Properties

Label 23.3.d.a.5.1
Level $23$
Weight $3$
Character 23.5
Analytic conductor $0.627$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [23,3,Mod(5,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\), degree \(10\), 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: \(0.626704608029\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 23.5
Dual form 23.3.d.a.14.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.10125 - 0.910608i) q^{2} +(-3.16934 + 3.65762i) q^{3} +(5.42352 + 3.48548i) q^{4} +(-5.40865 - 0.777647i) q^{5} +(13.1596 - 8.45714i) q^{6} +(-0.889564 + 0.406250i) q^{7} +(-5.17926 - 5.97719i) q^{8} +(-2.05259 - 14.2761i) q^{9} +O(q^{10})\) \(q+(-3.10125 - 0.910608i) q^{2} +(-3.16934 + 3.65762i) q^{3} +(5.42352 + 3.48548i) q^{4} +(-5.40865 - 0.777647i) q^{5} +(13.1596 - 8.45714i) q^{6} +(-0.889564 + 0.406250i) q^{7} +(-5.17926 - 5.97719i) q^{8} +(-2.05259 - 14.2761i) q^{9} +(16.0654 + 7.33684i) q^{10} +(3.66991 + 12.4986i) q^{11} +(-29.9375 + 8.79045i) q^{12} +(-5.85520 + 12.8211i) q^{13} +(3.12869 - 0.449838i) q^{14} +(19.9862 - 17.3181i) q^{15} +(-0.0933341 - 0.204373i) q^{16} +(-7.74290 - 12.0482i) q^{17} +(-6.63433 + 46.1428i) q^{18} +(-3.48690 + 5.42572i) q^{19} +(-26.6234 - 23.0693i) q^{20} +(1.33343 - 4.54123i) q^{21} -42.1030i q^{22} +(14.0512 + 18.2089i) q^{23} +38.2771 q^{24} +(4.66147 + 1.36873i) q^{25} +(29.8334 - 34.4296i) q^{26} +(22.0789 + 14.1893i) q^{27} +(-6.24054 - 0.897254i) q^{28} +(-2.47928 + 1.59333i) q^{29} +(-77.7522 + 35.5083i) q^{30} +(5.65792 + 6.52959i) q^{31} +(4.60559 + 32.0326i) q^{32} +(-57.3462 - 26.1891i) q^{33} +(13.0415 + 44.4152i) q^{34} +(5.12726 - 1.50550i) q^{35} +(38.6268 - 84.5809i) q^{36} +(30.2033 - 4.34258i) q^{37} +(15.7544 - 13.6513i) q^{38} +(-28.3375 - 62.0505i) q^{39} +(23.3647 + 36.3562i) q^{40} +(-4.02842 + 28.0183i) q^{41} +(-8.27056 + 12.8692i) q^{42} +(-25.3186 - 21.9387i) q^{43} +(-23.6597 + 80.5777i) q^{44} +78.8106i q^{45} +(-26.9951 - 69.2654i) q^{46} +28.3043 q^{47} +(1.04333 + 0.306348i) q^{48} +(-31.4619 + 36.3090i) q^{49} +(-13.2100 - 8.48954i) q^{50} +(68.6075 + 9.86427i) q^{51} +(-76.4435 + 49.1272i) q^{52} +(74.4829 - 34.0152i) q^{53} +(-55.5514 - 64.1097i) q^{54} +(-10.1298 - 70.4544i) q^{55} +(7.03552 + 3.21301i) q^{56} +(-8.79403 - 29.9497i) q^{57} +(9.13975 - 2.68367i) q^{58} +(-37.0343 + 81.0938i) q^{59} +(168.758 - 24.2637i) q^{60} +(13.9664 - 12.1020i) q^{61} +(-11.6007 - 25.4020i) q^{62} +(7.62557 + 11.8656i) q^{63} +(14.7582 - 102.645i) q^{64} +(41.6390 - 64.7916i) q^{65} +(153.997 + 133.439i) q^{66} +(-23.0835 + 78.6152i) q^{67} -92.3312i q^{68} +(-111.134 - 6.31624i) q^{69} -17.2718 q^{70} +(-70.4488 - 20.6856i) q^{71} +(-74.6999 + 86.2083i) q^{72} +(-62.8153 - 40.3690i) q^{73} +(-97.6223 - 14.0360i) q^{74} +(-19.7801 + 12.7119i) q^{75} +(-37.8225 + 17.2730i) q^{76} +(-8.34217 - 9.62738i) q^{77} +(31.3780 + 218.239i) q^{78} +(109.498 + 50.0059i) q^{79} +(0.345882 + 1.17796i) q^{80} +(2.67333 - 0.784960i) q^{81} +(38.0068 - 83.2233i) q^{82} +(-119.345 + 17.1592i) q^{83} +(23.0602 - 19.9818i) q^{84} +(32.5094 + 71.1857i) q^{85} +(58.5417 + 91.0926i) q^{86} +(2.02987 - 14.1181i) q^{87} +(55.6989 - 86.6692i) q^{88} +(-25.2210 - 21.8541i) q^{89} +(71.7656 - 244.411i) q^{90} -13.7839i q^{91} +(12.7402 + 147.731i) q^{92} -41.8146 q^{93} +(-87.7787 - 25.7741i) q^{94} +(23.0787 - 26.6343i) q^{95} +(-131.760 - 84.6768i) q^{96} +(118.310 + 17.0104i) q^{97} +(130.634 - 83.9536i) q^{98} +(170.898 - 78.0465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.10125 0.910608i −1.55062 0.455304i −0.609337 0.792912i \(-0.708564\pi\)
−0.941287 + 0.337607i \(0.890382\pi\)
\(3\) −3.16934 + 3.65762i −1.05645 + 1.21921i −0.0815227 + 0.996671i \(0.525978\pi\)
−0.974925 + 0.222534i \(0.928567\pi\)
\(4\) 5.42352 + 3.48548i 1.35588 + 0.871370i
\(5\) −5.40865 0.777647i −1.08173 0.155529i −0.421676 0.906747i \(-0.638558\pi\)
−0.660055 + 0.751217i \(0.729467\pi\)
\(6\) 13.1596 8.45714i 2.19326 1.40952i
\(7\) −0.889564 + 0.406250i −0.127081 + 0.0580357i −0.477941 0.878392i \(-0.658617\pi\)
0.350860 + 0.936428i \(0.385889\pi\)
\(8\) −5.17926 5.97719i −0.647408 0.747148i
\(9\) −2.05259 14.2761i −0.228066 1.58623i
\(10\) 16.0654 + 7.33684i 1.60654 + 0.733684i
\(11\) 3.66991 + 12.4986i 0.333629 + 1.13623i 0.940035 + 0.341079i \(0.110792\pi\)
−0.606406 + 0.795155i \(0.707389\pi\)
\(12\) −29.9375 + 8.79045i −2.49479 + 0.732538i
\(13\) −5.85520 + 12.8211i −0.450400 + 0.986239i 0.539171 + 0.842196i \(0.318737\pi\)
−0.989571 + 0.144043i \(0.953990\pi\)
\(14\) 3.12869 0.449838i 0.223478 0.0321313i
\(15\) 19.9862 17.3181i 1.33241 1.15454i
\(16\) −0.0933341 0.204373i −0.00583338 0.0127733i
\(17\) −7.74290 12.0482i −0.455465 0.708717i 0.535247 0.844695i \(-0.320218\pi\)
−0.990712 + 0.135979i \(0.956582\pi\)
\(18\) −6.63433 + 46.1428i −0.368574 + 2.56349i
\(19\) −3.48690 + 5.42572i −0.183521 + 0.285564i −0.920809 0.390015i \(-0.872470\pi\)
0.737288 + 0.675579i \(0.236106\pi\)
\(20\) −26.6234 23.0693i −1.33117 1.15347i
\(21\) 1.33343 4.54123i 0.0634964 0.216249i
\(22\) 42.1030i 1.91377i
\(23\) 14.0512 + 18.2089i 0.610922 + 0.791691i
\(24\) 38.2771 1.59488
\(25\) 4.66147 + 1.36873i 0.186459 + 0.0547492i
\(26\) 29.8334 34.4296i 1.14744 1.32422i
\(27\) 22.0789 + 14.1893i 0.817739 + 0.525529i
\(28\) −6.24054 0.897254i −0.222876 0.0320448i
\(29\) −2.47928 + 1.59333i −0.0854922 + 0.0549425i −0.582689 0.812696i \(-0.697999\pi\)
0.497196 + 0.867638i \(0.334363\pi\)
\(30\) −77.7522 + 35.5083i −2.59174 + 1.18361i
\(31\) 5.65792 + 6.52959i 0.182514 + 0.210632i 0.839632 0.543155i \(-0.182770\pi\)
−0.657119 + 0.753787i \(0.728225\pi\)
\(32\) 4.60559 + 32.0326i 0.143925 + 1.00102i
\(33\) −57.3462 26.1891i −1.73776 0.793610i
\(34\) 13.0415 + 44.4152i 0.383573 + 1.30633i
\(35\) 5.12726 1.50550i 0.146493 0.0430143i
\(36\) 38.6268 84.5809i 1.07297 2.34947i
\(37\) 30.2033 4.34258i 0.816305 0.117367i 0.278500 0.960436i \(-0.410163\pi\)
0.537805 + 0.843069i \(0.319254\pi\)
\(38\) 15.7544 13.6513i 0.414591 0.359245i
\(39\) −28.3375 62.0505i −0.726603 1.59104i
\(40\) 23.3647 + 36.3562i 0.584117 + 0.908904i
\(41\) −4.02842 + 28.0183i −0.0982541 + 0.683372i 0.879849 + 0.475253i \(0.157643\pi\)
−0.978103 + 0.208120i \(0.933266\pi\)
\(42\) −8.27056 + 12.8692i −0.196918 + 0.306411i
\(43\) −25.3186 21.9387i −0.588805 0.510202i 0.308728 0.951150i \(-0.400097\pi\)
−0.897532 + 0.440948i \(0.854642\pi\)
\(44\) −23.6597 + 80.5777i −0.537721 + 1.83131i
\(45\) 78.8106i 1.75135i
\(46\) −26.9951 69.2654i −0.586851 1.50577i
\(47\) 28.3043 0.602219 0.301110 0.953590i \(-0.402643\pi\)
0.301110 + 0.953590i \(0.402643\pi\)
\(48\) 1.04333 + 0.306348i 0.0217360 + 0.00638226i
\(49\) −31.4619 + 36.3090i −0.642079 + 0.740999i
\(50\) −13.2100 8.48954i −0.264200 0.169791i
\(51\) 68.6075 + 9.86427i 1.34525 + 0.193417i
\(52\) −76.4435 + 49.1272i −1.47007 + 0.944755i
\(53\) 74.4829 34.0152i 1.40534 0.641796i 0.438862 0.898554i \(-0.355382\pi\)
0.966476 + 0.256758i \(0.0826543\pi\)
\(54\) −55.5514 64.1097i −1.02873 1.18722i
\(55\) −10.1298 70.4544i −0.184178 1.28099i
\(56\) 7.03552 + 3.21301i 0.125634 + 0.0573752i
\(57\) −8.79403 29.9497i −0.154281 0.525434i
\(58\) 9.13975 2.68367i 0.157582 0.0462702i
\(59\) −37.0343 + 81.0938i −0.627700 + 1.37447i 0.282084 + 0.959390i \(0.408974\pi\)
−0.909784 + 0.415081i \(0.863753\pi\)
\(60\) 168.758 24.2637i 2.81263 0.404395i
\(61\) 13.9664 12.1020i 0.228958 0.198393i −0.532825 0.846225i \(-0.678870\pi\)
0.761783 + 0.647832i \(0.224324\pi\)
\(62\) −11.6007 25.4020i −0.187108 0.409710i
\(63\) 7.62557 + 11.8656i 0.121041 + 0.188343i
\(64\) 14.7582 102.645i 0.230597 1.60383i
\(65\) 41.6390 64.7916i 0.640601 0.996794i
\(66\) 153.997 + 133.439i 2.33328 + 2.02180i
