Properties

Label 33.3.h.b.5.1
Level $33$
Weight $3$
Character 33.5
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 5.1
Root \(-2.91048 + 0.945671i\) of defining polynomial
Character \(\chi\) \(=\) 33.5
Dual form 33.3.h.b.20.1

$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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 −0.926612 0.376020i \(-0.877293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(3\) 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 0.862518 0.506027i \(-0.168886\pi\)
0.400357 + 0.916359i \(0.368886\pi\)
\(6\) −2.46650 + 8.84324i −0.411083 + 1.47387i
\(7\) 2.47800 1.80037i 0.354000 0.257196i −0.396545 0.918015i \(-0.629791\pi\)
0.750545 + 0.660819i \(0.229791\pi\)
\(8\) −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 0.935647 + 0.352938i \(0.114817\pi\)
−0.549503 + 0.835492i \(0.685183\pi\)
\(14\) −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 0.286394 0.958112i \(-0.407543\pi\)
−0.331466 + 0.943467i \(0.607543\pi\)
\(18\) 18.0080 + 20.8396i 1.00044 + 1.15776i
\(19\) −16.7481 12.1682i −0.881479 0.640432i 0.0521636 0.998639i \(-0.483388\pi\)
−0.933642 + 0.358207i \(0.883388\pi\)
\(20\) 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 \(0.202438\pi\)
−0.804491 + 0.593965i \(0.797562\pi\)
\(24\) 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 0.845629 0.533771i \(-0.179226\pi\)
−0.768960 + 0.639297i \(0.779226\pi\)
\(30\) −33.7177 + 50.7790i −1.12392 + 1.69263i
\(31\) −6.42137 19.7630i −0.207141 0.637515i −0.999619 0.0276136i \(-0.991209\pi\)
0.792478 0.609901i \(-0.208791\pi\)
\(32\) 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 −0.923204 0.384311i \(-0.874439\pi\)
0.0802160 + 0.996778i \(0.474439\pi\)
\(38\) 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 −0.894043 0.447981i \(-0.852143\pi\)
0.702330 + 0.711852i \(0.252143\pi\)
\(42\) 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 −0.666323 0.745663i \(-0.732133\pi\)
0.915073 + 0.403289i \(0.132133\pi\)
\(48\) 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 −0.146102 0.989269i \(-0.546673\pi\)
0.463279 + 0.886213i \(0.346673\pi\)
\(54\) 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 0.535158 0.844752i \(-0.320252\pi\)
−0.968780 + 0.247923i \(0.920252\pi\)
\(60\) 28.7098 102.934i 0.478496 1.71557i
\(61\) 3.29249 10.1333i 0.0539753 0.166119i −0.920435 0.390896i \(-0.872165\pi\)
0.974410 + 0.224777i \(0.0721653\pi\)
\(62\) 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 0.326178 0.945308i \(-0.394239\pi\)
−0.291754 + 0.956493i \(0.594239\pi\)
\(72\) 36.6108 + 8.56611i 0.508484 + 0.118974i
\(73\) 36.7931 26.7318i 0.504015 0.366188i −0.306533 0.951860i \(-0.599169\pi\)
0.810549 + 0.585671i \(0.199169\pi\)
\(74\) 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 −0.936998 0.349336i \(-0.886407\pi\)
0.552712 0.833372i \(-0.313593\pi\)
\(80\) −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 0.120491 0.992714i \(-0.461553\pi\)
−0.486024 + 0.873945i \(0.661553\pi\)
\(84\) −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 \(0.0332161\pi\)
−0.994560 + 0.104162i \(0.966784\pi\)
\(90\) 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 −0.999834 0.0182248i \(-0.994199\pi\)
0.798170 0.602432i \(-0.205801\pi\)
\(98\) 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 0.501561 0.865122i \(-0.332759\pi\)
0.914277 + 0.405089i \(0.132759\pi\)
\(102\) 4.09147 6.16178i 0.0401125 0.0604096i
\(103\) 121.164 88.0311i 1.17635 0.854671i 0.184597 0.982814i \(-0.440902\pi\)
0.991756 + 0.128144i \(0.0409019\pi\)
\(104\) −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 −0.862202 0.506565i \(-0.830915\pi\)
0.748207 + 0.663465i \(0.230915\pi\)
\(108\) −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 −0.309384 0.950937i \(-0.600123\pi\)
