131.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.25162 + 0.932652i) q^{2} +(-2.66909 - 1.78343i) q^{3} +(2.78574 + 2.78574i) q^{4} +(2.54233 - 0.505701i) q^{5} +(-4.34645 - 6.50493i) q^{6} +(0.607350 - 3.05336i) q^{7} +(1.80901 + 4.36732i) q^{8} +(2.79536 + 6.74860i) q^{9} +O(q^{10})\) \(q+(2.25162 + 0.932652i) q^{2} +(-2.66909 - 1.78343i) q^{3} +(2.78574 + 2.78574i) q^{4} +(2.54233 - 0.505701i) q^{5} +(-4.34645 - 6.50493i) q^{6} +(0.607350 - 3.05336i) q^{7} +(1.80901 + 4.36732i) q^{8} +(2.79536 + 6.74860i) q^{9} +(6.19601 + 1.23246i) q^{10} +(-1.60711 + 2.90124i) q^{11} +(-2.46722 - 12.4036i) q^{12} +(0.635496 + 0.635496i) q^{13} +(4.21524 - 6.30855i) q^{14} +(-7.68758 - 3.18430i) q^{15} +3.64146i q^{16} +(-4.11200 - 0.302469i) q^{17} +17.8024i q^{18} +(0.134678 + 0.0557855i) q^{19} +(8.49104 + 5.67353i) q^{20} +(-7.06650 + 7.06650i) q^{21} +(-6.32445 + 5.03362i) q^{22} +(-2.79819 + 1.86969i) q^{23} +(2.96041 - 14.8830i) q^{24} +(1.58832 - 0.657904i) q^{25} +(0.838199 + 2.02359i) q^{26} +(2.69580 - 13.5527i) q^{27} +(10.1978 - 6.81394i) q^{28} +(-4.51218 + 0.897529i) q^{29} +(-14.3397 - 14.3397i) q^{30} +(-1.47824 + 2.21234i) q^{31} +(0.221796 - 0.535464i) q^{32} +(9.46366 - 4.87749i) q^{33} +(-8.97656 - 4.51611i) q^{34} -8.06978i q^{35} +(-11.0127 + 26.5870i) q^{36} +(6.78648 + 4.53458i) q^{37} +(0.251216 + 0.251216i) q^{38} +(-0.562833 - 2.82955i) q^{39} +(6.80765 + 10.1884i) q^{40} +(-0.970630 + 4.87969i) q^{41} +(-22.5017 + 9.32050i) q^{42} +(-5.85136 + 2.42371i) q^{43} +(-12.5591 + 3.60511i) q^{44} +(10.5195 + 15.7436i) q^{45} +(-8.04423 + 1.60010i) q^{46} +(6.83807 - 6.83807i) q^{47} +(6.49427 - 9.71937i) q^{48} +(-2.48695 - 1.03013i) q^{49} +4.18989 q^{50} +(10.4358 + 8.14076i) q^{51} +3.54066i q^{52} +(1.46144 - 3.52823i) q^{53} +(18.7099 - 28.0013i) q^{54} +(-2.61865 + 8.18863i) q^{55} +(14.4337 - 2.87104i) q^{56} +(-0.259978 - 0.389085i) q^{57} +(-10.9968 - 2.18740i) q^{58} +(-2.72536 + 1.12888i) q^{59} +(-12.5450 - 30.2863i) q^{60} +(3.48744 + 0.693694i) q^{61} +(-5.39177 + 3.60267i) q^{62} +(22.3036 - 4.43647i) q^{63} +(6.14860 - 6.14860i) q^{64} +(1.93701 + 1.29427i) q^{65} +(25.8576 - 2.15596i) q^{66} +1.66326i q^{67} +(-10.6124 - 12.2976i) q^{68} +10.8031 q^{69} +(7.52630 - 18.1701i) q^{70} +(-0.679474 - 0.454010i) q^{71} +(-24.4165 + 24.4165i) q^{72} +(-2.83470 - 14.2510i) q^{73} +(11.0514 + 16.5396i) q^{74} +(-5.41269 - 1.07665i) q^{75} +(0.219775 + 0.530583i) q^{76} +(7.88244 + 6.66915i) q^{77} +(1.37170 - 6.89601i) q^{78} +(8.45997 - 5.65277i) q^{79} +(1.84149 + 9.25780i) q^{80} +(-15.8701 + 15.8701i) q^{81} +(-6.73654 + 10.0819i) q^{82} +(-3.57555 + 8.63215i) q^{83} -39.3709 q^{84} +(-10.6070 + 1.31046i) q^{85} -15.4355 q^{86} +(13.6441 + 5.65156i) q^{87} +(-15.5779 - 1.77042i) q^{88} +(-3.83604 - 3.83604i) q^{89} +(9.00268 + 45.2595i) q^{90} +(2.32636 - 1.55443i) q^{91} +(-13.0035 - 2.58656i) q^{92} +(7.89108 - 3.26859i) q^{93} +(21.7743 - 9.01921i) q^{94} +(0.370607 + 0.0737184i) q^{95} +(-1.54695 + 1.03364i) q^{96} +(-1.57061 - 7.89597i) q^{97} +(-4.63891 - 4.63891i) q^{98} +(-24.0717 - 2.73573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38} - 112 q^{42} - 72 q^{44} - 16 q^{45} - 16 q^{47} + 32 q^{48} + 48 q^{49} - 16 q^{53} - 8 q^{55} - 16 q^{56} - 128 q^{58} + 48 q^{59} + 112 q^{60} + 48 q^{64} + 72 q^{66} - 192 q^{69} + 128 q^{70} - 16 q^{71} + 48 q^{75} + 8 q^{77} - 16 q^{78} + 112 q^{80} - 16 q^{82} + 32 q^{86} - 168 q^{88} - 16 q^{89} + 144 q^{91} - 176 q^{92} + 48 q^{93} + 48 q^{97} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{16}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.25162 + 0.932652i 1.59214 + 0.659484i 0.990276 0.139117i \(-0.0444264\pi\)
0.601860 + 0.798601i \(0.294426\pi\)
\(3\) −2.66909 1.78343i −1.54100 1.02966i −0.979323 0.202303i \(-0.935157\pi\)
−0.561674 0.827358i \(-0.689843\pi\)
\(4\) 2.78574 + 2.78574i 1.39287 + 1.39287i
\(5\) 2.54233 0.505701i 1.13697 0.226156i 0.409506 0.912307i \(-0.365701\pi\)
0.727459 + 0.686151i \(0.240701\pi\)
\(6\) −4.34645 6.50493i −1.77443 2.65563i
\(7\) 0.607350 3.05336i 0.229557 1.15406i −0.678302 0.734783i \(-0.737284\pi\)
0.907859 0.419276i \(-0.137716\pi\)
\(8\) 1.80901 + 4.36732i 0.639580 + 1.54408i
\(9\) 2.79536 + 6.74860i 0.931787 + 2.24953i
\(10\) 6.19601 + 1.23246i 1.95935 + 0.389739i
\(11\) −1.60711 + 2.90124i −0.484562 + 0.874757i
\(12\) −2.46722 12.4036i −0.712225 3.58060i
\(13\) 0.635496 + 0.635496i 0.176255 + 0.176255i 0.789721 0.613466i \(-0.210225\pi\)
−0.613466 + 0.789721i \(0.710225\pi\)
\(14\) 4.21524 6.30855i 1.12657 1.68603i
\(15\) −7.68758 3.18430i −1.98493 0.822183i
\(16\) 3.64146i 0.910365i
\(17\) −4.11200 0.302469i −0.997306 0.0733596i
\(18\) 17.8024i 4.19606i
\(19\) 0.134678 + 0.0557855i 0.0308973 + 0.0127981i 0.398079 0.917351i \(-0.369677\pi\)
−0.367181 + 0.930149i \(0.619677\pi\)
\(20\) 8.49104 + 5.67353i 1.89865 + 1.26864i
\(21\) −7.06650 + 7.06650i −1.54204 + 1.54204i
\(22\) −6.32445 + 5.03362i −1.34838 + 1.07317i
\(23\) −2.79819 + 1.86969i −0.583462 + 0.389857i −0.811982 0.583682i \(-0.801611\pi\)
0.228520 + 0.973539i \(0.426611\pi\)
\(24\) 2.96041 14.8830i 0.604291 3.03798i
\(25\) 1.58832 0.657904i 0.317664 0.131581i
\(26\) 0.838199 + 2.02359i 0.164384 + 0.396859i
\(27\) 2.69580 13.5527i 0.518807 2.60822i
\(28\) 10.1978 6.81394i 1.92720 1.28771i
\(29\) −4.51218 + 0.897529i −0.837892 + 0.166667i −0.595342 0.803472i \(-0.702984\pi\)
−0.242549 + 0.970139i \(0.577984\pi\)
\(30\) −14.3397 14.3397i −2.61805 2.61805i
\(31\) −1.47824 + 2.21234i −0.265499 + 0.397348i −0.940135 0.340804i \(-0.889301\pi\)
0.674635 + 0.738151i \(0.264301\pi\)
\(32\) 0.221796 0.535464i 0.0392084 0.0946575i
\(33\) 9.46366 4.87749i 1.64741 0.849063i
\(34\) −8.97656 4.51611i −1.53947 0.774506i
\(35\) 8.06978i 1.36404i
\(36\) −11.0127 + 26.5870i −1.83545 + 4.43117i
\(37\) 6.78648 + 4.53458i 1.11569 + 0.745480i 0.969820 0.243823i \(-0.0784018\pi\)
0.145870 + 0.989304i \(0.453402\pi\)
\(38\) 0.251216 + 0.251216i 0.0407526 + 0.0407526i
\(39\) −0.562833 2.82955i −0.0901254 0.453091i
\(40\) 6.80765 + 10.1884i 1.07638 + 1.61092i
\(41\) −0.970630 + 4.87969i −0.151587 + 0.762079i 0.827948 + 0.560805i \(0.189508\pi\)
−0.979535 + 0.201274i \(0.935492\pi\)
\(42\) −22.5017 + 9.32050i −3.47208 + 1.43818i
\(43\) −5.85136 + 2.42371i −0.892324 + 0.369613i −0.781264 0.624201i \(-0.785425\pi\)
−0.111060 + 0.993814i \(0.535425\pi\)
\(44\) −12.5591 + 3.60511i −1.89336 + 0.543491i
\(45\) 10.5195 + 15.7436i 1.56816 + 2.34691i
\(46\) −8.04423 + 1.60010i −1.18606 + 0.235921i
\(47\) 6.83807 6.83807i 0.997435 0.997435i −0.00256132 0.999997i \(-0.500815\pi\)
0.999997 + 0.00256132i \(0.000815296\pi\)
\(48\) 6.49427 9.71937i 0.937368 1.40287i
\(49\) −2.48695 1.03013i −0.355278 0.147161i
\(50\) 4.18989 0.592540
\(51\) 10.4358 + 8.14076i 1.46131 + 1.13993i
\(52\) 3.54066i 0.491001i
\(53\) 1.46144 3.52823i 0.200744 0.484639i −0.791163 0.611605i \(-0.790524\pi\)
0.991907 + 0.126966i \(0.0405240\pi\)
\(54\) 18.7099 28.0013i 2.54609 3.81049i
\(55\) −2.61865 + 8.18863i −0.353099 + 1.10416i
\(56\) 14.4337 2.87104i 1.92878 0.383659i
\(57\) −0.259978 0.389085i −0.0344350 0.0515356i
\(58\) −10.9968 2.18740i −1.44395 0.287220i
\(59\) −2.72536 + 1.12888i −0.354812 + 0.146968i −0.552968 0.833203i \(-0.686505\pi\)
0.198156 + 0.980170i \(0.436505\pi\)
\(60\) −12.5450 30.2863i −1.61955 3.90994i
\(61\) 3.48744 + 0.693694i 0.446520 + 0.0888184i 0.413229 0.910627i \(-0.364401\pi\)
0.0332917 + 0.999446i \(0.489401\pi\)
\(62\) −5.39177 + 3.60267i −0.684755 + 0.457539i
\(63\) 22.3036 4.43647i 2.80999 0.558942i
\(64\) 6.14860 6.14860i 0.768575 0.768575i
\(65\) 1.93701 + 1.29427i 0.240257 + 0.160534i