\(67\) −23.0835 + 78.6152i −0.344530 + 1.17336i 0.586967 + 0.809611i \(0.300322\pi\)
−0.931497 + 0.363750i \(0.881496\pi\)
\(68\) 92.3312i 1.35781i
\(69\) −111.134 6.31624i −1.61064 0.0915397i
\(70\) −17.2718 −0.246740
\(71\) −70.4488 20.6856i −0.992237 0.291347i −0.254970 0.966949i \(-0.582066\pi\)
−0.737267 + 0.675602i \(0.763884\pi\)
\(72\) −74.6999 + 86.2083i −1.03750 + 1.19734i
\(73\) −62.8153 40.3690i −0.860484 0.552999i 0.0343443 0.999410i \(-0.489066\pi\)
−0.894828 + 0.446411i \(0.852702\pi\)
\(74\) −97.6223 14.0360i −1.31922 0.189675i
\(75\) −19.7801 + 12.7119i −0.263734 + 0.169492i
\(76\) −37.8225 + 17.2730i −0.497665 + 0.227276i
\(77\) −8.34217 9.62738i −0.108340 0.125031i
\(78\) 31.3780 + 218.239i 0.402282 + 2.79793i
\(79\) 109.498 + 50.0059i 1.38605 + 0.632986i 0.962099 0.272702i \(-0.0879171\pi\)
0.423947 + 0.905687i \(0.360644\pi\)
\(80\) 0.345882 + 1.17796i 0.00432352 + 0.0147246i
\(81\) 2.67333 0.784960i 0.0330040 0.00969086i
\(82\) 38.0068 83.2233i 0.463498 1.01492i
\(83\) −119.345 + 17.1592i −1.43789 + 0.206738i −0.816764 0.576972i \(-0.804234\pi\)
−0.621127 + 0.783710i \(0.713325\pi\)
\(84\) 23.0602 19.9818i 0.274526 0.237879i
\(85\) 32.5094 + 71.1857i 0.382464 + 0.837479i
\(86\) 58.5417 + 91.0926i 0.680717 + 1.05922i
\(87\) 2.02987 14.1181i 0.0233318 0.162277i
\(88\) 55.6989 86.6692i 0.632942 0.984877i
\(89\) −25.2210 21.8541i −0.283382 0.245552i 0.501558 0.865124i \(-0.332761\pi\)
−0.784939 + 0.619572i \(0.787306\pi\)
\(90\) 71.7656 244.411i 0.797396 2.71568i
\(91\) 13.7839i 0.151471i
\(92\) 12.7402 + 147.731i 0.138481 + 1.60578i
\(93\) −41.8146 −0.449620
\(94\) −87.7787 25.7741i −0.933816 0.274193i
\(95\) 23.0787 26.6343i 0.242934 0.280361i
\(96\) −131.760 84.6768i −1.37250 0.882050i
\(97\) 118.310 + 17.0104i 1.21969 + 0.175365i 0.721941 0.691955i \(-0.243250\pi\)
0.497751 + 0.867320i \(0.334159\pi\)
\(98\) 130.634 83.9536i 1.33300 0.856669i
\(99\) 170.898 78.0465i 1.72624 0.788348i
\(100\) 20.5109 + 23.6708i 0.205109 + 0.236708i
\(101\) −5.57360 38.7653i −0.0551842 0.383815i −0.998632 0.0522928i \(-0.983347\pi\)
0.943448 0.331522i \(-0.107562\pi\)
\(102\) −203.786 93.0662i −1.99791 0.912413i
\(103\) 15.5668 + 53.0155i 0.151134 + 0.514714i 0.999901 0.0140523i \(-0.00447312\pi\)
−0.848768 + 0.528766i \(0.822655\pi\)
\(104\) 106.960 31.4062i 1.02846 0.301983i
\(105\) −10.7435 + 23.5250i −0.102319 + 0.224048i
\(106\) −261.965 + 37.6648i −2.47136 + 0.355328i
\(107\) 28.5114 24.7053i 0.266462 0.230890i −0.511374 0.859358i \(-0.670863\pi\)
0.777835 + 0.628468i \(0.216318\pi\)
\(108\) 70.2890 + 153.911i 0.650824 + 1.42511i
\(109\) 67.9227 + 105.690i 0.623144 + 0.969631i 0.999076 + 0.0429835i \(0.0136863\pi\)
−0.375932 + 0.926647i \(0.622677\pi\)
\(110\) −32.7413 + 227.721i −0.297648 + 2.07019i
\(111\) −79.8411 + 124.235i −0.719289 + 1.11924i
\(112\) 0.166053 + 0.143886i 0.00148262 + 0.00128470i
\(113\) 56.6517 192.938i 0.501343 1.70742i −0.187289 0.982305i \(-0.559970\pi\)
0.688631 0.725112i \(-0.258212\pi\)
\(114\) 100.889i 0.884995i
\(115\) −61.8381 109.412i −0.537722 0.951412i
\(116\) −18.9999 −0.163792
\(117\) 195.054 + 57.2729i 1.66712 + 0.489512i
\(118\) 188.697 217.768i 1.59913 1.84549i
\(119\) 11.7824 + 7.57207i 0.0990116 + 0.0636309i
\(120\) −207.028 29.7661i −1.72523 0.248051i
\(121\) −40.9545 + 26.3199i −0.338467 + 0.217520i
\(122\) −54.3336 + 24.8133i −0.445357 + 0.203388i
\(123\) −89.7127 103.534i −0.729371 0.841739i
\(124\) 7.92706 + 55.1339i 0.0639279 + 0.444628i
\(125\) 100.114 + 45.7205i 0.800912 + 0.365764i
\(126\) −12.8439 43.7422i −0.101935 0.347160i
\(127\) −74.4291 + 21.8544i −0.586056 + 0.172082i −0.561301 0.827612i \(-0.689699\pi\)
−0.0247555 + 0.999694i \(0.507881\pi\)
\(128\) −85.4639 + 187.140i −0.667686 + 1.46203i
\(129\) 160.487 23.0745i 1.24408 0.178872i
\(130\) −188.133 + 163.018i −1.44718 + 1.25398i
\(131\) −8.75733 19.1759i −0.0668499 0.146381i 0.873258 0.487259i \(-0.162003\pi\)
−0.940108 + 0.340878i \(0.889276\pi\)
\(132\) −219.736 341.916i −1.66467 2.59028i
\(133\) 0.897619 6.24308i 0.00674902 0.0469404i
\(134\) 143.175 222.785i 1.06847 1.66258i
\(135\) −108.383 93.9145i −0.802838 0.695663i
\(136\) −31.9118 + 108.681i −0.234645 + 0.799128i
\(137\) 169.870i 1.23993i 0.784630 + 0.619965i \(0.212853\pi\)
−0.784630 + 0.619965i \(0.787147\pi\)
\(138\) 338.903 + 120.788i 2.45582 + 0.875275i
\(139\) −31.2547 −0.224854 −0.112427 0.993660i \(-0.535862\pi\)
−0.112427 + 0.993660i \(0.535862\pi\)
\(140\) 33.0552 + 9.70587i 0.236108 + 0.0693277i
\(141\) −89.7061 + 103.526i −0.636213 + 0.734229i
\(142\) 199.643 + 128.303i 1.40594 + 0.903540i
\(143\) −181.734 26.1294i −1.27086 0.182723i
\(144\) −2.72607 + 1.75194i −0.0189311 + 0.0121663i
\(145\) 14.6486 6.68979i 0.101025 0.0461365i
\(146\) 158.046 + 182.394i 1.08250 + 1.24928i
\(147\) −33.0907 230.151i −0.225107 1.56565i
\(148\) 178.944 + 81.7210i 1.20908 + 0.552169i
\(149\) −40.7866 138.906i −0.273735 0.932257i −0.975528 0.219876i \(-0.929435\pi\)
0.701792 0.712381i \(-0.252383\pi\)
\(150\) 72.9185 21.4108i 0.486123 0.142739i
\(151\) 40.3370 88.3258i 0.267133 0.584939i −0.727765 0.685826i \(-0.759441\pi\)
0.994898 + 0.100888i \(0.0321682\pi\)
\(152\) 50.4901 7.25938i 0.332172 0.0477591i
\(153\) −156.108 + 135.268i −1.02031 + 0.884107i
\(154\) 17.1044 + 37.4533i 0.111067 + 0.243204i
\(155\) −25.5240 39.7162i −0.164671 0.256233i
\(156\) 62.5870 435.302i 0.401199 2.79040i
\(157\) −84.1467 + 130.935i −0.535966 + 0.833980i −0.998618 0.0525603i \(-0.983262\pi\)
0.462651 + 0.886540i \(0.346898\pi\)
\(158\) −294.043 254.790i −1.86103 1.61260i
\(159\) −111.647 + 380.236i −0.702184 + 2.39142i
\(160\) 176.835i 1.10522i
\(161\) −19.8968 10.4897i −0.123583 0.0651531i
\(162\) −9.00544 −0.0555891
\(163\) 31.2644 + 9.18007i 0.191806 + 0.0563194i 0.376225 0.926528i \(-0.377222\pi\)
−0.184419 + 0.982848i \(0.559040\pi\)
\(164\) −119.505 + 137.917i −0.728691 + 0.840955i
\(165\) 289.800 + 186.243i 1.75636 + 1.12875i
\(166\) 385.744 + 55.4616i 2.32376 + 0.334106i
\(167\) 118.325 76.0431i 0.708536 0.455348i −0.136096 0.990696i \(-0.543456\pi\)
0.844632 + 0.535347i \(0.179819\pi\)
\(168\) −34.0499 + 15.5501i −0.202678 + 0.0925600i
\(169\) −19.4258 22.4186i −0.114946 0.132654i
\(170\) −35.9975 250.368i −0.211750 1.47275i
\(171\) 84.6153 + 38.6425i 0.494826 + 0.225980i
\(172\) −60.8489 207.232i −0.353773 1.20484i
\(173\) −81.9298 + 24.0568i −0.473583 + 0.139056i −0.509810 0.860287i \(-0.670284\pi\)
0.0362271 + 0.999344i \(0.488466\pi\)
\(174\) −19.1512 + 41.9352i −0.110064 + 0.241007i
\(175\) −4.70272 + 0.676149i −0.0268727 + 0.00386371i
\(176\) 2.21185 1.91658i 0.0125673 0.0108896i
\(177\) −179.236 392.471i −1.01263 2.21735i
\(178\) 58.3160 + 90.7414i 0.327618 + 0.509783i
\(179\) 3.26607 22.7160i 0.0182462 0.126905i −0.978662 0.205475i \(-0.934126\pi\)
0.996909 + 0.0785695i \(0.0250353\pi\)
\(180\) −274.693 + 427.431i −1.52607 + 2.37461i
\(181\) 125.528 + 108.771i 0.693526 + 0.600943i 0.928621 0.371029i \(-0.120995\pi\)
−0.235096 + 0.971972i \(0.575540\pi\)
\(182\) −12.5517 + 42.7472i −0.0689654 + 0.234875i
\(183\) 89.4393i 0.488739i
\(184\) 36.0630 178.295i 0.195994 0.968996i
\(185\) −166.736 −0.901277
\(186\) 129.678 + 38.0768i 0.697191 + 0.204714i
\(187\) 122.169 140.991i 0.653312 0.753963i
\(188\) 153.509 + 98.6542i 0.816536 + 0.524756i
\(189\) −25.4050 3.65269i −0.134418 0.0193264i
\(190\) −95.8262 + 61.5838i −0.504349 + 0.324125i
\(191\) −55.2883 + 25.2493i −0.289467 + 0.132195i −0.554856 0.831946i \(-0.687227\pi\)
0.265389 + 0.964141i \(0.414500\pi\)
\(192\) 328.664 + 379.298i 1.71179 + 1.97551i
\(193\) 0.790541 + 5.49834i 0.00409607 + 0.0284888i 0.991767 0.128056i \(-0.0408736\pi\)
−0.987671 + 0.156544i \(0.949965\pi\)
\(194\) −351.419 160.488i −1.81144 0.827257i
\(195\) 105.014 + 357.646i 0.538536 + 1.83408i
