Properties

Label 56.3.j.a.45.2
Level $56$
Weight $3$
Character 56.45
Analytic conductor $1.526$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [56,3,Mod(5,56)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(56, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("56.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 56.j (of order \(6\), degree \(2\), 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: \(1.52588948042\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 45.2
Character \(\chi\) \(=\) 56.45
Dual form 56.3.j.a.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.87135 + 0.705725i) q^{2} +(-0.126628 + 0.219326i) q^{3} +(3.00390 - 2.64132i) q^{4} +(1.78589 + 3.09325i) q^{5} +(0.0821813 - 0.499801i) q^{6} +(2.89466 + 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 + 7.73868i) q^{9} +O(q^{10})\) \(q+(-1.87135 + 0.705725i) q^{2} +(-0.126628 + 0.219326i) q^{3} +(3.00390 - 2.64132i) q^{4} +(1.78589 + 3.09325i) q^{5} +(0.0821813 - 0.499801i) q^{6} +(2.89466 + 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 + 7.73868i) q^{9} +(-5.52501 - 4.52821i) q^{10} +(-6.82675 - 3.94142i) q^{11} +(0.198932 + 0.993300i) q^{12} +18.1529 q^{13} +(-9.91483 - 9.88414i) q^{14} -0.904575 q^{15} +(2.04687 - 15.8685i) q^{16} +(-8.26180 - 4.76995i) q^{17} +(-13.8224 - 11.3287i) q^{18} +(-12.4094 - 21.4938i) q^{19} +(13.5349 + 4.57472i) q^{20} +(-1.76441 - 0.172184i) q^{21} +(15.5568 + 2.55798i) q^{22} +(2.14949 + 3.72303i) q^{23} +(-1.07327 - 1.71842i) q^{24} +(6.12120 - 10.6022i) q^{25} +(-33.9704 + 12.8110i) q^{26} -4.54237 q^{27} +(25.5296 + 11.4995i) q^{28} +28.3630i q^{29} +(1.69278 - 0.638381i) q^{30} +(-28.2372 - 16.3027i) q^{31} +(7.36842 + 31.1401i) q^{32} +(1.72891 - 0.998189i) q^{33} +(18.8270 + 3.09569i) q^{34} +(-14.5452 + 20.3362i) q^{35} +(33.8616 + 11.4450i) q^{36} +(25.9006 - 14.9537i) q^{37} +(38.3911 + 31.4648i) q^{38} +(-2.29867 + 3.98141i) q^{39} +(-28.5570 + 0.991016i) q^{40} -45.2606i q^{41} +(3.42334 - 0.922973i) q^{42} +24.9109i q^{43} +(-30.9174 + 6.19196i) q^{44} +(-15.9585 + 27.6409i) q^{45} +(-6.64990 - 5.45015i) q^{46} +(44.0432 - 25.4284i) q^{47} +(3.22119 + 2.45833i) q^{48} +(-32.2419 + 36.8979i) q^{49} +(-3.97264 + 24.1604i) q^{50} +(2.09235 - 1.20802i) q^{51} +(54.5296 - 47.9476i) q^{52} +(-54.3930 - 31.4038i) q^{53} +(8.50036 - 3.20566i) q^{54} -28.1558i q^{55} +(-55.8903 - 3.50277i) q^{56} +6.28554 q^{57} +(-20.0165 - 53.0771i) q^{58} +(37.0048 - 64.0942i) q^{59} +(-2.71725 + 2.38927i) q^{60} +(-25.2994 - 43.8198i) q^{61} +(64.3469 + 10.5804i) q^{62} +(-36.3890 + 50.8770i) q^{63} +(-35.7653 - 53.0740i) q^{64} +(32.4191 + 56.1515i) q^{65} +(-2.53096 + 3.08810i) q^{66} +(108.673 + 62.7422i) q^{67} +(-37.4166 + 7.49357i) q^{68} -1.08875 q^{69} +(12.8673 - 48.3210i) q^{70} -5.33822 q^{71} +(-71.4439 + 2.47932i) q^{72} +(-23.6569 - 13.6583i) q^{73} +(-37.9159 + 46.2624i) q^{74} +(1.55023 + 2.68508i) q^{75} +(-94.0487 - 31.7880i) q^{76} +(5.35941 - 54.9191i) q^{77} +(1.49183 - 9.07283i) q^{78} +(51.5380 + 89.2664i) q^{79} +(52.7408 - 22.0080i) q^{80} +(-39.6362 + 68.6519i) q^{81} +(31.9415 + 84.6984i) q^{82} -51.5695 q^{83} +(-5.75491 + 4.14315i) q^{84} -34.0744i q^{85} +(-17.5802 - 46.6170i) q^{86} +(-6.22075 - 3.59155i) q^{87} +(53.4875 - 33.4066i) q^{88} +(133.222 - 76.9158i) q^{89} +(10.3570 - 62.9880i) q^{90} +(52.5464 + 115.697i) q^{91} +(16.2906 + 5.50613i) q^{92} +(7.15123 - 4.12877i) q^{93} +(-64.4749 + 78.6678i) q^{94} +(44.3238 - 76.7711i) q^{95} +(-7.76289 - 2.32712i) q^{96} +47.0436i q^{97} +(34.2961 - 91.8029i) q^{98} -70.4400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87135 + 0.705725i −0.935675 + 0.352863i
\(3\) −0.126628 + 0.219326i −0.0422093 + 0.0731087i −0.886358 0.463000i \(-0.846773\pi\)
0.844149 + 0.536109i \(0.180106\pi\)
\(4\) 3.00390 2.64132i 0.750976 0.660330i
\(5\) 1.78589 + 3.09325i 0.357178 + 0.618650i 0.987488 0.157693i \(-0.0504056\pi\)
−0.630310 + 0.776343i \(0.717072\pi\)
\(6\) 0.0821813 0.499801i 0.0136969 0.0833001i
\(7\) 2.89466 + 6.37346i 0.413522 + 0.910494i
\(8\) −3.75731 + 7.06276i −0.469664 + 0.882845i
\(9\) 4.46793 + 7.73868i 0.496437 + 0.859854i
\(10\) −5.52501 4.52821i −0.552501 0.452821i
\(11\) −6.82675 3.94142i −0.620613 0.358311i 0.156494 0.987679i \(-0.449981\pi\)
−0.777108 + 0.629368i \(0.783314\pi\)
\(12\) 0.198932 + 0.993300i 0.0165777 + 0.0827750i
\(13\) 18.1529 1.39638 0.698189 0.715914i \(-0.253990\pi\)
0.698189 + 0.715914i \(0.253990\pi\)
\(14\) −9.91483 9.88414i −0.708202 0.706010i
\(15\) −0.904575 −0.0603050
\(16\) 2.04687 15.8685i 0.127929 0.991783i
\(17\) −8.26180 4.76995i −0.485988 0.280585i 0.236920 0.971529i \(-0.423862\pi\)
−0.722909 + 0.690944i \(0.757195\pi\)
\(18\) −13.8224 11.3287i −0.767914 0.629370i
\(19\) −12.4094 21.4938i −0.653129 1.13125i −0.982359 0.187003i \(-0.940123\pi\)
0.329231 0.944250i \(-0.393211\pi\)
\(20\) 13.5349 + 4.57472i 0.676745 + 0.228736i
\(21\) −1.76441 0.172184i −0.0840196 0.00819925i
\(22\) 15.5568 + 2.55798i 0.707127 + 0.116272i
\(23\) 2.14949 + 3.72303i 0.0934563 + 0.161871i 0.908963 0.416876i \(-0.136875\pi\)
−0.815507 + 0.578747i \(0.803542\pi\)
\(24\) −1.07327 1.71842i −0.0447195 0.0716008i
\(25\) 6.12120 10.6022i 0.244848 0.424089i
\(26\) −33.9704 + 12.8110i −1.30656 + 0.492729i
\(27\) −4.54237 −0.168236
\(28\) 25.5296 + 11.4995i 0.911772 + 0.410698i
\(29\) 28.3630i 0.978035i 0.872274 + 0.489017i \(0.162644\pi\)
−0.872274 + 0.489017i \(0.837356\pi\)
\(30\) 1.69278 0.638381i 0.0564259 0.0212794i
\(31\) −28.2372 16.3027i −0.910876 0.525895i −0.0301634 0.999545i \(-0.509603\pi\)
−0.880713 + 0.473650i \(0.842936\pi\)
\(32\) 7.36842 + 31.1401i 0.230263 + 0.973128i
\(33\) 1.72891 0.998189i 0.0523914 0.0302482i
\(34\) 18.8270 + 3.09569i 0.553735 + 0.0910497i
\(35\) −14.5452 + 20.3362i −0.415576 + 0.581034i
\(36\) 33.8616 + 11.4450i 0.940599 + 0.317917i
\(37\) 25.9006 14.9537i 0.700017 0.404155i −0.107337 0.994223i \(-0.534232\pi\)
0.807354 + 0.590068i \(0.200899\pi\)
\(38\) 38.3911 + 31.4648i 1.01029 + 0.828020i
\(39\) −2.29867 + 3.98141i −0.0589402 + 0.102087i
\(40\) −28.5570 + 0.991016i −0.713926 + 0.0247754i
\(41\) 45.2606i 1.10392i −0.833872 0.551958i \(-0.813881\pi\)
0.833872 0.551958i \(-0.186119\pi\)
\(42\) 3.42334 0.922973i 0.0815082 0.0219755i
\(43\) 24.9109i 0.579323i 0.957129 + 0.289661i \(0.0935427\pi\)
−0.957129 + 0.289661i \(0.906457\pi\)
\(44\) −30.9174 + 6.19196i −0.702669 + 0.140726i
\(45\) −15.9585 + 27.6409i −0.354632 + 0.614242i
\(46\) −6.64990 5.45015i −0.144563 0.118481i
\(47\) 44.0432 25.4284i 0.937090 0.541029i 0.0480430 0.998845i \(-0.484702\pi\)
0.889047 + 0.457816i \(0.151368\pi\)
\(48\) 3.22119 + 2.45833i 0.0671082 + 0.0512153i
\(49\) −32.2419 + 36.8979i −0.657998 + 0.753019i
\(50\) −3.97264 + 24.1604i −0.0794529 + 0.483207i
\(51\) 2.09235 1.20802i 0.0410265 0.0236867i
\(52\) 54.5296 47.9476i 1.04865 0.922069i
\(53\) −54.3930 31.4038i −1.02628 0.592525i −0.110365 0.993891i \(-0.535202\pi\)
−0.915918 + 0.401366i \(0.868535\pi\)
\(54\) 8.50036 3.20566i 0.157414 0.0593641i
\(55\) 28.1558i 0.511924i
\(56\) −55.8903 3.50277i −0.998042 0.0625494i
\(57\) 6.28554 0.110273
\(58\) −20.0165 53.0771i −0.345112 0.915123i
\(59\) 37.0048 64.0942i 0.627200 1.08634i −0.360912 0.932600i \(-0.617534\pi\)
0.988111 0.153741i \(-0.0491323\pi\)
\(60\) −2.71725 + 2.38927i −0.0452876 + 0.0398212i
\(61\) −25.2994 43.8198i −0.414743 0.718357i 0.580658 0.814148i \(-0.302795\pi\)
−0.995401 + 0.0957908i \(0.969462\pi\)
\(62\) 64.3469 + 10.5804i 1.03785 + 0.170652i
\(63\) −36.3890 + 50.8770i −0.577604 + 0.807571i
\(64\) −35.7653 53.0740i −0.558832 0.829281i
\(65\) 32.4191 + 56.1515i 0.498755 + 0.863869i
\(66\) −2.53096 + 3.08810i −0.0383478 + 0.0467894i
\(67\) 108.673 + 62.7422i 1.62198 + 0.936451i 0.986389 + 0.164426i \(0.0525772\pi\)