\(66\) 25.8576 2.15596i 3.18285 0.265381i
\(67\) 1.66326i 0.203199i 0.994825 + 0.101600i \(0.0323961\pi\)
−0.994825 + 0.101600i \(0.967604\pi\)
\(68\) −10.6124 12.2976i −1.28694 1.49130i
\(69\) 10.8031 1.30053
\(70\) 7.52630 18.1701i 0.899564 2.17174i
\(71\) −0.679474 0.454010i −0.0806387 0.0538811i 0.514597 0.857432i \(-0.327941\pi\)
−0.595236 + 0.803551i \(0.702941\pi\)
\(72\) −24.4165 + 24.4165i −2.87751 + 2.87751i
\(73\) −2.83470 14.2510i −0.331776 1.66795i −0.682050 0.731305i \(-0.738911\pi\)
0.350274 0.936647i \(-0.386089\pi\)
\(74\) 11.0514 + 16.5396i 1.28470 + 1.92269i
\(75\) −5.41269 1.07665i −0.625003 0.124321i
\(76\) 0.219775 + 0.530583i 0.0252099 + 0.0608620i
\(77\) 7.88244 + 6.66915i 0.898287 + 0.760020i
\(78\) 1.37170 6.89601i 0.155315 0.780819i
\(79\) 8.45997 5.65277i 0.951821 0.635986i 0.0203464 0.999793i \(-0.493523\pi\)
0.931475 + 0.363807i \(0.118523\pi\)
\(80\) 1.84149 + 9.25780i 0.205885 + 1.03505i
\(81\) −15.8701 + 15.8701i −1.76334 + 1.76334i
\(82\) −6.73654 + 10.0819i −0.743926 + 1.11336i
\(83\) −3.57555 + 8.63215i −0.392468 + 0.947502i 0.596933 + 0.802291i \(0.296386\pi\)
−0.989401 + 0.145210i \(0.953614\pi\)
\(84\) −39.3709 −4.29572
\(85\) −10.6070 + 1.31046i −1.15049 + 0.142140i
\(86\) −15.4355 −1.66445
\(87\) 13.6441 + 5.65156i 1.46280 + 0.605911i
\(88\) −15.5779 1.77042i −1.66061 0.188727i
\(89\) −3.83604 3.83604i −0.406620 0.406620i 0.473938 0.880558i \(-0.342832\pi\)
−0.880558 + 0.473938i \(0.842832\pi\)
\(90\) 9.00268 + 45.2595i 0.948966 + 4.77078i
\(91\) 2.32636 1.55443i 0.243869 0.162948i
\(92\) −13.0035 2.58656i −1.35571 0.269667i
\(93\) 7.89108 3.26859i 0.818267 0.338937i
\(94\) 21.7743 9.01921i 2.24585 0.930260i
\(95\) 0.370607 + 0.0737184i 0.0380235 + 0.00756335i
\(96\) −1.54695 + 1.03364i −0.157885 + 0.105496i
\(97\) −1.57061 7.89597i −0.159471 0.801714i −0.974863 0.222805i \(-0.928479\pi\)
0.815392 0.578909i \(-0.196521\pi\)
\(98\) −4.63891 4.63891i −0.468601 0.468601i
\(99\) −24.0717 2.73573i −2.41930 0.274952i
\(100\) 6.25740 + 2.59190i 0.625740 + 0.259190i
\(101\) 3.28428 0.326798 0.163399 0.986560i \(-0.447754\pi\)
0.163399 + 0.986560i \(0.447754\pi\)
\(102\) 15.9051 + 28.0629i 1.57484 + 2.77864i
\(103\) 10.4739 1.03203 0.516013 0.856581i \(-0.327416\pi\)
0.516013 + 0.856581i \(0.327416\pi\)
\(104\) −1.62580 + 3.92503i −0.159423 + 0.384881i
\(105\) −14.3919 + 21.5389i −1.40450 + 2.10198i
\(106\) 6.58122 6.58122i 0.639224 0.639224i
\(107\) −1.69172 8.50486i −0.163545 0.822196i −0.972243 0.233972i \(-0.924828\pi\)
0.808698 0.588224i \(-0.200172\pi\)
\(108\) 45.2641 30.2445i 4.35554 2.91028i
\(109\) 1.62682 8.17857i 0.155821 0.783365i −0.821270 0.570540i \(-0.806734\pi\)
0.977090 0.212824i \(-0.0682662\pi\)
\(110\) −13.5333 + 15.9954i −1.29035 + 1.52510i
\(111\) −10.0266 24.2064i −0.951683 2.29757i
\(112\) 11.1187 + 2.21164i 1.05062 + 0.208980i
\(113\) 1.95257 + 2.92223i 0.183683 + 0.274900i 0.911871 0.410476i \(-0.134638\pi\)
−0.728189 + 0.685377i \(0.759638\pi\)
\(114\) −0.222492 1.11854i −0.0208382 0.104761i
\(115\) −6.16842 + 6.16842i −0.575208 + 0.575208i
\(116\) −15.0701 10.0695i −1.39922 0.934930i
\(117\) −2.51226 + 6.06514i −0.232259 + 0.560723i
\(118\) −7.18933 −0.661832
\(119\) −3.42097 + 12.3717i −0.313600 + 1.13411i
\(120\) 39.3346i 3.59074i
\(121\) −5.83439 9.32523i −0.530399 0.847748i
\(122\) 7.20541 + 4.81450i 0.652347 + 0.435884i
\(123\) 11.2933 11.2933i 1.01828 1.01828i
\(124\) −10.2810 + 2.04502i −0.923260 + 0.183648i
\(125\) −7.07109 + 4.72475i −0.632458 + 0.422595i
\(126\) 54.3570 + 10.8123i 4.84250 + 0.963234i
\(127\) 0.387799 + 0.936230i 0.0344116 + 0.0830769i 0.940151 0.340758i \(-0.110684\pi\)
−0.905739 + 0.423835i \(0.860684\pi\)
\(128\) 18.5079 7.66622i 1.63588 0.677605i
\(129\) 19.9403 + 3.96637i 1.75564 + 0.349219i
\(130\) 3.15431 + 4.72076i 0.276652 + 0.414038i
\(131\) −17.9044 + 3.56141i −1.56432 + 0.311162i −0.899864 0.436170i \(-0.856335\pi\)
−0.664451 + 0.747332i \(0.731335\pi\)
\(132\) 39.9508 + 12.7759i 3.47727 + 1.11200i
\(133\) 0.252130 0.377339i 0.0218624 0.0327194i
\(134\) −1.55124 + 3.74503i −0.134007 + 0.323521i
\(135\) 35.8187i 3.08278i
\(136\) −6.11764 18.5056i −0.524583 1.58684i
\(137\) −5.55931 −0.474964 −0.237482 0.971392i \(-0.576322\pi\)
−0.237482 + 0.971392i \(0.576322\pi\)
\(138\) 24.3244 + 10.0755i 2.07063 + 0.857683i
\(139\) 2.53534 3.79440i 0.215045 0.321837i −0.708227 0.705985i \(-0.750505\pi\)
0.923272 + 0.384148i \(0.125505\pi\)
\(140\) 22.4803 22.4803i 1.89994 1.89994i
\(141\) −30.4466 + 6.05620i −2.56407 + 0.510024i
\(142\) −1.10648 1.65597i −0.0928541 0.138966i
\(143\) −2.86504 + 0.822414i −0.239587 + 0.0687737i
\(144\) −24.5747 + 10.1792i −2.04789 + 0.848266i
\(145\) −11.0176 + 4.56363i −0.914961 + 0.378989i
\(146\) 6.90855 34.7316i 0.571756 2.87441i
\(147\) 4.80072 + 7.18479i 0.395957 + 0.592591i
\(148\) 6.27321 + 31.5376i 0.515655 + 2.59237i
\(149\) 11.6445 + 11.6445i 0.953953 + 0.953953i 0.998986 0.0450327i \(-0.0143392\pi\)
−0.0450327 + 0.998986i \(0.514339\pi\)
\(150\) −11.1832 7.47236i −0.913102 0.610116i
\(151\) 3.21996 7.77367i 0.262037 0.632612i −0.737028 0.675862i \(-0.763771\pi\)
0.999064 + 0.0432504i \(0.0137713\pi\)
\(152\) 0.689100i 0.0558934i
\(153\) −9.45327 28.5957i −0.764251 2.31183i
\(154\) 11.5283 + 22.3680i 0.928974 + 1.80246i
\(155\) −2.63939 + 6.37204i −0.212001 + 0.511815i
\(156\) 6.31450 9.45032i 0.505565 0.756631i
\(157\) −10.3629 10.3629i −0.827052 0.827052i 0.160056 0.987108i \(-0.448832\pi\)
−0.987108 + 0.160056i \(0.948832\pi\)
\(158\) 24.3207 4.83769i 1.93485 0.384866i
\(159\) −10.1930 + 6.81077i −0.808361 + 0.540129i
\(160\) 0.293095 1.47349i 0.0231712 0.116490i
\(161\) 4.00935 + 9.67942i 0.315981 + 0.762845i
\(162\) −50.5347 + 20.9322i −3.97038 + 1.64459i
\(163\) −3.64214 + 18.3103i −0.285274 + 1.43417i 0.526487 + 0.850183i \(0.323509\pi\)
−0.811762 + 0.583989i \(0.801491\pi\)
\(164\) −16.2975 + 10.8896i −1.27262 + 0.850337i
\(165\) 21.5932 17.1860i 1.68103 1.33793i
\(166\) −16.1016 + 16.1016i −1.24973 + 1.24973i
\(167\) 5.20717 + 3.47932i 0.402943 + 0.269238i 0.740486 0.672072i \(-0.234596\pi\)
−0.337542 + 0.941310i \(0.609596\pi\)
\(168\) −43.6451 18.0784i −3.36729 1.39478i
\(169\) 12.1923i 0.937868i
\(170\) −25.1052 6.94199i −1.92548 0.532426i
\(171\) 1.06483i 0.0814295i
\(172\) −23.0522 9.54854i −1.75772 0.728069i
\(173\) −0.0557685 + 0.0834635i −0.00424000 + 0.00634561i −0.833584 0.552393i \(-0.813715\pi\)
0.829344 + 0.558739i \(0.188715\pi\)
\(174\) 25.4504 + 25.4504i 1.92939 + 1.92939i
\(175\) −1.04415 5.24928i −0.0789301 0.396809i
\(176\) −10.5647 5.85223i −0.796348 0.441128i
\(177\) 9.28750 + 1.84740i 0.698091 + 0.138859i
\(178\) −5.05962 12.2150i −0.379235 0.915553i
\(179\) 10.0868 + 24.3516i 0.753920 + 1.82012i 0.536149 + 0.844123i \(0.319878\pi\)
0.217771 + 0.976000i \(0.430122\pi\)
\(180\) −14.5529 + 73.1621i −1.08471 + 5.45318i
\(181\) 0.532252 + 0.796571i 0.0395620 + 0.0592087i 0.850723 0.525614i \(-0.176164\pi\)
−0.811161 + 0.584822i \(0.801164\pi\)
\(182\) 6.68783 1.33029i 0.495735 0.0986078i
\(183\) −8.07111 8.07111i −0.596634 0.596634i
\(184\) −13.2275 8.83832i −0.975142 0.651569i
\(185\) 19.5466 + 8.09648i 1.43710 + 0.595265i
\(186\) 20.8162 1.52632
\(187\) 7.48597 11.4438i 0.547428 0.836853i
\(188\) 38.0982 2.77860
\(189\) −39.7439 16.4625i −2.89094 1.19747i
\(190\) 0.765714 + 0.511634i 0.0555507 + 0.0371178i
\(191\) −9.47851 9.47851i −0.685841 0.685841i 0.275469 0.961310i \(-0.411167\pi\)
−0.961310 + 0.275469i \(0.911167\pi\)
\(192\) −27.3767 + 5.44557i −1.97575 + 0.393000i
\(193\) −8.65546 12.9538i −0.623033 0.932435i −0.999981 0.00620069i \(-0.998026\pi\)
0.376947 0.926235i \(-0.376974\pi\)