\(196\) −297.188 + 87.2624i −1.51627 + 0.445216i
\(197\) −59.0035 + 129.200i −0.299510 + 0.655836i −0.998224 0.0595649i \(-0.981029\pi\)
0.698714 + 0.715401i \(0.253756\pi\)
\(198\) −601.067 + 86.4204i −3.03569 + 0.436466i
\(199\) 5.89878 5.11132i 0.0296421 0.0256850i −0.639914 0.768447i \(-0.721030\pi\)
0.669556 + 0.742762i \(0.266484\pi\)
\(200\) −15.9618 34.9515i −0.0798090 0.174757i
\(201\) −214.385 333.589i −1.06659 1.65965i
\(202\) −18.0149 + 125.296i −0.0891825 + 0.620278i
\(203\) 1.55818 2.42458i 0.00767577 0.0119437i
\(204\) 337.712 + 292.629i 1.65545 + 1.43446i
\(205\) 43.5766 148.408i 0.212569 0.723944i
\(206\) 178.589i 0.866939i
\(207\) 231.110 237.972i 1.11647 1.14962i
\(208\) 3.16678 0.0152249
\(209\) −80.6104 23.6694i −0.385696 0.113251i
\(210\) 54.7403 63.1737i 0.260668 0.300827i
\(211\) −293.762 188.789i −1.39224 0.894736i −0.392549 0.919731i \(-0.628407\pi\)
−0.999688 + 0.0249949i \(0.992043\pi\)
\(212\) 522.519 + 75.1268i 2.46471 + 0.354372i
\(213\) 298.937 192.115i 1.40346 0.901948i
\(214\) −110.918 + 50.6544i −0.518307 + 0.236703i
\(215\) 119.879 + 138.348i 0.557576 + 0.643478i
\(216\) −29.5407 205.460i −0.136762 0.951203i
\(217\) −7.68573 3.50996i −0.0354181 0.0161749i
\(218\) −114.403 389.621i −0.524785 1.78725i
\(219\) 346.737 101.811i 1.58328 0.464892i
\(220\) 190.628 417.418i 0.866492 1.89735i
\(221\) 199.807 28.7279i 0.904105 0.129991i
\(222\) 360.737 312.580i 1.62494 1.40802i
\(223\) 159.619 + 349.517i 0.715780 + 1.56734i 0.819726 + 0.572757i \(0.194126\pi\)
−0.103946 + 0.994583i \(0.533147\pi\)
\(224\) −17.1102 26.6240i −0.0763849 0.118857i
\(225\) 9.97203 69.3570i 0.0443201 0.308253i
\(226\) −351.382 + 546.761i −1.55479 + 2.41930i
\(227\) 190.299 + 164.895i 0.838322 + 0.726410i 0.964069 0.265652i \(-0.0855873\pi\)
−0.125747 + 0.992062i \(0.540133\pi\)
\(228\) 56.6946 193.084i 0.248661 0.846860i
\(229\) 201.638i 0.880514i −0.897872 0.440257i \(-0.854887\pi\)
0.897872 0.440257i \(-0.145113\pi\)
\(230\) 92.1433 + 395.625i 0.400623 + 1.72011i
\(231\) 61.6525 0.266894
\(232\) 22.3645 + 6.56680i 0.0963986 + 0.0283052i
\(233\) −217.430 + 250.927i −0.933174 + 1.07694i 0.0637030 + 0.997969i \(0.479709\pi\)
−0.996877 + 0.0789712i \(0.974836\pi\)
\(234\) −552.756 355.235i −2.36221 1.51810i
\(235\) −153.088 22.0108i −0.651439 0.0936628i
\(236\) −483.507 + 310.731i −2.04876 + 1.31666i
\(237\) −529.938 + 242.014i −2.23602 + 1.02116i
\(238\) −29.6449 34.2120i −0.124558 0.143748i
\(239\) 38.1832 + 265.570i 0.159762 + 1.11117i 0.899070 + 0.437804i \(0.144244\pi\)
−0.739308 + 0.673368i \(0.764847\pi\)
\(240\) −5.40476 2.46827i −0.0225198 0.0102845i
\(241\) −14.2327 48.4723i −0.0590570 0.201130i 0.924680 0.380746i \(-0.124333\pi\)
−0.983737 + 0.179616i \(0.942514\pi\)
\(242\) 150.977 44.3309i 0.623873 0.183186i
\(243\) −103.726 + 227.128i −0.426855 + 0.934682i
\(244\) 117.928 16.9556i 0.483314 0.0694900i
\(245\) 198.402 171.916i 0.809804 0.701699i
\(246\) 183.942 + 402.777i 0.747733 + 1.63731i
\(247\) −49.1472 76.4746i −0.198977 0.309614i
\(248\) 9.72472 67.6369i 0.0392126 0.272730i
\(249\) 315.483 490.902i 1.26700 1.97149i
\(250\) −268.845 232.955i −1.07538 0.931822i
\(251\) −7.46870 + 25.4361i −0.0297558 + 0.101339i −0.973032 0.230670i \(-0.925908\pi\)
0.943276 + 0.332009i \(0.107726\pi\)
\(252\) 90.9322i 0.360842i
\(253\) −176.018 + 242.445i −0.695725 + 0.958282i
\(254\) 250.724 0.987102
\(255\) −363.403 106.705i −1.42511 0.418451i
\(256\) 163.817 189.055i 0.639910 0.738496i
\(257\) 350.507 + 225.257i 1.36384 + 0.876486i 0.998519 0.0543958i \(-0.0173233\pi\)
0.365320 + 0.930882i \(0.380960\pi\)
\(258\) −518.721 74.5808i −2.01054 0.289073i
\(259\) −25.1036 + 16.1331i −0.0969251 + 0.0622899i
\(260\) 451.660 206.266i 1.73715 0.793332i
\(261\) 27.8355 + 32.1239i 0.106649 + 0.123080i
\(262\) 9.69694 + 67.4437i 0.0370112 + 0.257419i
\(263\) 146.205 + 66.7697i 0.555913 + 0.253877i 0.673502 0.739185i \(-0.264789\pi\)
−0.117589 + 0.993062i \(0.537517\pi\)
\(264\) 140.474 + 478.410i 0.532097 + 1.81216i
\(265\) −429.304 + 126.055i −1.62002 + 0.475679i
\(266\) −8.46874 + 18.5440i −0.0318374 + 0.0697141i
\(267\) 159.868 22.9855i 0.598756 0.0860881i
\(268\) −399.205 + 345.914i −1.48957 + 1.29072i
\(269\) −18.6398 40.8155i −0.0692929 0.151730i 0.871816 0.489833i \(-0.162942\pi\)
−0.941109 + 0.338103i \(0.890215\pi\)
\(270\) 250.603 + 389.947i 0.928161 + 1.44425i
\(271\) 56.2390 391.151i 0.207524 1.44336i −0.573677 0.819082i \(-0.694484\pi\)
0.781201 0.624280i \(-0.214607\pi\)
\(272\) −1.73965 + 2.70695i −0.00639577 + 0.00995201i
\(273\) 50.4161 + 43.6858i 0.184674 + 0.160021i
\(274\) 154.685 526.810i 0.564545 1.92266i
\(275\) 63.2848i 0.230127i
\(276\) −580.723 421.613i −2.10407 1.52758i
\(277\) −343.340 −1.23949 −0.619747 0.784801i \(-0.712765\pi\)
−0.619747 + 0.784801i \(0.712765\pi\)
\(278\) 96.9284 + 28.4608i 0.348663 + 0.102377i
\(279\) 81.6036 94.1756i 0.292486 0.337547i
\(280\) −35.5541 22.8492i −0.126979 0.0816044i
\(281\) 90.3158 + 12.9855i 0.321409 + 0.0462116i 0.301131 0.953583i \(-0.402636\pi\)
0.0202777 + 0.999794i \(0.493545\pi\)
\(282\) 372.473 239.374i 1.32083 0.848843i
\(283\) 389.627 177.937i 1.37677 0.628751i 0.416840 0.908980i \(-0.363137\pi\)
0.959933 + 0.280228i \(0.0904102\pi\)
\(284\) −309.981 357.737i −1.09148 1.25964i
\(285\) 24.2736 + 168.826i 0.0851704 + 0.592373i
\(286\) 539.807 + 246.522i 1.88744 + 0.861964i
\(287\) −7.79889 26.5606i −0.0271738 0.0925456i
\(288\) 447.847 131.500i 1.55502 0.456596i
\(289\) 34.8487 76.3079i 0.120584 0.264041i
\(290\) −51.5207 + 7.40756i −0.177658 + 0.0255433i
\(291\) −437.183 + 378.821i −1.50235 + 1.30179i
\(292\) −199.975 437.883i −0.684845 1.49960i
\(293\) −146.965 228.682i −0.501588 0.780485i 0.494470 0.869195i \(-0.335362\pi\)
−0.996058 + 0.0887092i \(0.971726\pi\)
\(294\) −106.955 + 743.888i −0.363792 + 2.53023i
\(295\) 263.368 409.809i 0.892773 1.38918i
\(296\) −182.387 158.039i −0.616173 0.533917i
\(297\) −96.3179 + 328.029i −0.324303 + 1.10447i
\(298\) 467.924i 1.57021i
\(299\) −315.731 + 73.5354i −1.05596 + 0.245938i
\(300\) −151.585 −0.505282
\(301\) 31.4351 + 9.23018i 0.104436 + 0.0306650i
\(302\) −205.525 + 237.189i −0.680547 + 0.785393i
\(303\) 159.453 + 102.474i 0.526248 + 0.338199i
\(304\) 1.43432 + 0.206224i 0.00471815 + 0.000678368i
\(305\) −84.9507 + 54.5945i −0.278527 + 0.178998i
\(306\) 607.306 277.347i 1.98466 0.906364i
\(307\) −176.795 204.032i −0.575878 0.664599i 0.390835 0.920461i \(-0.372186\pi\)
−0.966713 + 0.255862i \(0.917641\pi\)
\(308\) −11.6878 81.2907i −0.0379475 0.263931i
\(309\) −243.247 111.087i −0.787206 0.359505i
\(310\) 42.9905 + 146.412i 0.138679 + 0.472297i
\(311\) 284.965 83.6733i 0.916287 0.269046i 0.210602 0.977572i \(-0.432458\pi\)
0.705685 + 0.708526i \(0.250639\pi\)
\(312\) −224.120 + 490.755i −0.718334 + 1.57293i
\(313\) 411.987 59.2348i 1.31625 0.189249i 0.551827 0.833959i \(-0.313931\pi\)
0.764427 + 0.644710i \(0.223022\pi\)
\(314\) 380.190 329.437i 1.21080 1.04916i
\(315\) −32.0168 70.1071i −0.101641 0.222562i
\(316\) 419.567 + 652.859i 1.32774 + 2.06601i
\(317\) −1.41146 + 9.81691i −0.00445255 + 0.0309682i −0.991927 0.126813i \(-0.959525\pi\)
0.987474 + 0.157782i \(0.0504342\pi\)
\(318\) 692.492 1077.54i 2.17765 3.38849i
\(319\) −29.0131 25.1400i −0.0909503 0.0788088i
\(320\) −159.644 + 543.697i −0.498887 + 1.69905i
\(321\) 182.583i 0.568795i
\(322\) 52.1530 + 50.6492i 0.161966 + 0.157296i
\(323\) 92.3688 0.285972
\(324\) 17.2348 + 5.06059i 0.0531938 + 0.0156191i
\(325\) −44.8425 + 51.7510i −0.137977 + 0.159234i
\(326\) −88.5993 56.9393i −0.271777 0.174661i
\(327\) −601.843 86.5319i −1.84050 0.264624i
\(328\) 188.335 121.035i 0.574191 0.369010i
\(329\) −25.1785 + 11.4986i −0.0765304 + 0.0349502i
\(330\) −729.147 841.480i −2.20954 2.54994i
