Properties

Label 336.3.bv.a.325.20
Level $336$
Weight $3$
Character 336.325
Analytic conductor $9.155$
Analytic rank $0$
Dimension $256$
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] = [336,3,Mod(61,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 10]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.61");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.bv (of order \(12\), 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: \(9.15533688251\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(64\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 325.20
Character \(\chi\) \(=\) 336.325
Dual form 336.3.bv.a.61.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.08869 + 1.67772i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-1.62949 - 3.65305i) q^{4} +(4.74630 + 1.27177i) q^{5} +(1.06932 - 3.29493i) q^{6} +(-6.99296 - 0.313761i) q^{7} +(7.90281 + 1.24322i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-1.08869 + 1.67772i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-1.62949 - 3.65305i) q^{4} +(4.74630 + 1.27177i) q^{5} +(1.06932 - 3.29493i) q^{6} +(-6.99296 - 0.313761i) q^{7} +(7.90281 + 1.24322i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-7.30094 + 6.57840i) q^{10} +(-0.461633 + 0.123694i) q^{11} +(4.36381 + 5.38119i) q^{12} +(5.87506 + 5.87506i) q^{13} +(8.13960 - 11.3907i) q^{14} -8.51084 q^{15} +(-10.6895 + 11.9052i) q^{16} +(-3.44573 - 1.98939i) q^{17} +(-0.311929 + 5.99189i) q^{18} +(-6.74992 + 25.1911i) q^{19} +(-3.08823 - 19.4108i) q^{20} +(11.8401 - 2.60993i) q^{21} +(0.295053 - 0.909156i) q^{22} +(-22.3169 + 12.8847i) q^{23} +(-13.7790 + 1.46279i) q^{24} +(-0.740644 - 0.427611i) q^{25} +(-16.2528 + 3.46056i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(10.2488 + 26.0569i) q^{28} +(-1.30568 + 1.30568i) q^{29} +(9.26569 - 14.2788i) q^{30} +(-7.89680 - 4.55922i) q^{31} +(-8.33603 - 30.8952i) q^{32} +(0.716877 - 0.413889i) q^{33} +(7.08899 - 3.61513i) q^{34} +(-32.7917 - 10.3826i) q^{35} +(-9.71312 - 7.04666i) q^{36} +(-2.45126 + 9.14823i) q^{37} +(-34.9149 - 38.7498i) q^{38} +(-12.4629 - 7.19544i) q^{39} +(35.9280 + 15.9512i) q^{40} -36.6020 q^{41} +(-8.51153 + 22.7058i) q^{42} +(-44.4923 - 44.4923i) q^{43} +(1.20409 + 1.48481i) q^{44} +(14.2389 - 3.81530i) q^{45} +(2.67940 - 51.4690i) q^{46} +(-29.6352 + 17.1099i) q^{47} +(12.5469 - 24.7098i) q^{48} +(48.8031 + 4.38824i) q^{49} +(1.52375 - 0.777056i) q^{50} +(6.65664 + 1.78364i) q^{51} +(11.8885 - 31.0352i) q^{52} +(-64.8766 + 17.3836i) q^{53} +(-2.16422 - 10.1645i) q^{54} -2.34836 q^{55} +(-54.8740 - 11.1734i) q^{56} -45.1714i q^{57} +(-0.769078 - 3.61204i) q^{58} +(-9.62420 - 35.9180i) q^{59} +(13.8683 + 31.0905i) q^{60} +(5.04685 - 18.8351i) q^{61} +(16.2463 - 8.28503i) q^{62} +(-18.6389 + 9.67427i) q^{63} +(60.9088 + 19.6498i) q^{64} +(20.4131 + 35.3565i) q^{65} +(-0.0860692 + 1.65332i) q^{66} +(27.3644 + 102.126i) q^{67} +(-1.65256 + 15.8291i) q^{68} +(31.5609 - 31.5609i) q^{69} +(53.1193 - 43.7118i) q^{70} -36.6862i q^{71} +(22.3969 - 8.62424i) q^{72} +(-35.8516 + 62.0967i) q^{73} +(-12.6795 - 14.0722i) q^{74} +(1.43081 + 0.383385i) q^{75} +(103.023 - 16.3908i) q^{76} +(3.26699 - 0.720147i) q^{77} +(25.6402 - 13.0756i) q^{78} +(31.4824 + 54.5291i) q^{79} +(-65.8763 + 42.9112i) q^{80} +(4.50000 - 7.79423i) q^{81} +(39.8484 - 61.4079i) q^{82} +(-1.88968 - 1.88968i) q^{83} +(-28.8276 - 38.9996i) q^{84} +(-13.8244 - 13.8244i) q^{85} +(123.084 - 26.2072i) q^{86} +(1.59912 - 2.76976i) q^{87} +(-3.80198 + 0.403621i) q^{88} +(-3.53701 - 6.12629i) q^{89} +(-9.10080 + 28.0426i) q^{90} +(-39.2407 - 42.9274i) q^{91} +(83.4336 + 60.5293i) q^{92} +(15.2554 + 4.08768i) q^{93} +(3.55804 - 68.3470i) q^{94} +(-64.0743 + 110.980i) q^{95} +(27.7964 + 47.9517i) q^{96} +154.578i q^{97} +(-60.4939 + 77.1005i) q^{98} +(-1.01382 + 1.01382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 12 q^{4} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50} + 720 q^{52} + 160 q^{53} - 56 q^{56} - 312 q^{58} + 384 q^{59} + 72 q^{60} - 96 q^{64} - 216 q^{66} - 320 q^{67} - 780 q^{68} - 828 q^{70} + 60 q^{72} - 88 q^{74} - 72 q^{78} - 612 q^{80} + 1152 q^{81} + 780 q^{82} - 72 q^{84} - 212 q^{86} - 464 q^{88} - 480 q^{91} - 488 q^{92} - 612 q^{94} + 768 q^{95} - 900 q^{96} - 196 q^{98} + 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08869 + 1.67772i −0.544347 + 0.838860i
\(3\) −1.67303 + 0.448288i −0.557678 + 0.149429i
\(4\) −1.62949 3.65305i −0.407373 0.913262i
\(5\) 4.74630 + 1.27177i 0.949260 + 0.254354i 0.700048 0.714095i \(-0.253162\pi\)
0.249212 + 0.968449i \(0.419828\pi\)
\(6\) 1.06932 3.29493i 0.178220 0.549155i
\(7\) −6.99296 0.313761i −0.998995 0.0448230i
\(8\) 7.90281 + 1.24322i 0.987851 + 0.155402i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −7.30094 + 6.57840i −0.730094 + 0.657840i
\(11\) −0.461633 + 0.123694i −0.0419666 + 0.0112449i −0.279741 0.960075i \(-0.590249\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(12\) 4.36381 + 5.38119i 0.363651 + 0.448432i
\(13\) 5.87506 + 5.87506i 0.451927 + 0.451927i 0.895994 0.444066i \(-0.146465\pi\)
−0.444066 + 0.895994i \(0.646465\pi\)
\(14\) 8.13960 11.3907i 0.581400 0.813618i
\(15\) −8.51084 −0.567389
\(16\) −10.6895 + 11.9052i −0.668095 + 0.744076i
\(17\) −3.44573 1.98939i −0.202690 0.117023i 0.395220 0.918587i \(-0.370669\pi\)
−0.597910 + 0.801564i \(0.704002\pi\)
\(18\) −0.311929 + 5.99189i −0.0173294 + 0.332883i
\(19\) −6.74992 + 25.1911i −0.355259 + 1.32584i 0.524899 + 0.851164i \(0.324103\pi\)
−0.880158 + 0.474680i \(0.842564\pi\)
\(20\) −3.08823 19.4108i −0.154412 0.970540i
\(21\) 11.8401 2.60993i 0.563815 0.124282i
\(22\) 0.295053 0.909156i 0.0134115 0.0413253i
\(23\) −22.3169 + 12.8847i −0.970301 + 0.560203i −0.899328 0.437275i \(-0.855944\pi\)
−0.0709729 + 0.997478i \(0.522610\pi\)
\(24\) −13.7790 + 1.46279i −0.574124 + 0.0609495i
\(25\) −0.740644 0.427611i −0.0296257 0.0171044i
\(26\) −16.2528 + 3.46056i −0.625109 + 0.133099i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 10.2488 + 26.0569i 0.366028 + 0.930604i
\(29\) −1.30568 + 1.30568i −0.0450233 + 0.0450233i −0.729260 0.684237i \(-0.760136\pi\)
0.684237 + 0.729260i \(0.260136\pi\)
\(30\) 9.26569 14.2788i 0.308856 0.475960i
\(31\) −7.89680 4.55922i −0.254735 0.147072i 0.367195 0.930144i \(-0.380318\pi\)
−0.621931 + 0.783072i \(0.713651\pi\)
\(32\) −8.33603 30.8952i −0.260501 0.965474i
\(33\) 0.716877 0.413889i 0.0217235 0.0125421i
\(34\) 7.08899 3.61513i 0.208500 0.106327i
\(35\) −32.7917 10.3826i −0.936906 0.296647i
\(36\) −9.71312 7.04666i −0.269809 0.195741i
\(37\) −2.45126 + 9.14823i −0.0662503 + 0.247250i −0.991107 0.133066i \(-0.957518\pi\)
0.924857 + 0.380315i \(0.124185\pi\)
\(38\) −34.9149 38.7498i −0.918814 1.01973i
\(39\) −12.4629 7.19544i −0.319561 0.184499i
\(40\) 35.9280 + 15.9512i 0.898201 + 0.398781i
\(41\) −36.6020 −0.892731 −0.446366 0.894851i \(-0.647282\pi\)
−0.446366 + 0.894851i \(0.647282\pi\)
\(42\) −8.51153 + 22.7058i −0.202655 + 0.540615i
\(43\) −44.4923 44.4923i −1.03470 1.03470i −0.999376 0.0353291i \(-0.988752\pi\)
−0.0353291 0.999376i \(-0.511248\pi\)
\(44\) 1.20409 + 1.48481i 0.0273656 + 0.0337457i
\(45\) 14.2389 3.81530i 0.316420 0.0847845i
\(46\) 2.67940 51.4690i 0.0582478 1.11889i
\(47\) −29.6352 + 17.1099i −0.630536 + 0.364040i −0.780960 0.624582i \(-0.785270\pi\)
0.150424 + 0.988622i \(0.451936\pi\)
\(48\) 12.5469 24.7098i 0.261395 0.514788i
\(49\) 48.8031 + 4.38824i 0.995982 + 0.0895559i
\(50\) 1.52375 0.777056i 0.0304749 0.0155411i
\(51\) 6.65664 + 1.78364i 0.130522 + 0.0349734i
\(52\) 11.8885 31.0352i 0.228625 0.596831i
\(53\) −64.8766 + 17.3836i −1.22409 + 0.327993i −0.812274 0.583276i \(-0.801771\pi\)
−0.411812 + 0.911269i \(0.635104\pi\)
\(54\) −2.16422 10.1645i −0.0400782 0.188231i
\(55\) −2.34836 −0.0426975
\(56\) −54.8740 11.1734i −0.979893 0.199525i
\(57\) 45.1714i 0.792480i
\(58\) −0.769078 3.61204i −0.0132600 0.0622765i
