Properties

Label 33.3.h.b.20.1
Level $33$
Weight $3$
Character 33.20
Analytic conductor $0.899$
Analytic rank $0$
Dimension $16$
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] = [33,3,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), 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: \(0.899184872389\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 20.1
Root \(-2.91048 - 0.945671i\) of defining polynomial
Character \(\chi\) \(=\) 33.20
Dual form 33.3.h.b.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.91048 - 0.945671i) q^{2} +(1.65950 + 2.49921i) q^{3} +(4.34051 + 3.15356i) q^{4} +(6.31437 - 2.05166i) q^{5} +(-2.46650 - 8.84324i) q^{6} +(2.47800 + 1.80037i) q^{7} +(-2.45561 - 3.37986i) q^{8} +(-3.49213 + 8.29488i) q^{9} +O(q^{10})\) \(q+(-2.91048 - 0.945671i) q^{2} +(1.65950 + 2.49921i) q^{3} +(4.34051 + 3.15356i) q^{4} +(6.31437 - 2.05166i) q^{5} +(-2.46650 - 8.84324i) q^{6} +(2.47800 + 1.80037i) q^{7} +(-2.45561 - 3.37986i) q^{8} +(-3.49213 + 8.29488i) q^{9} -20.3180 q^{10} +(-10.9529 + 1.01736i) q^{11} +(-0.678356 + 16.0812i) q^{12} +(5.01988 - 15.4496i) q^{13} +(-5.50960 - 7.58331i) q^{14} +(15.6062 + 12.3762i) q^{15} +(-2.68094 - 8.25108i) q^{16} +(-0.766216 + 0.248959i) q^{17} +(18.0080 - 20.8396i) q^{18} +(-16.7481 + 12.1682i) q^{19} +(33.8776 + 11.0075i) q^{20} +(-0.387274 + 9.18076i) q^{21} +(32.8401 + 7.39680i) q^{22} -27.3224i q^{23} +(4.37190 - 11.7460i) q^{24} +(15.4365 - 11.2153i) q^{25} +(-29.2204 + 40.2185i) q^{26} +(-26.5259 + 5.03778i) q^{27} +(5.07819 + 15.6291i) q^{28} +(2.22341 - 3.06025i) q^{29} +(-33.7177 - 50.7790i) q^{30} +(-6.42137 + 19.7630i) q^{31} +43.2608i q^{32} +(-20.7188 - 25.6852i) q^{33} +2.46549 q^{34} +(19.3408 + 6.28420i) q^{35} +(-41.3160 + 24.9913i) q^{36} +(-31.1905 - 22.6613i) q^{37} +(60.2520 - 19.5771i) q^{38} +(46.9423 - 13.0928i) q^{39} +(-22.4400 - 16.3036i) q^{40} +(-7.86024 - 10.8187i) q^{41} +(9.80913 - 26.3542i) q^{42} +43.4125 q^{43} +(-50.7492 - 30.1247i) q^{44} +(-5.03227 + 59.5416i) q^{45} +(-25.8380 + 79.5212i) q^{46} +(11.6912 + 16.0916i) q^{47} +(16.1722 - 20.3929i) q^{48} +(-12.2427 - 37.6791i) q^{49} +(-55.5336 + 18.0440i) q^{50} +(-1.89374 - 1.50179i) q^{51} +(70.5100 - 51.2285i) q^{52} +(16.8103 + 5.46201i) q^{53} +(81.9669 + 10.4224i) q^{54} +(-67.0731 + 28.8955i) q^{55} -12.7963i q^{56} +(-58.2044 - 21.6639i) q^{57} +(-9.36516 + 6.80419i) q^{58} +(-25.5837 + 35.2129i) q^{59} +(28.7098 + 102.934i) q^{60} +(3.29249 + 10.1333i) q^{61} +(37.3785 - 51.4471i) q^{62} +(-23.5874 + 14.2676i) q^{63} +(30.1867 - 92.9052i) q^{64} -107.854i q^{65} +(36.0119 + 94.3494i) q^{66} +72.2963 q^{67} +(-4.11087 - 1.33570i) q^{68} +(68.2845 - 45.3415i) q^{69} +(-50.3481 - 36.5800i) q^{70} +(2.44412 - 0.794142i) q^{71} +(36.6108 - 8.56611i) q^{72} +(36.7931 + 26.7318i) q^{73} +(69.3492 + 95.4510i) q^{74} +(53.6463 + 19.9674i) q^{75} -111.068 q^{76} +(-28.9728 - 17.1982i) q^{77} +(-149.006 - 6.28555i) q^{78} +(-30.3585 + 93.4339i) q^{79} +(-33.8569 - 46.6000i) q^{80} +(-56.6101 - 57.9335i) q^{81} +(12.6461 + 38.9207i) q^{82} +(-30.3393 + 9.85783i) q^{83} +(-30.6331 + 38.6279i) q^{84} +(-4.32739 + 3.14404i) q^{85} +(-126.351 - 41.0540i) q^{86} +(11.3380 + 0.478272i) q^{87} +(30.3345 + 34.5209i) q^{88} -18.5409i q^{89} +(70.9531 - 168.536i) q^{90} +(40.2543 - 29.2464i) q^{91} +(86.1629 - 118.593i) q^{92} +(-60.0481 + 16.7482i) q^{93} +(-18.8097 - 57.8902i) q^{94} +(-80.7886 + 111.196i) q^{95} +(-108.118 + 71.7913i) q^{96} +(-19.5614 + 60.2037i) q^{97} +121.242i q^{98} +(29.8099 - 94.4054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9} - 12 q^{10} + 106 q^{12} - 42 q^{13} + 82 q^{15} - 88 q^{16} - 43 q^{18} - 134 q^{19} - 12 q^{21} + 78 q^{22} + 41 q^{24} + 134 q^{25} + 80 q^{27} + 264 q^{28} - 120 q^{30} + 124 q^{31} - 79 q^{33} - 132 q^{34} - 219 q^{36} + 90 q^{37} - 174 q^{39} - 284 q^{40} - 102 q^{42} - 156 q^{43} - 72 q^{45} - 22 q^{46} + 30 q^{48} - 30 q^{49} + 111 q^{51} + 326 q^{52} + 1046 q^{54} - 172 q^{55} + 281 q^{57} - 116 q^{58} + 54 q^{60} - 126 q^{61} - 138 q^{63} + 236 q^{64} - 236 q^{66} + 368 q^{67} + 198 q^{69} - 322 q^{70} - 562 q^{72} + 24 q^{73} - 21 q^{75} - 900 q^{76} - 492 q^{78} - 314 q^{79} - 388 q^{81} + 270 q^{84} + 318 q^{85} + 132 q^{87} + 1064 q^{88} + 176 q^{90} + 374 q^{91} - 10 q^{93} + 990 q^{94} - 332 q^{96} + 72 q^{97} - 530 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.91048 0.945671i −1.45524 0.472835i −0.528626 0.848855i \(-0.677293\pi\)
−0.926612 + 0.376020i \(0.877293\pi\)
\(3\) 1.65950 + 2.49921i 0.553166 + 0.833071i
\(4\) 4.34051 + 3.15356i 1.08513 + 0.788390i
\(5\) 6.31437 2.05166i 1.26287 0.410333i 0.400357 0.916359i \(-0.368886\pi\)
0.862518 + 0.506027i \(0.168886\pi\)
\(6\) −2.46650 8.84324i −0.411083 1.47387i
\(7\) 2.47800 + 1.80037i 0.354000 + 0.257196i 0.750545 0.660819i \(-0.229791\pi\)
−0.396545 + 0.918015i \(0.629791\pi\)
\(8\) −2.45561 3.37986i −0.306951 0.422482i
\(9\) −3.49213 + 8.29488i −0.388014 + 0.921653i
\(10\) −20.3180 −2.03180
\(11\) −10.9529 + 1.01736i −0.995714 + 0.0924869i
\(12\) −0.678356 + 16.0812i −0.0565297 + 1.34010i
\(13\) 5.01988 15.4496i 0.386144 1.18843i −0.549503 0.835492i \(-0.685183\pi\)
0.935647 0.352938i \(-0.114817\pi\)
\(14\) −5.50960 7.58331i −0.393543 0.541665i
\(15\) 15.6062 + 12.3762i 1.04042 + 0.825081i
\(16\) −2.68094 8.25108i −0.167559 0.515693i
\(17\) −0.766216 + 0.248959i −0.0450715 + 0.0146446i −0.331466 0.943467i \(-0.607543\pi\)
0.286394 + 0.958112i \(0.407543\pi\)
\(18\) 18.0080 20.8396i 1.00044 1.15776i
\(19\) −16.7481 + 12.1682i −0.881479 + 0.640432i −0.933642 0.358207i \(-0.883388\pi\)
0.0521636 + 0.998639i \(0.483388\pi\)
\(20\) 33.8776 + 11.0075i 1.69388 + 0.550375i
\(21\) −0.387274 + 9.18076i −0.0184416 + 0.437179i
\(22\) 32.8401 + 7.39680i 1.49273 + 0.336218i
\(23\) 27.3224i 1.18793i −0.804491 0.593965i \(-0.797562\pi\)
0.804491 0.593965i \(-0.202438\pi\)
\(24\) 4.37190 11.7460i 0.182163 0.489415i
\(25\) 15.4365 11.2153i 0.617462 0.448612i
\(26\) −29.2204 + 40.2185i −1.12386 + 1.54687i
\(27\) −26.5259 + 5.03778i −0.982439 + 0.186585i
\(28\) 5.07819 + 15.6291i 0.181364 + 0.558180i
\(29\) 2.22341 3.06025i 0.0766691 0.105526i −0.768960 0.639297i \(-0.779226\pi\)
0.845629 + 0.533771i \(0.179226\pi\)
\(30\) −33.7177 50.7790i −1.12392 1.69263i
\(31\) −6.42137 + 19.7630i −0.207141 + 0.637515i 0.792478 + 0.609901i \(0.208791\pi\)
−0.999619 + 0.0276136i \(0.991209\pi\)
\(32\) 43.2608i 1.35190i
\(33\) −20.7188 25.6852i −0.627844 0.778340i
\(34\) 2.46549 0.0725143
\(35\) 19.3408 + 6.28420i 0.552593 + 0.179548i
\(36\) −41.3160 + 24.9913i −1.14767 + 0.694204i
\(37\) −31.1905 22.6613i −0.842988 0.612466i 0.0802160 0.996778i \(-0.474439\pi\)
−0.923204 + 0.384311i \(0.874439\pi\)
\(38\) 60.2520 19.5771i 1.58558 0.515186i
\(39\) 46.9423 13.0928i 1.20365 0.335714i
\(40\) −22.4400 16.3036i −0.560999 0.407590i
\(41\) −7.86024 10.8187i −0.191713 0.263871i 0.702330 0.711852i \(-0.252143\pi\)
−0.894043 + 0.447981i \(0.852143\pi\)
\(42\) 9.80913 26.3542i 0.233551 0.627480i
\(43\) 43.4125 1.00959 0.504797 0.863238i \(-0.331567\pi\)
0.504797 + 0.863238i \(0.331567\pi\)
\(44\) −50.7492 30.1247i −1.15339 0.684651i
\(45\) −5.03227 + 59.5416i −0.111828 + 1.32315i
\(46\) −25.8380 + 79.5212i −0.561695 + 1.72872i
\(47\) 11.6912 + 16.0916i 0.248749 + 0.342374i 0.915073 0.403289i \(-0.132133\pi\)
−0.666323 + 0.745663i \(0.732133\pi\)
\(48\) 16.1722 20.3929i 0.336921 0.424852i
\(49\) −12.2427 37.6791i −0.249851 0.768962i
\(50\) −55.5336 + 18.0440i −1.11067 + 0.360880i
\(51\) −1.89374 1.50179i −0.0371321 0.0294469i
\(52\) 70.5100 51.2285i 1.35596 0.985164i
\(53\) 16.8103 + 5.46201i 0.317176 + 0.103057i 0.463279 0.886213i \(-0.346673\pi\)
−0.146102 + 0.989269i \(0.546673\pi\)
\(54\) 81.9669 + 10.4224i 1.51791 + 0.193007i
\(55\) −67.0731 + 28.8955i −1.21951 + 0.525373i
\(56\) 12.7963i 0.228505i
