Properties

Label 36.5.f.a.31.11
Level $36$
Weight $5$
Character 36.31
Analytic conductor $3.721$
Analytic rank $0$
Dimension $44$
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] = [36,5,Mod(7,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 36.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.72131867102\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.11
Character \(\chi\) \(=\) 36.31
Dual form 36.5.f.a.7.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.485844 + 3.97038i) q^{2} +(-4.25251 + 7.93197i) q^{3} +(-15.5279 - 3.85798i) q^{4} +(1.01545 - 1.75881i) q^{5} +(-29.4269 - 20.7378i) q^{6} +(-20.0352 + 11.5673i) q^{7} +(22.8618 - 59.7774i) q^{8} +(-44.8324 - 67.4615i) q^{9} +O(q^{10})\) \(q+(-0.485844 + 3.97038i) q^{2} +(-4.25251 + 7.93197i) q^{3} +(-15.5279 - 3.85798i) q^{4} +(1.01545 - 1.75881i) q^{5} +(-29.4269 - 20.7378i) q^{6} +(-20.0352 + 11.5673i) q^{7} +(22.8618 - 59.7774i) q^{8} +(-44.8324 - 67.4615i) q^{9} +(6.48981 + 4.88624i) q^{10} +(-4.32958 + 2.49968i) q^{11} +(96.6339 - 106.761i) q^{12} +(-137.824 + 238.718i) q^{13} +(-36.1928 - 85.1675i) q^{14} +(9.63264 + 15.5339i) q^{15} +(226.232 + 119.813i) q^{16} -266.009 q^{17} +(289.630 - 145.226i) q^{18} +367.194i q^{19} +(-22.5533 + 23.3931i) q^{20} +(-6.55189 - 208.109i) q^{21} +(-7.82120 - 18.4045i) q^{22} +(544.473 + 314.352i) q^{23} +(376.933 + 435.543i) q^{24} +(310.438 + 537.694i) q^{25} +(-880.842 - 663.194i) q^{26} +(725.753 - 68.7283i) q^{27} +(355.732 - 102.321i) q^{28} +(-319.481 - 553.357i) q^{29} +(-66.3555 + 30.6982i) q^{30} +(-1191.19 - 687.735i) q^{31} +(-585.616 + 840.018i) q^{32} +(-1.41585 - 44.9720i) q^{33} +(129.239 - 1056.16i) q^{34} +46.9843i q^{35} +(435.888 + 1220.50i) q^{36} +1466.19 q^{37} +(-1457.90 - 178.399i) q^{38} +(-1307.41 - 2108.37i) q^{39} +(-81.9222 - 100.911i) q^{40} +(593.019 - 1027.14i) q^{41} +(829.456 + 75.0950i) q^{42} +(-1430.33 + 825.804i) q^{43} +(76.8730 - 22.1114i) q^{44} +(-164.177 + 10.3478i) q^{45} +(-1512.63 + 2009.04i) q^{46} +(-307.864 + 177.745i) q^{47} +(-1912.40 + 1284.96i) q^{48} +(-932.893 + 1615.82i) q^{49} +(-2285.68 + 971.322i) q^{50} +(1131.21 - 2109.98i) q^{51} +(3061.09 - 3175.07i) q^{52} +5297.49 q^{53} +(-79.7250 + 2914.91i) q^{54} +10.1532i q^{55} +(233.424 + 1462.10i) q^{56} +(-2912.57 - 1561.50i) q^{57} +(2352.26 - 999.617i) q^{58} +(5223.32 + 3015.68i) q^{59} +(-89.6454 - 278.371i) q^{60} +(-833.364 - 1443.43i) q^{61} +(3309.31 - 4395.36i) q^{62} +(1678.58 + 833.016i) q^{63} +(-3050.68 - 2733.24i) q^{64} +(279.907 + 484.814i) q^{65} +(179.244 + 16.2279i) q^{66} +(1908.36 + 1101.79i) q^{67} +(4130.57 + 1026.26i) q^{68} +(-4808.81 + 2981.96i) q^{69} +(-186.546 - 22.8270i) q^{70} -524.299i q^{71} +(-5057.62 + 1137.67i) q^{72} -1492.29 q^{73} +(-712.338 + 5821.33i) q^{74} +(-5585.11 + 175.836i) q^{75} +(1416.63 - 5701.76i) q^{76} +(57.8293 - 100.163i) q^{77} +(9006.23 - 4166.58i) q^{78} +(-4448.35 + 2568.25i) q^{79} +(440.456 - 276.236i) q^{80} +(-2541.12 + 6048.92i) q^{81} +(3790.02 + 2853.54i) q^{82} +(-6918.39 + 3994.33i) q^{83} +(-701.143 + 3256.78i) q^{84} +(-270.120 + 467.861i) q^{85} +(-2583.84 - 6080.19i) q^{86} +(5747.81 - 180.958i) q^{87} +(50.4426 + 315.958i) q^{88} -8860.17 q^{89} +(38.6797 - 656.875i) q^{90} -6377.03i q^{91} +(-7241.77 - 6981.79i) q^{92} +(10520.7 - 6523.91i) q^{93} +(-556.144 - 1308.70i) q^{94} +(645.826 + 372.868i) q^{95} +(-4172.66 - 8217.27i) q^{96} +(-3409.33 - 5905.14i) q^{97} +(-5962.18 - 4488.98i) q^{98} +(362.737 + 180.013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.485844 + 3.97038i −0.121461 + 0.992596i
\(3\) −4.25251 + 7.93197i −0.472501 + 0.881330i
\(4\) −15.5279 3.85798i −0.970494 0.241124i
\(5\) 1.01545 1.75881i 0.0406181 0.0703525i −0.845002 0.534764i \(-0.820401\pi\)
0.885620 + 0.464411i \(0.153734\pi\)
\(6\) −29.4269 20.7378i −0.817415 0.576050i
\(7\) −20.0352 + 11.5673i −0.408882 + 0.236068i −0.690309 0.723514i \(-0.742526\pi\)
0.281427 + 0.959583i \(0.409192\pi\)
\(8\) 22.8618 59.7774i 0.357216 0.934022i
\(9\) −44.8324 67.4615i −0.553486 0.832859i
\(10\) 6.48981 + 4.88624i 0.0648981 + 0.0488624i
\(11\) −4.32958 + 2.49968i −0.0357816 + 0.0206585i −0.517784 0.855511i \(-0.673243\pi\)
0.482002 + 0.876170i \(0.339910\pi\)
\(12\) 96.6339 106.761i 0.671069 0.741395i
\(13\) −137.824 + 238.718i −0.815527 + 1.41253i 0.0934218 + 0.995627i \(0.470219\pi\)
−0.908949 + 0.416908i \(0.863114\pi\)
\(14\) −36.1928 85.1675i −0.184657 0.434528i
\(15\) 9.63264 + 15.5339i 0.0428117 + 0.0690395i
\(16\) 226.232 + 119.813i 0.883719 + 0.468018i
\(17\) −266.009 −0.920447 −0.460224 0.887803i \(-0.652231\pi\)
−0.460224 + 0.887803i \(0.652231\pi\)
\(18\) 289.630 145.226i 0.893919 0.448228i
\(19\) 367.194i 1.01716i 0.861015 + 0.508579i \(0.169829\pi\)
−0.861015 + 0.508579i \(0.830171\pi\)
\(20\) −22.5533 + 23.3931i −0.0563832 + 0.0584828i
\(21\) −6.55189 208.109i −0.0148569 0.471902i
\(22\) −7.82120 18.4045i −0.0161595 0.0380259i
\(23\) 544.473 + 314.352i 1.02925 + 0.594238i 0.916770 0.399416i \(-0.130787\pi\)
0.112481 + 0.993654i \(0.464120\pi\)
\(24\) 376.933 + 435.543i 0.654397 + 0.756151i
\(25\) 310.438 + 537.694i 0.496700 + 0.860310i
\(26\) −880.842 663.194i −1.30302 0.981057i
\(27\) 725.753 68.7283i 0.995546 0.0942775i
\(28\) 355.732 102.321i 0.453739 0.130512i
\(29\) −319.481 553.357i −0.379882 0.657975i 0.611163 0.791505i \(-0.290702\pi\)
−0.991045 + 0.133530i \(0.957369\pi\)
\(30\) −66.3555 + 30.6982i −0.0737284 + 0.0341092i
\(31\) −1191.19 687.735i −1.23953 0.715645i −0.270535 0.962710i \(-0.587201\pi\)
−0.968999 + 0.247065i \(0.920534\pi\)
\(32\) −585.616 + 840.018i −0.571891 + 0.820330i
\(33\) −1.41585 44.9720i −0.00130014 0.0412966i
\(34\) 129.239 1056.16i 0.111799 0.913633i
\(35\) 46.9843i 0.0383545i
\(36\) 435.888 + 1220.50i 0.336333 + 0.941743i
\(37\) 1466.19 1.07099 0.535496 0.844538i \(-0.320125\pi\)
0.535496 + 0.844538i \(0.320125\pi\)
\(38\) −1457.90 178.399i −1.00963 0.123545i
\(39\) −1307.41 2108.37i −0.859572 1.38617i
\(40\) −81.9222 100.911i −0.0512014 0.0630692i
\(41\) 593.019 1027.14i 0.352777 0.611028i −0.633958 0.773368i \(-0.718571\pi\)
0.986735 + 0.162339i \(0.0519040\pi\)
\(42\) 829.456 + 75.0950i 0.470213 + 0.0425709i
\(43\) −1430.33 + 825.804i −0.773572 + 0.446622i −0.834147 0.551542i \(-0.814040\pi\)
0.0605755 + 0.998164i \(0.480706\pi\)
\(44\) 76.8730 22.1114i 0.0397071 0.0114212i
\(45\) −164.177 + 10.3478i −0.0810752 + 0.00511004i
\(46\) −1512.63 + 2009.04i −0.714852 + 0.949453i
\(47\) −307.864 + 177.745i −0.139368 + 0.0804642i −0.568063 0.822985i \(-0.692307\pi\)
0.428695 + 0.903449i \(0.358974\pi\)
\(48\) −1912.40 + 1284.96i −0.830036 + 0.557709i
\(49\) −932.893 + 1615.82i −0.388544 + 0.672977i
\(50\) −2285.68 + 971.322i −0.914270 + 0.388529i
\(51\) 1131.21 2109.98i 0.434912 0.811218i
\(52\) 3061.09 3175.07i 1.13206 1.17421i
\(53\) 5297.49 1.88590 0.942950 0.332934i \(-0.108039\pi\)
0.942950 + 0.332934i \(0.108039\pi\)
\(54\) −79.7250 + 2914.91i −0.0273405 + 0.999626i
\(55\) 10.1532i 0.00335644i
\(56\) 233.424 + 1462.10i 0.0744338 + 0.466232i
\(57\) −2912.57 1561.50i −0.896452 0.480608i
\(58\) 2352.26 999.617i 0.699245 0.297151i
\(59\) 5223.32 + 3015.68i 1.50052 + 0.866327i 1.00000 0.000603027i \(0.000191950\pi\)
0.500522 + 0.865724i \(0.333141\pi\)
\(60\) −89.6454 278.371i −0.0249015 0.0773254i
\(61\) −833.364 1443.43i −0.223962 0.387914i 0.732045 0.681256i \(-0.238566\pi\)
−0.956008 + 0.293342i \(0.905233\pi\)
\(62\) 3309.31 4395.36i 0.860902 1.14343i
\(63\) 1678.58 + 833.016i 0.422922 + 0.209880i
\(64\) −3050.68 2733.24i −0.744794 0.667295i
\(65\) 279.907 + 484.814i 0.0662502 + 0.114749i
\(66\) 179.244 + 16.2279i 0.0411488 + 0.00372541i
\(67\) 1908.36 + 1101.79i 0.425119 + 0.245443i 0.697265 0.716813i \(-0.254400\pi\)
−0.272146 + 0.962256i \(0.587733\pi\)