0.635592 + 0.772025i \(0.280756\pi\)
\(68\) −37.4166 + 7.49357i −0.550244 + 0.110200i
\(69\) −1.08875 −0.0157789
\(70\) 12.8673 48.3210i 0.183819 0.690301i
\(71\) −5.33822 −0.0751863 −0.0375931 0.999293i \(-0.511969\pi\)
−0.0375931 + 0.999293i \(0.511969\pi\)
\(72\) −71.4439 + 2.47932i −0.992276 + 0.0344350i
\(73\) −23.6569 13.6583i −0.324067 0.187100i 0.329137 0.944282i \(-0.393242\pi\)
−0.653204 + 0.757182i \(0.726576\pi\)
\(74\) −37.9159 + 46.2624i −0.512378 + 0.625168i
\(75\) 1.55023 + 2.68508i 0.0206697 + 0.0358010i
\(76\) −94.0487 31.7880i −1.23748 0.418263i
\(77\) 5.35941 54.9191i 0.0696027 0.713234i
\(78\) 1.49183 9.07283i 0.0191260 0.116318i
\(79\) 51.5380 + 89.2664i 0.652380 + 1.12995i 0.982544 + 0.186031i \(0.0595626\pi\)
−0.330164 + 0.943924i \(0.607104\pi\)
\(80\) 52.7408 22.0080i 0.659261 0.275100i
\(81\) −39.6362 + 68.6519i −0.489336 + 0.847554i
\(82\) 31.9415 + 84.6984i 0.389531 + 1.03291i
\(83\) −51.5695 −0.621319 −0.310660 0.950521i \(-0.600550\pi\)
−0.310660 + 0.950521i \(0.600550\pi\)
\(84\) −5.75491 + 4.14315i −0.0685109 + 0.0493232i
\(85\) 34.0744i 0.400876i
\(86\) −17.5802 46.6170i −0.204421 0.542058i
\(87\) −6.22075 3.59155i −0.0715029 0.0412822i
\(88\) 53.4875 33.4066i 0.607813 0.379620i
\(89\) 133.222 76.9158i 1.49688 0.864222i 0.496883 0.867818i \(-0.334478\pi\)
0.999994 + 0.00359545i \(0.00114447\pi\)
\(90\) 10.3570 62.9880i 0.115078 0.699867i
\(91\) 52.5464 + 115.697i 0.577433 + 1.27139i
\(92\) 16.2906 + 5.50613i 0.177072 + 0.0598493i
\(93\) 7.15123 4.12877i 0.0768950 0.0443953i
\(94\) −64.4749 + 78.6678i −0.685903 + 0.836892i
\(95\) 44.3238 76.7711i 0.466566 0.808117i
\(96\) −7.76289 2.32712i −0.0808634 0.0242409i
\(97\) 47.0436i 0.484986i 0.970153 + 0.242493i \(0.0779651\pi\)
−0.970153 + 0.242493i \(0.922035\pi\)
\(98\) 34.2961 91.8029i 0.349960 0.936765i
\(99\) 70.4400i 0.711516i
\(100\) −9.61637 48.0161i −0.0961637 0.480161i
\(101\) −74.6727 + 129.337i −0.739333 + 1.28056i 0.213462 + 0.976951i \(0.431526\pi\)
−0.952796 + 0.303612i \(0.901807\pi\)
\(102\) −3.06299 + 3.73725i −0.0300293 + 0.0366397i
\(103\) −17.1847 + 9.92160i −0.166842 + 0.0963262i −0.581096 0.813835i \(-0.697376\pi\)
0.414254 + 0.910161i \(0.364043\pi\)
\(104\) −68.2061 + 128.210i −0.655827 + 1.23279i
\(105\) −2.61843 5.76527i −0.0249375 0.0549073i
\(106\) 123.951 + 20.3810i 1.16935 + 0.192274i
\(107\) 7.91877 4.57190i 0.0740072 0.0427281i −0.462540 0.886599i \(-0.653062\pi\)
0.536547 + 0.843870i \(0.319728\pi\)
\(108\) −13.6448 + 11.9978i −0.126341 + 0.111091i
\(109\) −103.229 59.5992i −0.947053 0.546781i −0.0548888 0.998492i \(-0.517480\pi\)
−0.892164 + 0.451711i \(0.850814\pi\)
\(110\) 19.8703 + 52.6894i 0.180639 + 0.478994i
\(111\) 7.57425i 0.0682365i
\(112\) 107.062 32.8883i 0.955914 0.293646i
\(113\) −124.011 −1.09744 −0.548720 0.836006i \(-0.684885\pi\)
−0.548720 + 0.836006i \(0.684885\pi\)
\(114\) −11.7624 + 4.43586i −0.103179 + 0.0389111i
\(115\) −7.67752 + 13.2979i −0.0667611 + 0.115634i
\(116\) 74.9157 + 85.1997i 0.645825 + 0.734480i
\(117\) 81.1059 + 140.480i 0.693213 + 1.20068i
\(118\) −24.0160 + 146.058i −0.203526 + 1.23778i
\(119\) 6.48601 66.4636i 0.0545043 0.558518i
\(120\) 3.39877 6.38880i 0.0283231 0.0532400i
\(121\) −29.4303 50.9749i −0.243226 0.421280i
\(122\) 78.2687 + 64.1477i 0.641546 + 0.525801i
\(123\) 9.92683 + 5.73126i 0.0807059 + 0.0465956i
\(124\) −127.882 + 25.6115i −1.03131 + 0.206545i
\(125\) 133.022 1.06417
\(126\) 32.1914 120.889i 0.255488 0.959439i
\(127\) −57.6144 −0.453656 −0.226828 0.973935i \(-0.572836\pi\)
−0.226828 + 0.973935i \(0.572836\pi\)
\(128\) 104.385 + 74.0795i 0.815508 + 0.578746i
\(129\) −5.46361 3.15441i −0.0423535 0.0244528i
\(130\) −100.295 82.2001i −0.771500 0.632309i
\(131\) −62.1497 107.646i −0.474425 0.821728i 0.525146 0.851012i \(-0.324011\pi\)
−0.999571 + 0.0292837i \(0.990677\pi\)
\(132\) 2.55696 7.56508i 0.0193709 0.0573112i
\(133\) 101.069 141.308i 0.759915 1.06247i
\(134\) −247.644 40.7196i −1.84809 0.303877i
\(135\) −8.11216 14.0507i −0.0600901 0.104079i
\(136\) 64.7312 40.4290i 0.475965 0.297272i
\(137\) 84.7404 146.775i 0.618543 1.07135i −0.371208 0.928550i \(-0.621056\pi\)
0.989752 0.142799i \(-0.0456102\pi\)
\(138\) 2.03742 0.768355i 0.0147639 0.00556779i
\(139\) −266.497 −1.91725 −0.958624 0.284677i \(-0.908114\pi\)
−0.958624 + 0.284677i \(0.908114\pi\)
\(140\) 10.0221 + 99.5064i 0.0715864 + 0.710760i
\(141\) 12.8798i 0.0913459i
\(142\) 9.98969 3.76732i 0.0703499 0.0265304i
\(143\) −123.925 71.5483i −0.866610 0.500338i
\(144\) 131.947 55.0594i 0.916297 0.382357i
\(145\) −87.7339 + 50.6532i −0.605061 + 0.349332i
\(146\) 53.9093 + 8.86421i 0.369242 + 0.0607138i
\(147\) −4.00996 11.7438i −0.0272786 0.0798899i
\(148\) 38.3054 113.331i 0.258820 0.765753i
\(149\) 26.6902 15.4096i 0.179129 0.103420i −0.407754 0.913092i \(-0.633688\pi\)
0.586883 + 0.809672i \(0.300355\pi\)
\(150\) −4.79595 3.93068i −0.0319730 0.0262046i
\(151\) −11.7448 + 20.3425i −0.0777800 + 0.134719i −0.902292 0.431126i \(-0.858116\pi\)
0.824512 + 0.565845i \(0.191450\pi\)
\(152\) 198.432 6.88618i 1.30547 0.0453038i
\(153\) 85.2473i 0.557172i
\(154\) 28.7284 + 106.555i 0.186548 + 0.691916i
\(155\) 116.460i 0.751352i
\(156\) 3.61119 + 18.0313i 0.0231487 + 0.115585i
\(157\) −63.8147 + 110.530i −0.406463 + 0.704015i −0.994491 0.104826i \(-0.966571\pi\)
0.588028 + 0.808841i \(0.299905\pi\)
\(158\) −159.443 130.677i −1.00913 0.827070i
\(159\) 13.7754 7.95320i 0.0866374 0.0500202i
\(160\) −83.1650 + 78.4052i −0.519781 + 0.490032i
\(161\) −17.5065 + 24.4766i −0.108736 + 0.152029i
\(162\) 25.7238 156.444i 0.158789 0.965704i
\(163\) −138.291 + 79.8421i −0.848409 + 0.489829i −0.860114 0.510103i \(-0.829607\pi\)
0.0117050 + 0.999931i \(0.496274\pi\)
\(164\) −119.548 135.958i −0.728949 0.829015i
\(165\) 6.17530 + 3.56531i 0.0374261 + 0.0216080i
\(166\) 96.5046 36.3939i 0.581353 0.219240i
\(167\) 142.792i 0.855042i 0.904005 + 0.427521i \(0.140613\pi\)
−0.904005 + 0.427521i \(0.859387\pi\)
\(168\) 7.84553 11.8147i 0.0466996 0.0703254i
\(169\) 160.528 0.949869
\(170\) 24.0472 + 63.7652i 0.141454 + 0.375089i
\(171\) 110.889 192.066i 0.648474 1.12319i
\(172\) 65.7976 + 74.8299i 0.382544 + 0.435057i
\(173\) 97.8898 + 169.550i 0.565837 + 0.980059i 0.996971 + 0.0777710i \(0.0247803\pi\)
−0.431134 + 0.902288i \(0.641886\pi\)
\(174\) 14.1758 + 2.33091i 0.0814704 + 0.0133960i
\(175\) 85.2916 + 8.32338i 0.487380 + 0.0475622i
\(176\) −76.5181 + 100.263i −0.434762 + 0.569675i
\(177\) 9.37168 + 16.2322i 0.0529474 + 0.0917075i
\(178\) −195.024 + 237.955i −1.09564 + 1.33682i
\(179\) 129.477 + 74.7535i 0.723334 + 0.417617i 0.815979 0.578082i \(-0.196199\pi\)
−0.0926444 + 0.995699i \(0.529532\pi\)
\(180\) 25.0707 + 125.182i 0.139282 + 0.695455i
\(181\) 91.2994 0.504417 0.252208 0.967673i \(-0.418843\pi\)
0.252208 + 0.967673i \(0.418843\pi\)
\(182\) −179.983 179.426i −0.988917 0.985856i
\(183\) 12.8144 0.0700242
\(184\) −34.3712 + 1.19279i −0.186800 + 0.00648253i
\(185\) 92.5114 + 53.4115i 0.500062 + 0.288711i
\(186\) −10.4687 + 12.7732i −0.0562833 + 0.0686730i
\(187\) 37.6008 + 65.1265i 0.201074 + 0.348270i
\(188\) 65.1372 192.717i 0.346474 1.02509i
\(189\) −13.1486 28.9506i −0.0695693 0.153178i
\(190\) −28.7661 + 174.946i −0.151400 + 0.920769i
\(191\) −13.9140 24.0997i −0.0728480 0.126176i 0.827300 0.561760i \(-0.189875\pi\)
−0.900148 + 0.435583i \(0.856542\pi\)
\(192\) 16.1694 1.12361i 0.0842156 0.00585212i
\(193\) −121.192 + 209.911i −0.627938 + 1.08762i 0.360027 + 0.932942i \(0.382767\pi\)
−0.987965 + 0.154678i \(0.950566\pi\)
\(194\) −33.1999 88.0351i −0.171133 0.453789i
\(195\) −16.4207 −0.0842085
\(196\) 0.607652 + 195.999i 0.00310026 + 0.999995i
\(197\) 94.7050i 0.480736i 0.970682 + 0.240368i \(0.0772682\pi\)
−0.970682 + 0.240368i \(0.922732\pi\)