\(57\) −58.2044 21.6639i −1.02113 0.380069i
\(58\) −9.36516 + 6.80419i −0.161468 + 0.117314i
\(59\) −25.5837 + 35.2129i −0.433621 + 0.596828i −0.968780 0.247923i \(-0.920252\pi\)
0.535158 + 0.844752i \(0.320252\pi\)
\(60\) 28.7098 + 102.934i 0.478496 + 1.71557i
\(61\) 3.29249 + 10.1333i 0.0539753 + 0.166119i 0.974410 0.224777i \(-0.0721653\pi\)
−0.920435 + 0.390896i \(0.872165\pi\)
\(62\) 37.3785 51.4471i 0.602879 0.829792i
\(63\) −23.5874 + 14.2676i −0.374403 + 0.226470i
\(64\) 30.1867 92.9052i 0.471667 1.45164i
\(65\) 107.854i 1.65929i
\(66\) 36.0119 + 94.3494i 0.545635 + 1.42954i
\(67\) 72.2963 1.07905 0.539525 0.841970i \(-0.318604\pi\)
0.539525 + 0.841970i \(0.318604\pi\)
\(68\) −4.11087 1.33570i −0.0604540 0.0196427i
\(69\) 68.2845 45.3415i 0.989630 0.657123i
\(70\) −50.3481 36.5800i −0.719258 0.522571i
\(71\) 2.44412 0.794142i 0.0344242 0.0111851i −0.291754 0.956493i \(-0.594239\pi\)
0.326178 + 0.945308i \(0.394239\pi\)
\(72\) 36.6108 8.56611i 0.508484 0.118974i
\(73\) 36.7931 + 26.7318i 0.504015 + 0.366188i 0.810549 0.585671i \(-0.199169\pi\)
−0.306533 + 0.951860i \(0.599169\pi\)
\(74\) 69.3492 + 95.4510i 0.937152 + 1.28988i
\(75\) 53.6463 + 19.9674i 0.715285 + 0.266232i
\(76\) −111.068 −1.46143
\(77\) −28.9728 17.1982i −0.376270 0.223353i
\(78\) −149.006 6.28555i −1.91033 0.0805840i
\(79\) −30.3585 + 93.4339i −0.384285 + 1.18271i 0.552712 + 0.833372i \(0.313593\pi\)
−0.936998 + 0.349336i \(0.886407\pi\)
\(80\) −33.8569 46.6000i −0.423211 0.582500i
\(81\) −56.6101 57.9335i −0.698890 0.715229i
\(82\) 12.6461 + 38.9207i 0.154221 + 0.474643i
\(83\) −30.3393 + 9.85783i −0.365534 + 0.118769i −0.486024 0.873945i \(-0.661553\pi\)
0.120491 + 0.992714i \(0.461553\pi\)
\(84\) −30.6331 + 38.6279i −0.364679 + 0.459855i
\(85\) −4.32739 + 3.14404i −0.0509105 + 0.0369887i
\(86\) −126.351 41.0540i −1.46920 0.477372i
\(87\) 11.3380 + 0.478272i 0.130321 + 0.00549738i
\(88\) 30.3345 + 34.5209i 0.344710 + 0.392283i
\(89\) 18.5409i 0.208325i −0.994560 0.104162i \(-0.966784\pi\)
0.994560 0.104162i \(-0.0332161\pi\)
\(90\) 70.9531 168.536i 0.788368 1.87262i
\(91\) 40.2543 29.2464i 0.442354 0.321389i
\(92\) 86.1629 118.593i 0.936553 1.28905i
\(93\) −60.0481 + 16.7482i −0.645678 + 0.180088i
\(94\) −18.8097 57.8902i −0.200103 0.615853i
\(95\) −80.7886 + 111.196i −0.850407 + 1.17048i
\(96\) −108.118 + 71.7913i −1.12623 + 0.747826i
\(97\) −19.5614 + 60.2037i −0.201664 + 0.620657i 0.798170 + 0.602432i \(0.205801\pi\)
−0.999834 + 0.0182248i \(0.994199\pi\)
\(98\) 121.242i 1.23716i
\(99\) 29.8099 94.4054i 0.301110 0.953589i
\(100\) 102.371 1.02371
\(101\) 143.000 + 46.4634i 1.41584 + 0.460034i 0.914277 0.405089i \(-0.132759\pi\)
0.501561 + 0.865122i \(0.332759\pi\)
\(102\) 4.09147 + 6.16178i 0.0401125 + 0.0604096i
\(103\) 121.164 + 88.0311i 1.17635 + 0.854671i 0.991756 0.128144i \(-0.0409019\pi\)
0.184597 + 0.982814i \(0.440902\pi\)
\(104\) −64.5443 + 20.9717i −0.620618 + 0.201651i
\(105\) 16.3904 + 58.7653i 0.156099 + 0.559670i
\(106\) −43.7608 31.7941i −0.412838 0.299944i
\(107\) −12.1974 16.7883i −0.113995 0.156900i 0.748207 0.663465i \(-0.230915\pi\)
−0.862202 + 0.506565i \(0.830915\pi\)
\(108\) −131.023 61.7844i −1.21317 0.572078i
\(109\) −105.794 −0.970583 −0.485291 0.874352i \(-0.661286\pi\)
−0.485291 + 0.874352i \(0.661286\pi\)
\(110\) 222.540 20.6707i 2.02309 0.187915i
\(111\) 4.87462 115.558i 0.0439155 1.04106i
\(112\) 8.21165 25.2729i 0.0733183 0.225651i
\(113\) 78.0396 + 107.412i 0.690616 + 0.950552i 1.00000 0.000385488i \(-0.000122705\pi\)
−0.309384 + 0.950937i \(0.600123\pi\)
\(114\) 148.915 + 118.094i 1.30628 + 1.03592i
\(115\) −56.0564 172.524i −0.487447 1.50021i
\(116\) 19.3014 6.27141i 0.166391 0.0540638i
\(117\) 110.622 + 95.5912i 0.945491 + 0.817019i
\(118\) 107.760 78.2925i 0.913224 0.663496i
\(119\) −2.34690 0.762555i −0.0197219 0.00640802i
\(120\) 3.50703 83.1381i 0.0292253 0.692817i
\(121\) 118.930 22.2859i 0.982892 0.184181i
\(122\) 32.6062i 0.267264i
\(123\) 13.9942 37.5980i 0.113774 0.305675i
\(124\) −90.1957 + 65.5310i −0.727385 + 0.528476i
\(125\) −23.1004 + 31.7950i −0.184803 + 0.254360i
\(126\) 82.1429 19.2196i 0.651928 0.152536i
\(127\) −45.3190 139.478i −0.356843 1.09825i −0.954933 0.296820i \(-0.904074\pi\)
0.598091 0.801428i \(-0.295926\pi\)
\(128\) −74.0031 + 101.857i −0.578150 + 0.795755i
\(129\) 72.0431 + 108.497i 0.558473 + 0.841063i
\(130\) −101.994 + 313.905i −0.784569 + 2.41465i
\(131\) 149.467i 1.14097i −0.821309 0.570484i \(-0.806756\pi\)
0.821309 0.570484i \(-0.193244\pi\)
\(132\) −8.93035 176.825i −0.0676542 1.33958i
\(133\) −63.4091 −0.476760
\(134\) −210.417 68.3685i −1.57027 0.510213i
\(135\) −157.158 + 86.2326i −1.16414 + 0.638760i
\(136\) 2.72298 + 1.97836i 0.0200219 + 0.0145467i
\(137\) −144.757 + 47.0345i −1.05662 + 0.343318i −0.785264 0.619161i \(-0.787473\pi\)
−0.271359 + 0.962478i \(0.587473\pi\)
\(138\) −241.618 + 67.3907i −1.75086 + 0.488338i
\(139\) −90.4769 65.7353i −0.650913 0.472916i 0.212669 0.977124i \(-0.431784\pi\)
−0.863582 + 0.504208i \(0.831784\pi\)
\(140\) 64.1311 + 88.2689i 0.458079 + 0.630492i
\(141\) −20.8147 + 55.9228i −0.147622 + 0.396616i
\(142\) −7.86454 −0.0553841
\(143\) −39.2642 + 174.324i −0.274575 + 1.21905i
\(144\) 77.8039 + 6.57574i 0.540305 + 0.0456649i
\(145\) 7.76079 23.8853i 0.0535227 0.164726i
\(146\) −81.8060 112.596i −0.560315 0.771207i
\(147\) 73.8514 93.1256i 0.502391 0.633507i
\(148\) −63.9190 196.723i −0.431885 1.32921i
\(149\) 246.985 80.2503i 1.65762 0.538592i 0.677247 0.735756i \(-0.263173\pi\)
0.980371 + 0.197164i \(0.0631730\pi\)
\(150\) −137.254 108.846i −0.915025 0.725643i
\(151\) −71.2078 + 51.7355i −0.471575 + 0.342619i −0.798055 0.602585i \(-0.794137\pi\)
0.326480 + 0.945204i \(0.394137\pi\)
\(152\) 82.2536 + 26.7258i 0.541142 + 0.175828i
\(153\) 0.610640 7.22507i 0.00399111 0.0472227i
\(154\) 68.0607 + 77.4537i 0.441953 + 0.502946i
\(155\) 137.965i 0.890098i
\(156\) 245.042 + 91.2058i 1.57078 + 0.584653i
\(157\) 6.19326 4.49967i 0.0394475 0.0286603i −0.567887 0.823107i \(-0.692239\pi\)
0.607334 + 0.794446i \(0.292239\pi\)
\(158\) 176.715 243.228i 1.11845 1.53942i
\(159\) 14.2460 + 51.0768i 0.0895977 + 0.321238i
\(160\) 88.7566 + 273.165i 0.554729 + 1.70728i
\(161\) 49.1905 67.7049i 0.305531 0.420527i
\(162\) 109.976 + 222.149i 0.678866 + 1.37129i
\(163\) 81.1315 249.697i 0.497739 1.53188i −0.314905 0.949123i \(-0.601973\pi\)
0.812644 0.582760i \(-0.198027\pi\)
\(164\) 71.7464i 0.437478i
\(165\) −183.524 119.678i −1.11227 0.725320i
\(166\) 97.6240 0.588096
\(167\) −152.175 49.4447i −0.911228 0.296076i −0.184364 0.982858i \(-0.559023\pi\)
−0.726863 + 0.686782i \(0.759023\pi\)
\(168\) 31.9807 21.2355i 0.190361 0.126402i
\(169\) −76.7667 55.7743i −0.454241 0.330025i
\(170\) 15.5680 5.05835i 0.0915765 0.0297550i
\(171\) −42.4474 181.416i −0.248230 1.06091i
\(172\) 188.432 + 136.904i 1.09554 + 0.795954i
\(173\) −97.2924 133.912i −0.562384 0.774055i 0.429243 0.903189i \(-0.358780\pi\)
−0.991627 + 0.129134i \(0.958780\pi\)
\(174\) −32.5466 12.1140i −0.187049 0.0696206i
\(175\) 58.4435 0.333963
\(176\) 37.7582 + 87.6454i 0.214535 + 0.497985i
\(177\) −130.461 5.50325i −0.737065 0.0310918i
\(178\) −17.5336 + 53.9628i −0.0985032 + 0.303162i
\(179\) 34.4072 + 47.3575i 0.192219 + 0.264567i 0.894238 0.447591i \(-0.147718\pi\)
−0.702019 + 0.712158i \(0.747718\pi\)
\(180\) −209.611 + 242.571i −1.16450 + 1.34762i
\(181\) 87.9703 + 270.745i 0.486024 + 1.49583i 0.830492 + 0.557030i \(0.188059\pi\)
−0.344468 + 0.938798i \(0.611941\pi\)
\(182\) −144.817 + 47.0537i −0.795695 + 0.258537i
\(183\) −19.8613 + 25.0448i −0.108531 + 0.136857i
\(184\) −92.3459 + 67.0932i −0.501880 + 0.364637i
\(185\) −243.442 79.0991i −1.31590 0.427563i
\(186\) 190.607 + 8.04041i 1.02477 + 0.0432280i
\(187\) 8.13897 3.50632i 0.0435239 0.0187504i
\(188\) 106.715i 0.567631i
\(189\) −74.8009 35.2728i −0.395772 0.186628i
\(190\) 340.288 247.234i 1.79099 1.30123i
