Properties

Label 36.5.f.a.31.20
Level $36$
Weight $5$
Character 36.31
Analytic conductor $3.721$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 31.20
Character \(\chi\) \(=\) 36.31
Dual form 36.5.f.a.7.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.68138 + 1.56444i) q^{2} +(4.25251 - 7.93197i) q^{3} +(11.1051 + 11.5186i) q^{4} +(1.01545 - 1.75881i) q^{5} +(28.0642 - 22.5478i) q^{6} +(20.0352 - 11.5673i) q^{7} +(22.8618 + 59.7774i) q^{8} +(-44.8324 - 67.4615i) q^{9} +O(q^{10})\) \(q+(3.68138 + 1.56444i) q^{2} +(4.25251 - 7.93197i) q^{3} +(11.1051 + 11.5186i) q^{4} +(1.01545 - 1.75881i) q^{5} +(28.0642 - 22.5478i) 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} +(138.589 - 39.1022i) q^{12} +(-137.824 + 238.718i) q^{13} +(91.8536 - 11.2399i) q^{14} +(-9.63264 - 15.5339i) q^{15} +(-9.35520 + 255.829i) q^{16} -266.009 q^{17} +(-59.5053 - 318.489i) q^{18} -367.194i q^{19} +(31.5357 - 7.83518i) q^{20} +(-6.55189 - 208.109i) q^{21} +(19.8494 - 2.42891i) q^{22} +(-544.473 - 314.352i) q^{23} +(571.373 + 72.8647i) 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} +(-11.1595 - 72.2558i) q^{30} +(1191.19 + 687.735i) q^{31} +(-434.669 + 927.167i) q^{32} +(-1.41585 - 44.9720i) q^{33} +(-979.280 - 416.155i) q^{34} -46.9843i q^{35} +(279.195 - 1265.57i) q^{36} +1466.19 q^{37} +(574.453 - 1351.78i) q^{38} +(1307.41 + 2108.37i) q^{39} +(128.352 + 20.4914i) q^{40} +(593.019 - 1027.14i) q^{41} +(301.454 - 776.378i) 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} +(1989.45 + 1162.12i) q^{48} +(-932.893 + 1615.82i) q^{49} +(301.649 + 2465.11i) q^{50} +(-1131.21 + 2109.98i) q^{51} +(-4280.24 + 1063.44i) q^{52} +5297.49 q^{53} +(-2779.29 - 882.381i) q^{54} -10.1532i q^{55} +(1149.51 + 933.203i) q^{56} +(-2912.57 - 1561.50i) q^{57} +(-310.436 - 2536.92i) q^{58} +(-5223.32 - 3015.68i) q^{59} +(71.9573 - 283.459i) 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} +(65.1436 - 167.774i) q^{66} +(-1908.36 - 1101.79i) q^{67} +(-2954.05 - 3064.05i) q^{68} +(-4808.81 + 2981.96i) q^{69} +(73.5040 - 172.967i) q^{70} +524.299i q^{71} +(3007.73 - 4222.25i) q^{72} -1492.29 q^{73} +(5397.59 + 2293.76i) q^{74} +(5585.11 - 175.836i) q^{75} +(4229.55 - 4077.71i) q^{76} +(57.8293 - 100.163i) q^{77} +(1514.65 + 9807.06i) 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} +(2324.36 - 2386.53i) q^{84} +(-270.120 + 467.861i) q^{85} +(6557.52 - 802.424i) q^{86} +(-5747.81 + 180.958i) q^{87} +(248.406 + 201.664i) q^{88} -8860.17 q^{89} +(-620.587 - 218.751i) q^{90} +6377.03i q^{91} +(-2425.53 - 9762.46i) q^{92} +(10520.7 - 6523.91i) q^{93} +(1411.44 - 172.713i) q^{94} +(-645.826 - 372.868i) q^{95} +(5505.83 + 7390.57i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.68138 + 1.56444i 0.920344 + 0.391110i
\(3\) 4.25251 7.93197i 0.472501 0.881330i
\(4\) 11.1051 + 11.5186i 0.694066 + 0.719911i
\(5\) 1.01545 1.75881i 0.0406181 0.0703525i −0.845002 0.534764i \(-0.820401\pi\)
0.885620 + 0.464411i \(0.153734\pi\)
\(6\) 28.0642 22.5478i 0.779560 0.626327i
\(7\) 20.0352 11.5673i 0.408882 0.236068i −0.281427 0.959583i \(-0.590808\pi\)
0.690309 + 0.723514i \(0.257474\pi\)
\(8\) 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 −0.482002 0.876170i \(-0.660090\pi\)
0.517784 + 0.855511i \(0.326757\pi\)
\(12\) 138.589 39.1022i 0.962426 0.271543i
\(13\) −137.824 + 238.718i −0.815527 + 1.41253i 0.0934218 + 0.995627i \(0.470219\pi\)
−0.908949 + 0.416908i \(0.863114\pi\)
\(14\) 91.8536 11.2399i 0.468641 0.0573462i
\(15\) −9.63264 15.5339i −0.0428117 0.0690395i
\(16\) −9.35520 + 255.829i −0.0365438 + 0.999332i
\(17\) −266.009 −0.920447 −0.460224 0.887803i \(-0.652231\pi\)
−0.460224 + 0.887803i \(0.652231\pi\)
\(18\) −59.5053 318.489i −0.183658 0.982990i
\(19\) 367.194i 1.01716i −0.861015 0.508579i \(-0.830171\pi\)
0.861015 0.508579i \(-0.169829\pi\)
\(20\) 31.5357 7.83518i 0.0788392 0.0195879i
\(21\) −6.55189 208.109i −0.0148569 0.471902i
\(22\) 19.8494 2.42891i 0.0410111 0.00501841i
\(23\) −544.473 314.352i −1.02925 0.594238i −0.112481 0.993654i \(-0.535880\pi\)
−0.916770 + 0.399416i \(0.869213\pi\)
\(24\) 571.373 + 72.8647i 0.991966 + 0.126501i
\(25\) 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 \(0.957369\pi\)
\(30\) −11.1595 72.2558i −0.0123995 0.0802842i
\(31\) 1191.19 + 687.735i 1.23953 + 0.715645i 0.968999 0.247065i \(-0.0794660\pi\)
0.270535 + 0.962710i \(0.412799\pi\)
\(32\) −434.669 + 927.167i −0.424481 + 0.905437i
\(33\) −1.41585 44.9720i −0.00130014 0.0412966i
\(34\) −979.280 416.155i −0.847128 0.359996i
\(35\) 46.9843i 0.0383545i
\(36\) 279.195 1265.57i 0.215428 0.976520i
\(37\) 1466.19 1.07099 0.535496 0.844538i \(-0.320125\pi\)
0.535496 + 0.844538i \(0.320125\pi\)
\(38\) 574.453 1351.78i 0.397820 0.936135i
\(39\) 1307.41 + 2108.37i 0.859572 + 1.38617i
\(40\) 128.352 + 20.4914i 0.0802202 + 0.0128071i
\(41\) 593.019 1027.14i 0.352777 0.611028i −0.633958 0.773368i \(-0.718571\pi\)
0.986735 + 0.162339i \(0.0519040\pi\)
\(42\) 301.454 776.378i 0.170892 0.440123i
\(43\) 1430.33 825.804i 0.773572 0.446622i −0.0605755 0.998164i \(-0.519294\pi\)
0.834147 + 0.551542i \(0.185960\pi\)
\(44\) 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 −0.428695 0.903449i \(-0.641026\pi\)
0.568063 + 0.822985i \(0.307693\pi\)
\(48\) 1989.45 + 1162.12i 0.863475 + 0.504392i
\(49\) −932.893 + 1615.82i −0.388544 + 0.672977i
\(50\) 301.649 + 2465.11i 0.120660 + 0.986046i
\(51\) −1131.21 + 2109.98i −0.434912 + 0.811218i
\(52\) −4280.24 + 1063.44i −1.58293 + 0.393286i
\(53\) 5297.49 1.88590 0.942950 0.332934i \(-0.108039\pi\)
0.942950 + 0.332934i \(0.108039\pi\)
\(54\) −2779.29 882.381i −0.953118 0.302600i
\(55\) 10.1532i 0.00335644i
\(56\) 1149.51 + 933.203i 0.366552 + 0.297578i
\(57\) −2912.57 1561.50i −0.896452 0.480608i
\(58\) −310.436 2536.92i −0.0922818 0.754139i
\(59\) −5223.32 3015.68i −1.50052 0.866327i −1.00000 0.000603027i \(-0.999808\pi\)
−0.500522 0.865724i \(-0.666859\pi\)
\(60\) 71.9573 283.459i 0.0199881 0.0787387i
\(61\) −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
\(66\) 65.1436 167.774i 0.0149549 0.0385156i
\(67\) −1908.36 1101.79i −0.425119 0.245443i 0.272146 0.962256i \(-0.412267\pi\)
−0.697265 + 0.716813i \(0.745600\pi\)
\(68\) −2954.05 3064.05i −0.638852 0.662640i
\(69\) −4808.81 + 2981.96i −1.01004 + 0.626332i
