Properties

Label 72.3.p.b.43.9
Level $72$
Weight $3$
Character 72.43
Analytic conductor $1.962$
Analytic rank $0$
Dimension $40$
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] = [72,3,Mod(43,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.p (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: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.9
Character \(\chi\) \(=\) 72.43
Dual form 72.3.p.b.67.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.564251 - 1.91875i) q^{2} +(1.21551 - 2.74272i) q^{3} +(-3.36324 + 2.16532i) q^{4} +(5.15803 - 2.97799i) q^{5} +(-5.94847 - 0.784682i) q^{6} +(-4.09037 - 2.36158i) q^{7} +(6.05243 + 5.23145i) q^{8} +(-6.04507 - 6.66762i) q^{9} +O(q^{10})\) \(q+(-0.564251 - 1.91875i) q^{2} +(1.21551 - 2.74272i) q^{3} +(-3.36324 + 2.16532i) q^{4} +(5.15803 - 2.97799i) q^{5} +(-5.94847 - 0.784682i) q^{6} +(-4.09037 - 2.36158i) q^{7} +(6.05243 + 5.23145i) q^{8} +(-6.04507 - 6.66762i) q^{9} +(-8.62446 - 8.21666i) q^{10} +(-6.94921 + 12.0364i) q^{11} +(1.85082 + 11.8564i) q^{12} +(4.03163 - 2.32766i) q^{13} +(-2.22329 + 9.18095i) q^{14} +(-1.89816 - 17.7668i) q^{15} +(6.62277 - 14.5650i) q^{16} +21.5221 q^{17} +(-9.38260 + 15.3612i) q^{18} +3.83672 q^{19} +(-10.8994 + 21.1845i) q^{20} +(-11.4491 + 8.34824i) q^{21} +(27.0160 + 6.54228i) q^{22} +(30.0178 - 17.3308i) q^{23} +(21.7052 - 10.2413i) q^{24} +(5.23684 - 9.07047i) q^{25} +(-6.74106 - 6.42232i) q^{26} +(-25.6353 + 8.47537i) q^{27} +(18.8705 - 0.914414i) q^{28} +(39.3950 + 22.7447i) q^{29} +(-33.0191 + 13.6671i) q^{30} +(-31.8750 + 18.4030i) q^{31} +(-31.6836 - 4.48916i) q^{32} +(24.5656 + 33.6901i) q^{33} +(-12.1439 - 41.2956i) q^{34} -28.1310 q^{35} +(34.7685 + 9.33531i) q^{36} +36.0613i q^{37} +(-2.16488 - 7.36173i) q^{38} +(-1.48364 - 13.8869i) q^{39} +(46.7978 + 8.95988i) q^{40} +(-10.2409 - 17.7377i) q^{41} +(22.4784 + 17.2574i) q^{42} +(3.50522 - 6.07122i) q^{43} +(-2.69077 - 55.5285i) q^{44} +(-51.0367 - 16.3896i) q^{45} +(-50.1912 - 47.8179i) q^{46} +(-53.1514 - 30.6870i) q^{47} +(-31.8977 - 35.8683i) q^{48} +(-13.3459 - 23.1158i) q^{49} +(-20.3589 - 4.93018i) q^{50} +(26.1603 - 59.0291i) q^{51} +(-8.51920 + 16.5582i) q^{52} +58.7545i q^{53} +(30.7269 + 44.4056i) q^{54} +82.7787i q^{55} +(-12.4022 - 35.6919i) q^{56} +(4.66358 - 10.5231i) q^{57} +(21.4128 - 88.4230i) q^{58} +(11.0410 + 19.1235i) q^{59} +(44.8548 + 55.6440i) q^{60} +(-47.1047 - 27.1959i) q^{61} +(53.2964 + 50.7763i) q^{62} +(8.98046 + 41.5490i) q^{63} +(9.26389 + 63.3260i) q^{64} +(13.8635 - 24.0123i) q^{65} +(50.7819 - 66.1451i) q^{66} +(56.9612 + 98.6596i) q^{67} +(-72.3839 + 46.6022i) q^{68} +(-11.0466 - 103.396i) q^{69} +(15.8730 + 53.9765i) q^{70} +8.30318i q^{71} +(-1.70603 - 71.9798i) q^{72} -114.051 q^{73} +(69.1928 - 20.3476i) q^{74} +(-18.5124 - 25.3885i) q^{75} +(-12.9038 + 8.30773i) q^{76} +(56.8497 - 32.8222i) q^{77} +(-25.8085 + 10.6825i) q^{78} +(47.5352 + 27.4445i) q^{79} +(-9.21392 - 94.8492i) q^{80} +(-7.91437 + 80.6124i) q^{81} +(-28.2559 + 29.6582i) q^{82} +(15.6347 - 27.0802i) q^{83} +(20.4293 - 52.8680i) q^{84} +(111.011 - 64.0925i) q^{85} +(-13.6270 - 3.29996i) q^{86} +(110.267 - 80.4031i) q^{87} +(-105.027 + 36.4950i) q^{88} +47.7407 q^{89} +(-2.65017 + 107.175i) q^{90} -21.9878 q^{91} +(-63.4304 + 123.286i) q^{92} +(11.7300 + 109.793i) q^{93} +(-28.8900 + 119.300i) q^{94} +(19.7899 - 11.4257i) q^{95} +(-50.8242 + 81.4426i) q^{96} +(-28.7623 + 49.8177i) q^{97} +(-36.8231 + 38.6506i) q^{98} +(122.262 - 26.4260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.564251 1.91875i −0.282126 0.959377i
\(3\) 1.21551 2.74272i 0.405170 0.914241i
\(4\) −3.36324 + 2.16532i −0.840810 + 0.541330i
\(5\) 5.15803 2.97799i 1.03161 0.595598i 0.114161 0.993462i \(-0.463582\pi\)
0.917444 + 0.397864i \(0.130249\pi\)
\(6\) −5.94847 0.784682i −0.991411 0.130780i
\(7\) −4.09037 2.36158i −0.584339 0.337368i 0.178517 0.983937i \(-0.442870\pi\)
−0.762856 + 0.646569i \(0.776203\pi\)
\(8\) 6.05243 + 5.23145i 0.756554 + 0.653931i
\(9\) −6.04507 6.66762i −0.671674 0.740847i
\(10\) −8.62446 8.21666i −0.862446 0.821666i
\(11\) −6.94921 + 12.0364i −0.631746 + 1.09422i 0.355448 + 0.934696i \(0.384328\pi\)
−0.987195 + 0.159521i \(0.949005\pi\)
\(12\) 1.85082 + 11.8564i 0.154235 + 0.988034i
\(13\) 4.03163 2.32766i 0.310125 0.179051i −0.336857 0.941556i \(-0.609364\pi\)
0.646982 + 0.762505i \(0.276031\pi\)
\(14\) −2.22329 + 9.18095i −0.158806 + 0.655782i
\(15\) −1.89816 17.7668i −0.126544 1.18446i
\(16\) 6.62277 14.5650i 0.413923 0.910312i
\(17\) 21.5221 1.26600 0.633002 0.774150i \(-0.281822\pi\)
0.633002 + 0.774150i \(0.281822\pi\)
\(18\) −9.38260 + 15.3612i −0.521255 + 0.853401i
\(19\) 3.83672 0.201933 0.100966 0.994890i \(-0.467807\pi\)
0.100966 + 0.994890i \(0.467807\pi\)
\(20\) −10.8994 + 21.1845i −0.544969 + 1.05922i
\(21\) −11.4491 + 8.34824i −0.545193 + 0.397535i
\(22\) 27.0160 + 6.54228i 1.22800 + 0.297376i
\(23\) 30.0178 17.3308i 1.30512 0.753513i 0.323845 0.946110i \(-0.395024\pi\)
0.981278 + 0.192597i \(0.0616910\pi\)
\(24\) 21.7052 10.2413i 0.904384 0.426719i
\(25\) 5.23684 9.07047i 0.209474 0.362819i
\(26\) −6.74106 6.42232i −0.259272 0.247012i
\(27\) −25.6353 + 8.47537i −0.949455 + 0.313903i
\(28\) 18.8705 0.914414i 0.673946 0.0326577i
\(29\) 39.3950 + 22.7447i 1.35845 + 0.784300i 0.989415 0.145116i \(-0.0463556\pi\)
0.369033 + 0.929416i \(0.379689\pi\)
\(30\) −33.0191 + 13.6671i −1.10064 + 0.455569i
\(31\) −31.8750 + 18.4030i −1.02822 + 0.593646i −0.916476 0.400091i \(-0.868979\pi\)
−0.111749 + 0.993736i \(0.535645\pi\)
\(32\) −31.6836 4.48916i −0.990111 0.140286i
\(33\) 24.5656 + 33.6901i 0.744413 + 1.02091i
\(34\) −12.1439 41.2956i −0.357172 1.21458i
\(35\) −28.1310 −0.803743
\(36\) 34.7685 + 9.33531i 0.965793 + 0.259314i
\(37\) 36.0613i 0.974630i 0.873226 + 0.487315i \(0.162024\pi\)
−0.873226 + 0.487315i \(0.837976\pi\)
\(38\) −2.16488 7.36173i −0.0569704 0.193730i
\(39\) −1.48364 13.8869i −0.0380421 0.356075i
\(40\) 46.7978 + 8.95988i 1.16995 + 0.223997i
\(41\) −10.2409 17.7377i −0.249777 0.432627i 0.713687 0.700465i \(-0.247024\pi\)
−0.963464 + 0.267838i \(0.913691\pi\)
\(42\) 22.4784 + 17.2574i 0.535199 + 0.410891i
\(43\) 3.50522 6.07122i 0.0815167 0.141191i −0.822385 0.568932i \(-0.807357\pi\)
0.903902 + 0.427740i \(0.140690\pi\)
\(44\) −2.69077 55.5285i −0.0611538 1.26201i
\(45\) −51.0367 16.3896i −1.13415 0.364214i
\(46\) −50.1912 47.8179i −1.09111 1.03952i
\(47\) −53.1514 30.6870i −1.13088 0.652914i −0.186724 0.982412i \(-0.559787\pi\)
−0.944156 + 0.329499i \(0.893120\pi\)
\(48\) −31.8977 35.8683i −0.664535 0.747257i
\(49\) −13.3459 23.1158i −0.272365 0.471750i
\(50\) −20.3589 4.93018i −0.407178 0.0986037i
\(51\) 26.1603 59.0291i 0.512947 1.15743i
\(52\) −8.51920 + 16.5582i −0.163831 + 0.318428i
\(53\) 58.7545i 1.10858i 0.832325 + 0.554288i \(0.187009\pi\)
−0.832325 + 0.554288i \(0.812991\pi\)
\(54\) 30.7269 + 44.4056i 0.569017 + 0.822326i
\(55\) 82.7787i 1.50507i
\(56\) −12.4022 35.6919i −0.221468 0.637355i
\(57\) 4.66358 10.5231i 0.0818171 0.184615i
\(58\) 21.4128 88.4230i 0.369187 1.52454i
\(59\) 11.0410 + 19.1235i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(60\) 44.8548 + 55.6440i 0.747581 + 0.927400i
\(61\) −47.1047 27.1959i −0.772209 0.445835i 0.0614532 0.998110i \(-0.480427\pi\)
−0.833662 + 0.552275i \(0.813760\pi\)
\(62\) 53.2964 + 50.7763i 0.859619 + 0.818973i
\(63\) 8.98046 + 41.5490i 0.142547 + 0.659507i
\(64\) 9.26389 + 63.3260i 0.144748 + 0.989469i
\(65\) 13.8635 24.0123i 0.213285 0.369420i
\(66\) 50.7819 66.1451i 0.769422 1.00220i
\(67\) 56.9612 + 98.6596i 0.850167 + 1.47253i 0.881058 + 0.473009i \(0.156832\pi\)
−0.0308908 + 0.999523i \(0.509834\pi\)
\(68\) −72.3839 + 46.6022i −1.06447 + 0.685326i
\(69\) −11.0466 103.396i −0.160096 1.49850i
\(70\) 15.8730 + 53.9765i 0.226757 + 0.771093i