\(198\) 49.7113 + 131.818i 0.251067 + 0.665747i
\(199\) 267.738 + 154.579i 1.34542 + 0.776778i 0.987597 0.157011i \(-0.0501859\pi\)
0.357823 + 0.933790i \(0.383519\pi\)
\(200\) 51.8818 + 83.0684i 0.259409 + 0.415342i
\(201\) −27.5220 + 15.8899i −0.136926 + 0.0790540i
\(202\) 48.4624 294.733i 0.239913 1.45907i
\(203\) −180.770 + 82.1012i −0.890494 + 0.404439i
\(204\) 3.09445 9.15534i 0.0151689 0.0448791i
\(205\) 140.002 80.8304i 0.682938 0.394295i
\(206\) 25.1567 30.6945i 0.122120 0.149002i
\(207\) −19.2076 + 33.2685i −0.0927903 + 0.160717i
\(208\) 37.1566 288.060i 0.178637 1.38490i
\(209\) 195.644i 0.936094i
\(210\) 8.96870 + 8.94094i 0.0427081 + 0.0425759i
\(211\) 125.864i 0.596514i 0.954486 + 0.298257i \(0.0964052\pi\)
−0.954486 + 0.298257i \(0.903595\pi\)
\(212\) −246.339 + 49.3352i −1.16198 + 0.232713i
\(213\) 0.675969 1.17081i 0.00317356 0.00549677i
\(214\) −11.5923 + 14.1441i −0.0541695 + 0.0660940i
\(215\) −77.0556 + 44.4881i −0.358398 + 0.206921i
\(216\) 17.0671 32.0817i 0.0790142 0.148526i
\(217\) 22.1679 227.159i 0.102156 1.04682i
\(218\) 235.238 + 38.6797i 1.07907 + 0.177430i
\(219\) 5.99125 3.45905i 0.0273573 0.0157947i
\(220\) −74.3684 84.5773i −0.338038 0.384442i
\(221\) −149.976 86.5885i −0.678623 0.391803i
\(222\) −5.34534 14.1741i −0.0240781 0.0638472i
\(223\) 8.94619i 0.0401174i −0.999799 0.0200587i \(-0.993615\pi\)
0.999799 0.0200587i \(-0.00638532\pi\)
\(224\) −177.141 + 137.102i −0.790809 + 0.612064i
\(225\) 109.396 0.486206
\(226\) 232.067 87.5175i 1.02685 0.387246i
\(227\) 136.347 236.160i 0.600647 1.04035i −0.392076 0.919933i \(-0.628243\pi\)
0.992723 0.120419i \(-0.0384237\pi\)
\(228\) 18.8811 16.6021i 0.0828120 0.0728162i
\(229\) −165.611 286.846i −0.723191 1.25260i −0.959714 0.280978i \(-0.909341\pi\)
0.236523 0.971626i \(-0.423992\pi\)
\(230\) 4.98269 30.3032i 0.0216639 0.131753i
\(231\) 11.3665 + 8.12975i 0.0492058 + 0.0351937i
\(232\) −200.321 106.569i −0.863453 0.459347i
\(233\) −79.1185 137.037i −0.339564 0.588143i 0.644786 0.764363i \(-0.276946\pi\)
−0.984351 + 0.176220i \(0.943613\pi\)
\(234\) −250.918 205.648i −1.07230 0.878837i
\(235\) 157.313 + 90.8245i 0.669416 + 0.386487i
\(236\) −58.1343 290.274i −0.246332 1.22997i
\(237\) −26.1046 −0.110146
\(238\) 34.7675 + 128.954i 0.146082 + 0.541824i
\(239\) 48.9981 0.205013 0.102507 0.994732i \(-0.467314\pi\)
0.102507 + 0.994732i \(0.467314\pi\)
\(240\) −1.85154 + 14.3543i −0.00771477 + 0.0598095i
\(241\) 170.914 + 98.6771i 0.709186 + 0.409449i 0.810759 0.585379i \(-0.199054\pi\)
−0.101574 + 0.994828i \(0.532388\pi\)
\(242\) 91.0487 + 74.6221i 0.376234 + 0.308356i
\(243\) −30.4787 52.7907i −0.125427 0.217246i
\(244\) −191.739 64.8067i −0.785815 0.265601i
\(245\) −171.715 33.8367i −0.700878 0.138109i
\(246\) −22.6213 3.71957i −0.0919564 0.0151202i
\(247\) −225.267 390.175i −0.912014 1.57965i
\(248\) 221.238 138.178i 0.892089 0.557170i
\(249\) 6.53014 11.3105i 0.0262255 0.0454239i
\(250\) −248.930 + 93.8767i −0.995720 + 0.375507i
\(251\) 315.497 1.25696 0.628480 0.777826i \(-0.283677\pi\)
0.628480 + 0.777826i \(0.283677\pi\)
\(252\) 25.0732 + 248.945i 0.0994970 + 0.987876i
\(253\) 33.8883i 0.133946i
\(254\) 107.817 40.6599i 0.424475 0.160078i
\(255\) 7.47341 + 4.31478i 0.0293075 + 0.0169207i
\(256\) −247.621 64.9616i −0.967268 0.253756i
\(257\) −329.533 + 190.256i −1.28223 + 0.740296i −0.977256 0.212065i \(-0.931981\pi\)
−0.304974 + 0.952361i \(0.598648\pi\)
\(258\) 12.4505 + 2.04721i 0.0482576 + 0.00793492i
\(259\) 170.281 + 121.791i 0.657454 + 0.470234i
\(260\) 245.698 + 83.0445i 0.944991 + 0.319402i
\(261\) −219.492 + 126.724i −0.840967 + 0.485532i
\(262\) 192.273 + 157.584i 0.733865 + 0.601464i
\(263\) −98.1636 + 170.024i −0.373246 + 0.646480i −0.990063 0.140626i \(-0.955088\pi\)
0.616817 + 0.787106i \(0.288422\pi\)
\(264\) 0.553910 + 15.9614i 0.00209814 + 0.0604599i
\(265\) 224.335i 0.846547i
\(266\) −89.4101 + 335.764i −0.336128 + 1.26227i
\(267\) 38.9588i 0.145913i
\(268\) 492.165 98.5678i 1.83644 0.367790i
\(269\) 51.1557 88.6043i 0.190170 0.329384i −0.755137 0.655568i \(-0.772429\pi\)
0.945306 + 0.326184i \(0.105763\pi\)
\(270\) 25.0966 + 20.5688i 0.0929504 + 0.0761807i
\(271\) −221.981 + 128.161i −0.819118 + 0.472918i −0.850112 0.526602i \(-0.823466\pi\)
0.0309944 + 0.999520i \(0.490133\pi\)
\(272\) −92.6030 + 121.339i −0.340452 + 0.446100i
\(273\) −32.0292 3.12564i −0.117323 0.0114492i
\(274\) −54.9964 + 334.470i −0.200717 + 1.22070i
\(275\) −83.5757 + 48.2525i −0.303912 + 0.175464i
\(276\) −3.27048 + 2.87572i −0.0118496 + 0.0104193i
\(277\) −170.372 98.3646i −0.615063 0.355107i 0.159881 0.987136i \(-0.448889\pi\)
−0.774944 + 0.632029i \(0.782222\pi\)
\(278\) 498.710 188.074i 1.79392 0.676525i
\(279\) 291.358i 1.04429i
\(280\) −88.9790 179.138i −0.317782 0.639780i
\(281\) −70.2923 −0.250151 −0.125075 0.992147i \(-0.539917\pi\)
−0.125075 + 0.992147i \(0.539917\pi\)
\(282\) −9.08959 24.1026i −0.0322326 0.0854701i
\(283\) −148.495 + 257.201i −0.524718 + 0.908838i 0.474868 + 0.880057i \(0.342496\pi\)
−0.999586 + 0.0287807i \(0.990838\pi\)
\(284\) −16.0355 + 14.1000i −0.0564631 + 0.0496477i
\(285\) 11.2253 + 19.4427i 0.0393869 + 0.0682201i
\(286\) 282.401 + 46.4347i 0.987416 + 0.162359i
\(287\) 288.466 131.014i 1.00511 0.456494i
\(288\) −208.062 + 196.154i −0.722437 + 0.681089i
\(289\) −98.9951 171.465i −0.342544 0.593303i
\(290\) 128.434 156.706i 0.442874 0.540365i
\(291\) −10.3179 5.95704i −0.0354567 0.0204709i
\(292\) −107.139 + 21.4571i −0.366914 + 0.0734834i
\(293\) 135.561 0.462665 0.231333 0.972875i \(-0.425691\pi\)
0.231333 + 0.972875i \(0.425691\pi\)
\(294\) 15.7919 + 19.1469i 0.0537141 + 0.0651254i
\(295\) 264.346 0.896087
\(296\) 8.29805 + 239.116i 0.0280339 + 0.807824i
\(297\) 31.0096 + 17.9034i 0.104409 + 0.0602808i
\(298\) −39.0718 + 47.6727i −0.131113 + 0.159976i
\(299\) 39.0196 + 67.5839i 0.130500 + 0.226033i
\(300\) 11.7489 + 3.97106i 0.0391630 + 0.0132369i
\(301\) −158.768 + 72.1084i −0.527470 + 0.239563i
\(302\) 7.62233 46.3566i 0.0252395 0.153499i
\(303\) −18.9113 32.7553i −0.0624136 0.108103i
\(304\) −366.475 + 152.925i −1.20551 + 0.503042i
\(305\) 90.3637 156.515i 0.296274 0.513162i
\(306\) 60.1612 + 159.527i 0.196605 + 0.521332i
\(307\) 76.2052 0.248225 0.124113 0.992268i \(-0.460392\pi\)
0.124113 + 0.992268i \(0.460392\pi\)
\(308\) −128.960 179.127i −0.418700 0.581583i
\(309\) 5.02541i 0.0162635i
\(310\) 82.1885 + 217.937i 0.265124 + 0.703021i
\(311\) −171.554 99.0468i −0.551621 0.318479i 0.198154 0.980171i \(-0.436505\pi\)
−0.749776 + 0.661692i \(0.769839\pi\)
\(312\) −19.4829 31.1943i −0.0624453 0.0999817i
\(313\) −47.9693 + 27.6951i −0.153257 + 0.0884827i −0.574667 0.818387i \(-0.694868\pi\)
0.421411 + 0.906870i \(0.361535\pi\)
\(314\) 41.4156 251.877i 0.131897 0.802155i
\(315\) −222.362 21.6997i −0.705912 0.0688881i
\(316\) 390.596 + 132.019i 1.23606 + 0.417783i
\(317\) −259.080 + 149.580i −0.817289 + 0.471862i −0.849481 0.527620i \(-0.823085\pi\)
0.0321920 + 0.999482i \(0.489751\pi\)
\(318\) −20.1657 + 24.6048i −0.0634143 + 0.0773737i
\(319\) 111.791 193.627i 0.350441 0.606981i
\(320\) 100.298 205.415i 0.313432 0.641923i
\(321\) 2.31572i 0.00721409i
\(322\) 15.4871 58.1591i 0.0480966 0.180618i
\(323\) 236.770i 0.733034i
\(324\) 62.2683 + 310.915i 0.192186 + 0.959616i
\(325\) 111.117 192.461i 0.341900 0.592188i
\(326\) 202.444 247.008i 0.620992 0.757693i
\(327\) 26.1433 15.0938i 0.0799490 0.0461586i
\(328\) 319.665 + 170.058i 0.974588 + 0.518469i
\(329\) 289.557 + 207.101i 0.880111 + 0.629487i
\(330\) −14.0723 2.31388i −0.0426433 0.00701176i
\(331\) 325.087 187.689i 0.982135 0.567036i 0.0792209 0.996857i \(-0.474757\pi\)
0.902914 + 0.429821i \(0.141423\pi\)
\(332\) −154.910 + 136.212i −0.466596 + 0.410276i
\(333\) 231.445 + 133.625i 0.695029 + 0.401275i