\(68\) 4130.57 + 1026.26i 0.893289 + 0.221942i
\(69\) −4808.81 + 2981.96i −1.01004 + 0.626332i
\(70\) −186.546 22.8270i −0.0380705 0.00465858i
\(71\) 524.299i 0.104007i −0.998647 0.0520035i \(-0.983439\pi\)
0.998647 0.0520035i \(-0.0165607\pi\)
\(72\) −5057.62 + 1137.67i −0.975622 + 0.219458i
\(73\) −1492.29 −0.280032 −0.140016 0.990149i \(-0.544715\pi\)
−0.140016 + 0.990149i \(0.544715\pi\)
\(74\) −712.338 + 5821.33i −0.130084 + 1.06306i
\(75\) −5585.11 + 175.836i −0.992909 + 0.0312597i
\(76\) 1416.63 5701.76i 0.245261 0.987146i
\(77\) 57.8293 100.163i 0.00975364 0.0168938i
\(78\) 9006.23 4166.58i 1.48031 0.684842i
\(79\) −4448.35 + 2568.25i −0.712762 + 0.411513i −0.812083 0.583542i \(-0.801666\pi\)
0.0993209 + 0.995055i \(0.468333\pi\)
\(80\) 440.456 276.236i 0.0688212 0.0431619i
\(81\) −2541.12 + 6048.92i −0.387307 + 0.921951i
\(82\) 3790.02 + 2853.54i 0.563656 + 0.424382i
\(83\) −6918.39 + 3994.33i −1.00427 + 0.579813i −0.909508 0.415687i \(-0.863541\pi\)
−0.0947580 + 0.995500i \(0.530208\pi\)
\(84\) −701.143 + 3256.78i −0.0993683 + 0.461561i
\(85\) −270.120 + 467.861i −0.0373868 + 0.0647558i
\(86\) −2583.84 6080.19i −0.349356 0.822092i
\(87\) 5747.81 180.958i 0.759388 0.0239078i
\(88\) 50.4426 + 315.958i 0.00651376 + 0.0408004i
\(89\) −8860.17 −1.11857 −0.559283 0.828977i \(-0.688924\pi\)
−0.559283 + 0.828977i \(0.688924\pi\)
\(90\) 38.6797 656.875i 0.00477527 0.0810956i
\(91\) 6377.03i 0.770080i
\(92\) −7241.77 6981.79i −0.855597 0.824881i
\(93\) 10520.7 6523.91i 1.21640 0.754296i
\(94\) −556.144 1308.70i −0.0629407 0.148110i
\(95\) 645.826 + 372.868i 0.0715596 + 0.0413150i
\(96\) −4172.66 8217.27i −0.452763 0.891631i
\(97\) −3409.33 5905.14i −0.362348 0.627606i 0.625999 0.779824i \(-0.284692\pi\)
−0.988347 + 0.152219i \(0.951358\pi\)
\(98\) −5962.18 4488.98i −0.620802 0.467408i
\(99\) 362.737 + 180.013i 0.0370103 + 0.0183668i
\(100\) −2746.04 9546.92i −0.274604 0.954692i
\(101\) −1545.53 2676.93i −0.151507 0.262418i 0.780274 0.625437i \(-0.215079\pi\)
−0.931782 + 0.363019i \(0.881746\pi\)
\(102\) 7827.84 + 5516.45i 0.752387 + 0.530224i
\(103\) 9409.35 + 5432.49i 0.886922 + 0.512065i 0.872934 0.487838i \(-0.162214\pi\)
0.0139875 + 0.999902i \(0.495547\pi\)
\(104\) 11119.1 + 13696.3i 1.02802 + 1.26630i
\(105\) −372.678 199.801i −0.0338030 0.0181225i
\(106\) −2573.76 + 21033.1i −0.229063 + 1.87194i
\(107\) 14106.5i 1.23212i −0.787699 0.616060i \(-0.788728\pi\)
0.787699 0.616060i \(-0.211272\pi\)
\(108\) −11534.6 1732.73i −0.988904 0.148554i
\(109\) 16328.3 1.37432 0.687160 0.726506i \(-0.258857\pi\)
0.687160 + 0.726506i \(0.258857\pi\)
\(110\) −40.3122 4.93288i −0.00333159 0.000407676i
\(111\) −6234.97 + 11629.8i −0.506044 + 0.943897i
\(112\) −5918.52 + 216.430i −0.471821 + 0.0172536i
\(113\) −5911.44 + 10238.9i −0.462952 + 0.801857i −0.999107 0.0422631i \(-0.986543\pi\)
0.536154 + 0.844120i \(0.319877\pi\)
\(114\) 7614.79 10805.4i 0.585934 0.831440i
\(115\) 1105.77 638.418i 0.0836123 0.0482736i
\(116\) 2826.03 + 9825.03i 0.210020 + 0.730160i
\(117\) 22283.3 1404.48i 1.62782 0.102599i
\(118\) −14511.1 + 19273.4i −1.04217 + 1.38419i
\(119\) 5329.56 3077.02i 0.376354 0.217288i
\(120\) 1148.80 220.682i 0.0797775 0.0153251i
\(121\) −7308.00 + 12657.8i −0.499146 + 0.864547i
\(122\) 6135.85 2607.49i 0.412245 0.175188i
\(123\) 5625.42 + 9071.72i 0.371830 + 0.599625i
\(124\) 15843.5 + 15274.7i 1.03040 + 0.993411i
\(125\) 2530.25 0.161936
\(126\) −4122.92 + 6259.88i −0.259695 + 0.394298i
\(127\) 20979.9i 1.30076i −0.759609 0.650379i \(-0.774610\pi\)
0.759609 0.650379i \(-0.225390\pi\)
\(128\) 12334.2 10784.4i 0.752817 0.658229i
\(129\) −467.746 14857.1i −0.0281081 0.892802i
\(130\) −2060.89 + 875.796i −0.121946 + 0.0518222i
\(131\) −24723.9 14274.3i −1.44070 0.831789i −0.442804 0.896618i \(-0.646016\pi\)
−0.997896 + 0.0648298i \(0.979350\pi\)
\(132\) −151.516 + 703.783i −0.00869580 + 0.0403916i
\(133\) −4247.46 7356.81i −0.240119 0.415898i
\(134\) −5301.70 + 7041.62i −0.295261 + 0.392160i
\(135\) 616.087 1346.25i 0.0338045 0.0738685i
\(136\) −6081.45 + 15901.3i −0.328798 + 0.859718i
\(137\) 309.436 + 535.959i 0.0164866 + 0.0285556i 0.874151 0.485654i \(-0.161419\pi\)
−0.857664 + 0.514210i \(0.828085\pi\)
\(138\) −9503.22 20541.6i −0.499014 1.07864i
\(139\) 16819.9 + 9710.99i 0.870552 + 0.502613i 0.867532 0.497382i \(-0.165705\pi\)
0.00302027 + 0.999995i \(0.499039\pi\)
\(140\) 181.264 729.568i 0.00924818 0.0372228i
\(141\) −100.677 3197.83i −0.00506400 0.160849i
\(142\) 2081.67 + 254.728i 0.103237 + 0.0126328i
\(143\) 1378.07i 0.0673903i
\(144\) −2059.77 20633.4i −0.0993330 0.995054i
\(145\) −1297.67 −0.0617203
\(146\) 725.022 5924.98i 0.0340130 0.277959i
\(147\) −8849.49 14271.0i −0.409528 0.660418i
\(148\) −22766.8 5656.52i −1.03939 0.258241i
\(149\) −309.641 + 536.313i −0.0139471 + 0.0241572i −0.872915 0.487873i \(-0.837773\pi\)
0.858968 + 0.512030i \(0.171106\pi\)
\(150\) 2015.36 22260.5i 0.0895715 0.989354i
\(151\) 3758.08 2169.73i 0.164821 0.0951593i −0.415321 0.909675i \(-0.636331\pi\)
0.580141 + 0.814516i \(0.302997\pi\)
\(152\) 21949.9 + 8394.72i 0.950048 + 0.363345i
\(153\) 11925.8 + 17945.4i 0.509455 + 0.766603i
\(154\) 369.591 + 278.268i 0.0155840 + 0.0117334i
\(155\) −2419.20 + 1396.72i −0.100695 + 0.0581362i
\(156\) 12167.3 + 37782.5i 0.499971 + 1.55254i
\(157\) 3103.88 5376.08i 0.125923 0.218105i −0.796170 0.605073i \(-0.793144\pi\)
0.922093 + 0.386967i \(0.126477\pi\)
\(158\) −8035.75 18909.4i −0.321894 0.757468i
\(159\) −22527.6 + 42019.6i −0.891090 + 1.66210i
\(160\) 882.770 + 1882.99i 0.0344832 + 0.0735541i
\(161\) −14544.9 −0.561123
\(162\) −22782.0 13028.1i −0.868082 0.496420i
\(163\) 15857.0i 0.596824i 0.954437 + 0.298412i \(0.0964569\pi\)
−0.954437 + 0.298412i \(0.903543\pi\)
\(164\) −13171.0 + 13661.5i −0.489702 + 0.507937i
\(165\) −80.5351 43.1766i −0.00295813 0.00158592i
\(166\) −12497.8 29409.3i −0.453541 1.06725i
\(167\) 362.861 + 209.498i 0.0130109 + 0.00751186i 0.506491 0.862245i \(-0.330942\pi\)
−0.493480 + 0.869757i \(0.664276\pi\)
\(168\) −12590.0 4366.09i −0.446074 0.154694i
\(169\) −23710.4 41067.7i −0.830169 1.43789i
\(170\) −1726.35 1299.79i −0.0597353 0.0449753i
\(171\) 24771.5 16462.2i 0.847149 0.562983i
\(172\) 25396.0 7304.81i 0.858438 0.246918i
\(173\) 9600.40 + 16628.4i 0.320772 + 0.555594i 0.980648 0.195781i \(-0.0627242\pi\)
−0.659875 + 0.751375i \(0.729391\pi\)
\(174\) −2074.07 + 22908.9i −0.0685053 + 0.756670i
\(175\) −12439.4 7181.88i −0.406184 0.234510i
\(176\) −1278.98 + 46.7701i −0.0412895 + 0.00150988i
\(177\) −46132.5 + 28607.0i −1.47252 + 0.913115i
\(178\) 4304.66 35178.3i 0.135862 1.11028i
\(179\) 49821.7i 1.55494i 0.628922 + 0.777468i \(0.283496\pi\)
−0.628922 + 0.777468i \(0.716504\pi\)
\(180\) 2589.25 + 472.712i 0.0799152 + 0.0145899i
\(181\) 13970.7 0.426443 0.213222 0.977004i \(-0.431604\pi\)
0.213222 + 0.977004i \(0.431604\pi\)
\(182\) 25319.3 + 3098.24i 0.764378 + 0.0935347i
\(183\) 14993.1 472.028i 0.447703 0.0140950i
\(184\) 31238.8 25360.6i 0.922696 0.749071i
\(185\) 1488.84 2578.75i 0.0435016 0.0753469i
\(186\) 20791.0 + 44940.6i 0.600966 + 1.29901i
\(187\) 1151.71 664.939i 0.0329351 0.0190151i
\(188\) 5466.22 1572.28i 0.154658 0.0444851i
\(189\) −13745.6 + 9772.02i −0.384805 + 0.273565i
\(190\) −1794.20 + 2383.02i −0.0497008 + 0.0660117i
\(191\) 26994.8 15585.5i 0.739969 0.427221i −0.0820893 0.996625i \(-0.526159\pi\)
0.822058 + 0.569404i \(0.192826\pi\)
\(192\) 34653.0 12574.8i 0.940023 0.341112i
\(193\) −13498.2 + 23379.5i −0.362377 + 0.627655i −0.988351 0.152189i \(-0.951368\pi\)
0.625975 + 0.779843i \(0.284701\pi\)
\(194\) 25102.1 10667.4i 0.666970 0.283436i
\(195\) −5035.84 + 158.543i −0.132435 + 0.00416944i
\(196\) 20719.7 21491.2i 0.539350 0.559434i
\(197\) 10416.4 0.268402 0.134201 0.990954i \(-0.457153\pi\)