\(71\) 8.30318i 0.116946i 0.998289 + 0.0584731i \(0.0186232\pi\)
−0.998289 + 0.0584731i \(0.981377\pi\)
\(72\) −1.70603 71.9798i −0.0236948 0.999719i
\(73\) −114.051 −1.56234 −0.781172 0.624316i \(-0.785378\pi\)
−0.781172 + 0.624316i \(0.785378\pi\)
\(74\) 69.1928 20.3476i 0.935038 0.274968i
\(75\) −18.5124 25.3885i −0.246831 0.338513i
\(76\) −12.9038 + 8.30773i −0.169787 + 0.109312i
\(77\) 56.8497 32.8222i 0.738308 0.426262i
\(78\) −25.8085 + 10.6825i −0.330878 + 0.136955i
\(79\) 47.5352 + 27.4445i 0.601712 + 0.347399i 0.769715 0.638388i \(-0.220398\pi\)
−0.168003 + 0.985787i \(0.553732\pi\)
\(80\) −9.21392 94.8492i −0.115174 1.18561i
\(81\) −7.91437 + 80.6124i −0.0977083 + 0.995215i
\(82\) −28.2559 + 29.6582i −0.344584 + 0.361686i
\(83\) 15.6347 27.0802i 0.188370 0.326267i −0.756337 0.654183i \(-0.773013\pi\)
0.944707 + 0.327916i \(0.106346\pi\)
\(84\) 20.4293 52.8680i 0.243206 0.629381i
\(85\) 111.011 64.0925i 1.30602 0.754029i
\(86\) −13.6270 3.29996i −0.158454 0.0383717i
\(87\) 110.267 80.4031i 1.26744 0.924174i
\(88\) −105.027 + 36.4950i −1.19349 + 0.414715i
\(89\) 47.7407 0.536413 0.268206 0.963361i \(-0.413569\pi\)
0.268206 + 0.963361i \(0.413569\pi\)
\(90\) −2.65017 + 107.175i −0.0294463 + 1.19083i
\(91\) −21.9878 −0.241624
\(92\) −63.4304 + 123.286i −0.689461 + 1.34006i
\(93\) 11.7300 + 109.793i 0.126129 + 1.18057i
\(94\) −28.8900 + 119.300i −0.307340 + 1.26914i
\(95\) 19.7899 11.4257i 0.208315 0.120271i
\(96\) −50.8242 + 81.4426i −0.529419 + 0.848360i
\(97\) −28.7623 + 49.8177i −0.296518 + 0.513585i −0.975337 0.220721i \(-0.929159\pi\)
0.678819 + 0.734306i \(0.262492\pi\)
\(98\) −36.8231 + 38.6506i −0.375745 + 0.394394i
\(99\) 122.262 26.4260i 1.23497 0.266929i
\(100\) 2.02773 + 41.8456i 0.0202773 + 0.418456i
\(101\) −114.007 65.8222i −1.12879 0.651705i −0.185157 0.982709i \(-0.559279\pi\)
−0.943629 + 0.331004i \(0.892613\pi\)
\(102\) −128.023 16.8880i −1.25513 0.165568i
\(103\) −37.1176 + 21.4299i −0.360365 + 0.208057i −0.669241 0.743045i \(-0.733381\pi\)
0.308876 + 0.951102i \(0.400047\pi\)
\(104\) 36.5782 + 7.00324i 0.351713 + 0.0673388i
\(105\) −34.1936 + 77.1556i −0.325653 + 0.734815i
\(106\) 112.735 33.1523i 1.06354 0.312758i
\(107\) −91.6085 −0.856154 −0.428077 0.903742i \(-0.640809\pi\)
−0.428077 + 0.903742i \(0.640809\pi\)
\(108\) 67.8657 84.0133i 0.628387 0.777901i
\(109\) 152.712i 1.40102i −0.713641 0.700512i \(-0.752955\pi\)
0.713641 0.700512i \(-0.247045\pi\)
\(110\) 158.832 46.7080i 1.44393 0.424618i
\(111\) 98.9062 + 43.8329i 0.891046 + 0.394891i
\(112\) −61.4860 + 43.9360i −0.548982 + 0.392286i
\(113\) 8.45762 + 14.6490i 0.0748462 + 0.129637i 0.901019 0.433779i \(-0.142820\pi\)
−0.826173 + 0.563416i \(0.809487\pi\)
\(114\) −22.8226 3.01061i −0.200198 0.0264088i
\(115\) 103.222 178.786i 0.897582 1.55466i
\(116\) −181.744 + 8.80686i −1.56676 + 0.0759212i
\(117\) −39.8914 12.8105i −0.340952 0.109491i
\(118\) 30.4634 31.9754i 0.258165 0.270978i
\(119\) −88.0333 50.8261i −0.739776 0.427110i
\(120\) 81.4578 117.463i 0.678815 0.978855i
\(121\) −36.0830 62.4976i −0.298206 0.516509i
\(122\) −25.6034 + 105.728i −0.209864 + 0.866621i
\(123\) −61.0975 + 6.52749i −0.496727 + 0.0530690i
\(124\) 67.3547 130.913i 0.543183 1.05575i
\(125\) 86.5185i 0.692148i
\(126\) 74.6550 40.6754i 0.592500 0.322820i
\(127\) 144.231i 1.13568i −0.823140 0.567839i \(-0.807780\pi\)
0.823140 0.567839i \(-0.192220\pi\)
\(128\) 116.280 53.5069i 0.908437 0.418023i
\(129\) −12.3910 16.9935i −0.0960546 0.131732i
\(130\) −53.8962 13.0517i −0.414586 0.100398i
\(131\) 8.71188 + 15.0894i 0.0665029 + 0.115186i 0.897360 0.441300i \(-0.145482\pi\)
−0.830857 + 0.556486i \(0.812149\pi\)
\(132\) −155.570 60.1155i −1.17856 0.455420i
\(133\) −15.6936 9.06072i −0.117997 0.0681257i
\(134\) 157.163 164.963i 1.17286 1.23107i
\(135\) −106.988 + 120.058i −0.792504 + 0.889317i
\(136\) 130.261 + 112.592i 0.957801 + 0.827879i
\(137\) 46.5748 80.6699i 0.339962 0.588831i −0.644463 0.764635i \(-0.722919\pi\)
0.984425 + 0.175804i \(0.0562525\pi\)
\(138\) −192.159 + 79.5373i −1.39246 + 0.576357i
\(139\) 22.0873 + 38.2563i 0.158902 + 0.275226i 0.934473 0.356034i \(-0.115871\pi\)
−0.775571 + 0.631260i \(0.782538\pi\)
\(140\) 94.6114 60.9127i 0.675796 0.435091i
\(141\) −148.772 + 108.479i −1.05512 + 0.769356i
\(142\) 15.9318 4.68508i 0.112196 0.0329935i
\(143\) 64.7016i 0.452459i
\(144\) −137.149 + 43.8881i −0.952423 + 0.304779i
\(145\) 270.934 1.86851
\(146\) 64.3535 + 218.836i 0.440777 + 1.49888i
\(147\) −79.6222 + 8.50663i −0.541648 + 0.0578682i
\(148\) −78.0843 121.283i −0.527596 0.819478i
\(149\) −27.3905 + 15.8139i −0.183829 + 0.106134i −0.589090 0.808067i \(-0.700514\pi\)
0.405261 + 0.914201i \(0.367180\pi\)
\(150\) −38.2686 + 49.8462i −0.255124 + 0.332308i
\(151\) −15.3552 8.86531i −0.101690 0.0587106i 0.448293 0.893887i \(-0.352032\pi\)
−0.549982 + 0.835176i \(0.685366\pi\)
\(152\) 23.2215 + 20.0716i 0.152773 + 0.132050i
\(153\) −130.102 143.501i −0.850342 0.937915i
\(154\) −95.0553 90.5607i −0.617242 0.588056i
\(155\) −109.608 + 189.847i −0.707148 + 1.22482i
\(156\) 35.0595 + 43.4925i 0.224740 + 0.278798i
\(157\) 76.4244 44.1236i 0.486780 0.281042i −0.236458 0.971642i \(-0.575987\pi\)
0.723237 + 0.690599i \(0.242653\pi\)
\(158\) 25.8374 106.694i 0.163528 0.675279i
\(159\) 161.147 + 71.4168i 1.01351 + 0.449162i
\(160\) −176.793 + 71.1980i −1.10496 + 0.444988i
\(161\) −163.712 −1.01685
\(162\) 159.141 30.2999i 0.982353 0.187037i
\(163\) 33.8559 0.207705 0.103852 0.994593i \(-0.466883\pi\)
0.103852 + 0.994593i \(0.466883\pi\)
\(164\) 72.8503 + 37.4814i 0.444209 + 0.228545i
\(165\) 227.039 + 100.618i 1.37599 + 0.609808i
\(166\) −60.7821 14.7192i −0.366157 0.0886699i
\(167\) −50.0218 + 28.8801i −0.299531 + 0.172935i −0.642232 0.766510i \(-0.721992\pi\)
0.342701 + 0.939445i \(0.388658\pi\)
\(168\) −112.968 9.36797i −0.672429 0.0557617i
\(169\) −73.6640 + 127.590i −0.435882 + 0.754969i
\(170\) −185.616 176.839i −1.09186 1.04023i
\(171\) −23.1932 25.5818i −0.135633 0.149601i
\(172\) 1.35724 + 28.0089i 0.00789092 + 0.162842i
\(173\) −15.6471 9.03387i −0.0904458 0.0522189i 0.454095 0.890953i \(-0.349963\pi\)
−0.544541 + 0.838734i \(0.683296\pi\)
\(174\) −216.492 166.209i −1.24421 0.955222i
\(175\) −42.8413 + 24.7344i −0.244807 + 0.141340i
\(176\) 129.287 + 180.929i 0.734584 + 1.02801i
\(177\) 65.8709 7.03747i 0.372152 0.0397597i
\(178\) −26.9378 91.6028i −0.151336 0.514622i
\(179\) 264.511 1.47771 0.738857 0.673862i \(-0.235366\pi\)
0.738857 + 0.673862i \(0.235366\pi\)
\(180\) 207.138 55.3885i 1.15076 0.307714i
\(181\) 185.479i 1.02475i 0.858762 + 0.512374i \(0.171234\pi\)
−0.858762 + 0.512374i \(0.828766\pi\)
\(182\) 12.4067 + 42.1892i 0.0681684 + 0.231809i
\(183\) −131.847 + 96.1383i −0.720477 + 0.525346i
\(184\) 272.346 + 52.1432i 1.48014 + 0.283387i
\(185\) 107.390 + 186.005i 0.580487 + 1.00543i
\(186\) 204.048 84.4581i 1.09703 0.454076i
\(187\) −149.561 + 259.048i −0.799793 + 1.38528i
\(188\) 245.208 11.8821i 1.30430 0.0632028i
\(189\) 124.873 + 25.8723i 0.660705 + 0.136890i
\(190\) −33.0896 31.5250i −0.174156 0.165921i
\(191\) −79.8243 46.0866i −0.417928 0.241291i 0.276262 0.961082i \(-0.410904\pi\)
−0.694191 + 0.719791i \(0.744237\pi\)
\(192\) 184.946 + 51.5652i 0.963261 + 0.268569i
\(193\) −135.169 234.120i −0.700359 1.21306i −0.968341 0.249633i \(-0.919690\pi\)
0.267982 0.963424i \(-0.413643\pi\)
\(194\) 111.817 + 27.0780i 0.576377 + 0.139578i
\(195\) −49.0078 67.2109i −0.251322 0.344671i
\(196\) 94.9385 + 48.8457i 0.484380 + 0.249213i
\(197\) 140.218i 0.711765i 0.934531 + 0.355883i \(0.115820\pi\)
−0.934531 + 0.355883i \(0.884180\pi\)
\(198\) −119.692 219.681i −0.604504 1.10950i
\(199\) 272.949i 1.37160i −0.727788 0.685802i \(-0.759452\pi\)
0.727788 0.685802i \(-0.240548\pi\)
\(200\) 79.1473 27.5022i 0.395737 0.137511i