\(194\) 3.82778 19.2436i 0.274819 1.38161i
\(195\) −2.86182 6.90904i −0.204939 0.494766i
\(196\) −4.05833 9.79767i −0.289881 0.699833i
\(197\) 24.5219 + 4.87772i 1.74712 + 0.347523i 0.962255 0.272149i \(-0.0877344\pi\)
0.784861 + 0.619672i \(0.212734\pi\)
\(198\) −51.6490 28.6104i −3.67053 2.03325i
\(199\) −0.0454625 0.228555i −0.00322275 0.0162019i 0.979140 0.203185i \(-0.0651292\pi\)
−0.982363 + 0.186983i \(0.940129\pi\)
\(200\) 5.74656 + 5.74656i 0.406343 + 0.406343i
\(201\) 2.96630 4.43938i 0.209227 0.313130i
\(202\) 7.39496 + 3.06309i 0.520307 + 0.215518i
\(203\) 14.3224i 1.00524i
\(204\) 6.39351 + 51.7496i 0.447635 + 3.62320i
\(205\) 12.8966i 0.900740i
\(206\) 23.5833 + 9.76852i 1.64313 + 0.680605i
\(207\) −20.4397 13.6574i −1.42066 0.949254i
\(208\) −2.31413 + 2.31413i −0.160456 + 0.160456i
\(209\) −0.378290 + 0.301080i −0.0261669 + 0.0208262i
\(210\) −52.4933 + 35.0749i −3.62238 + 2.42040i
\(211\) −5.26789 + 26.4835i −0.362657 + 1.82320i 0.180509 + 0.983573i \(0.442225\pi\)
−0.543166 + 0.839625i \(0.682775\pi\)
\(212\) 13.8999 5.75754i 0.954651 0.395429i
\(213\) 1.00388 + 2.42358i 0.0687848 + 0.166061i
\(214\) 4.12296 20.7275i 0.281840 1.41690i
\(215\) −13.6504 + 9.12092i −0.930951 + 0.622041i
\(216\) 64.0657 12.7435i 4.35912 0.867083i
\(217\) 5.85725 + 5.85725i 0.397616 + 0.397616i
\(218\) 11.2907 16.8978i 0.764705 1.14446i
\(219\) −17.8495 + 43.0926i −1.20616 + 2.91193i
\(220\) −30.1063 + 15.5165i −2.02977 + 1.04613i
\(221\) −2.42094 2.80537i −0.162850 0.188710i
\(222\) 63.8549i 4.28566i
\(223\) 3.11802 7.52758i 0.208798 0.504084i −0.784436 0.620210i \(-0.787048\pi\)
0.993235 + 0.116126i \(0.0370476\pi\)
\(224\) −1.50025 1.00244i −0.100240 0.0669781i
\(225\) 8.87985 + 8.87985i 0.591990 + 0.591990i
\(226\) 1.67103 + 8.40083i 0.111155 + 0.558815i
\(227\) 5.57902 + 8.34960i 0.370293 + 0.554182i 0.969087 0.246721i \(-0.0793531\pi\)
−0.598794 + 0.800903i \(0.704353\pi\)
\(228\) 0.359658 1.80812i 0.0238189 0.119746i
\(229\) 6.61566 2.74030i 0.437175 0.181084i −0.153231 0.988190i \(-0.548968\pi\)
0.590406 + 0.807107i \(0.298968\pi\)
\(230\) −19.6419 + 8.13595i −1.29515 + 0.536469i
\(231\) −9.14496 31.8583i −0.601695 2.09612i
\(232\) −12.0824 18.0825i −0.793246 1.18718i
\(233\) 13.2524 2.63607i 0.868194 0.172695i 0.259156 0.965835i \(-0.416556\pi\)
0.609038 + 0.793141i \(0.291556\pi\)
\(234\) −11.3133 + 11.3133i −0.739576 + 0.739576i
\(235\) 13.9266 20.8427i 0.908473 1.35963i
\(236\) −10.7369 4.44738i −0.698915 0.289500i
\(237\) −32.6617 −2.12160
\(238\) −19.2412 + 24.6658i −1.24722 + 1.59884i
\(239\) 23.1841i 1.49966i −0.661632 0.749828i \(-0.730136\pi\)
0.661632 0.749828i \(-0.269864\pi\)
\(240\) 11.5955 27.9940i 0.748486 1.80701i
\(241\) 5.99275 8.96878i 0.386027 0.577730i −0.586665 0.809830i \(-0.699560\pi\)
0.972692 + 0.232100i \(0.0745595\pi\)
\(242\) −4.43963 26.4383i −0.285390 1.69952i
\(243\) 30.0037 5.96810i 1.92474 0.382854i
\(244\) 7.78265 + 11.6476i 0.498233 + 0.745658i
\(245\) −6.84358 1.36127i −0.437220 0.0869686i
\(246\) 35.9608 14.8954i 2.29278 0.949699i
\(247\) 0.0501360 + 0.121039i 0.00319007 + 0.00770152i
\(248\) −12.3361 2.45381i −0.783345 0.155817i
\(249\) 24.9383 16.6632i 1.58040 1.05599i
\(250\) −20.3280 + 4.04348i −1.28565 + 0.255732i
\(251\) 13.1048 13.1048i 0.827167 0.827167i −0.159957 0.987124i \(-0.551136\pi\)
0.987124 + 0.159957i \(0.0511356\pi\)
\(252\) 74.4910 + 49.7733i 4.69249 + 3.13542i
\(253\) −0.927418 11.1230i −0.0583063 0.699298i
\(254\) 2.46972i 0.154964i
\(255\) 30.6482 + 15.4191i 1.91926 + 0.965581i
\(256\) 31.4318 1.96449
\(257\) −3.10743 + 7.50199i −0.193836 + 0.467961i −0.990678 0.136227i \(-0.956502\pi\)
0.796842 + 0.604188i \(0.206502\pi\)
\(258\) 41.1987 + 27.5281i 2.56492 + 1.71382i
\(259\) 17.9674 17.9674i 1.11644 1.11644i
\(260\) 1.79051 + 9.00152i 0.111043 + 0.558251i
\(261\) −18.6702 27.9420i −1.15566 1.72957i
\(262\) −43.6355 8.67964i −2.69581 0.536230i
\(263\) 9.40359 + 22.7023i 0.579850 + 1.39988i 0.892948 + 0.450161i \(0.148633\pi\)
−0.313097 + 0.949721i \(0.601367\pi\)
\(264\) 38.4214 + 32.5075i 2.36467 + 2.00070i
\(265\) 1.93124 9.70898i 0.118635 0.596418i
\(266\) 0.919627 0.614475i 0.0563859 0.0376759i
\(267\) 3.39743 + 17.0800i 0.207919 + 1.04528i
\(268\) −4.63341 + 4.63341i −0.283031 + 0.283031i
\(269\) −13.5845 + 20.3306i −0.828261 + 1.23958i 0.140128 + 0.990133i \(0.455249\pi\)
−0.968389 + 0.249446i \(0.919751\pi\)
\(270\) 33.4064 80.6502i 2.03305 4.90821i
\(271\) −7.15635 −0.434717 −0.217359 0.976092i \(-0.569744\pi\)
−0.217359 + 0.976092i \(0.569744\pi\)
\(272\) 1.10143 14.9737i 0.0667840 0.907912i
\(273\) −8.98147 −0.543583
\(274\) −12.5175 5.18491i −0.756208 0.313232i
\(275\) −0.643870 + 5.66542i −0.0388268 + 0.341638i
\(276\) 30.0945 + 30.0945i 1.81148 + 1.81148i
\(277\) 2.16488 + 10.8836i 0.130075 + 0.653931i 0.989718 + 0.143035i \(0.0456862\pi\)
−0.859643 + 0.510896i \(0.829314\pi\)
\(278\) 9.24748 6.17897i 0.554627 0.370590i
\(279\) −19.0624 3.79174i −1.14123 0.227006i
\(280\) 35.2434 14.5983i 2.10619 0.872414i
\(281\) −13.3984 + 5.54982i −0.799284 + 0.331074i −0.744670 0.667433i \(-0.767393\pi\)
−0.0546146 + 0.998508i \(0.517393\pi\)
\(282\) −74.2025 14.7598i −4.41870 0.878933i
\(283\) −9.96772 + 6.66022i −0.592519 + 0.395909i −0.815367 0.578945i \(-0.803465\pi\)
0.222848 + 0.974853i \(0.428465\pi\)
\(284\) −0.628085 3.15760i −0.0372700 0.187369i
\(285\) −0.857712 0.857712i −0.0508065 0.0508065i
\(286\) −7.21801 0.820320i −0.426810 0.0485066i
\(287\) 14.3099 + 5.92736i 0.844687 + 0.349881i
\(288\) 4.23363 0.249469
\(289\) 16.8170 + 2.48750i 0.989237 + 0.146324i
\(290\) −29.0637 −1.70668
\(291\) −9.88980 + 23.8761i −0.579750 + 1.39964i
\(292\) 31.8029 47.5964i 1.86112 2.78537i
\(293\) −11.6944 + 11.6944i −0.683197 + 0.683197i −0.960719 0.277522i \(-0.910487\pi\)
0.277522 + 0.960719i \(0.410487\pi\)
\(294\) 4.10850 + 20.6548i 0.239612 + 1.20461i
\(295\) −6.35790 + 4.24821i −0.370171 + 0.247340i
\(296\) −7.52721 + 37.8418i −0.437510 + 2.19951i
\(297\) 34.9872 + 29.6018i 2.03016 + 1.71767i
\(298\) 15.3587 + 37.0792i 0.889706 + 2.14794i
\(299\) −2.96642 0.590057i −0.171552 0.0341239i
\(300\) −12.0791 18.0776i −0.697386 1.04371i
\(301\) 3.84663 + 19.3383i 0.221716 + 1.11464i
\(302\) 14.5003 14.5003i 0.834396 0.834396i
\(303\) −8.76603 5.85727i −0.503595 0.336492i
\(304\) −0.203141 + 0.490425i −0.0116509 + 0.0281278i
\(305\) 9.21702 0.527765
\(306\) 5.38467 73.2033i 0.307821 4.18475i
\(307\) 1.08264i 0.0617895i 0.999523 + 0.0308948i \(0.00983567\pi\)
−0.999523 + 0.0308948i \(0.990164\pi\)
\(308\) 3.37991 + 40.5370i 0.192588 + 2.30981i
\(309\) −27.9558 18.6795i −1.59035 1.06264i
\(310\) −11.8858 + 11.8858i −0.675068 + 0.675068i
\(311\) 1.09414 0.217638i 0.0620431 0.0123411i −0.163971 0.986465i \(-0.552430\pi\)
0.226014 + 0.974124i \(0.427430\pi\)
\(312\) 11.3394 7.57675i 0.641968 0.428949i
\(313\) −32.5071 6.46606i −1.83741 0.365483i −0.850399 0.526138i \(-0.823639\pi\)
−0.987011 + 0.160655i \(0.948639\pi\)
\(314\) −13.6684 32.9984i −0.771351 1.86221i
\(315\) 54.4597 22.5579i 3.06846 1.27100i
\(316\) 39.3145 + 7.82013i 2.21161 + 0.439917i
\(317\) 5.50001 + 8.23135i 0.308911 + 0.462319i 0.953147 0.302509i \(-0.0978242\pi\)
−0.644235 + 0.764827i \(0.722824\pi\)
\(318\) −29.3029 + 5.82872i −1.64323 + 0.326858i
\(319\) 4.64763 14.5334i 0.260218 0.813712i
\(320\) 12.5224 18.7411i 0.700025 1.04766i
\(321\) −10.6524 + 25.7173i −0.594561 + 1.43540i
\(322\) 25.5337i 1.42294i
\(323\) −0.536923 0.270126i −0.0298752 0.0150302i
\(324\) −88.4200 −4.91222
\(325\) 1.42747 + 0.591276i 0.0791816 + 0.0327981i
\(326\) −25.2778 + 37.8310i −1.40001 + 2.09526i
\(327\) −18.9280 + 18.9280i −1.04672 + 1.04672i