\(191\) −80.7867 + 111.193i −0.422967 + 0.582164i −0.966321 0.257339i \(-0.917154\pi\)
0.543354 + 0.839504i \(0.317154\pi\)
\(192\) 282.285 78.7330i 1.47023 0.410068i
\(193\) 92.1162 + 283.505i 0.477286 + 1.46894i 0.842850 + 0.538149i \(0.180876\pi\)
−0.365563 + 0.930786i \(0.619124\pi\)
\(194\) 113.866 156.723i 0.586937 0.807849i
\(195\) 269.549 178.983i 1.38230 0.917861i
\(196\) 65.6840 202.155i 0.335122 1.03140i
\(197\) 58.1375i 0.295114i 0.989054 + 0.147557i \(0.0471410\pi\)
−0.989054 + 0.147557i \(0.952859\pi\)
\(198\) −176.037 + 246.574i −0.889077 + 1.24532i
\(199\) −125.049 −0.628385 −0.314193 0.949359i \(-0.601734\pi\)
−0.314193 + 0.949359i \(0.601734\pi\)
\(200\) −75.8123 24.6329i −0.379061 0.123165i
\(201\) 119.976 + 180.684i 0.596894 + 0.898925i
\(202\) −372.258 270.461i −1.84286 1.33892i
\(203\) 11.0192 3.58035i 0.0542818 0.0176372i
\(204\) −3.48378 12.4905i −0.0170774 0.0612282i
\(205\) −71.8288 52.1867i −0.350384 0.254569i
\(206\) −269.397 370.794i −1.30775 1.79997i
\(207\) 226.636 + 95.4133i 1.09486 + 0.460934i
\(208\) −140.934 −0.677566
\(209\) 171.060 150.315i 0.818469 0.719212i
\(210\) 7.86865 186.535i 0.0374698 0.888262i
\(211\) −14.9542 + 46.0242i −0.0708728 + 0.218124i −0.980219 0.197916i \(-0.936583\pi\)
0.909346 + 0.416040i \(0.136583\pi\)
\(212\) 55.7406 + 76.7204i 0.262927 + 0.361889i
\(213\) 6.04074 + 4.79049i 0.0283603 + 0.0224906i
\(214\) 19.6241 + 60.3967i 0.0917013 + 0.282228i
\(215\) 274.123 89.0679i 1.27499 0.414269i
\(216\) 82.1642 + 77.2828i 0.380390 + 0.357791i
\(217\) −51.4928 + 37.4117i −0.237294 + 0.172404i
\(218\) 307.909 + 100.046i 1.41243 + 0.458926i
\(219\) −5.75021 + 136.315i −0.0262567 + 0.622444i
\(220\) −382.255 86.0980i −1.73752 0.391354i
\(221\) 13.0875i 0.0592193i
\(222\) −123.467 + 331.719i −0.556159 + 1.49423i
\(223\) −171.282 + 124.444i −0.768082 + 0.558044i −0.901378 0.433032i \(-0.857444\pi\)
0.133297 + 0.991076i \(0.457444\pi\)
\(224\) −77.8855 + 107.200i −0.347703 + 0.478573i
\(225\) 39.1233 + 167.210i 0.173881 + 0.743153i
\(226\) −125.556 386.421i −0.555556 1.70983i
\(227\) −71.3484 + 98.2027i −0.314310 + 0.432611i −0.936719 0.350081i \(-0.886154\pi\)
0.622409 + 0.782692i \(0.286154\pi\)
\(228\) −184.318 277.583i −0.808412 1.21747i
\(229\) 99.7951 307.138i 0.435786 1.34121i −0.456492 0.889727i \(-0.650894\pi\)
0.892279 0.451485i \(-0.149106\pi\)
\(230\) 555.137i 2.41364i
\(231\) −5.09835 100.950i −0.0220708 0.437011i
\(232\) −15.8030 −0.0681166
\(233\) 382.714 + 124.351i 1.64255 + 0.533697i 0.977106 0.212752i \(-0.0682427\pi\)
0.665443 + 0.746449i \(0.268243\pi\)
\(234\) −231.566 382.828i −0.989599 1.63602i
\(235\) 106.837 + 77.6218i 0.454626 + 0.330305i
\(236\) −222.092 + 72.1621i −0.941068 + 0.305771i
\(237\) −283.891 + 79.1811i −1.19785 + 0.334098i
\(238\) 6.10948 + 4.43879i 0.0256701 + 0.0186504i
\(239\) 0.188940 + 0.260053i 0.000790543 + 0.00108809i 0.809412 0.587241i \(-0.199786\pi\)
−0.808622 + 0.588329i \(0.799786\pi\)
\(240\) 60.2779 161.948i 0.251158 0.674784i
\(241\) 290.799 1.20664 0.603318 0.797500i \(-0.293845\pi\)
0.603318 + 0.797500i \(0.293845\pi\)
\(242\) −367.218 47.6060i −1.51743 0.196719i
\(243\) 50.8438 237.621i 0.209234 0.977866i
\(244\) −17.6648 + 54.3665i −0.0723965 + 0.222814i
\(245\) −154.610 212.802i −0.631060 0.868580i
\(246\) −76.2850 + 96.1943i −0.310102 + 0.391034i
\(247\) 103.920 + 319.834i 0.420730 + 1.29487i
\(248\) 82.5644 26.8268i 0.332921 0.108173i
\(249\) −74.9848 59.4653i −0.301144 0.238816i
\(250\) 97.3007 70.6931i 0.389203 0.282772i
\(251\) 107.109 + 34.8019i 0.426730 + 0.138653i 0.514505 0.857487i \(-0.327976\pi\)
−0.0877748 + 0.996140i \(0.527976\pi\)
\(252\) −147.375 12.4557i −0.584821 0.0494272i
\(253\) 27.7966 + 299.258i 0.109868 + 1.18284i
\(254\) 448.803i 1.76694i
\(255\) −15.0389 5.59755i −0.0589762 0.0219512i
\(256\) −4.41230 + 3.20572i −0.0172355 + 0.0125224i
\(257\) −115.540 + 159.027i −0.449572 + 0.618783i −0.972306 0.233713i \(-0.924912\pi\)
0.522733 + 0.852496i \(0.324912\pi\)
\(258\) −107.077 383.907i −0.415027 1.48801i
\(259\) −36.4915 112.309i −0.140894 0.433626i
\(260\) 340.123 468.139i 1.30816 1.80053i
\(261\) 17.6200 + 29.1297i 0.0675097 + 0.111608i
\(262\) −141.346 + 435.020i −0.539490 + 1.66038i
\(263\) 378.327i 1.43850i −0.694749 0.719252i \(-0.744485\pi\)
0.694749 0.719252i \(-0.255515\pi\)
\(264\) −35.9350 + 133.100i −0.136117 + 0.504165i
\(265\) 117.353 0.442842
\(266\) 184.551 + 59.9641i 0.693799 + 0.225429i
\(267\) 46.3376 30.7686i 0.173549 0.115238i
\(268\) 313.803 + 227.991i 1.17090 + 0.850712i
\(269\) 191.309 62.1601i 0.711186 0.231078i 0.0689882 0.997617i \(-0.478023\pi\)
0.642198 + 0.766539i \(0.278023\pi\)
\(270\) 538.953 102.358i 1.99612 0.379103i
\(271\) −64.8950 47.1490i −0.239465 0.173981i 0.461580 0.887099i \(-0.347283\pi\)
−0.701045 + 0.713117i \(0.747283\pi\)
\(272\) 4.10836 + 5.65467i 0.0151043 + 0.0207892i
\(273\) 139.895 + 52.0695i 0.512436 + 0.190731i
\(274\) 465.792 1.69997
\(275\) −157.664 + 138.544i −0.573324 + 0.503796i
\(276\) 439.376 + 18.5343i 1.59194 + 0.0671533i
\(277\) 67.6484 208.200i 0.244218 0.751626i −0.751546 0.659681i \(-0.770692\pi\)
0.995764 0.0919450i \(-0.0293084\pi\)
\(278\) 201.167 + 276.882i 0.723622 + 0.995980i
\(279\) −141.507 122.279i −0.507194 0.438277i
\(280\) −26.2537 80.8006i −0.0937633 0.288574i
\(281\) −472.140 + 153.407i −1.68021 + 0.545934i −0.984953 0.172825i \(-0.944711\pi\)
−0.695260 + 0.718759i \(0.744711\pi\)
\(282\) 113.465 143.078i 0.402359 0.507369i
\(283\) 248.936 180.862i 0.879632 0.639090i −0.0535221 0.998567i \(-0.517045\pi\)
0.933154 + 0.359477i \(0.117045\pi\)
\(284\) 13.1131 + 4.26070i 0.0461728 + 0.0150025i
\(285\) −411.971 17.3783i −1.44551 0.0609764i
\(286\) 279.131 470.235i 0.975981 1.64418i
\(287\) 40.9601i 0.142718i
\(288\) −358.843 151.072i −1.24598 0.524556i
\(289\) −233.281 + 169.488i −0.807200 + 0.586465i
\(290\) −45.1752 + 62.1783i −0.155777 + 0.214408i
\(291\) −182.924 + 51.0200i −0.628604 + 0.175326i
\(292\) 75.4004 + 232.059i 0.258221 + 0.794721i
\(293\) 199.670 274.822i 0.681466 0.937957i −0.318484 0.947928i \(-0.603174\pi\)
0.999950 + 0.00997075i \(0.00317384\pi\)
\(294\) −303.009 + 201.201i −1.03064 + 0.684355i
\(295\) −89.2997 + 274.836i −0.302711 + 0.931648i
\(296\) 161.067i 0.544145i
\(297\) 285.409 82.1643i 0.960971 0.276648i
\(298\) −794.734 −2.66689
\(299\) −422.120 137.155i −1.41177 0.458712i
\(300\) 169.884 + 255.846i 0.566279 + 0.852819i
\(301\) 107.576 + 78.1587i 0.357396 + 0.259664i
\(302\) 256.173 83.2358i 0.848256 0.275615i
\(303\) 121.186 + 434.492i 0.399953 + 1.43397i
\(304\) 145.301 + 105.568i 0.477965 + 0.347262i
\(305\) 41.5801 + 57.2300i 0.136328 + 0.187639i
\(306\) −8.60979 + 20.4509i −0.0281366 + 0.0668331i
\(307\) −396.129 −1.29032 −0.645161 0.764047i \(-0.723210\pi\)
−0.645161 + 0.764047i \(0.723210\pi\)
\(308\) −71.5209 166.016i −0.232211 0.539014i
\(309\) −18.9362 + 448.903i −0.0612821 + 1.45276i
\(310\) 130.470 401.544i 0.420870 1.29530i
\(311\) −51.1584 70.4134i −0.164496 0.226410i 0.718809 0.695207i \(-0.244687\pi\)
−0.883306 + 0.468797i \(0.844687\pi\)
\(312\) −159.524 126.507i −0.511295 0.405472i
\(313\) −185.075 569.601i −0.591292 1.81981i −0.572378 0.819990i \(-0.693979\pi\)
−0.0189146 0.999821i \(-0.506021\pi\)
\(314\) −22.2805 + 7.23939i −0.0709572 + 0.0230554i
\(315\) −119.667 + 138.484i −0.379895 + 0.439632i
\(316\) −426.421 + 309.813i −1.34943 + 0.980421i
\(317\) 2.33475 + 0.758605i 0.00736513 + 0.00239308i 0.312697 0.949853i \(-0.398767\pi\)
−0.305332 + 0.952246i \(0.598767\pi\)
\(318\) 6.83917 162.130i 0.0215068 0.509843i
\(319\) −21.2393 + 35.7805i −0.0665808 + 0.112165i
\(320\) 648.571i 2.02678i
\(321\) 21.7159 58.3441i 0.0676509 0.181757i
\(322\) −207.194 + 150.535i −0.643460 + 0.467501i
\(323\) 9.80328 13.4931i 0.0303507 0.0417742i
\(324\) −63.0195 429.984i −0.194505 1.32711i