\(70\) 73.5040 172.967i 0.0150008 0.0352993i
\(71\) 524.299i 0.104007i 0.998647 + 0.0520035i \(0.0165607\pi\)
−0.998647 + 0.0520035i \(0.983439\pi\)
\(72\) 3007.73 4222.25i 0.580194 0.814478i
\(73\) −1492.29 −0.280032 −0.140016 0.990149i \(-0.544715\pi\)
−0.140016 + 0.990149i \(0.544715\pi\)
\(74\) 5397.59 + 2293.76i 0.985680 + 0.418875i
\(75\) 5585.11 175.836i 0.992909 0.0312597i
\(76\) 4229.55 4077.71i 0.732263 0.705975i
\(77\) 57.8293 100.163i 0.00975364 0.0168938i
\(78\) 1514.65 + 9807.06i 0.248956 + 1.61194i
\(79\) 4448.35 2568.25i 0.712762 0.411513i −0.0993209 0.995055i \(-0.531667\pi\)
0.812083 + 0.583542i \(0.198334\pi\)
\(80\) 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 0.0947580 0.995500i \(-0.469792\pi\)
0.909508 + 0.415687i \(0.136459\pi\)
\(84\) 2324.36 2386.53i 0.329416 0.338227i
\(85\) −270.120 + 467.861i −0.0373868 + 0.0647558i
\(86\) 6557.52 802.424i 0.886630 0.108494i
\(87\) −5747.81 + 180.958i −0.759388 + 0.0239078i
\(88\) 248.406 + 201.664i 0.0320773 + 0.0260413i
\(89\) −8860.17 −1.11857 −0.559283 0.828977i \(-0.688924\pi\)
−0.559283 + 0.828977i \(0.688924\pi\)
\(90\) −620.587 218.751i −0.0766157 0.0270063i
\(91\) 6377.03i 0.770080i
\(92\) −2425.53 9762.46i −0.286570 1.15341i
\(93\) 10520.7 6523.91i 1.21640 0.754296i
\(94\) 1411.44 172.713i 0.159737 0.0195465i
\(95\) −645.826 372.868i −0.0715596 0.0413150i
\(96\) 5505.83 + 7390.57i 0.597421 + 0.801928i
\(97\) −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 \(0.881746\pi\)
\(102\) −7465.33 + 5997.92i −0.717544 + 0.576501i
\(103\) −9409.35 5432.49i −0.886922 0.512065i −0.0139875 0.999902i \(-0.504453\pi\)
−0.872934 + 0.487838i \(0.837786\pi\)
\(104\) −17420.9 2781.23i −1.61066 0.257141i
\(105\) −372.678 199.801i −0.0338030 0.0181225i
\(106\) 19502.1 + 8287.61i 1.73568 + 0.737594i
\(107\) 14106.5i 1.23212i 0.787699 + 0.616060i \(0.211272\pi\)
−0.787699 + 0.616060i \(0.788728\pi\)
\(108\) −8851.18 7596.41i −0.758846 0.651270i
\(109\) 16328.3 1.37432 0.687160 0.726506i \(-0.258857\pi\)
0.687160 + 0.726506i \(0.258857\pi\)
\(110\) 15.8841 37.3778i 0.00131273 0.00308908i
\(111\) 6234.97 11629.8i 0.506044 0.943897i
\(112\) 2771.83 + 5233.81i 0.220968 + 0.417236i
\(113\) −5911.44 + 10238.9i −0.462952 + 0.801857i −0.999107 0.0422631i \(-0.986543\pi\)
0.536154 + 0.844120i \(0.319877\pi\)
\(114\) −8279.41 10305.0i −0.637074 0.792936i
\(115\) −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
\(120\) 708.356 930.947i 0.0491914 0.0646491i
\(121\) −7308.00 + 12657.8i −0.499146 + 0.864547i
\(122\) −809.770 6617.55i −0.0544054 0.444608i
\(123\) −5625.42 9071.72i −0.371830 0.599625i
\(124\) 5306.53 + 21358.2i 0.345118 + 1.38906i
\(125\) 2530.25 0.161936
\(126\) −4876.27 5692.67i −0.307147 0.358571i
\(127\) 20979.9i 1.30076i 0.759609 + 0.650379i \(0.225390\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(128\) −15506.7 + 5289.48i −0.946452 + 0.322844i
\(129\) −467.746 14857.1i −0.0281081 0.892802i
\(130\) 271.983 + 2222.68i 0.0160936 + 0.131519i
\(131\) 24723.9 + 14274.3i 1.44070 + 0.831789i 0.997896 0.0648298i \(-0.0206504\pi\)
0.442804 + 0.896618i \(0.353984\pi\)
\(132\) 502.290 515.725i 0.0288275 0.0295986i
\(133\) −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 \(0.828085\pi\)
\(138\) −22368.1 + 3454.65i −1.17455 + 0.181403i
\(139\) −16819.9 9710.99i −0.870552 0.502613i −0.00302027 0.999995i \(-0.500961\pi\)
−0.867532 + 0.497382i \(0.834295\pi\)
\(140\) 541.192 521.763i 0.0276118 0.0266206i
\(141\) −100.677 3197.83i −0.00506400 0.160849i
\(142\) −820.234 + 1930.14i −0.0406781 + 0.0957222i
\(143\) 1378.07i 0.0673903i
\(144\) 17678.0 10838.3i 0.852529 0.522680i
\(145\) −1297.67 −0.0617203
\(146\) −5493.69 2334.60i −0.257726 0.109523i
\(147\) 8849.49 + 14271.0i 0.409528 + 0.660418i
\(148\) 16282.1 + 16888.4i 0.743339 + 0.771018i
\(149\) −309.641 + 536.313i −0.0139471 + 0.0241572i −0.872915 0.487873i \(-0.837773\pi\)
0.858968 + 0.512030i \(0.171106\pi\)
\(150\) 20836.0 + 8090.25i 0.926044 + 0.359567i
\(151\) −3758.08 + 2169.73i −0.164821 + 0.0951593i −0.580141 0.814516i \(-0.697003\pi\)
0.415321 + 0.909675i \(0.363669\pi\)
\(152\) 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
\(156\) −9766.54 + 38473.0i −0.401321 + 1.58091i
\(157\) 3103.88 5376.08i 0.125923 0.218105i −0.796170 0.605073i \(-0.793144\pi\)
0.922093 + 0.386967i \(0.126477\pi\)
\(158\) 20393.9 2495.54i 0.816933 0.0999657i
\(159\) 22527.6 42019.6i 0.891090 1.66210i
\(160\) 1189.33 + 1705.99i 0.0464582 + 0.0666404i
\(161\) −14544.9 −0.561123
\(162\) −18818.0 + 18292.9i −0.717039 + 0.697033i
\(163\) 15857.0i 0.596824i −0.954437 0.298412i \(-0.903543\pi\)
0.954437 0.298412i \(-0.0964569\pi\)
\(164\) 18416.7 4575.71i 0.684737 0.170126i
\(165\) −80.5351 43.1766i −0.00295813 0.00158592i
\(166\) 31718.1 3881.25i 1.15104 0.140849i
\(167\) −362.861 209.498i −0.0130109 0.00751186i 0.493480 0.869757i \(-0.335724\pi\)
−0.506491 + 0.862245i \(0.669058\pi\)
\(168\) 12290.4 5149.40i 0.435460 0.182448i
\(169\) −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 \(0.729391\pi\)
\(174\) −21442.9 8325.92i −0.708249 0.275001i
\(175\) 12439.4 + 7181.88i 0.406184 + 0.234510i
\(176\) 598.987 + 1131.02i 0.0193371 + 0.0365127i
\(177\) −46132.5 + 28607.0i −1.47252 + 0.913115i
\(178\) −32617.6 13861.2i −1.02947 0.437482i
\(179\) 49821.7i 1.55494i −0.628922 0.777468i \(-0.716504\pi\)
0.628922 0.777468i \(-0.283496\pi\)
\(180\) −1942.39 1776.18i −0.0599504 0.0548202i
\(181\) 13970.7 0.426443 0.213222 0.977004i \(-0.431604\pi\)
0.213222 + 0.977004i \(0.431604\pi\)
\(182\) −9976.48 + 23476.3i −0.301186 + 0.708738i
\(183\) −14993.1 + 472.028i −0.447703 + 0.0140950i
\(184\) 6343.50 39733.9i 0.187367 1.17361i
\(185\) 1488.84 2578.75i 0.0435016 0.0753469i
\(186\) 48936.7 7558.03i 1.41452 0.218466i
\(187\) −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 −0.822058 0.569404i \(-0.807174\pi\)
0.0820893 + 0.996625i \(0.473841\pi\)
\(192\) 8706.95 + 35821.0i 0.236191 + 0.971707i
\(193\) −13498.2 + 23379.5i −0.362377 + 0.627655i −0.988351 0.152189i \(-0.951368\pi\)
0.625975 + 0.779843i \(0.284701\pi\)
\(194\) −3312.81 27072.7i −0.0880224 0.719331i
\(195\) 5035.84 158.543i 0.132435 0.00416944i
\(196\) −28971.8 + 7198.16i −0.754159 + 0.187374i
\(197\) 10416.4 0.268402 0.134201 0.990954i \(-0.457153\pi\)