\(328\) −23.0670 + 4.58832i −1.27366 + 0.253348i
\(329\) −16.7260 25.0322i −0.922132 1.38007i
\(330\) 64.6483 18.5574i 3.55877 1.02155i
\(331\) −10.5013 + 4.34977i −0.577202 + 0.239085i −0.652134 0.758104i \(-0.726126\pi\)
0.0749320 + 0.997189i \(0.476126\pi\)
\(332\) −34.0075 + 14.0864i −1.86641 + 0.773091i
\(333\) −11.6314 + 58.4750i −0.637396 + 3.20441i
\(334\) 8.47959 + 12.6906i 0.463982 + 0.694399i
\(335\) 0.841112 + 4.22856i 0.0459549 + 0.231031i
\(336\) −25.7324 25.7324i −1.40382 1.40382i
\(337\) 14.1844 + 9.47770i 0.772672 + 0.516283i 0.878293 0.478123i \(-0.158683\pi\)
−0.105620 + 0.994407i \(0.533683\pi\)
\(338\) 11.3712 27.4524i 0.618510 1.49321i
\(339\) 11.2820i 0.612752i
\(340\) −33.1990 25.8978i −1.80047 1.40451i
\(341\) −4.04283 7.84419i −0.218932 0.424787i
\(342\) −0.993115 + 2.39759i −0.0537015 + 0.129647i
\(343\) 7.45131 11.1517i 0.402333 0.602134i
\(344\) −21.1703 21.1703i −1.14142 1.14142i
\(345\) 27.4649 5.46312i 1.47866 0.294124i
\(346\) −0.203412 + 0.135915i −0.0109355 + 0.00730686i
\(347\) 4.41350 22.1882i 0.236929 1.19112i −0.660795 0.750566i \(-0.729781\pi\)
0.897724 0.440558i \(-0.145219\pi\)
\(348\) 22.2651 + 53.7527i 1.19354 + 2.88145i
\(349\) 23.5408 9.75092i 1.26011 0.521955i 0.350167 0.936687i \(-0.386125\pi\)
0.909943 + 0.414732i \(0.136125\pi\)
\(350\) 2.54473 12.7932i 0.136022 0.683827i
\(351\) 10.3258 6.89951i 0.551153 0.368269i
\(352\) 1.19706 + 1.50403i 0.0638034 + 0.0801653i
\(353\) 0.326674 0.326674i 0.0173871 0.0173871i −0.698360 0.715747i \(-0.746086\pi\)
0.715747 + 0.698360i \(0.246086\pi\)
\(354\) 19.1889 + 12.8216i 1.01988 + 0.681463i
\(355\) −1.95704 0.810633i −0.103869 0.0430240i
\(356\) 21.3725i 1.13274i
\(357\) 31.1948 26.9200i 1.65101 1.42476i
\(358\) 64.2380i 3.39508i
\(359\) 3.37656 + 1.39862i 0.178208 + 0.0738161i 0.470003 0.882665i \(-0.344253\pi\)
−0.291796 + 0.956481i \(0.594253\pi\)
\(360\) −49.7274 + 74.4223i −2.62086 + 3.92240i
\(361\) −13.4200 13.4200i −0.706316 0.706316i
\(362\) 0.455506 + 2.28998i 0.0239409 + 0.120359i
\(363\) −1.05838 + 35.2950i −0.0555506 + 1.85251i
\(364\) 10.8109 + 2.15042i 0.566644 + 0.112713i
\(365\) −14.4135 34.7972i −0.754437 1.82137i
\(366\) −10.6455 25.7006i −0.556452 1.34339i
\(367\) −3.40539 + 17.1200i −0.177760 + 0.893659i 0.784208 + 0.620497i \(0.213069\pi\)
−0.961968 + 0.273161i \(0.911931\pi\)
\(368\) −6.80840 10.1895i −0.354912 0.531164i
\(369\) −35.6443 + 7.09009i −1.85557 + 0.369095i
\(370\) 36.4604 + 36.4604i 1.89549 + 1.89549i
\(371\) −9.88533 6.60516i −0.513221 0.342923i
\(372\) 31.0880 + 12.8771i 1.61184 + 0.667645i
\(373\) 12.9757 0.671856 0.335928 0.941888i \(-0.390950\pi\)
0.335928 + 0.941888i \(0.390950\pi\)
\(374\) 27.5286 18.7853i 1.42347 0.971363i
\(375\) 27.2996 1.40974
\(376\) 42.2342 + 17.4940i 2.17806 + 0.902183i
\(377\) −3.43785 2.29710i −0.177058 0.118307i
\(378\) −74.1344 74.1344i −3.81306 3.81306i
\(379\) 8.45912 1.68262i 0.434516 0.0864305i 0.0270141 0.999635i \(-0.491400\pi\)
0.407502 + 0.913205i \(0.366400\pi\)
\(380\) 0.827057 + 1.23778i 0.0424271 + 0.0634967i
\(381\) 0.634628 3.19049i 0.0325130 0.163454i
\(382\) −12.5019 30.1822i −0.639651 1.54425i
\(383\) −4.57225 11.0384i −0.233631 0.564036i 0.762968 0.646436i \(-0.223741\pi\)
−0.996599 + 0.0824005i \(0.973741\pi\)
\(384\) −63.0713 12.5457i −3.21860 0.640218i
\(385\) 23.4124 + 12.9690i 1.19320 + 0.660963i
\(386\) −7.40741 37.2396i −0.377027 1.89545i
\(387\) −32.7133 32.7133i −1.66291 1.66291i
\(388\) 17.6208 26.3714i 0.894563 1.33881i
\(389\) −25.2308 10.4509i −1.27925 0.529883i −0.363486 0.931600i \(-0.618414\pi\)
−0.915764 + 0.401717i \(0.868414\pi\)
\(390\) 18.2256i 0.922890i
\(391\) 12.0717 6.84179i 0.610490 0.346004i
\(392\) 12.7248i 0.642700i
\(393\) 54.1399 + 22.4255i 2.73100 + 1.13122i
\(394\) 50.6649 + 33.8532i 2.55246 + 1.70550i
\(395\) 18.6494 18.6494i 0.938355 0.938355i
\(396\) −59.4367 74.6788i −2.98680 3.75275i
\(397\) 15.6345 10.4466i 0.784672 0.524301i −0.0974959 0.995236i \(-0.531083\pi\)
0.882168 + 0.470935i \(0.156083\pi\)
\(398\) 0.110798 0.557021i 0.00555382 0.0279209i
\(399\) −1.34591 + 0.557495i −0.0673799 + 0.0279097i
\(400\) 2.39573 + 5.78380i 0.119786 + 0.289190i
\(401\) −0.907426 + 4.56194i −0.0453147 + 0.227812i −0.996806 0.0798640i \(-0.974551\pi\)
0.951491 + 0.307676i \(0.0995514\pi\)
\(402\) 10.8194 7.22928i 0.539622 0.360564i
\(403\) −2.34535 + 0.466518i −0.116830 + 0.0232389i
\(404\) 9.14917 + 9.14917i 0.455188 + 0.455188i
\(405\) −32.3215 + 48.3726i −1.60607 + 2.40365i
\(406\) −13.3578 + 32.2487i −0.662938 + 1.60047i
\(407\) −24.0625 + 12.4016i −1.19274 + 0.614726i
\(408\) −16.6748 + 60.3034i −0.825528 + 2.98546i
\(409\) 9.56857i 0.473135i 0.971615 + 0.236568i \(0.0760225\pi\)
−0.971615 + 0.236568i \(0.923978\pi\)
\(410\) −12.0281 + 29.0383i −0.594024 + 1.43410i
\(411\) 14.8383 + 9.91463i 0.731919 + 0.489052i
\(412\) 29.1776 + 29.1776i 1.43748 + 1.43748i
\(413\) 1.79163 + 9.00712i 0.0881602 + 0.443211i
\(414\) −33.2849 49.8144i −1.63586 2.44824i
\(415\) −4.72496 + 23.7540i −0.231939 + 1.16604i
\(416\) 0.481236 0.199334i 0.0235945 0.00977317i
\(417\) −13.5341 + 5.60599i −0.662766 + 0.274527i
\(418\) −1.13257 + 0.325105i −0.0553957 + 0.0159014i
\(419\) −18.2423 27.3015i −0.891194 1.33377i −0.942194 0.335068i \(-0.891241\pi\)
0.0509999 0.998699i \(-0.483759\pi\)
\(420\) −100.094 + 19.9099i −4.88409 + 0.971505i
\(421\) 6.53792 6.53792i 0.318639 0.318639i −0.529605 0.848244i \(-0.677660\pi\)
0.848244 + 0.529605i \(0.177660\pi\)
\(422\) −36.5612 + 54.7177i −1.77977 + 2.66361i
\(423\) 65.2623 + 27.0325i 3.17316 + 1.31437i
\(424\) 18.0527 0.876715
\(425\) −6.73016 + 2.22488i −0.326461 + 0.107923i
\(426\) 6.39326i 0.309755i
\(427\) 4.23619 10.2271i 0.205004 0.494922i
\(428\) 18.9797 28.4051i 0.917416 1.37301i
\(429\) 9.11375 + 2.91449i 0.440016 + 0.140713i
\(430\) −39.2422 + 7.80576i −1.89243 + 0.376427i
\(431\) 17.2001 + 25.7417i 0.828497 + 1.23993i 0.968309 + 0.249756i \(0.0803503\pi\)
−0.139811 + 0.990178i \(0.544650\pi\)
\(432\) 49.3516 + 9.81664i 2.37443 + 0.472303i
\(433\) −21.9031 + 9.07254i −1.05259 + 0.435999i −0.840817 0.541320i \(-0.817925\pi\)
−0.211777 + 0.977318i \(0.567925\pi\)
\(434\) 7.72553 + 18.6511i 0.370837 + 0.895280i
\(435\) 37.5458 + 7.46832i 1.80018 + 0.358079i
\(436\) 27.3153 18.2515i 1.30816 0.874088i
\(437\) −0.481156 + 0.0957079i −0.0230168 + 0.00457833i
\(438\) −80.3808 + 80.3808i −3.84074 + 3.84074i
\(439\) 18.2313 + 12.1818i 0.870133 + 0.581404i 0.908512 0.417859i \(-0.137219\pi\)
−0.0383787 + 0.999263i \(0.512219\pi\)
\(440\) −40.4996 + 3.37679i −1.93074 + 0.160982i
\(441\) 19.6630i 0.936332i
\(442\) −2.83460 8.57453i −0.134828 0.407849i
\(443\) −20.2147 −0.960428 −0.480214 0.877151i \(-0.659441\pi\)
−0.480214 + 0.877151i \(0.659441\pi\)
\(444\) 39.5012 95.3642i 1.87464 4.52579i
\(445\) −11.6924 7.81260i −0.554272 0.370353i
\(446\) 14.0412 14.0412i 0.664871 0.664871i
\(447\) −10.3130 51.8472i −0.487790 2.45229i
\(448\) −15.0395 22.5082i −0.710550 1.06341i
\(449\) 24.6921 + 4.91156i 1.16529 + 0.231791i 0.739580 0.673069i \(-0.235024\pi\)
0.425711 + 0.904859i \(0.360024\pi\)
\(450\) 11.7122 + 28.2759i 0.552121 + 1.33294i
\(451\) −12.5972 10.6582i −0.593180 0.501876i
\(452\) −2.70122 + 13.5800i −0.127055 + 0.638747i
\(453\) −22.4581 + 15.0060i −1.05517 + 0.705045i
\(454\) 4.77458 + 24.0034i 0.224082 + 1.12654i
\(455\) 5.12831 5.12831i 0.240419 0.240419i
\(456\) 1.22896 1.83927i 0.0575512 0.0861315i
\(457\) −4.03474 + 9.74073i −0.188737 + 0.455652i −0.989717 0.143039i \(-0.954312\pi\)
0.800980 + 0.598691i \(0.204312\pi\)
\(458\) 17.4517 0.815464
\(459\) −15.1844 + 54.9132i −0.708746 + 2.56313i
\(460\) −34.3673 −1.60238