\(201\) 339.833 36.3068i 1.69071 0.180631i
\(202\) −61.9678 + 255.893i −0.306771 + 1.26679i
\(203\) −107.427 186.069i −0.529196 0.916594i
\(204\) 39.8335 + 255.174i 0.195262 + 1.25086i
\(205\) −105.645 60.9944i −0.515343 0.297533i
\(206\) 62.0623 + 59.1278i 0.301273 + 0.287028i
\(207\) −297.015 95.3817i −1.43486 0.460781i
\(208\) −7.20180 74.1361i −0.0346240 0.356424i
\(209\) −26.6622 + 46.1802i −0.127570 + 0.220958i
\(210\) 167.336 + 22.0739i 0.796840 + 0.105114i
\(211\) −64.2535 111.290i −0.304519 0.527443i 0.672635 0.739974i \(-0.265162\pi\)
−0.977154 + 0.212532i \(0.931829\pi\)
\(212\) −127.222 197.606i −0.600105 0.932102i
\(213\) 22.7733 + 10.0926i 0.106917 + 0.0473831i
\(214\) 51.6902 + 175.774i 0.241543 + 0.821375i
\(215\) 41.7540i 0.194205i
\(216\) −199.494 82.8131i −0.923585 0.383394i
\(217\) 173.841 0.801109
\(218\) −293.016 + 86.1677i −1.34411 + 0.395265i
\(219\) −138.630 + 312.811i −0.633015 + 1.42836i
\(220\) −179.242 278.405i −0.814738 1.26548i
\(221\) 86.7689 50.0961i 0.392620 0.226679i
\(222\) 28.2967 214.509i 0.127462 0.966259i
\(223\) 251.240 + 145.054i 1.12664 + 0.650465i 0.943087 0.332546i \(-0.107908\pi\)
0.183551 + 0.983010i \(0.441241\pi\)
\(224\) 118.996 + 93.1855i 0.531232 + 0.416007i
\(225\) −92.1355 + 19.9143i −0.409491 + 0.0885081i
\(226\) 23.3357 24.4938i 0.103255 0.108380i
\(227\) 132.263 229.086i 0.582656 1.00919i −0.412507 0.910954i \(-0.635347\pi\)
0.995163 0.0982354i \(-0.0313198\pi\)
\(228\) 7.10108 + 45.4897i 0.0311451 + 0.199516i
\(229\) −143.260 + 82.7110i −0.625588 + 0.361183i −0.779041 0.626973i \(-0.784294\pi\)
0.153454 + 0.988156i \(0.450960\pi\)
\(230\) −401.289 97.1775i −1.74473 0.422511i
\(231\) −20.9208 195.819i −0.0905660 0.847700i
\(232\) 119.448 + 343.754i 0.514861 + 1.48170i
\(233\) 163.520 0.701803 0.350902 0.936412i \(-0.385875\pi\)
0.350902 + 0.936412i \(0.385875\pi\)
\(234\) −2.07143 + 83.7702i −0.00885225 + 0.357992i
\(235\) −365.542 −1.55550
\(236\) −78.5419 40.4097i −0.332805 0.171228i
\(237\) 133.052 97.0170i 0.561402 0.409354i
\(238\) −47.8498 + 197.593i −0.201050 + 0.830223i
\(239\) 79.7160 46.0240i 0.333540 0.192569i −0.323872 0.946101i \(-0.604985\pi\)
0.657412 + 0.753532i \(0.271651\pi\)
\(240\) −271.345 90.0190i −1.13060 0.375079i
\(241\) 16.0255 27.7570i 0.0664958 0.115174i −0.830861 0.556480i \(-0.812151\pi\)
0.897357 + 0.441306i \(0.145485\pi\)
\(242\) −99.5576 + 104.499i −0.411395 + 0.431813i
\(243\) 211.478 + 119.692i 0.870278 + 0.492561i
\(244\) 217.312 10.5304i 0.890625 0.0431573i
\(245\) −137.677 79.4879i −0.561947 0.324440i
\(246\) 46.9990 + 113.548i 0.191053 + 0.461577i
\(247\) 15.4682 8.93058i 0.0626244 0.0361562i
\(248\) −289.196 55.3692i −1.16611 0.223263i
\(249\) −55.2692 75.7980i −0.221965 0.304410i
\(250\) 166.008 48.8182i 0.664031 0.195273i
\(251\) −108.956 −0.434088 −0.217044 0.976162i \(-0.569641\pi\)
−0.217044 + 0.976162i \(0.569641\pi\)
\(252\) −120.170 120.294i −0.476866 0.477355i
\(253\) 481.741i 1.90412i
\(254\) −276.744 + 81.3826i −1.08954 + 0.320404i
\(255\) −40.8523 382.379i −0.160205 1.49952i
\(256\) −168.278 192.921i −0.657335 0.753599i
\(257\) −244.729 423.883i −0.952252 1.64935i −0.740535 0.672018i \(-0.765428\pi\)
−0.211717 0.977331i \(-0.567906\pi\)
\(258\) −25.6147 + 33.3640i −0.0992816 + 0.129318i
\(259\) 85.1616 147.504i 0.328809 0.569514i
\(260\) 5.36801 + 110.778i 0.0206462 + 0.426069i
\(261\) −86.4921 400.164i −0.331388 1.53320i
\(262\) 24.0372 25.2302i 0.0917451 0.0962984i
\(263\) 341.950 + 197.425i 1.30019 + 0.750666i 0.980437 0.196835i \(-0.0630662\pi\)
0.319755 + 0.947500i \(0.396400\pi\)
\(264\) −27.5663 + 332.421i −0.104418 + 1.25917i
\(265\) 174.970 + 303.057i 0.660265 + 1.14361i
\(266\) −8.53015 + 35.2247i −0.0320682 + 0.132424i
\(267\) 58.0294 130.940i 0.217339 0.490411i
\(268\) −405.204 208.477i −1.51195 0.777899i
\(269\) 359.184i 1.33526i −0.744494 0.667629i \(-0.767309\pi\)
0.744494 0.667629i \(-0.232691\pi\)
\(270\) 290.730 + 137.541i 1.07678 + 0.509411i
\(271\) 223.217i 0.823680i −0.911256 0.411840i \(-0.864886\pi\)
0.911256 0.411840i \(-0.135114\pi\)
\(272\) 142.536 313.469i 0.524029 1.15246i
\(273\) −26.7264 + 60.3065i −0.0978990 + 0.220903i
\(274\) −181.066 43.8475i −0.660824 0.160027i
\(275\) 72.7838 + 126.065i 0.264668 + 0.458419i
\(276\) 261.039 + 323.828i 0.945792 + 1.17329i
\(277\) 111.426 + 64.3319i 0.402260 + 0.232245i 0.687459 0.726223i \(-0.258726\pi\)
−0.285198 + 0.958468i \(0.592060\pi\)
\(278\) 60.9418 63.9663i 0.219215 0.230095i
\(279\) 315.391 + 101.283i 1.13043 + 0.363021i
\(280\) −170.261 147.166i −0.608075 0.525593i
\(281\) −169.623 + 293.796i −0.603642 + 1.04554i 0.388622 + 0.921397i \(0.372951\pi\)
−0.992264 + 0.124142i \(0.960382\pi\)
\(282\) 292.090 + 224.247i 1.03578 + 0.795203i
\(283\) 8.66907 + 15.0153i 0.0306327 + 0.0530575i 0.880935 0.473237i \(-0.156914\pi\)
−0.850303 + 0.526294i \(0.823581\pi\)
\(284\) −17.9790 27.9256i −0.0633065 0.0983295i
\(285\) −7.28271 68.1663i −0.0255534 0.239180i
\(286\) 124.146 36.5080i 0.434079 0.127650i
\(287\) 96.7384i 0.337068i
\(288\) 161.597 + 238.391i 0.561101 + 0.827747i
\(289\) 174.199 0.602766
\(290\) −152.875 519.856i −0.527155 1.79261i
\(291\) 101.675 + 139.441i 0.349400 + 0.479179i
\(292\) 383.581 246.957i 1.31363 0.845744i
\(293\) 136.021 78.5318i 0.464235 0.268026i −0.249588 0.968352i \(-0.580295\pi\)
0.713824 + 0.700326i \(0.246962\pi\)
\(294\) 61.2491 + 147.976i 0.208330 + 0.503319i
\(295\) 113.899 + 65.7597i 0.386099 + 0.222914i
\(296\) −188.653 + 218.259i −0.637341 + 0.737360i
\(297\) 76.1321 367.453i 0.256337 1.23722i
\(298\) 45.7982 + 43.6327i 0.153685 + 0.146418i
\(299\) 80.6804 139.743i 0.269834 0.467367i
\(300\) 117.236 + 45.3023i 0.390786 + 0.151008i
\(301\) −28.6753 + 16.5557i −0.0952668 + 0.0550023i
\(302\) −8.34618 + 34.4651i −0.0276364 + 0.114123i
\(303\) −319.109 + 232.683i −1.05317 + 0.767931i
\(304\) 25.4097 55.8818i 0.0835846 0.183822i
\(305\) −323.957 −1.06215
\(306\) −201.933 + 330.605i −0.659911 + 1.08041i
\(307\) −41.8176 −0.136214 −0.0681069 0.997678i \(-0.521696\pi\)
−0.0681069 + 0.997678i \(0.521696\pi\)
\(308\) −120.129 + 233.487i −0.390028 + 0.758074i
\(309\) 13.6593 + 127.852i 0.0442049 + 0.413759i
\(310\) 426.116 + 103.190i 1.37457 + 0.332870i
\(311\) 40.6974 23.4966i 0.130860 0.0755519i −0.433141 0.901326i \(-0.642595\pi\)
0.564001 + 0.825774i \(0.309261\pi\)
\(312\) 63.6691 91.8113i 0.204068 0.294267i
\(313\) −183.527 + 317.878i −0.586349 + 1.01559i 0.408357 + 0.912822i \(0.366102\pi\)
−0.994706 + 0.102763i \(0.967232\pi\)
\(314\) −127.785 121.743i −0.406959 0.387716i
\(315\) 170.054 + 187.567i 0.539853 + 0.595451i
\(316\) −219.299 + 10.6266i −0.693983 + 0.0336286i
\(317\) 67.3034 + 38.8576i 0.212313 + 0.122579i 0.602386 0.798205i \(-0.294217\pi\)
−0.390073 + 0.920784i \(0.627550\pi\)
\(318\) 46.1036 349.499i 0.144980 1.09905i
\(319\) −547.528 + 316.115i −1.71639 + 0.990957i
\(320\) 236.367 + 299.049i 0.738648 + 0.934530i
\(321\) −111.351 + 251.257i −0.346888 + 0.782731i
\(322\) 92.3748 + 314.124i 0.286878 + 0.975539i
\(323\) 82.5742 0.255648
\(324\) −147.934 288.256i −0.456586 0.889679i
\(325\) 48.7583i 0.150026i
\(326\) −19.1032 64.9611i −0.0585988 0.199267i
\(327\) −418.846 185.623i −1.28087 0.567653i
\(328\) 30.8117 160.931i 0.0939381 0.490643i
\(329\) 144.939 + 251.042i 0.440545 + 0.763046i
\(330\) 64.9549 492.406i 0.196833 1.49214i
\(331\) 251.153 435.010i 0.758771 1.31423i −0.184707 0.982794i \(-0.559134\pi\)
0.943478 0.331436i \(-0.107533\pi\)
\(332\) 6.05384 + 124.931i 0.0182345 + 0.376299i
\(333\) 240.443 217.993i 0.722051 0.654633i
\(334\) 83.6386 + 79.6839i 0.250415 + 0.238574i
\(335\) 587.615 + 339.259i 1.75407 + 1.01271i
\(336\) 45.7675 + 222.044i 0.136213 + 0.660845i
\(337\) 23.0951 + 40.0018i 0.0685314 + 0.118700i 0.898255 0.439475i \(-0.144835\pi\)