0.134201 + 0.990954i \(0.457153\pi\)
\(198\) −890.956 + 1352.75i −0.0227261 + 0.0345054i
\(199\) 8438.68i 0.213093i −0.994308 0.106546i \(-0.966021\pi\)
0.994308 0.106546i \(-0.0339793\pi\)
\(200\) 39239.1 6264.51i 0.980978 0.156613i
\(201\) −16854.7 + 10451.7i −0.417185 + 0.258699i
\(202\) 11379.3 4835.76i 0.278878 0.118512i
\(203\) 12801.7 + 7391.09i 0.310654 + 0.179356i
\(204\) −25705.5 + 28399.4i −0.617684 + 0.682415i
\(205\) −1204.36 2086.02i −0.0286583 0.0496376i
\(206\) −26140.6 + 34719.4i −0.616000 + 0.818159i
\(207\) −3203.37 50824.2i −0.0747594 1.18612i
\(208\) −59781.7 + 37492.7i −1.38179 + 0.866602i
\(209\) −917.868 1589.79i −0.0210130 0.0363956i
\(210\) 974.350 1382.60i 0.0220941 0.0313515i
\(211\) 19871.6 + 11472.8i 0.446341 + 0.257695i 0.706284 0.707929i \(-0.250370\pi\)
−0.259943 + 0.965624i \(0.583704\pi\)
\(212\) −82259.0 20437.6i −1.83026 0.454735i
\(213\) 4158.73 + 2229.59i 0.0916645 + 0.0491434i
\(214\) 56008.4 + 6853.58i 1.22300 + 0.149655i
\(215\) 3354.25i 0.0725637i
\(216\) 12483.6 44954.9i 0.267567 0.963539i
\(217\) 31821.1 0.675764
\(218\) −7933.01 + 64829.6i −0.166926 + 1.36414i
\(219\) 6345.99 11836.8i 0.132316 0.246801i
\(220\) 39.1709 157.658i 0.000809316 0.00325740i
\(221\) 36662.5 63501.3i 0.750650 1.30016i
\(222\) −43145.4 30405.5i −0.875444 0.616944i
\(223\) −55651.0 + 32130.1i −1.11909 + 0.646105i −0.941167 0.337941i \(-0.890270\pi\)
−0.177919 + 0.984045i \(0.556936\pi\)
\(224\) 2016.17 23604.0i 0.0401820 0.470423i
\(225\) 22356.0 45048.7i 0.441600 0.889851i
\(226\) −37780.4 28445.2i −0.739690 0.556919i
\(227\) −5807.02 + 3352.69i −0.112694 + 0.0650641i −0.555288 0.831658i \(-0.687392\pi\)
0.442593 + 0.896722i \(0.354059\pi\)
\(228\) 39202.0 + 35483.4i 0.754116 + 0.682583i
\(229\) −17775.1 + 30787.4i −0.338955 + 0.587087i −0.984236 0.176858i \(-0.943407\pi\)
0.645281 + 0.763945i \(0.276740\pi\)
\(230\) 1997.53 + 4700.51i 0.0377605 + 0.0888566i
\(231\) 548.573 + 884.646i 0.0102804 + 0.0165785i
\(232\) −40382.2 + 6447.00i −0.750263 + 0.119779i
\(233\) 62439.9 1.15014 0.575070 0.818105i \(-0.304975\pi\)
0.575070 + 0.818105i \(0.304975\pi\)
\(234\) −5249.88 + 89155.6i −0.0958777 + 1.62823i
\(235\) 721.967i 0.0130732i
\(236\) −69472.8 66978.7i −1.24736 1.20258i
\(237\) −1454.69 46205.7i −0.0258985 0.822619i
\(238\) 9627.62 + 22655.3i 0.169967 + 0.399960i
\(239\) 3250.59 + 1876.73i 0.0569070 + 0.0328553i 0.528184 0.849130i \(-0.322873\pi\)
−0.471277 + 0.881985i \(0.656207\pi\)
\(240\) 318.055 + 4668.38i 0.00552178 + 0.0810482i
\(241\) 44832.6 + 77652.3i 0.771898 + 1.33697i 0.936522 + 0.350610i \(0.114026\pi\)
−0.164624 + 0.986356i \(0.552641\pi\)
\(242\) −46705.9 35165.3i −0.797519 0.600460i
\(243\) −37173.7 45879.2i −0.629541 0.776968i
\(244\) 7371.68 + 25628.5i 0.123819 + 0.430471i
\(245\) 1894.62 + 3281.57i 0.0315638 + 0.0546701i
\(246\) −38751.3 + 17927.6i −0.640348 + 0.296246i
\(247\) −87655.9 50608.2i −1.43677 0.829520i
\(248\) −68343.8 + 55483.5i −1.11121 + 0.902112i
\(249\) −2262.44 71862.4i −0.0364904 1.15905i
\(250\) −1229.31 + 10046.1i −0.0196689 + 0.160737i
\(251\) 9246.49i 0.146767i 0.997304 + 0.0733836i \(0.0233798\pi\)
−0.997304 + 0.0733836i \(0.976620\pi\)
\(252\) −22851.0 19410.9i −0.359836 0.305664i
\(253\) −3143.12 −0.0491043
\(254\) 83298.4 + 10193.0i 1.29113 + 0.157992i
\(255\) −2562.37 4132.16i −0.0394060 0.0635473i
\(256\) 36825.9 + 54210.9i 0.561918 + 0.827193i
\(257\) −7624.85 + 13206.6i −0.115442 + 0.199952i −0.917956 0.396681i \(-0.870162\pi\)
0.802514 + 0.596633i \(0.203495\pi\)
\(258\) 59215.7 + 5361.11i 0.889605 + 0.0805407i
\(259\) −29375.4 + 16959.9i −0.437909 + 0.252827i
\(260\) −2475.97 8608.02i −0.0366268 0.127338i
\(261\) −23007.2 + 46361.0i −0.337741 + 0.680568i
\(262\) 68686.5 91228.1i 1.00062 1.32900i
\(263\) 89478.0 51660.2i 1.29361 0.746869i 0.314322 0.949317i \(-0.398223\pi\)
0.979293 + 0.202448i \(0.0648896\pi\)
\(264\) −2720.68 943.505i −0.0390364 0.0135374i
\(265\) 5379.35 9317.30i 0.0766016 0.132678i
\(266\) 31273.0 13289.8i 0.441983 0.187825i
\(267\) 37677.9 70278.6i 0.528524 0.985826i
\(268\) −25382.2 24470.9i −0.353394 0.340707i
\(269\) −86017.8 −1.18873 −0.594366 0.804195i \(-0.702597\pi\)
−0.594366 + 0.804195i \(0.702597\pi\)
\(270\) 5045.83 + 3100.17i 0.0692157 + 0.0425263i
\(271\) 15629.0i 0.212810i −0.994323 0.106405i \(-0.966066\pi\)
0.994323 0.106405i \(-0.0339340\pi\)
\(272\) −60179.8 31871.3i −0.813417 0.430786i
\(273\) 50582.4 + 27118.4i 0.678695 + 0.363863i
\(274\) −2278.30 + 968.188i −0.0303466 + 0.0128961i
\(275\) −2688.13 1551.99i −0.0355455 0.0205222i
\(276\) 86175.1 27751.4i 1.13126 0.364306i
\(277\) 28307.3 + 49029.7i 0.368926 + 0.638998i 0.989398 0.145231i \(-0.0463924\pi\)
−0.620472 + 0.784228i \(0.713059\pi\)
\(278\) −46728.2 + 62063.6i −0.604630 + 0.803059i
\(279\) 7008.29 + 111192.i 0.0900334 + 1.42846i
\(280\) 2808.60 + 1074.15i 0.0358240 + 0.0137008i
\(281\) −55533.5 96186.8i −0.703303 1.21816i −0.967301 0.253633i \(-0.918374\pi\)
0.263998 0.964523i \(-0.414959\pi\)
\(282\) 12745.5 + 1153.92i 0.160273 + 0.0145104i
\(283\) 78979.6 + 45598.9i 0.986148 + 0.569353i 0.904121 0.427278i \(-0.140527\pi\)
0.0820271 + 0.996630i \(0.473861\pi\)
\(284\) −2022.73 + 8141.27i −0.0250785 + 0.100938i
\(285\) −5703.95 + 3537.05i −0.0702241 + 0.0435463i
\(286\) 5471.45 + 669.525i 0.0668914 + 0.00818530i
\(287\) 27438.6i 0.333118i
\(288\) 82923.4 + 1846.57i 0.999752 + 0.0222628i
\(289\) −12760.0 −0.152776
\(290\) 630.465 5152.25i 0.00749661 0.0612633i
\(291\) 61337.6 1931.09i 0.724338 0.0228043i
\(292\) 23172.2 + 5757.23i 0.271770 + 0.0675224i
\(293\) −41507.5 + 71893.1i −0.483494 + 0.837436i −0.999820 0.0189556i \(-0.993966\pi\)
0.516326 + 0.856392i \(0.327299\pi\)
\(294\) 60960.7 28202.4i 0.705270 0.326281i
\(295\) 10608.0 6124.56i 0.121897 0.0703770i
\(296\) 33519.7 87644.8i 0.382575 1.00033i
\(297\) −2970.40 + 2111.72i −0.0336746 + 0.0239399i
\(298\) −1978.93 1489.96i −0.0222843 0.0167780i
\(299\) −150083. + 86650.5i −1.67876 + 0.969234i
\(300\) 87403.5 + 18816.9i 0.971150 + 0.209076i
\(301\) 19104.7 33090.3i 0.210866 0.365231i
\(302\) 6788.81 + 15975.2i 0.0744355 + 0.175159i
\(303\) 27805.7 875.407i 0.302865 0.00953508i
\(304\) −43994.5 + 83071.0i −0.476048 + 0.898882i
\(305\) −3384.96 −0.0363876
\(306\) −77044.2 + 38631.4i −0.822806 + 0.412570i
\(307\) 65201.8i 0.691803i 0.938271 + 0.345902i \(0.112427\pi\)
−0.938271 + 0.345902i \(0.887573\pi\)
\(308\) −1284.40 + 1332.22i −0.0135393 + 0.0140435i
\(309\) −83103.7 + 51533.0i −0.870369 + 0.539720i
\(310\) −4370.18 10283.7i −0.0454753 0.107011i
\(311\) 115786. + 66849.3i 1.19712 + 0.691156i 0.959911 0.280303i \(-0.0904350\pi\)
0.237206 + 0.971459i \(0.423768\pi\)
\(312\) −155922. + 29952.4i −1.60177 + 0.307697i
\(313\) −5620.04 9734.19i −0.0573655 0.0993599i 0.835917 0.548857i \(-0.184937\pi\)
−0.893282 + 0.449497i \(0.851603\pi\)
\(314\) 19837.1 + 14935.5i 0.201196 + 0.151482i
\(315\) 3169.63 2106.42i 0.0319439 0.0212287i
\(316\) 78981.8 22718.0i 0.790957 0.227508i
\(317\) 19603.1 + 33953.5i 0.195077 + 0.337883i 0.946926 0.321452i \(-0.104171\pi\)
−0.751849 + 0.659336i \(0.770838\pi\)
\(318\) −155889. 109858.i −1.54156 1.08637i
\(319\) 2766.43 + 1597.20i 0.0271856 + 0.0156956i
\(320\) −7905.07 + 2590.10i −0.0771979 + 0.0252939i
\(321\) 111893. + 59988.2i 1.08590 + 0.582178i
\(322\) 7066.54 57748.7i 0.0681546 0.556968i
\(323\) 97677.0i 0.936240i
\(324\) 62794.9 84123.5i 0.598183 0.801359i
\(325\) −171143. −1.62029
\(326\) −62958.4 7704.04i −0.592405 0.0724908i
\(327\) −69436.2 + 129516.i −0.649367 + 1.21123i
\(328\) −47842.2 58931.4i −0.444696 0.547771i
\(329\) 4112.08 7122.34i 0.0379901 0.0658007i
\(330\) 210.555 298.778i 0.00193347 0.00274360i
\(331\) 64736.6 37375.7i 0.590873 0.341141i −0.174570 0.984645i \(-0.555853\pi\)
0.765443 + 0.643504i \(0.222520\pi\)