\(461\) −2.21700 0.918311i −0.103256 0.0427700i 0.330457 0.943821i \(-0.392797\pi\)
−0.433713 + 0.901051i \(0.642797\pi\)
\(462\) 9.12169 80.2618i 0.424379 3.73412i
\(463\) −8.39076 8.39076i −0.389952 0.389952i 0.484719 0.874670i \(-0.338922\pi\)
−0.874670 + 0.484719i \(0.838922\pi\)
\(464\) −3.26832 16.4309i −0.151728 0.762787i
\(465\) 18.4088 12.3004i 0.853688 0.570416i
\(466\) 32.2979 + 6.42446i 1.49617 + 0.297607i
\(467\) −1.72352 + 0.713903i −0.0797548 + 0.0330355i −0.422204 0.906501i \(-0.638743\pi\)
0.342449 + 0.939536i \(0.388743\pi\)
\(468\) −23.8945 + 9.89741i −1.10452 + 0.457508i
\(469\) 5.07852 + 1.01018i 0.234504 + 0.0466458i
\(470\) 50.7964 33.9411i 2.34307 1.56559i
\(471\) 9.17803 + 46.1411i 0.422901 + 2.12607i
\(472\) −9.86038 9.86038i −0.453861 0.453861i
\(473\) 2.37201 20.8714i 0.109065 0.959666i
\(474\) −73.5417 30.4620i −3.37788 1.39916i
\(475\) 0.250614 0.0114989
\(476\) −43.9943 + 24.9344i −2.01647 + 1.14287i
\(477\) 27.8958 1.27726
\(478\) 21.6227 52.2019i 0.989000 2.38766i
\(479\) −14.0449 + 21.0196i −0.641726 + 0.960411i 0.357919 + 0.933753i \(0.383486\pi\)
−0.999645 + 0.0266579i \(0.991514\pi\)
\(480\) −3.41015 + 3.41015i −0.155652 + 0.155652i
\(481\) 1.43107 + 7.19448i 0.0652513 + 0.328040i
\(482\) 21.8581 14.6051i 0.995611 0.665246i
\(483\) 6.56124 32.9856i 0.298547 1.50090i
\(484\) 9.72459 42.2308i 0.442027 1.91958i
\(485\) −7.98600 19.2799i −0.362626 0.875456i
\(486\) 73.1231 + 14.5451i 3.31693 + 0.659778i
\(487\) −4.60128 6.88630i −0.208504 0.312048i 0.712448 0.701725i \(-0.247587\pi\)
−0.920952 + 0.389677i \(0.872587\pi\)
\(488\) 3.27920 + 16.4857i 0.148443 + 0.746271i
\(489\) 42.3762 42.3762i 1.91632 1.91632i
\(490\) −14.1396 9.44775i −0.638760 0.426806i
\(491\) −0.807684 + 1.94992i −0.0364503 + 0.0879988i −0.941056 0.338250i \(-0.890165\pi\)
0.904606 + 0.426249i \(0.140165\pi\)
\(492\) 62.9202 2.83666
\(493\) 18.8256 2.32584i 0.847861 0.104751i
\(494\) 0.319293i 0.0143657i
\(495\) −62.5818 + 5.21797i −2.81284 + 0.234530i
\(496\) −8.05614 5.38294i −0.361731 0.241701i
\(497\) −1.79893 + 1.79893i −0.0806932 + 0.0806932i
\(498\) 71.6925 14.2605i 3.21262 0.639029i
\(499\) −24.4023 + 16.3051i −1.09240 + 0.729916i −0.965083 0.261946i \(-0.915636\pi\)
−0.127314 + 0.991862i \(0.540636\pi\)
\(500\) −32.8602 6.53630i −1.46955 0.292312i
\(501\) −7.69328 18.5732i −0.343710 0.829790i
\(502\) 41.7292 17.2848i 1.86247 0.771459i
\(503\) −26.5636 5.28383i −1.18441 0.235594i −0.436694 0.899610i \(-0.643851\pi\)
−0.747718 + 0.664016i \(0.768851\pi\)
\(504\) 59.7229 + 89.3816i 2.66027 + 3.98137i
\(505\) 8.34973 1.66087i 0.371558 0.0739075i
\(506\) 8.28570 25.9098i 0.368344 1.15183i
\(507\) −21.7440 + 32.5423i −0.965687 + 1.44525i
\(508\) −1.52779 + 3.68840i −0.0677846 + 0.163646i
\(509\) 24.3374i 1.07874i 0.842070 + 0.539369i \(0.181337\pi\)
−0.842070 + 0.539369i \(0.818663\pi\)
\(510\) 54.6274 + 63.3020i 2.41894 + 2.80306i
\(511\) −45.2350 −2.00108
\(512\) 33.7567 + 13.9825i 1.49185 + 0.617945i
\(513\) 1.11911 1.67487i 0.0494099 0.0739471i
\(514\) −13.9935 + 13.9935i −0.617226 + 0.617226i
\(515\) 26.6282 5.29667i 1.17338 0.233399i
\(516\) 44.4992 + 66.5978i 1.95897 + 2.93180i
\(517\) 8.84935 + 30.8284i 0.389194 + 1.35583i
\(518\) 57.2133 23.6985i 2.51381 1.04125i
\(519\) 0.297702 0.123312i 0.0130677 0.00541280i
\(520\) −2.14843 + 10.8009i −0.0942150 + 0.473651i
\(521\) 3.22007 + 4.81918i 0.141074 + 0.211132i 0.895278 0.445508i \(-0.146977\pi\)
−0.754204 + 0.656640i \(0.771977\pi\)
\(522\) −15.9782 80.3276i −0.699345 3.51584i
\(523\) −7.73739 7.73739i −0.338333 0.338333i 0.517407 0.855740i \(-0.326897\pi\)
−0.855740 + 0.517407i \(0.826897\pi\)
\(524\) −59.7983 39.9559i −2.61230 1.74548i
\(525\) −6.57479 + 15.8729i −0.286947 + 0.692752i
\(526\) 59.8872i 2.61120i
\(527\) 6.74767 8.65000i 0.293933 0.376800i
\(528\) 17.7612 + 34.4615i 0.772957 + 1.49975i
\(529\) −4.46760 + 10.7857i −0.194244 + 0.468946i
\(530\) 13.4035 20.0598i 0.582211 0.871340i
\(531\) −15.2367 15.2367i −0.661218 0.661218i
\(532\) 1.75354 0.348801i 0.0760255 0.0151224i
\(533\) −3.71785 + 2.48419i −0.161038 + 0.107602i
\(534\) −8.28000 + 41.6263i −0.358310 + 1.80135i
\(535\) −8.60184 20.7667i −0.371890 0.897821i
\(536\) −7.26399 + 3.00884i −0.313757 + 0.129962i
\(537\) 16.5068 82.9855i 0.712323 3.58109i
\(538\) −49.5485 + 33.1072i −2.13619 + 1.42735i
\(539\) 6.98545 5.55970i 0.300885 0.239473i
\(540\) 99.7817 99.7817i 4.29392 4.29392i
\(541\) −3.19307 2.13354i −0.137281 0.0917280i 0.485034 0.874496i \(-0.338807\pi\)
−0.622314 + 0.782768i \(0.713807\pi\)
\(542\) −16.1134 6.67438i −0.692129 0.286689i
\(543\) 3.07535i 0.131976i
\(544\) −1.07399 + 2.13474i −0.0460468 + 0.0915261i
\(545\) 21.6153i 0.925898i
\(546\) −20.2229 8.37658i −0.865458 0.358485i
\(547\) −0.678413 + 1.01532i −0.0290068 + 0.0434118i −0.845690 0.533675i \(-0.820811\pi\)
0.816683 + 0.577087i \(0.195811\pi\)
\(548\) −15.4868 15.4868i −0.661564 0.661564i
\(549\) 5.06718 + 25.4744i 0.216262 + 1.08722i
\(550\) −6.73362 + 12.1559i −0.287122 + 0.518328i
\(551\) −0.657762 0.130837i −0.0280216 0.00557384i
\(552\) 19.5428 + 47.1804i 0.831796 + 2.00813i
\(553\) −12.1218 29.2645i −0.515469 1.24445i
\(554\) −5.27611 + 26.5248i −0.224160 + 1.12693i
\(555\) −37.7321 56.4701i −1.60164 2.39702i
\(556\) 17.6330 3.50743i 0.747807 0.148748i
\(557\) −8.70024 8.70024i −0.368641 0.368641i 0.498341 0.866981i \(-0.333943\pi\)
−0.866981 + 0.498341i \(0.833943\pi\)
\(558\) −39.3849 26.3161i −1.66729 1.11405i
\(559\) −5.25877 2.17825i −0.222422 0.0921304i
\(560\) 29.3858 1.24178
\(561\) −40.3898 + 17.1938i −1.70526 + 0.725922i
\(562\) −35.3443 −1.49091
\(563\) −9.65350 3.99861i −0.406846 0.168521i 0.169869 0.985467i \(-0.445666\pi\)
−0.576715 + 0.816945i \(0.695666\pi\)
\(564\) −101.687 67.9454i −4.28181 2.86102i
\(565\) 6.44187 + 6.44187i 0.271011 + 0.271011i
\(566\) −28.6552 + 5.69987i −1.20447 + 0.239583i
\(567\) 38.8183 + 58.0957i 1.63022 + 2.43979i
\(568\) 0.753637 3.78879i 0.0316219 0.158974i
\(569\) 14.3870 + 34.7333i 0.603134 + 1.45609i 0.870338 + 0.492454i \(0.163900\pi\)
−0.267205 + 0.963640i \(0.586100\pi\)
\(570\) −1.13130 2.73119i −0.0473847 0.114397i
\(571\) −15.4483 3.07286i −0.646492 0.128595i −0.139056 0.990285i \(-0.544407\pi\)
−0.507436 + 0.861689i \(0.669407\pi\)
\(572\) −10.2723 5.69023i −0.429506 0.237920i
\(573\) 8.39473 + 42.2032i 0.350695 + 1.76306i
\(574\) 26.6923 + 26.6923i 1.11412 + 1.11412i
\(575\) −3.21434 + 4.81060i −0.134047 + 0.200616i
\(576\) 58.6820 + 24.3069i 2.44508 + 1.01279i
\(577\) 13.7024i 0.570440i −0.958462 0.285220i \(-0.907933\pi\)
0.958462 0.285220i \(-0.0920667\pi\)
\(578\) 35.5456 + 21.2853i 1.47850 + 0.885354i
\(579\) 50.0112i 2.07839i
\(580\) −43.4053 17.9791i −1.80231 0.746540i
\(581\) 24.1854 + 16.1602i 1.00338 + 0.670437i
\(582\) −44.5361 + 44.5361i −1.84608 + 1.84608i
\(583\) 7.88754 + 9.91024i 0.326668 + 0.410440i
\(584\) 57.1107 38.1602i 2.36326 1.57908i
\(585\) −3.31986 + 16.6901i −0.137259 + 0.690049i
\(586\) −37.2383 + 15.4246i −1.53830 + 0.637185i
\(587\) −4.05031 9.77831i −0.167174 0.403594i 0.817985 0.575240i \(-0.195091\pi\)
−0.985159 + 0.171646i \(0.945091\pi\)
\(588\) −6.64139 + 33.3885i −0.273886 + 1.37692i
\(589\) −0.322503 + 0.215489i −0.0132885 + 0.00887909i
\(590\) −18.2777 + 3.63565i −0.752480 + 0.149678i
\(591\) −56.7521 56.7521i −2.33447 2.33447i
\(592\) −16.5125 + 24.7127i −0.678659 + 1.01568i
\(593\) −3.53910 + 8.54415i −0.145334 + 0.350866i −0.979737 0.200288i \(-0.935812\pi\)
0.834404 + 0.551154i \(0.185812\pi\)
\(594\) 51.1696 + 99.2830i 2.09951 + 4.07363i
\(595\) −2.44086 + 33.1829i −0.100066 + 1.36037i
\(596\) 64.8771i 2.65747i
\(597\) −0.286268 + 0.691113i −0.0117162 + 0.0282854i