0.134201 + 0.990954i \(0.457153\pi\)
\(198\) −1053.75 1230.18i −0.0268787 0.0313789i
\(199\) 8438.68i 0.213093i 0.994308 + 0.106546i \(0.0339793\pi\)
−0.994308 + 0.106546i \(0.966021\pi\)
\(200\) −25044.8 + 30849.8i −0.626119 + 0.771245i
\(201\) −16854.7 + 10451.7i −0.417185 + 0.258699i
\(202\) −1501.77 12272.7i −0.0368045 0.300771i
\(203\) −12801.7 7391.09i −0.310654 0.179356i
\(204\) −36866.1 + 10401.6i −0.885863 + 0.249941i
\(205\) −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
\(210\) −1059.39 1318.57i −0.0240225 0.0298997i
\(211\) −19871.6 11472.8i −0.446341 0.257695i 0.259943 0.965624i \(-0.416296\pi\)
−0.706284 + 0.707929i \(0.749630\pi\)
\(212\) 58829.0 + 61019.6i 1.30894 + 1.35768i
\(213\) 4158.73 + 2229.59i 0.0916645 + 0.0491434i
\(214\) −22068.8 + 51931.5i −0.481894 + 1.13397i
\(215\) 3354.25i 0.0725637i
\(216\) −20700.4 41812.4i −0.443682 0.896184i
\(217\) 31821.1 0.675764
\(218\) 60110.6 + 25544.6i 1.26485 + 0.537510i
\(219\) −6345.99 + 11836.8i −0.132316 + 0.246801i
\(220\) 116.951 112.752i 0.00241634 0.00232959i
\(221\) 36662.5 63501.3i 0.750650 1.30016i
\(222\) 41147.3 33059.3i 0.834902 0.670791i
\(223\) 55651.0 32130.1i 1.11909 0.646105i 0.177919 0.984045i \(-0.443064\pi\)
0.941167 + 0.337941i \(0.109730\pi\)
\(224\) 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 −0.442593 0.896722i \(-0.645941\pi\)
0.555288 + 0.831658i \(0.312608\pi\)
\(228\) −14358.1 50889.2i −0.276202 0.978940i
\(229\) −17775.1 + 30787.4i −0.338955 + 0.587087i −0.984236 0.176858i \(-0.943407\pi\)
0.645281 + 0.763945i \(0.276740\pi\)
\(230\) −5069.53 + 620.344i −0.0958323 + 0.0117267i
\(231\) −548.573 884.646i −0.0102804 0.0165785i
\(232\) 25774.4 31748.5i 0.478864 0.589857i
\(233\) 62439.9 1.15014 0.575070 0.818105i \(-0.304975\pi\)
0.575070 + 0.818105i \(0.304975\pi\)
\(234\) 84230.4 + 29690.4i 1.53829 + 0.542231i
\(235\) 721.967i 0.0130732i
\(236\) −23268.9 93654.5i −0.417784 1.68153i
\(237\) −1454.69 46205.7i −0.0258985 0.822619i
\(238\) −24433.9 + 2989.91i −0.431359 + 0.0527841i
\(239\) −3250.59 1876.73i −0.0569070 0.0328553i 0.471277 0.881985i \(-0.343793\pi\)
−0.528184 + 0.849130i \(0.677127\pi\)
\(240\) 4064.14 2318.99i 0.0705579 0.0402602i
\(241\) 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
\(246\) −6517.12 42197.1i −0.107693 0.697288i
\(247\) 87655.9 + 50608.2i 1.43677 + 0.829520i
\(248\) −13878.2 + 86929.3i −0.225647 + 1.41339i
\(249\) −2262.44 71862.4i −0.0364904 1.15905i
\(250\) 9314.81 + 3958.42i 0.149037 + 0.0633348i
\(251\) 9246.49i 0.146767i −0.997304 0.0733836i \(-0.976620\pi\)
0.997304 0.0733836i \(-0.0233798\pi\)
\(252\) −9045.54 28585.5i −0.142441 0.450137i
\(253\) −3143.12 −0.0491043
\(254\) −32821.8 + 77235.1i −0.508739 + 1.19715i
\(255\) 2562.37 + 4132.16i 0.0394060 + 0.0635473i
\(256\) −65361.0 4786.66i −0.997329 0.0730387i
\(257\) −7624.85 + 13206.6i −0.115442 + 0.199952i −0.917956 0.396681i \(-0.870162\pi\)
0.802514 + 0.596633i \(0.203495\pi\)
\(258\) 21521.1 55426.4i 0.323314 0.832678i
\(259\) 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 −0.979293 0.202448i \(-0.935110\pi\)
−0.314322 + 0.949317i \(0.601777\pi\)
\(264\) 2655.94 1112.78i 0.0381075 0.0159661i
\(265\) 5379.35 9317.30i 0.0766016 0.132678i
\(266\) −4127.21 33728.1i −0.0583301 0.476682i
\(267\) −37677.9 + 70278.6i −0.528524 + 0.985826i
\(268\) −8501.38 34217.1i −0.118364 0.476402i
\(269\) −86017.8 −1.18873 −0.594366 0.804195i \(-0.702597\pi\)
−0.594366 + 0.804195i \(0.702597\pi\)
\(270\) −4374.18 + 3992.24i −0.0600025 + 0.0547632i
\(271\) 15629.0i 0.212810i 0.994323 + 0.106405i \(0.0339340\pi\)
−0.994323 + 0.106405i \(0.966066\pi\)
\(272\) 2488.57 68052.9i 0.0336366 0.919833i
\(273\) 50582.4 + 27118.4i 0.678695 + 0.363863i
\(274\) 300.676 + 2457.16i 0.00400495 + 0.0327290i
\(275\) 2688.13 + 1551.99i 0.0355455 + 0.0205222i
\(276\) −87750.1 22275.7i −1.15194 0.292424i
\(277\) 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 \(-0.414959\pi\)
\(282\) 4632.18 11929.9i 0.0582489 0.150017i
\(283\) −78979.6 45598.9i −0.986148 0.569353i −0.0820271 0.996630i \(-0.526139\pi\)
−0.904121 + 0.427278i \(0.859473\pi\)
\(284\) −6039.18 + 5822.37i −0.0748758 + 0.0721877i
\(285\) −5703.95 + 3537.05i −0.0702241 + 0.0435463i
\(286\) −2155.90 + 5073.18i −0.0263570 + 0.0620223i
\(287\) 27438.6i 0.333118i
\(288\) 82035.4 12243.7i 0.989045 0.147614i
\(289\) −12760.0 −0.152776
\(290\) −4777.21 2030.12i −0.0568039 0.0241394i
\(291\) −61337.6 + 1931.09i −0.724338 + 0.0228043i
\(292\) −16572.0 17189.1i −0.194361 0.201598i
\(293\) −41507.5 + 71893.1i −0.483494 + 0.837436i −0.999820 0.0189556i \(-0.993966\pi\)
0.516326 + 0.856392i \(0.327299\pi\)
\(294\) 10252.3 + 66381.3i 0.118611 + 0.767982i
\(295\) −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
\(300\) 64048.4 + 62379.9i 0.711649 + 0.693110i
\(301\) 19104.7 33090.3i 0.210866 0.365231i
\(302\) −17229.3 + 2108.30i −0.188910 + 0.0231163i
\(303\) −27805.7 + 875.407i −0.302865 + 0.00953508i
\(304\) 93938.9 + 3435.17i 1.01648 + 0.0371708i
\(305\) −3384.96 −0.0363876
\(306\) 15829.0 + 84721.0i 0.169048 + 0.904791i
\(307\) 65201.8i 0.691803i −0.938271 0.345902i \(-0.887573\pi\)
0.938271 0.345902i \(-0.112427\pi\)
\(308\) 1795.94 446.209i 0.0189317 0.00470367i
\(309\) −83103.7 + 51533.0i −0.870369 + 0.539720i
\(310\) 11091.1 1357.18i 0.115412 0.0141226i
\(311\) −115786. 66849.3i −1.19712 0.691156i −0.237206 0.971459i \(-0.576232\pi\)
−0.959911 + 0.280303i \(0.909565\pi\)
\(312\) −96143.0 + 126355.i −0.987663 + 1.29802i
\(313\) −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 \(0.770838\pi\)
\(318\) 148670. 119447.i 1.47017 1.18119i
\(319\) −2766.43 1597.20i −0.0271856 0.0156956i
\(320\) 1709.44 + 8141.04i 0.0166938 + 0.0795023i
\(321\) 111893. + 59988.2i 1.08590 + 0.582178i
\(322\) −53545.1 22754.5i −0.516426 0.219461i
\(323\) 97677.0i 0.936240i
\(324\) −97894.2 + 37903.6i −0.932539 + 0.361069i
\(325\) −171143. −1.62029
\(326\) 24807.3 58375.6i 0.233424 0.549283i
\(327\) 69436.2 129516.i 0.649367 1.21123i
\(328\) 74957.2 + 11966.9i 0.696732 + 0.111233i
\(329\) 4112.08 7122.34i 0.0379901 0.0658007i
\(330\) −228.933 284.942i −0.00210223 0.00261654i
\(331\) −64736.6 + 37375.7i −0.590873 + 0.341141i −0.765443 0.643504i \(-0.777480\pi\)
0.174570 + 0.984645i \(0.444147\pi\)