\(332\) 122838. 35332.7i 1.11444 0.320553i
\(333\) −65732.6 98911.2i −0.592779 0.891984i
\(334\) −1008.08 + 1338.92i −0.00903656 + 0.0120022i
\(335\) 3875.69 2237.63i 0.0345350 0.0199388i
\(336\) 23451.8 47865.9i 0.207730 0.423982i
\(337\) 70909.1 122818.i 0.624370 1.08144i −0.364293 0.931285i \(-0.618689\pi\)
0.988662 0.150156i \(-0.0479775\pi\)
\(338\) 174574. 74187.1i 1.52808 0.649374i
\(339\) −56076.3 90430.4i −0.487955 0.786892i
\(340\) 5999.39 6222.78i 0.0518978 0.0538303i
\(341\) 6876.48 0.0591367
\(342\) 53326.1 + 106350.i 0.455919 + 0.909257i
\(343\) 98710.7i 0.839027i
\(344\) 16664.4 + 104381.i 0.140823 + 0.882073i
\(345\) 361.608 + 11485.8i 0.00303809 + 0.0964994i
\(346\) −70685.3 + 30038.5i −0.590442 + 0.250914i
\(347\) −158508. 91514.6i −1.31641 0.760032i −0.333264 0.942834i \(-0.608150\pi\)
−0.983150 + 0.182802i \(0.941483\pi\)
\(348\) −89949.6 19365.0i −0.742747 0.159904i
\(349\) −67279.0 116531.i −0.552368 0.956729i −0.998103 0.0615644i \(-0.980391\pi\)
0.445735 0.895165i \(-0.352942\pi\)
\(350\) 34558.4 45899.8i 0.282110 0.374693i
\(351\) −83619.5 + 182723.i −0.678724 + 1.48313i
\(352\) 435.691 5100.77i 0.00351636 0.0411671i
\(353\) 100139. + 173446.i 0.803626 + 1.39192i 0.917215 + 0.398393i \(0.130432\pi\)
−0.113589 + 0.993528i \(0.536235\pi\)
\(354\) −91167.5 197062.i −0.727501 1.57252i
\(355\) −922.144 532.400i −0.00731715 0.00422456i
\(356\) 137580. + 34182.3i 1.08556 + 0.269713i
\(357\) 1742.86 + 55358.9i 0.0136750 + 0.434361i
\(358\) −197811. 24205.6i −1.54342 0.188864i
\(359\) 161179.i 1.25060i −0.780385 0.625300i \(-0.784977\pi\)
0.780385 0.625300i \(-0.215023\pi\)
\(360\) −3134.82 + 10050.7i −0.0241884 + 0.0775514i
\(361\) −4510.46 −0.0346104
\(362\) −6787.59 + 55469.1i −0.0517962 + 0.423286i
\(363\) −69324.2 111794.i −0.526104 0.848412i
\(364\) −24602.4 + 99022.0i −0.185684 + 0.747358i
\(365\) −1515.35 + 2624.66i −0.0113744 + 0.0197010i
\(366\) −5410.19 + 59757.8i −0.0403878 + 0.446100i
\(367\) 172828. 99782.5i 1.28317 0.740836i 0.305740 0.952115i \(-0.401096\pi\)
0.977426 + 0.211279i \(0.0677627\pi\)
\(368\) 85514.0 + 136351.i 0.631454 + 1.00685i
\(369\) −95878.8 + 6043.09i −0.704158 + 0.0443820i
\(370\) 9515.28 + 7164.14i 0.0695053 + 0.0523312i
\(371\) −106136. + 61277.9i −0.771111 + 0.445201i
\(372\) −188533. + 60714.2i −1.36239 + 0.438737i
\(373\) 2894.35 5013.15i 0.0208033 0.0360324i −0.855436 0.517908i \(-0.826711\pi\)
0.876240 + 0.481876i \(0.160044\pi\)
\(374\) 2080.51 + 4895.78i 0.0148740 + 0.0350008i
\(375\) −10759.9 + 20069.9i −0.0765149 + 0.142719i
\(376\) 3586.83 + 22466.9i 0.0253709 + 0.158916i
\(377\) 176129. 1.23922
\(378\) −32120.4 59323.1i −0.224801 0.415183i
\(379\) 217930.i 1.51719i 0.651565 + 0.758593i \(0.274113\pi\)
−0.651565 + 0.758593i \(0.725887\pi\)
\(380\) −8589.81 8281.44i −0.0594862 0.0573507i
\(381\) 166412. + 89217.4i 1.14640 + 0.614610i
\(382\) 48765.0 + 114752.i 0.334181 + 0.786381i
\(383\) 60187.2 + 34749.1i 0.410305 + 0.236890i 0.690921 0.722930i \(-0.257205\pi\)
−0.280616 + 0.959820i \(0.590539\pi\)
\(384\) 33090.7 + 143695.i 0.224411 + 0.974495i
\(385\) −117.446 203.422i −0.000792348 0.00137239i
\(386\) −86267.6 64951.7i −0.578993 0.435929i
\(387\) 119835. + 59469.8i 0.800134 + 0.397077i
\(388\) 30157.9 + 104848.i 0.200326 + 0.696458i
\(389\) −28733.0 49767.0i −0.189881 0.328884i 0.755329 0.655345i \(-0.227477\pi\)
−0.945210 + 0.326462i \(0.894144\pi\)
\(390\) 1817.15 20071.2i 0.0119471 0.131961i
\(391\) −144835. 83620.5i −0.947371 0.546965i
\(392\) 75261.8 + 92706.5i 0.489782 + 0.603306i
\(393\) 218362. 135407.i 1.41381 0.876712i
\(394\) −5060.76 + 41357.2i −0.0326004 + 0.266415i
\(395\) 10431.7i 0.0668595i
\(396\) −4938.07 4194.66i −0.0314896 0.0267489i
\(397\) 13255.8 0.0841056 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(398\) 33504.8 + 4099.89i 0.211515 + 0.0258825i
\(399\) 76416.4 2405.82i 0.479999 0.0151118i
\(400\) 5808.42 + 158838.i 0.0363026 + 0.992737i
\(401\) 2687.66 4655.16i 0.0167142 0.0289498i −0.857547 0.514405i \(-0.828013\pi\)
0.874262 + 0.485455i \(0.161346\pi\)
\(402\) −33308.4 71997.5i −0.206111 0.445518i
\(403\) 328350. 189573.i 2.02175 1.16726i
\(404\) 13671.3 + 47529.7i 0.0837618 + 0.291208i
\(405\) 8058.54 + 10611.7i 0.0491299 + 0.0646959i
\(406\) −35565.1 + 47236.9i −0.215761 + 0.286569i
\(407\) −6347.97 + 3665.00i −0.0383218 + 0.0221251i
\(408\) −100268. 115859.i −0.602338 0.695997i
\(409\) 120347. 208446.i 0.719427 1.24608i −0.241800 0.970326i \(-0.577738\pi\)
0.961227 0.275758i \(-0.0889289\pi\)
\(410\) 8867.43 3768.31i 0.0527509 0.0224170i
\(411\) −5567.10 + 175.269i −0.0329568 + 0.00103758i
\(412\) −125149. 120656.i −0.737282 0.710814i
\(413\) −139534. −0.818049
\(414\) 203348. + 11974.0i 1.18642 + 0.0698618i
\(415\) 16224.2i 0.0942035i
\(416\) −119816. 255572.i −0.692352 1.47682i
\(417\) −148554. + 92119.2i −0.854305 + 0.529758i
\(418\) 6758.04 2871.90i 0.0386784 0.0164368i
\(419\) −30669.6 17707.1i −0.174695 0.100860i 0.410103 0.912039i \(-0.365493\pi\)
−0.584798 + 0.811179i \(0.698826\pi\)
\(420\) 5016.08 + 4540.28i 0.0284358 + 0.0257385i
\(421\) 82548.0 + 142977.i 0.465739 + 0.806683i 0.999235 0.0391198i \(-0.0124554\pi\)
−0.533496 + 0.845803i \(0.679122\pi\)
\(422\) −55206.1 + 73323.7i −0.310000 + 0.411737i
\(423\) 25793.3 + 12800.2i 0.144154 + 0.0715381i
\(424\) 121110. 316670.i 0.673673 1.76147i
\(425\) −82579.3 143032.i −0.457187 0.791870i
\(426\) −10872.8 + 15428.5i −0.0599132 + 0.0850168i
\(427\) 33393.2 + 19279.6i 0.183148 + 0.105741i
\(428\) −54422.7 + 219045.i −0.297093 + 1.19577i
\(429\) 10930.8 + 5860.23i 0.0593931 + 0.0318420i
\(430\) −13317.7 1629.65i −0.0720264 0.00881366i
\(431\) 161673.i 0.870327i −0.900351 0.435163i \(-0.856691\pi\)
0.900351 0.435163i \(-0.143309\pi\)
\(432\) 172423. + 71405.8i 0.923906 + 0.382619i
\(433\) −61835.3 −0.329808 −0.164904 0.986310i \(-0.552731\pi\)
−0.164904 + 0.986310i \(0.552731\pi\)
\(434\) −15460.1 + 126342.i −0.0820791 + 0.670761i
\(435\) 5518.35 10293.1i 0.0291629 0.0543960i
\(436\) −253544. 62994.2i −1.33377 0.331381i
\(437\) −115428. + 199927.i −0.604434 + 1.04691i
\(438\) 43913.6 + 30946.9i 0.228903 + 0.161313i
\(439\) −268021. + 154742.i −1.39072 + 0.802933i −0.993395 0.114744i \(-0.963395\pi\)
−0.397326 + 0.917677i \(0.630062\pi\)
\(440\) 606.933 + 232.121i 0.00313499 + 0.00119897i
\(441\) 150829. 9506.54i 0.775548 0.0488816i
\(442\) 234312. + 176416.i 1.19936 + 0.903011i
\(443\) 40615.5 23449.4i 0.206959 0.119488i −0.392938 0.919565i \(-0.628541\pi\)
0.599897 + 0.800077i \(0.295208\pi\)
\(444\) 141683. 156531.i 0.718709 0.794027i
\(445\) −8997.07 + 15583.4i −0.0454340 + 0.0786940i
\(446\) −100531. 236566.i −0.505396 1.18928i
\(447\) −2937.27 4736.74i −0.0147004 0.0237063i
\(448\) 92737.3 + 19472.8i 0.462060 + 0.0970226i
\(449\) −124857. −0.619328 −0.309664 0.950846i \(-0.600217\pi\)
−0.309664 + 0.950846i \(0.600217\pi\)
\(450\) 167999. + 110649.i 0.829625 + 0.546413i
\(451\) 5929.43i 0.0291514i
\(452\) 131294. 136183.i 0.642639 0.666569i
\(453\) 1228.96 + 39035.8i 0.00598883 + 0.190224i
\(454\) −10490.1 24685.0i −0.0508944 0.119763i
\(455\) −11216.0 6475.56i −0.0541771 0.0312791i
\(456\) −159929. + 138407.i −0.769125 + 0.665625i
\(457\) 62748.5 + 108684.i 0.300449 + 0.520393i 0.976238 0.216703i \(-0.0695302\pi\)
−0.675789 + 0.737095i \(0.736197\pi\)
\(458\) −113602. 85532.1i −0.541571 0.407754i
\(459\) −193057. + 18282.4i −0.916348 + 0.0867775i
\(460\) −19633.3 + 5647.25i −0.0927852 + 0.0266883i
\(461\) −51647.4 89455.9i −0.243022 0.420927i 0.718551 0.695474i \(-0.244806\pi\)
−0.961574 + 0.274547i \(0.911472\pi\)
\(462\) −3778.91 + 1748.25i −0.0177044 + 0.00819066i
\(463\) −277564. 160252.i −1.29480 0.747552i −0.315297 0.948993i \(-0.602104\pi\)
−0.979501 + 0.201442i \(0.935437\pi\)