\(598\) −6.12893 4.09522i −0.250630 0.167466i
\(599\) −2.69666 2.69666i −0.110183 0.110183i 0.649866 0.760049i \(-0.274825\pi\)
−0.760049 + 0.649866i \(0.774825\pi\)
\(600\) −5.08950 25.5866i −0.207778 1.04457i
\(601\) −13.4069 20.0648i −0.546877 0.818459i 0.450352 0.892851i \(-0.351298\pi\)
−0.997229 + 0.0743919i \(0.976298\pi\)
\(602\) −9.37476 + 47.1301i −0.382087 + 1.92088i
\(603\) −11.2247 + 4.64941i −0.457104 + 0.189338i
\(604\) 30.6254 12.6855i 1.24613 0.516164i
\(605\) −19.5487 20.7574i −0.794769 0.843907i
\(606\) −14.2750 21.3640i −0.579881 0.867854i
\(607\) 33.4577 6.65514i 1.35800 0.270124i 0.538224 0.842802i \(-0.319095\pi\)
0.819780 + 0.572678i \(0.194095\pi\)
\(608\) 0.0597422 0.0597422i 0.00242287 0.00242287i
\(609\) 25.5430 38.2278i 1.03505 1.54907i
\(610\) 20.7532 + 8.59627i 0.840274 + 0.348053i
\(611\) 8.69113 0.351606
\(612\) 53.3259 105.995i 2.15557 4.28458i
\(613\) 10.3283i 0.417155i −0.978006 0.208577i \(-0.933117\pi\)
0.978006 0.208577i \(-0.0668833\pi\)
\(614\) −1.00973 + 2.43769i −0.0407492 + 0.0983773i
\(615\) 23.0002 34.4222i 0.927457 1.38804i
\(616\) −14.8670 + 46.4897i −0.599007 + 1.87312i
\(617\) 24.2427 4.82217i 0.975974 0.194133i 0.318759 0.947836i \(-0.396734\pi\)
0.657216 + 0.753703i \(0.271734\pi\)
\(618\) −45.5244 68.1321i −1.83126 2.74067i
\(619\) 31.4844 + 6.26263i 1.26546 + 0.251716i 0.781795 0.623535i \(-0.214304\pi\)
0.483668 + 0.875251i \(0.339304\pi\)
\(620\) −25.1035 + 10.3982i −1.00818 + 0.417603i
\(621\) 17.7960 + 42.9633i 0.714128 + 1.72406i
\(622\) 2.66657 + 0.530414i 0.106920 + 0.0212677i
\(623\) −14.0426 + 9.38298i −0.562606 + 0.375921i
\(624\) 10.3037 2.04953i 0.412478 0.0820470i
\(625\) −21.6660 + 21.6660i −0.866639 + 0.866639i
\(626\) −67.1631 44.8769i −2.68438 1.79364i
\(627\) 1.54664 0.128957i 0.0617670 0.00515003i
\(628\) 57.7369i 2.30395i
\(629\) −26.5344 20.6989i −1.05800 0.825318i
\(630\) 143.661 5.72360
\(631\) −3.85329 + 9.30267i −0.153397 + 0.370333i −0.981832 0.189752i \(-0.939232\pi\)
0.828435 + 0.560085i \(0.189232\pi\)
\(632\) 39.9916 + 26.7215i 1.59078 + 1.06293i
\(633\) 61.2918 61.2918i 2.43613 2.43613i
\(634\) 4.70696 + 23.6635i 0.186937 + 0.939796i
\(635\) 1.45937 + 2.18410i 0.0579132 + 0.0866732i
\(636\) −47.3682 9.42213i −1.87827 0.373612i
\(637\) −0.925803 2.23509i −0.0366817 0.0885574i
\(638\) 24.0193 28.3890i 0.950932 1.12393i
\(639\) 1.16456 5.85462i 0.0460691 0.231605i
\(640\) 43.1764 28.8496i 1.70670 1.14038i
\(641\) −6.74839 33.9265i −0.266545 1.34001i −0.849534 0.527534i \(-0.823117\pi\)
0.582989 0.812480i \(-0.301883\pi\)
\(642\) −47.9705 + 47.9705i −1.89324 + 1.89324i
\(643\) 25.5420 38.2263i 1.00728 1.50750i 0.152635 0.988283i \(-0.451224\pi\)
0.854643 0.519216i \(-0.173776\pi\)
\(644\) −15.7954 + 38.1334i −0.622424 + 1.50267i
\(645\) 52.7006 2.07508
\(646\) −0.957013 1.10898i −0.0376532 0.0436324i
\(647\) 11.3386 0.445767 0.222883 0.974845i \(-0.428453\pi\)
0.222883 + 0.974845i \(0.428453\pi\)
\(648\) −98.0189 40.6008i −3.85055 1.59495i
\(649\) 1.10480 9.72116i 0.0433673 0.381589i
\(650\) 2.66266 + 2.66266i 0.104438 + 0.104438i
\(651\) −5.18753 26.0795i −0.203315 1.02213i
\(652\) −61.1538 + 40.8617i −2.39497 + 1.60027i
\(653\) −42.9864 8.55052i −1.68219 0.334608i −0.740746 0.671785i \(-0.765528\pi\)
−0.941441 + 0.337177i \(0.890528\pi\)
\(654\) −60.2719 + 24.9654i −2.35682 + 0.976225i
\(655\) −43.7179 + 18.1086i −1.70820 + 0.707560i
\(656\) −17.7692 3.53451i −0.693770 0.137999i
\(657\) 88.2502 58.9669i 3.44297 2.30052i
\(658\) −14.3142 71.9625i −0.558026 2.80539i
\(659\) 25.2806 + 25.2806i 0.984791 + 0.984791i 0.999886 0.0150951i \(-0.00480509\pi\)
−0.0150951 + 0.999886i \(0.504805\pi\)
\(660\) 108.029 + 12.2774i 4.20502 + 0.477897i
\(661\) 25.3479 + 10.4994i 0.985918 + 0.408380i 0.816614 0.577184i \(-0.195848\pi\)
0.169303 + 0.985564i \(0.445848\pi\)
\(662\) −27.7017 −1.07666
\(663\) 1.45851 + 11.8054i 0.0566440 + 0.458482i
\(664\) −44.1676 −1.71404
\(665\) 0.450177 1.08682i 0.0174571 0.0421452i
\(666\) −80.7263 + 120.815i −3.12808 + 4.68150i
\(667\) 10.9478 10.9478i 0.423902 0.423902i
\(668\) 4.81335 + 24.1984i 0.186234 + 0.936262i
\(669\) −21.7471 + 14.5310i −0.840793 + 0.561800i
\(670\) −2.04991 + 10.3056i −0.0791948 + 0.398139i
\(671\) −7.61727 + 9.00305i −0.294061 + 0.347559i
\(672\) 2.21653 + 5.35118i 0.0855045 + 0.206426i
\(673\) −20.3152 4.04095i −0.783094 0.155767i −0.212677 0.977123i \(-0.568218\pi\)
−0.570417 + 0.821356i \(0.693218\pi\)
\(674\) 23.0984 + 34.5693i 0.889719 + 1.33156i
\(675\) −4.63458 23.2996i −0.178385 0.896802i
\(676\) 33.9646 33.9646i 1.30633 1.30633i
\(677\) −15.8679 10.6026i −0.609854 0.407491i 0.211935 0.977284i \(-0.432024\pi\)
−0.821789 + 0.569793i \(0.807024\pi\)
\(678\) 10.5221 25.4027i 0.404100 0.975585i
\(679\) −25.0631 −0.961834
\(680\) −24.9114 43.9537i −0.955308 1.68555i
\(681\) 32.2356i 1.23527i
\(682\) −1.78702 21.4327i −0.0684287 0.820701i
\(683\) 37.9949 + 25.3874i 1.45383 + 0.971420i 0.996627 + 0.0820595i \(0.0261498\pi\)
0.457206 + 0.889361i \(0.348850\pi\)
\(684\) −2.96634 + 2.96634i −0.113421 + 0.113421i
\(685\) −14.1336 + 2.81135i −0.540018 + 0.107416i
\(686\) 27.1782 18.1599i 1.03767 0.693347i
\(687\) −22.5449 4.48445i −0.860141 0.171093i
\(688\) −8.82585 21.3075i −0.336482 0.812340i
\(689\) 3.17091 1.31343i 0.120802 0.0500379i
\(690\) 66.9358 + 13.3144i 2.54820 + 0.506869i
\(691\) 12.1511 + 18.1853i 0.462248 + 0.691803i 0.987228 0.159311i \(-0.0509273\pi\)
−0.524980 + 0.851114i \(0.675927\pi\)
\(692\) −0.387864 + 0.0771510i −0.0147444 + 0.00293284i
\(693\) −22.9731 + 71.8381i −0.872678 + 2.72890i
\(694\) 30.6314 45.8431i 1.16275 1.74018i
\(695\) 4.52684 10.9288i 0.171713 0.414551i
\(696\) 69.8119i 2.64621i
\(697\) 5.46718 19.7717i 0.207084 0.748905i
\(698\) 62.0992 2.35049
\(699\) −40.0730 16.5988i −1.51570 0.627824i
\(700\) 11.7144 17.5319i 0.442764 0.662643i
\(701\) −4.67090 + 4.67090i −0.176418 + 0.176418i −0.789792 0.613375i \(-0.789812\pi\)
0.613375 + 0.789792i \(0.289812\pi\)
\(702\) 29.6847 5.90466i 1.12038 0.222857i
\(703\) 0.661026 + 0.989296i 0.0249311 + 0.0373120i
\(704\) 7.95708 + 27.7201i 0.299894 + 1.04474i
\(705\) −74.3427 + 30.7938i −2.79991 + 1.15976i
\(706\) 1.04022 0.430873i 0.0391492 0.0162161i
\(707\) 1.99471 10.0281i 0.0750188 0.377145i
\(708\) 20.7262 + 31.0190i 0.778939 + 1.16576i
\(709\) −2.06564 10.3847i −0.0775769 0.390005i −0.999993 0.00380716i \(-0.998788\pi\)
0.922416 0.386198i \(-0.126212\pi\)
\(710\) −3.65048 3.65048i −0.137000 0.137000i
\(711\) 61.7969 + 41.2914i 2.31757 + 1.54855i
\(712\) 9.81382 23.6927i 0.367788 0.887920i
\(713\) 8.95438i 0.335344i
\(714\) 95.3460 31.5198i 3.56823 1.17960i
\(715\) −6.86798 + 3.53970i −0.256848 + 0.132377i
\(716\) −39.7382 + 95.9364i −1.48508 + 3.58531i
\(717\) −41.3472 + 61.8804i −1.54414 + 2.31097i
\(718\) 6.29830 + 6.29830i 0.235051 + 0.235051i
\(719\) 5.01677 0.997898i 0.187094 0.0372153i −0.100654 0.994922i \(-0.532093\pi\)
0.287748 + 0.957706i \(0.407093\pi\)
\(720\) −57.3295 + 38.3064i −2.13654 + 1.42759i
\(721\) 6.36133 31.9806i 0.236908 1.19102i
\(722\) −17.7006 42.7329i −0.658747 1.59036i
\(723\) −31.9903 + 13.2508i −1.18973 + 0.492803i
\(724\) −0.736326 + 3.70176i −0.0273653 + 0.137575i
\(725\) −6.57631 + 4.39415i −0.244238 + 0.163195i
\(726\) −35.3011 + 78.4839i −1.31015 + 2.91281i
\(727\) −36.9658 + 36.9658i −1.37099 + 1.37099i −0.512000 + 0.858985i \(0.671095\pi\)
−0.858985 + 0.512000i \(0.828905\pi\)
\(728\) 10.9971 + 7.34802i 0.407579 + 0.272336i
\(729\) −28.5202 11.8135i −1.05631 0.437536i
\(730\) 91.7930i 3.39741i
\(731\) 24.7939 8.19644i 0.917034 0.303156i
\(732\) 44.9681i 1.66207i