\(331\) −1.55056 10.7844i −0.00468449 0.0325813i 0.987345 0.158586i \(-0.0506936\pi\)
−0.992030 + 0.126005i \(0.959784\pi\)
\(332\) −707.078 322.911i −2.12975 0.972625i
\(333\) −123.990 422.271i −0.372343 1.26808i
\(334\) −436.202 + 128.080i −1.30599 + 0.383474i
\(335\) 185.985 407.251i 0.555181 1.21568i
\(336\) −1.05256 + 0.151335i −0.00313262 + 0.000450402i
\(337\) −266.757 + 231.146i −0.791564 + 0.685894i −0.953662 0.300881i \(-0.902719\pi\)
0.162098 + 0.986775i \(0.448174\pi\)
\(338\) 39.8297 + 87.2149i 0.117839 + 0.258032i
\(339\) 526.145 + 818.697i 1.55205 + 2.41504i
\(340\) −71.8011 + 499.388i −0.211180 + 1.46879i
\(341\) −60.8465 + 94.6790i −0.178436 + 0.277651i
\(342\) −227.225 196.891i −0.664400 0.575706i
\(343\) 26.7372 91.0584i 0.0779509 0.265476i
\(344\) 264.960i 0.770233i
\(345\) 596.175 + 120.586i 1.72804 + 0.349523i
\(346\) 275.991 0.797661
\(347\) −164.645 48.3442i −0.474482 0.139321i 0.0357436 0.999361i \(-0.488620\pi\)
−0.510226 + 0.860040i \(0.670438\pi\)
\(348\) 60.2173 69.4944i 0.173038 0.199697i
\(349\) −79.2149 50.9083i −0.226977 0.145869i 0.422210 0.906498i \(-0.361254\pi\)
−0.649187 + 0.760629i \(0.724891\pi\)
\(350\) 15.2000 + 2.18543i 0.0434286 + 0.00624409i
\(351\) −311.199 + 199.995i −0.886606 + 0.569787i
\(352\) −383.460 + 175.120i −1.08937 + 0.497501i
\(353\) −38.6544 44.6096i −0.109503 0.126373i 0.698352 0.715754i \(-0.253917\pi\)
−0.807855 + 0.589382i \(0.799371\pi\)
\(354\) 198.466 + 1380.36i 0.560640 + 3.89933i
\(355\) 364.947 + 166.666i 1.02802 + 0.469481i
\(356\) −60.6143 206.433i −0.170265 0.579869i
\(357\) −65.0381 + 19.0969i −0.182180 + 0.0534928i
\(358\) −30.8143 + 67.4739i −0.0860735 + 0.188475i
\(359\) −231.145 + 33.2337i −0.643859 + 0.0925729i −0.456507 0.889720i \(-0.650900\pi\)
−0.187352 + 0.982293i \(0.559990\pi\)
\(360\) 471.066 408.181i 1.30852 1.13384i
\(361\) 132.685 + 290.539i 0.367548 + 0.804818i
\(362\) −290.246 451.632i −0.801785 1.24760i
\(363\) 33.5309 233.213i 0.0923717 0.642459i
\(364\) 48.0434 74.7570i 0.131987 0.205376i
\(365\) 308.354 + 267.190i 0.844804 + 0.732027i
\(366\) 81.4441 277.373i 0.222525 0.757851i
\(367\) 466.001i 1.26976i −0.772612 0.634879i \(-0.781050\pi\)
0.772612 0.634879i \(-0.218950\pi\)
\(368\) 2.40995 4.57120i 0.00654878 0.0124217i
\(369\) 408.260 1.10640
\(370\) 517.090 + 151.831i 1.39754 + 0.410355i
\(371\) −52.4386 + 60.5174i −0.141344 + 0.163120i
\(372\) −226.782 145.744i −0.609630 0.391785i
\(373\) −426.128 61.2680i −1.14244 0.164257i −0.454992 0.890496i \(-0.650358\pi\)
−0.687443 + 0.726238i \(0.741267\pi\)
\(374\) −507.265 + 326.000i −1.35632 + 0.871657i
\(375\) −484.524 + 221.275i −1.29206 + 0.590066i
\(376\) −146.595 169.180i −0.389881 0.449947i
\(377\) −5.91164 41.1163i −0.0156807 0.109062i
\(378\) 75.4611 + 34.4619i 0.199633 + 0.0911691i
\(379\) 54.7723 + 186.537i 0.144518 + 0.492183i 0.999656 0.0262168i \(-0.00834604\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(380\) 218.001 64.0109i 0.573687 0.168450i
\(381\) 155.957 341.497i 0.409335 0.896318i
\(382\) 194.455 27.9584i 0.509044 0.0731895i
\(383\) −31.8478 + 27.5963i −0.0831536 + 0.0720530i −0.695446 0.718579i \(-0.744793\pi\)
0.612292 + 0.790632i \(0.290248\pi\)
\(384\) −413.621 905.704i −1.07714 2.35860i
\(385\) 37.6332 + 58.5584i 0.0977486 + 0.152100i
\(386\) 2.55517 17.7716i 0.00661960 0.0460403i
\(387\) −261.230 + 406.482i −0.675013 + 1.05034i
\(388\) 582.367 + 504.624i 1.50095 + 1.30058i
\(389\) 86.1483 293.394i 0.221461 0.754226i −0.771546 0.636173i \(-0.780516\pi\)
0.993007 0.118053i \(-0.0376654\pi\)
\(390\) 1204.78i 3.08917i
\(391\) 110.587 310.281i 0.282831 0.793558i
\(392\) 379.975 0.969324
\(393\) 97.8930 + 28.7440i 0.249092 + 0.0731399i
\(394\) 300.635 346.951i 0.763033 0.880587i
\(395\) −553.347 355.615i −1.40088 0.900291i
\(396\) 1198.90 + 172.375i 3.02752 + 0.435292i
\(397\) 111.820 71.8621i 0.281662 0.181013i −0.392181 0.919888i \(-0.628279\pi\)
0.673842 + 0.738875i \(0.264643\pi\)
\(398\) −22.9480 + 10.4800i −0.0576582 + 0.0263316i
\(399\) 19.9899 + 23.0696i 0.0501001 + 0.0578186i
\(400\) −0.155342 1.08043i −0.000388355 0.00270107i
\(401\) −434.725 198.532i −1.08410 0.495093i −0.208449 0.978033i \(-0.566842\pi\)
−0.875653 + 0.482940i \(0.839569\pi\)
\(402\) 361.091 + 1229.76i 0.898236 + 3.05911i
\(403\) −116.845 + 34.3087i −0.289938 + 0.0851333i
\(404\) 104.887 229.671i 0.259622 0.568492i
\(405\) −15.0695 + 2.16667i −0.0372087 + 0.00534980i
\(406\) −7.04015 + 6.10032i −0.0173403 + 0.0150254i
\(407\) 165.120 + 361.561i 0.405699 + 0.888357i
\(408\) −296.376 461.170i −0.726411 1.13032i
\(409\) −50.8160 + 353.433i −0.124244 + 0.864139i 0.828418 + 0.560110i \(0.189241\pi\)
−0.952663 + 0.304029i \(0.901668\pi\)
\(410\) −270.284 + 420.570i −0.659229 + 1.02578i
\(411\) −621.320 538.377i −1.51173 1.30992i
\(412\) −100.358 + 341.788i −0.243587 + 0.829583i
\(413\) 87.1833i 0.211098i
\(414\) −933.429 + 527.558i −2.25466 + 1.27430i
\(415\) 658.839 1.58756
\(416\) −437.660 128.509i −1.05207 0.308915i
\(417\) 99.0567 114.318i 0.237546 0.274143i
\(418\) 228.439 + 146.809i 0.546506 + 0.351218i
\(419\) 666.662 + 95.8515i 1.59108 + 0.228763i 0.880218 0.474570i \(-0.157396\pi\)
0.710861 + 0.703333i \(0.248306\pi\)
\(420\) −140.264 + 90.1419i −0.333961 + 0.214624i
\(421\) 432.269 197.411i 1.02677 0.468909i 0.170455 0.985366i \(-0.445476\pi\)
0.856314 + 0.516456i \(0.172749\pi\)
\(422\) 739.115 + 852.985i 1.75146 + 2.02129i
\(423\) −58.0972 404.075i −0.137346 0.955260i
\(424\) −589.082 269.025i −1.38934 0.634492i
\(425\) −19.6026 66.7602i −0.0461237 0.157083i
\(426\) −1102.02 + 323.582i −2.58690 + 0.759582i
\(427\) −7.50761 + 16.4394i −0.0175822 + 0.0384997i
\(428\) 240.742 34.6134i 0.562481 0.0808725i
\(429\) 671.547 581.899i 1.56538 1.35641i
\(430\) −245.794 538.213i −0.571613 1.25166i
\(431\) 419.135 + 652.186i 0.972470 + 1.51319i 0.854025 + 0.520232i \(0.174155\pi\)
0.118445 + 0.992961i \(0.462209\pi\)
\(432\) 0.839189 5.83669i 0.00194257 0.0135108i
\(433\) −284.450 + 442.613i −0.656928 + 1.02220i 0.339731 + 0.940523i \(0.389664\pi\)
−0.996659 + 0.0816775i \(0.973972\pi\)
\(434\) 20.6392 + 17.8839i 0.0475557 + 0.0412072i
\(435\) −21.9577 + 74.7812i −0.0504775 + 0.171911i
\(436\) 809.953i 1.85769i
\(437\) −147.791 + 12.7454i −0.338196 + 0.0291657i
\(438\) −1168.03 −2.66673
\(439\) −406.664 119.407i −0.926341 0.271998i −0.216437 0.976297i \(-0.569444\pi\)
−0.709904 + 0.704298i \(0.751262\pi\)
\(440\) −368.654 + 425.449i −0.837850 + 0.966931i
\(441\) 582.928 + 374.625i 1.32183 + 0.849490i
\(442\) −645.812 92.8537i −1.46111 0.210076i
\(443\) 48.8393 31.3871i 0.110247 0.0708512i −0.484356 0.874871i \(-0.660946\pi\)
0.594602 + 0.804020i \(0.297310\pi\)
\(444\) −866.039 + 395.507i −1.95054 + 0.890781i
\(445\) 119.417 + 137.814i 0.268352 + 0.309695i
\(446\) −176.745 1229.29i −0.396289 2.75625i
\(447\) 637.333 + 291.060i 1.42580 + 0.651141i
\(448\) 28.5714 + 97.3051i 0.0637754 + 0.217199i
\(449\) 480.449 141.072i 1.07004 0.314193i 0.301153 0.953576i \(-0.402628\pi\)
0.768888 + 0.639383i \(0.220810\pi\)
\(450\) −94.0828 + 206.013i −0.209073 + 0.457806i
\(451\) −364.973 + 52.4751i −0.809252 + 0.116353i
\(452\) 979.734 848.944i 2.16755 1.87819i
\(453\) 195.220 + 427.472i 0.430949 + 0.943647i
\(454\) −440.010 684.668i −0.969184 1.50808i
\(455\) −10.7190 + 74.5521i −0.0235582 + 0.163851i
\(456\) −133.468 + 207.681i −0.292694 + 0.455441i
\(457\) −117.286 101.629i −0.256643 0.222383i 0.517030 0.855967i \(-0.327037\pi\)
−0.773673 + 0.633585i \(0.781583\pi\)
\(458\) −183.613 + 625.329i −0.400902 + 1.36535i
\(459\) 375.877i 0.818905i
\(460\) 45.9753 808.935i 0.0999463 1.75856i
\(461\) −37.1200 −0.0805207 −0.0402603 0.999189i \(-0.512819\pi\)
−0.0402603 + 0.999189i \(0.512819\pi\)
\(462\) −191.200 56.1413i −0.413852 0.121518i