\(332\) 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
\(336\) 53301.6 + 270.738i 0.472130 + 0.00239812i
\(337\) 70909.1 122818.i 0.624370 1.08144i −0.364293 0.931285i \(-0.618689\pi\)
0.988662 0.150156i \(-0.0479775\pi\)
\(338\) −23039.2 188279.i −0.201666 1.64804i
\(339\) 56076.3 + 90430.4i 0.487955 + 0.786892i
\(340\) −8388.78 + 2084.23i −0.0725673 + 0.0180297i
\(341\) 6876.48 0.0591367
\(342\) −116947. + 21850.0i −0.999856 + 0.186810i
\(343\) 98710.7i 0.839027i
\(344\) 82064.4 + 66622.3i 0.693487 + 0.562993i
\(345\) 361.608 + 11485.8i 0.00303809 + 0.0964994i
\(346\) 9328.60 + 76234.5i 0.0779227 + 0.636795i
\(347\) 158508. + 91514.6i 1.31641 + 0.760032i 0.983150 0.182802i \(-0.0585168\pi\)
0.333264 + 0.942834i \(0.391850\pi\)
\(348\) −65914.2 64197.0i −0.544277 0.530098i
\(349\) −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 \(0.536235\pi\)
\(354\) −214585. + 33141.6i −1.71235 + 0.264464i
\(355\) 922.144 + 532.400i 0.00731715 + 0.00422456i
\(356\) −98392.7 102056.i −0.776359 0.805268i
\(357\) 1742.86 + 55358.9i 0.0136750 + 0.434361i
\(358\) 77943.1 183413.i 0.608151 1.43108i
\(359\) 161179.i 1.25060i 0.780385 + 0.625300i \(0.215023\pi\)
−0.780385 + 0.625300i \(0.784977\pi\)
\(360\) −4371.96 9577.52i −0.0337342 0.0739006i
\(361\) −4510.46 −0.0346104
\(362\) 51431.4 + 21856.3i 0.392474 + 0.166786i
\(363\) 69324.2 + 111794.i 0.526104 + 0.848412i
\(364\) −73454.3 + 70817.3i −0.554389 + 0.534487i
\(365\) −1515.35 + 2624.66i −0.0113744 + 0.0197010i
\(366\) −55933.8 21718.1i −0.417553 0.162129i
\(367\) −172828. + 99782.5i −1.28317 + 0.740836i −0.977426 0.211279i \(-0.932237\pi\)
−0.305740 + 0.952115i \(0.598904\pi\)
\(368\) 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
\(372\) 191979. + 48734.6i 1.38729 + 0.352169i
\(373\) 2894.35 5013.15i 0.0208033 0.0360324i −0.855436 0.517908i \(-0.826711\pi\)
0.876240 + 0.481876i \(0.160044\pi\)
\(374\) −5280.12 + 646.113i −0.0377486 + 0.00461919i
\(375\) 10759.9 20069.9i 0.0765149 0.142719i
\(376\) 17663.5 + 14339.7i 0.124940 + 0.101430i
\(377\) 176129. 1.23922
\(378\) −65890.5 + 14470.3i −0.461147 + 0.101273i
\(379\) 217930.i 1.51719i −0.651565 0.758593i \(-0.725887\pi\)
0.651565 0.758593i \(-0.274113\pi\)
\(380\) −2877.03 11579.7i −0.0199240 0.0801919i
\(381\) 166412. + 89217.4i 1.14640 + 0.614610i
\(382\) −123760. + 15144.2i −0.848116 + 0.103781i
\(383\) −60187.2 34749.1i −0.410305 0.236890i 0.280616 0.959820i \(-0.409461\pi\)
−0.690921 + 0.722930i \(0.742795\pi\)
\(384\) −23986.2 + 145492.i −0.162667 + 0.986681i
\(385\) −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 \(0.894144\pi\)
\(390\) 18786.8 + 7294.60i 0.123516 + 0.0479592i
\(391\) 144835. + 83620.5i 0.947371 + 0.546965i
\(392\) −117917. 18825.4i −0.767369 0.122510i
\(393\) 218362. 135407.i 1.41381 0.876712i
\(394\) 38346.8 + 16295.9i 0.247023 + 0.104975i
\(395\) 10431.7i 0.0668595i
\(396\) −1954.73 6177.28i −0.0124651 0.0393919i
\(397\) 13255.8 0.0841056 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(398\) −13201.8 + 31066.0i −0.0833426 + 0.196119i
\(399\) −76416.4 + 2405.82i −0.479999 + 0.0151118i
\(400\) −140462. + 74388.7i −0.877887 + 0.464930i
\(401\) 2687.66 4655.16i 0.0167142 0.0289498i −0.857547 0.514405i \(-0.828013\pi\)
0.874262 + 0.485455i \(0.161346\pi\)
\(402\) −78399.5 + 12108.4i −0.485133 + 0.0749265i
\(403\) −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
\(408\) −151990. 19382.7i −0.913053 0.116438i
\(409\) 120347. 208446.i 0.719427 1.24608i −0.241800 0.970326i \(-0.577738\pi\)
0.961227 0.275758i \(-0.0889289\pi\)
\(410\) −1170.27 9563.57i −0.00696173 0.0568922i
\(411\) 5567.10 175.269i 0.0329568 0.00103758i
\(412\) −41916.9 168711.i −0.246942 0.993912i
\(413\) −139534. −0.818049
\(414\) −67718.5 + 192114.i −0.395100 + 1.12088i
\(415\) 16224.2i 0.0942035i
\(416\) −161424. 231549.i −0.932784 1.33800i
\(417\) −148554. + 92119.2i −0.854305 + 0.529758i
\(418\) −891.882 7288.58i −0.00510452 0.0417148i
\(419\) 30669.6 + 17707.1i 0.174695 + 0.100860i 0.584798 0.811179i \(-0.301174\pi\)
−0.410103 + 0.912039i \(0.634507\pi\)
\(420\) −1837.19 6511.52i −0.0104149 0.0369134i
\(421\) 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
\(426\) 11821.8 + 14714.0i 0.0651424 + 0.0810797i
\(427\) −33393.2 19279.6i −0.183148 0.105741i
\(428\) −162487. + 156654.i −0.887017 + 0.855173i
\(429\) 10930.8 + 5860.23i 0.0593931 + 0.0318420i
\(430\) 5247.53 12348.3i 0.0283803 0.0667835i
\(431\) 161673.i 0.870327i 0.900351 + 0.435163i \(0.143309\pi\)
−0.900351 + 0.435163i \(0.856691\pi\)
\(432\) −10793.1 186312.i −0.0578336 0.998326i
\(433\) −61835.3 −0.329808 −0.164904 0.986310i \(-0.552731\pi\)
−0.164904 + 0.986310i \(0.552731\pi\)
\(434\) 117145. + 49782.1i 0.621936 + 0.264298i
\(435\) −5518.35 + 10293.1i −0.0291629 + 0.0543960i
\(436\) 181327. + 188079.i 0.953869 + 0.989388i
\(437\) −115428. + 199927.i −0.604434 + 1.04691i
\(438\) −41880.0 + 33647.9i −0.218302 + 0.175392i
\(439\) 268021. 154742.i 1.39072 0.802933i 0.397326 0.917677i \(-0.369938\pi\)
0.993395 + 0.114744i \(0.0366049\pi\)
\(440\) 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 −0.599897 0.800077i \(-0.704792\pi\)
0.392938 + 0.919565i \(0.371459\pi\)
\(444\) 203198. 57331.1i 1.03075 0.290820i
\(445\) −8997.07 + 15583.4i −0.0454340 + 0.0786940i
\(446\) 255138. 31220.5i 1.28264 0.156953i
\(447\) 2937.27 + 4736.74i 0.0147004 + 0.0237063i
\(448\) −29504.7 + 90049.2i −0.147006 + 0.448667i
\(449\) −124857. −0.619328 −0.309664 0.950846i \(-0.600217\pi\)
−0.309664 + 0.950846i \(0.600217\pi\)
\(450\) 152777. 130867.i 0.754453 0.646255i
\(451\) 5929.43i 0.0291514i
\(452\) −183585. + 45612.4i −0.898585 + 0.223257i
\(453\) 1228.96 + 39035.8i 0.00598883 + 0.190224i
\(454\) 26622.9 3257.77i 0.129165 0.0158055i
\(455\) 11216.0 + 6475.56i 0.0541771 + 0.0312791i
\(456\) 26755.5 209805.i 0.128672 1.00899i
\(457\) 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 \(0.911472\pi\)
\(462\) −635.530 4114.92i −0.00297750 0.0192787i
\(463\) 277564. + 160252.i 1.29480 + 0.747552i 0.979501 0.201442i \(-0.0645626\pi\)
0.315297 + 0.948993i \(0.397896\pi\)
\(464\) 144554. 76555.7i 0.671418 0.355584i
\(465\) −791.122 25128.6i −0.00365879 0.116215i
\(466\) 229865. + 97683.4i 1.05852 + 0.449831i
\(467\) 427381.i 1.95967i −0.199820 0.979833i \(-0.564036\pi\)
0.199820 0.979833i \(-0.435964\pi\)