\(464\) −5977.62 163465.i −0.0277646 0.759257i
\(465\) −791.122 25128.6i −0.00365879 0.116215i
\(466\) −30336.1 + 247910.i −0.139697 + 1.14162i
\(467\) 427381.i 1.95967i 0.199820 + 0.979833i \(0.435964\pi\)
−0.199820 + 0.979833i \(0.564036\pi\)
\(468\) −351431. 64159.8i −1.60453 0.292935i
\(469\) −50979.2 −0.231765
\(470\) −2866.49 350.764i −0.0129764 0.00158788i
\(471\) 29443.6 + 47481.7i 0.132724 + 0.214035i
\(472\) 299684. 243292.i 1.34518 1.09205i
\(473\) 4128.49 7150.76i 0.0184531 0.0319617i
\(474\) 184161. + 16673.1i 0.819674 + 0.0742094i
\(475\) −197438. + 113991.i −0.875071 + 0.505223i
\(476\) −94627.9 + 27218.4i −0.417643 + 0.120129i
\(477\) −237499. 357377.i −1.04382 1.57069i
\(478\) −9030.61 + 11994.3i −0.0395240 + 0.0524951i
\(479\) 166330. 96030.5i 0.724935 0.418541i −0.0916316 0.995793i \(-0.529208\pi\)
0.816566 + 0.577252i \(0.195875\pi\)
\(480\) −18689.8 1005.30i −0.0811188 0.00436330i
\(481\) −202076. + 350006.i −0.873422 + 1.51281i
\(482\) −330091. + 140276.i −1.42082 + 0.603793i
\(483\) 61852.1 115369.i 0.265131 0.494534i
\(484\) 162312. 168356.i 0.692882 0.718682i
\(485\) −13848.1 −0.0588715
\(486\) 200219. 125304.i 0.847680 0.530508i
\(487\) 52885.1i 0.222985i 0.993765 + 0.111492i \(0.0355631\pi\)
−0.993765 + 0.111492i \(0.964437\pi\)
\(488\) −105337. + 16816.9i −0.442323 + 0.0706167i
\(489\) −125777. 67432.0i −0.525999 0.282000i
\(490\) −13949.6 + 5928.02i −0.0580991 + 0.0246898i
\(491\) −6368.89 3677.08i −0.0264180 0.0152525i 0.486733 0.873551i \(-0.338189\pi\)
−0.513151 + 0.858298i \(0.671522\pi\)
\(492\) −52352.5 162568.i −0.216275 0.671590i
\(493\) 84984.9 + 147198.i 0.349662 + 0.605632i
\(494\) 243521. 323440.i 0.997890 1.32538i
\(495\) 684.952 455.193i 0.00279544 0.00185774i
\(496\) −187086. 298308.i −0.760465 1.21255i
\(497\) 6064.75 + 10504.4i 0.0245527 + 0.0425266i
\(498\) 286420. + 25931.2i 1.15490 + 0.104559i
\(499\) 359442. + 207524.i 1.44354 + 0.833426i 0.998084 0.0618804i \(-0.0197097\pi\)
0.445452 + 0.895306i \(0.353043\pi\)
\(500\) −39289.5 9761.65i −0.157158 0.0390466i
\(501\) −3204.80 + 1987.31i −0.0127681 + 0.00791756i
\(502\) −36712.1 4492.35i −0.145681 0.0178265i
\(503\) 53242.3i 0.210436i 0.994449 + 0.105218i \(0.0335541\pi\)
−0.994449 + 0.105218i \(0.966446\pi\)
\(504\) 88170.8 81296.7i 0.347107 0.320046i
\(505\) −6277.63 −0.0246157
\(506\) 1527.07 12479.4i 0.00596426 0.0487408i
\(507\) 426577. 13429.9i 1.65952 0.0522465i
\(508\) −80940.1 + 325775.i −0.313644 + 1.26238i
\(509\) 248630. 430640.i 0.959662 1.66218i 0.236344 0.971669i \(-0.424051\pi\)
0.723319 0.690515i \(-0.242616\pi\)
\(510\) 17651.2 8166.02i 0.0678631 0.0313957i
\(511\) 29898.4 17261.9i 0.114500 0.0661068i
\(512\) −233130. + 119875.i −0.889320 + 0.457286i
\(513\) 25236.6 + 266492.i 0.0958952 + 1.01263i
\(514\) −48730.9 36689.9i −0.184450 0.138874i
\(515\) 19109.5 11032.9i 0.0720501 0.0415981i
\(516\) −50055.3 + 232504.i −0.187997 + 0.873236i
\(517\) 888.614 1539.12i 0.00332454 0.00575828i
\(518\) −53065.4 124871.i −0.197766 0.465375i
\(519\) −172722. + 5437.79i −0.641227 + 0.0201877i
\(520\) 35380.1 5648.42i 0.130843 0.0208891i
\(521\) −58965.8 −0.217233 −0.108616 0.994084i \(-0.534642\pi\)
−0.108616 + 0.994084i \(0.534642\pi\)
\(522\) −172893. 113872.i −0.634507 0.417903i
\(523\) 117488.i 0.429527i 0.976666 + 0.214763i \(0.0688980\pi\)
−0.976666 + 0.214763i \(0.931102\pi\)
\(524\) 328840. + 317035.i 1.19763 + 1.15463i
\(525\) 109865. 68127.8i 0.398603 0.247176i
\(526\) 161638. + 380361.i 0.584215 + 1.37475i
\(527\) 316868. + 182944.i 1.14093 + 0.658714i
\(528\) 5067.90 10343.7i 0.0181786 0.0371031i
\(529\) 57713.8 + 99963.2i 0.206238 + 0.357214i
\(530\) 34379.8 + 25884.8i 0.122391 + 0.0921497i
\(531\) −30731.0 487573.i −0.108990 1.72922i
\(532\) 37571.7 + 130623.i 0.132751 + 0.461525i
\(533\) 163465. + 283129.i 0.575399 + 0.996620i
\(534\) 260727. + 183740.i 0.914333 + 0.644350i
\(535\) −24810.8 14324.5i −0.0866828 0.0500463i
\(536\) 109491. 88887.9i 0.381108 0.309395i
\(537\) −395185. 211867.i −1.37041 0.734709i
\(538\) 41791.3 341524.i 0.144385 1.17993i
\(539\) 9327.75i 0.0321070i
\(540\) −14760.4 + 18527.7i −0.0506185 + 0.0635380i
\(541\) −16461.8 −0.0562448 −0.0281224 0.999604i \(-0.508953\pi\)
−0.0281224 + 0.999604i \(0.508953\pi\)
\(542\) 62053.1 + 7593.26i 0.211235 + 0.0258482i
\(543\) −59410.5 + 110815.i −0.201495 + 0.375837i
\(544\) 155779. 223453.i 0.526395 0.755071i
\(545\) 16580.6 28718.4i 0.0558222 0.0966869i
\(546\) −132246. + 187656.i −0.443604 + 0.629474i
\(547\) −337391. + 194793.i −1.12761 + 0.651026i −0.943333 0.331848i \(-0.892328\pi\)
−0.184277 + 0.982874i \(0.558994\pi\)
\(548\) −2737.18 9516.13i −0.00911470 0.0316883i
\(549\) −60014.2 + 120932.i −0.199118 + 0.401234i
\(550\) 7468.01 9918.87i 0.0246876 0.0327897i
\(551\) 203189. 117312.i 0.669265 0.386400i
\(552\) 68316.1 + 355631.i 0.224205 + 1.16714i
\(553\) 59415.7 102911.i 0.194290 0.336521i
\(554\) −208420. + 88570.1i −0.679077 + 0.288581i
\(555\) 14123.3 + 22775.6i 0.0458510 + 0.0739407i
\(556\) −223714. 215682.i −0.723674 0.697694i
\(557\) 434133. 1.39931 0.699653 0.714483i \(-0.253338\pi\)
0.699653 + 0.714483i \(0.253338\pi\)
\(558\) −444882. 26196.6i −1.42882 0.0841350i
\(559\) 455263.i 1.45693i
\(560\) −5629.31 + 10629.3i −0.0179506 + 0.0338946i
\(561\) 376.630 + 11963.0i 0.00119671 + 0.0380113i
\(562\) 408879. 173758.i 1.29456 0.550137i
\(563\) −192477. 111127.i −0.607244 0.350592i 0.164642 0.986353i \(-0.447353\pi\)
−0.771886 + 0.635761i \(0.780686\pi\)
\(564\) −10773.9 + 50044.1i −0.0338698 + 0.157324i
\(565\) 12005.6 + 20794.2i 0.0376084 + 0.0651397i
\(566\) −219417. + 291425.i −0.684916 + 0.909692i
\(567\) −19058.0 150585.i −0.0592805 0.468400i
\(568\) −31341.2 11986.4i −0.0971448 0.0371529i
\(569\) −1962.56 3399.25i −0.00606175 0.0104993i 0.862979 0.505240i \(-0.168596\pi\)
−0.869040 + 0.494741i \(0.835263\pi\)
\(570\) −11272.2 24365.3i −0.0346944 0.0749934i
\(571\) −331554. 191423.i −1.01691 0.587112i −0.103702 0.994608i \(-0.533069\pi\)
−0.913207 + 0.407496i \(0.866402\pi\)
\(572\) −5316.54 + 21398.5i −0.0162494 + 0.0654020i
\(573\) 8827.80 + 280399.i 0.0268871 + 0.854019i
\(574\) −108942. 13330.9i −0.330652 0.0404609i
\(575\) 390347.i 1.18063i
\(576\) −47619.5 + 328341.i −0.143529 + 0.989646i
\(577\) 18219.2 0.0547239 0.0273620 0.999626i \(-0.491289\pi\)
0.0273620 + 0.999626i \(0.491289\pi\)
\(578\) 6199.39 50662.3i 0.0185564 0.151645i
\(579\) −128045. 206489.i −0.381948 0.615941i
\(580\) 20150.1 + 5006.38i 0.0598992 + 0.0148822i
\(581\) 92407.6 160055.i 0.273751 0.474150i
\(582\) −22133.4 + 244472.i −0.0653433 + 0.721745i
\(583\) −22935.9 + 13242.0i −0.0674806 + 0.0389599i
\(584\) −34116.5 + 89205.4i −0.100032 + 0.261556i
\(585\) 20157.4 40618.3i 0.0589009 0.118689i
\(586\) −265277. 199730.i −0.772510 0.581630i
\(587\) −45835.0 + 26462.8i −0.133021 + 0.0767998i −0.565034 0.825068i \(-0.691137\pi\)
0.432013 + 0.901868i \(0.357804\pi\)
\(588\) 82357.1 + 255739.i 0.238202 + 0.739678i
\(589\) 252532. 437399.i 0.727924 1.26080i
\(590\) 19163.0 + 45093.6i 0.0550503 + 0.129542i
\(591\) −44295.9 + 82622.8i −0.126820 + 0.236551i
\(592\) 331698. + 175668.i 0.946455 + 0.501243i
\(593\) 216280. 0.615046 0.307523 0.951541i \(-0.400500\pi\)
0.307523 + 0.951541i \(0.400500\pi\)
\(594\) −6941.17 12819.6i −0.0196725 0.0363331i
\(595\) 12498.3i 0.0353033i
\(596\) 6877.16 7133.24i 0.0193605 0.0200814i
\(597\) 66935.4 + 35885.6i 0.187805 + 0.100686i
\(598\) −271119. 637986.i −0.758154 1.78406i
\(599\) −260151. 150198.i −0.725057 0.418612i 0.0915543 0.995800i \(-0.470816\pi\)
−0.816611 + 0.577188i \(0.804150\pi\)
\(600\) −117175. + 337883.i −0.325485 + 0.938565i
\(601\) −255485. 442514.i −0.707322 1.22512i −0.965847 0.259113i \(-0.916570\pi\)
0.258525 0.966005i \(-0.416764\pi\)
\(602\) 122099. + 91929.8i 0.336915 + 0.253667i