\(325\) −95.7823 294.788i −0.294715 0.907039i
\(326\) −472.262 + 650.013i −1.44866 + 1.99391i
\(327\) −175.564 264.400i −0.536894 0.808564i
\(328\) −17.2640 + 53.1330i −0.0526340 + 0.161991i
\(329\) 60.9235i 0.185178i
\(330\) 420.966 + 521.873i 1.27565 + 1.58143i
\(331\) 368.074 1.11200 0.556002 0.831181i \(-0.312335\pi\)
0.556002 + 0.831181i \(0.312335\pi\)
\(332\) −162.775 52.8888i −0.490286 0.159304i
\(333\) 296.894 179.586i 0.891573 0.539297i
\(334\) 396.143 + 287.815i 1.18606 + 0.861721i
\(335\) 456.506 148.328i 1.36270 0.442769i
\(336\) 76.7895 21.4176i 0.228540 0.0637430i
\(337\) −478.841 347.898i −1.42089 1.03234i −0.991624 0.129162i \(-0.958771\pi\)
−0.429269 0.903177i \(-0.641229\pi\)
\(338\) 170.684 + 234.926i 0.504981 + 0.695047i
\(339\) −138.940 + 373.288i −0.409851 + 1.10115i
\(340\) −28.6980 −0.0844059
\(341\) 50.2264 222.994i 0.147291 0.653940i
\(342\) −48.0182 + 568.149i −0.140404 + 1.66125i
\(343\) 83.8781 258.150i 0.244543 0.752625i
\(344\) −106.604 146.728i −0.309896 0.426536i
\(345\) 338.148 426.400i 0.980139 1.23594i
\(346\) 156.531 + 481.753i 0.452402 + 1.39235i
\(347\) 280.182 91.0367i 0.807442 0.262354i 0.123928 0.992291i \(-0.460451\pi\)
0.683514 + 0.729938i \(0.260451\pi\)
\(348\) 47.7042 + 37.8309i 0.137081 + 0.108710i
\(349\) −333.322 + 242.172i −0.955076 + 0.693903i −0.952002 0.306092i \(-0.900979\pi\)
−0.00307413 + 0.999995i \(0.500979\pi\)
\(350\) −170.098 55.2683i −0.485995 0.157909i
\(351\) −55.3248 + 435.102i −0.157620 + 1.23961i
\(352\) −44.0117 473.829i −0.125033 1.34611i
\(353\) 135.577i 0.384070i 0.981388 + 0.192035i \(0.0615086\pi\)
−0.981388 + 0.192035i \(0.938491\pi\)
\(354\) 374.498 + 139.390i 1.05790 + 0.393756i
\(355\) 13.8038 10.0290i 0.0388838 0.0282507i
\(356\) 58.4698 80.4768i 0.164241 0.226058i
\(357\) −1.98890 7.13087i −0.00557114 0.0199744i
\(358\) −55.3568 170.371i −0.154628 0.475896i
\(359\) −163.860 + 225.534i −0.456435 + 0.628229i −0.973765 0.227557i \(-0.926926\pi\)
0.517330 + 0.855786i \(0.326926\pi\)
\(360\) 213.600 129.203i 0.593332 0.358896i
\(361\) 20.8784 64.2571i 0.0578349 0.177997i
\(362\) 871.187i 2.40659i
\(363\) 253.061 + 260.248i 0.697139 + 0.716936i
\(364\) 266.954 0.733391
\(365\) 287.170 + 93.3072i 0.786767 + 0.255636i
\(366\) 81.4898 54.1100i 0.222650 0.147841i
\(367\) 142.701 + 103.678i 0.388830 + 0.282502i 0.764976 0.644059i \(-0.222751\pi\)
−0.376146 + 0.926560i \(0.622751\pi\)
\(368\) −225.439 + 73.2497i −0.612607 + 0.199048i
\(369\) 117.189 27.4195i 0.317585 0.0743077i
\(370\) 633.730 + 460.432i 1.71278 + 1.24441i
\(371\) 31.8224 + 43.7998i 0.0857746 + 0.118059i
\(372\) −313.456 116.670i −0.842623 0.313628i
\(373\) 163.109 0.437289 0.218645 0.975805i \(-0.429836\pi\)
0.218645 + 0.975805i \(0.429836\pi\)
\(374\) −27.0041 + 2.50828i −0.0722035 + 0.00670663i
\(375\) −117.797 4.96908i −0.314126 0.0132509i
\(376\) 25.6782 79.0293i 0.0682930 0.210184i
\(377\) −36.1185 49.7128i −0.0958049 0.131864i
\(378\) 184.350 + 173.398i 0.487698 + 0.458724i
\(379\) 16.4492 + 50.6253i 0.0434015 + 0.133576i 0.970409 0.241466i \(-0.0776283\pi\)
−0.927008 + 0.375042i \(0.877628\pi\)
\(380\) −701.327 + 227.875i −1.84560 + 0.599671i
\(381\) 273.377 344.725i 0.717526 0.904790i
\(382\) 340.280 247.228i 0.890785 0.647193i
\(383\) −85.2768 27.7081i −0.222655 0.0723449i 0.195565 0.980691i \(-0.437346\pi\)
−0.418220 + 0.908346i \(0.637346\pi\)
\(384\) −377.369 15.9187i −0.982733 0.0414549i
\(385\) −218.230 49.1534i −0.566831 0.127671i
\(386\) 912.245i 2.36333i
\(387\) −151.602 + 360.102i −0.391736 + 0.930496i
\(388\) −274.762 + 199.626i −0.708150 + 0.514501i
\(389\) −158.468 + 218.112i −0.407372 + 0.560699i −0.962575 0.271016i \(-0.912640\pi\)
0.555203 + 0.831715i \(0.312640\pi\)
\(390\) −953.774 + 266.021i −2.44557 + 0.682104i
\(391\) 6.80215 + 20.9349i 0.0173968 + 0.0535419i
\(392\) −97.2868 + 133.904i −0.248181 + 0.341591i
\(393\) 373.549 248.040i 0.950508 0.631145i
\(394\) 54.9789 169.208i 0.139540 0.429461i
\(395\) 652.262i 1.65130i
\(396\) 427.103 315.760i 1.07854 0.797373i
\(397\) 211.490 0.532720 0.266360 0.963874i \(-0.414179\pi\)
0.266360 + 0.963874i \(0.414179\pi\)
\(398\) 363.951 + 118.255i 0.914450 + 0.297123i
\(399\) −105.227 158.473i −0.263728 0.397175i
\(400\) −133.923 97.3006i −0.334807 0.243252i
\(401\) −427.784 + 138.995i −1.06679 + 0.346622i −0.789237 0.614088i \(-0.789524\pi\)
−0.277555 + 0.960710i \(0.589524\pi\)
\(402\) −178.319 639.333i −0.443579 1.59038i
\(403\) 273.095 + 198.415i 0.677655 + 0.492345i
\(404\) 474.165 + 652.633i 1.17368 + 1.61543i
\(405\) −476.317 249.669i −1.17609 0.616467i
\(406\) −35.4569 −0.0873323
\(407\) 364.680 + 216.474i 0.896020 + 0.531876i
\(408\) −0.425560 + 10.0884i −0.00104304 + 0.0247264i
\(409\) −47.6795 + 146.742i −0.116576 + 0.358783i −0.992272 0.124078i \(-0.960403\pi\)
0.875697 + 0.482862i \(0.160403\pi\)
\(410\) 159.705 + 219.814i 0.389523 + 0.536133i
\(411\) −357.774 283.726i −0.870496 0.690330i
\(412\) 248.303 + 764.199i 0.602678 + 1.85485i
\(413\) −126.793 + 41.1974i −0.307004 + 0.0997516i
\(414\) −569.389 492.021i −1.37534 1.18846i
\(415\) −171.349 + 124.492i −0.412888 + 0.299981i
\(416\) 668.362 + 217.164i 1.60664 + 0.522028i
\(417\) 14.1402 335.209i 0.0339093 0.803858i
\(418\) −640.015 + 275.723i −1.53114 + 0.659623i
\(419\) 755.530i 1.80317i −0.432599 0.901587i \(-0.642403\pi\)
0.432599 0.901587i \(-0.357597\pi\)
\(420\) −114.177 + 306.759i −0.271851 + 0.730380i
\(421\) 353.452 256.798i 0.839553 0.609971i −0.0826929 0.996575i \(-0.526352\pi\)
0.922246 + 0.386604i \(0.126352\pi\)
\(422\) 87.0474 119.810i 0.206274 0.283911i
\(423\) −174.305 + 40.7834i −0.412068 + 0.0964147i
\(424\) −22.8188 70.2292i −0.0538180 0.165635i
\(425\) −9.03558 + 12.4364i −0.0212602 + 0.0292621i
\(426\) −13.0512 19.6552i −0.0306366 0.0461389i
\(427\) −10.0848 + 31.0379i −0.0236179 + 0.0726883i
\(428\) 111.335i 0.260129i
\(429\) −500.832 + 191.161i −1.16744 + 0.445597i
\(430\) −882.057 −2.05129
\(431\) −9.25765 3.00799i −0.0214795 0.00697910i 0.298258 0.954485i \(-0.403595\pi\)
−0.319737 + 0.947506i \(0.603595\pi\)
\(432\) 112.681 + 205.361i 0.260837 + 0.475373i
\(433\) 47.9543 + 34.8408i 0.110749 + 0.0804638i 0.641781 0.766888i \(-0.278196\pi\)
−0.531032 + 0.847352i \(0.678196\pi\)
\(434\) 185.248 60.1907i 0.426838 0.138688i
\(435\) 72.5734 20.2417i 0.166835 0.0465327i
\(436\) −459.197 333.626i −1.05320 0.765198i
\(437\) 332.465 + 457.598i 0.760788 + 1.04714i
\(438\) 145.645 391.304i 0.332523 0.893388i
\(439\) 444.724 1.01304 0.506519 0.862229i \(-0.330932\pi\)
0.506519 + 0.862229i \(0.330932\pi\)
\(440\) 262.368 + 155.741i 0.596292 + 0.353958i
\(441\) 355.297 + 30.0286i 0.805662 + 0.0680920i
\(442\) 12.3764 38.0908i 0.0280010 0.0861782i
\(443\) −314.672 433.108i −0.710320 0.977671i −0.999790 0.0204842i \(-0.993479\pi\)
0.289470 0.957187i \(-0.406521\pi\)
\(444\) 385.578 486.208i 0.868419 1.09506i
\(445\) −38.0397 117.074i −0.0854824 0.263088i
\(446\) 616.196 200.214i 1.38160 0.448910i
\(447\) 610.434 + 484.093i 1.36562 + 1.08298i
\(448\) 242.067 175.872i 0.540327 0.392571i
\(449\) −731.756 237.762i −1.62975 0.529537i −0.655534 0.755166i \(-0.727556\pi\)
−0.974213 + 0.225629i \(0.927556\pi\)
\(450\) 44.2578 523.657i 0.0983508 1.16368i
\(451\) 97.0986 + 110.499i 0.215296 + 0.245009i
\(452\) 712.327i 1.57594i
\(453\) −247.467 92.1084i −0.546285 0.203330i
\(454\) 300.525 218.344i 0.661950 0.480935i
\(455\) 194.177 267.261i 0.426762 0.587387i
\(456\) 69.7063 + 249.921i 0.152865 + 0.548072i
\(457\) 52.4263 + 161.352i 0.114718 + 0.353067i 0.991888 0.127113i \(-0.0405712\pi\)
−0.877170 + 0.480180i \(0.840571\pi\)
\(458\) −580.902 + 799.543i −1.26835 + 1.74573i
\(459\) 19.0703 10.4639i 0.0415476 0.0227971i
\(460\) 300.751 925.618i 0.653807 2.01221i
\(461\) 266.355i 0.577777i 0.957363 + 0.288888i \(0.0932857\pi\)
−0.957363 + 0.288888i \(0.906714\pi\)
\(462\) −80.6264 + 298.633i −0.174516 + 0.646391i