1.00000 0.000385488i \(0.000122705\pi\)
\(114\) 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 0.598091 + 0.801428i \(0.295926\pi\)
−0.954933 + 0.296820i \(0.904074\pi\)
\(128\) −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 \(0.193244\pi\)
−0.821309 + 0.570484i \(0.806756\pi\)
\(132\) −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 −0.271359 0.962478i \(-0.587473\pi\)
−0.785264 + 0.619161i \(0.787473\pi\)
\(138\) −241.618 67.3907i −1.75086 0.488338i
\(139\) −90.4769 + 65.7353i −0.650913 + 0.472916i −0.863582 0.504208i \(-0.831784\pi\)
0.212669 + 0.977124i \(0.431784\pi\)
\(140\) 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 0.980371 0.197164i \(-0.0631730\pi\)
0.677247 + 0.735756i \(0.263173\pi\)
\(150\) −137.254 + 108.846i −0.915025 + 0.725643i
\(151\) −71.2078 51.7355i −0.471575 0.342619i 0.326480 0.945204i \(-0.394137\pi\)
−0.798055 + 0.602585i \(0.794137\pi\)
\(152\) 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 0.607334 0.794446i \(-0.292239\pi\)
−0.567887 + 0.823107i \(0.692239\pi\)
\(158\) 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 0.812644 + 0.582760i \(0.198027\pi\)
−0.314905 + 0.949123i \(0.601973\pi\)
\(164\) 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 −0.726863 0.686782i \(-0.759023\pi\)
−0.184364 + 0.982858i \(0.559023\pi\)
\(168\) 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 −0.991627 0.129134i \(-0.958780\pi\)
0.429243 + 0.903189i \(0.358780\pi\)
\(174\) −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 −0.702019 0.712158i \(-0.747718\pi\)
0.894238 + 0.447591i \(0.147718\pi\)
\(180\) −209.611 242.571i −1.16450 1.34762i
\(181\) 87.9703 270.745i 0.486024 1.49583i −0.344468 0.938798i \(-0.611941\pi\)
0.830492 0.557030i \(-0.188059\pi\)
\(182\) −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 0.543354 0.839504i \(-0.317154\pi\)
−0.966321 + 0.257339i \(0.917154\pi\)
\(192\) 282.285 + 78.7330i 1.47023 + 0.410068i
\(193\) 92.1162 283.505i 0.477286 1.46894i −0.365563 0.930786i \(-0.619124\pi\)
0.842850 0.538149i \(-0.180876\pi\)
\(194\) 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 \(-0.952859\pi\)
0.989054 0.147557i \(-0.0471410\pi\)
\(198\) −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 0.909346 0.416040i \(-0.136583\pi\)
−0.980219 + 0.197916i \(0.936583\pi\)
\(212\) 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 0.133297 0.991076i \(-0.457444\pi\)
−0.901378 + 0.433032i \(0.857444\pi\)
\(224\) −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 0.622409 0.782692i \(-0.286154\pi\)
−0.936719 + 0.350081i \(0.886154\pi\)
\(228\) −184.318 + 277.583i −0.808412 + 1.21747i
\(229\) 99.7951 + 307.138i 0.435786 + 1.34121i 0.892279 + 0.451485i \(0.149106\pi\)
−0.456492 + 0.889727i \(0.650894\pi\)
\(230\) 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 0.665443 0.746449i \(-0.268243\pi\)
0.977106 + 0.212752i \(0.0682427\pi\)
\(234\) −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 −0.808622 0.588329i \(-0.799786\pi\)
0.809412 + 0.587241i \(0.199786\pi\)
\(240\) 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 −0.0877748 0.996140i \(-0.527976\pi\)
0.514505 + 0.857487i \(0.327976\pi\)
\(252\) −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 0.522733 0.852496i \(-0.324912\pi\)
−0.972306 + 0.233713i \(0.924912\pi\)
\(258\) −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 \(0.255515\pi\)
−0.694749 + 0.719252i \(0.744485\pi\)
\(264\) −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 0.642198 0.766539i \(-0.278023\pi\)
0.0689882 + 0.997617i \(0.478023\pi\)
\(270\) 538.953 + 102.358i 1.99612 + 0.379103i
\(271\) −64.8950 + 47.1490i −0.239465 + 0.173981i −0.701045 0.713117i \(-0.747283\pi\)