\(334\) −100.772 267.214i −0.301712 0.800041i
\(335\) 448.203i 1.33792i
\(336\) −6.34383 + 27.6462i −0.0188804 + 0.0822803i
\(337\) −4.99043 −0.0148084 −0.00740419 0.999973i \(-0.502357\pi\)
−0.00740419 + 0.999973i \(0.502357\pi\)
\(338\) −300.404 + 113.289i −0.888769 + 0.335173i
\(339\) 15.7032 27.1988i 0.0463222 0.0802324i
\(340\) −90.0014 102.356i −0.264710 0.301048i
\(341\) 128.512 + 222.589i 0.376868 + 0.652755i
\(342\) −71.9668 + 437.679i −0.210429 + 1.27976i
\(343\) −328.497 98.6856i −0.957717 0.287713i
\(344\) −175.940 93.5978i −0.511452 0.272087i
\(345\) −1.94438 3.36776i −0.00563588 0.00976163i
\(346\) −302.842 248.204i −0.875266 0.717354i
\(347\) −320.772 185.198i −0.924414 0.533711i −0.0393734 0.999225i \(-0.512536\pi\)
−0.885041 + 0.465514i \(0.845870\pi\)
\(348\) −28.1730 + 5.64231i −0.0809568 + 0.0162135i
\(349\) 25.6801 0.0735821 0.0367910 0.999323i \(-0.488286\pi\)
0.0367910 + 0.999323i \(0.488286\pi\)
\(350\) −165.484 + 44.6165i −0.472813 + 0.127476i
\(351\) −82.4571 −0.234921
\(352\) 72.4340 241.628i 0.205779 0.686442i
\(353\) −229.938 132.755i −0.651383 0.376076i 0.137603 0.990487i \(-0.456060\pi\)
−0.788986 + 0.614411i \(0.789394\pi\)
\(354\) −28.9932 23.7624i −0.0819017 0.0671253i
\(355\) −9.53348 16.5125i −0.0268549 0.0465140i
\(356\) 197.027 582.929i 0.553446 1.63744i
\(357\) 13.7559 + 9.83871i 0.0385319 + 0.0275594i
\(358\) −295.052 48.5148i −0.824167 0.135516i
\(359\) 275.228 + 476.709i 0.766651 + 1.32788i 0.939369 + 0.342908i \(0.111412\pi\)
−0.172718 + 0.984971i \(0.555255\pi\)
\(360\) −135.260 216.566i −0.375722 0.601573i
\(361\) −127.489 + 220.817i −0.353155 + 0.611682i
\(362\) −170.853 + 64.4323i −0.471970 + 0.177990i
\(363\) 14.9068 0.0410656
\(364\) 463.436 + 208.750i 1.27318 + 0.573489i
\(365\) 97.5689i 0.267312i
\(366\) −23.9803 + 9.04347i −0.0655199 + 0.0247089i
\(367\) 180.099 + 103.980i 0.490732 + 0.283324i 0.724878 0.688877i \(-0.241896\pi\)
−0.234146 + 0.972201i \(0.575229\pi\)
\(368\) 63.4788 26.4888i 0.172497 0.0719803i
\(369\) 350.257 202.221i 0.949207 0.548025i
\(370\) −210.815 34.6639i −0.569770 0.0936863i
\(371\) 42.7018 437.575i 0.115099 1.17945i
\(372\) 10.5762 31.2911i 0.0284307 0.0841159i
\(373\) 393.539 227.210i 1.05507 0.609142i 0.131002 0.991382i \(-0.458180\pi\)
0.924063 + 0.382240i \(0.124847\pi\)
\(374\) −116.326 95.3387i −0.311031 0.254916i
\(375\) −16.8443 + 29.1751i −0.0449180 + 0.0778003i
\(376\) 14.1106 + 406.609i 0.0375281 + 1.08141i
\(377\) 514.871i 1.36570i
\(378\) 45.0368 + 44.8974i 0.119145 + 0.118776i
\(379\) 373.244i 0.984813i −0.870365 0.492406i \(-0.836117\pi\)
0.870365 0.492406i \(-0.163883\pi\)
\(380\) −69.6325 347.686i −0.183243 0.914964i
\(381\) 7.29559 12.6363i 0.0191485 0.0331662i
\(382\) 43.0457 + 35.2796i 0.112685 + 0.0923549i
\(383\) −270.298 + 156.056i −0.705738 + 0.407458i −0.809481 0.587146i \(-0.800251\pi\)
0.103743 + 0.994604i \(0.466918\pi\)
\(384\) −29.4656 + 13.5138i −0.0767334 + 0.0351922i
\(385\) 179.450 81.5014i 0.466103 0.211692i
\(386\) 78.6533 478.345i 0.203765 1.23923i
\(387\) −192.777 + 111.300i −0.498133 + 0.287597i
\(388\) 124.257 + 141.314i 0.320251 + 0.364213i
\(389\) 439.628 + 253.819i 1.13015 + 0.652492i 0.943973 0.330024i \(-0.107057\pi\)
0.186177 + 0.982516i \(0.440390\pi\)
\(390\) 30.7288 11.5885i 0.0787918 0.0297140i
\(391\) 41.0120i 0.104890i
\(392\) −139.459 366.354i −0.355762 0.934577i
\(393\) 31.4796 0.0801007
\(394\) −66.8358 177.226i −0.169634 0.449813i
\(395\) −184.082 + 318.840i −0.466031 + 0.807190i
\(396\) −186.055 211.595i −0.469835 0.534331i
\(397\) −95.6487 165.668i −0.240929 0.417301i 0.720050 0.693922i \(-0.244119\pi\)
−0.960979 + 0.276621i \(0.910785\pi\)
\(398\) −610.123 100.321i −1.53297 0.252064i
\(399\) 18.1945 + 40.0606i 0.0456002 + 0.100402i
\(400\) −155.712 118.836i −0.389281 0.297089i
\(401\) 61.2011 + 106.004i 0.152621 + 0.264348i 0.932190 0.361968i \(-0.117895\pi\)
−0.779569 + 0.626316i \(0.784562\pi\)
\(402\) 40.2895 49.1585i 0.100223 0.122285i
\(403\) −512.587 295.942i −1.27193 0.734347i
\(404\) 117.310 + 585.750i 0.290372 + 1.44988i
\(405\) −283.143 −0.699120
\(406\) 280.344 281.214i 0.690502 0.692646i
\(407\) −235.756 −0.579254
\(408\) 0.670347 + 19.3167i 0.00164301 + 0.0473448i
\(409\) −4.57744 2.64279i −0.0111918 0.00646158i 0.494394 0.869238i \(-0.335390\pi\)
−0.505585 + 0.862777i \(0.668723\pi\)
\(410\) −204.949 + 250.065i −0.499877 + 0.609915i
\(411\) 21.4610 + 37.1716i 0.0522166 + 0.0904418i
\(412\) −25.4151 + 75.1939i −0.0616872 + 0.182509i
\(413\) 515.617 + 50.3178i 1.24847 + 0.121835i
\(414\) 12.4657 75.8123i 0.0301103 0.183122i
\(415\) −92.0975 159.517i −0.221922 0.384379i
\(416\) 133.758 + 565.283i 0.321534 + 1.35885i
\(417\) 33.7460 58.4498i 0.0809257 0.140167i
\(418\) −138.071 366.118i −0.330313 0.875880i
\(419\) −34.7160 −0.0828545 −0.0414272 0.999142i \(-0.513190\pi\)
−0.0414272 + 0.999142i \(0.513190\pi\)
\(420\) −23.0934 10.4022i −0.0549844 0.0247671i
\(421\) 394.337i 0.936669i 0.883551 + 0.468334i \(0.155146\pi\)
−0.883551 + 0.468334i \(0.844854\pi\)
\(422\) −88.8257 235.536i −0.210487 0.558143i
\(423\) 393.564 + 227.224i 0.930412 + 0.537173i
\(424\) 426.169 266.171i 1.00512 0.627762i
\(425\) −101.144 + 58.3956i −0.237986 + 0.137401i
\(426\) −0.438702 + 2.66805i −0.00102982 + 0.00626302i
\(427\) 206.050 288.088i 0.482554 0.674678i
\(428\) 11.7114 34.6495i 0.0273630 0.0809569i
\(429\) 31.3848 18.1200i 0.0731581 0.0422378i
\(430\) 112.802 137.633i 0.262329 0.320076i
\(431\) 215.872 373.901i 0.500862 0.867519i −0.499137 0.866523i \(-0.666350\pi\)
1.00000 0.000995912i \(-0.000317009\pi\)
\(432\) −9.29762 + 72.0807i −0.0215223 + 0.166853i
\(433\) 318.535i 0.735647i −0.929896 0.367823i \(-0.880103\pi\)
0.929896 0.367823i \(-0.119897\pi\)
\(434\) 118.828 + 440.739i 0.273798 + 1.01553i
\(435\) 25.6565i 0.0589803i
\(436\) −467.510 + 93.6300i −1.07227 + 0.214748i
\(437\) 53.3481 92.4016i 0.122078 0.211445i
\(438\) −8.77058 + 10.7013i −0.0200242 + 0.0244321i
\(439\) 532.799 307.612i 1.21366 0.700710i 0.250109 0.968218i \(-0.419533\pi\)
0.963556 + 0.267508i \(0.0862001\pi\)
\(440\) 198.858 + 105.790i 0.451949 + 0.240432i
\(441\) −429.596 84.6525i −0.974141 0.191956i
\(442\) 341.765 + 56.1957i 0.773223 + 0.127140i
\(443\) −86.4553 + 49.9150i −0.195159 + 0.112675i −0.594395 0.804173i \(-0.702609\pi\)
0.399237 + 0.916848i \(0.369275\pi\)
\(444\) 20.0060 + 22.7523i 0.0450586 + 0.0512440i
\(445\) 475.840 + 274.726i 1.06930 + 0.617362i
\(446\) 6.31355 + 16.7415i 0.0141559 + 0.0375369i
\(447\) 7.80515i 0.0174612i
\(448\) 234.736 381.579i 0.523965 0.851740i
\(449\) −75.3168 −0.167743 −0.0838717 0.996477i \(-0.526729\pi\)
−0.0838717 + 0.996477i \(0.526729\pi\)
\(450\) −204.719 + 77.2038i −0.454931 + 0.171564i
\(451\) −178.391 + 308.983i −0.395546 + 0.685105i
\(452\) −372.516 + 327.552i −0.824151 + 0.724672i
\(453\) −2.97443 5.15187i −0.00656608 0.0113728i
\(454\) −88.4889 + 538.161i −0.194909 + 1.18538i
\(455\) −264.037 + 369.161i −0.580301 + 0.811343i
\(456\) −23.6167 + 44.3932i −0.0517910 + 0.0973536i
\(457\) 104.447 + 180.907i 0.228549 + 0.395858i 0.957378 0.288837i \(-0.0932687\pi\)
−0.728830 + 0.684695i \(0.759935\pi\)
\(458\) 512.351 + 419.914i 1.11867 + 0.916843i
\(459\) 37.5281 + 21.6669i 0.0817606 + 0.0472045i
\(460\) 12.0614 + 60.2243i 0.0262203 + 0.130922i
\(461\) −751.461 −1.63007 −0.815034 0.579413i \(-0.803282\pi\)
−0.815034 + 0.579413i \(0.803282\pi\)
\(462\) −27.0081 7.19195i −0.0584592 0.0155670i
\(463\) −3.56075 −0.00769060 −0.00384530 0.999993i \(-0.501224\pi\)
−0.00384530 + 0.999993i \(0.501224\pi\)
\(464\) 450.079 + 58.0553i 0.969998 + 0.125119i
\(465\) 25.5426 + 14.7470i 0.0549304 + 0.0317141i
\(466\) 244.769 + 200.609i 0.525256 + 0.430491i
\(467\) 206.945 + 358.440i 0.443138 + 0.767537i 0.997920 0.0644583i \(-0.0205320\pi\)