\(59\) −9.62420 35.9180i −0.163122 0.608779i −0.998272 0.0587577i \(-0.981286\pi\)
0.835150 0.550022i \(-0.185381\pi\)
\(60\) 13.8683 + 31.0905i 0.231139 + 0.518175i
\(61\) 5.04685 18.8351i 0.0827352 0.308772i −0.912140 0.409878i \(-0.865571\pi\)
0.994876 + 0.101106i \(0.0322380\pi\)
\(62\) 16.2463 8.28503i 0.262037 0.133629i
\(63\) −18.6389 + 9.67427i −0.295855 + 0.153560i
\(64\) 60.9088 + 19.6498i 0.951700 + 0.307029i
\(65\) 20.4131 + 35.3565i 0.314047 + 0.543946i
\(66\) −0.0860692 + 1.65332i −0.00130408 + 0.0250503i
\(67\) 27.3644 + 102.126i 0.408425 + 1.52426i 0.797651 + 0.603119i \(0.206076\pi\)
−0.389226 + 0.921142i \(0.627258\pi\)
\(68\) −1.65256 + 15.8291i −0.0243023 + 0.232781i
\(69\) 31.5609 31.5609i 0.457404 0.457404i
\(70\) 53.1193 43.7118i 0.758847 0.624454i
\(71\) 36.6862i 0.516707i −0.966050 0.258353i \(-0.916820\pi\)
0.966050 0.258353i \(-0.0831799\pi\)
\(72\) 22.3969 8.62424i 0.311068 0.119781i
\(73\) −35.8516 + 62.0967i −0.491117 + 0.850640i −0.999948 0.0102268i \(-0.996745\pi\)
0.508831 + 0.860867i \(0.330078\pi\)
\(74\) −12.6795 14.0722i −0.171345 0.190164i
\(75\) 1.43081 + 0.383385i 0.0190775 + 0.00511180i
\(76\) 103.023 16.3908i 1.35557 0.215669i
\(77\) 3.26699 0.720147i 0.0424285 0.00935256i
\(78\) 25.6402 13.0756i 0.328721 0.167636i
\(79\) 31.4824 + 54.5291i 0.398512 + 0.690242i 0.993543 0.113461i \(-0.0361935\pi\)
−0.595031 + 0.803703i \(0.702860\pi\)
\(80\) −65.8763 + 42.9112i −0.823454 + 0.536390i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 39.8484 61.4079i 0.485955 0.748877i
\(83\) −1.88968 1.88968i −0.0227673 0.0227673i 0.695632 0.718399i \(-0.255125\pi\)
−0.718399 + 0.695632i \(0.755125\pi\)
\(84\) −28.8276 38.9996i −0.343185 0.464281i
\(85\) −13.8244 13.8244i −0.162640 0.162640i
\(86\) 123.084 26.2072i 1.43121 0.304734i
\(87\) 1.59912 2.76976i 0.0183807 0.0318363i
\(88\) −3.80198 + 0.403621i −0.0432043 + 0.00458661i
\(89\) −3.53701 6.12629i −0.0397417 0.0688347i 0.845470 0.534022i \(-0.179320\pi\)
−0.885212 + 0.465188i \(0.845987\pi\)
\(90\) −9.10080 + 28.0426i −0.101120 + 0.311584i
\(91\) −39.2407 42.9274i −0.431216 0.471730i
\(92\) 83.4336 + 60.5293i 0.906887 + 0.657927i
\(93\) 15.2554 + 4.08768i 0.164037 + 0.0439536i
\(94\) 3.55804 68.3470i 0.0378515 0.727096i
\(95\) −64.0743 + 110.980i −0.674467 + 1.16821i
\(96\) 27.7964 + 47.9517i 0.289546 + 0.499496i
\(97\) 154.578i 1.59359i 0.604251 + 0.796794i \(0.293472\pi\)
−0.604251 + 0.796794i \(0.706528\pi\)
\(98\) −60.4939 + 77.1005i −0.617284 + 0.786740i
\(99\) −1.01382 + 1.01382i −0.0102406 + 0.0102406i
\(100\) −0.355210 + 3.40239i −0.00355210 + 0.0340239i
\(101\) −1.58012 5.89707i −0.0156447 0.0583868i 0.957662 0.287894i \(-0.0929552\pi\)
−0.973307 + 0.229507i \(0.926288\pi\)
\(102\) −10.2395 + 9.22615i −0.100387 + 0.0904524i
\(103\) 31.4369 + 54.4503i 0.305213 + 0.528644i 0.977309 0.211820i \(-0.0679392\pi\)
−0.672096 + 0.740464i \(0.734606\pi\)
\(104\) 39.1255 + 53.7334i 0.376206 + 0.516668i
\(105\) 59.5160 + 2.67037i 0.566819 + 0.0254321i
\(106\) 41.4659 127.770i 0.391187 1.20538i
\(107\) −18.6087 + 69.4487i −0.173913 + 0.649053i 0.822821 + 0.568301i \(0.192399\pi\)
−0.996734 + 0.0807525i \(0.974268\pi\)
\(108\) 19.4093 + 7.43502i 0.179716 + 0.0688428i
\(109\) 35.1390 + 131.140i 0.322376 + 1.20312i 0.916924 + 0.399063i \(0.130664\pi\)
−0.594548 + 0.804060i \(0.702669\pi\)
\(110\) 2.55665 3.93989i 0.0232422 0.0358172i
\(111\) 16.4042i 0.147785i
\(112\) 78.4868 79.8988i 0.700775 0.713383i
\(113\) 140.502 1.24338 0.621690 0.783263i \(-0.286446\pi\)
0.621690 + 0.783263i \(0.286446\pi\)
\(114\) 75.7849 + 49.1778i 0.664780 + 0.431384i
\(115\) −122.309 + 32.7726i −1.06356 + 0.284979i
\(116\) 6.89728 + 2.64211i 0.0594593 + 0.0227768i
\(117\) 24.0764 + 6.45126i 0.205781 + 0.0551390i
\(118\) 70.7381 + 22.9570i 0.599476 + 0.194551i
\(119\) 23.4717 + 14.9929i 0.197241 + 0.125991i
\(120\) −67.2595 10.5808i −0.560496 0.0881736i
\(121\) −104.591 + 60.3858i −0.864391 + 0.499056i
\(122\) 26.1056 + 28.9729i 0.213980 + 0.237482i
\(123\) 61.2363 16.4082i 0.497856 0.133400i
\(124\) −3.78727 + 36.2766i −0.0305425 + 0.292553i
\(125\) −89.8349 89.8349i −0.718679 0.718679i
\(126\) 4.06133 41.8032i 0.0322327 0.331771i
\(127\) −152.373 −1.19979 −0.599894 0.800080i \(-0.704790\pi\)
−0.599894 + 0.800080i \(0.704790\pi\)
\(128\) −99.2780 + 80.7953i −0.775609 + 0.631213i
\(129\) 94.3824 + 54.4917i 0.731647 + 0.422416i
\(130\) −81.5419 4.24495i −0.627246 0.0326535i
\(131\) 58.9186 219.887i 0.449761 1.67853i −0.253291 0.967390i \(-0.581513\pi\)
0.703051 0.711139i \(-0.251820\pi\)
\(132\) −2.68010 1.94436i −0.0203038 0.0147300i
\(133\) 55.1059 174.042i 0.414330 1.30859i
\(134\) −201.130 65.2735i −1.50097 0.487116i
\(135\) −22.1118 + 12.7663i −0.163791 + 0.0945648i
\(136\) −24.7577 20.0056i −0.182042 0.147100i
\(137\) 29.6539 + 17.1207i 0.216452 + 0.124969i 0.604306 0.796752i \(-0.293450\pi\)
−0.387854 + 0.921721i \(0.626784\pi\)
\(138\) 18.5902 + 87.3105i 0.134712 + 0.632685i
\(139\) 24.5128 24.5128i 0.176351 0.176351i −0.613412 0.789763i \(-0.710203\pi\)
0.789763 + 0.613412i \(0.210203\pi\)
\(140\) 15.5055 + 136.708i 0.110754 + 0.976486i
\(141\) 41.9105 41.9105i 0.297237 0.297237i
\(142\) 61.5492 + 39.9400i 0.433445 + 0.281268i
\(143\) −3.43883 1.98541i −0.0240478 0.0138840i
\(144\) −9.91433 + 46.9649i −0.0688495 + 0.326145i
\(145\) −7.85764 + 4.53661i −0.0541907 + 0.0312870i
\(146\) −65.1496 127.753i −0.446230 0.875022i
\(147\) −83.6164 + 14.5362i −0.568819 + 0.0988855i
\(148\) 37.4132 5.95240i 0.252792 0.0402189i
\(149\) 18.3741 68.5730i 0.123316 0.460222i −0.876458 0.481478i \(-0.840100\pi\)
0.999774 + 0.0212565i \(0.00676668\pi\)
\(150\) −2.20093 + 1.98312i −0.0146729 + 0.0132208i
\(151\) 192.045 + 110.877i 1.27182 + 0.734286i 0.975330 0.220750i \(-0.0708505\pi\)
0.296490 + 0.955036i \(0.404184\pi\)
\(152\) −84.6613 + 190.688i −0.556982 + 1.25453i
\(153\) −11.9364 −0.0780155
\(154\) −2.34855 + 6.26512i −0.0152503 + 0.0406826i
\(155\) −31.6823 31.6823i −0.204402 0.204402i
\(156\) −5.97715 + 57.2524i −0.0383150 + 0.367003i
\(157\) 245.770 65.8539i 1.56542 0.419452i 0.631043 0.775748i \(-0.282627\pi\)
0.934373 + 0.356296i \(0.115961\pi\)
\(158\) −125.759 6.54684i −0.795945 0.0414357i
\(159\) 100.748 58.1668i 0.633634 0.365829i
\(160\) −0.273851 157.239i −0.00171157 0.982745i
\(161\) 160.104 83.0999i 0.994436 0.516149i
\(162\) 8.17741 + 16.0353i 0.0504779 + 0.0989831i
\(163\) −242.427 64.9582i −1.48728 0.398516i −0.578464 0.815708i \(-0.696348\pi\)
−0.908819 + 0.417191i \(0.863014\pi\)
\(164\) 59.6426 + 133.709i 0.363675 + 0.815297i
\(165\) 3.92888 1.05274i 0.0238114 0.00638025i
\(166\) 5.22765 1.11307i 0.0314919 0.00670527i
\(167\) 268.936 1.61040 0.805199 0.593005i \(-0.202058\pi\)
0.805199 + 0.593005i \(0.202058\pi\)
\(168\) 96.8149 5.90592i 0.576279 0.0351543i
\(169\) 99.9674i 0.591523i
\(170\) 38.2441 8.14296i 0.224965 0.0478998i
\(171\) 20.2498 + 75.5732i 0.118420 + 0.441948i
\(172\) −90.0327 + 235.032i −0.523446 + 1.36647i
\(173\) 37.1536 138.659i 0.214760 0.801497i −0.771490 0.636241i \(-0.780488\pi\)
0.986251 0.165256i \(-0.0528450\pi\)
\(174\) 2.90592 + 5.69829i 0.0167007 + 0.0327488i
\(175\) 5.04513 + 3.22265i 0.0288293 + 0.0184152i
\(176\) 3.46203 6.81808i 0.0196706 0.0387391i
\(177\) 32.2032 + 55.7776i 0.181939 + 0.315127i
\(178\) 14.1289 + 0.735530i 0.0793760 + 0.00413219i
\(179\) −51.7977 193.312i −0.289373 1.07995i −0.945584 0.325377i \(-0.894509\pi\)
0.656211 0.754577i \(-0.272158\pi\)
\(180\) −37.1397 45.7984i −0.206331 0.254436i
\(181\) 242.030 242.030i 1.33718 1.33718i 0.438403 0.898779i \(-0.355544\pi\)
0.898779 0.438403i \(-0.144456\pi\)
\(182\) 114.741 19.1001i 0.630447 0.104946i
\(183\) 33.7742i 0.184558i
\(184\) −192.385 + 74.0804i −1.04557 + 0.402611i
\(185\) −23.2689 + 40.3028i −0.125778 + 0.217853i
\(186\) −23.4665 + 21.1441i −0.126164 + 0.113678i
\(187\) 1.83674 + 0.492153i 0.00982214 + 0.00263184i
\(188\) 110.794 + 80.3783i 0.589327 + 0.427544i