0.461580 + 0.887099i \(0.347283\pi\)
\(272\) 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 0.995764 + 0.0919450i \(0.0293084\pi\)
−0.751546 + 0.659681i \(0.770692\pi\)
\(278\) 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 −0.695260 0.718759i \(-0.744711\pi\)
−0.984953 + 0.172825i \(0.944711\pi\)
\(282\) 113.465 + 143.078i 0.402359 + 0.507369i
\(283\) 248.936 + 180.862i 0.879632 + 0.639090i 0.933154 0.359477i \(-0.117045\pi\)
−0.0535221 + 0.998567i \(0.517045\pi\)
\(284\) 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 0.999950 0.00997075i \(-0.00317384\pi\)
−0.318484 + 0.947928i \(0.603174\pi\)
\(294\) −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 −0.883306 0.468797i \(-0.844687\pi\)
0.718809 + 0.695207i \(0.244687\pi\)
\(312\) −159.524 + 126.507i −0.511295 + 0.405472i
\(313\) −185.075 + 569.601i −0.591292 + 1.81981i −0.0189146 + 0.999821i \(0.506021\pi\)
−0.572378 + 0.819990i \(0.693979\pi\)
\(314\) −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 −0.305332 0.952246i \(-0.598767\pi\)
0.312697 + 0.949853i \(0.398767\pi\)
\(318\) 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 −0.429269 + 0.903177i \(0.641229\pi\)
−0.991624 + 0.129162i \(0.958771\pi\)
\(338\) 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 0.683514 0.729938i \(-0.260451\pi\)
0.123928 + 0.992291i \(0.460451\pi\)
\(348\) 47.7042 37.8309i 0.137081 0.108710i
\(349\) −333.322 242.172i −0.955076 0.693903i −0.00307413 0.999995i \(-0.500979\pi\)
−0.952002 + 0.306092i \(0.900979\pi\)
\(350\) −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 \(-0.938491\pi\)
0.981388 0.192035i \(-0.0615086\pi\)
\(354\) 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 0.517330 0.855786i \(-0.326926\pi\)
−0.973765 + 0.227557i \(0.926926\pi\)
\(360\) 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 −0.376146 0.926560i \(-0.622751\pi\)
0.764976 + 0.644059i \(0.222751\pi\)
\(368\) −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 −0.927008 0.375042i \(-0.877628\pi\)
0.970409 + 0.241466i \(0.0776283\pi\)
\(380\) −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 −0.418220 0.908346i \(-0.637346\pi\)
0.195565 + 0.980691i \(0.437346\pi\)
\(384\) −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 0.555203 0.831715i \(-0.312640\pi\)
−0.962575 + 0.271016i \(0.912640\pi\)
\(390\) −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 −0.277555 0.960710i \(-0.589524\pi\)
−0.789237 + 0.614088i \(0.789524\pi\)
\(402\) −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 0.875697 0.482862i \(-0.160403\pi\)
−0.992272 + 0.124078i \(0.960403\pi\)
\(410\) 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 \(0.357597\pi\)
−0.432599 + 0.901587i \(0.642403\pi\)
\(420\) −114.177 306.759i −0.271851 0.730380i
\(421\) 353.452 + 256.798i 0.839553 + 0.609971i 0.922246 0.386604i \(-0.126352\pi\)
−0.0826929 + 0.996575i \(0.526352\pi\)
\(422\) 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 −0.319737 0.947506i \(-0.603595\pi\)
0.298258 + 0.954485i \(0.403595\pi\)
\(432\) 112.681 205.361i 0.260837 0.475373i
\(433\) 47.9543 34.8408i 0.110749 0.0804638i −0.531032 0.847352i \(-0.678196\pi\)
0.641781 + 0.766888i \(0.278196\pi\)
\(434\) 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 0.289470 + 0.957187i \(0.406521\pi\)
−0.999790 + 0.0204842i \(0.993479\pi\)
\(444\) 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 −0.974213 0.225629i \(-0.927556\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(450\) 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 −0.877170 0.480180i \(-0.840571\pi\)
0.991888 + 0.127113i \(0.0405712\pi\)
\(458\) −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 \(-0.906714\pi\)
0.957363 0.288888i \(-0.0932857\pi\)