−0.554783 + 0.831995i \(0.687199\pi\)
\(468\) 614.686 + 207.760i 1.31343 + 0.443932i
\(469\) −85.3146 + 874.238i −0.181908 + 1.86405i
\(470\) −358.484 58.9449i −0.762733 0.125415i
\(471\) −16.1615 27.9925i −0.0343131 0.0594320i
\(472\) 313.643 + 502.177i 0.664499 + 1.06394i
\(473\) 98.1843 170.060i 0.207578 0.359535i
\(474\) 48.8509 18.4227i 0.103061 0.0388664i
\(475\) −303.843 −0.639669
\(476\) −156.068 216.782i −0.327874 0.455424i
\(477\) 561.240i 1.17660i
\(478\) −91.6927 + 34.5792i −0.191826 + 0.0723415i
\(479\) −785.798 453.681i −1.64050 0.947142i −0.980657 0.195737i \(-0.937290\pi\)
−0.659841 0.751405i \(-0.729376\pi\)
\(480\) −6.66529 28.1686i −0.0138860 0.0586845i
\(481\) 470.172 271.454i 0.977488 0.564353i
\(482\) −389.478 64.0412i −0.808047 0.132866i
\(483\) −3.15154 6.93907i −0.00652494 0.0143666i
\(484\) −223.047 75.3886i −0.460840 0.155762i
\(485\) −145.518 + 84.0147i −0.300037 + 0.173226i
\(486\) 94.2922 + 77.2803i 0.194017 + 0.159013i
\(487\) −421.452 + 729.977i −0.865405 + 1.49893i 0.00123943 + 0.999999i \(0.499605\pi\)
−0.866644 + 0.498926i \(0.833728\pi\)
\(488\) 404.546 14.0390i 0.828988 0.0287684i
\(489\) 40.4410i 0.0827014i
\(490\) 345.219 57.8634i 0.704528 0.118089i
\(491\) 144.126i 0.293535i 0.989171 + 0.146768i \(0.0468870\pi\)
−0.989171 + 0.146768i \(0.953113\pi\)
\(492\) 44.9573 9.00378i 0.0913766 0.0183004i
\(493\) 135.290 234.329i 0.274422 0.475313i
\(494\) 696.911 + 571.177i 1.41075 + 1.15623i
\(495\) 217.889 125.798i 0.440179 0.254138i
\(496\) −316.498 + 414.713i −0.638101 + 0.836115i
\(497\) −15.4523 34.0229i −0.0310912 0.0684566i
\(498\) −4.23805 + 25.7745i −0.00851014 + 0.0517560i
\(499\) 330.101 190.584i 0.661526 0.381932i −0.131332 0.991338i \(-0.541926\pi\)
0.792858 + 0.609406i \(0.208592\pi\)
\(500\) 399.584 351.352i 0.799168 0.702705i
\(501\) −31.3180 18.0815i −0.0625110 0.0360908i
\(502\) −590.405 + 222.654i −1.17611 + 0.443534i
\(503\) 936.429i 1.86169i −0.365418 0.930843i \(-0.619074\pi\)
0.365418 0.930843i \(-0.380926\pi\)
\(504\) −222.607 448.168i −0.441681 0.889222i
\(505\) −533.429 −1.05629
\(506\) 23.9158 + 63.4168i 0.0472645 + 0.125330i
\(507\) −20.3273 + 35.2080i −0.0400933 + 0.0694437i
\(508\) −173.068 + 152.178i −0.340685 + 0.299563i
\(509\) −167.592 290.278i −0.329258 0.570291i 0.653107 0.757265i \(-0.273465\pi\)
−0.982365 + 0.186975i \(0.940132\pi\)
\(510\) −17.0304 2.80028i −0.0333930 0.00549075i
\(511\) 18.5721 190.312i 0.0363446 0.372431i
\(512\) 509.230 53.1863i 0.994590 0.103880i
\(513\) 56.3682 + 97.6327i 0.109880 + 0.190317i
\(514\) 482.403 588.596i 0.938528 1.14513i
\(515\) −61.3800 35.4378i −0.119185 0.0688112i
\(516\) −24.7440 + 4.95557i −0.0479534 + 0.00960382i
\(517\) −400.896 −0.775427
\(518\) −404.605 107.742i −0.781091 0.207996i
\(519\) −49.5824 −0.0955345
\(520\) −518.393 + 17.9898i −0.996910 + 0.0345958i
\(521\) −421.675 243.454i −0.809357 0.467283i 0.0373754 0.999301i \(-0.488100\pi\)
−0.846733 + 0.532019i \(0.821434\pi\)
\(522\) 321.315 392.046i 0.615545 0.751046i
\(523\) 86.3132 + 149.499i 0.165035 + 0.285849i 0.936668 0.350220i \(-0.113893\pi\)
−0.771633 + 0.636068i \(0.780560\pi\)
\(524\) −471.020 159.202i −0.898894 0.303821i
\(525\) −12.6258 + 17.6527i −0.0240492 + 0.0336242i
\(526\) 63.7080 387.452i 0.121118 0.736600i
\(527\) 155.527 + 269.380i 0.295117 + 0.511157i
\(528\) −12.3009 29.4785i −0.0232972 0.0558305i
\(529\) 255.259 442.122i 0.482532 0.835770i
\(530\) 158.319 + 419.809i 0.298715 + 0.792093i
\(531\) 661.339 1.24546
\(532\) −69.6396 691.431i −0.130902 1.29968i
\(533\) 821.611i 1.54148i
\(534\) −27.4942 72.9055i −0.0514872 0.136527i
\(535\) 28.2841 + 16.3298i 0.0528675 + 0.0305230i
\(536\) −851.451 + 531.788i −1.58853 + 0.992142i
\(537\) −32.7908 + 18.9318i −0.0610629 + 0.0352547i
\(538\) −33.1999 + 201.912i −0.0617099 + 0.375300i
\(539\) 365.538 124.814i 0.678178 0.231566i
\(540\) −61.4805 20.7801i −0.113853 0.0384816i
\(541\) −500.736 + 289.100i −0.925574 + 0.534381i −0.885409 0.464812i \(-0.846122\pi\)
−0.0401652 + 0.999193i \(0.512788\pi\)
\(542\) 324.958 396.491i 0.599553 0.731534i
\(543\) −11.5611 + 20.0244i −0.0212911 + 0.0368773i
\(544\) 87.6604 292.420i 0.161140 0.537537i
\(545\) 425.750i 0.781193i
\(546\) 62.1436 16.7546i 0.113816 0.0306861i
\(547\) 454.579i 0.831040i −0.909584 0.415520i \(-0.863600\pi\)
0.909584 0.415520i \(-0.136400\pi\)
\(548\) −133.127 664.724i −0.242932 1.21300i
\(549\) 226.071 391.567i 0.411788 0.713237i
\(550\) 122.346 149.279i 0.222448 0.271416i
\(551\) 609.629 351.969i 1.10640 0.638783i
\(552\) 4.09075 7.68955i 0.00741078 0.0139303i
\(553\) −419.751 + 586.871i −0.759043 + 1.06125i
\(554\) 388.245 + 63.8384i 0.700803 + 0.115232i
\(555\) −23.4291 + 13.5268i −0.0422145 + 0.0243726i
\(556\) −800.532 + 703.905i −1.43981 + 1.26602i
\(557\) −25.2401 14.5724i −0.0453143 0.0261622i 0.477172 0.878810i \(-0.341662\pi\)
−0.522486 + 0.852648i \(0.674995\pi\)
\(558\) 205.619 + 545.233i 0.368492 + 0.977120i
\(559\) 452.205i 0.808953i
\(560\) 292.934 + 272.436i 0.523096 + 0.486493i
\(561\) −19.0453 −0.0339488
\(562\) 131.542 49.6071i 0.234060 0.0882688i
\(563\) −514.005 + 890.283i −0.912975 + 1.58132i −0.103136 + 0.994667i \(0.532888\pi\)
−0.809839 + 0.586652i \(0.800446\pi\)
\(564\) 34.0196 + 38.6896i 0.0603184 + 0.0685986i
\(565\) −221.469 383.596i −0.391981 0.678931i
\(566\) 96.3730 586.110i 0.170270 1.03553i
\(567\) −552.283 53.8959i −0.974044 0.0950544i
\(568\) 20.0574 37.7026i 0.0353122 0.0663778i
\(569\) 409.852 + 709.885i 0.720303 + 1.24760i 0.960878 + 0.276971i \(0.0893305\pi\)
−0.240576 + 0.970630i \(0.577336\pi\)
\(570\) −34.7277 28.4622i −0.0609257 0.0499337i
\(571\) −140.820 81.3023i −0.246620 0.142386i 0.371596 0.928395i \(-0.378811\pi\)
−0.618215 + 0.786009i \(0.712144\pi\)
\(572\) −561.241 + 112.402i −0.981191 + 0.196507i
\(573\) 7.04760 0.0122995
\(574\) −447.362 + 448.751i −0.779376 + 0.781796i
\(575\) 52.6299 0.0915303
\(576\) 250.926 513.907i 0.435635 0.892199i
\(577\) 131.878 + 76.1400i 0.228559 + 0.131958i 0.609907 0.792473i \(-0.291207\pi\)
−0.381348 + 0.924431i \(0.624540\pi\)
\(578\) 306.261 + 251.007i 0.529864 + 0.434268i
\(579\) −30.6926 53.1611i −0.0530097 0.0918154i
\(580\) −129.753 + 383.890i −0.223712 + 0.661880i
\(581\) −149.276 328.676i −0.256930 0.565708i
\(582\) 23.5124 + 3.86611i 0.0403994 + 0.00664279i
\(583\) 247.551 + 428.772i 0.424617 + 0.735457i
\(584\) 185.352 115.764i 0.317383 0.198227i
\(585\) −289.692 + 501.762i −0.495201 + 0.857713i
\(586\) −253.682 + 95.6688i −0.432905 + 0.163257i
\(587\) 894.404 1.52369 0.761843 0.647761i \(-0.224295\pi\)
0.761843 + 0.647761i \(0.224295\pi\)
\(588\) −43.0647 24.6857i −0.0732392 0.0419825i
\(589\) 809.232i 1.37391i
\(590\) −494.684 + 186.556i −0.838447 + 0.316196i
\(591\) −20.7713 11.9923i −0.0351460 0.0202916i
\(592\) −184.279 441.614i −0.311282 0.745969i
\(593\) 164.729 95.1064i 0.277789 0.160382i −0.354633 0.935006i \(-0.615394\pi\)
0.632422 + 0.774624i \(0.282061\pi\)
\(594\) −70.6647 11.6193i −0.118964 0.0195610i
\(595\) 217.172 98.6338i 0.364995 0.165771i
\(596\) 39.4731 116.786i 0.0662301 0.195950i
\(597\) −67.8064 + 39.1480i −0.113579 + 0.0655746i
\(598\) −120.715 98.9360i −0.201864 0.165445i
\(599\) 146.832 254.320i 0.245128 0.424574i −0.717040 0.697033i \(-0.754503\pi\)
0.962168 + 0.272458i \(0.0878366\pi\)
\(600\) −24.7888 + 0.860245i −0.0413146 + 0.00143374i
\(601\) 597.574i 0.994299i 0.867665 + 0.497150i \(0.165620\pi\)
−0.867665 + 0.497150i \(0.834380\pi\)
\(602\) 246.223 246.987i 0.409008 0.410278i
\(603\) 1121.31i 1.85956i
\(604\) 18.4510 + 92.1287i 0.0305480 + 0.152531i
\(605\) 105.119 182.071i 0.173750 0.300944i
\(606\) 58.5060 + 47.9505i 0.0965445 + 0.0791263i
\(607\) −10.6620 + 6.15569i −0.0175650 + 0.0101412i −0.508757 0.860910i \(-0.669895\pi\)