\(189\) 26.8466 24.5410i 0.142046 0.129846i
\(190\) −116.436 228.322i −0.612822 1.20170i
\(191\) 110.575 + 191.522i 0.578928 + 1.00273i 0.995603 + 0.0936773i \(0.0298622\pi\)
−0.416674 + 0.909056i \(0.636804\pi\)
\(192\) −110.711 5.57014i −0.576621 0.0290111i
\(193\) −83.4337 + 144.511i −0.432299 + 0.748763i −0.997071 0.0764836i \(-0.975631\pi\)
0.564772 + 0.825247i \(0.308964\pi\)
\(194\) −259.339 168.288i −1.33680 0.867464i
\(195\) −50.0016 50.0016i −0.256419 0.256419i
\(196\) −63.4938 185.431i −0.323948 0.946075i
\(197\) −11.9643 11.9643i −0.0607327 0.0607327i 0.676088 0.736821i \(-0.263674\pi\)
−0.736821 + 0.676088i \(0.763674\pi\)
\(198\) −0.597165 2.80464i −0.00301599 0.0141648i
\(199\) 62.2423 107.807i 0.312776 0.541743i −0.666187 0.745785i \(-0.732075\pi\)
0.978962 + 0.204042i \(0.0654079\pi\)
\(200\) −5.32155 4.30011i −0.0266078 0.0215005i
\(201\) −91.5632 158.592i −0.455538 0.789016i
\(202\) 11.6139 + 3.76911i 0.0574945 + 0.0186590i
\(203\) 9.54021 8.72087i 0.0469961 0.0429600i
\(204\) −4.33122 27.2235i −0.0212315 0.133448i
\(205\) −173.724 46.5492i −0.847435 0.227069i
\(206\) −125.578 6.53738i −0.609600 0.0317348i
\(207\) −38.6540 + 66.9508i −0.186734 + 0.323434i
\(208\) −132.745 + 7.14236i −0.638199 + 0.0343383i
\(209\) 12.4640i 0.0596361i
\(210\) −69.2748 + 96.9440i −0.329880 + 0.461638i
\(211\) −272.705 + 272.705i −1.29244 + 1.29244i −0.359170 + 0.933272i \(0.616940\pi\)
−0.933272 + 0.359170i \(0.883060\pi\)
\(212\) 169.219 + 208.671i 0.798203 + 0.984296i
\(213\) 16.4460 + 61.3772i 0.0772111 + 0.288156i
\(214\) −96.2563 106.829i −0.449796 0.499199i
\(215\) −154.590 267.758i −0.719023 1.24539i
\(216\) −33.6047 + 24.4689i −0.155577 + 0.113282i
\(217\) 53.7915 + 34.3602i 0.247887 + 0.158342i
\(218\) −258.273 83.8184i −1.18474 0.384488i
\(219\) 32.1436 119.962i 0.146775 0.547770i
\(220\) 3.82663 + 8.57867i 0.0173938 + 0.0389940i
\(221\) −8.55607 31.9317i −0.0387152 0.144487i
\(222\) 27.5216 + 17.8591i 0.123971 + 0.0804464i
\(223\) 263.287i 1.18066i −0.807163 0.590329i \(-0.798998\pi\)
0.807163 0.590329i \(-0.201002\pi\)
\(224\) 48.5999 + 218.664i 0.216964 + 0.976180i
\(225\) −2.56566 −0.0114030
\(226\) −152.964 + 235.723i −0.676830 + 1.04302i
\(227\) −317.145 + 84.9789i −1.39712 + 0.374356i −0.877308 0.479927i \(-0.840663\pi\)
−0.519808 + 0.854283i \(0.673997\pi\)
\(228\) −165.013 + 73.6064i −0.723742 + 0.322835i
\(229\) −59.1886 15.8595i −0.258466 0.0692556i 0.127259 0.991869i \(-0.459382\pi\)
−0.385725 + 0.922614i \(0.626049\pi\)
\(230\) 78.1739 240.880i 0.339886 1.04730i
\(231\) −5.14296 + 2.66938i −0.0222639 + 0.0115558i
\(232\) −11.9417 + 8.69526i −0.0514730 + 0.0374796i
\(233\) −301.116 + 173.849i −1.29234 + 0.746134i −0.979069 0.203529i \(-0.934759\pi\)
−0.313273 + 0.949663i \(0.601425\pi\)
\(234\) −37.0353 + 33.3701i −0.158270 + 0.142607i
\(235\) −162.417 + 43.5196i −0.691138 + 0.185190i
\(236\) −115.528 + 93.6857i −0.489524 + 0.396973i
\(237\) −77.1158 77.1158i −0.325383 0.325383i
\(238\) −50.7074 + 23.0563i −0.213056 + 0.0968750i
\(239\) 175.958 0.736225 0.368113 0.929781i \(-0.380004\pi\)
0.368113 + 0.929781i \(0.380004\pi\)
\(240\) 90.9767 101.323i 0.379070 0.422181i
\(241\) 59.9919 + 34.6363i 0.248929 + 0.143719i 0.619274 0.785175i \(-0.287427\pi\)
−0.370345 + 0.928894i \(0.620760\pi\)
\(242\) 12.5574 241.217i 0.0518900 0.996763i
\(243\) −4.03459 + 15.0573i −0.0166032 + 0.0619642i
\(244\) −77.0293 + 12.2553i −0.315694 + 0.0502265i
\(245\) 226.053 + 82.8941i 0.922667 + 0.338343i
\(246\) −39.1392 + 120.601i −0.159102 + 0.490248i
\(247\) −187.655 + 108.343i −0.759737 + 0.438634i
\(248\) −56.7388 45.8481i −0.228786 0.184871i
\(249\) 4.00863 + 2.31438i 0.0160989 + 0.00929470i
\(250\) 248.520 52.9151i 0.994082 0.211661i
\(251\) 286.303 286.303i 1.14065 1.14065i 0.152315 0.988332i \(-0.451327\pi\)
0.988332 0.152315i \(-0.0486730\pi\)
\(252\) 65.7125 + 52.3246i 0.260764 + 0.207637i
\(253\) 8.70847 8.70847i 0.0344208 0.0344208i
\(254\) 165.888 255.639i 0.653100 1.00645i
\(255\) 29.3261 + 16.9314i 0.115004 + 0.0663977i
\(256\) −27.4686 254.522i −0.107299 0.994227i
\(257\) −209.251 + 120.811i −0.814208 + 0.470083i −0.848415 0.529332i \(-0.822443\pi\)
0.0342070 + 0.999415i \(0.489109\pi\)
\(258\) −194.175 + 99.0225i −0.752618 + 0.383808i
\(259\) 20.0119 63.2042i 0.0772662 0.244032i
\(260\) 95.8960 132.183i 0.368831 0.508397i
\(261\) −1.43373 + 5.35076i −0.00549322 + 0.0205010i
\(262\) 304.765 + 338.239i 1.16323 + 1.29099i
\(263\) 322.487 + 186.188i 1.22619 + 0.707939i 0.966230 0.257681i \(-0.0829584\pi\)
0.259957 + 0.965620i \(0.416292\pi\)
\(264\) 6.17989 2.37965i 0.0234087 0.00901383i
\(265\) −330.032 −1.24540
\(266\) 232.001 + 281.931i 0.872183 + 1.05989i
\(267\) 8.66388 + 8.66388i 0.0324490 + 0.0324490i
\(268\) 328.479 266.376i 1.22567 0.993941i
\(269\) −286.930 + 76.8826i −1.06665 + 0.285809i −0.749117 0.662437i \(-0.769522\pi\)
−0.317536 + 0.948246i \(0.602855\pi\)
\(270\) 2.65477 50.9960i 0.00983249 0.188874i
\(271\) −2.25484 + 1.30184i −0.00832046 + 0.00480382i −0.504154 0.863614i \(-0.668196\pi\)
0.495834 + 0.868417i \(0.334862\pi\)
\(272\) 60.5174 19.7566i 0.222490 0.0726344i
\(273\) 84.8948 + 54.2279i 0.310970 + 0.198637i
\(274\) −61.0077 + 31.1118i −0.222656 + 0.113547i
\(275\) 0.394799 + 0.105786i 0.00143563 + 0.000384676i
\(276\) −166.722 63.8652i −0.604064 0.231396i
\(277\) 229.376 61.4611i 0.828072 0.221881i 0.180200 0.983630i \(-0.442326\pi\)
0.647873 + 0.761749i \(0.275659\pi\)
\(278\) 14.4387 + 67.8126i 0.0519377 + 0.243930i
\(279\) −27.3553 −0.0980477
\(280\) −246.239 122.819i −0.879424 0.438640i
\(281\) 486.481i 1.73125i 0.500693 + 0.865625i \(0.333078\pi\)
−0.500693 + 0.865625i \(0.666922\pi\)
\(282\) 24.6864 + 115.942i 0.0875404 + 0.411141i
\(283\) 114.267 + 426.452i 0.403772 + 1.50690i 0.806310 + 0.591493i \(0.201461\pi\)
−0.402538 + 0.915403i \(0.631872\pi\)
\(284\) −134.016 + 59.7798i −0.471889 + 0.210492i
\(285\) 57.4475 214.397i 0.201570 0.752270i
\(286\) 7.07480 3.60789i 0.0247371 0.0126150i
\(287\) 255.956 + 11.4843i 0.891834 + 0.0400149i
\(288\) −68.0004 67.7639i −0.236112 0.235291i
\(289\) −136.585 236.572i −0.472611 0.818587i
\(290\) 0.943400 18.1219i 0.00325310 0.0624894i
\(291\) −69.2954 258.614i −0.238129 0.888708i
\(292\) 285.262 + 29.7813i 0.976925 + 0.101991i
\(293\) 200.464 200.464i 0.684178 0.684178i −0.276761 0.960939i \(-0.589261\pi\)
0.960939 + 0.276761i \(0.0892611\pi\)
\(294\) 66.6450 156.110i 0.226684 0.530988i
\(295\) 182.717i 0.619381i
\(296\) −30.7451 + 69.2493i −0.103869 + 0.233950i
\(297\) 1.24167 2.15063i 0.00418070 0.00724118i
\(298\) 95.0426 + 105.482i 0.318935 + 0.353965i
\(299\) −206.811 55.4149i −0.691677 0.185334i
\(300\) −0.930974 5.85155i −0.00310325 0.0195052i
\(301\) 297.173 + 325.093i 0.987286 + 1.08004i
\(302\) −395.099 + 201.486i −1.30827 + 0.667173i
\(303\) 5.28717 + 9.15764i 0.0174494 + 0.0302232i
\(304\) −227.752 349.639i −0.749183 1.15013i
\(305\) 47.9078 82.9787i 0.157075 0.272061i
\(306\) 12.9950 20.0259i 0.0424675 0.0654441i
\(307\) 116.965 + 116.965i 0.380993 + 0.380993i 0.871460 0.490467i \(-0.163174\pi\)
−0.490467 + 0.871460i \(0.663174\pi\)
\(308\) −7.95427 10.7610i −0.0258256 0.0349384i
\(309\) −77.0043 77.0043i −0.249205 0.249205i
\(310\) 87.6464 18.6617i 0.282730 0.0601992i
\(311\) 279.510 484.126i 0.898747 1.55667i 0.0696487 0.997572i \(-0.477812\pi\)
0.829098 0.559103i \(-0.188855\pi\)
\(312\) −89.5462 72.3583i −0.287007 0.231918i
\(313\) −19.3439 33.5046i −0.0618016 0.107044i 0.833469 0.552566i \(-0.186351\pi\)
−0.895271 + 0.445522i \(0.853018\pi\)
\(314\) −157.084 + 484.029i −0.500268 + 1.54149i
\(315\) −100.769 + 22.2127i −0.319902 + 0.0705164i
\(316\) 147.897 203.862i 0.468029 0.645131i
\(317\) −48.1007 12.8886i −0.151737 0.0406579i 0.182151 0.983271i \(-0.441694\pi\)
−0.333888 + 0.942613i \(0.608361\pi\)
\(318\) −12.0959 + 232.352i −0.0380375 + 0.730668i
\(319\) 0.441238 0.764247i 0.00138319 0.00239576i
