Properties

Label 75.3.k.a.58.10
Level $75$
Weight $3$
Character 75.58
Analytic conductor $2.044$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,3,Mod(13,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.k (of order \(20\), degree \(8\), 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: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 58.10
Character \(\chi\) \(=\) 75.58
Dual form 75.3.k.a.22.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.93190 + 1.49388i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(4.01322 + 5.52372i) q^{4} +(-0.890939 + 4.91998i) q^{5} +(-4.61091 - 3.35002i) q^{6} +(4.34391 - 4.34391i) q^{7} +(1.45557 + 9.19012i) q^{8} +(2.85317 + 0.927051i) q^{9} +O(q^{10})\) \(q+(2.93190 + 1.49388i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(4.01322 + 5.52372i) q^{4} +(-0.890939 + 4.91998i) q^{5} +(-4.61091 - 3.35002i) q^{6} +(4.34391 - 4.34391i) q^{7} +(1.45557 + 9.19012i) q^{8} +(2.85317 + 0.927051i) q^{9} +(-9.96199 + 13.0939i) q^{10} +(-4.51369 - 13.8917i) q^{11} +(-5.36886 - 10.5370i) q^{12} +(6.86423 - 3.49750i) q^{13} +(19.2252 - 6.24664i) q^{14} +(2.85723 - 8.17534i) q^{15} +(-1.02182 + 3.14483i) q^{16} +(-25.6357 + 4.06030i) q^{17} +(6.98030 + 6.98030i) q^{18} +(-1.24222 + 1.70977i) q^{19} +(-30.7522 + 14.8237i) q^{20} +(-8.60824 + 6.25425i) q^{21} +(7.51883 - 47.4720i) q^{22} +(-2.15443 + 4.22830i) q^{23} -16.1162i q^{24} +(-23.4125 - 8.76681i) q^{25} +25.3501 q^{26} +(-4.62981 - 2.35900i) q^{27} +(41.4277 + 6.56150i) q^{28} +(32.6254 + 44.9050i) q^{29} +(20.5901 - 19.7009i) q^{30} +(27.1558 + 19.7298i) q^{31} +(18.6237 - 18.6237i) q^{32} +(3.95770 + 24.9879i) q^{33} +(-81.2269 - 26.3922i) q^{34} +(17.5018 + 25.2421i) q^{35} +(6.32962 + 19.4806i) q^{36} +(-18.7363 - 36.7721i) q^{37} +(-6.19627 + 3.15716i) q^{38} +(-12.6905 + 4.12339i) q^{39} +(-46.5120 - 1.02645i) q^{40} +(-1.20677 + 3.71404i) q^{41} +(-34.5816 + 5.47718i) q^{42} +(-32.8976 - 32.8976i) q^{43} +(58.6196 - 80.6829i) q^{44} +(-7.10308 + 13.2116i) q^{45} +(-12.6331 + 9.17851i) q^{46} +(-12.8776 + 81.3060i) q^{47} +(2.60015 - 5.10308i) q^{48} +11.2608i q^{49} +(-55.5464 - 60.6787i) q^{50} +44.9558 q^{51} +(46.8669 + 23.8799i) q^{52} +(-81.1884 - 12.8590i) q^{53} +(-10.0501 - 13.8327i) q^{54} +(72.3684 - 9.83061i) q^{55} +(46.2440 + 33.5982i) q^{56} +(2.58837 - 2.58837i) q^{57} +(28.5718 + 180.395i) q^{58} +(-10.7101 - 3.47991i) q^{59} +(56.6250 - 17.0269i) q^{60} +(-9.84864 - 30.3110i) q^{61} +(50.1440 + 98.4132i) q^{62} +(16.4210 - 8.36689i) q^{63} +(95.0038 - 30.8686i) q^{64} +(11.0920 + 36.8880i) q^{65} +(-25.7253 + 79.1744i) q^{66} +(-0.351533 + 0.0556774i) q^{67} +(-125.310 - 125.310i) q^{68} +(4.83131 - 6.64972i) q^{69} +(13.6049 + 100.153i) q^{70} +(88.5525 - 64.3371i) q^{71} +(-4.36672 + 27.5704i) q^{72} +(-20.1163 + 39.4805i) q^{73} -135.802i q^{74} +(37.6769 + 21.3413i) q^{75} -14.4296 q^{76} +(-79.9515 - 40.7373i) q^{77} +(-43.3670 - 6.86866i) q^{78} +(33.1447 + 45.6197i) q^{79} +(-14.5621 - 7.82918i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-9.08644 + 9.08644i) q^{82} +(-2.71085 - 17.1156i) q^{83} +(-69.0935 - 22.4499i) q^{84} +(2.86327 - 129.745i) q^{85} +(-47.3074 - 145.597i) q^{86} +(-43.6460 - 85.6602i) q^{87} +(121.097 - 61.7018i) q^{88} +(-85.2857 + 27.7110i) q^{89} +(-40.5620 + 28.1239i) q^{90} +(14.6248 - 45.0105i) q^{91} +(-32.0022 + 5.06865i) q^{92} +(-41.1102 - 41.1102i) q^{93} +(-159.217 + 219.143i) q^{94} +(-7.30531 - 7.63503i) q^{95} +(-36.9063 + 26.8140i) q^{96} +(1.37908 - 8.70714i) q^{97} +(-16.8223 + 33.0156i) q^{98} -43.8198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.93190 + 1.49388i 1.46595 + 0.746939i 0.991099 0.133128i \(-0.0425021\pi\)