\(463\) −704.848 −1.52235 −0.761175 0.648547i \(-0.775377\pi\)
−0.761175 + 0.648547i \(0.775377\pi\)
\(464\) −31.2112 10.1411i −0.0672656 0.0218559i
\(465\) −344.804 + 228.953i −0.741514 + 0.492372i
\(466\) −996.284 723.843i −2.13795 1.55331i
\(467\) 642.132 208.641i 1.37502 0.446770i 0.473988 0.880531i \(-0.342814\pi\)
0.901028 + 0.433762i \(0.142814\pi\)
\(468\) 178.705 + 763.769i 0.381848 + 1.63198i
\(469\) 179.150 + 130.160i 0.381983 + 0.277527i
\(470\) −237.542 326.949i −0.505409 0.695636i
\(471\) 21.5233 + 8.01109i 0.0456971 + 0.0170087i
\(472\) 181.838 0.385250
\(473\) −475.491 + 44.1660i −1.00527 + 0.0933742i
\(474\) 901.138 + 38.0129i 1.90113 + 0.0801960i
\(475\) −122.063 + 375.670i −0.256974 + 0.790884i
\(476\) −7.78198 10.7110i −0.0163487 0.0225020i
\(477\) −104.011 + 120.366i −0.218052 + 0.252339i
\(478\) −0.303980 0.935553i −0.000635941 0.00195722i
\(479\) −665.556 + 216.252i −1.38947 + 0.451466i −0.905771 0.423768i \(-0.860707\pi\)
−0.483700 + 0.875234i \(0.660707\pi\)
\(480\) −535.405 + 675.138i −1.11543 + 1.40654i
\(481\) −506.680 + 368.124i −1.05339 + 0.765331i
\(482\) −846.365 275.001i −1.75594 0.570541i
\(483\) 250.841 + 10.5813i 0.519339 + 0.0219074i
\(484\) 586.496 + 278.321i 1.21177 + 0.575043i
\(485\) 420.282i 0.866560i
\(486\) −372.691 + 643.510i −0.766854 + 1.32409i
\(487\) 528.569 384.028i 1.08536 0.788558i 0.106747 0.994286i \(-0.465956\pi\)
0.978609 + 0.205729i \(0.0659564\pi\)
\(488\) 26.1639 36.0115i 0.0536145 0.0737941i
\(489\) 758.683 211.607i 1.55150 0.432734i
\(490\) 248.747 + 765.565i 0.507647 + 1.56238i
\(491\) 36.3470 50.0274i 0.0740265 0.101889i −0.770398 0.637563i \(-0.779943\pi\)
0.844425 + 0.535674i \(0.179943\pi\)
\(492\) 179.309 119.063i 0.364450 0.241998i
\(493\) −0.941732 + 2.89835i −0.00191021 + 0.00587901i
\(494\) 1029.14i 2.08329i
\(495\) −5.45732 657.270i −0.0110249 1.32782i
\(496\) 180.281 0.363470
\(497\) 7.48628 + 2.43244i 0.0150629 + 0.00489424i
\(498\) 162.007 + 243.983i 0.325315 + 0.489926i
\(499\) −266.970 193.965i −0.535010 0.388707i 0.287219 0.957865i \(-0.407269\pi\)
−0.822228 + 0.569158i \(0.807269\pi\)
\(500\) −200.535 + 65.1577i −0.401069 + 0.130315i
\(501\) −128.962 462.371i −0.257408 0.922897i
\(502\) −278.828 202.580i −0.555434 0.403547i
\(503\) 204.067 + 280.874i 0.405700 + 0.558398i 0.962163 0.272474i \(-0.0878420\pi\)
−0.556463 + 0.830872i \(0.687842\pi\)
\(504\) 106.144 + 44.6863i 0.210603 + 0.0886633i
\(505\) 998.280 1.97679
\(506\) 202.098 897.270i 0.399404 1.77326i
\(507\) 11.9975 284.414i 0.0236637 0.560974i
\(508\) 243.144 748.320i 0.478630 1.47307i
\(509\) 503.258 + 692.675i 0.988719 + 1.36086i 0.931997 + 0.362465i \(0.118065\pi\)
0.0567219 + 0.998390i \(0.481935\pi\)
\(510\) 38.4770 + 30.5134i 0.0754450 + 0.0598302i
\(511\) 43.0462 + 132.483i 0.0842391 + 0.259261i
\(512\) 494.832 160.781i 0.966468 0.314025i
\(513\) 382.957 407.145i 0.746504 0.793655i
\(514\) 486.664 353.582i 0.946817 0.687903i
\(515\) 945.687 + 307.272i 1.83629 + 0.596645i
\(516\) −29.4492 + 698.125i −0.0570720 + 1.35295i
\(517\) −144.423 164.355i −0.279348 0.317901i
\(518\) 361.382i 0.697649i
\(519\) 173.217 465.381i 0.333751 0.896687i
\(520\) −364.530 + 264.846i −0.701019 + 0.509320i
\(521\) 418.891 576.554i 0.804013 1.10663i −0.188207 0.982129i \(-0.560268\pi\)
0.992220 0.124499i \(-0.0397325\pi\)
\(522\) −23.7356 101.444i −0.0454705 0.194337i
\(523\) 155.721 + 479.261i 0.297746 + 0.916369i 0.982285 + 0.187392i \(0.0600036\pi\)
−0.684539 + 0.728976i \(0.739996\pi\)
\(524\) 471.353 648.762i 0.899529 1.23809i
\(525\) 96.9869 + 146.063i 0.184737 + 0.278215i
\(526\) −357.772 + 1101.11i −0.680176 + 2.09337i
\(527\) 16.7414i 0.0317673i
\(528\) −156.385 + 239.813i −0.296183 + 0.454192i
\(529\) −217.513 −0.411179
\(530\) −341.553 110.977i −0.644440 0.209391i
\(531\) −202.745 335.181i −0.381818 0.631226i
\(532\) −275.227 199.964i −0.517345 0.375873i
\(533\) −206.602 + 67.1290i −0.387621 + 0.125946i
\(534\) −163.961 + 45.7311i −0.307044 + 0.0856387i
\(535\) −111.463 80.9826i −0.208342 0.151369i
\(536\) −177.532 244.351i −0.331216 0.455879i
\(537\) −61.2576 + 164.581i −0.114074 + 0.306482i
\(538\) −615.583 −1.14421
\(539\) 172.425 + 400.239i 0.319899 + 0.742558i
\(540\) −954.086 121.315i −1.76683 0.224658i
\(541\) −181.281 + 557.925i −0.335085 + 1.03128i 0.631596 + 0.775298i \(0.282400\pi\)
−0.966680 + 0.255987i \(0.917600\pi\)
\(542\) 144.288 + 198.595i 0.266214 + 0.366412i
\(543\) −530.662 + 669.157i −0.977279 + 1.23233i
\(544\) −10.7702 33.1471i −0.0197981 0.0609322i
\(545\) −668.020 + 217.053i −1.22572 + 0.398262i
\(546\) −357.920 283.842i −0.655531 0.519856i
\(547\) −557.289 + 404.894i −1.01881 + 0.740209i −0.966039 0.258398i \(-0.916805\pi\)
−0.0527711 + 0.998607i \(0.516805\pi\)
\(548\) −776.646 252.348i −1.41724 0.460489i
\(549\) −95.5519 8.07575i −0.174047 0.0147099i
\(550\) 589.895 254.131i 1.07254 0.462056i
\(551\) 78.3083i 0.142120i
\(552\) −320.928 119.451i −0.581391 0.216396i
\(553\) −243.444 + 176.873i −0.440225 + 0.319842i
\(554\) −393.778 + 541.989i −0.710790 + 0.978319i
\(555\) −206.306 739.678i −0.371723 1.33275i
\(556\) −185.415 570.649i −0.333480 1.02635i
\(557\) 363.725 500.624i 0.653007 0.898787i −0.346218 0.938154i \(-0.612534\pi\)
0.999225 + 0.0393671i \(0.0125342\pi\)
\(558\) 296.217 + 489.710i 0.530855 + 0.877616i
\(559\) 217.925 670.706i 0.389849 1.19983i
\(560\) 176.430i 0.315053i
\(561\) 22.2697 + 14.5223i 0.0396964 + 0.0258864i
\(562\) 1519.22 2.70325
\(563\) −541.408 175.914i −0.961648 0.312458i −0.214208 0.976788i \(-0.568717\pi\)
−0.747440 + 0.664330i \(0.768717\pi\)
\(564\) −266.702 + 177.093i −0.472876 + 0.313994i
\(565\) 713.145 + 518.130i 1.26220 + 0.917045i
\(566\) −895.558 + 290.984i −1.58226 + 0.514107i
\(567\) −35.9779 245.479i −0.0634531 0.432943i
\(568\) −8.68589 6.31067i −0.0152921 0.0111103i
\(569\) −529.905 729.352i −0.931292 1.28181i −0.959354 0.282207i \(-0.908934\pi\)
0.0280618 0.999606i \(-0.491066\pi\)
\(570\) 1182.60 + 440.168i 2.07473 + 0.772225i
\(571\) −804.182 −1.40837 −0.704187 0.710014i \(-0.748688\pi\)
−0.704187 + 0.710014i \(0.748688\pi\)
\(572\) −720.168 + 632.832i −1.25904 + 1.10635i
\(573\) −411.961 17.3779i −0.718955 0.0303279i
\(574\) −38.7348 + 119.213i −0.0674822 + 0.207689i
\(575\) −306.429 421.763i −0.532920 0.733501i
\(576\) 665.221 + 574.832i 1.15490 + 0.997972i
\(577\) −243.227 748.576i −0.421538 1.29736i −0.906271 0.422697i \(-0.861083\pi\)
0.484733 0.874662i \(-0.338917\pi\)
\(578\) 839.238 272.685i 1.45197 0.471773i
\(579\) −555.671 + 700.694i −0.959709 + 1.21018i
\(580\) 109.009 79.2000i 0.187947 0.136552i
\(581\) −92.9285 30.1943i −0.159946 0.0519695i
\(582\) 580.643 + 24.4934i 0.997669 + 0.0420849i
\(583\) −189.678 42.7225i −0.325348 0.0732805i
\(584\) 189.998i 0.325340i
\(585\) 894.632 + 376.638i 1.52929 + 0.643826i
\(586\) −841.024 + 611.040i −1.43519 + 1.04273i
\(587\) 107.287 147.667i 0.182771 0.251563i −0.707794 0.706419i \(-0.750309\pi\)
0.890565 + 0.454856i \(0.150309\pi\)
\(588\) 614.230 171.317i 1.04461 0.291355i
\(589\) −132.934 409.128i −0.225694 0.694615i
\(590\) 519.809 715.456i 0.881033 1.21264i
\(591\) −145.298 + 96.4791i −0.245851 + 0.163247i
\(592\) −103.360 + 318.109i −0.174595 + 0.537347i
\(593\) 685.071i 1.15526i 0.816297 + 0.577632i \(0.196023\pi\)
−0.816297 + 0.577632i \(0.803977\pi\)
\(594\) −908.375 30.7652i −1.52925 0.0517932i
\(595\) −16.3837 −0.0275357
\(596\) 1325.11 + 430.556i 2.22335 + 0.722409i
\(597\) −207.518 312.523i −0.347602 0.523489i
\(598\) 1098.87 + 798.373i 1.83757 + 1.33507i
\(599\) −343.213 + 111.517i −0.572977 + 0.186171i −0.581152 0.813795i \(-0.697398\pi\)
0.00817505 + 0.999967i \(0.497398\pi\)
\(600\) −64.2476 230.349i −0.107079 0.383915i
\(601\) 339.372 + 246.568i 0.564679 + 0.410264i 0.833169 0.553019i \(-0.186524\pi\)
−0.268489 + 0.963283i \(0.586524\pi\)
\(602\) −239.186 329.211i −0.397318 0.546862i