\(463\) −369.627 + 426.572i −0.798331 + 0.921323i −0.998288 0.0584819i \(-0.981374\pi\)
0.199958 + 0.979804i \(0.435919\pi\)
\(464\) 0.557036 + 0.357985i 0.00120051 + 0.000771519i
\(465\) 226.161 + 32.5170i 0.486367 + 0.0699291i
\(466\) 902.799 580.194i 1.93734 1.24505i
\(467\) −307.154 + 140.273i −0.657718 + 0.300370i −0.716175 0.697920i \(-0.754109\pi\)
0.0584577 + 0.998290i \(0.481382\pi\)
\(468\) 858.252 + 990.476i 1.83387 + 2.11640i
\(469\) −11.4032 79.3109i −0.0243138 0.169106i
\(470\) 454.721 + 207.664i 0.967492 + 0.441839i
\(471\) −212.220 722.754i −0.450573 1.53451i
\(472\) 676.523 198.645i 1.43331 0.420858i
\(473\) 181.285 396.960i 0.383267 0.839238i
\(474\) 1863.85 267.981i 3.93217 0.565361i
\(475\) −23.6804 + 20.5192i −0.0498535 + 0.0431983i
\(476\) 37.5096 + 82.1345i 0.0788016 + 0.172552i
\(477\) −638.487 993.505i −1.33855 2.08282i
\(478\) 123.415 858.369i 0.258190 1.79575i
\(479\) −110.203 + 171.480i −0.230070 + 0.357995i −0.937025 0.349263i \(-0.886432\pi\)
0.706955 + 0.707258i \(0.250068\pi\)
\(480\) 646.794 + 560.450i 1.34749 + 1.16760i
\(481\) −121.170 + 412.666i −0.251912 + 0.857934i
\(482\) 163.285i 0.338765i
\(483\) 101.427 39.5296i 0.209994 0.0818418i
\(484\) −313.855 −0.648461
\(485\) −626.670 184.007i −1.29210 0.379396i
\(486\) 528.504 609.926i 1.08746 1.25499i
\(487\) 106.619 + 68.5200i 0.218931 + 0.140698i 0.645510 0.763752i \(-0.276645\pi\)
−0.426579 + 0.904450i \(0.640281\pi\)
\(488\) −144.672 20.8007i −0.296458 0.0426243i
\(489\) −132.665 + 85.2586i −0.271298 + 0.174353i
\(490\) −771.842 + 352.489i −1.57519 + 0.719364i
\(491\) −100.797 116.326i −0.205289 0.236916i 0.643764 0.765224i \(-0.277372\pi\)
−0.849053 + 0.528308i \(0.822827\pi\)
\(492\) −125.692 874.210i −0.255472 1.77685i
\(493\) 38.3936 + 17.5337i 0.0778774 + 0.0355654i
\(494\) 82.7793 + 281.921i 0.167570 + 0.570689i
\(495\) −985.021 + 289.228i −1.98994 + 0.584299i
\(496\) 0.806396 1.76576i 0.00162580 0.00356000i
\(497\) 71.0723 10.2187i 0.143003 0.0205607i
\(498\) −1425.41 + 1235.13i −2.86227 + 2.48017i
\(499\) 112.222 + 245.732i 0.224894 + 0.492448i 0.988120 0.153683i \(-0.0491133\pi\)
−0.763227 + 0.646131i \(0.776386\pi\)
\(500\) 383.612 + 596.912i 0.767224 + 1.19382i
\(501\) −96.8772 + 673.796i −0.193368 + 1.34490i
\(502\) 46.3246 72.0825i 0.0922801 0.143591i
\(503\) −147.693 127.977i −0.293625 0.254427i 0.495573 0.868566i \(-0.334958\pi\)
−0.789198 + 0.614139i \(0.789504\pi\)
\(504\) 31.4282 107.035i 0.0623576 0.212370i
\(505\) 214.002i 0.423767i
\(506\) 766.649 591.599i 1.51512 1.16917i
\(507\) 143.566 0.283167
\(508\) −479.841 140.894i −0.944568 0.277350i
\(509\) −464.703 + 536.296i −0.912973 + 1.05363i 0.0853854 + 0.996348i \(0.472788\pi\)
−0.998358 + 0.0572788i \(0.981758\pi\)
\(510\) 1029.84 + 661.837i 2.01929 + 1.29772i
\(511\) 72.2781 + 10.3920i 0.141444 + 0.0203366i
\(512\) 12.0962 7.77378i 0.0236255 0.0151832i
\(513\) −153.974 + 70.3176i −0.300144 + 0.137071i
\(514\) −881.887 1017.75i −1.71573 1.98006i
\(515\) −42.9678 298.848i −0.0834327 0.580287i
\(516\) 950.827 + 434.228i 1.84269 + 0.841528i
\(517\) 103.874 + 353.764i 0.200918 + 0.684262i
\(518\) 92.5434 27.1732i 0.178655 0.0524579i
\(519\) 171.673 375.912i 0.330777 0.724300i
\(520\) −602.931 + 86.6884i −1.15948 + 0.166708i
\(521\) −58.3153 + 50.5305i −0.111929 + 0.0969875i −0.709027 0.705181i \(-0.750866\pi\)
0.597098 + 0.802168i \(0.296320\pi\)
\(522\) −57.0725 124.971i −0.109334 0.239409i
\(523\) −388.831 605.032i −0.743462 1.15685i −0.982577 0.185858i \(-0.940494\pi\)
0.239115 0.970991i \(-0.423143\pi\)
\(524\) 19.3417 134.524i 0.0369116 0.256726i
\(525\) 12.4314 19.3437i 0.0236789 0.0368451i
\(526\) −392.617 340.205i −0.746421 0.646777i
\(527\) 34.8610 118.726i 0.0661499 0.225286i
\(528\) 14.1644i 0.0268265i
\(529\) −134.127 + 511.714i −0.253548 + 0.967323i
\(530\) 1446.17 2.72861
\(531\) 1233.72 + 362.252i 2.32339 + 0.682208i
\(532\) 26.6284 30.7308i 0.0500534 0.0577647i
\(533\) −335.638 215.701i −0.629715 0.404693i
\(534\) −516.721 74.2932i −0.967642 0.139126i
\(535\) −173.420 + 111.450i −0.324150 + 0.208319i
\(536\) 589.453 269.194i 1.09973 0.502228i
\(537\) 72.7352 + 83.9409i 0.135447 + 0.156315i
\(538\) 20.6397 + 143.552i 0.0383638 + 0.266826i
\(539\) −569.273 259.978i −1.05616 0.482334i
\(540\) −260.480 887.114i −0.482371 1.64280i
\(541\) 846.574 248.577i 1.56483 0.459476i 0.619341 0.785122i \(-0.287400\pi\)
0.945492 + 0.325646i \(0.105582\pi\)
\(542\) −530.596 + 1161.84i −0.978960 + 2.14362i
\(543\) −795.683 + 114.402i −1.46535 + 0.210685i
\(544\) 350.274 303.514i 0.643886 0.557931i
\(545\) −285.181 624.459i −0.523268 1.14580i
\(546\) −116.572 181.390i −0.213502 0.332216i
\(547\) −5.41018 + 37.6286i −0.00989064 + 0.0687909i −0.994169 0.107833i \(-0.965609\pi\)
0.984278 + 0.176624i \(0.0565178\pi\)
\(548\) −592.080 + 921.294i −1.08044 + 1.68119i
\(549\) −201.437 174.546i −0.366915 0.317934i
\(550\) 57.6277 196.262i 0.104778 0.356840i
\(551\) 19.0077i 0.0344966i
\(552\) 537.840 + 696.984i 0.974348 + 1.26265i
\(553\) −117.720 −0.212875
\(554\) 1064.78 + 312.648i 1.92199 + 0.564347i
\(555\) 528.444 609.857i 0.952152 1.09884i
\(556\) −169.510 108.938i −0.304874 0.195931i
\(557\) 95.3735 + 13.7126i 0.171227 + 0.0246187i 0.227395 0.973803i \(-0.426979\pi\)
−0.0561680 + 0.998421i \(0.517888\pi\)
\(558\) −338.830 + 217.753i −0.607222 + 0.390238i
\(559\) 429.524 196.157i 0.768379 0.350907i
\(560\) −0.786232 0.907360i −0.00140399 0.00162029i
\(561\) 128.494 + 893.698i 0.229045 + 1.59304i
\(562\) −268.267 122.513i −0.477344 0.217996i
\(563\) −167.219 569.496i −0.297015 1.01154i −0.963875 0.266356i \(-0.914180\pi\)
0.666860 0.745183i \(-0.267638\pi\)
\(564\) −847.361 + 248.808i −1.50241 + 0.441148i
\(565\) −456.447 + 999.480i −0.807871 + 1.76899i
\(566\) −1370.36 + 197.028i −2.42113 + 0.348106i
\(567\) −2.05920 + 1.78431i −0.00363175 + 0.00314693i
\(568\) 241.231 + 528.222i 0.424703 + 0.929969i
\(569\) 315.775 + 491.356i 0.554966 + 0.863543i 0.999481 0.0322281i \(-0.0102603\pi\)
−0.444515 + 0.895771i \(0.646624\pi\)
\(570\) 78.4563 545.676i 0.137643 0.957326i
\(571\) 86.1621 134.071i 0.150897 0.234800i −0.757573 0.652750i \(-0.773615\pi\)
0.908470 + 0.417950i \(0.137251\pi\)
\(572\) −894.562 775.142i −1.56392 1.35514i
\(573\) 82.8752 282.247i 0.144634 0.492578i
\(574\) 89.4727i 0.155876i
\(575\) 40.5762 + 104.112i 0.0705674 + 0.181065i
\(576\) −1495.67 −2.59664
\(577\) 946.244 + 277.842i 1.63994 + 0.481529i 0.966275 0.257511i \(-0.0829022\pi\)
0.673662 + 0.739040i \(0.264720\pi\)
\(578\) −177.561 + 204.916i −0.307199 + 0.354526i
\(579\) −22.6163 14.5346i −0.0390610 0.0251030i
\(580\) 102.764 + 14.7752i 0.177179 + 0.0254745i
\(581\) 99.1940 63.7481i 0.170730 0.109721i
\(582\) 1700.77 776.716i 2.92229 1.33456i
\(583\) 698.488 + 806.098i 1.19809 + 1.38267i
\(584\) 84.0442 + 584.540i 0.143911 + 1.00093i
\(585\) −1010.44 461.452i −1.72725 0.788807i
\(586\) 247.535 + 843.028i 0.422415 + 1.43861i
\(587\) −410.642 + 120.575i −0.699561 + 0.205410i −0.612126 0.790761i \(-0.709685\pi\)
−0.0874353 + 0.996170i \(0.527867\pi\)
\(588\) 622.719 1363.57i 1.05905 2.31899i
\(589\) −55.1564 + 7.93029i −0.0936441 + 0.0134640i
\(590\) −1189.94 + 1031.09i −2.01686 + 1.74761i
\(591\) −285.561 625.290i −0.483182 1.05802i
\(592\) −3.70651 5.76743i −0.00626099 0.00974229i
\(593\) 57.8337 402.242i 0.0975273 0.678317i −0.881138 0.472858i \(-0.843222\pi\)
0.978666 0.205459i \(-0.0658687\pi\)
\(594\) 597.412 929.591i 1.00574 1.56497i
\(595\) −57.8384 50.1173i −0.0972074 0.0842307i
\(596\) 262.949 895.522i 0.441189 1.50255i
\(597\) 37.7750i 0.0632747i
\(598\) 1046.12 + 59.4556i 1.74937 + 0.0994241i
\(599\) 194.807 0.325220 0.162610 0.986690i \(-0.448009\pi\)
0.162610 + 0.986690i \(0.448009\pi\)