\(320\) 264.102 + 170.726i 0.825318 + 0.533519i
\(321\) 124.532i 0.387950i
\(322\) −34.8859 + 359.080i −0.108341 + 1.11516i
\(323\) 73.3734 73.3734i 0.227162 0.227162i
\(324\) −35.8054 3.73808i −0.110510 0.0115373i
\(325\) −1.83909 6.86356i −0.00565872 0.0211186i
\(326\) 372.911 336.005i 1.14390 1.03069i
\(327\) −117.577 203.650i −0.359564 0.622782i
\(328\) −289.259 45.5043i −0.881886 0.138732i
\(329\) 212.606 110.350i 0.646220 0.335412i
\(330\) −2.51115 + 7.73768i −0.00760953 + 0.0234475i
\(331\) −96.0246 + 358.369i −0.290105 + 1.08269i 0.654923 + 0.755695i \(0.272701\pi\)
−0.945028 + 0.326990i \(0.893966\pi\)
\(332\) −3.82388 + 9.98233i −0.0115177 + 0.0300673i
\(333\) 7.35379 + 27.4447i 0.0220834 + 0.0824165i
\(334\) −292.789 + 451.200i −0.876615 + 1.35090i
\(335\) 519.520i 1.55081i
\(336\) −95.4933 + 168.858i −0.284206 + 0.502554i
\(337\) 219.472 0.651251 0.325626 0.945499i \(-0.394425\pi\)
0.325626 + 0.945499i \(0.394425\pi\)
\(338\) 167.717 + 108.834i 0.496205 + 0.321994i
\(339\) −235.064 + 62.9853i −0.693405 + 0.185797i
\(340\) −27.9745 + 73.0281i −0.0822780 + 0.214789i
\(341\) 4.20937 + 1.12790i 0.0123442 + 0.00330762i
\(342\) −148.836 48.3026i −0.435194 0.141236i
\(343\) −339.902 45.9993i −0.990967 0.134109i
\(344\) −296.301 406.928i −0.861339 1.18293i
\(345\) 189.936 109.659i 0.550538 0.317853i
\(346\) 192.182 + 213.290i 0.555440 + 0.616446i
\(347\) 278.183 74.5389i 0.801680 0.214809i 0.165358 0.986234i \(-0.447122\pi\)
0.636321 + 0.771424i \(0.280455\pi\)
\(348\) −12.7238 1.32836i −0.0365626 0.00381714i
\(349\) 215.487 + 215.487i 0.617442 + 0.617442i 0.944875 0.327433i \(-0.106183\pi\)
−0.327433 + 0.944875i \(0.606183\pi\)
\(350\) −10.8993 + 4.95583i −0.0311409 + 0.0141595i
\(351\) −43.1727 −0.122999
\(352\) 7.66974 + 13.2311i 0.0217890 + 0.0375884i
\(353\) −410.770 237.158i −1.16366 0.671837i −0.211478 0.977383i \(-0.567828\pi\)
−0.952177 + 0.305546i \(0.901161\pi\)
\(354\) −128.639 6.69673i −0.363386 0.0189173i
\(355\) 46.6563 174.124i 0.131426 0.490489i
\(356\) −16.6161 + 22.9036i −0.0466744 + 0.0643360i
\(357\) −45.9900 14.5615i −0.128824 0.0407886i
\(358\) 380.715 + 123.555i 1.06345 + 0.345126i
\(359\) 244.461 141.139i 0.680949 0.393146i −0.119263 0.992863i \(-0.538053\pi\)
0.800213 + 0.599716i \(0.204720\pi\)
\(360\) 117.271 12.4496i 0.325752 0.0345821i
\(361\) −276.393 159.575i −0.765630 0.442037i
\(362\) 142.562 + 669.555i 0.393818 + 1.84960i
\(363\) 147.914 147.914i 0.407478 0.407478i
\(364\) −92.8735 + 213.298i −0.255147 + 0.585984i
\(365\) −249.135 + 249.135i −0.682561 + 0.682561i
\(366\) −56.6636 36.7697i −0.154819 0.100464i
\(367\) 354.164 + 204.477i 0.965025 + 0.557157i 0.897716 0.440575i \(-0.145225\pi\)
0.0673088 + 0.997732i \(0.478559\pi\)
\(368\) 85.1620 403.419i 0.231419 1.09625i
\(369\) −95.0947 + 54.9030i −0.257709 + 0.148789i
\(370\) −42.2842 82.9161i −0.114282 0.224098i
\(371\) 459.134 101.207i 1.23756 0.272796i
\(372\) −9.92612 62.3897i −0.0266831 0.167714i
\(373\) −59.4166 + 221.746i −0.159294 + 0.594493i 0.839405 + 0.543506i \(0.182903\pi\)
−0.998699 + 0.0509870i \(0.983763\pi\)
\(374\) −2.82534 + 2.54573i −0.00755439 + 0.00680677i
\(375\) 190.569 + 110.025i 0.508183 + 0.293399i
\(376\) −255.473 + 98.3732i −0.679448 + 0.261631i
\(377\) −15.3418 −0.0406945
\(378\) 11.9451 + 71.7587i 0.0316008 + 0.189838i
\(379\) −128.585 128.585i −0.339273 0.339273i 0.516821 0.856094i \(-0.327115\pi\)
−0.856094 + 0.516821i \(0.827115\pi\)
\(380\) 509.824 + 53.2256i 1.34164 + 0.140067i
\(381\) 254.925 68.3069i 0.669094 0.179283i
\(382\) −441.703 22.9944i −1.15629 0.0601948i
\(383\) −12.1280 + 7.00211i −0.0316658 + 0.0182823i −0.515749 0.856740i \(-0.672486\pi\)
0.484084 + 0.875022i \(0.339153\pi\)
\(384\) 129.876 179.678i 0.338218 0.467912i
\(385\) 16.4220 + 0.736824i 0.0426546 + 0.00191383i
\(386\) −151.616 297.307i −0.392787 0.770225i
\(387\) −182.333 48.8559i −0.471144 0.126243i
\(388\) 564.681 251.884i 1.45536 0.649185i
\(389\) −446.158 + 119.548i −1.14694 + 0.307321i −0.781737 0.623608i \(-0.785666\pi\)
−0.365200 + 0.930929i \(0.618999\pi\)
\(390\) 138.325 29.4523i 0.354680 0.0755187i
\(391\) 102.531 0.262227
\(392\) 380.226 + 95.3523i 0.969965 + 0.243246i
\(393\) 394.291i 1.00329i
\(394\) 33.0983 7.04732i 0.0840059 0.0178866i
\(395\) 80.0766 + 298.850i 0.202726 + 0.756583i
\(396\) 5.35553 + 2.05151i 0.0135241 + 0.00518059i
\(397\) −107.803 + 402.325i −0.271543 + 1.01341i 0.686579 + 0.727055i \(0.259111\pi\)
−0.958123 + 0.286358i \(0.907555\pi\)
\(398\) 113.107 + 221.794i 0.284188 + 0.557271i
\(399\) −14.1730 + 315.882i −0.0355213 + 0.791684i
\(400\) 13.0079 4.24658i 0.0325198 0.0106164i
\(401\) 90.5199 + 156.785i 0.225735 + 0.390985i 0.956540 0.291602i \(-0.0941882\pi\)
−0.730804 + 0.682587i \(0.760855\pi\)
\(402\) 365.758 + 19.0408i 0.909845 + 0.0473652i
\(403\) −19.6085 73.1798i −0.0486563 0.181588i
\(404\) −18.9675 + 15.3815i −0.0469492 + 0.0380729i
\(405\) 31.2708 31.2708i 0.0772119 0.0772119i
\(406\) 4.24482 + 25.5002i 0.0104552 + 0.0628083i
\(407\) 4.52633i 0.0111212i
\(408\) 50.3887 + 22.3714i 0.123502 + 0.0548320i
\(409\) 136.865 237.058i 0.334634 0.579603i −0.648781 0.760976i \(-0.724721\pi\)
0.983414 + 0.181373i \(0.0580540\pi\)
\(410\) 267.229 240.783i 0.651778 0.587275i
\(411\) −57.2869 15.3500i −0.139384 0.0373479i
\(412\) 147.683 203.567i 0.358455 0.494094i
\(413\) 56.0320 + 254.193i 0.135671 + 0.615479i
\(414\) −70.2422 137.740i −0.169667 0.332704i
\(415\) −6.56577 11.3723i −0.0158211 0.0274030i
\(416\) 132.536 230.485i 0.318596 0.554051i
\(417\) −30.0219 + 51.9995i −0.0719950 + 0.124699i
\(418\) 20.9110 + 13.5694i 0.0500264 + 0.0324627i
\(419\) 451.112 + 451.112i 1.07664 + 1.07664i 0.996808 + 0.0798308i \(0.0254380\pi\)
0.0798308 + 0.996808i \(0.474562\pi\)
\(420\) −87.2258 221.766i −0.207681 0.528014i
\(421\) −118.463 118.463i −0.281384 0.281384i 0.552277 0.833661i \(-0.313759\pi\)
−0.833661 + 0.552277i \(0.813759\pi\)
\(422\) −160.631 754.416i −0.380642 1.78772i
\(423\) −51.3296 + 88.9056i −0.121347 + 0.210179i
\(424\) −534.319 + 56.7238i −1.26019 + 0.133783i
\(425\) 1.70137 + 2.94686i 0.00400323 + 0.00693380i
\(426\) −120.878 39.2292i −0.283752 0.0920874i
\(427\) −41.2022 + 130.130i −0.0964922 + 0.304753i
\(428\) 284.022 45.1875i 0.663603 0.105578i
\(429\) 6.64331 + 1.78007i 0.0154856 + 0.00414935i
\(430\) 617.524 + 32.1474i 1.43610 + 0.0747613i
\(431\) 130.773 226.505i 0.303417 0.525534i −0.673490 0.739196i \(-0.735206\pi\)
0.976908 + 0.213662i \(0.0685390\pi\)
\(432\) −4.46680 83.0184i −0.0103398 0.192172i
\(433\) 385.127i 0.889439i 0.895670 + 0.444720i \(0.146697\pi\)
−0.895670 + 0.444720i \(0.853303\pi\)
\(434\) −116.209 + 52.8395i −0.267763 + 0.121750i
\(435\) 11.1124 11.1124i 0.0255457 0.0255457i
\(436\) 421.804 342.057i 0.967439 0.784533i
\(437\) −173.941 649.157i −0.398035 1.48549i
\(438\) 166.268 + 184.529i 0.379606 + 0.421300i
\(439\) −9.23347 15.9928i −0.0210330 0.0364301i 0.855317 0.518104i \(-0.173362\pi\)
−0.876350 + 0.481674i \(0.840029\pi\)
\(440\) −18.5586 2.91952i −0.0421787 0.00663528i
\(441\) 133.377 61.8037i 0.302441 0.140144i
\(442\) 62.8874 + 20.4091i 0.142279 + 0.0461745i
\(443\) 161.761 603.700i 0.365149 1.36275i −0.502070 0.864827i \(-0.667428\pi\)
0.867219 0.497928i \(-0.165905\pi\)
\(444\) −59.9252 + 26.7304i −0.134967 + 0.0602037i
\(445\) −8.99652 33.5755i −0.0202169 0.0754505i
\(446\) 441.722 + 286.639i 0.990407 + 0.642688i
\(447\) 122.962i 0.275082i
\(448\) −419.768 156.521i −0.936982 0.349378i
\(449\) −654.486 −1.45765 −0.728827 0.684698i \(-0.759934\pi\)
−0.728827 + 0.684698i \(0.759934\pi\)
\(450\) 2.79322 4.30447i 0.00620716 0.00956548i
\(451\) 16.8967 4.52745i 0.0374649 0.0100387i
\(452\) −228.947 513.260i −0.506519 1.13553i
\(453\) −371.002 99.4098i −0.818990 0.219448i
\(454\) 202.703 624.597i 0.446483 1.37577i
\(455\) −131.654 253.652i −0.289351 0.557476i
\(456\) 56.1579 356.981i 0.123153 0.782852i
\(457\) −361.990 + 208.995i −0.792101 + 0.457319i −0.840702 0.541499i \(-0.817857\pi\)