−0.829724 + 0.558174i \(0.811502\pi\)
\(338\) 286.379 + 69.3504i 0.847274 + 0.205179i
\(339\) 50.4585 5.39085i 0.148845 0.0159022i
\(340\) −234.577 + 455.934i −0.689934 + 1.34098i
\(341\) 511.546i 1.50013i
\(342\) −35.9984 + 58.9367i −0.105258 + 0.172329i
\(343\) 357.504i 1.04229i
\(344\) 52.9764 18.4083i 0.154001 0.0535124i
\(345\) −364.892 500.425i −1.05766 1.45051i
\(346\) −8.50487 + 35.1204i −0.0245805 + 0.101504i
\(347\) 127.082 + 220.112i 0.366230 + 0.634329i 0.988973 0.148097i \(-0.0473149\pi\)
−0.622743 + 0.782427i \(0.713982\pi\)
\(348\) −196.758 + 509.179i −0.565395 + 1.46316i
\(349\) −213.501 123.265i −0.611750 0.353194i 0.161900 0.986807i \(-0.448238\pi\)
−0.773650 + 0.633613i \(0.781571\pi\)
\(350\) 71.6325 + 68.2454i 0.204664 + 0.194987i
\(351\) −83.6241 + 93.8398i −0.238245 + 0.267350i
\(352\) 274.209 350.159i 0.779002 0.994770i
\(353\) −76.3516 + 132.245i −0.216293 + 0.374631i −0.953672 0.300849i \(-0.902730\pi\)
0.737379 + 0.675480i \(0.236063\pi\)
\(354\) −50.6709 122.419i −0.143138 0.345817i
\(355\) 24.7268 + 42.8280i 0.0696529 + 0.120642i
\(356\) −160.564 + 103.374i −0.451021 + 0.290376i
\(357\) −246.407 + 179.671i −0.690216 + 0.503281i
\(358\) −149.251 507.532i −0.416901 1.41769i
\(359\) 343.066i 0.955615i 0.878465 + 0.477807i \(0.158568\pi\)
−0.878465 + 0.477807i \(0.841432\pi\)
\(360\) −223.155 366.193i −0.619874 1.01720i
\(361\) −346.280 −0.959223
\(362\) 355.889 104.657i 0.983120 0.289108i
\(363\) −215.273 + 22.9992i −0.593038 + 0.0633586i
\(364\) 73.9503 47.6106i 0.203160 0.130798i
\(365\) −588.279 + 339.643i −1.61172 + 0.930529i
\(366\) 258.861 + 198.736i 0.707270 + 0.542996i
\(367\) −35.7464 20.6382i −0.0974016 0.0562348i 0.450508 0.892772i \(-0.351243\pi\)
−0.547910 + 0.836538i \(0.684576\pi\)
\(368\) −53.6216 551.987i −0.145711 1.49997i
\(369\) −56.3616 + 175.508i −0.152741 + 0.475631i
\(370\) 296.303 311.009i 0.800820 0.840565i
\(371\) 138.753 240.328i 0.373998 0.647784i
\(372\) −277.189 343.862i −0.745131 0.924360i
\(373\) −93.5900 + 54.0342i −0.250911 + 0.144864i −0.620182 0.784458i \(-0.712941\pi\)
0.369270 + 0.929322i \(0.379608\pi\)
\(374\) 581.439 + 140.803i 1.55465 + 0.376480i
\(375\) 237.296 + 105.164i 0.632790 + 0.280438i
\(376\) −161.158 463.789i −0.428611 1.23348i
\(377\) 211.768 0.561718
\(378\) −20.8173 254.199i −0.0550721 0.672485i
\(379\) −290.232 −0.765783 −0.382891 0.923793i \(-0.625072\pi\)
−0.382891 + 0.923793i \(0.625072\pi\)
\(380\) −41.8179 + 81.2789i −0.110047 + 0.213892i
\(381\) −395.586 175.315i −1.03828 0.460143i
\(382\) −43.3879 + 179.168i −0.113581 + 0.469025i
\(383\) −39.2004 + 22.6324i −0.102351 + 0.0590924i −0.550302 0.834966i \(-0.685487\pi\)
0.447951 + 0.894058i \(0.352154\pi\)
\(384\) −5.41516 383.962i −0.0141020 0.999901i
\(385\) 195.488 338.596i 0.507762 0.879469i
\(386\) −372.949 + 391.459i −0.966190 + 1.01414i
\(387\) −61.6699 + 13.3294i −0.159354 + 0.0344430i
\(388\) −11.1369 229.829i −0.0287033 0.592342i
\(389\) 473.733 + 273.510i 1.21782 + 0.703110i 0.964452 0.264259i \(-0.0851274\pi\)
0.253371 + 0.967369i \(0.418461\pi\)
\(390\) −101.309 + 131.958i −0.259766 + 0.338353i
\(391\) 646.046 372.995i 1.65229 0.953951i
\(392\) 40.1538 209.725i 0.102433 0.535013i
\(393\) 51.9755 5.55292i 0.132253 0.0141296i
\(394\) 269.043 79.1180i 0.682851 0.200807i
\(395\) 326.918 0.827639
\(396\) −353.977 + 353.614i −0.893882 + 0.892966i
\(397\) 360.883i 0.909026i 0.890740 + 0.454513i \(0.150187\pi\)
−0.890740 + 0.454513i \(0.849813\pi\)
\(398\) −523.723 + 154.012i −1.31589 + 0.386965i
\(399\) −43.9268 + 32.0299i −0.110092 + 0.0802753i
\(400\) −97.4289 136.346i −0.243572 0.340865i
\(401\) 64.5497 + 111.803i 0.160972 + 0.278812i 0.935218 0.354074i \(-0.115204\pi\)
−0.774246 + 0.632885i \(0.781870\pi\)
\(402\) −261.415 631.570i −0.650287 1.57107i
\(403\) −85.6720 + 148.388i −0.212585 + 0.368209i
\(404\) 525.961 25.4867i 1.30188 0.0630858i
\(405\) 199.240 + 439.370i 0.491952 + 1.08486i
\(406\) −296.404 + 311.115i −0.730060 + 0.766294i
\(407\) −434.047 250.597i −1.06646 0.615718i
\(408\) 467.141 220.413i 1.14495 0.540229i
\(409\) −201.124 348.356i −0.491745 0.851727i 0.508210 0.861233i \(-0.330307\pi\)
−0.999955 + 0.00950593i \(0.996974\pi\)
\(410\) −57.4227 + 237.124i −0.140055 + 0.578350i
\(411\) −164.643 225.797i −0.400591 0.549384i
\(412\) 78.4329 152.445i 0.190371 0.370013i
\(413\) 104.296i 0.252534i
\(414\) −15.4230 + 623.718i −0.0372536 + 1.50657i
\(415\) 186.240i 0.448772i
\(416\) −138.185 + 55.6499i −0.332177 + 0.133774i
\(417\) 131.774 14.0784i 0.316005 0.0337611i
\(418\) 103.653 + 25.1009i 0.247973 + 0.0600500i
\(419\) −35.6383 61.7274i −0.0850557 0.147321i 0.820359 0.571848i \(-0.193773\pi\)
−0.905415 + 0.424528i \(0.860440\pi\)
\(420\) −52.0654 333.533i −0.123965 0.794126i
\(421\) −594.980 343.512i −1.41326 0.815943i −0.417562 0.908649i \(-0.637115\pi\)
−0.995694 + 0.0927053i \(0.970449\pi\)
\(422\) −177.284 + 186.083i −0.420104 + 0.440954i
\(423\) 116.694 + 539.898i 0.275873 + 1.27635i
\(424\) −307.371 + 355.608i −0.724932 + 0.838697i
\(425\) 112.708 195.215i 0.265194 0.459330i
\(426\) 6.51535 49.3912i 0.0152943 0.115942i
\(427\) 128.451 + 222.483i 0.300821 + 0.521038i
\(428\) 308.101 198.362i 0.719863 0.463462i
\(429\) 177.459 + 78.6455i 0.413656 + 0.183323i
\(430\) −80.1157 + 23.5598i −0.186316 + 0.0547902i
\(431\) 411.731i 0.955292i −0.878552 0.477646i \(-0.841490\pi\)
0.878552 0.477646i \(-0.158510\pi\)
\(432\) −46.3330 + 429.508i −0.107252 + 0.994232i
\(433\) 812.833 1.87721 0.938606 0.344992i \(-0.112118\pi\)
0.938606 + 0.344992i \(0.112118\pi\)
\(434\) −98.0899 333.558i −0.226014 0.768566i
\(435\) 329.323 743.097i 0.757065 1.70827i
\(436\) 330.670 + 513.606i 0.758416 + 1.17799i
\(437\) 115.170 66.4935i 0.263547 0.152159i
\(438\) 678.429 + 89.4939i 1.54893 + 0.204324i
\(439\) −436.189 251.834i −0.993597 0.573653i −0.0872494 0.996186i \(-0.527808\pi\)
−0.906348 + 0.422533i \(0.861141\pi\)
\(440\) −433.052 + 501.012i −0.984210 + 1.13866i
\(441\) −73.4504 + 228.722i −0.166554 + 0.518643i
\(442\) −145.082 138.222i −0.328239 0.312718i
\(443\) −163.387 + 282.994i −0.368819 + 0.638813i −0.989381 0.145344i \(-0.953571\pi\)
0.620562 + 0.784157i \(0.286904\pi\)
\(444\) −427.557 + 66.7429i −0.962967 + 0.150322i
\(445\) 246.248 142.171i 0.553366 0.319486i
\(446\) 136.560 563.915i 0.306188 1.26438i
\(447\) 10.0797 + 94.3466i 0.0225498 + 0.211066i
\(448\) 111.657 280.904i 0.249233 0.627019i
\(449\) −482.106 −1.07373 −0.536866 0.843667i \(-0.680392\pi\)
−0.536866 + 0.843667i \(0.680392\pi\)
\(450\) 90.1983 + 165.549i 0.200441 + 0.367886i
\(451\) 284.664 0.631183
\(452\) −60.1648 30.9547i −0.133108 0.0684839i
\(453\) −42.9795 + 31.3391i −0.0948774 + 0.0691812i
\(454\) −514.190 124.518i −1.13258 0.274269i
\(455\) −113.414 + 65.4794i −0.249261 + 0.143911i
\(456\) 83.2769 39.2929i 0.182625 0.0861686i
\(457\) −128.853 + 223.180i −0.281954 + 0.488359i −0.971866 0.235534i \(-0.924316\pi\)
0.689912 + 0.723893i \(0.257649\pi\)
\(458\) 239.536 + 228.210i 0.523005 + 0.498276i
\(459\) −551.724 + 182.408i −1.20201 + 0.397402i
\(460\) 39.9680 + 824.807i 0.0868870 + 1.79306i
\(461\) 102.474 + 59.1634i 0.222286 + 0.128337i 0.607008 0.794695i \(-0.292369\pi\)
−0.384722 + 0.923032i \(0.625703\pi\)
\(462\) −363.924 + 150.633i −0.787714 + 0.326045i
\(463\) 332.975 192.243i 0.719168 0.415212i −0.0952784 0.995451i \(-0.530374\pi\)
0.814446 + 0.580239i \(0.197041\pi\)
\(464\) 592.180 423.154i 1.27625 0.911971i
\(465\) 387.467 + 531.385i 0.833262 + 1.14276i
\(466\) −92.2665 313.755i −0.197997 0.673294i
\(467\) −881.059 −1.88664 −0.943318 0.331891i \(-0.892314\pi\)
−0.943318 + 0.331891i \(0.892314\pi\)
\(468\) 161.903 43.2929i 0.345947 0.0925061i
\(469\) 538.073i 1.14728i
\(470\) 206.257 + 701.385i 0.438846 + 1.49231i
\(471\) −28.1243 263.244i −0.0597118 0.558904i