\(462\) −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 0.901028 0.433762i \(-0.142814\pi\)
0.473988 + 0.880531i \(0.342814\pi\)
\(468\) 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 −0.483700 0.875234i \(-0.660707\pi\)
−0.905771 + 0.423768i \(0.860707\pi\)
\(480\) −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 0.978609 0.205729i \(-0.0659564\pi\)
0.106747 + 0.994286i \(0.465956\pi\)
\(488\) 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 0.844425 0.535674i \(-0.179943\pi\)
−0.770398 + 0.637563i \(0.779943\pi\)
\(492\) 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 −0.822228 0.569158i \(-0.807269\pi\)
0.287219 + 0.957865i \(0.407269\pi\)
\(500\) −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 −0.556463 0.830872i \(-0.687842\pi\)
0.962163 + 0.272474i \(0.0878420\pi\)
\(504\) 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 0.0567219 0.998390i \(-0.481935\pi\)
0.931997 0.362465i \(-0.118065\pi\)
\(510\) 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 0.992220 + 0.124499i \(0.0397325\pi\)
−0.188207 + 0.982129i \(0.560268\pi\)
\(522\) −23.7356 + 101.444i −0.0454705 + 0.194337i
\(523\) 155.721 479.261i 0.297746 0.916369i −0.684539 0.728976i \(-0.739996\pi\)
0.982285 0.187392i \(-0.0600036\pi\)
\(524\) 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 −0.966680 0.255987i \(-0.917600\pi\)
0.631596 0.775298i \(-0.282400\pi\)
\(542\) 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 −0.0527711 0.998607i \(-0.516805\pi\)
−0.966039 + 0.258398i \(0.916805\pi\)
\(548\) −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 0.999225 0.0393671i \(-0.0125342\pi\)
−0.346218 + 0.938154i \(0.612534\pi\)
\(558\) 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 −0.747440 0.664330i \(-0.768717\pi\)
−0.214208 + 0.976788i \(0.568717\pi\)
\(564\) −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 0.0280618 + 0.999606i \(0.491066\pi\)
−0.959354 + 0.282207i \(0.908934\pi\)
\(570\) 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 0.484733 + 0.874662i \(0.338917\pi\)
−0.906271 + 0.422697i \(0.861083\pi\)
\(578\) 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 0.890565 0.454856i \(-0.150309\pi\)
−0.707794 + 0.706419i \(0.750309\pi\)
\(588\) 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 \(-0.803977\pi\)
0.816297 0.577632i \(-0.196023\pi\)
\(594\) −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 0.00817505 0.999967i \(-0.497398\pi\)
−0.581152 + 0.813795i \(0.697398\pi\)
\(600\) −64.2476 + 230.349i −0.107079 + 0.383915i
\(601\) 339.372 246.568i 0.564679 0.410264i −0.268489 0.963283i \(-0.586524\pi\)
0.833169 + 0.553019i \(0.186524\pi\)
\(602\) −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 0.786856 + 0.617137i \(0.211707\pi\)
−0.273836 + 0.961776i \(0.588293\pi\)
\(608\) −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 0.889196 0.457527i \(-0.151265\pi\)
−0.160358 + 0.987059i \(0.551265\pi\)
\(614\) 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 \(-0.815598\pi\)
0.836837 0.547452i \(-0.184402\pi\)
\(618\) 479.628 + 1288.61i 0.776097 + 2.08514i
\(619\) 217.722 + 158.184i 0.351732 + 0.255548i 0.749595 0.661896i \(-0.230248\pi\)
−0.397863 + 0.917445i \(0.630248\pi\)
\(620\) −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 −0.646017 0.763323i \(-0.723567\pi\)
0.526333 + 0.850279i \(0.323567\pi\)
\(632\) 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 −0.815735 0.578425i \(-0.803667\pi\)
0.802191 + 0.597067i \(0.203667\pi\)
\(642\) −118.378 149.273i −0.184389 0.232512i
\(643\) −134.744 + 414.698i −0.209555 + 0.644943i 0.789941 + 0.613183i \(0.210111\pi\)
−0.999496 + 0.0317599i \(0.989889\pi\)
\(644\) 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 −0.0687036 0.997637i \(-0.521886\pi\)