\(468\) 263635. + 241075.i 1.20368 + 1.10068i
\(469\) −50979.2 −0.231765
\(470\) 1129.47 2657.83i 0.00511305 0.0120318i
\(471\) −29443.6 47481.7i −0.132724 0.214035i
\(472\) 60855.3 381180.i 0.273158 1.71099i
\(473\) 4128.49 7150.76i 0.0184531 0.0319617i
\(474\) 66930.7 172376.i 0.297899 0.767222i
\(475\) 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 −0.816566 0.577252i \(-0.804125\pi\)
0.0916316 + 0.995793i \(0.470792\pi\)
\(480\) 18589.5 2178.97i 0.0806837 0.00945733i
\(481\) −202076. + 350006.i −0.873422 + 1.51281i
\(482\) 43563.3 + 356005.i 0.187511 + 1.53237i
\(483\) −61852.1 + 115369.i −0.265131 + 0.494534i
\(484\) −226956. + 56388.2i −0.968838 + 0.240712i
\(485\) −13848.1 −0.0588715
\(486\) 65075.4 + 227055.i 0.275514 + 0.961297i
\(487\) 52885.1i 0.222985i −0.993765 0.111492i \(-0.964437\pi\)
0.993765 0.111492i \(-0.0355631\pi\)
\(488\) 67232.2 82815.7i 0.282317 0.347755i
\(489\) −125777. 67432.0i −0.525999 0.282000i
\(490\) 1840.98 + 15044.7i 0.00766754 + 0.0626602i
\(491\) 6368.89 + 3677.08i 0.0264180 + 0.0152525i 0.513151 0.858298i \(-0.328478\pi\)
−0.486733 + 0.873551i \(0.661811\pi\)
\(492\) 42022.7 165539.i 0.173602 0.683864i
\(493\) 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
\(498\) 104095. 268092.i 0.419733 1.08100i
\(499\) −359442. 207524.i −1.44354 0.833426i −0.445452 0.895306i \(-0.646957\pi\)
−0.998084 + 0.0618804i \(0.980290\pi\)
\(500\) 28098.6 + 29144.9i 0.112394 + 0.116580i
\(501\) −3204.80 + 1987.31i −0.0127681 + 0.00791756i
\(502\) 14465.6 34039.8i 0.0574021 0.135076i
\(503\) 53242.3i 0.210436i −0.994449 0.105218i \(-0.966446\pi\)
0.994449 0.105218i \(-0.0335541\pi\)
\(504\) 11420.2 119385.i 0.0449587 0.469991i
\(505\) −6277.63 −0.0246157
\(506\) −11571.0 4917.22i −0.0451929 0.0192052i
\(507\) −426577. + 13429.9i −1.65952 + 0.0522465i
\(508\) −241659. + 232984.i −0.936431 + 0.902813i
\(509\) 248630. 430640.i 0.959662 1.66218i 0.236344 0.971669i \(-0.424051\pi\)
0.723319 0.690515i \(-0.242616\pi\)
\(510\) 2968.54 + 19220.7i 0.0114131 + 0.0738974i
\(511\) −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
\(516\) 165938. 170377.i 0.623229 0.639899i
\(517\) 888.614 1539.12i 0.00332454 0.00575828i
\(518\) 134675. 16479.7i 0.501910 0.0614173i
\(519\) 172722. 5437.79i 0.641227 0.0201877i
\(520\) −22581.7 + 27815.8i −0.0835123 + 0.102869i
\(521\) −58965.8 −0.217233 −0.108616 0.994084i \(-0.534642\pi\)
−0.108616 + 0.994084i \(0.534642\pi\)
\(522\) −157227. + 134679.i −0.577015 + 0.494263i
\(523\) 117488.i 0.429527i −0.976666 0.214763i \(-0.931102\pi\)
0.976666 0.214763i \(-0.0688980\pi\)
\(524\) 110140. + 443301.i 0.401128 + 1.61449i
\(525\) 109865. 68127.8i 0.398603 0.247176i
\(526\) −410222. + 50197.6i −1.48268 + 0.181431i
\(527\) −316868. 182944.i −1.14093 0.658714i
\(528\) 11518.4 + 58.5059i 0.0413165 + 0.000209861i
\(529\) 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
\(534\) −248653. + 199777.i −0.871990 + 0.700589i
\(535\) 24810.8 + 14324.5i 0.0866828 + 0.0500463i
\(536\) 22233.7 139266.i 0.0773896 0.484747i
\(537\) −395185. 211867.i −1.37041 0.734709i
\(538\) −316664. 134570.i −1.09404 0.464925i
\(539\) 9327.75i 0.0321070i
\(540\) −22348.6 + 7853.80i −0.0766413 + 0.0269335i
\(541\) −16461.8 −0.0562448 −0.0281224 0.999604i \(-0.508953\pi\)
−0.0281224 + 0.999604i \(0.508953\pi\)
\(542\) −24450.6 + 57536.2i −0.0832322 + 0.195859i
\(543\) 59410.5 110815.i 0.201495 0.375837i
\(544\) 115626. 246635.i 0.390713 0.833407i
\(545\) 16580.6 28718.4i 0.0558222 0.0966869i
\(546\) 143788. + 178966.i 0.482322 + 0.600324i
\(547\) 337391. 194793.i 1.12761 0.651026i 0.184277 0.982874i \(-0.441006\pi\)
0.943333 + 0.331848i \(0.107672\pi\)
\(548\) −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
\(552\) −288192. 219285.i −0.945810 0.719666i
\(553\) 59415.7 102911.i 0.194290 0.336521i
\(554\) 27505.9 + 224782.i 0.0896202 + 0.732388i
\(555\) −14123.3 22775.6i −0.0458510 0.0739407i
\(556\) −74929.6 301583.i −0.242384 0.975567i
\(557\) 434133. 1.39931 0.699653 0.714483i \(-0.253338\pi\)
0.699653 + 0.714483i \(0.253338\pi\)
\(558\) 148154. 420305.i 0.475821 1.34988i
\(559\) 455263.i 1.45693i
\(560\) 12019.9 + 439.547i 0.0383289 + 0.00140162i
\(561\) 376.630 + 11963.0i 0.00119671 + 0.0380113i
\(562\) −53961.3 440979.i −0.170848 1.39619i
\(563\) 192477. + 111127.i 0.607244 + 0.350592i 0.771886 0.635761i \(-0.219314\pi\)
−0.164642 + 0.986353i \(0.552647\pi\)
\(564\) 35716.5 36671.8i 0.112282 0.115285i
\(565\) 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 \(0.835263\pi\)
\(570\) −26531.9 + 4097.72i −0.0816617 + 0.0126123i
\(571\) 331554. + 191423.i 1.01691 + 0.587112i 0.913207 0.407496i \(-0.133598\pi\)
0.103702 + 0.994608i \(0.466931\pi\)
\(572\) −15873.3 + 15303.5i −0.0485151 + 0.0467734i
\(573\) 8827.80 + 280399.i 0.0268871 + 0.854019i
\(574\) 42926.0 101012.i 0.130286 0.306583i
\(575\) 390347.i 1.18063i
\(576\) 321157. + 83265.8i 0.967995 + 0.250970i
\(577\) 18219.2 0.0547239 0.0273620 0.999626i \(-0.491289\pi\)
0.0273620 + 0.999626i \(0.491289\pi\)
\(578\) −46974.5 19962.3i −0.140607 0.0597524i
\(579\) 128045. + 206489.i 0.381948 + 0.615941i
\(580\) −14410.7 14947.3i −0.0428380 0.0444331i
\(581\) 92407.6 160055.i 0.273751 0.474150i
\(582\) −228828. 88849.9i −0.675559 0.262308i
\(583\) 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 −0.432013 0.901868i \(-0.642196\pi\)
0.565034 + 0.825068i \(0.308863\pi\)
\(588\) −66107.0 + 260413.i −0.191202 + 0.753197i
\(589\) 252532. 437399.i 0.727924 1.26080i
\(590\) −48633.7 + 5951.16i −0.139712 + 0.0170961i
\(591\) 44295.9 82622.8i 0.126820 0.236551i
\(592\) −13716.5 + 375093.i −0.0391380 + 1.07028i
\(593\) 216280. 0.615046 0.307523 0.951541i \(-0.400500\pi\)
0.307523 + 0.951541i \(0.400500\pi\)
\(594\) −14238.8 + 3127.01i −0.0403554 + 0.00886249i
\(595\) 12498.3i 0.0353033i
\(596\) −9616.14 + 2389.17i −0.0270713 + 0.00672597i
\(597\) 66935.4 + 35885.6i 0.187805 + 0.100686i
\(598\) 688072. 84197.3i 1.92412 0.235448i
\(599\) 260151. + 150198.i 0.725057 + 0.418612i 0.816611 0.577188i \(-0.195850\pi\)
−0.0915543 + 0.995800i \(0.529184\pi\)
\(600\) 138197. + 329844.i 0.383880 + 0.916232i
\(601\) −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
\(606\) −103733. 40277.6i −0.282469 0.109678i