\(600\) 178.428 + 52.3911i 0.297379 + 0.0873184i
\(601\) 654.528 755.365i 1.08906 1.25685i 0.124721 0.992192i \(-0.460196\pi\)
0.964343 0.264656i \(-0.0852583\pi\)
\(602\) −89.0829 57.2501i −0.147978 0.0950999i
\(603\) 1169.70 + 168.177i 1.93980 + 0.278901i
\(604\) 526.626 338.442i 0.871898 0.560335i
\(605\) 241.976 110.507i 0.399961 0.182656i
\(606\) −401.190 462.998i −0.662029 0.764023i
\(607\) 152.687 + 1061.96i 0.251544 + 1.74953i 0.588953 + 0.808168i \(0.299540\pi\)
−0.337409 + 0.941358i \(0.609550\pi\)
\(608\) −189.859 86.7058i −0.312268 0.142608i
\(609\) 3.92976 + 13.3835i 0.00645281 + 0.0219763i
\(610\) 313.167 91.9543i 0.513389 0.150745i
\(611\) −165.727 + 362.892i −0.271240 + 0.593932i
\(612\) −1318.13 + 189.518i −2.15381 + 0.309671i
\(613\) 636.423 551.464i 1.03821 0.899615i 0.0431688 0.999068i \(-0.486255\pi\)
0.995042 + 0.0994527i \(0.0317092\pi\)
\(614\) 362.491 + 793.744i 0.590376 + 1.29274i
\(615\) 404.712 + 629.744i 0.658068 + 1.02397i
\(616\) −14.3384 + 99.7254i −0.0232765 + 0.161892i
\(617\) 628.913 978.608i 1.01931 1.58607i 0.228943 0.973440i \(-0.426473\pi\)
0.790366 0.612635i \(-0.209890\pi\)
\(618\) 653.212 + 566.011i 1.05698 + 0.915876i
\(619\) −48.1634 + 164.030i −0.0778084 + 0.264991i −0.989205 0.146538i \(-0.953187\pi\)
0.911397 + 0.411529i \(0.135005\pi\)
\(620\) 304.365i 0.490911i
\(621\) 51.8651 + 601.409i 0.0835187 + 0.968453i
\(622\) −959.941 −1.54331
\(623\) 31.3139 + 9.19459i 0.0502631 + 0.0147586i
\(624\) −10.0366 + 11.5829i −0.0160843 + 0.0185623i
\(625\) −608.103 390.804i −0.972965 0.625287i
\(626\) −1331.61 191.457i −2.12718 0.305842i
\(627\) 342.056 219.826i 0.545543 0.350599i
\(628\) −912.742 + 416.835i −1.45341 + 0.663751i
\(629\) −286.181 330.271i −0.454978 0.525073i
\(630\) 35.4520 + 246.574i 0.0562730 + 0.391388i
\(631\) −554.063 253.032i −0.878071 0.401002i −0.0752099 0.997168i \(-0.523963\pi\)
−0.802861 + 0.596166i \(0.796690\pi\)
\(632\) −268.222 913.481i −0.424402 1.44538i
\(633\) 1621.55 476.130i 2.56169 0.752181i
\(634\) 13.3166 29.1594i 0.0210042 0.0459927i
\(635\) 419.556 60.3231i 0.660719 0.0949970i
\(636\) −1930.83 + 1673.07i −3.03589 + 2.63061i
\(637\) −281.305 615.972i −0.441609 0.966990i
\(638\) 67.0842 + 104.385i 0.105148 + 0.163613i
\(639\) −150.707 + 1048.19i −0.235849 + 1.64036i
\(640\) 607.773 945.713i 0.949645 1.47768i
\(641\) 48.5119 + 42.0358i 0.0756816 + 0.0655785i 0.691880 0.722012i \(-0.256783\pi\)
−0.616199 + 0.787591i \(0.711328\pi\)
\(642\) 166.262 566.236i 0.258975 0.881987i
\(643\) 761.478i 1.18426i −0.805843 0.592129i \(-0.798288\pi\)
0.805843 0.592129i \(-0.201712\pi\)
\(644\) −71.3492 126.241i −0.110791 0.196026i
\(645\) −885.960 −1.37358
\(646\) −286.459 84.1118i −0.443434 0.130204i
\(647\) 409.930 473.085i 0.633586 0.731197i −0.344641 0.938735i \(-0.611999\pi\)
0.978227 + 0.207537i \(0.0665448\pi\)
\(648\) −18.5377 11.9135i −0.0286076 0.0183850i
\(649\) −1149.47 165.269i −1.77114 0.254651i
\(650\) 186.192 119.659i 0.286450 0.184090i
\(651\) 37.1968 16.9872i 0.0571379 0.0260940i
\(652\) 137.566 + 158.760i 0.210991 + 0.243497i
\(653\) −18.2619 127.014i −0.0279661 0.194509i 0.971049 0.238881i \(-0.0767804\pi\)
−0.999015 + 0.0443719i \(0.985871\pi\)
\(654\) 1787.67 + 816.400i 2.73344 + 1.24832i
\(655\) 32.4533 + 110.526i 0.0495470 + 0.168742i
\(656\) 6.10217 1.79176i 0.00930209 0.00273134i
\(657\) −447.377 + 979.618i −0.680939 + 1.49105i
\(658\) 88.5555 12.7324i 0.134583 0.0193501i
\(659\) −14.9685 + 12.9703i −0.0227140 + 0.0196818i −0.666144 0.745823i \(-0.732056\pi\)
0.643430 + 0.765505i \(0.277511\pi\)
\(660\) 922.587 + 2020.18i 1.39786 + 3.06089i
\(661\) −210.035 326.820i −0.317753 0.494433i 0.645233 0.763986i \(-0.276760\pi\)
−0.962986 + 0.269553i \(0.913124\pi\)
\(662\) −5.01169 + 34.8571i −0.00757053 + 0.0526542i
\(663\) −528.182 + 821.867i −0.796654 + 1.23962i
\(664\) 720.683 + 624.475i 1.08537 + 0.940475i
\(665\) −9.70982 + 33.0686i −0.0146012 + 0.0497272i
\(666\) 1422.47i 2.13585i
\(667\) −63.8496 22.7566i −0.0957266 0.0341178i
\(668\) 906.787 1.35747
\(669\) −1784.29 523.913i −2.66709 0.783129i
\(670\) −947.634 + 1093.63i −1.41438 + 1.63228i
\(671\) 202.513 + 130.147i 0.301808 + 0.193960i
\(672\) 151.609 + 21.7980i 0.225608 + 0.0324375i
\(673\) −1033.54 + 664.218i −1.53573 + 0.986951i −0.547013 + 0.837124i \(0.684235\pi\)
−0.988712 + 0.149827i \(0.952128\pi\)
\(674\) 1037.76 473.930i 1.53971 0.703161i
\(675\) 83.4990 + 96.3630i 0.123702 + 0.142760i
\(676\) −27.2166 189.296i −0.0402613 0.280023i
\(677\) 541.466 + 247.279i 0.799802 + 0.365257i 0.773018 0.634384i \(-0.218746\pi\)
0.0267838 + 0.999641i \(0.491473\pi\)
\(678\) −886.193 3018.09i −1.30707 4.45147i
\(679\) −112.155 + 32.9316i −0.165177 + 0.0485002i
\(680\) 257.115 563.004i 0.378111 0.827947i
\(681\) −1206.25 + 173.432i −1.77129 + 0.254672i
\(682\) 274.916 238.216i 0.403102 0.349290i
\(683\) 384.043 + 840.938i 0.562289 + 1.23124i 0.950802 + 0.309798i \(0.100261\pi\)
−0.388514 + 0.921443i \(0.627011\pi\)
\(684\) 324.224 + 504.503i 0.474012 + 0.737578i
\(685\) 132.099 918.769i 0.192845 1.34127i
\(686\) −165.837 + 258.048i −0.241745 + 0.376163i
\(687\) 737.514 + 639.059i 1.07353 + 0.930217i
\(688\) −2.12059 + 7.22207i −0.00308225 + 0.0104972i
\(689\) 1154.12i 1.67506i
\(690\) −1739.08 916.847i −2.52040 1.32876i
\(691\) −304.936 −0.441296 −0.220648 0.975353i \(-0.570817\pi\)
−0.220648 + 0.975353i \(0.570817\pi\)
\(692\) −528.197 155.093i −0.763290 0.224122i
\(693\) −120.318 + 138.855i −0.173619 + 0.200367i
\(694\) 466.583 + 299.855i 0.672310 + 0.432068i
\(695\) 169.046 + 24.3051i 0.243231 + 0.0349713i
\(696\) −94.8995 + 60.9882i −0.136350 + 0.0876267i
\(697\) 368.761 168.407i 0.529069 0.241618i
\(698\) 199.307 + 230.013i 0.285541 + 0.329532i
\(699\) −228.686 1590.55i −0.327162 2.27546i
\(700\) −27.8620 12.7241i −0.0398028 0.0181773i
\(701\) 281.867 + 959.952i 0.402093 + 1.36940i 0.873215 + 0.487335i \(0.162031\pi\)
−0.471122 + 0.882068i \(0.656151\pi\)
\(702\) 1147.22 336.855i 1.63422 0.479850i
\(703\) −81.7543 + 179.017i −0.116293 + 0.254647i
\(704\) 1337.08 192.243i 1.89926 0.273073i
\(705\) 565.696 490.178i 0.802405 0.695288i
\(706\) 79.2550 + 173.544i 0.112259 + 0.245814i
\(707\) 20.7065 + 32.2199i 0.0292878 + 0.0455727i
\(708\) 395.864 2753.30i 0.559130 3.88884i
\(709\) 244.971 381.182i 0.345516 0.537634i −0.624390 0.781113i \(-0.714652\pi\)
0.969906 + 0.243479i \(0.0782888\pi\)
\(710\) −980.024 849.196i −1.38032 1.19605i
\(711\) 489.134 1665.84i 0.687953 2.34295i
\(712\) 263.939i 0.370700i
\(713\) −39.3959 + 194.773i −0.0552537 + 0.273174i
\(714\) 219.089 0.306848
\(715\) 962.615 + 282.649i 1.34631 + 0.395314i
\(716\) 96.8899 111.817i 0.135321 0.156169i
\(717\) −1092.37 702.023i −1.52353 0.979112i
\(718\) 747.102 + 107.417i 1.04053 + 0.149606i
\(719\) 127.002 81.6191i 0.176637 0.113518i −0.449335 0.893363i \(-0.648339\pi\)
0.625972 + 0.779846i \(0.284703\pi\)
\(720\) 16.1068 7.35572i 0.0223705 0.0102163i
\(721\) −35.3852 40.8367i −0.0490779 0.0566389i
\(722\) −146.921 1021.86i −0.203492 1.41532i
\(723\) 222.401 + 101.567i 0.307609 + 0.140480i
\(724\) 301.685 + 1027.45i 0.416692 + 1.41912i
\(725\) −13.7379 + 4.03381i −0.0189488 + 0.00556388i
\(726\) −316.353 + 692.717i −0.435748 + 0.954155i
\(727\) 652.318 93.7892i 0.897274 0.129009i 0.321780 0.946814i \(-0.395719\pi\)
0.575494 + 0.817806i \(0.304810\pi\)
\(728\) −82.3887 + 71.3902i −0.113171 + 0.0980635i
\(729\) −491.587 1076.43i −0.674331 1.47658i
\(730\) −712.975 1109.41i −0.976679 1.51974i
\(731\) −68.2821 + 474.912i −0.0934091 + 0.649675i
\(732\) −311.739 + 485.075i −0.425873 + 0.662671i
\(733\) 1047.40 + 907.578i 1.42892 + 1.23817i 0.927949 + 0.372707i \(0.121570\pi\)
0.500975 + 0.865462i \(0.332975\pi\)
\(734\) −424.345 + 1445.18i −0.578126 + 1.96892i