\(603\) −252.468 + 599.689i −0.418686 + 0.994510i
\(604\) −472.229 −0.781836
\(605\) 705.245 384.726i 1.16569 0.635910i
\(606\) 58.1783 1379.18i 0.0960039 2.27588i
\(607\) 311.403 958.400i 0.513020 1.57891i −0.273836 0.961776i \(-0.588293\pi\)
0.786856 0.617137i \(-0.211707\pi\)
\(608\) −526.406 724.536i −0.865800 1.19167i
\(609\) 27.2344 + 21.5977i 0.0447199 + 0.0354642i
\(610\) −66.8970 205.888i −0.109667 0.337521i
\(611\) 307.297 99.8468i 0.502941 0.163415i
\(612\) 25.4352 29.4348i 0.0415608 0.0480960i
\(613\) 446.778 324.603i 0.728838 0.529532i −0.160358 0.987059i \(-0.551265\pi\)
0.889196 + 0.457527i \(0.151265\pi\)
\(614\) 1152.92 + 374.608i 1.87773 + 0.610110i
\(615\) 11.2258 266.119i 0.0182533 0.432714i
\(616\) 13.0184 + 140.156i 0.0211338 + 0.227526i
\(617\) 675.556i 1.09490i 0.836837 + 0.547452i \(0.184402\pi\)
−0.836837 + 0.547452i \(0.815598\pi\)
\(618\) 479.628 1288.61i 0.776097 2.08514i
\(619\) 217.722 158.184i 0.351732 0.255548i −0.397863 0.917445i \(-0.630248\pi\)
0.749595 + 0.661896i \(0.230248\pi\)
\(620\) −435.082 + 598.838i −0.701744 + 0.965868i
\(621\) 137.644 + 724.750i 0.221650 + 1.16707i
\(622\) 82.3072 + 253.316i 0.132327 + 0.407260i
\(623\) 33.3805 45.9443i 0.0535802 0.0737469i
\(624\) −233.880 352.224i −0.374807 0.564461i
\(625\) −228.038 + 701.828i −0.364860 + 1.12292i
\(626\) 1832.83i 2.92784i
\(627\) 659.544 + 178.067i 1.05190 + 0.283999i
\(628\) 41.0719 0.0654011
\(629\) 29.5404 + 9.59826i 0.0469641 + 0.0152596i
\(630\) 479.249 289.889i 0.760712 0.460142i
\(631\) −75.5208 54.8691i −0.119684 0.0869558i 0.526333 0.850279i \(-0.323567\pi\)
−0.646017 + 0.763323i \(0.723567\pi\)
\(632\) 390.342 126.830i 0.617630 0.200680i
\(633\) −139.841 + 39.0034i −0.220917 + 0.0616168i
\(634\) −6.07783 4.41580i −0.00958649 0.00696499i
\(635\) −572.322 787.734i −0.901295 1.24053i
\(636\) −99.2390 + 266.625i −0.156036 + 0.419222i
\(637\) −643.584 −1.01034
\(638\) 95.6529 84.0530i 0.149926 0.131744i
\(639\) −1.94785 + 23.0469i −0.00304828 + 0.0360672i
\(640\) −258.308 + 794.990i −0.403606 + 1.24217i
\(641\) −8.68174 11.9494i −0.0135441 0.0186418i 0.802191 0.597067i \(-0.203667\pi\)
−0.815735 + 0.578425i \(0.803667\pi\)
\(642\) −118.378 + 149.273i −0.184389 + 0.232512i
\(643\) −134.744 414.698i −0.209555 0.644943i −0.999496 0.0317599i \(-0.989889\pi\)
0.789941 0.613183i \(-0.210111\pi\)
\(644\) 427.023 138.748i 0.663079 0.215448i
\(645\) 677.506 + 537.283i 1.05040 + 0.832997i
\(646\) −41.2922 + 30.0005i −0.0639198 + 0.0464405i
\(647\) 298.985 + 97.1462i 0.462110 + 0.150149i 0.530814 0.847488i \(-0.321886\pi\)
−0.0687036 + 0.997637i \(0.521886\pi\)
\(648\) −56.7948 + 333.596i −0.0876462 + 0.514809i
\(649\) 244.390 411.709i 0.376564 0.634375i
\(650\) 948.550i 1.45931i
\(651\) −178.952 66.6068i −0.274888 0.102315i
\(652\) 1139.59 827.958i 1.74783 1.26987i
\(653\) 112.807 155.266i 0.172752 0.237773i −0.713858 0.700291i \(-0.753054\pi\)
0.886610 + 0.462517i \(0.153054\pi\)
\(654\) 260.940 + 935.557i 0.398990 + 1.43052i
\(655\) −306.656 943.789i −0.468177 1.44090i
\(656\) −68.1931 + 93.8598i −0.103953 + 0.143079i
\(657\) −350.223 + 211.844i −0.533064 + 0.322441i
\(658\) 57.6135 177.316i 0.0875586 0.269478i
\(659\) 127.678i 0.193745i −0.995297 0.0968724i \(-0.969116\pi\)
0.995297 0.0968724i \(-0.0308839\pi\)
\(660\) −419.175 1098.22i −0.635113 1.66396i
\(661\) 580.599 0.878364 0.439182 0.898398i \(-0.355268\pi\)
0.439182 + 0.898398i \(0.355268\pi\)
\(662\) −1071.27 348.076i −1.61823 0.525795i
\(663\) −32.7084 + 21.7186i −0.0493339 + 0.0327581i
\(664\) 107.820 + 78.3355i 0.162379 + 0.117975i
\(665\) −400.388 + 130.094i −0.602088 + 0.195630i
\(666\) −1033.93 + 241.917i −1.55245 + 0.363238i
\(667\) −83.6135 60.7488i −0.125358 0.0910776i
\(668\) −504.590 694.508i −0.755374 1.03968i
\(669\) −595.254 221.556i −0.889767 0.331175i
\(670\) −1468.92 −2.19241
\(671\) −46.3713 107.638i −0.0691078 0.160415i
\(672\) −397.167 16.7538i −0.591023 0.0249313i
\(673\) −168.866 + 519.715i −0.250915 + 0.772236i 0.743692 + 0.668522i \(0.233073\pi\)
−0.994607 + 0.103714i \(0.966927\pi\)
\(674\) 1064.66 + 1465.37i 1.57961 + 2.17415i
\(675\) −352.967 + 375.261i −0.522914 + 0.555943i
\(676\) −157.319 484.177i −0.232720 0.716238i
\(677\) 27.7389 9.01292i 0.0409733 0.0133130i −0.288459 0.957492i \(-0.593143\pi\)
0.329432 + 0.944179i \(0.393143\pi\)
\(678\) 757.388 955.055i 1.11709 1.40864i
\(679\) −156.862 + 113.967i −0.231019 + 0.167845i
\(680\) 21.2528 + 6.90545i 0.0312541 + 0.0101551i
\(681\) −363.832 15.3476i −0.534261 0.0225369i
\(682\) −357.061 + 601.520i −0.523550 + 0.881994i
\(683\) 82.4506i 0.120718i 0.998177 + 0.0603592i \(0.0192246\pi\)
−0.998177 + 0.0603592i \(0.980775\pi\)
\(684\) 387.865 921.299i 0.567054 1.34693i
\(685\) −817.553 + 593.987i −1.19351 + 0.867134i
\(686\) −488.251 + 672.019i −0.711735 + 0.979620i
\(687\) 933.212 260.286i 1.35839 0.378873i
\(688\) −116.386 358.200i −0.169166 0.520640i
\(689\) 168.772 232.294i 0.244952 0.337147i
\(690\) −1387.41 + 921.249i −2.01073 + 1.33514i
\(691\) 299.041 920.352i 0.432765 1.33191i −0.462595 0.886570i \(-0.653082\pi\)
0.895360 0.445344i \(-0.146918\pi\)
\(692\) 888.061i 1.28333i
\(693\) 243.834 180.268i 0.351852 0.260126i
\(694\) −901.554 −1.29907
\(695\) −706.172 229.449i −1.01607 0.330143i
\(696\) −26.2251 39.4952i −0.0376798 0.0567459i
\(697\) 8.71606 + 6.33259i 0.0125051 + 0.00908549i
\(698\) 1199.14 389.624i 1.71796 0.558201i
\(699\) 324.333 + 1162.84i 0.463996 + 1.66358i
\(700\) 253.674 + 184.305i 0.362392 + 0.263293i
\(701\) 184.624 + 254.112i 0.263372 + 0.362500i 0.920138 0.391594i \(-0.128076\pi\)
−0.656766 + 0.754094i \(0.728076\pi\)
\(702\) 572.485 1214.04i 0.815506 1.72940i
\(703\) 798.129 1.13532
\(704\) −236.113 + 1048.29i −0.335388 + 1.48904i
\(705\) −16.6971 + 395.822i −0.0236838 + 0.561450i
\(706\) 128.211 394.592i 0.181602 0.558912i
\(707\) 270.702 + 372.589i 0.382888 + 0.527000i
\(708\) −548.910 435.302i −0.775296 0.614834i
\(709\) 101.157 + 311.330i 0.142676 + 0.439111i 0.996705 0.0811142i \(-0.0258478\pi\)
−0.854029 + 0.520226i \(0.825848\pi\)
\(710\) −49.6596 + 16.1354i −0.0699432 + 0.0227259i
\(711\) −669.008 578.103i −0.940939 0.813085i
\(712\) −62.6656 + 45.5292i −0.0880134 + 0.0639455i
\(713\) 539.971 + 175.447i 0.757323 + 0.246069i
\(714\) −0.954820 + 22.6351i −0.00133728 + 0.0317018i
\(715\) 109.725 + 1181.30i 0.153462 + 1.65217i
\(716\) 314.061i 0.438632i
\(717\) −0.336383 + 0.903758i −0.000469153 + 0.00126047i
\(718\) 690.192 501.454i 0.961270 0.698404i
\(719\) 650.211 894.939i 0.904327 1.24470i −0.0647402 0.997902i \(-0.520622\pi\)
0.969067 0.246797i \(-0.0793781\pi\)
\(720\) 504.774 118.106i 0.701075 0.164036i
\(721\) 141.757 + 436.282i 0.196611 + 0.605107i
\(722\) −121.532 + 167.275i −0.168327 + 0.231682i
\(723\) 482.581 + 726.770i 0.667471 + 1.00521i
\(724\) −471.975 + 1452.59i −0.651899 + 2.00634i
\(725\) 72.1759i 0.0995530i
\(726\) −490.420 996.758i −0.675510 1.37294i
\(727\) 577.040 0.793727 0.396864 0.917878i \(-0.370099\pi\)
0.396864 + 0.917878i \(0.370099\pi\)
\(728\) −197.698 64.2359i −0.271563 0.0882361i
\(729\) 678.241 267.263i 0.930372 0.366616i
\(730\) −747.563 543.136i −1.02406 0.744023i
\(731\) −33.2634 + 10.8079i −0.0455040 + 0.0147851i
\(732\) −165.188 + 46.0732i −0.225667 + 0.0629416i
\(733\) −501.026 364.016i −0.683527 0.496612i 0.190999 0.981590i \(-0.438827\pi\)
−0.874526 + 0.484979i \(0.838827\pi\)
\(734\) −317.281 436.700i −0.432263 0.594959i
\(735\) 275.263 739.548i 0.374507 1.00619i
\(736\) 1181.99 1.60596
\(737\) −791.851 + 73.5511i −1.07442 + 0.0997980i
\(738\) −367.005 31.0181i −0.497297 0.0420299i
\(739\) −345.884 + 1064.52i −0.468044 + 1.44049i 0.387070 + 0.922050i \(0.373487\pi\)
−0.855114 + 0.518440i \(0.826513\pi\)
\(740\) −807.217 1111.04i −1.09083 1.50140i
\(741\) −626.877 + 790.483i −0.845988 + 1.06678i
\(742\) −51.1981 157.572i −0.0690002 0.212361i