0.491192 + 0.871051i \(0.336561\pi\)
\(608\) 577.881 544.807i 0.950462 0.896064i
\(609\) 4.88366 50.0440i 0.00801915 0.0821740i
\(610\) −58.6458 + 356.665i −0.0961407 + 0.584697i
\(611\) 799.512 461.599i 1.30853 0.755481i
\(612\) −225.165 256.075i −0.367917 0.418422i
\(613\) 118.897 + 68.6451i 0.193959 + 0.111982i 0.593835 0.804587i \(-0.297613\pi\)
−0.399876 + 0.916569i \(0.630947\pi\)
\(614\) −142.607 + 53.7800i −0.232258 + 0.0875895i
\(615\) 40.9416i 0.0665717i
\(616\) 367.743 + 244.200i 0.596986 + 0.396429i
\(617\) 290.516 0.470853 0.235427 0.971892i \(-0.424351\pi\)
0.235427 + 0.971892i \(0.424351\pi\)
\(618\) 3.54656 + 9.40430i 0.00573877 + 0.0152173i
\(619\) 51.1586 88.6092i 0.0826471 0.143149i −0.821739 0.569864i \(-0.806996\pi\)
0.904386 + 0.426715i \(0.140329\pi\)
\(620\) −307.607 349.833i −0.496140 0.564247i
\(621\) −9.76379 16.9114i −0.0157227 0.0272325i
\(622\) 390.938 + 64.2812i 0.628517 + 0.103346i
\(623\) 875.851 + 626.440i 1.40586 + 1.00552i
\(624\) 58.4740 + 44.6259i 0.0937083 + 0.0715158i
\(625\) 84.5320 + 146.414i 0.135251 + 0.234262i
\(626\) 70.2222 85.6804i 0.112176 0.136870i
\(627\) −42.9098 24.7740i −0.0684366 0.0395119i
\(628\) 100.253 + 500.577i 0.159638 + 0.797097i
\(629\) −285.315 −0.453600
\(630\) 431.432 116.319i 0.684812 0.184633i
\(631\) −562.739 −0.891820 −0.445910 0.895078i \(-0.647120\pi\)
−0.445910 + 0.895078i \(0.647120\pi\)
\(632\) −824.112 + 28.5992i −1.30397 + 0.0452519i
\(633\) −27.6054 15.9380i −0.0436104 0.0251785i
\(634\) 379.268 462.757i 0.598214 0.729900i
\(635\) −102.893 178.216i −0.162036 0.280655i
\(636\) 20.3729 60.2758i 0.0320328 0.0947732i
\(637\) −585.284 + 669.805i −0.918814 + 1.05150i
\(638\) −72.5519 + 441.237i −0.113718 + 0.691595i
\(639\) −23.8508 41.3108i −0.0373252 0.0646492i
\(640\) −42.7265 + 455.187i −0.0667602 + 0.711229i
\(641\) 376.275 651.727i 0.587012 1.01673i −0.407610 0.913156i \(-0.633638\pi\)
0.994621 0.103578i \(-0.0330291\pi\)
\(642\) −1.63427 4.33353i −0.00254558 0.00675005i
\(643\) −253.143 −0.393690 −0.196845 0.980435i \(-0.563070\pi\)
−0.196845 + 0.980435i \(0.563070\pi\)
\(644\) 12.0626 + 119.766i 0.0187307 + 0.185972i
\(645\) 22.5337i 0.0349360i
\(646\) −167.095 443.079i −0.258660 0.685881i
\(647\) 485.492 + 280.299i 0.750374 + 0.433229i 0.825829 0.563921i \(-0.190708\pi\)
−0.0754551 + 0.997149i \(0.524041\pi\)
\(648\) −335.947 537.887i −0.518436 0.830073i
\(649\) −505.244 + 291.703i −0.778497 + 0.449465i
\(650\) −72.1150 + 438.581i −0.110946 + 0.674739i
\(651\) 47.0149 + 33.6267i 0.0722195 + 0.0516539i
\(652\) −204.523 + 605.108i −0.313686 + 0.928079i
\(653\) 602.396 347.793i 0.922505 0.532609i 0.0380717 0.999275i \(-0.487878\pi\)
0.884433 + 0.466666i \(0.154545\pi\)
\(654\) −38.2712 + 46.6959i −0.0585186 + 0.0714004i
\(655\) 221.985 384.489i 0.338908 0.587007i
\(656\) −718.219 92.6424i −1.09485 0.141223i
\(657\) 244.097i 0.371533i
\(658\) −688.019 183.211i −1.04562 0.278437i
\(659\) 323.387i 0.490724i 0.969432 + 0.245362i \(0.0789068\pi\)
−0.969432 + 0.245362i \(0.921093\pi\)
\(660\) 27.9671 5.60109i 0.0423745 0.00848650i
\(661\) 15.5168 26.8758i 0.0234747 0.0406593i −0.854049 0.520192i \(-0.825860\pi\)
0.877524 + 0.479533i \(0.159194\pi\)
\(662\) −475.894 + 580.654i −0.718873 + 0.877120i
\(663\) 37.9822 21.9291i 0.0572884 0.0330755i
\(664\) 193.763 364.223i 0.291811 0.548529i
\(665\) 617.600 + 60.2699i 0.928721 + 0.0906315i
\(666\) −527.416 86.7221i −0.791916 0.130213i
\(667\) −105.596 + 60.9661i −0.158315 + 0.0914035i
\(668\) 377.159 + 428.933i 0.564610 + 0.642116i
\(669\) 1.96213 + 1.13284i 0.00293293 + 0.00169333i
\(670\) −316.308 838.745i −0.472102 1.25186i
\(671\) 398.862i 0.594429i
\(672\) −7.63908 56.2127i −0.0113677 0.0836498i
\(673\) 1011.75 1.50334 0.751670 0.659539i \(-0.229249\pi\)
0.751670 + 0.659539i \(0.229249\pi\)
\(674\) 9.33884 3.52187i 0.0138558 0.00522533i
\(675\) −27.8047 + 48.1592i −0.0411922 + 0.0713469i
\(676\) 482.210 424.005i 0.713328 0.627227i
\(677\) −34.7377 60.1674i −0.0513112 0.0888736i 0.839229 0.543778i \(-0.183007\pi\)
−0.890540 + 0.454905i \(0.849673\pi\)
\(678\) −10.1914 + 61.9806i −0.0150315 + 0.0914169i
\(679\) −299.831 + 136.175i −0.441577 + 0.200553i
\(680\) 240.660 + 128.028i 0.353911 + 0.188277i
\(681\) 34.5307 + 59.8089i 0.0507058 + 0.0878251i
\(682\) −397.578 325.848i −0.582959 0.477784i
\(683\) −824.530 476.042i −1.20722 0.696987i −0.245067 0.969506i \(-0.578810\pi\)
−0.962150 + 0.272519i \(0.912143\pi\)
\(684\) −174.206 869.840i −0.254688 1.27170i
\(685\) 605.348 0.883720
\(686\) 684.378 47.1533i 0.997635 0.0687366i
\(687\) 83.8839 0.122102
\(688\) 395.299 + 50.9893i 0.574563 + 0.0741123i
\(689\) −987.391 570.070i −1.43308 0.827388i
\(690\) 6.01533 + 4.93007i 0.00871787 + 0.00714502i
\(691\) −34.0754 59.0204i −0.0493132 0.0854130i 0.840315 0.542098i \(-0.182370\pi\)
−0.889628 + 0.456685i \(0.849037\pi\)
\(692\) 741.888 + 250.754i 1.07209 + 0.362361i
\(693\) 448.947 203.900i 0.647831 0.294228i
\(694\) 730.975 + 120.193i 1.05328 + 0.173189i
\(695\) −475.935 824.343i −0.684798 1.18611i
\(696\) 48.7395 30.4411i 0.0700281 0.0437372i
\(697\) −215.891 + 373.934i −0.309743 + 0.536490i
\(698\) −48.0565 + 18.1231i −0.0688489 + 0.0259644i
\(699\) 40.0745 0.0573311
\(700\) 278.192 200.280i 0.397418 0.286114i
\(701\) 1.67276i 0.00238625i −0.999999 0.00119312i \(-0.999620\pi\)
0.999999 0.00119312i \(-0.000379783\pi\)
\(702\) 154.306 58.1921i 0.219809 0.0828947i
\(703\) −642.825 371.135i −0.914403 0.527931i
\(704\) 34.9734 + 503.289i 0.0496781 + 0.714899i
\(705\) −39.8404 + 23.0019i −0.0565112 + 0.0326267i
\(706\) 523.984 + 86.1577i 0.742186 + 0.122036i
\(707\) −1040.47 101.537i −1.47168 0.143617i
\(708\) 71.0261 + 24.0064i 0.100319 + 0.0339074i
\(709\) 45.7969 26.4408i 0.0645936 0.0372931i −0.467355 0.884070i \(-0.654793\pi\)
0.531949 + 0.846776i \(0.321460\pi\)
\(710\) 29.4937 + 24.1726i 0.0415405 + 0.0340459i
\(711\) −460.536 + 797.673i −0.647731 + 1.12190i
\(712\) 42.6817 + 1229.91i 0.0599461 + 1.72740i
\(713\) 140.171i 0.196593i
\(714\) −32.6855 8.70378i −0.0457780 0.0121902i
\(715\) 511.109i 0.714838i
\(716\) 586.384 117.437i 0.818972 0.164019i
\(717\) −6.20454 + 10.7466i −0.00865347 + 0.0149882i
\(718\) −851.473 697.853i −1.18590 0.971941i
\(719\) −824.178 + 475.840i −1.14628 + 0.661808i −0.947979 0.318333i \(-0.896877\pi\)
−0.198305 + 0.980140i \(0.563544\pi\)
\(720\) 405.955 + 309.815i 0.563827 + 0.430298i
\(721\) −112.979 80.8064i −0.156697 0.112075i
\(722\) 82.7399 503.198i 0.114598 0.696950i
\(723\) −43.2849 + 24.9906i −0.0598685 + 0.0345651i
\(724\) 274.255 241.151i 0.378805 0.333081i
\(725\) 300.711 + 173.615i 0.414774 + 0.239470i
\(726\) −27.8959 + 10.5201i −0.0384241 + 0.0144905i
\(727\) 1061.98i 1.46078i −0.683032 0.730388i \(-0.739339\pi\)
0.683032 0.730388i \(-0.260661\pi\)
\(728\) −1014.57 63.5854i −1.39364 0.0873426i
\(729\) −698.013 −0.957494
\(730\) 68.8569 + 182.586i 0.0943245 + 0.250117i
\(731\) 118.824 205.809i 0.162550 0.281544i
\(732\) 38.4933 33.8470i 0.0525865 0.0462391i
\(733\) −0.148102 0.256519i −0.000202048 0.000349958i 0.865924 0.500175i \(-0.166731\pi\)
−0.866126 + 0.499825i \(0.833398\pi\)
\(734\) −410.409 67.4828i −0.559140 0.0919384i
\(735\) 29.1652 33.3769i 0.0396806 0.0454108i
\(736\) −100.097 + 94.3684i −0.136002 + 0.128218i
\(737\) −494.588 856.651i −0.671082 1.16235i
\(738\) −512.741 + 625.612i −0.694772 + 0.847713i
\(739\) 176.276 + 101.773i 0.238533 + 0.137717i 0.614502 0.788915i \(-0.289357\pi\)
−0.375969 + 0.926632i \(0.622690\pi\)
\(740\) 418.972 83.9092i 0.566178 0.113391i
\(741\) 114.101 0.153982
\(742\) 228.898 + 848.991i 0.308487 + 1.14419i
\(743\) 1142.13 1.53718 0.768592 0.639739i \(-0.220958\pi\)
0.768592 + 0.639739i \(0.220958\pi\)
\(744\) 2.29111 + 66.0205i 0.00307945 + 0.0887373i