\(735\) 1270.54i 1.72863i
\(736\) −518.564 + 533.960i −0.704570 + 0.725489i
\(737\) −1067.29 −1.44816
\(738\) −1266.12 371.765i −1.71560 0.503747i
\(739\) −679.026 + 783.638i −0.918845 + 1.06040i 0.0791345 + 0.996864i \(0.474784\pi\)
−0.997979 + 0.0635395i \(0.979761\pi\)
\(740\) −904.296 581.156i −1.22202 0.785346i
\(741\) 435.479 + 62.6124i 0.587691 + 0.0844972i
\(742\) 217.733 139.928i 0.293440 0.188583i
\(743\) 207.514 94.7685i 0.279292 0.127548i −0.270844 0.962623i \(-0.587303\pi\)
0.550137 + 0.835075i \(0.314576\pi\)
\(744\) 216.569 + 249.934i 0.291087 + 0.335933i
\(745\) 112.580 + 783.014i 0.151115 + 1.05103i
\(746\) 1265.74 + 578.043i 1.69670 + 0.774857i
\(747\) 489.933 + 1668.56i 0.655868 + 2.23368i
\(748\) 1154.01 338.848i 1.54279 0.453005i
\(749\) −15.3262 + 33.5597i −0.0204622 + 0.0448060i
\(750\) 1704.12 245.016i 2.27216 0.326688i
\(751\) −96.3917 + 83.5239i −0.128351 + 0.111217i −0.716671 0.697411i \(-0.754335\pi\)
0.588320 + 0.808628i \(0.299790\pi\)
\(752\) −2.64176 5.78464i −0.00351298 0.00769234i
\(753\) −69.3645 107.933i −0.0921175 0.143338i
\(754\) −19.1074 + 132.895i −0.0253414 + 0.176253i
\(755\) −286.855 + 446.355i −0.379941 + 0.591199i
\(756\) −125.053 108.359i −0.165414 0.143332i
\(757\) 319.858 1089.34i 0.422534 1.43902i −0.423504 0.905894i \(-0.639200\pi\)
0.846037 0.533124i \(-0.178982\pi\)
\(758\) 628.375i 0.828991i
\(759\) −328.909 1412.20i −0.433345 1.86061i
\(760\) −278.729 −0.366748
\(761\) 1454.43 + 427.059i 1.91121 + 0.561181i 0.980944 + 0.194291i \(0.0622407\pi\)
0.930264 + 0.366890i \(0.119577\pi\)
\(762\) −794.630 + 917.052i −1.04282 + 1.20348i
\(763\) −103.358 66.4242i −0.135463 0.0870566i
\(764\) −387.863 55.7662i −0.507674 0.0729925i
\(765\) 949.525 610.222i 1.24121 0.797676i
\(766\) 123.898 56.5821i 0.161746 0.0738670i
\(767\) −822.868 949.641i −1.07284 1.23812i
\(768\) 172.298 + 1198.36i 0.224347 + 1.56036i
\(769\) −1027.18 469.099i −1.33574 0.610012i −0.385840 0.922566i \(-0.626088\pi\)
−0.949900 + 0.312554i \(0.898816\pi\)
\(770\) −63.3861 215.873i −0.0823196 0.280355i
\(771\) −1934.78 + 568.103i −2.50944 + 0.736839i
\(772\) −14.8768 + 32.5757i −0.0192705 + 0.0421965i
\(773\) −850.070 + 122.222i −1.09970 + 0.158113i −0.668188 0.743993i \(-0.732930\pi\)
−0.431514 + 0.902106i \(0.642021\pi\)
\(774\) 1180.28 1022.72i 1.52492 1.32135i
\(775\) 17.4370 + 38.1817i 0.0224993 + 0.0492666i
\(776\) −511.085 795.263i −0.658614 1.02482i
\(777\) 20.5532 142.951i 0.0264520 0.183978i
\(778\) −534.334 + 831.440i −0.686805 + 1.06869i
\(779\) −137.973 119.554i −0.177115 0.153471i
\(780\) −677.023 + 2305.73i −0.867978 + 2.95606i
\(781\) 956.425i 1.22462i
\(782\) −625.502 + 861.557i −0.799875 + 1.10174i
\(783\) −77.3480 −0.0987842
\(784\) 10.3570 + 3.04110i 0.0132105 + 0.00387896i
\(785\) 556.942 642.745i 0.709480 0.818783i
\(786\) −277.416 178.284i −0.352947 0.226825i
\(787\) 287.889 + 41.3921i 0.365805 + 0.0525948i 0.322767 0.946479i \(-0.395387\pi\)
0.0430384 + 0.999073i \(0.486296\pi\)
\(788\) −770.330 + 495.061i −0.977576 + 0.628250i
\(789\) −707.592 + 323.146i −0.896821 + 0.409565i
\(790\) 1392.24 + 1606.73i 1.76233 + 2.03384i
\(791\) 27.9858 + 194.645i 0.0353803 + 0.246075i
\(792\) −1351.62 617.266i −1.70660 0.779376i
\(793\) 73.3845 + 249.925i 0.0925404 + 0.315164i
\(794\) −412.219 + 121.038i −0.519167 + 0.152441i
\(795\) 899.551 1969.74i 1.13151 2.47766i
\(796\) 49.8075 7.16124i 0.0625722 0.00899653i
\(797\) −693.547 + 600.962i −0.870197 + 0.754030i −0.970544 0.240923i \(-0.922550\pi\)
0.100348 + 0.994952i \(0.468004\pi\)
\(798\) −40.9863 89.7475i −0.0513613 0.112466i
\(799\) −219.157 341.016i −0.274290 0.426803i
\(800\) −22.3752 + 155.623i −0.0279690 + 0.194528i
\(801\) −260.223 + 404.915i −0.324872 + 0.505511i
\(802\) 1167.40 + 1011.56i 1.45562 + 1.26130i
\(803\) 274.028 933.253i 0.341255 1.16221i
\(804\) 2556.46i 3.17968i
\(805\) 99.4577 + 72.2076i 0.123550 + 0.0896989i
\(806\) 393.607 0.488346
\(807\) 208.363 + 61.1810i 0.258195 + 0.0758128i
\(808\) −202.840 + 234.090i −0.251040 + 0.289715i
\(809\) 749.248 + 481.513i 0.926141 + 0.595195i 0.914433 0.404737i \(-0.132637\pi\)
0.0117080 + 0.999931i \(0.496273\pi\)
\(810\) 48.7073 + 7.00305i 0.0601325 + 0.00864574i
\(811\) −1223.15 + 786.069i −1.50820 + 0.969259i −0.514460 + 0.857514i \(0.672008\pi\)
−0.993737 + 0.111745i \(0.964356\pi\)
\(812\) 16.9016 7.71872i 0.0208148 0.00950581i
\(813\) 1252.44 + 1445.39i 1.54052 + 1.77785i
\(814\) −182.836 1271.65i −0.224614 1.56222i
\(815\) −161.960 73.9645i −0.198724 0.0907540i
\(816\) −4.38743 14.9422i −0.00537675 0.0183115i
\(817\) 207.317 60.8736i 0.253753 0.0745087i
\(818\) 479.432 1049.81i 0.586103 1.28339i
\(819\) −196.780 + 28.2926i −0.240268 + 0.0345454i
\(820\) 753.613 653.010i 0.919041 0.796353i
\(821\) 125.587 + 274.997i 0.152968 + 0.334954i 0.970566 0.240836i \(-0.0774217\pi\)
−0.817597 + 0.575790i \(0.804694\pi\)
\(822\) 1436.62 + 2235.42i 1.74771 + 2.71949i
\(823\) 65.2056 453.515i 0.0792292 0.551051i −0.911086 0.412216i \(-0.864755\pi\)
0.990315 0.138835i \(-0.0443359\pi\)
\(824\) 236.259 367.627i 0.286722 0.446149i
\(825\) −231.472 200.571i −0.280572 0.243117i
\(826\) −79.3898 + 270.377i −0.0961136 + 0.327333i
\(827\) 217.299i 0.262756i 0.991332 + 0.131378i \(0.0419402\pi\)
−0.991332 + 0.131378i \(0.958060\pi\)
\(828\) 2082.88 485.113i 2.51555 0.585885i
\(829\) 1359.45 1.63987 0.819935 0.572456i \(-0.194009\pi\)
0.819935 + 0.572456i \(0.194009\pi\)
\(830\) −2043.22 599.945i −2.46172 0.722825i
\(831\) 1088.16 1255.81i 1.30946 1.51120i
\(832\) 1229.61 + 790.225i 1.47790 + 0.949790i
\(833\) 681.063 + 97.9221i 0.817603 + 0.117554i
\(834\) −411.298 + 264.325i −0.493163 + 0.316937i
\(835\) −699.116 + 319.276i −0.837265 + 0.382366i
\(836\) −354.693 409.337i −0.424274 0.489638i
\(837\) 32.2708 + 224.448i 0.0385553 + 0.268158i
\(838\) −1980.20 904.327i −2.36301 1.07915i
\(839\) −315.093 1073.11i −0.375558 1.27903i −0.903073 0.429487i \(-0.858694\pi\)
0.527515 0.849545i \(-0.323124\pi\)
\(840\) 196.257 57.6262i 0.233639 0.0686026i
\(841\) −345.756 + 757.100i −0.411125 + 0.900238i
\(842\) −1520.34 + 218.592i −1.80563 + 0.259610i
\(843\) −333.738 + 289.185i −0.395893 + 0.343043i
\(844\) −935.201 2047.80i −1.10806 2.42631i
\(845\) 87.6337 + 136.361i 0.103709 + 0.161374i
\(846\) −187.780 + 1306.04i −0.221962 + 1.54378i
\(847\) 25.7392 40.0510i 0.0303887 0.0472857i
\(848\) −13.9036 12.0475i −0.0163957 0.0142070i
\(849\) −584.037 + 1989.05i −0.687912 + 2.34281i
\(850\) 224.890i 0.264577i
\(851\) 503.467 + 488.950i 0.591618 + 0.574559i
\(852\) 2290.90 2.68885
\(853\) 179.937 + 52.8341i 0.210945 + 0.0619392i 0.385498 0.922709i \(-0.374030\pi\)
−0.174552 + 0.984648i \(0.555848\pi\)
\(854\) 38.2528 44.1460i 0.0447925 0.0516933i
\(855\) −427.604 274.805i −0.500122 0.321409i
\(856\) −295.336 42.4629i −0.345019 0.0496062i
\(857\) 299.616 192.551i 0.349610 0.224681i −0.354036 0.935232i \(-0.615191\pi\)
0.703645 + 0.710551i \(0.251554\pi\)
\(858\) −2612.52 + 1193.10i −3.04489 + 1.39056i
\(859\) −677.411 781.774i −0.788604 0.910098i 0.209095 0.977895i \(-0.432948\pi\)
−0.997699 + 0.0677973i \(0.978403\pi\)
\(860\) 167.957 + 1168.17i 0.195299 + 1.35833i
\(861\) 121.866 + 55.6542i 0.141540 + 0.0646391i
\(862\) −705.954 2404.26i −0.818972 2.78916i
\(863\) −1107.41 + 325.164i −1.28321 + 0.376784i −0.851083 0.525031i \(-0.824054\pi\)
−0.432124 + 0.901814i \(0.642236\pi\)
\(864\) −352.833 + 772.596i −0.408371 + 0.894208i
\(865\) 461.837 66.4022i 0.533916 0.0767656i
\(866\) 1285.20 1113.63i 1.48406 1.28595i
\(867\) 168.658 + 369.309i 0.194530 + 0.425962i
\(868\) −29.4498 45.8248i −0.0339283 0.0527935i
\(869\) −223.156 + 1552.08i −0.256796 + 1.78605i
\(870\) 136.193 211.920i 0.156543 0.243586i
\(871\) −872.775 756.264i −1.00204 0.868270i