\(472\) −33.2190 + 173.504i −0.0703791 + 0.367593i
\(473\) 48.7170 + 84.3803i 0.102996 + 0.178394i
\(474\) −261.227 200.553i −0.551111 0.423107i
\(475\) 20.0923 34.8009i 0.0422996 0.0732650i
\(476\) 406.132 19.6801i 0.853218 0.0413447i
\(477\) 391.753 355.175i 0.821285 0.744601i
\(478\) −133.289 126.986i −0.278847 0.265662i
\(479\) −410.614 237.068i −0.857232 0.494923i 0.00585234 0.999983i \(-0.498137\pi\)
−0.863084 + 0.505060i \(0.831470\pi\)
\(480\) −19.6177 + 571.437i −0.0408703 + 1.19049i
\(481\) 83.9384 + 145.386i 0.174508 + 0.302257i
\(482\) −62.3012 15.0871i −0.129256 0.0313010i
\(483\) −198.994 + 449.017i −0.411996 + 0.929642i
\(484\) 256.683 + 132.063i 0.530337 + 0.272858i
\(485\) 342.615i 0.706423i
\(486\) 110.334 473.310i 0.227024 0.973889i
\(487\) 67.4929i 0.138589i −0.997596 0.0692945i \(-0.977925\pi\)
0.997596 0.0692945i \(-0.0220748\pi\)
\(488\) −142.824 411.028i −0.292672 0.842270i
\(489\) 41.1522 92.8572i 0.0841558 0.189892i
\(490\) −74.8333 + 309.020i −0.152721 + 0.630652i
\(491\) −103.521 179.303i −0.210837 0.365180i 0.741140 0.671351i \(-0.234286\pi\)
−0.951977 + 0.306171i \(0.900952\pi\)
\(492\) 191.351 154.249i 0.388926 0.313515i
\(493\) 847.862 + 489.513i 1.71980 + 0.992927i
\(494\) −25.8636 24.6406i −0.0523554 0.0498798i
\(495\) 551.937 500.402i 1.11502 1.01091i
\(496\) 56.9391 + 586.138i 0.114797 + 1.18173i
\(497\) 19.6086 33.9631i 0.0394539 0.0683362i
\(498\) −114.252 + 148.817i −0.229422 + 0.298830i
\(499\) 136.696 + 236.765i 0.273940 + 0.474479i 0.969867 0.243634i \(-0.0783396\pi\)
−0.695927 + 0.718113i \(0.745006\pi\)
\(500\) −187.340 290.982i −0.374680 0.581965i
\(501\) 18.4081 + 172.300i 0.0367426 + 0.343912i
\(502\) 61.4786 + 209.060i 0.122467 + 0.416454i
\(503\) 801.394i 1.59323i −0.604488 0.796615i \(-0.706622\pi\)
0.604488 0.796615i \(-0.293378\pi\)
\(504\) −163.008 + 298.453i −0.323428 + 0.592169i
\(505\) −784.071 −1.55262
\(506\) 924.344 271.823i 1.82677 0.537200i
\(507\) 260.404 + 357.127i 0.513618 + 0.704392i
\(508\) 312.307 + 485.084i 0.614777 + 0.954890i
\(509\) −456.038 + 263.294i −0.895950 + 0.517277i −0.875884 0.482522i \(-0.839721\pi\)
−0.0200657 + 0.999799i \(0.506388\pi\)
\(510\) −710.640 + 294.143i −1.39341 + 0.576752i
\(511\) 466.512 + 269.341i 0.912939 + 0.527085i
\(512\) −275.218 + 431.740i −0.537534 + 0.843242i
\(513\) −98.3554 + 32.5176i −0.191726 + 0.0633872i
\(514\) −675.238 + 708.751i −1.31369 + 1.37889i
\(515\) −127.636 + 221.072i −0.247837 + 0.429265i
\(516\) 78.4704 + 30.3226i 0.152074 + 0.0587647i
\(517\) 738.720 426.500i 1.42886 0.824952i
\(518\) −331.077 80.1747i −0.639145 0.154777i
\(519\) −43.7966 + 31.9350i −0.0843866 + 0.0615317i
\(520\) 209.527 72.8065i 0.402936 0.140013i
\(521\) 860.976 1.65255 0.826273 0.563270i \(-0.190457\pi\)
0.826273 + 0.563270i \(0.190457\pi\)
\(522\) −719.013 + 391.750i −1.37742 + 0.750480i
\(523\) 233.126 0.445747 0.222873 0.974847i \(-0.428456\pi\)
0.222873 + 0.974847i \(0.428456\pi\)
\(524\) −61.9736 31.8853i −0.118270 0.0608499i
\(525\) 15.7656 + 147.567i 0.0300298 + 0.281079i
\(526\) 185.864 767.516i 0.353354 1.45916i
\(527\) −686.015 + 396.071i −1.30174 + 0.751558i
\(528\) 653.389 134.676i 1.23748 0.255068i
\(529\) 336.213 582.339i 0.635564 1.10083i
\(530\) 482.766 506.726i 0.910879 0.956086i
\(531\) 60.7650 189.220i 0.114435 0.356346i
\(532\) 72.4008 3.50835i 0.136092 0.00659465i
\(533\) −82.5746 47.6745i −0.154924 0.0894456i
\(534\) −283.984 37.4613i −0.531806 0.0701522i
\(535\) −472.519 + 272.809i −0.883213 + 0.509923i
\(536\) −171.379 + 895.120i −0.319737 + 1.67000i
\(537\) 321.516 725.480i 0.598726 1.35099i
\(538\) −689.187 + 202.670i −1.28102 + 0.376711i
\(539\) 370.974 0.688263
\(540\) 99.8626 635.447i 0.184931 1.17675i
\(541\) 735.170i 1.35891i −0.733718 0.679455i \(-0.762216\pi\)
0.733718 0.679455i \(-0.237784\pi\)
\(542\) −428.299 + 125.951i −0.790220 + 0.232381i
\(543\) 508.719 + 225.452i 0.936867 + 0.415197i
\(544\) −681.896 96.6161i −1.25348 0.177603i
\(545\) −454.773 787.691i −0.834447 1.44530i
\(546\) 130.794 + 17.2534i 0.239549 + 0.0315997i
\(547\) −252.906 + 438.046i −0.462351 + 0.800816i −0.999078 0.0429407i \(-0.986327\pi\)
0.536727 + 0.843756i \(0.319661\pi\)
\(548\) 18.0340 + 372.162i 0.0329087 + 0.679127i
\(549\) 103.419 + 478.478i 0.188377 + 0.871544i
\(550\) 200.820 210.787i 0.365127 0.383249i
\(551\) 151.148 + 87.2651i 0.274315 + 0.158376i
\(552\) 474.054 683.589i 0.858794 1.23839i
\(553\) −129.625 224.516i −0.234403 0.405997i
\(554\) 60.5648 250.099i 0.109323 0.451442i
\(555\) 640.695 68.4501i 1.15440 0.123334i
\(556\) −157.122 80.8392i −0.282594 0.145394i
\(557\) 240.438i 0.431666i 0.976430 + 0.215833i \(0.0692467\pi\)
−0.976430 + 0.215833i \(0.930753\pi\)
\(558\) 16.3772 662.306i 0.0293498 1.18693i
\(559\) 32.6358i 0.0583825i
\(560\) −186.305 + 409.728i −0.332688 + 0.731657i
\(561\) 528.703 + 725.081i 0.942430 + 1.29248i
\(562\) 659.434 + 159.691i 1.17337 + 0.284147i
\(563\) 71.8708 + 124.484i 0.127657 + 0.221108i 0.922768 0.385355i \(-0.125921\pi\)
−0.795112 + 0.606463i \(0.792588\pi\)
\(564\) 265.464 686.980i 0.470680 1.21805i
\(565\) 87.2493 + 50.3734i 0.154423 + 0.0891564i
\(566\) 23.9191 25.1062i 0.0422599 0.0443572i
\(567\) 222.745 311.045i 0.392849 0.548579i
\(568\) −43.4376 + 50.2544i −0.0764747 + 0.0884761i
\(569\) 468.006 810.610i 0.822506 1.42462i −0.0813051 0.996689i \(-0.525909\pi\)
0.903811 0.427932i \(-0.140758\pi\)
\(570\) −126.685 + 52.4367i −0.222255 + 0.0919942i
\(571\) −104.431 180.879i −0.182891 0.316776i 0.759973 0.649955i \(-0.225212\pi\)
−0.942864 + 0.333179i \(0.891879\pi\)
\(572\) −140.100 217.607i −0.244929 0.380432i
\(573\) −223.430 + 162.917i −0.389930 + 0.284323i
\(574\) 185.617 54.5848i 0.323375 0.0950954i
\(575\) 363.035i 0.631364i
\(576\) 366.233 444.578i 0.635821 0.771836i
\(577\) −707.574 −1.22630 −0.613149 0.789967i \(-0.710097\pi\)
−0.613149 + 0.789967i \(0.710097\pi\)
\(578\) −98.2923 334.246i −0.170056 0.578280i
\(579\) −806.426 + 86.1564i −1.39279 + 0.148802i
\(580\) −911.216 + 586.659i −1.57106 + 1.01148i
\(581\) −127.904 + 73.8453i −0.220144 + 0.127100i
\(582\) 210.183 273.770i 0.361139 0.470395i
\(583\) −707.192 408.297i −1.21302 0.700338i
\(584\) −690.287 596.652i −1.18200 1.02167i
\(585\) −243.910 + 52.7192i −0.416941 + 0.0901183i
\(586\) −227.433 216.679i −0.388111 0.369760i
\(587\) −172.823 + 299.339i −0.294418 + 0.509947i −0.974849 0.222865i \(-0.928459\pi\)
0.680431 + 0.732812i \(0.261792\pi\)
\(588\) 249.369 201.018i 0.424097 0.341867i
\(589\) −122.295 + 70.6073i −0.207632 + 0.119876i
\(590\) 61.9090 255.650i 0.104930 0.433304i
\(591\) 384.578 + 170.436i 0.650725 + 0.288386i
\(592\) 525.232 + 238.826i 0.887217 + 0.403422i
\(593\) 577.178 0.973318 0.486659 0.873592i \(-0.338215\pi\)
0.486659 + 0.873592i \(0.338215\pi\)
\(594\) −748.010 + 61.2571i −1.25928 + 0.103127i
\(595\) −605.438 −1.01754
\(596\) 57.8787 112.495i 0.0971119 0.188750i
\(597\) −748.624 331.773i −1.25398 0.555733i
\(598\) −313.656 75.9560i −0.524508 0.127017i
\(599\) −580.291 + 335.031i −0.968766 + 0.559317i −0.898860 0.438237i \(-0.855603\pi\)
−0.0699059 + 0.997554i \(0.522270\pi\)
\(600\) 20.7736 250.508i 0.0346227 0.417514i
\(601\) −474.923 + 822.591i −0.790221 + 1.36870i 0.135609 + 0.990762i \(0.456701\pi\)
−0.925830 + 0.377941i \(0.876632\pi\)
\(602\) 47.9464 + 45.6793i 0.0796452 + 0.0758793i
\(603\) 313.491 976.199i 0.519886 1.61890i
\(604\) 70.8393 3.43269i 0.117284 0.00568326i
\(605\) −372.234 214.909i −0.615263 0.355222i
\(606\) 626.520 + 481.001i 1.03386 + 0.793731i
\(607\) −247.947 + 143.152i −0.408479 + 0.235835i −0.690136 0.723680i \(-0.742449\pi\)
0.281657 + 0.959515i \(0.409116\pi\)
\(608\) −121.561 17.2237i −0.199936 0.0283284i
\(609\) −640.913 + 68.4735i −1.05240 + 0.112436i
\(610\) 182.793 + 621.594i 0.299661 + 1.01901i