\(603\) −11227.7 178137.i −0.0308785 0.489913i
\(604\) −66725.9 + 19192.8i −0.182903 + 0.0526094i
\(605\) 14841.8 + 25706.8i 0.0405487 + 0.0702324i
\(606\) −10033.5 + 110825.i −0.0273218 + 0.301780i
\(607\) 154217. + 89037.5i 0.418558 + 0.241655i 0.694460 0.719531i \(-0.255643\pi\)
−0.275902 + 0.961186i \(0.588976\pi\)
\(608\) −308450. 215035.i −0.834405 0.581703i
\(609\) −113065. + 70112.4i −0.304856 + 0.189043i
\(610\) 1644.56 13439.6i 0.00441968 0.0361182i
\(611\) 97990.4i 0.262483i
\(612\) −115950. 324664.i −0.309577 0.866825i
\(613\) 570495. 1.51821 0.759103 0.650970i \(-0.225638\pi\)
0.759103 + 0.650970i \(0.225638\pi\)
\(614\) −258876. 31677.9i −0.686681 0.0840272i
\(615\) 21667.8 682.167i 0.0572881 0.00180360i
\(616\) −4665.42 5746.80i −0.0122950 0.0151448i
\(617\) −107951. + 186976.i −0.283567 + 0.491153i −0.972261 0.233900i \(-0.924851\pi\)
0.688694 + 0.725052i \(0.258185\pi\)
\(618\) −164230. 354991.i −0.430008 0.929480i
\(619\) 158318. 91404.9i 0.413189 0.238555i −0.278970 0.960300i \(-0.589993\pi\)
0.692159 + 0.721745i \(0.256660\pi\)
\(620\) 42953.6 12355.0i 0.111742 0.0321410i
\(621\) 416758. + 190721.i 1.08069 + 0.494556i
\(622\) −321672. + 427238.i −0.831442 + 1.10431i
\(623\) 177515. 102489.i 0.457362 0.264058i
\(624\) −43168.6 633624.i −0.110866 1.62728i
\(625\) −191454. + 331608.i −0.490123 + 0.848918i
\(626\) 41378.9 17584.4i 0.105592 0.0448724i
\(627\) 16513.4 519.893i 0.0420052 0.00132245i
\(628\) −68937.6 + 71504.6i −0.174798 + 0.181307i
\(629\) −390019. −0.985791
\(630\) 6823.34 + 13608.0i 0.0171916 + 0.0342858i
\(631\) 153307.i 0.385037i 0.981293 + 0.192518i \(0.0616655\pi\)
−0.981293 + 0.192518i \(0.938335\pi\)
\(632\) 51826.4 + 324626.i 0.129753 + 0.812734i
\(633\) −175506. + 108832.i −0.438011 + 0.271613i
\(634\) −144333. + 61335.7i −0.359076 + 0.152593i
\(635\) −36899.8 21304.1i −0.0915117 0.0528343i
\(636\) 511918. 565565.i 1.26557 1.39820i
\(637\) −257150. 445397.i −0.633736 1.09766i
\(638\) −7685.56 + 10207.8i −0.0188814 + 0.0250779i
\(639\) −35370.0 + 23505.6i −0.0866231 + 0.0575664i
\(640\) −6443.06 32644.5i −0.0157301 0.0796986i
\(641\) −196626. 340566.i −0.478547 0.828869i 0.521150 0.853465i \(-0.325503\pi\)
−0.999697 + 0.0245966i \(0.992170\pi\)
\(642\) −292539. + 415112.i −0.709763 + 1.00715i
\(643\) 384971. + 222263.i 0.931120 + 0.537583i 0.887166 0.461451i \(-0.152671\pi\)
0.0439545 + 0.999034i \(0.486004\pi\)
\(644\) 225851. + 56113.7i 0.544566 + 0.135300i
\(645\) −26605.9 14264.0i −0.0639525 0.0342864i
\(646\) 387815. + 47455.8i 0.929309 + 0.113717i
\(647\) 152505.i 0.364314i 0.983269 + 0.182157i \(0.0583079\pi\)
−0.983269 + 0.182157i \(0.941692\pi\)
\(648\) 303494. + 290191.i 0.722770 + 0.691088i
\(649\) −30153.0 −0.0715881
\(650\) 83148.9 679504.i 0.196802 1.60829i
\(651\) −135319. + 252404.i −0.319299 + 0.595572i
\(652\) 61176.0 246226.i 0.143908 0.579214i
\(653\) 149617. 259144.i 0.350876 0.607736i −0.635527 0.772079i \(-0.719217\pi\)
0.986403 + 0.164343i \(0.0525504\pi\)
\(654\) −480492. 338613.i −1.12339 0.791677i
\(655\) −50211.7 + 28989.8i −0.117037 + 0.0675713i
\(656\) 257224. 161321.i 0.597728 0.374871i
\(657\) 66903.0 + 100672.i 0.154994 + 0.233227i
\(658\) 26280.6 + 19786.9i 0.0606992 + 0.0457010i
\(659\) −361192. + 208535.i −0.831702 + 0.480183i −0.854435 0.519558i \(-0.826097\pi\)
0.0227330 + 0.999742i \(0.492763\pi\)
\(660\) 1083.97 + 981.145i 0.00248844 + 0.00225240i
\(661\) −379775. + 657790.i −0.869208 + 1.50551i −0.00639999 + 0.999980i \(0.502037\pi\)
−0.862808 + 0.505532i \(0.831296\pi\)
\(662\) 116944. + 275188.i 0.266847 + 0.627933i
\(663\) 347783. + 560846.i 0.791191 + 1.27590i
\(664\) 80604.0 + 504881.i 0.182819 + 1.14512i
\(665\) −17252.3 −0.0390126
\(666\) 424651. 212928.i 0.957380 0.480048i
\(667\) 401718.i 0.902962i
\(668\) −4826.24 4652.98i −0.0108157 0.0104275i
\(669\) −18198.9 578056.i −0.0406625 1.29157i
\(670\) 7001.28 + 16475.1i 0.0155965 + 0.0367011i
\(671\) 7216.22 + 4166.29i 0.0160275 + 0.00925346i
\(672\) 178652. + 116368.i 0.395612 + 0.257689i
\(673\) 18836.0 + 32624.9i 0.0415871 + 0.0720309i 0.886070 0.463552i \(-0.153425\pi\)
−0.844483 + 0.535583i \(0.820092\pi\)
\(674\) 453184. + 341207.i 0.997597 + 0.751100i
\(675\) 262256. + 368897.i 0.575596 + 0.809651i
\(676\) 209735. + 729170.i 0.458964 + 1.59564i
\(677\) 347010. + 601039.i 0.757120 + 1.31137i 0.944313 + 0.329047i \(0.106728\pi\)
−0.187193 + 0.982323i \(0.559939\pi\)
\(678\) 386288. 178710.i 0.840334 0.388766i
\(679\) 136614. + 78873.9i 0.296315 + 0.171078i
\(680\) 21792.1 + 26843.2i 0.0471282 + 0.0580519i
\(681\) −1899.01 60318.5i −0.00409479 0.130064i
\(682\) −3340.90 + 27302.3i −0.00718281 + 0.0586989i
\(683\) 357197.i 0.765714i −0.923808 0.382857i \(-0.874940\pi\)
0.923808 0.382857i \(-0.125060\pi\)
\(684\) −448160. + 160055.i −0.957901 + 0.342104i
\(685\) 1256.87 0.00267861
\(686\) 391920. + 47958.0i 0.832815 + 0.101909i
\(687\) −168616. 271916.i −0.357261 0.576131i
\(688\) −422529. + 15451.1i −0.892647 + 0.0326425i
\(689\) −730122. + 1.26461e6i −1.53800 + 2.66390i
\(690\) −45778.9 4144.60i −0.0961539 0.00870532i
\(691\) 384473. 221976.i 0.805212 0.464889i −0.0400786 0.999197i \(-0.512761\pi\)
0.845290 + 0.534307i \(0.179427\pi\)
\(692\) −84922.2 295242.i −0.177341 0.616547i
\(693\) −9349.80 + 589.303i −0.0194686 + 0.00122708i
\(694\) 440359. 584876.i 0.914297 1.21435i
\(695\) 34159.6 19722.1i 0.0707202 0.0408304i
\(696\) 120588. 347726.i 0.248935 0.717826i
\(697\) −157749. + 273228.i −0.324713 + 0.562420i
\(698\) 495358. 210508.i 1.01674 0.432073i
\(699\) −265526. + 495272.i −0.543442 + 1.01365i
\(700\) 165450. + 159510.i 0.337653 + 0.325531i
\(701\) −483771. −0.984474 −0.492237 0.870461i \(-0.663821\pi\)
−0.492237 + 0.870461i \(0.663821\pi\)
\(702\) −684854. 420777.i −1.38971 0.853842i
\(703\) 538375.i 1.08937i
\(704\) 20040.4 + 4208.04i 0.0404353 + 0.00849053i
\(705\) −5726.62 3070.17i −0.0115218 0.00617710i
\(706\) −737299. + 313323.i −1.47922 + 0.628612i
\(707\) 61929.9 + 35755.3i 0.123897 + 0.0715321i
\(708\) 826707. 266229.i 1.64924 0.531114i
\(709\) −79169.5 137126.i −0.157494 0.272788i 0.776470 0.630154i \(-0.217008\pi\)
−0.933965 + 0.357366i \(0.883675\pi\)
\(710\) 2561.85 3402.60i 0.00508203 0.00674986i
\(711\) 372688. + 184951.i 0.737236 + 0.365863i
\(712\) −202559. + 529638.i −0.399569 + 1.04477i
\(713\) −432382. 748907.i −0.850527 1.47316i
\(714\) −220643. 19976.0i −0.432807 0.0391843i
\(715\) −2423.76 1399.36i −0.00474108 0.00273726i
\(716\) 192211. 773627.i 0.374932 1.50906i
\(717\) −28709.3 + 17802.8i −0.0558450 + 0.0346297i
\(718\) 639941. + 78307.7i 1.24134 + 0.151899i
\(719\) 781622.i 1.51196i −0.654597 0.755978i \(-0.727162\pi\)
0.654597 0.755978i \(-0.272838\pi\)
\(720\) −38382.0 17329.5i −0.0740393 0.0334288i
\(721\) −251358. −0.483529
\(722\) 2191.38 17908.3i 0.00420381 0.0343541i
\(723\) −806587. + 25393.8i −1.54303 + 0.0485792i
\(724\) −216936. 53898.7i −0.413861 0.102826i
\(725\) 198358. 343566.i 0.377375 0.653633i
\(726\) 477548. 220929.i 0.906032 0.419160i
\(727\) 51590.1 29785.6i 0.0976107 0.0563556i −0.450400 0.892827i \(-0.648719\pi\)
0.548011 + 0.836471i \(0.315385\pi\)
\(728\) −381202. 145790.i −0.719271 0.275085i
\(729\) 521994. 99759.6i 0.982223 0.187715i
\(730\) −9684.71 7291.71i −0.0181736 0.0136831i
\(731\) 380482. 219672.i 0.712032 0.411092i
\(732\) −234633. 50513.5i −0.437892 0.0942726i
\(733\) 106923. 185196.i 0.199004 0.344685i −0.749202 0.662342i \(-0.769563\pi\)
0.948206 + 0.317657i \(0.102896\pi\)
\(734\) 312207. + 734674.i 0.579497 + 1.36365i
\(735\) −34086.2 + 1073.13i −0.0630963 + 0.00198646i
\(736\) −582914. + 273278.i −1.07609 + 0.504486i
\(737\) −11016.5 −0.0202819
\(738\) 22588.8 383612.i 0.0414744 0.704335i
\(739\) 218903.i 0.400832i −0.979711 0.200416i \(-0.935771\pi\)