0.530814 + 0.847488i \(0.321886\pi\)
\(648\) −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 0.886610 0.462517i \(-0.153054\pi\)
−0.713858 + 0.700291i \(0.753054\pi\)
\(654\) 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 \(0.0308839\pi\)
−0.995297 + 0.0968724i \(0.969116\pi\)
\(660\) −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 −0.994607 0.103714i \(-0.966927\pi\)
0.743692 0.668522i \(-0.233073\pi\)
\(674\) 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 0.329432 0.944179i \(-0.393143\pi\)
−0.288459 + 0.957492i \(0.593143\pi\)
\(678\) 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 \(-0.980775\pi\)
0.998177 0.0603592i \(-0.0192246\pi\)
\(684\) 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 0.895360 + 0.445344i \(0.146918\pi\)
−0.462595 + 0.886570i \(0.653082\pi\)
\(692\) 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 −0.656766 0.754094i \(-0.728076\pi\)
0.920138 + 0.391594i \(0.128076\pi\)
\(702\) 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 −0.854029 0.520226i \(-0.825848\pi\)
0.996705 + 0.0811142i \(0.0258478\pi\)
\(710\) −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 0.969067 + 0.246797i \(0.0793781\pi\)
−0.0647402 + 0.997902i \(0.520622\pi\)
\(720\) 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 −0.874526 0.484979i \(-0.838827\pi\)
0.190999 + 0.981590i \(0.438827\pi\)
\(734\) −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 −0.855114 0.518440i \(-0.826513\pi\)
0.387070 0.922050i \(-0.373487\pi\)
\(740\) −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 0.931170 0.364586i \(-0.118790\pi\)
0.539034 + 0.842284i \(0.318790\pi\)
\(744\) 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 0.725346 0.688384i \(-0.241680\pi\)
−0.430548 + 0.902568i \(0.641680\pi\)
\(752\) 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 −0.997997 0.0632624i \(-0.979850\pi\)
0.770212 0.637788i \(-0.220150\pi\)
\(758\) 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 −0.0333725 0.999443i \(-0.510625\pi\)
0.560459 + 0.828182i \(0.310625\pi\)
\(762\) −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 0.210346 + 0.977627i \(0.432541\pi\)
−0.994779 + 0.102053i \(0.967459\pi\)
\(774\) 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 −0.902039 0.431655i \(-0.857930\pi\)
0.983485 + 0.180988i \(0.0579296\pi\)
\(788\) −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 0.173300 0.984869i \(-0.444557\pi\)
−0.438689 + 0.898639i \(0.644557\pi\)
\(798\) 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 −0.168833 0.985645i \(-0.554000\pi\)
−0.715936 + 0.698166i \(0.754000\pi\)
\(810\) 1150.21 1177.09i 1.42001 1.45320i
\(811\) −187.891 136.511i −0.231678 0.168324i 0.465890 0.884843i \(-0.345734\pi\)
−0.697568 + 0.716519i \(0.745734\pi\)
\(812\) 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 0.946528 0.322621i \(-0.104564\pi\)
−0.599324 + 0.800506i \(0.704564\pi\)
\(822\) 772.981 1164.11i 0.940367 1.41620i
\(823\) 48.4819 + 149.212i 0.0589088 + 0.181302i 0.976181 0.216959i \(-0.0696137\pi\)
−0.917272 + 0.398261i \(0.869614\pi\)
\(824\) 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 −0.216916 0.976190i \(-0.569600\pi\)
0.398302 + 0.917254i \(0.369600\pi\)
\(828\) 682.823 1128.85i 0.824666 1.36335i
\(829\) −1057.08 + 768.011i −1.27512 + 0.926431i −0.999394 0.0348051i \(-0.988919\pi\)
−0.275728 + 0.961236i \(0.588919\pi\)
\(830\) 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 −0.0716959 0.997427i \(-0.522841\pi\)
0.970764 0.240035i \(-0.0771589\pi\)
\(840\) 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 −0.819908 0.572495i \(-0.805976\pi\)
0.999824 + 0.0187721i \(0.00597570\pi\)
\(854\) 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 \(0.0903442\pi\)