\(611\) −285.715 −0.467619
\(612\) 748.291 + 200.915i 1.22270 + 0.328293i
\(613\) 461.893i 0.753496i 0.926316 + 0.376748i \(0.122958\pi\)
−0.926316 + 0.376748i \(0.877042\pi\)
\(614\) 23.5957 + 80.2378i 0.0384294 + 0.130680i
\(615\) −295.704 + 215.617i −0.480819 + 0.350596i
\(616\) 515.787 + 98.7522i 0.837316 + 0.160312i
\(617\) 307.736 + 533.015i 0.498763 + 0.863882i 0.999999 0.00142829i \(-0.000454640\pi\)
−0.501236 + 0.865310i \(0.667121\pi\)
\(618\) 237.609 98.3493i 0.384480 0.159141i
\(619\) 121.945 211.215i 0.197003 0.341219i −0.750552 0.660811i \(-0.770212\pi\)
0.947555 + 0.319592i \(0.103546\pi\)
\(620\) −42.4407 875.836i −0.0684528 1.41264i
\(621\) −622.631 + 698.692i −1.00263 + 1.12511i
\(622\) −68.0478 64.8302i −0.109402 0.104229i
\(623\) −195.277 112.743i −0.313447 0.180969i
\(624\) −212.089 70.3608i −0.339886 0.112758i
\(625\) 388.572 + 673.026i 0.621715 + 1.07684i
\(626\) 713.486 + 172.780i 1.13975 + 0.276007i
\(627\) 94.2514 + 129.260i 0.150321 + 0.206156i
\(628\) −161.492 + 313.882i −0.257152 + 0.499812i
\(629\) 776.114i 1.23388i
\(630\) 263.942 432.127i 0.418956 0.685915i
\(631\) 1132.71i 1.79510i 0.440912 + 0.897550i \(0.354655\pi\)
−0.440912 + 0.897550i \(0.645345\pi\)
\(632\) 144.129 + 414.784i 0.228053 + 0.656304i
\(633\) −383.340 + 40.9550i −0.605592 + 0.0646998i
\(634\) 36.5822 151.064i 0.0577007 0.238272i
\(635\) −429.519 743.948i −0.676408 1.17157i
\(636\) −696.618 + 108.744i −1.09531 + 0.170981i
\(637\) −107.611 62.1294i −0.168935 0.0975344i
\(638\) 915.491 + 872.203i 1.43494 + 1.36709i
\(639\) 55.3625 50.1932i 0.0866392 0.0785497i
\(640\) 440.432 622.270i 0.688175 0.972297i
\(641\) 104.496 180.992i 0.163020 0.282359i −0.772930 0.634491i \(-0.781210\pi\)
0.935950 + 0.352132i \(0.114543\pi\)
\(642\) 544.930 + 71.8835i 0.848801 + 0.111968i
\(643\) −88.2601 152.871i −0.137263 0.237746i 0.789197 0.614141i \(-0.210497\pi\)
−0.926460 + 0.376394i \(0.877164\pi\)
\(644\) 550.603 354.489i 0.854974 0.550449i
\(645\) −114.520 50.7525i −0.177550 0.0786860i
\(646\) −46.5926 158.440i −0.0721248 0.245263i
\(647\) 186.463i 0.288196i 0.989563 + 0.144098i \(0.0460281\pi\)
−0.989563 + 0.144098i \(0.953972\pi\)
\(648\) −469.621 + 446.498i −0.724724 + 0.689040i
\(649\) −306.904 −0.472887
\(650\) −93.5553 + 27.5120i −0.143931 + 0.0423261i
\(651\) 211.305 476.797i 0.324586 0.732407i
\(652\) −113.865 + 73.3088i −0.174640 + 0.112437i
\(653\) 757.512 437.350i 1.16005 0.669754i 0.208733 0.977973i \(-0.433066\pi\)
0.951316 + 0.308218i \(0.0997327\pi\)
\(654\) −119.830 + 908.400i −0.183226 + 1.38899i
\(655\) 89.8723 + 51.8878i 0.137210 + 0.0792180i
\(656\) −326.172 + 31.6853i −0.497214 + 0.0483008i
\(657\) 689.446 + 760.450i 1.04939 + 1.15746i
\(658\) 399.906 419.754i 0.607760 0.637924i
\(659\) −431.297 + 747.028i −0.654472 + 1.13358i 0.327554 + 0.944833i \(0.393776\pi\)
−0.982026 + 0.188746i \(0.939558\pi\)
\(660\) −981.458 + 153.208i −1.48706 + 0.232134i
\(661\) −361.406 + 208.658i −0.546757 + 0.315670i −0.747813 0.663910i \(-0.768896\pi\)
0.201056 + 0.979580i \(0.435563\pi\)
\(662\) −976.391 236.446i −1.47491 0.357170i
\(663\) −31.9311 298.875i −0.0481615 0.450793i
\(664\) 236.297 82.1085i 0.355869 0.123657i
\(665\) −107.931 −0.162302
\(666\) −553.945 338.349i −0.831750 0.508031i
\(667\) 1576.74 2.36392
\(668\) 105.701 205.444i 0.158234 0.307551i
\(669\) 703.227 512.768i 1.05116 0.766470i
\(670\) 319.393 1318.92i 0.476706 1.96853i
\(671\) 654.681 377.980i 0.975680 0.563309i
\(672\) 400.223 213.105i 0.595570 0.317121i
\(673\) 651.368 1128.20i 0.967857 1.67638i 0.266121 0.963940i \(-0.414258\pi\)
0.701736 0.712438i \(-0.252409\pi\)
\(674\) 63.7223 66.8849i 0.0945435 0.0992357i
\(675\) −57.3723 + 276.908i −0.0849959 + 0.410235i
\(676\) −28.5230 588.621i −0.0421939 0.870742i
\(677\) 408.374 + 235.775i 0.603211 + 0.348264i 0.770304 0.637677i \(-0.220105\pi\)
−0.167093 + 0.985941i \(0.553438\pi\)
\(678\) −38.8150 93.7758i −0.0572493 0.138312i
\(679\) 235.297 135.849i 0.346535 0.200072i
\(680\) 1007.19 + 192.835i 1.48116 + 0.283581i
\(681\) −467.553 641.217i −0.686568 0.941582i
\(682\) −981.531 + 288.640i −1.43919 + 0.423226i
\(683\) 316.113 0.462830 0.231415 0.972855i \(-0.425664\pi\)
0.231415 + 0.972855i \(0.425664\pi\)
\(684\) 133.397 + 35.8170i 0.195025 + 0.0523640i
\(685\) 554.797i 0.809922i
\(686\) 685.963 201.722i 0.999946 0.294056i
\(687\) 52.7197 + 493.458i 0.0767390 + 0.718279i
\(688\) −65.2129 91.2618i −0.0947863 0.132648i
\(689\) 136.761 + 236.876i 0.198491 + 0.343797i
\(690\) −754.302 + 982.504i −1.09319 + 1.42392i
\(691\) 14.4746 25.0708i 0.0209473 0.0362819i −0.855362 0.518031i \(-0.826665\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(692\) 72.1862 3.49796i 0.104315 0.00505485i
\(693\) −562.506 180.640i −0.811697 0.260664i
\(694\) 350.635 368.038i 0.505238 0.530314i
\(695\) 227.854 + 131.552i 0.327847 + 0.189283i
\(696\) 1088.01 + 90.2243i 1.56323 + 0.129633i
\(697\) −220.405 381.752i −0.316219 0.547707i
\(698\) −116.047 + 479.208i −0.166256 + 0.686544i
\(699\) 198.761 448.491i 0.284350 0.641618i
\(700\) 90.5275 175.953i 0.129325 0.251361i
\(701\) 181.322i 0.258662i 0.991601 + 0.129331i \(0.0412830\pi\)
−0.991601 + 0.129331i \(0.958717\pi\)
\(702\) 227.241 + 107.505i 0.323704 + 0.153141i
\(703\) 138.357i 0.196810i
\(704\) −826.592 328.562i −1.17414 0.466707i
\(705\) −444.320 + 1002.58i −0.630241 + 1.42210i
\(706\) 296.827 + 71.8806i 0.420435 + 0.101814i
\(707\) 310.889 + 538.475i 0.439729 + 0.761633i
\(708\) −206.301 + 166.300i −0.291386 + 0.234887i
\(709\) −56.7386 32.7581i −0.0800262 0.0462032i 0.459453 0.888202i \(-0.348045\pi\)
−0.539479 + 0.841999i \(0.681379\pi\)
\(710\) 68.2244 71.6104i 0.0960907 0.100860i
\(711\) −104.364 482.851i −0.146785 0.679115i
\(712\) 288.948 + 249.753i 0.405825 + 0.350777i
\(713\) −637.878 + 1104.84i −0.894640 + 1.54956i
\(714\) 483.781 + 371.415i 0.677564 + 0.520190i
\(715\) 192.681 + 333.733i 0.269483 + 0.466759i
\(716\) −889.614 + 572.751i −1.24248 + 0.799932i
\(717\) −29.3356 274.582i −0.0409143 0.382959i
\(718\) 658.259 193.575i 0.916795 0.269604i
\(719\) 583.213i 0.811144i 0.914063 + 0.405572i \(0.132928\pi\)
−0.914063 + 0.405572i \(0.867072\pi\)
\(720\) −576.720 + 634.804i −0.801000 + 0.881673i
\(721\) 202.433 0.280767
\(722\) 195.389 + 664.426i 0.270622 + 0.920257i
\(723\) −56.6505 77.6924i −0.0783548 0.107458i
\(724\) −401.622 623.812i −0.554727 0.861618i
\(725\) 412.610 238.221i 0.569118 0.328580i
\(726\) 165.598 + 400.078i 0.228096 + 0.551072i
\(727\) 870.370 + 502.508i 1.19721 + 0.691208i 0.959932 0.280234i \(-0.0904122\pi\)
0.237276 + 0.971442i \(0.423746\pi\)
\(728\) −133.080 115.028i −0.182802 0.158006i
\(729\) 585.336 434.537i 0.802930 0.596073i
\(730\) 983.629 + 937.119i 1.34744 + 1.28372i
\(731\) 75.4396 130.665i 0.103201 0.178749i
\(732\) 235.264 608.828i 0.321399 0.831732i
\(733\) −487.340 + 281.366i −0.664857 + 0.383855i −0.794125 0.607755i \(-0.792070\pi\)
0.129268 + 0.991610i \(0.458737\pi\)
\(734\) −19.4297 + 80.2337i −0.0264709 + 0.109310i
\(735\) −385.361 + 280.992i −0.524301 + 0.382302i
\(736\) −1028.87 + 414.346i −1.39792 + 0.562971i
\(737\) −1583.34 −2.14836
\(738\) 368.558 + 9.11353i 0.499402 + 0.0123490i
\(739\) 786.903 1.06482 0.532411 0.846486i \(-0.321286\pi\)
0.532411 + 0.846486i \(0.321286\pi\)
\(740\) −763.940 393.046i −1.03235 0.531143i
\(741\) −5.69232 53.2803i −0.00768194 0.0719032i
\(742\) −539.422 130.628i −0.726984 0.176049i
\(743\) 1259.40 727.115i 1.69502 0.978620i 0.744672 0.667430i \(-0.232606\pi\)
0.950348 0.311190i \(-0.100728\pi\)
\(744\) −503.383 + 725.882i −0.676590 + 0.975647i
\(745\) −94.1874 + 163.137i −0.126426 + 0.218976i
\(746\) 156.487 + 149.087i 0.209768 + 0.199849i
\(747\) −275.073 + 59.4548i −0.368237 + 0.0795915i
\(748\) −57.9109 1195.09i −0.0774209 1.59771i
\(749\) 374.713 + 216.341i 0.500284 + 0.288839i