\(743\) 1092.36 354.930i 1.47020 0.477698i 0.539034 0.842284i \(-0.318790\pi\)
0.931170 + 0.364586i \(0.118790\pi\)
\(744\) 204.061 + 161.827i 0.274276 + 0.217509i
\(745\) 1394.91 1013.46i 1.87236 1.36035i
\(746\) −474.724 154.247i −0.636360 0.206766i
\(747\) 24.1791 286.086i 0.0323682 0.382979i
\(748\) 46.3847 + 10.4475i 0.0620116 + 0.0139673i
\(749\) 63.5613i 0.0848616i
\(750\) 338.147 + 125.860i 0.450863 + 0.167813i
\(751\) 221.394 160.852i 0.294799 0.214184i −0.430548 0.902568i \(-0.641680\pi\)
0.725346 + 0.688384i \(0.241680\pi\)
\(752\) 101.430 139.606i 0.134880 0.185646i
\(753\) 90.7704 + 325.443i 0.120545 + 0.432195i
\(754\) 58.1099 + 178.844i 0.0770689 + 0.237194i
\(755\) −343.489 + 472.772i −0.454952 + 0.626188i
\(756\) −213.439 388.991i −0.282327 0.514538i
\(757\) −172.433 + 530.695i −0.227785 + 0.701051i 0.770212 + 0.637788i \(0.220150\pi\)
−0.997997 + 0.0632624i \(0.979850\pi\)
\(758\) 162.899i 0.214906i
\(759\) −701.781 + 566.088i −0.924613 + 0.745834i
\(760\) 574.212 0.755543
\(761\) 401.113 + 130.329i 0.527086 + 0.171261i 0.560459 0.828182i \(-0.310625\pi\)
−0.0333725 + 0.999443i \(0.510625\pi\)
\(762\) −1121.65 + 744.788i −1.47199 + 0.977412i
\(763\) −262.156 190.468i −0.343586 0.249630i
\(764\) −701.310 + 227.870i −0.917945 + 0.298259i
\(765\) −10.9676 46.8746i −0.0143367 0.0612740i
\(766\) 221.993 + 161.287i 0.289808 + 0.210558i
\(767\) 415.598 + 572.021i 0.541848 + 0.745790i
\(768\) −15.3340 5.70738i −0.0199661 0.00743148i
\(769\) −108.997 −0.141738 −0.0708692 0.997486i \(-0.522577\pi\)
−0.0708692 + 0.997486i \(0.522577\pi\)
\(770\) 588.670 + 349.433i 0.764506 + 0.453810i
\(771\) −589.181 24.8536i −0.764178 0.0322355i
\(772\) −494.218 + 1521.05i −0.640179 + 1.97027i
\(773\) −606.367 834.592i −0.784433 1.07968i −0.994779 0.102053i \(-0.967459\pi\)
0.210346 0.977627i \(-0.432541\pi\)
\(774\) 781.772 904.702i 1.01004 1.16887i
\(775\) 122.524 + 377.089i 0.158095 + 0.486567i
\(776\) 251.515 81.7222i 0.324117 0.105312i
\(777\) 220.127 277.577i 0.283304 0.357242i
\(778\) 667.478 484.951i 0.857941 0.623331i
\(779\) 263.288 + 85.5475i 0.337982 + 0.109817i
\(780\) 1734.41 + 73.1631i 2.22360 + 0.0937988i
\(781\) −25.9621 + 11.1847i −0.0332422 + 0.0143209i
\(782\) 67.3630i 0.0861420i
\(783\) −43.5608 + 92.3769i −0.0556332 + 0.117978i
\(784\) −278.072 + 202.031i −0.354683 + 0.257692i
\(785\) 29.8748 41.1191i 0.0380570 0.0523810i
\(786\) −1321.77 + 368.660i −1.68164 + 0.469033i
\(787\) 64.0985 + 197.275i 0.0814467 + 0.250667i 0.983485 0.180988i \(-0.0579296\pi\)
−0.902039 + 0.431655i \(0.857930\pi\)
\(788\) −183.340 + 252.346i −0.232665 + 0.320236i
\(789\) 945.519 627.833i 1.19838 0.795732i
\(790\) 616.825 1898.39i 0.780791 2.40303i
\(791\) 406.668i 0.514119i
\(792\) −392.278 + 131.070i −0.495301 + 0.165492i
\(793\) 173.082 0.218263
\(794\) −615.536 200.000i −0.775234 0.251889i
\(795\) 194.747 + 293.290i 0.244965 + 0.368918i
\(796\) −542.774 394.349i −0.681877 0.495413i
\(797\) −211.514 + 68.7252i −0.265388 + 0.0862298i −0.438689 0.898639i \(-0.644557\pi\)
0.173300 + 0.984869i \(0.444557\pi\)
\(798\) 156.398 + 560.741i 0.195988 + 0.702683i
\(799\) −12.9641 9.41900i −0.0162255 0.0117885i
\(800\) 485.183 + 667.797i 0.606479 + 0.834746i
\(801\) 153.794 + 64.7471i 0.192003 + 0.0808328i
\(802\) 1376.50 1.71633
\(803\) −430.185 255.357i −0.535723 0.318004i
\(804\) −49.0426 + 1162.61i −0.0609983 + 1.44603i
\(805\) 171.699 528.436i 0.213291 0.656443i
\(806\) −607.201 835.740i −0.753351 1.03690i
\(807\) 472.828 + 374.967i 0.585909 + 0.464643i
\(808\) −194.112 597.415i −0.240237 0.739375i
\(809\) −715.778 + 232.570i −0.884769 + 0.287479i −0.715936 0.698166i \(-0.754000\pi\)
−0.168833 + 0.985645i \(0.554000\pi\)
\(810\) 1150.21 + 1177.09i 1.42001 + 1.45320i
\(811\) −187.891 + 136.511i −0.231678 + 0.168324i −0.697568 0.716519i \(-0.745734\pi\)
0.465890 + 0.884843i \(0.345734\pi\)
\(812\) 59.1197 + 19.2092i 0.0728076 + 0.0236566i
\(813\) 10.1421 240.430i 0.0124749 0.295732i
\(814\) −856.679 974.908i −1.05243 1.19768i
\(815\) 1743.13i 2.13881i
\(816\) −7.31441 + 19.6516i −0.00896373 + 0.0240828i
\(817\) −727.077 + 528.252i −0.889935 + 0.646576i
\(818\) 277.540 382.001i 0.339291 0.466994i
\(819\) 102.023 + 436.037i 0.124570 + 0.532401i
\(820\) −147.199 453.033i −0.179511 0.552480i
\(821\) 285.054 392.343i 0.347204 0.477885i −0.599324 0.800506i \(-0.704564\pi\)
0.946528 + 0.322621i \(0.104564\pi\)
\(822\) 772.981 + 1164.11i 0.940367 + 1.41620i
\(823\) 48.4819 149.212i 0.0589088 0.181302i −0.917272 0.398261i \(-0.869614\pi\)
0.976181 + 0.216959i \(0.0696137\pi\)
\(824\) 625.689i 0.759331i
\(825\) −607.894 164.123i −0.736842 0.198937i
\(826\) 407.986 0.493930
\(827\) 150.007 + 48.7401i 0.181386 + 0.0589360i 0.398302 0.917254i \(-0.369600\pi\)
−0.216916 + 0.976190i \(0.569600\pi\)
\(828\) 682.823 + 1128.85i 0.824666 + 1.36335i
\(829\) −1057.08 768.011i −1.27512 0.926431i −0.275728 0.961236i \(-0.588919\pi\)
−0.999394 + 0.0348051i \(0.988919\pi\)
\(830\) 616.434 200.292i 0.742692 0.241315i
\(831\) 632.599 176.441i 0.761251 0.212323i
\(832\) −1283.81 932.745i −1.54304 1.12109i
\(833\) 18.7611 + 25.8224i 0.0225223 + 0.0309993i
\(834\) −358.152 + 962.245i −0.429439 + 1.15377i
\(835\) −1062.33 −1.27226
\(836\) 1216.52 112.996i 1.45516 0.135163i
\(837\) 70.7709 556.579i 0.0845530 0.664969i
\(838\) −714.482 + 2198.95i −0.852604 + 2.62405i
\(839\) 754.318 + 1038.23i 0.899068 + 1.23746i 0.970764 + 0.240035i \(0.0771589\pi\)
−0.0716959 + 0.997427i \(0.522841\pi\)
\(840\) 158.370 199.702i 0.188536 0.237741i
\(841\) 255.462 + 786.230i 0.303759 + 0.934875i
\(842\) −1271.56 + 413.154i −1.51016 + 0.490682i
\(843\) −1166.91 925.398i −1.38424 1.09774i
\(844\) −210.049 + 152.609i −0.248873 + 0.180817i
\(845\) −599.164 194.680i −0.709069 0.230391i
\(846\) 545.878 + 46.1359i 0.645246 + 0.0545342i
\(847\) 334.831 + 158.894i 0.395315 + 0.187596i
\(848\) 153.347i 0.180834i
\(849\) 865.123 + 322.002i 1.01899 + 0.379273i
\(850\) 38.0586 27.6512i 0.0447748 0.0325308i
\(851\) −619.160 + 852.200i −0.727567 + 1.00141i
\(852\) 11.1128 + 39.8430i 0.0130431 + 0.0467641i
\(853\) 153.468 + 472.325i 0.179915 + 0.553723i 0.999824 0.0187721i \(-0.00597570\pi\)
−0.819908 + 0.572495i \(0.805976\pi\)
\(854\) 58.7033 80.7982i 0.0687392 0.0946114i
\(855\) −640.234 1058.44i −0.748811 1.23794i
\(856\) −26.7900 + 82.4511i −0.0312967 + 0.0963214i
\(857\) 479.970i 0.560059i −0.959991 0.280029i \(-0.909656\pi\)
0.959991 0.280029i \(-0.0903442\pi\)
\(858\) 1638.43 82.7474i 1.90960 0.0964421i
\(859\) 658.810 0.766950 0.383475 0.923551i \(-0.374727\pi\)
0.383475 + 0.923551i \(0.374727\pi\)
\(860\) 1470.71 + 477.864i 1.71013 + 0.555655i
\(861\) 102.368 67.9732i 0.118894 0.0789468i
\(862\) 24.0996 + 17.5094i 0.0279578 + 0.0203125i
\(863\) −512.443 + 166.503i −0.593793 + 0.192935i −0.590470 0.807060i \(-0.701058\pi\)
−0.00332255 + 0.999994i \(0.501058\pi\)
\(864\) −217.939 1147.53i −0.252244 1.32816i
\(865\) −889.082 645.956i −1.02784 0.746770i
\(866\) −106.622 146.752i −0.123120 0.169460i
\(867\) −810.717 301.752i −0.935083 0.348042i
\(868\) −341.485 −0.393416
\(869\) 237.457 1054.25i 0.273253 1.21318i
\(870\) −230.365 9.71754i −0.264787 0.0111696i
\(871\) 362.918 1116.95i 0.416669 1.28237i
\(872\) 259.788 + 357.567i 0.297922 + 0.410054i
\(873\) −431.072 372.498i −0.493782 0.426687i
\(874\) −534.893 1646.23i −0.612005 1.88356i
\(875\) −114.486 + 37.1986i −0.130841 + 0.0425127i
\(876\) −454.837 + 573.543i −0.519220 + 0.654729i
\(877\) −68.5357 + 49.7941i −0.0781479 + 0.0567777i −0.626173 0.779684i \(-0.715380\pi\)
0.548025 + 0.836462i \(0.315380\pi\)
\(878\) −1294.36 420.562i −1.47421 0.479001i
\(879\) 1018.19 + 42.9505i 1.15835 + 0.0488629i
\(880\) 418.238 + 475.959i 0.475271 + 0.540862i
\(881\) 364.734i 0.414000i −0.978341 0.207000i \(-0.933630\pi\)
0.978341 0.207000i \(-0.0663701\pi\)
\(882\) −1005.69 423.391i −1.14023 0.480035i