0.0486010 + 0.998818i \(0.484524\pi\)
\(458\) 91.0461 82.0358i 0.198791 0.179117i
\(459\) 19.9699 5.35093i 0.0435075 0.0116578i
\(460\) 319.022 + 393.398i 0.693526 + 0.855214i
\(461\) −188.470 188.470i −0.408829 0.408829i 0.472501 0.881330i \(-0.343351\pi\)
−0.881330 + 0.472501i \(0.843351\pi\)
\(462\) 1.12063 11.5346i 0.00242560 0.0249666i
\(463\) −688.952 −1.48802 −0.744009 0.668170i \(-0.767078\pi\)
−0.744009 + 0.668170i \(0.767078\pi\)
\(464\) −1.58732 29.5014i −0.00342095 0.0635806i
\(465\) 67.2084 + 38.8028i 0.144534 + 0.0834468i
\(466\) 36.1524 694.456i 0.0775802 1.49025i
\(467\) 141.316 527.397i 0.302603 1.12933i −0.632386 0.774654i \(-0.717924\pi\)
0.934989 0.354677i \(-0.115409\pi\)
\(468\) −15.6656 98.4646i −0.0334735 0.210394i
\(469\) −159.316 722.746i −0.339692 1.54104i
\(470\) 103.809 319.870i 0.220870 0.680575i
\(471\) −381.660 + 220.352i −0.810319 + 0.467838i
\(472\) −31.4043 295.818i −0.0665345 0.626733i
\(473\) 26.0426 + 15.0357i 0.0550583 + 0.0317879i
\(474\) 213.334 45.4233i 0.450073 0.0958297i
\(475\) 15.7713 15.7713i 0.0332026 0.0332026i
\(476\) 16.5229 110.174i 0.0347119 0.231458i
\(477\) −142.479 + 142.479i −0.298698 + 0.298698i
\(478\) −191.564 + 295.208i −0.400762 + 0.617590i
\(479\) 511.956 + 295.578i 1.06880 + 0.617073i 0.927854 0.372944i \(-0.121652\pi\)
0.140948 + 0.990017i \(0.454985\pi\)
\(480\) 70.9466 + 262.944i 0.147805 + 0.547799i
\(481\) −68.1477 + 39.3451i −0.141679 + 0.0817985i
\(482\) −123.423 + 62.9413i −0.256064 + 0.130584i
\(483\) −230.607 + 210.802i −0.477447 + 0.436442i
\(484\) 391.023 + 283.679i 0.807898 + 0.586113i
\(485\) −196.587 + 733.674i −0.405335 + 1.51273i
\(486\) −20.8695 23.1617i −0.0429414 0.0476578i
\(487\) 708.741 + 409.192i 1.45532 + 0.840230i 0.998776 0.0494708i \(-0.0157535\pi\)
0.456545 + 0.889700i \(0.349087\pi\)
\(488\) 63.3004 142.576i 0.129714 0.292164i
\(489\) 434.708 0.888974
\(490\) −385.176 + 289.008i −0.786074 + 0.589813i
\(491\) 158.312 + 158.312i 0.322428 + 0.322428i 0.849698 0.527270i \(-0.176784\pi\)
−0.527270 + 0.849698i \(0.676784\pi\)
\(492\) −159.724 196.962i −0.324642 0.400329i
\(493\) 7.09651 1.90150i 0.0143945 0.00385701i
\(494\) 22.5301 432.785i 0.0456075 0.876082i
\(495\) −6.10122 + 3.52254i −0.0123257 + 0.00711624i
\(496\) 138.691 45.2773i 0.279620 0.0912849i
\(497\) −11.5107 + 256.545i −0.0231604 + 0.516188i
\(498\) −8.24705 + 4.20570i −0.0165603 + 0.00844518i
\(499\) 246.911 + 66.1597i 0.494812 + 0.132585i 0.497591 0.867412i \(-0.334218\pi\)
−0.00277907 + 0.999996i \(0.500885\pi\)
\(500\) −181.786 + 474.556i −0.363572 + 0.949112i
\(501\) −449.939 + 120.561i −0.898083 + 0.240641i
\(502\) 168.640 + 792.031i 0.335936 + 1.57775i
\(503\) −585.633 −1.16428 −0.582141 0.813088i \(-0.697785\pi\)
−0.582141 + 0.813088i \(0.697785\pi\)
\(504\) −159.327 + 53.2817i −0.316125 + 0.105718i
\(505\) 29.9988i 0.0594036i
\(506\) 5.12952 + 24.0912i 0.0101374 + 0.0476111i
\(507\) 44.8142 + 167.249i 0.0883909 + 0.329879i
\(508\) 248.291 + 556.626i 0.488761 + 1.09572i
\(509\) 4.65947 17.3894i 0.00915417 0.0341638i −0.961198 0.275860i \(-0.911037\pi\)
0.970352 + 0.241697i \(0.0777039\pi\)
\(510\) −60.3333 + 30.7678i −0.118301 + 0.0603290i
\(511\) 270.192 422.991i 0.528752 0.827772i
\(512\) 456.922 + 231.012i 0.892425 + 0.451195i
\(513\) −67.7570 117.359i −0.132080 0.228769i
\(514\) 25.1230 482.592i 0.0488775 0.938895i
\(515\) 79.9609 + 298.418i 0.155264 + 0.579452i
\(516\) 45.2654 433.577i 0.0877237 0.840266i
\(517\) 11.5642 11.5642i 0.0223679 0.0223679i
\(518\) 84.2520 + 102.384i 0.162649 + 0.197653i
\(519\) 248.636i 0.479068i
\(520\) 117.365 + 304.794i 0.225702 + 0.586142i
\(521\) 51.1015 88.5104i 0.0980835 0.169886i −0.812808 0.582532i \(-0.802062\pi\)
0.910891 + 0.412646i \(0.135395\pi\)
\(522\) −7.41618 8.23073i −0.0142072 0.0157677i
\(523\) −247.725 66.3778i −0.473662 0.126917i 0.0140877 0.999901i \(-0.495516\pi\)
−0.487750 + 0.872983i \(0.662182\pi\)
\(524\) −899.266 + 143.072i −1.71616 + 0.273038i
\(525\) −9.88534 3.12993i −0.0188292 0.00596178i
\(526\) −663.461 + 338.341i −1.26133 + 0.643235i
\(527\) 18.1402 + 31.4197i 0.0344216 + 0.0596199i
\(528\) −2.73562 + 12.9588i −0.00518110 + 0.0245433i
\(529\) 67.5299 116.965i 0.127656 0.221106i
\(530\) 359.304 553.701i 0.677931 1.04472i
\(531\) −78.8814 78.8814i −0.148552 0.148552i
\(532\) −725.579 + 82.2959i −1.36387 + 0.154691i
\(533\) −215.039 215.039i −0.403450 0.403450i
\(534\) −23.9679 + 5.10325i −0.0448837 + 0.00955666i
\(535\) −176.645 + 305.959i −0.330178 + 0.571885i
\(536\) 89.2917 + 841.098i 0.166589 + 1.56921i
\(537\) 173.319 + 300.197i 0.322754 + 0.559025i
\(538\) 183.391 565.090i 0.340876 1.05035i
\(539\) −23.0719 + 4.01091i −0.0428051 + 0.00744138i
\(540\) 82.6667 + 59.9730i 0.153087 + 0.111061i
\(541\) −221.770 59.4230i −0.409926 0.109839i 0.0479624 0.998849i \(-0.484727\pi\)
−0.457888 + 0.889010i \(0.651394\pi\)
\(542\) 0.270720 5.20030i 0.000499483 0.00959465i
\(543\) −296.425 + 513.423i −0.545902 + 0.945530i
\(544\) −32.7389 + 123.040i −0.0601818 + 0.226177i
\(545\) 667.121i 1.22407i
\(546\) −183.404 + 83.3922i −0.335904 + 0.152733i
\(547\) 684.070 684.070i 1.25059 1.25059i 0.295127 0.955458i \(-0.404638\pi\)
0.955458 0.295127i \(-0.0953621\pi\)
\(548\) 14.2219 136.225i 0.0259524 0.248586i
\(549\) −15.1406 56.5053i −0.0275784 0.102924i
\(550\) −0.607294 + 0.547193i −0.00110417 + 0.000994897i
\(551\) −24.0781 41.7045i −0.0436990 0.0756888i
\(552\) 288.657 210.183i 0.522929 0.380766i
\(553\) −203.046 391.198i −0.367172 0.707411i
\(554\) −146.606 + 451.741i −0.264631 + 0.815417i
\(555\) 20.8623 77.8591i 0.0375897 0.140287i
\(556\) −129.490 49.6030i −0.232895 0.0892141i
\(557\) −10.2832 38.3773i −0.0184617 0.0689000i 0.956080 0.293104i \(-0.0946884\pi\)
−0.974542 + 0.224204i \(0.928022\pi\)
\(558\) 29.7816 45.8946i 0.0533720 0.0822483i
\(559\) 522.790i 0.935223i
\(560\) 474.135 279.407i 0.846669 0.498941i
\(561\) −3.29355 −0.00587086
\(562\) −816.179 529.629i −1.45228 0.942400i
\(563\) −512.829 + 137.412i −0.910887 + 0.244071i −0.683686 0.729776i \(-0.739624\pi\)
−0.227201 + 0.973848i \(0.572957\pi\)
\(564\) −221.394 84.8082i −0.392542 0.150369i
\(565\) 666.865 + 178.686i 1.18029 + 0.316258i
\(566\) −839.869 272.567i −1.48387 0.481566i
\(567\) −33.9139 + 53.0928i −0.0598128 + 0.0936382i
\(568\) 45.6089 289.924i 0.0802974 0.510430i
\(569\) −438.433 + 253.129i −0.770532 + 0.444867i −0.833064 0.553176i \(-0.813416\pi\)
0.0625324 + 0.998043i \(0.480082\pi\)
\(570\) 297.155 + 329.793i 0.521325 + 0.578585i
\(571\) −42.1936 + 11.3057i −0.0738942 + 0.0197999i −0.295577 0.955319i \(-0.595512\pi\)
0.221683 + 0.975119i \(0.428845\pi\)
\(572\) −1.64925 + 15.7974i −0.00288330 + 0.0276179i
\(573\) −270.853 270.853i −0.472693 0.472693i
\(574\) −297.926 + 416.920i −0.519034 + 0.726342i
\(575\) 22.0385 0.0383278
\(576\) 187.721 40.3115i 0.325904 0.0699852i
\(577\) −130.713 75.4674i −0.226540 0.130793i 0.382435 0.923982i \(-0.375086\pi\)
−0.608975 + 0.793190i \(0.708419\pi\)
\(578\) 545.600 + 28.4031i 0.943944 + 0.0491403i
\(579\) 74.8046 279.174i 0.129196 0.482167i
\(580\) 29.3764 + 21.3120i 0.0506490 + 0.0367448i
\(581\) 12.6216 + 13.8074i 0.0217239 + 0.0237649i
\(582\) 509.324 + 165.293i 0.875126 + 0.284009i
\(583\) 27.7989 16.0497i 0.0476826 0.0275295i
\(584\) −360.528 + 446.167i −0.617342 + 0.763985i
\(585\) 106.069 + 61.2393i 0.181315 + 0.104682i
\(586\) 118.079 + 554.567i 0.201499 + 0.946359i
\(587\) −704.233 + 704.233i −1.19972 + 1.19972i −0.225464 + 0.974251i \(0.572390\pi\)
−0.974251 + 0.225464i \(0.927610\pi\)
\(588\) 189.354 + 281.768i 0.322030 + 0.479197i
\(589\) 168.154 168.154i 0.285491 0.285491i
\(590\) 306.549 + 198.923i 0.519574 + 0.337158i
\(591\) 25.3802 + 14.6533i 0.0429445 + 0.0247940i
\(592\) −82.7090 126.973i −0.139711 0.214481i
\(593\) −467.655 + 270.001i −0.788626 + 0.455313i −0.839479 0.543393i \(-0.817139\pi\)
0.0508527 + 0.998706i \(0.483806\pi\)