\(750\) 67.8895 514.652i 0.0905193 0.686203i
\(751\) −298.356 + 172.256i −0.397279 + 0.229369i −0.685309 0.728252i \(-0.740333\pi\)
0.288031 + 0.957621i \(0.407000\pi\)
\(752\) −798.965 + 570.916i −1.06245 + 0.759197i
\(753\) −132.437 + 298.836i −0.175879 + 0.396861i
\(754\) −119.490 406.330i −0.158475 0.538900i
\(755\) −105.603 −0.139872
\(756\) −476.000 + 183.376i −0.629630 + 0.242560i
\(757\) 1091.69i 1.44212i −0.692870 0.721062i \(-0.743654\pi\)
0.692870 0.721062i \(-0.256346\pi\)
\(758\) 163.764 + 556.883i 0.216047 + 0.734675i
\(759\) 1321.28 + 585.562i 1.74082 + 0.771492i
\(760\) 179.550 + 34.3766i 0.236250 + 0.0452323i
\(761\) 133.134 + 230.595i 0.174946 + 0.303015i 0.940143 0.340781i \(-0.110692\pi\)
−0.765197 + 0.643797i \(0.777358\pi\)
\(762\) −113.176 + 857.954i −0.148524 + 1.12592i
\(763\) −360.640 + 624.647i −0.472661 + 0.818673i
\(764\) 368.261 17.8449i 0.482016 0.0233572i
\(765\) −1098.42 352.739i −1.43584 0.461097i
\(766\) 65.5449 + 62.4457i 0.0855678 + 0.0815218i
\(767\) 89.0260 + 51.3992i 0.116070 + 0.0670133i
\(768\) −733.673 + 227.041i −0.955304 + 0.295627i
\(769\) −426.068 737.971i −0.554054 0.959650i −0.997976 0.0635850i \(-0.979747\pi\)
0.443922 0.896065i \(-0.353587\pi\)
\(770\) −759.987 184.041i −0.986996 0.239014i
\(771\) −1460.06 + 155.989i −1.89373 + 0.202321i
\(772\) 961.551 + 494.717i 1.24553 + 0.640825i
\(773\) 1203.58i 1.55702i −0.627630 0.778512i \(-0.715975\pi\)
0.627630 0.778512i \(-0.284025\pi\)
\(774\) 60.3732 + 110.808i 0.0780016 + 0.143163i
\(775\) 385.495i 0.497412i
\(776\) −434.701 + 151.050i −0.560181 + 0.194652i
\(777\) −301.048 412.868i −0.387450 0.531361i
\(778\) 257.494 1063.31i 0.330969 1.36672i
\(779\) −39.2913 68.0546i −0.0504382 0.0873615i
\(780\) 310.358 + 119.929i 0.397895 + 0.153755i
\(781\) −99.9402 57.7005i −0.127964 0.0738803i
\(782\) −1080.22 1029.14i −1.38135 1.31604i
\(783\) −1202.67 249.180i −1.53598 0.318237i
\(784\) −425.068 + 41.2923i −0.542178 + 0.0526687i
\(785\) 262.799 455.182i 0.334776 0.579850i
\(786\) −39.9819 96.5950i −0.0508676 0.122894i
\(787\) −353.524 612.322i −0.449205 0.778046i 0.549130 0.835737i \(-0.314959\pi\)
−0.998334 + 0.0576915i \(0.981626\pi\)
\(788\) −303.616 471.586i −0.385300 0.598459i
\(789\) 957.127 697.903i 1.21309 0.884541i
\(790\) −184.464 627.275i −0.233498 0.794019i
\(791\) 79.8933i 0.101003i
\(792\) 878.232 + 479.668i 1.10888 + 0.605642i
\(793\) −253.212 −0.319308
\(794\) 692.447 203.629i 0.872099 0.256460i
\(795\) 1043.88 111.525i 1.31306 0.140284i
\(796\) 591.022 + 917.994i 0.742491 + 1.15326i
\(797\) 802.601 463.382i 1.00703 0.581408i 0.0967079 0.995313i \(-0.469169\pi\)
0.910320 + 0.413905i \(0.135835\pi\)
\(798\) 86.2432 + 66.2119i 0.108074 + 0.0829723i
\(799\) −1143.93 660.447i −1.43170 0.826592i
\(800\) −206.641 + 263.876i −0.258301 + 0.329845i
\(801\) −288.596 318.317i −0.360294 0.397400i
\(802\) 178.101 186.940i 0.222071 0.233093i
\(803\) 792.565 1372.76i 0.987005 1.70954i
\(804\) −1064.32 + 857.956i −1.32379 + 1.06711i
\(805\) −844.432 + 487.533i −1.04898 + 0.605631i
\(806\) 333.061 + 80.6552i 0.413227 + 0.100069i
\(807\) −985.144 436.593i −1.22075 0.541007i
\(808\) −345.677 994.808i −0.427818 1.23120i
\(809\) 804.591 0.994551 0.497275 0.867593i \(-0.334334\pi\)
0.497275 + 0.867593i \(0.334334\pi\)
\(810\) 730.622 630.209i 0.902002 0.778035i
\(811\) 652.228 0.804227 0.402113 0.915590i \(-0.368276\pi\)
0.402113 + 0.915590i \(0.368276\pi\)
\(812\) 764.200 + 393.180i 0.941134 + 0.484212i
\(813\) −612.223 271.323i −0.753042 0.333731i
\(814\) −235.923 + 974.231i −0.289832 + 1.19684i
\(815\) 174.629 100.822i 0.214269 0.123708i
\(816\) −686.504 771.961i −0.841304 0.946031i
\(817\) 13.4485 23.2936i 0.0164609 0.0285111i
\(818\) −554.926 + 582.468i −0.678394 + 0.712063i
\(819\) 132.918 + 146.606i 0.162293 + 0.179007i
\(820\) 487.383 23.6173i 0.594369 0.0288016i
\(821\) −162.159 93.6225i −0.197514 0.114035i 0.397981 0.917393i \(-0.369711\pi\)
−0.595495 + 0.803359i \(0.703044\pi\)
\(822\) −340.349 + 443.316i −0.414050 + 0.539314i
\(823\) −260.354 + 150.315i −0.316347 + 0.182643i −0.649763 0.760137i \(-0.725132\pi\)
0.333416 + 0.942780i \(0.391799\pi\)
\(824\) −336.761 64.4761i −0.408691 0.0782477i
\(825\) 434.231 46.3921i 0.526341 0.0562329i
\(826\) −200.119 + 58.8494i −0.242275 + 0.0712462i
\(827\) 755.962 0.914101 0.457051 0.889441i \(-0.348906\pi\)
0.457051 + 0.889441i \(0.348906\pi\)
\(828\) 1205.46 322.341i 1.45588 0.389301i
\(829\) 205.363i 0.247724i 0.992299 + 0.123862i \(0.0395280\pi\)
−0.992299 + 0.123862i \(0.960472\pi\)
\(830\) −357.350 + 105.086i −0.430542 + 0.126610i
\(831\) 311.884 227.415i 0.375312 0.273664i
\(832\) 184.750 + 233.743i 0.222055 + 0.280942i
\(833\) −287.231 497.499i −0.344815 0.597238i
\(834\) −101.367 244.898i −0.121543 0.293643i
\(835\) −172.009 + 297.929i −0.205999 + 0.356801i
\(836\) −10.3237 213.047i −0.0123489 0.254841i
\(837\) 661.152 741.919i 0.789906 0.886403i
\(838\) −98.3308 + 103.211i −0.117340 + 0.123163i
\(839\) −249.008 143.765i −0.296791 0.171352i 0.344209 0.938893i \(-0.388147\pi\)
−0.641000 + 0.767541i \(0.721480\pi\)
\(840\) −610.590 + 288.097i −0.726893 + 0.342973i
\(841\) 614.143 + 1063.73i 0.730253 + 1.26484i
\(842\) −323.397 + 1335.45i −0.384082 + 1.58604i
\(843\) 599.623 + 822.343i 0.711297 + 0.975496i
\(844\) 457.080 + 235.167i 0.541563 + 0.278634i
\(845\) 877.482i 1.03844i
\(846\) 970.087 528.546i 1.14667 0.624759i
\(847\) 340.851i 0.402422i
\(848\) 855.759 + 389.118i 1.00915 + 0.458865i
\(849\) 51.7201 5.52563i 0.0609188 0.00650840i
\(850\) −438.166 106.108i −0.515489 0.124833i
\(851\) 624.971 + 1082.48i 0.734396 + 1.27201i
\(852\) −98.4459 + 15.3677i −0.115547 + 0.0180372i
\(853\) 1224.79 + 707.134i 1.43586 + 0.828997i 0.997559 0.0698290i \(-0.0222454\pi\)
0.438306 + 0.898826i \(0.355579\pi\)
\(854\) 354.412 372.002i 0.415002 0.435599i
\(855\) −195.814 62.8825i −0.229022 0.0735468i
\(856\) −554.454 479.245i −0.647727 0.559866i
\(857\) 214.812 372.065i 0.250656 0.434149i −0.713051 0.701113i \(-0.752687\pi\)
0.963707 + 0.266964i \(0.0860204\pi\)
\(858\) 50.7702 384.875i 0.0591727 0.448573i
\(859\) −820.973 1421.97i −0.955731 1.65537i −0.732687 0.680566i \(-0.761734\pi\)
−0.223043 0.974809i \(-0.571599\pi\)
\(860\) 90.4109 + 140.429i 0.105129 + 0.163289i
\(861\) 265.327 + 117.587i 0.308161 + 0.136570i
\(862\) −790.011 + 232.320i −0.916486 + 0.269512i
\(863\) 343.475i 0.398001i 0.979999 + 0.199000i \(0.0637695\pi\)
−0.979999 + 0.199000i \(0.936231\pi\)
\(864\) 850.264 153.449i 0.984102 0.177603i
\(865\) −107.611 −0.124406
\(866\) −458.642 1559.63i −0.529610 1.80095i
\(867\) 211.741 477.781i 0.244223 0.551074i
\(868\) −584.668 + 376.421i −0.673581 + 0.433665i
\(869\) −660.665 + 381.435i −0.760259 + 0.438935i
\(870\) −1611.64 212.597i −1.85246 0.244364i
\(871\) 459.292 + 265.172i 0.527316 + 0.304446i
\(872\) 798.903 924.277i 0.916173 1.05995i
\(873\) 506.036 109.375i 0.579652 0.125287i
\(874\) −192.569 183.464i −0.220331 0.209913i
\(875\) 204.320 353.893i 0.233509 0.404449i
\(876\) −211.088 1352.24i −0.240968 1.54365i
\(877\) −322.495 + 186.193i −0.367725 + 0.212306i −0.672464 0.740130i \(-0.734764\pi\)
0.304739 + 0.952436i \(0.401431\pi\)
\(878\) −237.087 + 979.038i −0.270031 + 1.11508i
\(879\) −50.0559 468.524i −0.0569464 0.533020i
\(880\) 1205.67 + 548.224i 1.37008 + 0.622982i
\(881\) −526.956 −0.598134 −0.299067 0.954232i \(-0.596675\pi\)
−0.299067 + 0.954232i \(0.596675\pi\)
\(882\) 480.305 + 11.8768i 0.544564 + 0.0134657i
\(883\) −1534.59 −1.73792 −0.868962 0.494879i \(-0.835212\pi\)
−0.868962 + 0.494879i \(0.835212\pi\)
\(884\) −183.351 + 356.368i −0.207410 + 0.403131i
\(885\) 318.806 232.462i 0.360233 0.262669i
\(886\) 635.188 + 153.819i 0.716916 + 0.173611i
\(887\) 525.057 303.142i 0.591946 0.341760i −0.173920 0.984760i \(-0.555644\pi\)