\(607\) −154217. 89037.5i −0.418558 0.241655i 0.275902 0.961186i \(-0.411024\pi\)
−0.694460 + 0.719531i \(0.744357\pi\)
\(608\) 340450. + 159608.i 0.920972 + 0.431765i
\(609\) −113065. + 70112.4i −0.304856 + 0.189043i
\(610\) −12461.3 5295.56i −0.0334892 0.0142316i
\(611\) 97990.4i 0.262483i
\(612\) −74268.4 + 336653.i −0.198290 + 0.898835i
\(613\) 570495. 1.51821 0.759103 0.650970i \(-0.225638\pi\)
0.759103 + 0.650970i \(0.225638\pi\)
\(614\) 102004. 240032.i 0.270571 0.636697i
\(615\) −21667.8 + 682.167i −0.0572881 + 0.00180360i
\(616\) 7309.59 + 1166.97i 0.0192633 + 0.00307538i
\(617\) −107951. + 186976.i −0.283567 + 0.491153i −0.972261 0.233900i \(-0.924851\pi\)
0.688694 + 0.725052i \(0.258185\pi\)
\(618\) −386556. + 59701.7i −1.01213 + 0.156318i
\(619\) −158318. + 91404.9i −0.413189 + 0.238555i −0.692159 0.721745i \(-0.743340\pi\)
0.278970 + 0.960300i \(0.410007\pi\)
\(620\) 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
\(624\) −551613. + 314749.i −1.41666 + 0.808342i
\(625\) −191454. + 331608.i −0.490123 + 0.848918i
\(626\) −5460.93 44627.4i −0.0139353 0.113881i
\(627\) −16513.4 + 519.893i −0.0420052 + 0.00132245i
\(628\) 96393.6 23949.4i 0.244415 0.0607261i
\(629\) −390019. −0.985791
\(630\) −14964.0 + 2795.82i −0.0377021 + 0.00704413i
\(631\) 153307.i 0.385037i −0.981293 0.192518i \(-0.938335\pi\)
0.981293 0.192518i \(-0.0616655\pi\)
\(632\) 255221. + 207196.i 0.638972 + 0.518736i
\(633\) −175506. + 108832.i −0.438011 + 0.271613i
\(634\) 19048.1 + 155664.i 0.0473885 + 0.387265i
\(635\) 36899.8 + 21304.1i 0.0915117 + 0.0528343i
\(636\) 734176. 207144.i 1.81504 0.512103i
\(637\) −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 \(0.992170\pi\)
\(642\) 318071. + 395888.i 0.771711 + 0.960512i
\(643\) −384971. 222263.i −0.931120 0.537583i −0.0439545 0.999034i \(-0.513996\pi\)
−0.887166 + 0.461451i \(0.847329\pi\)
\(644\) −161522. 167536.i −0.389456 0.403958i
\(645\) −26605.9 14264.0i −0.0639525 0.0342864i
\(646\) −152810. + 359586.i −0.366173 + 0.861663i
\(647\) 152505.i 0.364314i −0.983269 0.182157i \(-0.941692\pi\)
0.983269 0.182157i \(-0.0583079\pi\)
\(648\) −419683. 13612.3i −0.999474 0.0324176i
\(649\) −30153.0 −0.0715881
\(650\) −630042. 267743.i −1.49122 0.633711i
\(651\) 135319. 252404.i 0.319299 0.595572i
\(652\) 182650. 176093.i 0.429660 0.414235i
\(653\) 149617. 259144.i 0.350876 0.607736i −0.635527 0.772079i \(-0.719217\pi\)
0.986403 + 0.164343i \(0.0525504\pi\)
\(654\) 458240. 368167.i 1.07137 0.860774i
\(655\) 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 −0.0227330 0.999742i \(-0.507237\pi\)
0.854435 + 0.519558i \(0.173903\pi\)
\(660\) −397.013 1407.13i −0.000911417 0.00323032i
\(661\) −379775. + 657790.i −0.869208 + 1.50551i −0.00639999 + 0.999980i \(0.502037\pi\)
−0.862808 + 0.505532i \(0.831296\pi\)
\(662\) −296792. + 36317.5i −0.677230 + 0.0828706i
\(663\) −347783. 560846.i −0.791191 1.27590i
\(664\) 396938. + 322246.i 0.900298 + 0.730888i
\(665\) −17252.3 −0.0390126
\(666\) −87245.9 466964.i −0.196697 1.05277i
\(667\) 401718.i 0.902962i
\(668\) −1616.48 6506.14i −0.00362257 0.0145804i
\(669\) −18198.9 578056.i −0.0406625 1.29157i
\(670\) −17768.5 + 2174.28i −0.0395824 + 0.00484358i
\(671\) −7216.22 4166.29i −0.0160275 0.00925346i
\(672\) 195800. + 84383.8i 0.433584 + 0.186862i
\(673\) 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 \(0.559939\pi\)
\(678\) 64965.2 + 420636.i 0.141326 + 0.915056i
\(679\) −136614. 78873.9i −0.296315 0.171078i
\(680\) −34142.9 5450.90i −0.0738385 0.0117883i
\(681\) −1899.01 60318.5i −0.00409479 0.130064i
\(682\) 25314.9 + 10757.8i 0.0544261 + 0.0231289i
\(683\) 357197.i 0.765714i 0.923808 + 0.382857i \(0.125060\pi\)
−0.923808 + 0.382857i \(0.874940\pi\)
\(684\) −464710. 102519.i −0.993275 0.219124i
\(685\) 1256.87 0.00267861
\(686\) −154427. + 363391.i −0.328152 + 0.772194i
\(687\) 168616. + 271916.i 0.357261 + 0.576131i
\(688\) 197884. + 373647.i 0.418054 + 0.789376i
\(689\) −730122. + 1.26461e6i −1.53800 + 2.66390i
\(690\) −16637.7 + 42849.4i −0.0349457 + 0.0900008i
\(691\) −384473. + 221976.i −0.805212 + 0.464889i −0.845290 0.534307i \(-0.820573\pi\)
0.0400786 + 0.999197i \(0.487239\pi\)
\(692\) −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
\(696\) −142222. 339452.i −0.293596 0.700745i
\(697\) −157749. + 273228.i −0.324713 + 0.562420i
\(698\) −65374.2 534247.i −0.134182 1.09656i
\(699\) 265526. 495272.i 0.543442 1.01365i
\(700\) 55415.0 + 223039.i 0.113092 + 0.455182i
\(701\) −483771. −0.984474 −0.492237 0.870461i \(-0.663821\pi\)
−0.492237 + 0.870461i \(0.663821\pi\)
\(702\) 593694. 541854.i 1.20473 1.09953i
\(703\) 538375.i 1.08937i
\(704\) −6375.91 + 19459.5i −0.0128646 + 0.0392632i
\(705\) −5726.62 3070.17i −0.0115218 0.00617710i
\(706\) 97304.0 + 795181.i 0.195219 + 1.59535i
\(707\) −61929.9 35755.3i −0.123897 0.0715321i
\(708\) −841816. 213698.i −1.67939 0.426319i
\(709\) −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
\(714\) −80189.5 + 206524.i −0.157297 + 0.405110i
\(715\) 2423.76 + 1399.36i 0.00474108 + 0.00273726i
\(716\) 573875. 553273.i 1.11942 1.07923i
\(717\) −28709.3 + 17802.8i −0.0558450 + 0.0346297i
\(718\) −252154. + 593359.i −0.489122 + 1.15098i
\(719\) 781622.i 1.51196i 0.654597 + 0.755978i \(0.272838\pi\)
−0.654597 + 0.755978i \(0.727162\pi\)
\(720\) −1111.37 42098.1i −0.00214384 0.0812078i
\(721\) −251358. −0.483529
\(722\) −16604.7 7056.34i −0.0318535 0.0135365i
\(723\) 806587. 25393.8i 1.54303 0.0485792i
\(724\) 155146. + 160923.i 0.295980 + 0.307001i
\(725\) 198358. 343566.i 0.377375 0.653633i
\(726\) 80313.1 + 520011.i 0.152375 + 0.986595i
\(727\) −51590.1 + 29785.6i −0.0976107 + 0.0563556i −0.548011 0.836471i \(-0.684615\pi\)
0.450400 + 0.892827i \(0.351281\pi\)
\(728\) −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
\(732\) −171937. 167457.i −0.320883 0.312523i
\(733\) 106923. 185196.i 0.199004 0.344685i −0.749202 0.662342i \(-0.769563\pi\)
0.948206 + 0.317657i \(0.102896\pi\)
\(734\) −792350. + 96957.5i −1.47070 + 0.179966i
\(735\) 34086.2 1073.13i 0.0630963 0.00198646i
\(736\) 528122. 368179.i 0.974943 0.679678i
\(737\) −11016.5 −0.0202819
\(738\) −362420. 127750.i −0.665425 0.234556i
\(739\) 218903.i 0.400832i 0.979711 + 0.200416i \(0.0642294\pi\)
−0.979711 + 0.200416i \(0.935771\pi\)
\(740\) 46237.2 11487.8i 0.0844361 0.0209785i