\(594\) 2.25636 + 4.42455i 0.00379859 + 0.00744873i
\(595\) 92.3362 + 101.011i 0.155187 + 0.169767i
\(596\) −280.441 + 44.6178i −0.470539 + 0.0748621i
\(597\) −55.8050 + 208.267i −0.0934756 + 0.348856i
\(598\) 318.125 286.642i 0.531982 0.479334i
\(599\) −8.10018 4.67664i −0.0135228 0.00780741i 0.493223 0.869903i \(-0.335819\pi\)
−0.506746 + 0.862095i \(0.669152\pi\)
\(600\) 10.8308 + 4.80863i 0.0180514 + 0.00801439i
\(601\) −896.701 −1.49201 −0.746007 0.665938i \(-0.768032\pi\)
−0.746007 + 0.665938i \(0.768032\pi\)
\(602\) −868.946 + 144.647i −1.44343 + 0.240277i
\(603\) 224.283 + 224.283i 0.371946 + 0.371946i
\(604\) 92.1040 882.223i 0.152490 1.46063i
\(605\) −573.218 + 153.593i −0.947469 + 0.253873i
\(606\) −21.1201 1.09948i −0.0348516 0.00181432i
\(607\) 531.237 306.710i 0.875185 0.505288i 0.00611707 0.999981i \(-0.498053\pi\)
0.869068 + 0.494693i \(0.164720\pi\)
\(608\) 834.549 1.45347i 1.37261 0.00239057i
\(609\) −12.0516 + 18.8671i −0.0197892 + 0.0309804i
\(610\) 87.0581 + 170.714i 0.142718 + 0.279859i
\(611\) −274.630 73.5869i −0.449476 0.120437i
\(612\) 19.4502 + 43.6041i 0.0317814 + 0.0712485i
\(613\) −335.641 + 89.9346i −0.547538 + 0.146712i −0.521975 0.852961i \(-0.674805\pi\)
−0.0255630 + 0.999673i \(0.508138\pi\)
\(614\) −323.573 + 68.8954i −0.526992 + 0.112208i
\(615\) 311.513 0.506526
\(616\) 26.7137 1.62960i 0.0433665 0.00264545i
\(617\) 815.272i 1.32135i 0.750672 + 0.660675i \(0.229730\pi\)
−0.750672 + 0.660675i \(0.770270\pi\)
\(618\) 213.026 45.3576i 0.344702 0.0733942i
\(619\) 91.2147 + 340.418i 0.147358 + 0.549948i 0.999639 + 0.0268637i \(0.00855200\pi\)
−0.852281 + 0.523084i \(0.824781\pi\)
\(620\) −64.1110 + 167.363i −0.103405 + 0.269941i
\(621\) 34.6563 129.339i 0.0558072 0.208275i
\(622\) 507.927 + 996.005i 0.816603 + 1.60129i
\(623\) 22.8120 + 43.9507i 0.0366164 + 0.0705468i
\(624\) 218.885 71.4575i 0.350778 0.114515i
\(625\) −301.444 522.116i −0.482310 0.835386i
\(626\) 77.2710 + 4.02261i 0.123436 + 0.00642590i
\(627\) 5.58744 + 20.8526i 0.00891138 + 0.0332577i
\(628\) −641.048 790.502i −1.02078 1.25876i
\(629\) 26.6458 26.6458i 0.0423622 0.0423622i
\(630\) 72.4402 193.245i 0.114984 0.306739i
\(631\) 38.2521i 0.0606214i −0.999541 0.0303107i \(-0.990350\pi\)
0.999541 0.0303107i \(-0.00964968\pi\)
\(632\) 181.008 + 470.073i 0.286405 + 0.743786i
\(633\) 333.994 578.495i 0.527637 0.913895i
\(634\) 73.9904 66.6679i 0.116704 0.105154i
\(635\) −723.208 193.783i −1.13891 0.305170i
\(636\) −376.654 273.254i −0.592223 0.429645i
\(637\) 260.940 + 312.502i 0.409639 + 0.490584i
\(638\) 0.801820 + 1.57231i 0.00125677 + 0.00246443i
\(639\) −55.0293 95.3135i −0.0861178 0.149160i
\(640\) −573.956 + 257.220i −0.896807 + 0.401907i
\(641\) 461.184 798.794i 0.719476 1.24617i −0.241732 0.970343i \(-0.577716\pi\)
0.961208 0.275825i \(-0.0889511\pi\)
\(642\) 208.930 + 135.577i 0.325436 + 0.211179i
\(643\) 44.8400 + 44.8400i 0.0697356 + 0.0697356i 0.741114 0.671379i \(-0.234298\pi\)
−0.671379 + 0.741114i \(0.734298\pi\)
\(644\) −564.456 449.457i −0.876485 0.697915i
\(645\) 378.667 + 378.667i 0.587080 + 0.587080i
\(646\) 43.2189 + 202.981i 0.0669023 + 0.314212i
\(647\) −468.981 + 812.300i −0.724855 + 1.25549i 0.234178 + 0.972194i \(0.424760\pi\)
−0.959033 + 0.283293i \(0.908573\pi\)
\(648\) 45.2526 56.0018i 0.0698342 0.0864226i
\(649\) 8.88569 + 15.3905i 0.0136914 + 0.0237141i
\(650\) 13.5173 + 4.38684i 0.0207959 + 0.00674899i
\(651\) −105.398 33.3716i −0.161902 0.0512621i
\(652\) 157.738 + 991.447i 0.241929 + 1.52062i
\(653\) −903.088 241.982i −1.38298 0.370569i −0.510779 0.859712i \(-0.670643\pi\)
−0.872204 + 0.489143i \(0.837310\pi\)
\(654\) 469.673 + 24.4505i 0.718155 + 0.0373861i
\(655\) 559.291 968.721i 0.853880 1.47896i
\(656\) 391.257 435.755i 0.596429 0.664260i
\(657\) 215.109i 0.327411i
\(658\) −46.3259 + 476.832i −0.0704041 + 0.724668i
\(659\) 267.197 267.197i 0.405459 0.405459i −0.474693 0.880152i \(-0.657441\pi\)
0.880152 + 0.474693i \(0.157441\pi\)
\(660\) −10.2478 12.6370i −0.0155270 0.0191469i
\(661\) −84.6934 316.080i −0.128129 0.478184i 0.871803 0.489857i \(-0.162951\pi\)
−0.999932 + 0.0116727i \(0.996284\pi\)
\(662\) −496.701 551.256i −0.750304 0.832714i
\(663\) 28.6292 + 49.5871i 0.0431812 + 0.0747921i
\(664\) −12.5845 17.2831i −0.0189526 0.0260288i
\(665\) 482.891 755.975i 0.726152 1.13680i
\(666\) −54.0506 17.5413i −0.0811570 0.0263383i
\(667\) 12.3154 45.9619i 0.0184639 0.0689083i
\(668\) −438.230 982.438i −0.656033 1.47072i
\(669\) 118.028 + 440.487i 0.176425 + 0.658427i
\(670\) −871.609 565.598i −1.30091 0.844176i
\(671\) 9.31917i 0.0138885i
\(672\) −179.334 344.046i −0.266866 0.511973i
\(673\) 668.360 0.993106 0.496553 0.868006i \(-0.334599\pi\)
0.496553 + 0.868006i \(0.334599\pi\)
\(674\) −238.937 + 368.212i −0.354507 + 0.546309i
\(675\) 4.29244 1.15016i 0.00635917 0.00170393i
\(676\) −365.186 + 162.896i −0.540216 + 0.240971i
\(677\) 1286.06 + 344.600i 1.89965 + 0.509010i 0.996884 + 0.0788822i \(0.0251351\pi\)
0.902768 + 0.430128i \(0.141532\pi\)
\(678\) 150.241 462.944i 0.221595 0.682808i
\(679\) 48.5005 1080.96i 0.0714294 1.59199i
\(680\) −92.0651 126.439i −0.135390 0.185939i
\(681\) 492.500 284.345i 0.723201 0.417540i
\(682\) −6.47502 + 5.83422i −0.00949416 + 0.00855457i
\(683\) 835.054 223.752i 1.22263 0.327602i 0.410922 0.911670i \(-0.365207\pi\)
0.811704 + 0.584069i \(0.198540\pi\)
\(684\) 243.076 197.119i 0.355374 0.288186i
\(685\) 118.973 + 118.973i 0.173683 + 0.173683i
\(686\) 447.223 520.181i 0.651928 0.758281i
\(687\) 106.134 0.154489
\(688\) 1005.29 54.0897i 1.46118 0.0786188i
\(689\) −483.283 279.024i −0.701427 0.404969i
\(690\) −22.8039 + 438.044i −0.0330492 + 0.634847i
\(691\) −13.7966 + 51.4895i −0.0199661 + 0.0745145i −0.975190 0.221369i \(-0.928947\pi\)
0.955224 + 0.295884i \(0.0956141\pi\)
\(692\) −567.069 + 90.2199i −0.819464 + 0.130376i
\(693\) 7.40768 6.77149i 0.0106893 0.00977127i
\(694\) −177.801 + 547.863i −0.256197 + 0.789428i
\(695\) 147.520 85.1706i 0.212259 0.122548i
\(696\) 16.0809 19.9008i 0.0231048 0.0285931i
\(697\) 126.121 + 72.8158i 0.180948 + 0.104470i
\(698\) −596.127 + 126.928i −0.854050 + 0.181845i
\(699\) 425.842 425.842i 0.609216 0.609216i
\(700\) 3.55151 23.6814i 0.00507358 0.0338305i
\(701\) −276.351 + 276.351i −0.394225 + 0.394225i −0.876190 0.481966i \(-0.839923\pi\)
0.481966 + 0.876190i \(0.339923\pi\)
\(702\) 47.0018 72.4317i 0.0669542 0.103179i
\(703\) −213.908 123.500i −0.304279 0.175675i
\(704\) −30.5481 1.53695i −0.0433922 0.00218316i
\(705\) 252.220 145.619i 0.357759 0.206552i
\(706\) 845.088 430.965i 1.19701 0.610432i
\(707\) 9.19942 + 41.7338i 0.0130119 + 0.0590294i
\(708\) 151.283 208.529i 0.213677 0.294532i
\(709\) −72.2905 + 269.792i −0.101961 + 0.380524i −0.997983 0.0634863i \(-0.979778\pi\)
0.896022 + 0.444011i \(0.146445\pi\)
\(710\) 241.337 + 267.844i 0.339911 + 0.377245i
\(711\) 163.587 + 94.4472i 0.230081 + 0.132837i
\(712\) −20.3360 52.8122i −0.0285618 0.0741744i
\(713\) 234.976 0.329560
\(714\) 74.4993 61.3054i 0.104341 0.0858618i
\(715\) −13.7967 13.7967i −0.0192962 0.0192962i
\(716\) −621.773 + 504.220i −0.868398 + 0.704217i
\(717\) −294.383 + 78.8797i −0.410576 + 0.110014i
\(718\) −29.3503 + 563.794i −0.0408779 + 0.785229i
\(719\) −1005.04 + 580.258i −1.39783 + 0.807035i −0.994165 0.107874i \(-0.965596\pi\)
−0.403661 + 0.914909i \(0.632262\pi\)
\(720\) −106.785 + 210.301i −0.148312 + 0.292085i
\(721\) −202.753 390.633i −0.281210 0.541793i
\(722\) 568.630 289.981i 0.787576 0.401635i
\(723\) −115.895 31.0541i −0.160298 0.0429517i
\(724\) −1278.53 489.761i −1.76593 0.676465i
\(725\) 1.52536 0.408719i 0.00210395 0.000563751i
\(726\) 87.1255 + 409.192i 0.120008 + 0.563626i
\(727\) −769.974 −1.05911 −0.529556 0.848275i \(-0.677641\pi\)
−0.529556 + 0.848275i \(0.677641\pi\)
\(728\) −256.744 388.032i −0.352670 0.533011i
\(729\) 27.0000i 0.0370370i
\(730\) −146.747 689.210i −0.201023 0.944124i
\(731\) 64.7958 + 241.821i 0.0886400 + 0.330809i