0.765867 + 0.642999i \(0.222310\pi\)
\(888\) 369.313 + 782.718i 0.415893 + 0.881439i
\(889\) −340.613 + 589.959i −0.383142 + 0.663621i
\(890\) −411.738 392.269i −0.462627 0.440752i
\(891\) −915.283 655.453i −1.02725 0.735637i
\(892\) −1159.07 + 56.1654i −1.29940 + 0.0629657i
\(893\) −203.927 117.737i −0.228362 0.131845i
\(894\) 175.341 72.5758i 0.196130 0.0811810i
\(895\) 1364.36 787.711i 1.52442 0.880124i
\(896\) −601.989 55.7408i −0.671863 0.0622107i
\(897\) −285.207 391.143i −0.317957 0.436057i
\(898\) 272.029 + 925.043i 0.302927 + 1.03011i
\(899\) −1674.28 −1.86239
\(900\) 266.753 266.480i 0.296392 0.296088i
\(901\) 1264.52i 1.40346i
\(902\) −160.622 546.200i −0.178073 0.605543i
\(903\) 10.5525 + 98.7721i 0.0116861 + 0.109382i
\(904\) −25.4464 + 132.908i −0.0281487 + 0.147022i
\(905\) 552.355 + 956.708i 0.610338 + 1.05714i
\(906\) 84.3833 + 64.7839i 0.0931383 + 0.0715054i
\(907\) −297.755 + 515.726i −0.328285 + 0.568606i −0.982172 0.187986i \(-0.939804\pi\)
0.653887 + 0.756593i \(0.273137\pi\)
\(908\) 51.2128 + 1056.86i 0.0564018 + 1.16395i
\(909\) 250.305 + 1158.06i 0.275363 + 1.27399i
\(910\) 189.633 + 180.666i 0.208388 + 0.198534i
\(911\) −335.426 193.658i −0.368195 0.212578i 0.304475 0.952520i \(-0.401519\pi\)
−0.672670 + 0.739943i \(0.734852\pi\)
\(912\) −122.382 137.617i −0.134191 0.150896i
\(913\) 217.298 + 376.371i 0.238004 + 0.412236i
\(914\) 500.933 + 121.308i 0.548067 + 0.132722i
\(915\) −393.773 + 888.524i −0.430353 + 0.971064i
\(916\) 302.721 588.380i 0.330481 0.642336i
\(917\) 82.2952i 0.0897439i
\(918\) 661.307 + 955.700i 0.720378 + 1.04107i
\(919\) 1508.26i 1.64119i −0.571508 0.820597i \(-0.693641\pi\)
0.571508 0.820597i \(-0.306359\pi\)
\(920\) 1560.05 542.088i 1.69571 0.589226i
\(921\) −50.8298 + 114.694i −0.0551898 + 0.124532i
\(922\) 55.6989 230.005i 0.0604110 0.249464i
\(923\) 19.3270 + 33.4753i 0.0209393 + 0.0362679i
\(924\) 494.372 + 613.286i 0.535035 + 0.663729i
\(925\) 327.093 + 188.847i 0.353614 + 0.204159i
\(926\) −556.749 530.424i −0.601241 0.572812i
\(927\) 367.265 + 117.941i 0.396186 + 0.127229i
\(928\) −1146.07 897.483i −1.23499 0.967116i
\(929\) −346.221 + 599.672i −0.372681 + 0.645503i −0.989977 0.141228i \(-0.954895\pi\)
0.617296 + 0.786731i \(0.288228\pi\)
\(930\) 800.969 1043.29i 0.861257 1.12182i
\(931\) −51.2045 88.6887i −0.0549994 0.0952618i
\(932\) −549.958 + 354.074i −0.590083 + 0.379907i
\(933\) −14.9767 140.182i −0.0160522 0.150249i
\(934\) 497.139 + 1690.54i 0.532269 + 1.81000i
\(935\) 1781.57i 1.90542i
\(936\) −174.423 286.224i −0.186349 0.305795i
\(937\) 735.537 0.784991 0.392496 0.919754i \(-0.371612\pi\)
0.392496 + 0.919754i \(0.371612\pi\)
\(938\) −1032.43 + 303.609i −1.10067 + 0.323676i
\(939\) 648.773 + 889.749i 0.690919 + 0.947549i
\(940\) 1229.40 791.515i 1.30788 0.842037i
\(941\) 246.674 142.418i 0.262141 0.151347i −0.363170 0.931723i \(-0.618306\pi\)
0.625311 + 0.780376i \(0.284972\pi\)
\(942\) −489.231 + 202.499i −0.519354 + 0.214967i
\(943\) −614.817 354.965i −0.651980 0.376421i
\(944\) 351.655 34.1608i 0.372516 0.0361873i
\(945\) 721.147 238.421i 0.763118 0.252297i
\(946\) 134.417 141.088i 0.142089 0.149141i
\(947\) −327.212 + 566.748i −0.345525 + 0.598466i −0.985449 0.169972i \(-0.945632\pi\)
0.639924 + 0.768438i \(0.278966\pi\)
\(948\) −237.414 + 614.392i −0.250437 + 0.648093i
\(949\) −459.811 + 265.472i −0.484522 + 0.279739i
\(950\) −78.1114 18.9157i −0.0822226 0.0199113i
\(951\) 188.384 137.363i 0.198090 0.144440i
\(952\) −266.922 768.163i −0.280380 0.806894i
\(953\) 883.663 0.927243 0.463622 0.886033i \(-0.346550\pi\)
0.463622 + 0.886033i \(0.346550\pi\)
\(954\) −902.541 551.270i −0.946059 0.577851i
\(955\) −548.981 −0.574850
\(956\) −168.447 + 327.401i −0.176200 + 0.342469i
\(957\) 201.491 + 1885.96i 0.210544 + 1.97070i
\(958\) −223.186 + 921.634i −0.232971 + 0.962040i
\(959\) −381.017 + 219.980i −0.397306 + 0.229385i
\(960\) 1107.52 284.793i 1.15366 0.296659i
\(961\) 196.842 340.941i 0.204831 0.354777i
\(962\) 231.597 243.091i 0.240745 0.252694i
\(963\) 553.779 + 610.811i 0.575056 + 0.634279i
\(964\) 6.20514 + 128.054i 0.00643687 + 0.132836i
\(965\) −1394.41 805.065i −1.44499 0.834264i
\(966\) 973.837 + 128.462i 1.00811 + 0.132983i
\(967\) −93.5260 + 53.9973i −0.0967177 + 0.0558400i −0.547579 0.836754i \(-0.684450\pi\)
0.450861 + 0.892594i \(0.351117\pi\)
\(968\) 108.563 567.029i 0.112152 0.585773i
\(969\) 100.370 226.478i 0.103581 0.233724i
\(970\) 657.394 193.321i 0.677726 0.199300i
\(971\) 384.915 0.396411 0.198206 0.980160i \(-0.436489\pi\)
0.198206 + 0.980160i \(0.436489\pi\)
\(972\) −970.422 + 55.3630i −0.998377 + 0.0569578i
\(973\) 208.644i 0.214433i
\(974\) −129.502 + 38.0830i −0.132959 + 0.0390995i
\(975\) −133.731 59.2663i −0.137160 0.0607859i
\(976\) −708.072 + 505.967i −0.725484 + 0.518409i
\(977\) −791.946 1371.69i −0.810589 1.40398i −0.912452 0.409183i \(-0.865814\pi\)
0.101863 0.994798i \(-0.467520\pi\)
\(978\) −201.390 26.5661i −0.205921 0.0271637i
\(979\) −331.760 + 574.626i −0.338877 + 0.586952i
\(980\) 635.158 30.7781i 0.648120 0.0314062i
\(981\) −1018.22 + 923.152i −1.03794 + 0.941031i
\(982\) −285.628 + 299.803i −0.290863 + 0.305299i
\(983\) 48.2339 + 27.8478i 0.0490680 + 0.0283294i 0.524333 0.851513i \(-0.324315\pi\)
−0.475265 + 0.879843i \(0.657648\pi\)
\(984\) −403.937 280.121i −0.410505 0.284676i
\(985\) 417.567 + 723.247i 0.423926 + 0.734261i
\(986\) 460.848 1903.05i 0.467392 1.93007i
\(987\) 864.715 92.3838i 0.876104 0.0936006i
\(988\) −32.6858 + 63.5294i −0.0330828 + 0.0643010i
\(989\) 242.993i 0.245696i
\(990\) −1271.58 776.679i −1.28443 0.784524i
\(991\) 1622.31i 1.63704i 0.574477 + 0.818521i \(0.305205\pi\)
−0.574477 + 0.818521i \(0.694795\pi\)
\(992\) 1092.53 439.981i 1.10134 0.443529i
\(993\) −887.833 1217.60i −0.894091 1.22619i
\(994\) −76.2310 18.4604i −0.0766912 0.0185718i
\(995\) −812.840 1407.88i −0.816924 1.41495i
\(996\) 350.011 + 135.251i 0.351416 + 0.135795i
\(997\) 1233.43 + 712.120i 1.23714 + 0.714263i 0.968508 0.248981i \(-0.0800956\pi\)
0.268631 + 0.963243i \(0.413429\pi\)
\(998\) 377.163 395.882i 0.377919 0.396675i
\(999\) −305.633 924.442i −0.305939 0.925367i
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 72.3.p.b.43.9 40
3.2 odd 2 216.3.p.b.19.12 40
4.3 odd 2 288.3.t.b.79.8 40
8.3 odd 2 inner 72.3.p.b.43.19 yes 40
8.5 even 2 288.3.t.b.79.7 40
9.2 odd 6 648.3.b.e.163.17 20
9.4 even 3 inner 72.3.p.b.67.19 yes 40
9.5 odd 6 216.3.p.b.91.2 40
9.7 even 3 648.3.b.f.163.4 20
12.11 even 2 864.3.t.b.559.5 40
24.5 odd 2 864.3.t.b.559.16 40
24.11 even 2 216.3.p.b.19.2 40
36.7 odd 6 2592.3.b.e.1135.16 20
36.11 even 6 2592.3.b.f.1135.5 20
36.23 even 6 864.3.t.b.847.16 40
36.31 odd 6 288.3.t.b.175.7 40
72.5 odd 6 864.3.t.b.847.5 40
72.11 even 6 648.3.b.e.163.18 20
72.13 even 6 288.3.t.b.175.8 40
72.29 odd 6 2592.3.b.f.1135.16 20
72.43 odd 6 648.3.b.f.163.3 20
72.59 even 6 216.3.p.b.91.12 40
72.61 even 6 2592.3.b.e.1135.5 20
72.67 odd 6 inner 72.3.p.b.67.9 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.p.b.43.9 40 1.1 even 1 trivial
72.3.p.b.43.19 yes 40 8.3 odd 2 inner
72.3.p.b.67.9 yes 40 72.67 odd 6 inner
72.3.p.b.67.19 yes 40 9.4 even 3 inner
216.3.p.b.19.2 40 24.11 even 2
216.3.p.b.19.12 40 3.2 odd 2
216.3.p.b.91.2 40 9.5 odd 6
216.3.p.b.91.12 40 72.59 even 6
288.3.t.b.79.7 40 8.5 even 2
288.3.t.b.79.8 40 4.3 odd 2
288.3.t.b.175.7 40 36.31 odd 6
288.3.t.b.175.8 40 72.13 even 6
648.3.b.e.163.17 20 9.2 odd 6
648.3.b.e.163.18 20 72.11 even 6
648.3.b.f.163.3 20 72.43 odd 6
648.3.b.f.163.4 20 9.7 even 3
864.3.t.b.559.5 40 12.11 even 2
864.3.t.b.559.16 40 24.5 odd 2
864.3.t.b.847.5 40 72.5 odd 6
864.3.t.b.847.16 40 36.23 even 6
2592.3.b.e.1135.5 20 72.61 even 6
2592.3.b.e.1135.16 20 36.7 odd 6
2592.3.b.f.1135.5 20 36.11 even 6
2592.3.b.f.1135.16 20 72.29 odd 6