\(883\) −180.241 + 130.953i −0.204123 + 0.148304i −0.685151 0.728401i \(-0.740264\pi\)
0.481027 + 0.876706i \(0.340264\pi\)
\(884\) −41.2721 + 56.8062i −0.0466879 + 0.0642604i
\(885\) −835.067 + 232.912i −0.943578 + 0.263177i
\(886\) 506.266 + 1558.13i 0.571406 + 1.75861i
\(887\) −801.425 + 1103.07i −0.903523 + 1.24359i 0.0658073 + 0.997832i \(0.479038\pi\)
−0.969331 + 0.245761i \(0.920962\pi\)
\(888\) −402.540 + 267.290i −0.453311 + 0.301003i
\(889\) 138.811 427.217i 0.156143 0.480559i
\(890\) 376.714i 0.423274i
\(891\) 678.981 + 576.945i 0.762044 + 0.647525i
\(892\) −1135.89 −1.27342
\(893\) −391.611 127.242i −0.438534 0.142488i
\(894\) −1318.86 1986.21i −1.47524 2.22171i
\(895\) 314.422 + 228.441i 0.351309 + 0.255241i
\(896\) −366.760 + 119.167i −0.409330 + 0.132999i
\(897\) −357.728 1282.58i −0.398805 1.42985i
\(898\) 1904.91 + 1384.00i 2.12129 + 1.54120i
\(899\) 46.2024 + 63.5921i 0.0513931 + 0.0707365i
\(900\) −357.491 + 849.151i −0.397212 + 0.943502i
\(901\) −14.2402 −0.0158049
\(902\) −178.107 413.428i −0.197458 0.458345i
\(903\) −16.8126 + 398.560i −0.0186186 + 0.441373i
\(904\) 171.404 527.526i 0.189606 0.583546i
\(905\) 1110.95 + 1529.10i 1.22757 + 1.68961i
\(906\) 633.143 + 502.102i 0.698834 + 0.554196i
\(907\) 203.099 + 625.073i 0.223924 + 0.689166i 0.998399 + 0.0565619i \(0.0180138\pi\)
−0.774476 + 0.632604i \(0.781986\pi\)
\(908\) −619.376 + 201.248i −0.682132 + 0.221638i
\(909\) −884.781 + 1023.91i −0.973357 + 1.12641i
\(910\) −817.887 + 594.230i −0.898777 + 0.653000i
\(911\) −331.388 107.674i −0.363763 0.118194i 0.121432 0.992600i \(-0.461251\pi\)
−0.485195 + 0.874406i \(0.661251\pi\)
\(912\) −22.7085 + 538.329i −0.0248996 + 0.590273i
\(913\) 322.273 138.837i 0.352982 0.152067i
\(914\) 519.188i 0.568039i
\(915\) −74.0280 + 198.891i −0.0809049 + 0.217367i
\(916\) 1401.74 1018.42i 1.53028 1.11182i
\(917\) 269.096 370.379i 0.293453 0.403903i
\(918\) −65.3991 + 12.4206i −0.0712409 + 0.0135301i
\(919\) 197.588 + 608.115i 0.215004 + 0.661714i 0.999153 + 0.0411417i \(0.0130995\pi\)
−0.784150 + 0.620572i \(0.786901\pi\)
\(920\) −445.453 + 613.114i −0.484188 + 0.666428i
\(921\) −657.376 990.010i −0.713763 1.07493i
\(922\) 251.884 775.220i 0.273193 0.840803i
\(923\) 41.7471i 0.0452298i
\(924\) 296.221 454.250i 0.320586 0.491613i
\(925\) −735.627 −0.795272
\(926\) 2051.44 + 666.554i 2.21538 + 0.719821i
\(927\) −1153.33 + 697.629i −1.24415 + 0.752566i
\(928\) 132.389 + 96.1863i 0.142661 + 0.103649i
\(929\) 299.056 97.1692i 0.321912 0.104595i −0.143604 0.989635i \(-0.545869\pi\)
0.465515 + 0.885040i \(0.345869\pi\)
\(930\) 1220.06 340.291i 1.31189 0.365904i
\(931\) 663.529 + 482.082i 0.712706 + 0.517811i
\(932\) 1269.02 + 1746.66i 1.36161 + 1.87410i
\(933\) 91.0809 244.707i 0.0976215 0.262279i
\(934\) −2066.22 −2.21222
\(935\) 44.1987 38.8387i 0.0472714 0.0415387i
\(936\) 51.4389 608.623i 0.0549561 0.650238i
\(937\) 469.735 1445.70i 0.501318 1.54290i −0.305556 0.952174i \(-0.598842\pi\)
0.806874 0.590724i \(-0.201158\pi\)
\(938\) −398.324 548.245i −0.424652 0.584483i
\(939\) 1116.42 1407.79i 1.18895 1.49925i
\(940\) 218.942 + 673.835i 0.232917 + 0.716846i
\(941\) 1067.37 346.811i 1.13430 0.368556i 0.319090 0.947724i \(-0.396623\pi\)
0.815208 + 0.579169i \(0.196623\pi\)
\(942\) −55.0673 43.6701i −0.0584579 0.0463589i
\(943\) −295.593 + 214.761i −0.313460 + 0.227742i
\(944\) 359.133 + 116.689i 0.380437 + 0.123611i
\(945\) −544.689 69.2591i −0.576390 0.0732900i
\(946\) 1425.67 + 321.114i 1.50705 + 0.339444i
\(947\) 865.333i 0.913762i 0.889528 + 0.456881i \(0.151033\pi\)
−0.889528 + 0.456881i \(0.848967\pi\)
\(948\) −1481.93 551.582i −1.56322 0.581838i
\(949\) 597.691 434.248i 0.629812 0.457585i
\(950\) 710.520 977.947i 0.747916 1.02942i
\(951\) 1.97859 + 7.09393i 0.00208054 + 0.00745945i
\(952\) 3.18575 + 9.80474i 0.00334638 + 0.0102991i
\(953\) −298.122 + 410.330i −0.312825 + 0.430567i −0.936260 0.351309i \(-0.885737\pi\)
0.623435 + 0.781875i \(0.285737\pi\)
\(954\) 416.547 251.962i 0.436632 0.264111i
\(955\) −281.986 + 867.863i −0.295273 + 0.908757i
\(956\) 1.72460i 0.00180397i
\(957\) −124.670 + 6.29631i −0.130271 + 0.00657921i
\(958\) 2141.59 2.23548
\(959\) −443.388 144.066i −0.462345 0.150225i
\(960\) 1620.92 1076.30i 1.68845 1.12115i
\(961\) 428.125 + 311.051i 0.445500 + 0.323674i
\(962\) 1822.80 592.265i 1.89481 0.615660i
\(963\) 181.852 42.5493i 0.188839 0.0441841i
\(964\) 1262.22 + 917.054i 1.30935 + 0.951301i
\(965\) 1163.31 + 1601.16i 1.20550 + 1.65924i
\(966\) −720.059 268.009i −0.745402 0.277442i
\(967\) −569.116 −0.588537 −0.294269 0.955723i \(-0.595076\pi\)
−0.294269 + 0.955723i \(0.595076\pi\)
\(968\) −367.369 347.241i −0.379513 0.358720i
\(969\) 49.9906 + 2.10876i 0.0515899 + 0.00217623i
\(970\) 397.448 1223.22i 0.409740 1.26105i
\(971\) −736.695 1013.97i −0.758697 1.04426i −0.997321 0.0731450i \(-0.976696\pi\)
0.238624 0.971112i \(-0.423304\pi\)
\(972\) 970.041 871.058i 0.997985 0.896150i
\(973\) −105.854 325.784i −0.108791 0.334825i
\(974\) −1901.55 + 617.851i −1.95231 + 0.634344i
\(975\) 577.786 728.580i 0.592601 0.747262i
\(976\) 74.7833 54.3333i 0.0766223 0.0556693i
\(977\) 1085.77 + 352.788i 1.11133 + 0.361093i 0.806453 0.591298i \(-0.201384\pi\)
0.304878 + 0.952391i \(0.401384\pi\)
\(978\) −2408.24 101.587i −2.46241 0.103873i
\(979\) 18.8627 + 203.076i 0.0192673 + 0.207432i
\(980\) 1411.24i 1.44004i
\(981\) 369.444 877.545i 0.376600 0.894541i
\(982\) −153.097 + 111.231i −0.155903 + 0.113270i
\(983\) −391.031 + 538.208i −0.397793 + 0.547515i −0.960188 0.279353i \(-0.909880\pi\)
0.562395 + 0.826869i \(0.309880\pi\)
\(984\) −161.440 + 45.0279i −0.164065 + 0.0457600i
\(985\) 119.279 + 367.102i 0.121095 + 0.372692i
\(986\) 5.48178 7.54502i 0.00555961 0.00765215i
\(987\) −152.261 + 101.102i −0.154266 + 0.102434i
\(988\) −557.549 + 1715.96i −0.564321 + 1.73680i
\(989\) 1186.13i 1.19933i
\(990\) −605.678 + 1918.13i −0.611796 + 1.93750i
\(991\) −1471.97 −1.48534 −0.742670 0.669658i \(-0.766441\pi\)
−0.742670 + 0.669658i \(0.766441\pi\)
\(992\) −854.961 277.794i −0.861856 0.280034i
\(993\) 610.818 + 919.894i 0.615124 + 0.926379i
\(994\) −19.4883 14.1591i −0.0196060 0.0142446i
\(995\) −789.604 + 256.558i −0.793572 + 0.257847i
\(996\) −137.945 494.579i −0.138499 0.496565i
\(997\) −502.232 364.893i −0.503743 0.365991i 0.306702 0.951806i \(-0.400775\pi\)
−0.810445 + 0.585815i \(0.800775\pi\)
\(998\) 593.582 + 816.996i 0.594772 + 0.818633i
\(999\) 941.518 + 443.978i 0.942461 + 0.444422i
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 33.3.h.b.20.1 yes 16
3.2 odd 2 inner 33.3.h.b.20.4 yes 16
11.2 odd 10 363.3.h.n.245.1 16
11.3 even 5 363.3.h.o.323.1 16
11.4 even 5 363.3.b.m.122.2 8
11.5 even 5 inner 33.3.h.b.5.4 yes 16
11.6 odd 10 363.3.h.j.269.1 16
11.7 odd 10 363.3.b.l.122.7 8
11.8 odd 10 363.3.h.n.323.4 16
11.9 even 5 363.3.h.o.245.4 16
11.10 odd 2 363.3.h.j.251.4 16
33.2 even 10 363.3.h.n.245.4 16
33.5 odd 10 inner 33.3.h.b.5.1 16
33.8 even 10 363.3.h.n.323.1 16
33.14 odd 10 363.3.h.o.323.4 16
33.17 even 10 363.3.h.j.269.4 16
33.20 odd 10 363.3.h.o.245.1 16
33.26 odd 10 363.3.b.m.122.7 8
33.29 even 10 363.3.b.l.122.2 8
33.32 even 2 363.3.h.j.251.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.h.b.5.1 16 33.5 odd 10 inner
33.3.h.b.5.4 yes 16 11.5 even 5 inner
33.3.h.b.20.1 yes 16 1.1 even 1 trivial
33.3.h.b.20.4 yes 16 3.2 odd 2 inner
363.3.b.l.122.2 8 33.29 even 10
363.3.b.l.122.7 8 11.7 odd 10
363.3.b.m.122.2 8 11.4 even 5
363.3.b.m.122.7 8 33.26 odd 10
363.3.h.j.251.1 16 33.32 even 2
363.3.h.j.251.4 16 11.10 odd 2
363.3.h.j.269.1 16 11.6 odd 10
363.3.h.j.269.4 16 33.17 even 10
363.3.h.n.245.1 16 11.2 odd 10
363.3.h.n.245.4 16 33.2 even 10
363.3.h.n.323.1 16 33.8 even 10
363.3.h.n.323.4 16 11.8 odd 10
363.3.h.o.245.1 16 33.20 odd 10
363.3.h.o.245.4 16 11.9 even 5
363.3.h.o.323.1 16 11.3 even 5
363.3.h.o.323.4 16 33.14 odd 10