\(741\) 774180. 480073.i 1.40996 0.874320i
\(742\) 486594. 59543.1i 0.883810 0.108149i
\(743\) 431487. + 249119.i 0.781610 + 0.451263i 0.837001 0.547202i \(-0.184307\pi\)
−0.0553907 + 0.998465i \(0.517640\pi\)
\(744\) 630503. + 479749.i 1.13905 + 0.866699i
\(745\) 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
\(750\) 71009.4 57051.6i 0.126239 0.101425i
\(751\) −534346. 308505.i −0.947421 0.546994i −0.0551419 0.998479i \(-0.517561\pi\)
−0.892279 + 0.451485i \(0.850894\pi\)
\(752\) 42592.3 + 80423.4i 0.0753174 + 0.142215i
\(753\) −73342.9 39320.8i −0.129350 0.0693477i
\(754\) 648396. + 275543.i 1.14051 + 0.484670i
\(755\) 8813.01i 0.0154607i
\(756\) −265206. 49811.1i −0.464023 0.0871530i
\(757\) 483106. 0.843045 0.421523 0.906818i \(-0.361496\pi\)
0.421523 + 0.906818i \(0.361496\pi\)
\(758\) 340938. 802283.i 0.593386 1.39633i
\(759\) −13366.1 + 24931.1i −0.0232018 + 0.0432771i
\(760\) 7524.32 47130.2i 0.0130269 0.0815966i
\(761\) 68847.3 119247.i 0.118882 0.205910i −0.800443 0.599409i \(-0.795402\pi\)
0.919325 + 0.393499i \(0.128736\pi\)
\(762\) 473051. + 588785.i 0.814701 + 1.01402i
\(763\) 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
\(768\) −315916. + 498086.i −0.535610 + 0.844465i
\(769\) 173385. 300311.i 0.293196 0.507830i −0.681368 0.731941i \(-0.738614\pi\)
0.974564 + 0.224111i \(0.0719478\pi\)
\(770\) −114.121 932.610i −0.000192479 0.00157296i
\(771\) 72329.9 + 116641.i 0.121677 + 0.196220i
\(772\) −419197. + 104151.i −0.703369 + 0.174755i
\(773\) −456941. −0.764717 −0.382358 0.924014i \(-0.624888\pi\)
−0.382358 + 0.924014i \(0.624888\pi\)
\(774\) −348122. 406406.i −0.581098 0.678388i
\(775\) 853996.i 1.42185i
\(776\) 275050. 338803.i 0.456761 0.562632i
\(777\) −9606.30 305127.i −0.0159116 0.505403i
\(778\) −27919.5 228162.i −0.0461263 0.376951i
\(779\) −377159. 217753.i −0.621512 0.358830i
\(780\) 57749.5 + 56245.0i 0.0949202 + 0.0924474i
\(781\) 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
\(786\) 1.01571e6 156871.i 1.64408 0.253921i
\(787\) 602982. + 348132.i 0.973543 + 0.562075i 0.900314 0.435240i \(-0.143337\pi\)
0.0732283 + 0.997315i \(0.476670\pi\)
\(788\) 115675. + 119982.i 0.186289 + 0.193226i
\(789\) 29261.0 + 929423.i 0.0470040 + 1.49300i
\(790\) 16319.8 38403.2i 0.0261494 0.0615337i
\(791\) 273518.i 0.437153i
\(792\) 2467.89 25798.9i 0.00393437 0.0411293i
\(793\) 459430. 0.730589
\(794\) 48799.6 + 20737.9i 0.0774061 + 0.0328945i
\(795\) −51028.9 82290.7i −0.0807387 0.130202i
\(796\) −97201.6 + 93712.1i −0.153408 + 0.147900i
\(797\) −65680.3 + 113762.i −0.103399 + 0.179093i −0.913083 0.407773i \(-0.866305\pi\)
0.809684 + 0.586867i \(0.199639\pi\)
\(798\) −285081. 110692.i −0.447675 0.173824i
\(799\) −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
\(804\) −307561. 78075.6i −0.475794 0.120782i
\(805\) −14769.6 + 25581.7i −0.0227917 + 0.0394764i
\(806\) −1.50536e6 + 184206.i −2.31723 + 0.283552i
\(807\) −365791. + 682291.i −0.561677 + 1.04767i
\(808\) 124686. 153587.i 0.190984 0.235251i
\(809\) 796199. 1.21653 0.608267 0.793732i \(-0.291865\pi\)
0.608267 + 0.793732i \(0.291865\pi\)
\(810\) 13065.1 + 51672.9i 0.0199133 + 0.0787576i
\(811\) 116976.i 0.177851i −0.996038 0.0889253i \(-0.971657\pi\)
0.996038 0.0889253i \(-0.0283432\pi\)
\(812\) −57029.3 229536.i −0.0864940 0.348128i
\(813\) 123969. + 66462.4i 0.187556 + 0.100553i
\(814\) 29102.9 3561.24i 0.0439226 0.00537468i
\(815\) −27889.5 16102.0i −0.0419881 0.0242418i
\(816\) −529211. 309135.i −0.794783 0.464267i
\(817\) −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 \(0.903206\pi\)
\(822\) 20768.8 + 8064.15i 0.0307374 + 0.0119348i
\(823\) −198711. 114726.i −0.293375 0.169380i 0.346088 0.938202i \(-0.387510\pi\)
−0.639463 + 0.768822i \(0.720843\pi\)
\(824\) 109626. 686663.i 0.161457 1.01132i
\(825\) 23741.6 14722.3i 0.0348821 0.0216306i
\(826\) −513676. 218292.i −0.752886 0.319947i
\(827\) 673431.i 0.984651i 0.870411 + 0.492326i \(0.163853\pi\)
−0.870411 + 0.492326i \(0.836147\pi\)
\(828\) −549848. + 601304.i −0.802015 + 0.877068i
\(829\) 268282. 0.390375 0.195188 0.980766i \(-0.437468\pi\)
0.195188 + 0.980766i \(0.437468\pi\)
\(830\) 25381.8 59727.4i 0.0368439 0.0866996i
\(831\) 509279. 16033.6i 0.737486 0.0232183i
\(832\) −232017. 1.10496e6i −0.335177 1.59624i
\(833\) 248158. 429823.i 0.357634 0.619440i
\(834\) −690999. + 106721.i −0.993448 + 0.153433i
\(835\) −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 −0.967651 0.252292i \(-0.918816\pi\)
−0.265334 + 0.964156i \(0.585482\pi\)
\(840\) 3423.49 26845.5i 0.00485189 0.0380464i
\(841\) 149504. 258949.i 0.211379 0.366119i
\(842\) 80210.9 + 655494.i 0.113138 + 0.924581i
\(843\) −999108. + 31454.9i −1.40591 + 0.0442622i
\(844\) −88524.0 356299.i −0.124273 0.500183i
\(845\) −96307.2 −0.134879
\(846\) −74929.5 87474.5i −0.104692 0.122220i
\(847\) 338137.i 0.471330i
\(848\) −49559.1 + 1.35525e6i −0.0689179 + 1.88464i
\(849\) −697550. + 432554.i −0.967743 + 0.600102i
\(850\) −80241.4 655743.i −0.111061 0.907603i
\(851\) −798300. 460899.i −1.10232 0.636424i
\(852\) 20501.3 + 72662.3i 0.0282424 + 0.100099i
\(853\) −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 \(0.617669\pi\)
\(858\) 31072.3 + 38674.2i 0.0422084 + 0.0525348i
\(859\) −520799. 300684.i −0.705804 0.407496i 0.103702 0.994608i \(-0.466931\pi\)
−0.809505 + 0.587112i \(0.800265\pi\)
\(860\) 38636.2 37249.2i 0.0522394 0.0503640i
\(861\) −217642. 116683.i −0.293587 0.157399i
\(862\) −252927. + 595178.i −0.340393 + 0.801000i
\(863\) 1.01872e6i 1.36783i −0.729560 0.683917i \(-0.760275\pi\)
0.729560 0.683917i \(-0.239725\pi\)
\(864\) 251740. 702768.i 0.337228 0.941423i
\(865\) 38994.9 0.0521166
\(866\) −227639. 96737.6i −0.303536 0.128991i
\(867\) −54262.2 + 101212.i −0.0721870 + 0.134647i
\(868\) 353375. + 366533.i 0.469025 + 0.486490i
\(869\) 12839.6 22238.9i 0.0170025 0.0294492i
\(870\) −36418.0 + 29259.6i −0.0481147 + 0.0386571i
\(871\) 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
\(876\) −206816. + 58352.0i −0.269511 + 0.0760409i
\(877\) −432672. + 749411.i −0.562549 + 0.974363i 0.434724 + 0.900564i \(0.356846\pi\)
−0.997273 + 0.0737993i \(0.976488\pi\)
\(878\) 1.22877e6 150361.i 1.59398 0.195050i
\(879\) 393743. + 634962.i 0.509607 + 0.821807i
\(880\) 2597.49 + 94.9854i 0.00335419 + 0.000122657i