\(732\) 123.379 55.0348i 0.168550 0.0751841i
\(733\) 316.504 1181.21i 0.431793 1.61147i −0.316833 0.948482i \(-0.602619\pi\)
0.748626 0.662993i \(-0.230714\pi\)
\(734\) −728.631 + 371.576i −0.992685 + 0.506234i
\(735\) −415.355 37.3476i −0.565109 0.0508130i
\(736\) 584.109 + 582.078i 0.793626 + 0.790866i
\(737\) −25.2647 43.7597i −0.0342804 0.0593754i
\(738\) 11.4172 219.315i 0.0154705 0.297175i
\(739\) 314.410 + 1173.39i 0.425453 + 1.58781i 0.762932 + 0.646478i \(0.223759\pi\)
−0.337480 + 0.941333i \(0.609574\pi\)
\(740\) 185.145 + 19.3291i 0.250195 + 0.0261204i
\(741\) 265.384 265.384i 0.358143 0.358143i
\(742\) −330.059 + 880.482i −0.444823 + 1.18663i
\(743\) 68.3881i 0.0920433i −0.998940 0.0460216i \(-0.985346\pi\)
0.998940 0.0460216i \(-0.0146543\pi\)
\(744\) 115.479 + 51.2700i 0.155214 + 0.0689113i
\(745\) 174.418 302.101i 0.234118 0.405504i
\(746\) −307.341 341.098i −0.411985 0.457235i
\(747\) −7.74407 2.07502i −0.0103669 0.00277780i
\(748\) −1.19509 7.51166i −0.00159772 0.0100423i
\(749\) 151.920 479.814i 0.202831 0.640606i
\(750\) −392.062 + 199.937i −0.522749 + 0.266583i
\(751\) −533.902 924.745i −0.710921 1.23135i −0.964512 0.264040i \(-0.914945\pi\)
0.253591 0.967312i \(-0.418388\pi\)
\(752\) 113.089 535.710i 0.150384 0.712380i
\(753\) −350.648 + 607.339i −0.465667 + 0.806560i
\(754\) 16.7026 25.7393i 0.0221519 0.0341370i
\(755\) 770.493 + 770.493i 1.02052 + 1.02052i
\(756\) −133.396 58.0827i −0.176449 0.0768290i
\(757\) 348.651 + 348.651i 0.460570 + 0.460570i 0.898842 0.438272i \(-0.144409\pi\)
−0.438272 + 0.898842i \(0.644409\pi\)
\(758\) 355.718 75.7397i 0.469285 0.0999205i
\(759\) −10.6657 + 18.4735i −0.0140522 + 0.0243392i
\(760\) −644.340 + 797.396i −0.847815 + 1.04920i
\(761\) −233.726 404.825i −0.307130 0.531965i 0.670603 0.741816i \(-0.266035\pi\)
−0.977733 + 0.209852i \(0.932702\pi\)
\(762\) −162.935 + 502.058i −0.213826 + 0.658869i
\(763\) −204.579 928.086i −0.268124 1.21636i
\(764\) 519.457 716.020i 0.679918 0.937199i
\(765\) −56.6536 15.1803i −0.0740570 0.0198435i
\(766\) 1.45610 27.9705i 0.00190092 0.0365151i
\(767\) 154.477 267.563i 0.201405 0.348843i
\(768\) 160.055 + 413.510i 0.208405 + 0.538424i
\(769\) 794.625i 1.03332i 0.856190 + 0.516661i \(0.172825\pi\)
−0.856190 + 0.516661i \(0.827175\pi\)
\(770\) −19.1147 + 26.7494i −0.0248243 + 0.0347394i
\(771\) 295.926 295.926i 0.383821 0.383821i
\(772\) 663.861 + 69.3071i 0.859924 + 0.0897760i
\(773\) 13.0468 + 48.6914i 0.0168782 + 0.0629901i 0.973851 0.227186i \(-0.0729527\pi\)
−0.956973 + 0.290176i \(0.906286\pi\)
\(774\) 280.471 252.714i 0.362366 0.326504i
\(775\) 3.89914 + 6.75351i 0.00503115 + 0.00871421i
\(776\) −192.174 + 1221.60i −0.247647 + 1.57423i
\(777\) −5.14699 + 114.714i −0.00662418 + 0.147637i
\(778\) 285.162 878.680i 0.366532 1.12941i
\(779\) 247.061 922.043i 0.317151 1.18362i
\(780\) −101.181 + 264.136i −0.129719 + 0.338635i
\(781\) 4.53787 + 16.9356i 0.00581033 + 0.0216845i
\(782\) −111.625 + 172.018i −0.142743 + 0.219972i
\(783\) 9.59471i 0.0122538i
\(784\) −573.924 + 534.104i −0.732046 + 0.681255i
\(785\) 1250.25 1.59268
\(786\) −661.510 429.262i −0.841616 0.546135i
\(787\) −78.9004 + 21.1413i −0.100255 + 0.0268631i −0.308598 0.951193i \(-0.599860\pi\)
0.208343 + 0.978056i \(0.433193\pi\)
\(788\) −24.2105 + 63.2021i −0.0307240 + 0.0802057i
\(789\) −622.997 166.932i −0.789604 0.211574i
\(790\) −588.566 191.010i −0.745020 0.241785i
\(791\) −982.525 44.0840i −1.24213 0.0557320i
\(792\) −9.27240 + 6.75161i −0.0117076 + 0.00852475i
\(793\) 140.308 81.0067i 0.176933 0.102152i
\(794\) −557.625 618.872i −0.702298 0.779435i
\(795\) 552.154 147.949i 0.694534 0.186100i
\(796\) −495.247 51.7038i −0.622170 0.0649545i
\(797\) 181.021 + 181.021i 0.227128 + 0.227128i 0.811492 0.584364i \(-0.198656\pi\)
−0.584364 + 0.811492i \(0.698656\pi\)
\(798\) −514.531 367.677i −0.644776 0.460748i
\(799\) 136.153 0.170405
\(800\) −7.03707 + 26.4469i −0.00879634 + 0.0330586i
\(801\) −18.3789 10.6110i −0.0229449 0.0132472i
\(802\) −361.590 18.8238i −0.450860 0.0234711i
\(803\) 8.86926 33.1005i 0.0110452 0.0412211i
\(804\) −430.143 + 592.909i −0.535004 + 0.737450i
\(805\) 865.586 190.802i 1.07526 0.237021i
\(806\) 144.123 + 46.7729i 0.178813 + 0.0580309i
\(807\) 445.577 257.254i 0.552140 0.318778i
\(808\) −5.15601 48.5679i −0.00638119 0.0601087i
\(809\) 457.698 + 264.252i 0.565758 + 0.326641i 0.755453 0.655202i \(-0.227417\pi\)
−0.189695 + 0.981843i \(0.560750\pi\)
\(810\) 18.4193 + 86.5080i 0.0227399 + 0.106800i
\(811\) −995.155 + 995.155i −1.22707 + 1.22707i −0.262006 + 0.965066i \(0.584384\pi\)
−0.965066 + 0.262006i \(0.915616\pi\)
\(812\) −47.4034 20.6403i −0.0583786 0.0254190i
\(813\) 3.18883 3.18883i 0.00392230 0.00392230i
\(814\) 7.59392 + 4.92779i 0.00932914 + 0.00605380i
\(815\) −1068.02 616.622i −1.31045 0.756591i
\(816\) −92.3909 + 60.1826i −0.113224 + 0.0737531i
\(817\) 1421.13 820.488i 1.73945 1.00427i
\(818\) 248.712 + 487.705i 0.304049 + 0.596216i
\(819\) −166.341 52.6677i −0.203103 0.0643073i
\(820\) 113.035 + 710.474i 0.137848 + 0.866432i
\(821\) −397.142 + 1482.15i −0.483729 + 1.80530i 0.101987 + 0.994786i \(0.467480\pi\)
−0.585716 + 0.810516i \(0.699187\pi\)
\(822\) 88.1209 79.4000i 0.107203 0.0965937i
\(823\) 591.308 + 341.392i 0.718479 + 0.414814i 0.814193 0.580595i \(-0.197180\pi\)
−0.0957135 + 0.995409i \(0.530513\pi\)
\(824\) 180.746 + 469.393i 0.219352 + 0.569652i
\(825\) −0.707933 −0.000858101
\(826\) −487.466 182.732i −0.590153 0.221225i
\(827\) −264.449 264.449i −0.319769 0.319769i 0.528910 0.848678i \(-0.322601\pi\)
−0.848678 + 0.528910i \(0.822601\pi\)
\(828\) 307.561 + 32.1093i 0.371450 + 0.0387794i
\(829\) 806.013 215.971i 0.972272 0.260519i 0.262485 0.964936i \(-0.415458\pi\)
0.709787 + 0.704417i \(0.248791\pi\)
\(830\) 26.2276 + 1.36537i 0.0315995 + 0.00164502i
\(831\) −356.201 + 205.653i −0.428642 + 0.247476i
\(832\) 242.399 + 473.287i 0.291345 + 0.568854i
\(833\) −159.432 112.209i −0.191396 0.134705i
\(834\) −54.5559 106.980i −0.0654148 0.128273i
\(835\) 1276.45 + 342.025i 1.52869 + 0.409610i
\(836\) −45.5314 + 20.3099i −0.0544634 + 0.0242941i
\(837\) 45.7663 12.2631i 0.0546790 0.0146512i
\(838\) −1247.96 + 265.717i −1.48922 + 0.317085i
\(839\) 119.715 0.142688 0.0713441 0.997452i \(-0.477271\pi\)
0.0713441 + 0.997452i \(0.477271\pi\)
\(840\) 467.024 + 95.0948i 0.555981 + 0.113208i
\(841\) 837.590i 0.995946i
\(842\) 327.717 69.7778i 0.389213 0.0828715i
\(843\) −218.083 813.899i −0.258699 0.965479i
\(844\) 1440.58 + 551.834i 1.70684 + 0.653832i
\(845\) 127.135 474.476i 0.150456 0.561510i
\(846\) −93.2764 182.908i −0.110256 0.216203i
\(847\) 750.350 389.459i 0.885891 0.459810i
\(848\) 486.543 958.193i 0.573754 1.12994i
\(849\) −382.346 662.243i −0.450349 0.780027i
\(850\) −6.79629 0.353805i −0.00799563 0.000416241i
\(851\) −63.1674 235.744i −0.0742273 0.277020i
\(852\) 197.415 160.092i 0.231708 0.187901i
\(853\) 18.2725 18.2725i 0.0214215 0.0214215i −0.696315 0.717736i \(-0.745178\pi\)
0.717736 + 0.696315i \(0.245178\pi\)
\(854\) −173.465 210.797i −0.203120 0.246835i
\(855\) 384.446i 0.449645i
\(856\) −233.401 + 525.705i −0.272665 + 0.614142i
\(857\) 670.958 1162.13i 0.782914 1.35605i −0.147323 0.989088i \(-0.547066\pi\)
0.930237 0.366959i \(-0.119601\pi\)
\(858\) −10.2190 + 9.20767i −0.0119102 + 0.0107315i
\(859\) 297.288 + 79.6580i 0.346086 + 0.0927334i 0.427675 0.903933i \(-0.359333\pi\)
−0.0815891 + 0.996666i \(0.526000\pi\)
\(860\) −726.229 + 1001.03i −0.844452 + 1.16399i
\(861\) −433.372 + 95.5285i −0.503335 + 0.110951i
\(862\) 237.641 + 465.995i 0.275685 + 0.540598i
\(863\) 151.816 + 262.954i 0.175917 + 0.304697i 0.940478 0.339854i \(-0.110378\pi\)
−0.764561 + 0.644551i \(0.777044\pi\)
\(864\) 144.145 + 82.8875i 0.166834 + 0.0959346i
\(865\) 352.684 610.867i 0.407727 0.706204i
\(866\) −646.136 419.286i −0.746115 0.484163i
\(867\) 334.563 + 334.563i 0.385885 + 0.385885i
\(868\) 37.8665 252.493i 0.0436250 0.290890i