−0.959991 + 0.280029i \(0.909656\pi\)
\(858\) 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 −0.00332255 0.999994i \(-0.501058\pi\)
−0.590470 + 0.807060i \(0.701058\pi\)
\(864\) −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 0.548025 0.836462i \(-0.315380\pi\)
−0.626173 + 0.779684i \(0.715380\pi\)
\(878\) −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 \(0.0663701\pi\)
−0.978341 + 0.207000i \(0.933630\pi\)
\(882\) −1005.69 + 423.391i −1.14023 + 0.480035i
\(883\) −180.241 130.953i −0.204123 0.148304i 0.481027 0.876706i \(-0.340264\pi\)
−0.685151 + 0.728401i \(0.740264\pi\)
\(884\) −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 −0.969331 0.245761i \(-0.920962\pi\)
0.0658073 0.997832i \(-0.479038\pi\)
\(888\) −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 −0.774476 0.632604i \(-0.781986\pi\)
0.998399 0.0565619i \(-0.0180138\pi\)
\(908\) −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 −0.485195 0.874406i \(-0.661251\pi\)
0.121432 + 0.992600i \(0.461251\pi\)
\(912\) −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 −0.784150 0.620572i \(-0.786901\pi\)
0.999153 0.0411417i \(-0.0130995\pi\)
\(920\) −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 0.465515 0.885040i \(-0.345869\pi\)
−0.143604 + 0.989635i \(0.545869\pi\)
\(930\) 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 0.806874 + 0.590724i \(0.201158\pi\)
−0.305556 + 0.952174i \(0.598842\pi\)
\(938\) −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 0.815208 0.579169i \(-0.196623\pi\)
0.319090 + 0.947724i \(0.396623\pi\)
\(942\) −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 \(-0.848967\pi\)
0.889528 0.456881i \(-0.151033\pi\)
\(948\) −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 0.623435 0.781875i \(-0.285737\pi\)
−0.936260 + 0.351309i \(0.885737\pi\)
\(954\) 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 0.238624 + 0.971112i \(0.423304\pi\)
−0.997321 + 0.0731450i \(0.976696\pi\)
\(972\) 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 0.304878 0.952391i \(-0.401384\pi\)
0.806453 + 0.591298i \(0.201384\pi\)
\(978\) −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 0.562395 0.826869i \(-0.309880\pi\)
−0.960188 + 0.279353i \(0.909880\pi\)
\(984\) −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 −0.810445 0.585815i \(-0.800775\pi\)
0.306702 + 0.951806i \(0.400775\pi\)
\(998\) 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.5.1 16
3.2 odd 2 inner 33.3.h.b.5.4 yes 16
11.2 odd 10 363.3.h.j.251.1 16
11.3 even 5 363.3.b.m.122.7 8
11.4 even 5 363.3.h.o.245.1 16
11.5 even 5 363.3.h.o.323.4 16
11.6 odd 10 363.3.h.n.323.1 16
11.7 odd 10 363.3.h.n.245.4 16
11.8 odd 10 363.3.b.l.122.2 8
11.9 even 5 inner 33.3.h.b.20.4 yes 16
11.10 odd 2 363.3.h.j.269.4 16
33.2 even 10 363.3.h.j.251.4 16
33.5 odd 10 363.3.h.o.323.1 16
33.8 even 10 363.3.b.l.122.7 8
33.14 odd 10 363.3.b.m.122.2 8
33.17 even 10 363.3.h.n.323.4 16
33.20 odd 10 inner 33.3.h.b.20.1 yes 16
33.26 odd 10 363.3.h.o.245.4 16
33.29 even 10 363.3.h.n.245.1 16
33.32 even 2 363.3.h.j.269.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.h.b.5.1 16 1.1 even 1 trivial
33.3.h.b.5.4 yes 16 3.2 odd 2 inner
33.3.h.b.20.1 yes 16 33.20 odd 10 inner
33.3.h.b.20.4 yes 16 11.9 even 5 inner
363.3.b.l.122.2 8 11.8 odd 10
363.3.b.l.122.7 8 33.8 even 10
363.3.b.m.122.2 8 33.14 odd 10
363.3.b.m.122.7 8 11.3 even 5
363.3.h.j.251.1 16 11.2 odd 10
363.3.h.j.251.4 16 33.2 even 10
363.3.h.j.269.1 16 33.32 even 2
363.3.h.j.269.4 16 11.10 odd 2
363.3.h.n.245.1 16 33.29 even 10
363.3.h.n.245.4 16 11.7 odd 10
363.3.h.n.323.1 16 11.6 odd 10
363.3.h.n.323.4 16 33.17 even 10
363.3.h.o.245.1 16 11.4 even 5
363.3.h.o.245.4 16 33.26 odd 10
363.3.h.o.323.1 16 33.5 odd 10
363.3.h.o.323.4 16 11.5 even 5