0.979711 0.200416i \(-0.0642294\pi\)
\(740\) −33067.3 + 34298.7i −0.0603860 + 0.0626345i
\(741\) 774180. 480073.i 1.40996 0.874320i
\(742\) −191731. 451174.i −0.348245 0.819476i
\(743\) −431487. 249119.i −0.781610 0.451263i 0.0553907 0.998465i \(-0.482360\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(744\) −149461. 778045.i −0.270012 1.40559i
\(745\) 628.850 + 1089.20i 0.00113301 + 0.00196243i
\(746\) 18497.9 + 13927.3i 0.0332388 + 0.0250258i
\(747\) 579631. + 287650.i 1.03875 + 0.515493i
\(748\) −20448.9 + 5881.85i −0.0365483 + 0.0105126i
\(749\) 163175. + 282628.i 0.290864 + 0.503792i
\(750\) −74457.5 52471.8i −0.132369 0.0932833i
\(751\) 534346. + 308505.i 0.947421 + 0.546994i 0.892279 0.451485i \(-0.149106\pi\)
0.0551419 + 0.998479i \(0.482439\pi\)
\(752\) −90944.9 + 3325.69i −0.160821 + 0.00588093i
\(753\) −73342.9 39320.8i −0.129350 0.0693477i
\(754\) −85571.1 + 699299.i −0.150517 + 1.23004i
\(755\) 8813.01i 0.0154607i
\(756\) 251141. 98708.7i 0.439414 0.172708i
\(757\) 483106. 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(758\) −865266. 105880.i −1.50595 0.184279i
\(759\) 13366.1 24931.1i 0.0232018 0.0432771i
\(760\) 37053.8 30081.4i 0.0641513 0.0520799i
\(761\) 68847.3 119247.i 0.118882 0.205910i −0.800443 0.599409i \(-0.795402\pi\)
0.919325 + 0.393499i \(0.128736\pi\)
\(762\) −435078. + 617375.i −0.749302 + 1.06326i
\(763\) −327141. + 188875.i −0.561935 + 0.324433i
\(764\) −479301. + 137864.i −0.821148 + 0.236192i
\(765\) 43672.7 2752.62i 0.0746255 0.00470353i
\(766\) −167209. + 222084.i −0.284972 + 0.378494i
\(767\) −1.43980e6 + 831268.i −2.44743 + 1.41303i
\(768\) −586602. + 61569.3i −0.994537 + 0.104386i
\(769\) 173385. 300311.i 0.293196 0.507830i −0.681368 0.731941i \(-0.738614\pi\)
0.974564 + 0.224111i \(0.0719478\pi\)
\(770\) 864.724 367.473i 0.00145847 0.000619790i
\(771\) −72329.9 116641.i −0.121677 0.196220i
\(772\) 299796. 310959.i 0.503027 0.521758i
\(773\) −456941. −0.764717 −0.382358 0.924014i \(-0.624888\pi\)
−0.382358 + 0.924014i \(0.624888\pi\)
\(774\) −294339. + 446899.i −0.491322 + 0.745981i
\(775\) 853996.i 1.42185i
\(776\) −430938. + 68799.0i −0.715634 + 0.114251i
\(777\) −9606.30 305127.i −0.0159116 0.505403i
\(778\) 211554. 89902.1i 0.349512 0.148529i
\(779\) 377159. + 217753.i 0.621512 + 0.358830i
\(780\) 78807.7 + 16966.3i 0.129533 + 0.0278867i
\(781\) 1310.58 + 2269.99i 0.00214863 + 0.00372154i
\(782\) 402373. 534424.i 0.657984 0.873922i
\(783\) −269896. 379643.i −0.440223 0.619230i
\(784\) −404646. + 253777.i −0.658329 + 0.412877i
\(785\) −6303.68 10918.3i −0.0102295 0.0177180i
\(786\) 431529. + 932768.i 0.698498 + 1.50983i
\(787\) −602982. 348132.i −0.973543 0.562075i −0.0732283 0.997315i \(-0.523330\pi\)
−0.900314 + 0.435240i \(0.856663\pi\)
\(788\) −161745. 40186.4i −0.260483 0.0647182i
\(789\) 29261.0 + 929423.i 0.0470040 + 1.49300i
\(790\) −41418.1 5068.21i −0.0663645 0.00812082i
\(791\) 273518.i 0.437153i
\(792\) 19053.6 17568.1i 0.0303757 0.0280075i
\(793\) 459430. 0.730589
\(794\) −6440.25 + 52630.6i −0.0102156 + 0.0834829i
\(795\) 51028.9 + 82290.7i 0.0807387 + 0.130202i
\(796\) −32556.3 + 131035.i −0.0513817 + 0.206805i
\(797\) −65680.3 + 113762.i −0.103399 + 0.179093i −0.913083 0.407773i \(-0.866305\pi\)
0.809684 + 0.586867i \(0.199639\pi\)
\(798\) −27574.4 + 304571.i −0.0433013 + 0.478281i
\(799\) 81894.7 47281.9i 0.128281 0.0740631i
\(800\) −633470. 54108.9i −0.989796 0.0845451i
\(801\) 397222. + 597720.i 0.619111 + 0.931608i
\(802\) 17177.0 + 12932.7i 0.0267053 + 0.0201067i
\(803\) 6461.00 3730.26i 0.0100200 0.00578506i
\(804\) 302041. 97267.7i 0.467254 0.150472i
\(805\) −14769.6 + 25581.7i −0.0227917 + 0.0394764i
\(806\) 593151. + 1.39578e6i 0.913051 + 2.14855i
\(807\) 365791. 682291.i 0.561677 1.04767i
\(808\) −195353. + 31188.1i −0.299225 + 0.0477712i
\(809\) 796199. 1.21653 0.608267 0.793732i \(-0.291865\pi\)
0.608267 + 0.793732i \(0.291865\pi\)
\(810\) −46047.9 + 26839.8i −0.0701842 + 0.0409082i
\(811\) 116976.i 0.177851i 0.996038 + 0.0889253i \(0.0283432\pi\)
−0.996038 + 0.0889253i \(0.971657\pi\)
\(812\) −170270. 164157.i −0.258241 0.248970i
\(813\) 123969. + 66462.4i 0.187556 + 0.100553i
\(814\) −11467.3 26984.5i −0.0173067 0.0407254i
\(815\) 27889.5 + 16102.0i 0.0419881 + 0.0242418i
\(816\) 508717. 341812.i 0.764005 0.513342i
\(817\) −303230. 525210.i −0.454285 0.786845i
\(818\) 769142. + 579094.i 1.14948 + 0.865451i
\(819\) −430204. + 285897.i −0.641368 + 0.426228i
\(820\) 10653.4 + 37037.9i 0.0158439 + 0.0550832i
\(821\) −146773. 254219.i −0.217751 0.377157i 0.736369 0.676580i \(-0.236539\pi\)
−0.954120 + 0.299424i \(0.903206\pi\)
\(822\) 2008.86 22188.7i 0.00297307 0.0328388i
\(823\) 198711. + 114726.i 0.293375 + 0.169380i 0.639463 0.768822i \(-0.279157\pi\)
−0.346088 + 0.938202i \(0.612490\pi\)
\(824\) 539855. 438270.i 0.795102 0.645487i
\(825\) 23741.6 14722.3i 0.0348821 0.0216306i
\(826\) 67791.7 554003.i 0.0993611 0.811992i
\(827\) 673431.i 0.984651i −0.870411 0.492326i \(-0.836147\pi\)
0.870411 0.492326i \(-0.163853\pi\)
\(828\) −146337. + 801552.i −0.213448 + 1.16915i
\(829\) 268282. 0.390375 0.195188 0.980766i \(-0.437468\pi\)
0.195188 + 0.980766i \(0.437468\pi\)
\(830\) −64416.3 7882.43i −0.0935060 0.0114421i
\(831\) −509279. + 16033.6i −0.737486 + 0.0232183i
\(832\) 1.07293e6 351546.i 1.54998 0.507850i
\(833\) 248158. 429823.i 0.357634 0.619440i
\(834\) −293574. 634573.i −0.422071 0.912325i
\(835\) 736.936 425.470i 0.00105696 0.000610234i
\(836\) 8119.18 + 28227.3i 0.0116172 + 0.0403884i
\(837\) −911778. 417257.i −1.30148 0.595598i
\(838\) 85204.7 113167.i 0.121332 0.161151i
\(839\) 867924. 501096.i 1.23299 0.711865i 0.265334 0.964156i \(-0.414518\pi\)
0.967651 + 0.252292i \(0.0811843\pi\)
\(840\) −20463.7 + 17709.9i −0.0290018 + 0.0250991i
\(841\) 149504. 258949.i 0.211379 0.366119i
\(842\) −607780. + 258283.i −0.857279 + 0.364310i
\(843\) 999108. 31454.9i 1.40591 0.0442622i
\(844\) −264302. 254813.i −0.371035 0.357715i
\(845\) −96307.2 −0.134879
\(846\) −63353.4 + 96190.2i −0.0885175 + 0.134397i
\(847\) 338137.i 0.471330i
\(848\) 1.19846e6 + 634707.i 1.66661 + 0.882636i
\(849\) −697550. + 432554.i −0.967743 + 0.600102i
\(850\) 608011. 258381.i 0.841538 0.357620i
\(851\) 798300. + 460899.i 1.10232 + 0.636424i
\(852\) −55974.6 50665.1i −0.0771102 0.0697958i
\(853\) −205795. 356448.i −0.282837 0.489889i 0.689245 0.724528i \(-0.257942\pi\)
−0.972082 + 0.234640i \(0.924609\pi\)
\(854\) −92771.3 + 123217.i −0.127203 + 0.168949i
\(855\) −3799.67 60284.9i −0.00519772 0.0824663i
\(856\) −843253. 322501.i −1.15083 0.440133i
\(857\) 460403. + 797442.i 0.626869 + 1.08577i 0.988176 + 0.153322i \(0.0489972\pi\)
−0.361307 + 0.932447i \(0.617669\pi\)
\(858\) −28578.0 + 40552.2i −0.0388202 + 0.0550859i
\(859\) 520799. + 300684.i 0.705804 + 0.407496i 0.809505 0.587112i \(-0.199735\pi\)
−0.103702 + 0.994608i \(0.533069\pi\)
\(860\) 12940.6 52084.6i 0.0174968 0.0704226i
\(861\) −217642. 116683.i −0.293587 0.157399i
\(862\) 641903. + 78547.8i 0.863883 + 0.105711i
\(863\) 1.01872e6i 1.36783i 0.729560 + 0.683917i \(0.239725\pi\)
−0.729560 + 0.683917i \(0.760275\pi\)
\(864\) −367279. + 649894.i −0.492005 + 0.870593i
\(865\) 38994.9 0.0521166
\(866\) 30042.3 245510.i 0.0400588 0.327366i
\(867\) 54262.2 101212.i 0.0721870 0.134647i
\(868\) −494115. 122765.i −0.655826 0.162943i
\(869\) 12839.6 22238.9i 0.0170025 0.0294492i
\(870\) 38186.4 + 26910.8i 0.0504511 + 0.0355540i
\(871\) −526036. + 303707.i −0.693392 + 0.400330i
\(872\) 373294. 976063.i 0.490929 1.28365i
\(873\) −245521. + 494740.i −0.322152 + 0.649156i
\(874\) −737709. 555428.i −0.965744 0.727118i
\(875\) −50694.1 + 29268.3i −0.0662128 + 0.0382280i
\(876\) −144206. + 159319.i −0.187921 + 0.207615i
\(877\) −432672. + 749411.i −0.562549 + 0.974363i 0.434724 + 0.900564i \(0.356846\pi\)