\(745\) 95.3315 + 55.0397i 0.127962 + 0.0738788i
\(746\) −576.102 + 702.920i −0.772255 + 0.942253i
\(747\) −230.409 399.080i −0.308446 0.534244i
\(748\) 284.969 + 96.3180i 0.380975 + 0.128767i
\(749\) 52.0610 + 37.2358i 0.0695073 + 0.0497141i
\(750\) 10.9319 66.4843i 0.0145759 0.0886457i
\(751\) 396.068 + 686.010i 0.527387 + 0.913462i 0.999490 + 0.0319185i \(0.0101617\pi\)
−0.472103 + 0.881543i \(0.656505\pi\)
\(752\) −313.360 750.950i −0.416702 0.998604i
\(753\) −39.9508 + 69.1967i −0.0530554 + 0.0918947i
\(754\) −363.357 963.503i −0.481906 1.27786i
\(755\) −83.8995 −0.111125
\(756\) −115.965 52.2351i −0.153393 0.0690940i
\(757\) 1179.34i 1.55792i 0.627076 + 0.778958i \(0.284252\pi\)
−0.627076 + 0.778958i \(0.715748\pi\)
\(758\) 263.408 + 698.470i 0.347504 + 0.921465i
\(759\) 7.43259 + 4.29121i 0.00979260 + 0.00565376i
\(760\) 375.678 + 601.501i 0.494313 + 0.791449i
\(761\) 197.869 114.240i 0.260011 0.150118i −0.364328 0.931271i \(-0.618701\pi\)
0.624340 + 0.781153i \(0.285368\pi\)
\(762\) −4.73482 + 28.7957i −0.00621368 + 0.0377896i
\(763\) 81.0408 830.443i 0.106213 1.08839i
\(764\) −105.451 35.6420i −0.138025 0.0466518i
\(765\) 263.691 152.242i 0.344694 0.199009i
\(766\) 395.689 482.792i 0.516565 0.630277i
\(767\) 671.744 1163.49i 0.875807 1.51694i
\(768\) 45.6035 46.0837i 0.0593795 0.0600049i
\(769\) 83.4232i 0.108483i −0.998528 0.0542414i \(-0.982726\pi\)
0.998528 0.0542414i \(-0.0172740\pi\)
\(770\) −278.296 + 279.160i −0.361423 + 0.362545i
\(771\) 96.3670i 0.124990i
\(772\) 190.392 + 950.658i 0.246622 + 1.23142i
\(773\) −285.318 + 494.186i −0.369105 + 0.639309i −0.989426 0.145039i \(-0.953669\pi\)
0.620321 + 0.784348i \(0.287002\pi\)
\(774\) 282.207 344.329i 0.364608 0.444870i
\(775\) −345.691 + 199.585i −0.446052 + 0.257528i
\(776\) −332.258 176.757i −0.428168 0.227780i
\(777\) −48.2742 + 21.9249i −0.0621289 + 0.0282173i
\(778\) −1001.83 164.728i −1.28769 0.211733i
\(779\) −972.822 + 561.659i −1.24881 + 0.721000i
\(780\) −49.3261 + 43.3722i −0.0632385 + 0.0556054i
\(781\) 36.4427 + 21.0402i 0.0466616 + 0.0269401i
\(782\) 28.9432 + 76.7477i 0.0370117 + 0.0981429i
\(783\) 128.835i 0.164540i
\(784\) 519.521 + 587.157i 0.662655 + 0.748925i
\(785\) −455.864 −0.580718
\(786\) −58.9093 + 22.2159i −0.0749482 + 0.0282645i
\(787\) 382.719 662.888i 0.486301 0.842298i −0.513575 0.858045i \(-0.671679\pi\)
0.999876 + 0.0157470i \(0.00501262\pi\)
\(788\) 250.146 + 284.485i 0.317444 + 0.361021i
\(789\) −24.8605 43.0597i −0.0315089 0.0545750i
\(790\) 119.469 726.573i 0.151227 0.919713i
\(791\) −358.968 790.377i −0.453816 0.999212i
\(792\) 497.501 + 264.665i 0.628158 + 0.334173i
\(793\) −459.257 795.456i −0.579138 1.00310i
\(794\) 295.909 + 242.522i 0.372681 + 0.305443i
\(795\) 49.2025 + 28.4071i 0.0618900 + 0.0357322i
\(796\) 1212.55 242.843i 1.52331 0.305079i
\(797\) 577.729 0.724880 0.362440 0.932007i \(-0.381944\pi\)
0.362440 + 0.932007i \(0.381944\pi\)
\(798\) −62.3200 62.1271i −0.0780952 0.0778535i
\(799\) −485.168 −0.607220
\(800\) 375.258 + 112.493i 0.469072 + 0.140616i
\(801\) 1190.45 + 687.309i 1.48621 + 0.858063i
\(802\) −189.338 155.178i −0.236082 0.193489i
\(803\) 107.666 + 186.484i 0.134080 + 0.232234i
\(804\) −40.7033 + 120.426i −0.0506260 + 0.149784i
\(805\) −106.977 10.4396i −0.132891 0.0129685i
\(806\) 1168.08 + 192.066i 1.44923 + 0.238295i
\(807\) 12.9555 + 22.4396i 0.0160539 + 0.0278062i
\(808\) −632.908 1013.35i −0.783301 1.25415i
\(809\) 41.4824 71.8496i 0.0512761 0.0888128i −0.839248 0.543749i \(-0.817004\pi\)
0.890524 + 0.454936i \(0.150338\pi\)
\(810\) 529.860 199.822i 0.654149 0.246693i
\(811\) −525.164 −0.647552 −0.323776 0.946134i \(-0.604952\pi\)
−0.323776 + 0.946134i \(0.604952\pi\)
\(812\) −326.161 + 724.096i −0.401677 + 0.891744i
\(813\) 64.9150i 0.0798462i
\(814\) 441.182 166.379i 0.541993 0.204397i
\(815\) −493.944 285.178i −0.606066 0.349912i
\(816\) −14.8867 35.6752i −0.0182435 0.0437196i
\(817\) 535.429 309.130i 0.655360 0.378372i
\(818\) 10.4311 + 1.71516i 0.0127519 + 0.00209677i
\(819\) −660.567 + 923.565i −0.806553 + 1.12767i
\(820\) 207.055 612.598i 0.252506 0.747070i
\(821\) −506.369 + 292.352i −0.616771 + 0.356093i −0.775611 0.631211i \(-0.782558\pi\)
0.158840 + 0.987304i \(0.449225\pi\)
\(822\) −66.3940 54.4155i −0.0807713 0.0661989i
\(823\) −590.484 + 1022.75i −0.717478 + 1.24271i 0.244518 + 0.969645i \(0.421370\pi\)
−0.961996 + 0.273063i \(0.911963\pi\)
\(824\) −5.50564 158.650i −0.00668160 0.192537i
\(825\) 24.4405i 0.0296248i
\(826\) −1000.41 + 269.722i −1.21115 + 0.326540i
\(827\) 336.806i 0.407262i 0.979048 + 0.203631i \(0.0652743\pi\)
−0.979048 + 0.203631i \(0.934726\pi\)
\(828\) 30.1750 + 150.669i 0.0364433 + 0.181967i
\(829\) 184.145 318.949i 0.222130 0.384740i −0.733325 0.679878i \(-0.762033\pi\)
0.955454 + 0.295139i \(0.0953658\pi\)
\(830\) 284.922 + 233.518i 0.343280 + 0.281346i
\(831\) 43.1479 24.9114i 0.0519228 0.0299777i
\(832\) −649.243 963.446i −0.780340 1.15799i
\(833\) 442.378 151.051i 0.531066 0.181334i
\(834\) −21.9011 + 133.196i −0.0262603 + 0.159707i
\(835\) −441.692 + 255.011i −0.528972 + 0.305402i
\(836\) 516.757 + 587.694i 0.618131 + 0.702984i
\(837\) 128.264 + 74.0530i 0.153242 + 0.0884743i
\(838\) 64.9658 24.5000i 0.0775249 0.0292363i
\(839\) 709.889i 0.846113i 0.906103 + 0.423056i \(0.139043\pi\)
−0.906103 + 0.423056i \(0.860957\pi\)
\(840\) 50.5570 + 3.16851i 0.0601869 + 0.00377204i
\(841\) 36.5402 0.0434485
\(842\) −278.294 737.943i −0.330515 0.876417i
\(843\) 8.90098 15.4169i 0.0105587 0.0182882i
\(844\) 332.448 + 378.084i 0.393896 + 0.447967i
\(845\) 286.685 + 496.553i 0.339272 + 0.587637i
\(846\) −896.854 147.468i −1.06011 0.174312i
\(847\) 239.695 335.128i 0.282993 0.395664i
\(848\) −609.668 + 798.858i −0.718948 + 0.942049i
\(849\) −37.6073 65.1377i −0.0442960 0.0767229i
\(850\) 148.065 180.659i 0.174194 0.212540i
\(851\) 111.347 + 64.2860i 0.130842 + 0.0755417i
\(852\) −1.06194 5.30246i −0.00124641 0.00622354i
\(853\) 1136.65 1.33253 0.666267 0.745713i \(-0.267891\pi\)
0.666267 + 0.745713i \(0.267891\pi\)
\(854\) −182.282 + 684.528i −0.213445 + 0.801555i
\(855\) 792.143 0.926483
\(856\) 2.53701 + 73.1064i 0.00296380 + 0.0854047i
\(857\) 578.645 + 334.081i 0.675198 + 0.389826i 0.798043 0.602600i \(-0.205869\pi\)
−0.122845 + 0.992426i \(0.539202\pi\)
\(858\) −45.9442 + 56.0580i −0.0535480 + 0.0653357i
\(859\) 100.378 + 173.859i 0.116854 + 0.202397i 0.918519 0.395376i \(-0.129386\pi\)
−0.801665 + 0.597773i \(0.796052\pi\)
\(860\) −113.960 + 337.166i −0.132512 + 0.392054i
\(861\) −7.79316 + 79.8582i −0.00905129 + 0.0927506i
\(862\) −140.100 + 852.045i −0.162529 + 0.988451i
\(863\) −21.7855 37.7337i −0.0252440 0.0437238i 0.853127 0.521703i \(-0.174703\pi\)
−0.878371 + 0.477979i \(0.841370\pi\)
\(864\) −33.4701 141.450i −0.0387385 0.163715i
\(865\) −349.641 + 605.596i −0.404209 + 0.700111i
\(866\) 224.798 + 596.091i 0.259582 + 0.688326i
\(867\) 50.1422 0.0578342
\(868\) −533.410 740.917i −0.614527 0.853591i
\(869\) 812.533i 0.935020i
\(870\) 18.1064 + 48.0122i 0.0208120 + 0.0551864i
\(871\) 1972.73 + 1138.95i 2.26490 + 1.30764i
\(872\) 808.797 505.148i 0.927520 0.579298i
\(873\) −364.056 + 210.188i −0.417017 + 0.240765i
\(874\) −34.6228 + 210.565i −0.0396142 + 0.240921i
\(875\) 385.052 + 847.808i 0.440059 + 0.968923i
\(876\) 8.86068 26.2154i 0.0101149 0.0299263i
\(877\) −129.242 + 74.6180i −0.147368 + 0.0850832i −0.571871 0.820343i \(-0.693782\pi\)
0.424503 + 0.905427i \(0.360449\pi\)
\(878\) −779.964 + 951.659i −0.888342 + 1.08389i
\(879\) −17.1658 + 29.7321i −0.0195288 + 0.0338249i
\(880\) −446.791 57.6312i −0.507717 0.0654900i
\(881\) 865.257i 0.982130i 0.871123 + 0.491065i \(0.163392\pi\)
−0.871123 + 0.491065i \(0.836608\pi\)
\(882\) 863.666 144.762i 0.979214 0.164130i
\(883\) 1476.24i 1.67184i −0.548850 0.835921i \(-0.684934\pi\)