\(872\) 279.938 953.382i 0.321030 1.09333i
\(873\) 1723.92i 1.97471i
\(874\) 469.944 + 95.0535i 0.537694 + 0.108757i
\(875\) −107.632 −0.123008
\(876\) 2235.40 + 656.372i 2.55182 + 0.749283i
\(877\) 451.316 520.847i 0.514614 0.593896i −0.437660 0.899140i \(-0.644193\pi\)
0.952274 + 0.305244i \(0.0987382\pi\)
\(878\) 1152.43 + 740.623i 1.31256 + 0.843534i
\(879\) 1302.21 + 187.230i 1.48147 + 0.213004i
\(880\) −13.4535 + 8.64606i −0.0152881 + 0.00982507i
\(881\) 166.371 75.9791i 0.188843 0.0862419i −0.318749 0.947839i \(-0.603263\pi\)
0.507593 + 0.861597i \(0.330536\pi\)
\(882\) −1466.67 1692.63i −1.66289 1.91908i
\(883\) 113.499 + 789.400i 0.128537 + 0.893997i 0.947410 + 0.320022i \(0.103690\pi\)
−0.818873 + 0.573975i \(0.805401\pi\)
\(884\) 1183.79 + 540.618i 1.33913 + 0.611559i
\(885\) 664.219 + 2262.12i 0.750530 + 2.55607i
\(886\) −180.044 + 52.8657i −0.203210 + 0.0596678i
\(887\) 585.620 1282.33i 0.660226 1.44569i −0.222085 0.975027i \(-0.571286\pi\)
0.882311 0.470666i \(-0.155986\pi\)
\(888\) 1156.10 166.221i 1.30191 0.187186i
\(889\) 57.3311 49.6777i 0.0644895 0.0558804i
\(890\) −244.846 536.138i −0.275108 0.602402i
\(891\) 19.6218 + 30.5321i 0.0220222 + 0.0342672i
\(892\) −352.538 + 2451.96i −0.395222 + 2.74883i
\(893\) −98.6943 + 153.571i −0.110520 + 0.171972i
\(894\) −1711.48 1483.01i −1.91441 1.65885i
\(895\) −35.3301 + 120.323i −0.0394750 + 0.134439i
\(896\) 201.192i 0.224545i
\(897\) 731.694 1387.88i 0.815713 1.54725i
\(898\) −1618.45 −1.80229
\(899\) −24.4314 7.17370i −0.0271762 0.00797964i
\(900\) 295.826 341.401i 0.328695 0.379335i
\(901\) −986.535 634.008i −1.09493 0.703671i
\(902\) 1179.65 + 169.609i 1.30782 + 0.188036i
\(903\) −133.389 + 85.7239i −0.147718 + 0.0949324i
\(904\) −1446.64 + 660.659i −1.60027 + 0.730817i
\(905\) −594.353 685.920i −0.656744 0.757922i
\(906\) −216.166 1503.47i −0.238593 1.65945i
\(907\) 1180.19 + 538.976i 1.30121 + 0.594241i 0.940929 0.338604i \(-0.109955\pi\)
0.360277 + 0.932845i \(0.382682\pi\)
\(908\) 457.351 + 1557.59i 0.503691 + 1.71541i
\(909\) −541.976 + 159.139i −0.596233 + 0.175070i
\(910\) 101.130 221.444i 0.111132 0.243345i
\(911\) −705.378 + 101.418i −0.774290 + 0.111326i −0.518123 0.855306i \(-0.673369\pi\)
−0.256167 + 0.966632i \(0.582460\pi\)
\(912\) −5.30014 + 4.59259i −0.00581155 + 0.00503574i
\(913\) −652.452 1428.67i −0.714624 1.56481i
\(914\) 271.189 + 421.978i 0.296705 + 0.461682i
\(915\) 69.5522 483.746i 0.0760133 0.528684i
\(916\) 702.805 1093.59i 0.767254 1.19387i
\(917\) 15.5804 + 13.5005i 0.0169906 + 0.0147225i
\(918\) −342.277 + 1165.69i −0.372851 + 1.26981i
\(919\) 1453.27i 1.58136i 0.612229 + 0.790680i \(0.290273\pi\)
−0.612229 + 0.790680i \(0.709727\pi\)
\(920\) −333.703 + 936.293i −0.362721 + 1.01771i
\(921\) 1306.59 1.41867
\(922\) 115.118 + 33.8018i 0.124857 + 0.0366614i
\(923\) 677.705 782.113i 0.734242 0.847360i
\(924\) 334.373 + 214.889i 0.361876 + 0.232563i
\(925\) 146.736 + 21.0974i 0.158633 + 0.0228080i
\(926\) 1534.75 986.321i 1.65739 1.06514i
\(927\) 724.902 331.052i 0.781987 0.357121i
\(928\) −62.4572 72.0794i −0.0673030 0.0776718i
\(929\) −32.1369 223.517i −0.0345930 0.240600i 0.965187 0.261560i \(-0.0842369\pi\)
−0.999780 + 0.0209599i \(0.993328\pi\)
\(930\) −671.771 306.787i −0.722334 0.329879i
\(931\) −87.2978 297.309i −0.0937678 0.319344i
\(932\) −2053.83 + 603.060i −2.20368 + 0.647060i
\(933\) −597.107 + 1307.48i −0.639986 + 1.40137i
\(934\) 1080.29 155.323i 1.15663 0.166299i
\(935\) −770.413 + 667.567i −0.823971 + 0.713975i
\(936\) −667.903 1462.50i −0.713571 1.56250i
\(937\) −78.0792 121.494i −0.0833289 0.129662i 0.797087 0.603864i \(-0.206373\pi\)
−0.880416 + 0.474202i \(0.842737\pi\)
\(938\) −36.8571 + 256.347i −0.0392932 + 0.273291i
\(939\) −1089.07 + 1694.63i −1.15982 + 1.80471i
\(940\) −753.558 652.962i −0.801658 0.694640i
\(941\) −135.597 + 461.802i −0.144099 + 0.490757i −0.999636 0.0269856i \(-0.991409\pi\)
0.855537 + 0.517742i \(0.173227\pi\)
\(942\) 2434.69i 2.58459i
\(943\) −566.786 + 320.338i −0.601045 + 0.339701i
\(944\) 20.0300 0.0212182
\(945\) 134.566 + 39.5123i 0.142398 + 0.0418119i
\(946\) −923.686 + 1065.99i −0.976412 + 1.12684i
\(947\) 874.786 + 562.191i 0.923745 + 0.593655i 0.913742 0.406295i \(-0.133180\pi\)
0.0100027 + 0.999950i \(0.496816\pi\)
\(948\) −3717.66 534.519i −3.92158 0.563839i
\(949\) 885.371 568.993i 0.932951 0.599571i
\(950\) 92.1238 42.0715i 0.0969724 0.0442858i
\(951\) −31.4331 36.2757i −0.0330527 0.0381448i
\(952\) −15.7643 109.643i −0.0165592 0.115171i
\(953\) 137.184 + 62.6496i 0.143949 + 0.0657394i 0.486087 0.873910i \(-0.338424\pi\)
−0.342138 + 0.939650i \(0.611151\pi\)
\(954\) 1075.41 + 3662.52i 1.12727 + 3.83912i
\(955\) 318.670 93.5700i 0.333686 0.0979790i
\(956\) −718.552 + 1573.41i −0.751624 + 1.64583i
\(957\) 183.905 26.4416i 0.192168 0.0276296i
\(958\) 497.919 431.449i 0.519748 0.450364i
\(959\) −69.0098 151.110i −0.0719602 0.157571i
\(960\) −1482.67 2307.08i −1.54445 2.40320i
\(961\) 126.141 877.331i 0.131260 0.912935i
\(962\) 751.555 1169.44i 0.781242 1.21564i
\(963\) −411.217 356.322i −0.427017 0.370012i
\(964\) 91.7577 312.498i 0.0951843 0.324168i
\(965\) 30.3533i 0.0314542i
\(966\) −350.546 + 30.2308i −0.362884 + 0.0312949i
\(967\) −858.605 −0.887905 −0.443953 0.896050i \(-0.646424\pi\)
−0.443953 + 0.896050i \(0.646424\pi\)
\(968\) 369.433 + 108.475i 0.381646 + 0.112061i
\(969\) −292.748 + 337.850i −0.302114 + 0.348658i
\(970\) 1775.90 + 1141.30i 1.83083 + 1.17660i
\(971\) −471.201 67.7485i −0.485274 0.0697719i −0.104664 0.994508i \(-0.533377\pi\)
−0.380610 + 0.924736i \(0.624286\pi\)
\(972\) −1354.21 + 870.297i −1.39322 + 0.895367i
\(973\) 27.8030 12.6972i 0.0285745 0.0130495i
\(974\) −268.258 309.586i −0.275419 0.317850i
\(975\) −47.1640 328.033i −0.0483734 0.336444i
\(976\) −3.77687 1.72484i −0.00386974 0.00176725i
\(977\) −406.072 1382.95i −0.415631 1.41551i −0.855666 0.517529i \(-0.826852\pi\)
0.440035 0.897981i \(-0.354966\pi\)
\(978\) 489.064 143.602i 0.500065 0.146832i
\(979\) 180.586 395.429i 0.184460 0.403911i
\(980\) 1675.25 240.864i 1.70944 0.245780i
\(981\) 1369.42 1186.61i 1.39594 1.20959i
\(982\) 206.669 + 452.541i 0.210457 + 0.460836i
\(983\) 213.637 + 332.426i 0.217332 + 0.338175i 0.932752 0.360520i \(-0.117401\pi\)
−0.715419 + 0.698695i \(0.753764\pi\)
\(984\) −154.196 + 1072.46i −0.156704 + 1.08990i
\(985\) 419.601 652.912i 0.425991 0.662855i
\(986\) −103.102 89.3380i −0.104565 0.0906065i
\(987\) 37.7417 128.536i 0.0382388 0.130229i
\(988\) 586.063i 0.593181i
\(989\) 43.7220 769.288i 0.0442083 0.777845i
\(990\) 3318.17 3.35168
\(991\) −471.222 138.363i −0.475502 0.139620i 0.0351956 0.999380i \(-0.488795\pi\)
−0.510697 + 0.859761i \(0.670613\pi\)
\(992\) −183.102 + 211.311i −0.184578 + 0.213015i
\(993\) 44.3595 + 28.5081i 0.0446722 + 0.0287091i
\(994\) −229.718 33.0285i −0.231105 0.0332278i
\(995\) −35.8792 + 23.0582i −0.0360595 + 0.0231741i
\(996\) 3422.06 1562.80i 3.43580 1.56908i
\(997\) 504.917 + 582.706i 0.506437 + 0.584459i 0.950183 0.311693i \(-0.100896\pi\)
−0.443746 + 0.896153i \(0.646351\pi\)
\(998\) −124.263 864.265i −0.124512 0.865997i
\(999\) 728.475 + 332.683i 0.729204 + 0.333016i
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 23.3.d.a.5.1 30
3.2 odd 2 207.3.j.a.28.3 30
4.3 odd 2 368.3.p.a.97.3 30
23.3 even 11 529.3.b.b.528.29 30
23.14 odd 22 inner 23.3.d.a.14.1 yes 30
23.20 odd 22 529.3.b.b.528.30 30
69.14 even 22 207.3.j.a.37.3 30
92.83 even 22 368.3.p.a.129.3 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.3.d.a.5.1 30 1.1 even 1 trivial
23.3.d.a.14.1 yes 30 23.14 odd 22 inner
207.3.j.a.28.3 30 3.2 odd 2
207.3.j.a.37.3 30 69.14 even 22
368.3.p.a.97.3 30 4.3 odd 2
368.3.p.a.129.3 30 92.83 even 22
529.3.b.b.528.29 30 23.3 even 11
529.3.b.b.528.30 30 23.20 odd 22