−0.997273 + 0.0737993i \(0.976488\pi\)
\(878\) −484169. 1.13933e6i −0.628070 1.47795i
\(879\) −393743. 634962.i −0.509607 0.821807i
\(880\) −1216.48 + 2296.98i −0.00157087 + 0.00296615i
\(881\) 1.46275e6 1.88459 0.942296 0.334780i \(-0.108662\pi\)
0.942296 + 0.334780i \(0.108662\pi\)
\(882\) −35535.0 + 603470.i −0.0456792 + 0.775744i
\(883\) 162909.i 0.208941i −0.994528 0.104470i \(-0.966685\pi\)
0.994528 0.104470i \(-0.0333148\pi\)
\(884\) −814278. + 844599.i −1.04200 + 1.08080i
\(885\) 3469.03 + 110187.i 0.00442916 + 0.140684i
\(886\) 73370.2 + 172652.i 0.0934657 + 0.219940i
\(887\) 192525. + 111154.i 0.244703 + 0.141280i 0.617337 0.786699i \(-0.288212\pi\)
−0.372633 + 0.927979i \(0.621545\pi\)
\(888\) 552654. + 638587.i 0.700853 + 0.809831i
\(889\) 242682. + 420338.i 0.307068 + 0.531857i
\(890\) −57500.8 43292.9i −0.0725929 0.0546559i
\(891\) −4118.41 32541.2i −0.00518769 0.0409901i
\(892\) 988102. 284213.i 1.24186 0.357203i
\(893\) −65267.1 113046.i −0.0818448 0.141759i
\(894\) 20233.7 9360.79i 0.0253163 0.0117122i
\(895\) 87627.1 + 50591.5i 0.109394 + 0.0631585i
\(896\) −122370. + 358742.i −0.152427 + 0.446854i
\(897\) −49080.0 1.55894e6i −0.0609986 1.93751i
\(898\) 60661.2 495731.i 0.0752243 0.614743i
\(899\) 878873.i 1.08744i
\(900\) −520939. + 613263.i −0.643134 + 0.757115i
\(901\) −1.40918e6 −1.73587
\(902\) −23542.1 2880.78i −0.0289356 0.00354077i
\(903\) 181229. + 292255.i 0.222255 + 0.358415i
\(904\) 476909. + 587450.i 0.583578 + 0.718844i
\(905\) 14186.6 24571.9i 0.0173213 0.0300014i
\(906\) −155584. 14085.8i −0.189543 0.0171604i
\(907\) −1.03664e6 + 598505.i −1.26013 + 0.727534i −0.973099 0.230388i \(-0.926001\pi\)
−0.287028 + 0.957922i \(0.592667\pi\)
\(908\) 103106. 29656.8i 0.125058 0.0359711i
\(909\) −111300. + 224277.i −0.134700 + 0.271429i
\(910\) 31159.7 41385.7i 0.0376280 0.0499767i
\(911\) −806036. + 465365.i −0.971220 + 0.560734i −0.899608 0.436698i \(-0.856148\pi\)
−0.0716123 + 0.997433i \(0.522814\pi\)
\(912\) −471830. 702223.i −0.567278 0.844278i
\(913\) 19969.1 34587.5i 0.0239562 0.0414933i
\(914\) −462001. + 196332.i −0.553033 + 0.235017i
\(915\) 14394.6 26849.4i 0.0171932 0.0320695i
\(916\) 394788. 409489.i 0.470515 0.488035i
\(917\) 660464. 0.785435
\(918\) 21207.6 775393.i 0.0251655 0.920103i
\(919\) 1.46503e6i 1.73467i 0.497725 + 0.867335i \(0.334169\pi\)
−0.497725 + 0.867335i \(0.665831\pi\)
\(920\) −12883.0 80695.6i −0.0152210 0.0953398i
\(921\) −517178. 277271.i −0.609707 0.326878i
\(922\) 380267. 161598.i 0.447329 0.190097i
\(923\) 125160. + 72261.0i 0.146913 + 0.0848205i
\(924\) −5105.25 15853.1i −0.00597961 0.0185682i
\(925\) 455160. + 788360.i 0.531962 + 0.921385i
\(926\) 771115. 1.02418e6i 0.899284 1.19441i
\(927\) −55359.2 878321.i −0.0644214 1.02210i
\(928\) 651923. + 55685.1i 0.757008 + 0.0646611i
\(929\) −493591. 854925.i −0.571921 0.990596i −0.996369 0.0851437i \(-0.972865\pi\)
0.424448 0.905452i \(-0.360468\pi\)
\(930\) 100154. + 9067.51i 0.115799 + 0.0104839i
\(931\) −593319. 342553.i −0.684524 0.395210i
\(932\) −969561. 240892.i −1.11620 0.277326i
\(933\) −1.02263e6 + 634137.i −1.17478 + 0.728484i
\(934\) −1.69687e6 207641.i −1.94516 0.238023i
\(935\) 2700.85i 0.00308942i
\(936\) 425480. 1.36415e6i 0.485654 1.55707i
\(937\) −287243. −0.327167 −0.163584 0.986529i \(-0.552305\pi\)
−0.163584 + 0.986529i \(0.552305\pi\)
\(938\) 24768.0 202407.i 0.0281504 0.230049i
\(939\) 101111. 3183.26i 0.114674 0.00361028i
\(940\) 2785.33 11210.6i 0.00315226 0.0126875i
\(941\) 149097. 258244.i 0.168380 0.291643i −0.769470 0.638683i \(-0.779480\pi\)
0.937850 + 0.347040i \(0.112813\pi\)
\(942\) −202826. + 93833.8i −0.228571 + 0.105744i
\(943\) 645766. 372833.i 0.726193 0.419267i
\(944\) 820364. + 1.30806e6i 0.920583 + 1.46786i
\(945\) 3229.15 + 34099.0i 0.00361597 + 0.0381837i
\(946\) 26385.5 + 19865.9i 0.0294837 + 0.0221986i
\(947\) 904210. 522046.i 1.00825 0.582115i 0.0975732 0.995228i \(-0.468892\pi\)
0.910680 + 0.413113i \(0.135559\pi\)
\(948\) −155672. + 723090.i −0.173219 + 0.804592i
\(949\) 205674. 356238.i 0.228374 0.395555i
\(950\) −356664. 839287.i −0.395195 0.929957i
\(951\) −352681. + 11103.4i −0.389961 + 0.0122771i
\(952\) −62093.0 388933.i −0.0685124 0.429142i
\(953\) −1.38691e6 −1.52708 −0.763539 0.645762i \(-0.776540\pi\)
−0.763539 + 0.645762i \(0.776540\pi\)
\(954\) 1.53431e6 769334.i 1.68584 0.845314i
\(955\) 63305.1i 0.0694115i
\(956\) −43234.4 41682.3i −0.0473058 0.0456075i
\(957\) −24433.2 + 15151.2i −0.0266782 + 0.0165433i
\(958\) 300468. + 707049.i 0.327391 + 0.770404i
\(959\) −12399.2 7158.71i −0.0134821 0.00778391i
\(960\) 13071.8 73717.2i 0.0141838 0.0799883i
\(961\) 484199. + 838657.i 0.524297 + 0.908109i
\(962\) −1.29148e6 972367.i −1.39552 1.05070i
\(963\) −951649. + 632430.i −1.02618 + 0.681961i
\(964\) −396576. 1.37874e6i −0.426748 1.48364i
\(965\) 27413.5 + 47481.5i 0.0294381 + 0.0509882i
\(966\) 428011. + 301628.i 0.458670 + 0.323235i
\(967\) −697159. 402505.i −0.745554 0.430446i 0.0785311 0.996912i \(-0.474977\pi\)
−0.824085 + 0.566466i \(0.808310\pi\)
\(968\) 589578. + 726234.i 0.629203 + 0.775043i
\(969\) 774772. + 415372.i 0.825137 + 0.442374i
\(970\) 6728.00 54982.1i 0.00715060 0.0584356i
\(971\) 643421.i 0.682428i −0.939986 0.341214i \(-0.889162\pi\)
0.939986 0.341214i \(-0.110838\pi\)
\(972\) 400230. + 855823.i 0.423620 + 0.905840i
\(973\) −449321. −0.474604
\(974\) −209974. 25693.9i −0.221334 0.0270840i
\(975\) 727788. 1.35750e6i 0.765588 1.42801i
\(976\) −15592.6 426397.i −0.0163688 0.447625i
\(977\) 63505.8 109995.i 0.0665311 0.115235i −0.830841 0.556510i \(-0.812140\pi\)
0.897372 + 0.441275i \(0.145474\pi\)
\(978\) 328839. 466623.i 0.343800 0.487852i
\(979\) 38360.8 22147.6i 0.0400241 0.0231079i
\(980\) −16759.2 58265.3i −0.0174502 0.0606678i
\(981\) −732036. 1.10153e6i −0.760667 1.14461i
\(982\) 17693.7 23500.5i 0.0183483 0.0243699i
\(983\) −158662. + 91603.6i −0.164197 + 0.0947994i −0.579847 0.814725i \(-0.696888\pi\)
0.415650 + 0.909525i \(0.363554\pi\)
\(984\) 670891. 128877.i 0.692886 0.133102i
\(985\) 10577.4 18320.6i 0.0109020 0.0188828i
\(986\) −625723. + 265907.i −0.643618 + 0.273512i
\(987\) 39007.5 + 62904.7i 0.0400418 + 0.0645727i
\(988\) 1.16587e6 + 1.12401e6i 1.19436 + 1.15148i
\(989\) −1.03837e6 −1.06160
\(990\) 1474.51 + 2940.68i 0.00150445 + 0.00300038i
\(991\) 684255.i 0.696740i 0.937357 + 0.348370i \(0.113265\pi\)
−0.937357 + 0.348370i \(0.886735\pi\)
\(992\) 1.27529e6 597874.i 1.29594 0.607556i
\(993\) 21170.1 + 672429.i 0.0214696 + 0.681943i
\(994\) −44653.2 + 18975.8i −0.0451939 + 0.0192056i
\(995\) −14842.1 8569.07i −0.0149916 0.00865541i
\(996\) −242112. + 1.12460e6i −0.244061 + 1.13365i
\(997\) 271816. + 470800.i 0.273455 + 0.473637i 0.969744 0.244124i \(-0.0785003\pi\)
−0.696289 + 0.717761i \(0.745167\pi\)
\(998\) −998582. + 1.32630e6i −1.00259 + 1.33162i
\(999\) 1.06409e6 100769.i 1.06622 0.100970i
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 36.5.f.a.31.11 yes 44
3.2 odd 2 108.5.f.a.91.12 44
4.3 odd 2 inner 36.5.f.a.31.20 yes 44
9.2 odd 6 108.5.f.a.19.3 44
9.4 even 3 324.5.d.f.163.5 22
9.5 odd 6 324.5.d.e.163.18 22
9.7 even 3 inner 36.5.f.a.7.20 yes 44
12.11 even 2 108.5.f.a.91.3 44
36.7 odd 6 inner 36.5.f.a.7.11 44
36.11 even 6 108.5.f.a.19.12 44
36.23 even 6 324.5.d.e.163.17 22
36.31 odd 6 324.5.d.f.163.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.5.f.a.7.11 44 36.7 odd 6 inner
36.5.f.a.7.20 yes 44 9.7 even 3 inner
36.5.f.a.31.11 yes 44 1.1 even 1 trivial
36.5.f.a.31.20 yes 44 4.3 odd 2 inner
108.5.f.a.19.3 44 9.2 odd 6
108.5.f.a.19.12 44 36.11 even 6
108.5.f.a.91.3 44 12.11 even 2
108.5.f.a.91.12 44 3.2 odd 2
324.5.d.e.163.17 22 36.23 even 6
324.5.d.e.163.18 22 9.5 odd 6
324.5.d.f.163.5 22 9.4 even 3
324.5.d.f.163.6 22 36.31 odd 6