\(733\) 1.88239 + 0.779713i 0.0695278 + 0.0287994i 0.417176 0.908826i \(-0.363020\pi\)
−0.347649 + 0.937625i \(0.613020\pi\)
\(734\) −23.6347 + 35.3718i −0.872372 + 1.30560i
\(735\) 15.8384 + 15.8384i 0.584207 + 0.584207i
\(736\) 0.380523 + 1.91302i 0.0140263 + 0.0705148i
\(737\) −4.82551 2.67304i −0.177750 0.0984628i
\(738\) −86.8700 17.2795i −3.19773 0.636068i
\(739\) −4.88830 11.8014i −0.179819 0.434122i 0.808109 0.589032i \(-0.200491\pi\)
−0.987928 + 0.154911i \(0.950491\pi\)
\(740\) 31.8972 + 77.0066i 1.17256 + 2.83082i
\(741\) 0.0820468 0.412477i 0.00301406 0.0151527i
\(742\) −16.0977 24.0919i −0.590965 0.884441i
\(743\) 48.1877 9.58513i 1.76784 0.351644i 0.799379 0.600827i \(-0.205162\pi\)
0.968456 + 0.249183i \(0.0801620\pi\)
\(744\) 28.5500 + 28.5500i 1.04669 + 1.04669i
\(745\) 35.4928 + 23.7155i 1.30035 + 0.868869i
\(746\) 29.2163 + 12.1018i 1.06969 + 0.443079i
\(747\) −68.2499 −2.49713
\(748\) 52.7334 11.0255i 1.92813 0.403131i
\(749\) −26.9958 −0.986406
\(750\) 61.4683 + 25.4610i 2.24451 + 0.929705i
\(751\) 16.0582 + 10.7298i 0.585974 + 0.391535i 0.812923 0.582372i \(-0.197875\pi\)
−0.226949 + 0.973907i \(0.572875\pi\)
\(752\) 24.9006 + 24.9006i 0.908030 + 0.908030i
\(753\) −58.3492 + 11.6064i −2.12636 + 0.422960i
\(754\) −5.59834 8.37851i −0.203880 0.305127i
\(755\) 4.25505 21.3916i 0.154857 0.778519i
\(756\) −64.8561 156.576i −2.35879 5.69463i
\(757\) −8.63415 20.8447i −0.313814 0.757613i −0.999557 0.0297695i \(-0.990523\pi\)
0.685743 0.727844i \(-0.259477\pi\)
\(758\) 20.6160 + 4.10078i 0.748808 + 0.148947i
\(759\) −17.3617 + 31.3423i −0.630190 + 1.13765i
\(760\) 0.348479 + 1.75192i 0.0126406 + 0.0635488i
\(761\) 11.7309 + 11.7309i 0.425246 + 0.425246i 0.887005 0.461759i \(-0.152782\pi\)
−0.461759 + 0.887005i \(0.652782\pi\)
\(762\) 4.40456 6.59188i 0.159560 0.238799i
\(763\) −23.9840 9.93451i −0.868280 0.359653i
\(764\) 52.8094i 1.91058i
\(765\) −38.4942 67.9193i −1.39176 2.45563i
\(766\) 29.1186i 1.05210i
\(767\) −2.44936 1.01456i −0.0884411 0.0366335i
\(768\) −83.8942 56.0563i −3.02727 2.02276i
\(769\) −8.65082 + 8.65082i −0.311957 + 0.311957i −0.845667 0.533711i \(-0.820797\pi\)
0.533711 + 0.845667i \(0.320797\pi\)
\(770\) 40.6202 + 51.0369i 1.46385 + 1.83924i
\(771\) 21.6732 14.4816i 0.780542 0.521542i
\(772\) 11.9741 60.1979i 0.430957 2.16657i
\(773\) 26.2214 10.8613i 0.943119 0.390653i 0.142479 0.989798i \(-0.454493\pi\)
0.800640 + 0.599145i \(0.204493\pi\)
\(774\) −43.1478 104.168i −1.55092 3.74424i
\(775\) −0.892408 + 4.48644i −0.0320562 + 0.161158i
\(776\) 31.6430 21.1432i 1.13592 0.758996i
\(777\) −80.0003 + 15.9130i −2.86999 + 0.570877i
\(778\) −47.0630 47.0630i −1.68729 1.68729i
\(779\) −0.402938 + 0.603040i −0.0144368 + 0.0216062i
\(780\) 11.2745 27.2191i 0.403692 0.974600i
\(781\) 2.40918 1.24167i 0.0862073 0.0444305i
\(782\) 33.5618 4.14646i 1.20017 0.148277i
\(783\) 63.5718i 2.27187i
\(784\) 3.75117 9.05612i 0.133970 0.323433i
\(785\) −31.5866 21.1055i −1.12737 0.753286i
\(786\) 100.987 + 100.987i 3.60210 + 3.60210i
\(787\) 7.59156 + 38.1653i 0.270610 + 1.36045i 0.841871 + 0.539679i \(0.181454\pi\)
−0.571261 + 0.820768i \(0.693546\pi\)
\(788\) 54.7238 + 81.8999i 1.94945 + 2.91756i
\(789\) 15.3888 77.3649i 0.547857 2.75426i
\(790\) 59.3849 24.5980i 2.11282 0.875159i
\(791\) 10.1085 4.18708i 0.359417 0.148875i
\(792\) −31.5981 110.078i −1.12279 3.91145i
\(793\) 1.77541 + 2.65709i 0.0630467 + 0.0943561i
\(794\) 44.9460 8.94031i 1.59507 0.317280i
\(795\) −22.4699 + 22.4699i −0.796924 + 0.796924i
\(796\) 0.510050 0.763344i 0.0180782 0.0270560i
\(797\) −36.7521 15.2232i −1.30183 0.539234i −0.379338 0.925258i \(-0.623848\pi\)
−0.922489 + 0.386024i \(0.873848\pi\)
\(798\) −3.55043 −0.125684
\(799\) −30.1864 + 26.0498i −1.06792 + 0.921576i
\(800\) 0.996408i 0.0352284i
\(801\) 15.1648 36.6110i 0.535821 1.29359i
\(802\) −6.29788 + 9.42545i −0.222386 + 0.332824i
\(803\) 45.9012 + 14.6788i 1.61982 + 0.518003i
\(804\) 20.6303 4.10363i 0.727575 0.144724i
\(805\) 15.0880 + 22.5808i 0.531781 + 0.795867i
\(806\) −5.71593 1.13697i −0.201335 0.0400480i
\(807\) 72.5163 30.0372i 2.55269 1.05736i
\(808\) 5.94128 + 14.3435i 0.209014 + 0.504603i
\(809\) 23.9243 + 4.75884i 0.841134 + 0.167312i 0.596811 0.802382i \(-0.296434\pi\)
0.244323 + 0.969694i \(0.421434\pi\)
\(810\) −117.891 + 78.7719i −4.14225 + 2.76776i
\(811\) 12.2028 2.42728i 0.428497 0.0852333i 0.0238696 0.999715i \(-0.492401\pi\)
0.404627 + 0.914482i \(0.367401\pi\)
\(812\) −39.8986 + 39.8986i −1.40017 + 1.40017i
\(813\) 19.1009 + 12.7628i 0.669898 + 0.447611i
\(814\) −65.7461 + 5.48180i −2.30440 + 0.192137i
\(815\) 48.3926i 1.69512i
\(816\) −29.6442 + 38.0017i −1.03776 + 1.33032i
\(817\) −0.923258 −0.0323007
\(818\) −8.92414 + 21.5448i −0.312025 + 0.753296i
\(819\) 16.9932 + 11.3545i 0.593791 + 0.396758i
\(820\) −35.9267 + 35.9267i −1.25461 + 1.25461i
\(821\) −8.17356 41.0913i −0.285259 1.43409i −0.811795 0.583942i \(-0.801509\pi\)
0.526536 0.850153i \(-0.323491\pi\)
\(822\) 24.1633 + 36.1629i 0.842792 + 1.26133i
\(823\) 17.2252 + 3.42630i 0.600431 + 0.119433i 0.485942 0.873991i \(-0.338477\pi\)
0.114490 + 0.993424i \(0.463477\pi\)
\(824\) 18.9474 + 45.7430i 0.660063 + 1.59353i
\(825\) 11.8224 13.9732i 0.411603 0.486484i
\(826\) −4.36644 + 21.9516i −0.151928 + 0.763793i
\(827\) −13.4679 + 8.99898i −0.468326 + 0.312925i −0.767246 0.641353i \(-0.778374\pi\)
0.298920 + 0.954278i \(0.403374\pi\)
\(828\) −18.8938 94.9858i −0.656606 3.30098i
\(829\) 15.5999 15.5999i 0.541807 0.541807i −0.382252 0.924058i \(-0.624851\pi\)
0.924058 + 0.382252i \(0.124851\pi\)
\(830\) −32.7930 + 49.0782i −1.13826 + 1.70353i
\(831\) 13.6318 32.9101i 0.472882 1.14164i
\(832\) 7.81482 0.270930
\(833\) 9.91474 + 4.98811i 0.343525 + 0.172828i
\(834\) −35.7020 −1.23626
\(835\) 14.9979 + 6.21232i 0.519022 + 0.214986i
\(836\) −1.89255 0.215087i −0.0654552 0.00743893i
\(837\) 25.9981 + 25.9981i 0.898626 + 0.898626i
\(838\) −15.6119 78.4864i −0.539304 2.71127i
\(839\) −33.6727 + 22.4994i −1.16251 + 0.776766i −0.978518 0.206162i \(-0.933903\pi\)
−0.183994 + 0.982927i \(0.558903\pi\)
\(840\) −120.102 23.8899i −4.14393 0.824279i
\(841\) −7.23826 + 2.99818i −0.249595 + 0.103386i
\(842\) 20.8185 8.62332i 0.717454 0.297179i
\(843\) 45.6593 + 9.08220i 1.57259 + 0.312808i
\(844\) −88.4512 + 59.1012i −3.04462 + 2.03435i
\(845\) −6.16566 30.9968i −0.212105 1.06632i
\(846\) 121.734 + 121.734i 4.18530 + 4.18530i
\(847\) −32.0168 + 12.1508i −1.10011 + 0.417506i
\(848\) 12.8479 + 5.32177i 0.441199 + 0.182750i
\(849\) 38.4827 1.32072
\(850\) −17.2288 1.26731i −0.590943 0.0434685i
\(851\) −27.4681 −0.941594
\(852\) −3.95493 + 9.54804i −0.135494 + 0.327110i
\(853\) −29.8976 + 44.7450i −1.02368 + 1.53204i −0.188488 + 0.982076i \(0.560359\pi\)
−0.835188 + 0.549964i \(0.814641\pi\)
\(854\) 19.0766 19.0766i 0.652787 0.652787i
\(855\) 0.538485 + 2.70715i 0.0184158 + 0.0925825i
\(856\) 34.0832 22.7736i 1.16494 0.778387i
\(857\) −5.90751 + 29.6991i −0.201797 + 1.01450i 0.738528 + 0.674223i \(0.235521\pi\)
−0.940325 + 0.340278i \(0.889479\pi\)
\(858\) 17.8025 + 15.0623i 0.607767 + 0.514218i
\(859\) −6.32326 15.2657i −0.215747 0.520859i 0.778541 0.627594i \(-0.215960\pi\)
−0.994287 + 0.106735i \(0.965960\pi\)
\(860\) −63.4351 12.6180i −2.16312 0.430271i
\(861\) −27.6234 41.3413i −0.941401 1.40891i
\(862\) 14.7200 + 74.0022i 0.501364 + 2.52053i
\(863\) 19.5240 19.5240i 0.664605 0.664605i −0.291857 0.956462i \(-0.594273\pi\)
0.956462 + 0.291857i \(0.0942730\pi\)
\(864\) −6.65906 4.44944i −0.226546 0.151373i
\(865\) −0.0995745 + 0.240394i −0.00338563 + 0.00817364i
\(866\) −57.7789 −1.96341
\(867\) −40.4498 36.6313i −1.37375 1.24406i
\(868\) 32.6336i 1.10766i