0.548850 0.835921i \(-0.315066\pi\)
\(884\) −679.220 + 136.030i −0.768348 + 0.153880i
\(885\) −33.4736 + 57.9779i −0.0378233 + 0.0655118i
\(886\) 126.562 154.422i 0.142846 0.174291i
\(887\) −518.166 + 299.163i −0.584178 + 0.337275i −0.762792 0.646644i \(-0.776172\pi\)
0.178614 + 0.983919i \(0.442839\pi\)
\(888\) −53.4951 28.4588i −0.0602423 0.0320482i
\(889\) −166.774 367.203i −0.187597 0.413051i
\(890\) −1084.34 178.297i −1.21836 0.200333i
\(891\) 541.172 312.446i 0.607376 0.350669i
\(892\) −23.6297 26.8735i −0.0264907 0.0301272i
\(893\) −1093.10 631.104i −1.22408 0.706723i
\(894\) −5.50829 14.6062i −0.00616140 0.0163380i
\(895\) 534.006i 0.596655i
\(896\) −169.984 + 879.728i −0.189714 + 0.981839i
\(897\) −19.7639 −0.0220333
\(898\) 140.944 53.1530i 0.156953 0.0591904i
\(899\) 462.395 800.891i 0.514343 0.890869i
\(900\) 328.616 288.951i 0.365129 0.321056i
\(901\) 299.589 + 518.904i 0.332508 + 0.575920i
\(902\) 115.775 704.110i 0.128354 0.780609i
\(903\) 4.28926 43.9530i 0.00475001 0.0486744i
\(904\) 465.946 875.858i 0.515428 0.968870i
\(905\) 163.051 + 282.412i 0.180167 + 0.312058i
\(906\) 9.20202 + 7.54182i 0.0101568 + 0.00832431i
\(907\) 1463.00 + 844.666i 1.61301 + 0.931274i 0.988667 + 0.150128i \(0.0479687\pi\)
0.624348 + 0.781146i \(0.285365\pi\)
\(908\) −214.200 1069.54i −0.235904 1.17790i
\(909\) −1334.53 −1.46813
\(910\) 233.579 877.167i 0.256681 0.963920i
\(911\) −813.339 −0.892798 −0.446399 0.894834i \(-0.647294\pi\)
−0.446399 + 0.894834i \(0.647294\pi\)
\(912\) 12.8657 99.7422i 0.0141071 0.109366i
\(913\) 352.052 + 203.257i 0.385599 + 0.222626i
\(914\) −323.127 264.830i −0.353531 0.289748i
\(915\) 22.8852 + 39.6382i 0.0250111 + 0.0433205i
\(916\) −1255.13 424.228i −1.37023 0.463131i
\(917\) 506.178 707.708i 0.551993 0.771764i
\(918\) −85.5191 14.0617i −0.0931581 0.0153178i
\(919\) −751.489 1301.62i −0.817724 1.41634i −0.907355 0.420365i \(-0.861902\pi\)
0.0896310 0.995975i \(-0.471431\pi\)
\(920\) −65.0728 104.189i −0.0707313 0.113249i
\(921\) −9.64971 + 16.7138i −0.0104774 + 0.0181474i
\(922\) 1406.25 530.325i 1.52521 0.575190i
\(923\) −96.9043 −0.104988
\(924\) 55.6172 5.60166i 0.0601918 0.00606241i
\(925\) 366.139i 0.395826i
\(926\) 6.66340 2.51291i 0.00719590 0.00271373i
\(927\) −153.560 88.6581i −0.165653 0.0956398i
\(928\) −883.227 + 208.991i −0.951753 + 0.225205i
\(929\) −1301.71 + 751.543i −1.40120 + 0.808981i −0.994515 0.104589i \(-0.966647\pi\)
−0.406681 + 0.913570i \(0.633314\pi\)
\(930\) −58.2066 9.57080i −0.0625877 0.0102912i
\(931\) 1193.18 + 235.118i 1.28161 + 0.252543i
\(932\) −599.623 202.669i −0.643373 0.217456i
\(933\) 43.4471 25.0842i 0.0465671 0.0268855i
\(934\) −640.227 524.720i −0.685468 0.561798i
\(935\) −134.302 + 232.618i −0.143638 + 0.248789i
\(936\) −1296.91 + 45.0068i −1.38559 + 0.0480842i
\(937\) 419.349i 0.447545i −0.974641 0.223772i \(-0.928163\pi\)
0.974641 0.223772i \(-0.0718372\pi\)
\(938\) −457.319 1696.21i −0.487547 1.80833i
\(939\) 14.0279i 0.0149392i
\(940\) 712.449 142.685i 0.757924 0.151792i
\(941\) −261.680 + 453.243i −0.278087 + 0.481661i −0.970909 0.239448i \(-0.923034\pi\)
0.692822 + 0.721108i \(0.256367\pi\)
\(942\) 49.9987 + 40.9781i 0.0530772 + 0.0435012i
\(943\) 168.507 97.2874i 0.178692 0.103168i
\(944\) −941.336 718.404i −0.997178 0.761021i
\(945\) 66.0695 92.3744i 0.0699148 0.0977507i
\(946\) −63.7214 + 387.533i −0.0673588 + 0.409655i
\(947\) 311.949 180.104i 0.329408 0.190184i −0.326170 0.945311i \(-0.605758\pi\)
0.655578 + 0.755127i \(0.272425\pi\)
\(948\) −78.4157 + 68.9506i −0.0827170 + 0.0727327i
\(949\) −429.441 247.938i −0.452520 0.261262i
\(950\) 568.596 214.430i 0.598522 0.225715i
\(951\) 75.7642i 0.0796679i
\(952\) 445.047 + 295.533i 0.467486 + 0.310434i
\(953\) 1242.81 1.30410 0.652051 0.758175i \(-0.273909\pi\)
0.652051 + 0.758175i \(0.273909\pi\)
\(954\) 396.081 + 1050.28i 0.415180 + 1.10092i
\(955\) 49.6976 86.0789i 0.0520394 0.0901349i
\(956\) 147.186 129.420i 0.153960 0.135376i
\(957\) 28.3116 + 49.0372i 0.0295838 + 0.0512406i
\(958\) 1790.68 + 294.438i 1.86918 + 0.307346i
\(959\) 1180.76 + 115.227i 1.23124 + 0.120153i
\(960\) 32.3524 + 48.0094i 0.0337004 + 0.0500098i
\(961\) 51.0585 + 88.4359i 0.0531306 + 0.0920248i
\(962\) −688.284 + 839.797i −0.715472 + 0.872970i
\(963\) 70.7610 + 40.8539i 0.0734798 + 0.0424236i
\(964\) 774.046 155.021i 0.802952 0.160810i
\(965\) −865.742 −0.897142
\(966\) 10.7947 + 10.7613i 0.0111747 + 0.0111401i
\(967\) 81.8793 0.0846735 0.0423368 0.999103i \(-0.486520\pi\)
0.0423368 + 0.999103i \(0.486520\pi\)
\(968\) 470.602 16.3313i 0.486159 0.0168712i
\(969\) −51.9298 29.9817i −0.0535912 0.0309409i
\(970\) 213.023 259.917i 0.219612 0.267955i
\(971\) −409.052 708.499i −0.421269 0.729660i 0.574795 0.818298i \(-0.305082\pi\)
−0.996064 + 0.0886380i \(0.971749\pi\)
\(972\) −230.992 78.0742i −0.237646 0.0803232i
\(973\) −771.419 1698.51i −0.792825 1.74564i
\(974\) 273.522 1663.47i 0.280823 1.70788i
\(975\) 28.1412 + 48.7419i 0.0288627 + 0.0499917i
\(976\) −747.140 + 311.770i −0.765512 + 0.319437i
\(977\) −448.155 + 776.227i −0.458705 + 0.794500i −0.998893 0.0470441i \(-0.985020\pi\)
0.540188 + 0.841544i \(0.318353\pi\)
\(978\) 28.5402 + 75.6793i 0.0291823 + 0.0773817i
\(979\) −1212.63 −1.23864
\(980\) −605.189 + 351.912i −0.617540 + 0.359094i
\(981\) 1065.14i 1.08577i
\(982\) −101.713 269.710i −0.103578 0.274654i
\(983\) 852.404 + 492.136i 0.867146 + 0.500647i 0.866399 0.499353i \(-0.166429\pi\)
0.000746983 1.00000i \(0.499762\pi\)
\(984\) −77.7767 + 48.5767i −0.0790413 + 0.0493666i
\(985\) −292.947 + 169.133i −0.297408 + 0.171708i
\(986\) −87.8030 + 533.990i −0.0890497 + 0.541572i
\(987\) −82.0887 + 37.2825i −0.0831699 + 0.0377736i
\(988\) −1707.26 577.044i −1.72799 0.584052i
\(989\) −92.7440 + 53.5458i −0.0937756 + 0.0541414i
\(990\) −318.967 + 389.182i −0.322189 + 0.393113i
\(991\) 612.037 1060.08i 0.617596 1.06971i −0.372327 0.928101i \(-0.621440\pi\)
0.989923 0.141606i \(-0.0452265\pi\)
\(992\) 299.606 999.434i 0.302022 1.00749i
\(993\) 95.0667i 0.0957368i
\(994\) 52.9276 + 52.7637i 0.0532471 + 0.0530822i
\(995\) 1104.24i 1.10979i
\(996\) −10.2588 51.2240i −0.0103000 0.0514297i
\(997\) −186.825 + 323.590i −0.187387 + 0.324563i −0.944378 0.328861i \(-0.893335\pi\)
0.756991 + 0.653425i \(0.226668\pi\)
\(998\) −483.235 + 589.610i −0.484203 + 0.590792i
\(999\) −117.650 + 67.9254i −0.117768 + 0.0679934i
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 56.3.j.a.45.2 yes 28
4.3 odd 2 224.3.n.a.17.8 28
7.2 even 3 392.3.j.e.117.12 28
7.3 odd 6 392.3.h.a.293.13 28
7.4 even 3 392.3.h.a.293.14 28
7.5 odd 6 inner 56.3.j.a.5.12 yes 28
7.6 odd 2 392.3.j.e.325.2 28
8.3 odd 2 224.3.n.a.17.7 28
8.5 even 2 inner 56.3.j.a.45.12 yes 28
28.3 even 6 1568.3.h.a.881.15 28
28.11 odd 6 1568.3.h.a.881.13 28
28.19 even 6 224.3.n.a.145.7 28
56.3 even 6 1568.3.h.a.881.14 28
56.5 odd 6 inner 56.3.j.a.5.2 28
56.11 odd 6 1568.3.h.a.881.16 28
56.13 odd 2 392.3.j.e.325.12 28
56.19 even 6 224.3.n.a.145.8 28
56.37 even 6 392.3.j.e.117.2 28
56.45 odd 6 392.3.h.a.293.16 28
56.53 even 6 392.3.h.a.293.15 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.j.a.5.2 28 56.5 odd 6 inner
56.3.j.a.5.12 yes 28 7.5 odd 6 inner
56.3.j.a.45.2 yes 28 1.1 even 1 trivial
56.3.j.a.45.12 yes 28 8.5 even 2 inner
224.3.n.a.17.7 28 8.3 odd 2
224.3.n.a.17.8 28 4.3 odd 2
224.3.n.a.145.7 28 28.19 even 6
224.3.n.a.145.8 28 56.19 even 6
392.3.h.a.293.13 28 7.3 odd 6
392.3.h.a.293.14 28 7.4 even 3
392.3.h.a.293.15 28 56.53 even 6
392.3.h.a.293.16 28 56.45 odd 6
392.3.j.e.117.2 28 56.37 even 6
392.3.j.e.117.12 28 7.2 even 3
392.3.j.e.325.2 28 7.6 odd 2
392.3.j.e.325.12 28 56.13 odd 2
1568.3.h.a.881.13 28 28.11 odd 6
1568.3.h.a.881.14 28 56.3 even 6
1568.3.h.a.881.15 28 28.3 even 6
1568.3.h.a.881.16 28 56.11 odd 6