\(881\) 1.46275e6 1.88459 0.942296 0.334780i \(-0.108662\pi\)
0.942296 + 0.334780i \(0.108662\pi\)
\(882\) 570132. + 200966.i 0.732889 + 0.258337i
\(883\) 162909.i 0.208941i 0.994528 + 0.104470i \(0.0333148\pi\)
−0.994528 + 0.104470i \(0.966685\pi\)
\(884\) 1.13858e6 282886.i 1.45700 0.361999i
\(885\) 3469.03 + 110187.i 0.00442916 + 0.140684i
\(886\) −186206. + 22785.5i −0.237206 + 0.0290262i
\(887\) −192525. 111154.i −0.244703 0.141280i 0.372633 0.927979i \(-0.378455\pi\)
−0.617337 + 0.786699i \(0.711788\pi\)
\(888\) 837739. + 106833.i 1.06239 + 0.135482i
\(889\) 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
\(894\) 3402.87 + 22032.9i 0.00425766 + 0.0275674i
\(895\) −87627.1 50591.5i −0.109394 0.0631585i
\(896\) −249494. + 285347.i −0.310774 + 0.355432i
\(897\) −49080.0 1.55894e6i −0.0609986 1.93751i
\(898\) −459646. 195332.i −0.569995 0.242225i
\(899\) 878873.i 1.08744i
\(900\) 767162. 242759.i 0.947113 0.299703i
\(901\) −1.40918e6 −1.73587
\(902\) 9276.24 21828.5i 0.0114014 0.0268294i
\(903\) −181229. 292255.i −0.222255 0.358415i
\(904\) −747202. 119290.i −0.914326 0.145972i
\(905\) 14186.6 24571.9i 0.0173213 0.0300014i
\(906\) −56544.8 + 145628.i −0.0688868 + 0.177414i
\(907\) 1.03664e6 598505.i 1.26013 0.727534i 0.287028 0.957922i \(-0.407333\pi\)
0.973099 + 0.230388i \(0.0739995\pi\)
\(908\) 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 0.0716123 0.997433i \(-0.477186\pi\)
0.899608 + 0.436698i \(0.143852\pi\)
\(912\) 426724. 730513.i 0.513047 0.878290i
\(913\) 19969.1 34587.5i 0.0239562 0.0414933i
\(914\) 60972.0 + 498271.i 0.0729857 + 0.596449i
\(915\) −14394.6 + 26849.4i −0.0171932 + 0.0320695i
\(916\) −552022. + 137152.i −0.657908 + 0.163460i
\(917\) 660464. 0.785435
\(918\) 739317. + 234722.i 0.877295 + 0.278527i
\(919\) 1.46503e6i 1.73467i −0.497725 0.867335i \(-0.665831\pi\)
0.497725 0.867335i \(-0.334169\pi\)
\(920\) −63442.9 51504.8i −0.0749562 0.0608516i
\(921\) −517178. 277271.i −0.609707 0.326878i
\(922\) −50185.2 410120.i −0.0590355 0.482446i
\(923\) −125160. 72261.0i −0.146913 0.0848205i
\(924\) 4097.92 16142.8i 0.00479976 0.0189076i
\(925\) 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 \(-0.360468\pi\)
\(930\) 36399.7 93745.4i 0.0420854 0.108389i
\(931\) 593319. + 342553.i 0.684524 + 0.395210i
\(932\) 693399. + 719219.i 0.798273 + 0.827998i
\(933\) −1.02263e6 + 634137.i −1.17478 + 0.728484i
\(934\) 668612. 1.57335e6i 0.766444 1.80357i
\(935\) 2700.85i 0.00308942i
\(936\) 593392. + 1.29993e6i 0.677314 + 1.48377i
\(937\) −287243. −0.327167 −0.163584 0.986529i \(-0.552305\pi\)
−0.163584 + 0.986529i \(0.552305\pi\)
\(938\) −187674. 79753.9i −0.213303 0.0906455i
\(939\) −101111. + 3183.26i −0.114674 + 0.00361028i
\(940\) 8316.04 8017.49i 0.00941154 0.00907367i
\(941\) 149097. 258244.i 0.168380 0.291643i −0.769470 0.638683i \(-0.779480\pi\)
0.937850 + 0.347040i \(0.112813\pi\)
\(942\) −34110.8 220861.i −0.0384407 0.248895i
\(943\) −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 −0.910680 0.413113i \(-0.864441\pi\)
−0.0975732 + 0.995228i \(0.531108\pi\)
\(948\) 516069. 529873.i 0.574237 0.589597i
\(949\) 205674. 356238.i 0.228374 0.395555i
\(950\) 905175. 110764.i 1.00296 0.122730i
\(951\) 352681. 11103.4i 0.389961 0.0122771i
\(952\) −305780. 248241.i −0.337392 0.273905i
\(953\) −1.38691e6 −1.52708 −0.763539 0.645762i \(-0.776540\pi\)
−0.763539 + 0.645762i \(0.776540\pi\)
\(954\) −315229. 1.68719e6i −0.346362 1.85382i
\(955\) 63305.1i 0.0694115i
\(956\) −14480.7 58283.3i −0.0158444 0.0637717i
\(957\) −24433.2 + 15151.2i −0.0266782 + 0.0165433i
\(958\) −762556. + 93311.7i −0.830885 + 0.101673i
\(959\) 12399.2 + 7158.71i 0.0134821 + 0.00778391i
\(960\) 71843.9 + 21060.6i 0.0779556 + 0.0228522i
\(961\) 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
\(966\) −408189. + 327954.i −0.437429 + 0.351447i
\(967\) 697159. + 402505.i 0.745554 + 0.430446i 0.824085 0.566466i \(-0.191690\pi\)
−0.0785311 + 0.996912i \(0.525023\pi\)
\(968\) −923727. 147473.i −0.985809 0.157384i
\(969\) 774772. + 415372.i 0.825137 + 0.442374i
\(970\) −50979.9 21664.4i −0.0541821 0.0230252i
\(971\) 643421.i 0.682428i 0.939986 + 0.341214i \(0.110838\pi\)
−0.939986 + 0.341214i \(0.889162\pi\)
\(972\) −115646. + 937679.i −0.122405 + 0.992480i
\(973\) −449321. −0.474604
\(974\) 82735.5 194690.i 0.0872116 0.205223i
\(975\) −727788. + 1.35750e6i −0.765588 + 1.42801i
\(976\) 377067. 199695.i 0.395839 0.209637i
\(977\) 63505.8 109995.i 0.0665311 0.115235i −0.830841 0.556510i \(-0.812140\pi\)
0.897372 + 0.441275i \(0.145474\pi\)
\(978\) −357540. 445014.i −0.373807 0.465260i
\(979\) −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 −0.415650 0.909525i \(-0.636446\pi\)
0.579847 + 0.814725i \(0.303112\pi\)
\(984\) 413677. 543669.i 0.427239 0.561493i
\(985\) 10577.4 18320.6i 0.0109020 0.0188828i
\(986\) 82578.9 + 674846.i 0.0849406 + 0.694146i
\(987\) −39007.5 62904.7i −0.0400418 0.0645727i
\(988\) 390490. + 1.57168e6i 0.400034 + 1.61009i
\(989\) −1.03837e6 −1.06160
\(990\) −3233.69 + 604.171i −0.00329934 + 0.000616438i
\(991\) 684255.i 0.696740i −0.937357 0.348370i \(-0.886735\pi\)
0.937357 0.348370i \(-0.113265\pi\)
\(992\) −1.15542e6 + 805497.i −1.17413 + 0.818542i
\(993\) 21170.1 + 672429.i 0.0214696 + 0.681943i
\(994\) 5893.04 + 48158.7i 0.00596440 + 0.0487419i
\(995\) 14842.1 + 8569.07i 0.0149916 + 0.00865541i
\(996\) 802628. 824096.i 0.809087 0.830729i
\(997\) 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.31.20 yes 44
3.2 odd 2 108.5.f.a.91.3 44
4.3 odd 2 inner 36.5.f.a.31.11 yes 44
9.2 odd 6 108.5.f.a.19.12 44
9.4 even 3 324.5.d.f.163.6 22
9.5 odd 6 324.5.d.e.163.17 22
9.7 even 3 inner 36.5.f.a.7.11 44
12.11 even 2 108.5.f.a.91.12 44
36.7 odd 6 inner 36.5.f.a.7.20 yes 44
36.11 even 6 108.5.f.a.19.3 44
36.23 even 6 324.5.d.e.163.18 22
36.31 odd 6 324.5.d.f.163.5 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.5.f.a.7.11 44 9.7 even 3 inner
36.5.f.a.7.20 yes 44 36.7 odd 6 inner
36.5.f.a.31.11 yes 44 4.3 odd 2 inner
36.5.f.a.31.20 yes 44 1.1 even 1 trivial
108.5.f.a.19.3 44 36.11 even 6
108.5.f.a.19.12 44 9.2 odd 6
108.5.f.a.91.3 44 3.2 odd 2
108.5.f.a.91.12 44 12.11 even 2
324.5.d.e.163.17 22 9.5 odd 6
324.5.d.e.163.18 22 36.23 even 6
324.5.d.f.163.5 22 36.31 odd 6
324.5.d.f.163.6 22 9.4 even 3