\(869\) −21.2783 21.2783i −0.0244859 0.0244859i
\(870\) 6.54549 + 30.7415i 0.00752356 + 0.0353350i
\(871\) −439.225 + 760.761i −0.504277 + 0.873434i
\(872\) 114.660 + 1080.06i 0.131491 + 1.23860i
\(873\) 231.867 + 401.605i 0.265598 + 0.460029i
\(874\) 1278.47 + 414.909i 1.46278 + 0.474724i
\(875\) 600.025 + 656.399i 0.685743 + 0.750170i
\(876\) −490.603 + 78.0543i −0.560049 + 0.0891031i
\(877\) 1586.29 + 425.044i 1.80876 + 0.484657i 0.995290 0.0969430i \(-0.0309065\pi\)
0.813475 + 0.581600i \(0.197573\pi\)
\(878\) 36.8839 + 1.92012i 0.0420090 + 0.00218693i
\(879\) −245.517 + 425.248i −0.279314 + 0.483787i
\(880\) 25.1028 27.9578i 0.0285259 0.0317702i
\(881\) 576.277i 0.654117i −0.945004 0.327058i \(-0.893943\pi\)
0.945004 0.327058i \(-0.106057\pi\)
\(882\) −41.5169 + 291.054i −0.0470713 + 0.329993i
\(883\) 299.829 299.829i 0.339557 0.339557i −0.516644 0.856201i \(-0.672819\pi\)
0.856201 + 0.516644i \(0.172819\pi\)
\(884\) −102.706 + 83.2881i −0.116183 + 0.0942173i
\(885\) 81.9100 + 305.692i 0.0925536 + 0.345415i
\(886\) 836.732 + 928.635i 0.944393 + 1.04812i
\(887\) 307.801 + 533.127i 0.347014 + 0.601045i 0.985717 0.168408i \(-0.0538625\pi\)
−0.638704 + 0.769453i \(0.720529\pi\)
\(888\) 20.3940 129.639i 0.0229662 0.145990i
\(889\) 1065.54 + 47.8087i 1.19858 + 0.0537781i
\(890\) 66.1247 + 21.4598i 0.0742974 + 0.0241121i
\(891\) −1.11325 + 4.15470i −0.00124944 + 0.00466296i
\(892\) −961.799 + 429.024i −1.07825 + 0.480968i
\(893\) −230.981 862.032i −0.258657 0.965321i
\(894\) −206.296 133.868i −0.230756 0.149740i
\(895\) 983.391i 1.09876i
\(896\) 719.598 533.849i 0.803123 0.595814i
\(897\) 370.844 0.413427
\(898\) 712.535 1098.05i 0.793469 1.22277i
\(899\) 16.2635 4.35780i 0.0180907 0.00484738i
\(900\) 4.18073 + 9.37249i 0.00464525 + 0.0104139i
\(901\) 258.130 + 69.1658i 0.286493 + 0.0767656i
\(902\) −10.7995 + 33.2769i −0.0119729 + 0.0368924i
\(903\) −642.916 410.672i −0.711977 0.454787i
\(904\) 1110.36 + 174.675i 1.22827 + 0.193224i
\(905\) 1456.55 840.941i 1.60945 0.929217i
\(906\) 570.690 514.211i 0.629900 0.567562i
\(907\) 15.5077 4.15528i 0.0170978 0.00458135i −0.250260 0.968179i \(-0.580516\pi\)
0.267358 + 0.963597i \(0.413849\pi\)
\(908\) 827.218 + 1020.08i 0.911033 + 1.12343i
\(909\) −12.9509 12.9509i −0.0142474 0.0142474i
\(910\) 568.888 + 55.2695i 0.625151 + 0.0607357i
\(911\) −909.033 −0.997841 −0.498920 0.866648i \(-0.666270\pi\)
−0.498920 + 0.866648i \(0.666270\pi\)
\(912\) 537.775 + 482.860i 0.589666 + 0.529452i
\(913\) 1.10608 + 0.638598i 0.00121148 + 0.000699450i
\(914\) 43.4610 834.849i 0.0475503 0.913402i
\(915\) −42.9529 + 160.302i −0.0469431 + 0.175194i
\(916\) 38.5117 + 242.062i 0.0420433 + 0.264260i
\(917\) −481.008 + 1519.18i −0.524545 + 1.65668i
\(918\) −12.7638 + 39.3295i −0.0139039 + 0.0428426i
\(919\) −613.945 + 354.462i −0.668058 + 0.385703i −0.795340 0.606163i \(-0.792708\pi\)
0.127282 + 0.991867i \(0.459375\pi\)
\(920\) −1007.33 + 106.939i −1.09492 + 0.116238i
\(921\) −248.120 143.252i −0.269403 0.155540i
\(922\) 521.387 111.014i 0.565495 0.120406i
\(923\) 215.533 215.533i 0.233514 0.233514i
\(924\) 18.1318 + 14.4377i 0.0196231 + 0.0156252i
\(925\) 5.72739 5.72739i 0.00619178 0.00619178i
\(926\) 750.058 1155.87i 0.809998 1.24824i
\(927\) 163.351 + 94.3107i 0.176215 + 0.101738i
\(928\) 51.2232 + 29.4549i 0.0551974 + 0.0317402i
\(929\) 741.347 428.017i 0.798006 0.460729i −0.0447678 0.998997i \(-0.514255\pi\)
0.842773 + 0.538269i \(0.180921\pi\)
\(930\) −138.270 + 70.5125i −0.148677 + 0.0758199i
\(931\) −439.962 + 1199.78i −0.472569 + 1.28870i
\(932\) 1125.74 + 816.704i 1.20788 + 0.876292i
\(933\) −250.602 + 935.259i −0.268598 + 1.00242i
\(934\) 730.976 + 811.262i 0.782629 + 0.868589i
\(935\) 8.09182 + 4.67182i 0.00865435 + 0.00499659i
\(936\) 182.251 + 80.9153i 0.194713 + 0.0864480i
\(937\) −1112.05 −1.18682 −0.593412 0.804899i \(-0.702219\pi\)
−0.593412 + 0.804899i \(0.702219\pi\)
\(938\) 1386.01 + 519.562i 1.47762 + 0.553904i
\(939\) 47.3827 + 47.3827i 0.0504608 + 0.0504608i
\(940\) 423.637 + 522.403i 0.450678 + 0.555748i
\(941\) 1111.64 297.862i 1.18134 0.316538i 0.385880 0.922549i \(-0.373898\pi\)
0.795457 + 0.606011i \(0.207231\pi\)
\(942\) 45.8226 880.214i 0.0486440 0.934410i
\(943\) 816.843 471.605i 0.866218 0.500111i
\(944\) 530.490 + 269.368i 0.561959 + 0.285347i
\(945\) 158.633 82.3361i 0.167865 0.0871282i
\(946\) −53.5780 + 27.3229i −0.0566364 + 0.0288825i
\(947\) −1666.79 446.616i −1.76008 0.471612i −0.773348 0.633981i \(-0.781420\pi\)
−0.986730 + 0.162370i \(0.948086\pi\)
\(948\) −156.048 + 407.368i −0.164608 + 0.429713i
\(949\) −575.452 + 154.192i −0.606377 + 0.162478i
\(950\) 9.28969 + 43.6298i 0.00977862 + 0.0459261i
\(951\) 86.2519 0.0906960
\(952\) 166.853 + 147.666i 0.175266 + 0.155112i
\(953\) 671.118i 0.704216i 0.935959 + 0.352108i \(0.114535\pi\)
−0.935959 + 0.352108i \(0.885465\pi\)
\(954\) −83.9239 394.156i −0.0879705 0.413161i
\(955\) 281.252 + 1049.65i 0.294505 + 1.09911i
\(956\) −286.722 642.782i −0.299918 0.672366i
\(957\) −0.395604 + 1.47641i −0.000413379 + 0.00154275i
\(958\) −1053.26 + 537.125i −1.09944 + 0.560673i
\(959\) −201.997 129.029i −0.210633 0.134545i
\(960\) −518.385 167.237i −0.539984 0.174205i
\(961\) −438.927 760.244i −0.456740 0.791097i
\(962\) 8.18191 157.168i 0.00850510 0.163376i
\(963\) 55.8262 + 208.346i 0.0579711 + 0.216351i
\(964\) 28.7719 275.593i 0.0298464 0.285885i
\(965\) −579.786 + 579.786i −0.600815 + 0.600815i
\(966\) −102.606 616.392i −0.106217 0.638087i
\(967\) 377.448i 0.390329i −0.980771 0.195165i \(-0.937476\pi\)
0.980771 0.195165i \(-0.0625241\pi\)
\(968\) −901.638 + 347.188i −0.931444 + 0.358665i
\(969\) −89.8637 + 155.648i −0.0927385 + 0.160628i
\(970\) −1016.88 1128.56i −1.04833 1.16347i
\(971\) −326.613 87.5158i −0.336368 0.0901295i 0.0866816 0.996236i \(-0.472374\pi\)
−0.423050 + 0.906107i \(0.639040\pi\)
\(972\) 61.5793 9.79719i 0.0633532 0.0100794i
\(973\) −179.108 + 163.726i −0.184078 + 0.168269i
\(974\) −1458.11 + 743.585i −1.49703 + 0.763434i
\(975\) 6.15370 + 10.6585i 0.00631149 + 0.0109318i
\(976\) 170.288 + 261.422i 0.174475 + 0.267850i
\(977\) −61.2092 + 106.017i −0.0626501 + 0.108513i −0.895649 0.444761i \(-0.853289\pi\)
0.832999 + 0.553274i \(0.186622\pi\)
\(978\) −473.264 + 729.319i −0.483910 + 0.745725i
\(979\) 2.39059 + 2.39059i 0.00244187 + 0.00244187i
\(980\) −65.5361 960.859i −0.0668736 0.980469i
\(981\) 288.004 + 288.004i 0.293582 + 0.293582i
\(982\) −437.957 + 93.2501i −0.445985 + 0.0949593i
\(983\) −692.928 + 1200.19i −0.704911 + 1.22094i 0.261812 + 0.965119i \(0.415680\pi\)
−0.966723 + 0.255824i \(0.917653\pi\)
\(984\) 504.338 53.5410i 0.512539 0.0544115i
\(985\) −41.5705 72.0023i −0.0422036 0.0730987i
\(986\) −4.53573 + 13.9761i −0.00460014 + 0.0141746i
\(987\) −306.228 + 279.929i −0.310262 + 0.283616i
\(988\) 701.563 + 508.969i 0.710084 + 0.515151i
\(989\) 1566.20 + 419.662i 1.58362 + 0.424330i
\(990\) 0.732521 14.0711i 0.000739920 0.0142132i
\(991\) −719.460 + 1246.14i −0.725993 + 1.25746i 0.232570 + 0.972580i \(0.425286\pi\)
−0.958564 + 0.284878i \(0.908047\pi\)
\(992\) −75.0298 + 281.979i −0.0756349 + 0.284253i
\(993\) 642.609i 0.647139i
\(994\) −417.880 298.611i −0.420402 0.300413i
\(995\) 432.526 432.526i 0.434700 0.434700i
\(996\) 1.92252 18.4150i 0.00193024 0.0184889i
\(997\) 245.467 + 916.097i 0.246206 + 0.918853i 0.972773 + 0.231758i \(0.0744478\pi\)
−0.726568 + 0.687095i \(0.758886\pi\)
\(998\) −379.808 + 342.221i −0.380569 + 0.342906i
\(999\) −24.6062 42.6193i −0.0246309 0.0426619i
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 336.3.bv.a.325.20 yes 256
7.5 odd 6 inner 336.3.bv.a.229.64 yes 256
16.13 even 4 inner 336.3.bv.a.157.64 yes 256
112.61 odd 12 inner 336.3.bv.a.61.20 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.3.bv.a.61.20 256 112.61 odd 12 inner
336.3.bv.a.157.64 yes 256 16.13 even 4 inner
336.3.bv.a.229.64 yes 256 7.5 odd 6 inner
336.3.bv.a.325.20 yes 256 1.1 even 1 trivial