\(869\) 2.80393 + 33.6290i 0.0951169 + 1.14079i
\(870\) 77.5735 + 51.8330i 2.62999 + 1.75730i
\(871\) −1.05699 + 1.05699i −0.0358149 + 0.0358149i
\(872\) 38.6614 7.69023i 1.30924 0.260424i
\(873\) 48.8963 32.6715i 1.65489 1.10576i
\(874\) −1.17264 0.233253i −0.0396653 0.00788991i
\(875\) 10.1317 + 24.4601i 0.342515 + 0.826903i
\(876\) −169.769 + 70.3207i −5.73597 + 2.37592i
\(877\) 34.0074 + 6.76449i 1.14835 + 0.228420i 0.732339 0.680940i \(-0.238429\pi\)
0.416008 + 0.909361i \(0.363429\pi\)
\(878\) 29.6887 + 44.4322i 1.00194 + 1.49951i
\(879\) 52.0697 10.3573i 1.75627 0.349343i
\(880\) −29.8186 9.53571i −1.00518 0.321449i
\(881\) −23.0674 + 34.5228i −0.777161 + 1.16310i 0.205674 + 0.978621i \(0.434061\pi\)
−0.982836 + 0.184484i \(0.940939\pi\)
\(882\) 18.3387 44.2736i 0.617497 1.49077i
\(883\) 13.7954i 0.464254i −0.972686 0.232127i \(-0.925432\pi\)
0.972686 0.232127i \(-0.0745684\pi\)
\(884\) 1.07094 14.5592i 0.0360196 0.489678i
\(885\) 24.5461 0.825109
\(886\) −45.5158 18.8533i −1.52913 0.633387i
\(887\) 22.8938 34.2630i 0.768698 1.15044i −0.216038 0.976385i \(-0.569313\pi\)
0.984736 0.174054i \(-0.0556866\pi\)
\(888\) 87.5789 87.5789i 2.93895 2.93895i
\(889\) 3.09417 0.615469i 0.103775 0.0206422i
\(890\) −19.0404 28.4959i −0.638235 0.955186i
\(891\) −20.5379 71.5479i −0.688047 2.39695i
\(892\) 29.6559 12.2839i 0.992953 0.411295i
\(893\) 1.30240 0.539474i 0.0435833 0.0180528i
\(894\) 25.1343 126.359i 0.840617 4.22607i
\(895\) 37.9585 + 56.8089i 1.26881 + 1.89891i
\(896\) −12.1669 61.1673i −0.406469 2.04346i
\(897\) 6.86530 + 6.86530i 0.229226 + 0.229226i
\(898\) 51.0164 + 34.0881i 1.70244 + 1.13753i
\(899\) 4.68444 11.3092i 0.156235 0.377184i
\(900\) 49.4740i 1.64913i
\(901\) −7.07661 + 14.0660i −0.235756 + 0.468607i
\(902\) −18.4238 35.7471i −0.613444 1.19025i
\(903\) 24.2215 58.4758i 0.806040 1.94595i
\(904\) −9.23012 + 13.8139i −0.306989 + 0.459442i
\(905\) 1.75599 + 1.75599i 0.0583710 + 0.0583710i
\(906\) −64.5625 + 12.8423i −2.14495 + 0.426656i
\(907\) −11.8545 + 7.92093i −0.393623 + 0.263010i −0.736593 0.676336i \(-0.763567\pi\)
0.342971 + 0.939346i \(0.388567\pi\)
\(908\) −7.71811 + 38.8016i −0.256134 + 1.28767i
\(909\) 9.18075 + 22.1643i 0.304506 + 0.735143i
\(910\) 16.3299 6.76408i 0.541332 0.224227i
\(911\) −4.02522 + 20.2362i −0.133362 + 0.670454i 0.855037 + 0.518568i \(0.173535\pi\)
−0.988398 + 0.151886i \(0.951465\pi\)
\(912\) 1.41684 0.946700i 0.0469162 0.0313484i
\(913\) −19.2976 24.2464i −0.638658 0.802438i
\(914\) −18.1694 + 18.1694i −0.600991 + 0.600991i
\(915\) −24.6010 16.4379i −0.813285 0.543419i
\(916\) 26.0633 + 10.7958i 0.861155 + 0.356702i
\(917\) 56.8315i 1.87674i
\(918\) −85.4044 + 109.482i −2.81877 + 3.61345i
\(919\) 2.75588i 0.0909082i 0.998966 + 0.0454541i \(0.0144735\pi\)
−0.998966 + 0.0454541i \(0.985527\pi\)
\(920\) −38.0982 15.7808i −1.25606 0.520277i
\(921\) 1.93081 2.88966i 0.0636223 0.0952175i
\(922\) −4.13538 4.13538i −0.136191 0.136191i
\(923\) −0.143281 0.720324i −0.00471617 0.0237098i
\(924\) 63.2735 114.225i 2.08154 3.75771i
\(925\) 13.7624 + 2.73751i 0.452505 + 0.0900089i
\(926\) −11.0671 26.7185i −0.363689 0.878023i
\(927\) 29.2784 + 70.6842i 0.961628 + 2.32157i
\(928\) −0.520192 + 2.61518i −0.0170761 + 0.0858475i
\(929\) 31.6760 + 47.4065i 1.03926 + 1.55536i 0.813835 + 0.581096i \(0.197376\pi\)
0.225422 + 0.974261i \(0.427624\pi\)
\(930\) 52.9216 10.5268i 1.73537 0.345186i
\(931\) −0.277471 0.277471i −0.00909376 0.00909376i
\(932\) 44.2612 + 29.5744i 1.44982 + 0.968742i
\(933\) −3.30850 1.37043i −0.108315 0.0448657i
\(934\) −4.54653 −0.148767
\(935\) 13.2447 32.8796i 0.433148 1.07528i
\(936\) −31.0332 −1.01435
\(937\) 42.8197 + 17.7365i 1.39886 + 0.579426i 0.949455 0.313903i \(-0.101637\pi\)
0.449403 + 0.893329i \(0.351637\pi\)
\(938\) 10.4928 + 7.01104i 0.342601 + 0.228918i
\(939\) 75.2325 + 75.2325i 2.45512 + 2.45512i
\(940\) 96.8583 19.2663i 3.15917 0.628398i
\(941\) −6.24719 9.34959i −0.203653 0.304788i 0.715558 0.698553i \(-0.246172\pi\)
−0.919211 + 0.393765i \(0.871172\pi\)
\(942\) −22.3681 + 112.452i −0.728792 + 3.66389i
\(943\) −6.40749 15.4690i −0.208657 0.503742i
\(944\) −4.11078 9.92429i −0.133794 0.323008i
\(945\) −109.367 21.7545i −3.55772 0.707674i
\(946\) 24.8066 44.7821i 0.806532 1.45599i
\(947\) −10.4812 52.6926i −0.340594 1.71228i −0.648799 0.760960i \(-0.724728\pi\)
0.308205 0.951320i \(-0.400272\pi\)
\(948\) −90.9871 90.9871i −2.95512 2.95512i
\(949\) 7.25501 10.8579i 0.235508 0.352462i
\(950\) 0.564287 + 0.233735i 0.0183079 + 0.00758337i
\(951\) 31.7790i 1.03051i
\(952\) −60.2197 + 7.43996i −1.95173 + 0.241130i
\(953\) 40.0153i 1.29622i −0.761546 0.648111i \(-0.775559\pi\)
0.761546 0.648111i \(-0.224441\pi\)
\(954\) 62.8108 + 26.0171i 2.03358 + 0.842335i
\(955\) −28.8908 19.3042i −0.934884 0.624670i
\(956\) 64.5850 64.5850i 2.08883 2.08883i
\(957\) −38.3241 + 30.5021i −1.23884 + 0.985992i
\(958\) −51.2277 + 34.2292i −1.65509 + 1.10590i
\(959\) −3.37645 + 16.9746i −0.109031 + 0.548137i
\(960\) −66.8469 + 27.6889i −2.15747 + 0.893655i
\(961\) 9.15393 + 22.0995i 0.295288 + 0.712889i
\(962\) −3.48772 + 17.5339i −0.112449 + 0.565317i
\(963\) 52.6669 35.1909i 1.69717 1.13401i
\(964\) 41.6790 8.29046i 1.34239 0.267018i
\(965\) −28.5558 28.5558i −0.919244 0.919244i
\(966\) 45.5375 68.1516i 1.46514 2.19274i
\(967\) 11.9161 28.7681i 0.383197 0.925119i −0.608146 0.793825i \(-0.708087\pi\)
0.991343 0.131295i \(-0.0419134\pi\)
\(968\) 30.1719 42.3501i 0.969761 1.36118i
\(969\) 0.951343 + 1.67855i 0.0305615 + 0.0539228i
\(970\) 50.8592i 1.63299i
\(971\) 21.5160 51.9442i 0.690481 1.66697i −0.0533271 0.998577i \(-0.516983\pi\)
0.743809 0.668393i \(-0.233017\pi\)
\(972\) 100.208 + 66.9569i 3.21418 + 2.14764i
\(973\) −10.0458 10.0458i −0.322054 0.322054i
\(974\) −3.93781 19.7967i −0.126176 0.634328i
\(975\) −2.75553 4.12395i −0.0882477 0.132072i
\(976\) −2.52606 + 12.6994i −0.0808572 + 0.406497i
\(977\) 8.00494 3.31576i 0.256101 0.106080i −0.250939 0.968003i \(-0.580740\pi\)
0.507040 + 0.861922i \(0.330740\pi\)
\(978\) 134.937 55.8929i 4.31482 1.78726i
\(979\) 17.2942 4.96433i 0.552726 0.158661i
\(980\) −15.2723 22.8566i −0.487856 0.730128i
\(981\) 59.7414 11.8833i 1.90740 0.379405i
\(982\) −3.63720 + 3.63720i −0.116068 + 0.116068i
\(983\) −1.43162 + 2.14257i −0.0456617 + 0.0683375i −0.853598 0.520932i \(-0.825584\pi\)
0.807936 + 0.589270i \(0.200584\pi\)
\(984\) 69.7508 + 28.8917i 2.22358 + 0.921035i
\(985\) 64.8096 2.06500
\(986\) 44.5572 + 12.3208i 1.41899 + 0.392374i
\(987\) 96.6425i 3.07617i
\(988\) −0.197517 + 0.476849i −0.00628387 + 0.0151706i
\(989\) 11.8416 17.7222i 0.376541 0.563534i
\(990\) −145.777 46.6182i −4.63310 1.48162i
\(991\) −40.5803 + 8.07192i −1.28908 + 0.256413i −0.791587 0.611057i \(-0.790745\pi\)
−0.497489 + 0.867470i \(0.665745\pi\)
\(992\) 0.856759 + 1.28223i 0.0272021 + 0.0407109i
\(993\) 35.7863 + 7.11833i 1.13564 + 0.225893i
\(994\) −5.72829 + 2.37274i −0.181690 + 0.0752586i
\(995\) −0.231162 0.558073i −0.00732831 0.0176921i
\(996\) 115.891 + 23.0522i 3.67215 + 0.730436i
\(997\) −48.2791 + 32.2591i −1.52902 + 1.02166i −0.546074 + 0.837737i \(0.683878\pi\)
−0.982942 + 0.183918i \(0.941122\pi\)
\(998\) −70.1517 + 13.9540i −2.22061 + 0.441707i
\(999\) 79.7507 79.7507i 2.52320 2.52320i
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 187.2.m.a.10.15 yes 128
11.10 odd 2 inner 187.2.m.a.10.2 128
17.12 odd 16 inner 187.2.m.a.131.2 yes 128
187.131 even 16 inner 187.2.m.a.131.15 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.m.a.10.2 128 11.10 odd 2 inner
187.2.m.a.10.15 yes 128 1.1 even 1 trivial
187.2.m.a.131.2 yes 128 17.12 odd 16 inner
187.2.m.a.131.15 yes 128 187.131 even 16 inner