0.474850 + 0.880066i \(0.342502\pi\)
\(3\) −1.71073 0.270952i −0.570242 0.0903175i
\(4\) 4.01322 + 5.52372i 1.00331 + 1.38093i
\(5\) −0.890939 + 4.91998i −0.178188 + 0.983996i
\(6\) −4.61091 3.35002i −0.768484 0.558337i
\(7\) 4.34391 4.34391i 0.620559 0.620559i −0.325115 0.945674i \(-0.605403\pi\)
0.945674 + 0.325115i \(0.105403\pi\)
\(8\) 1.45557 + 9.19012i 0.181946 + 1.14876i
\(9\) 2.85317 + 0.927051i 0.317019 + 0.103006i
\(10\) −9.96199 + 13.0939i −0.996199 + 1.30939i
\(11\) −4.51369 13.8917i −0.410336 1.26288i −0.916357 0.400362i \(-0.868884\pi\)
0.506021 0.862521i \(-0.331116\pi\)
\(12\) −5.36886 10.5370i −0.447405 0.878081i
\(13\) 6.86423 3.49750i 0.528018 0.269039i −0.169595 0.985514i \(-0.554246\pi\)
0.697612 + 0.716475i \(0.254246\pi\)
\(14\) 19.2252 6.24664i 1.37323 0.446189i
\(15\) 2.85723 8.17534i 0.190482 0.545023i
\(16\) −1.02182 + 3.14483i −0.0638636 + 0.196552i
\(17\) −25.6357 + 4.06030i −1.50798 + 0.238841i −0.855039 0.518564i \(-0.826467\pi\)
−0.652945 + 0.757405i \(0.726467\pi\)
\(18\) 6.98030 + 6.98030i 0.387795 + 0.387795i
\(19\) −1.24222 + 1.70977i −0.0653802 + 0.0899881i −0.840455 0.541881i \(-0.817712\pi\)
0.775075 + 0.631870i \(0.217712\pi\)
\(20\) −30.7522 + 14.8237i −1.53761 + 0.741184i
\(21\) −8.60824 + 6.25425i −0.409916 + 0.297822i
\(22\) 7.51883 47.4720i 0.341765 2.15782i
\(23\) −2.15443 + 4.22830i −0.0936708 + 0.183839i −0.933088 0.359649i \(-0.882897\pi\)
0.839417 + 0.543488i \(0.182897\pi\)
\(24\) 16.1162i 0.671507i
\(25\) −23.4125 8.76681i −0.936498 0.350672i
\(26\) 25.3501 0.975003
\(27\) −4.62981 2.35900i −0.171474 0.0873705i
\(28\) 41.4277 + 6.56150i 1.47956 + 0.234339i
\(29\) 32.6254 + 44.9050i 1.12501 + 1.54845i 0.797208 + 0.603704i \(0.206309\pi\)
0.327806 + 0.944745i \(0.393691\pi\)
\(30\) 20.5901 19.7009i 0.686336 0.656697i
\(31\) 27.1558 + 19.7298i 0.875993 + 0.636446i 0.932188 0.361974i \(-0.117897\pi\)
−0.0561957 + 0.998420i \(0.517897\pi\)
\(32\) 18.6237 18.6237i 0.581992 0.581992i
\(33\) 3.95770 + 24.9879i 0.119930 + 0.757210i
\(34\) −81.2269 26.3922i −2.38903 0.776242i
\(35\) 17.5018 + 25.2421i 0.500052 + 0.721204i
\(36\) 6.32962 + 19.4806i 0.175823 + 0.541127i
\(37\) −18.7363 36.7721i −0.506388 0.993842i −0.992763 0.120092i \(-0.961681\pi\)
0.486375 0.873750i \(-0.338319\pi\)
\(38\) −6.19627 + 3.15716i −0.163060 + 0.0830831i
\(39\) −12.6905 + 4.12339i −0.325397 + 0.105728i
\(40\) −46.5120 1.02645i −1.16280 0.0256613i
\(41\) −1.20677 + 3.71404i −0.0294333 + 0.0905864i −0.964694 0.263373i \(-0.915165\pi\)
0.935261 + 0.353960i \(0.115165\pi\)
\(42\) −34.5816 + 5.47718i −0.823371 + 0.130409i
\(43\) −32.8976 32.8976i −0.765060 0.765060i 0.212172 0.977232i \(-0.431946\pi\)
−0.977232 + 0.212172i \(0.931946\pi\)
\(44\) 58.6196 80.6829i 1.33226 1.83370i
\(45\) −7.10308 + 13.2116i −0.157846 + 0.293591i
\(46\) −12.6331 + 9.17851i −0.274633 + 0.199533i
\(47\) −12.8776 + 81.3060i −0.273991 + 1.72991i 0.339846 + 0.940481i \(0.389625\pi\)
−0.613837 + 0.789433i \(0.710375\pi\)
\(48\) 2.60015 5.10308i 0.0541698 0.106314i
\(49\) 11.2608i 0.229813i
\(50\) −55.5464 60.6787i −1.11093 1.21357i
\(51\) 44.9558 0.881487
\(52\) 46.8669 + 23.8799i 0.901287 + 0.459229i
\(53\) −81.1884 12.8590i −1.53186 0.242622i −0.667159 0.744916i \(-0.732490\pi\)
−0.864697 + 0.502293i \(0.832490\pi\)
\(54\) −10.0501 13.8327i −0.186112 0.256161i
\(55\) 72.3684 9.83061i 1.31579 0.178738i
\(56\) 46.2440 + 33.5982i 0.825785 + 0.599968i
\(57\) 2.58837 2.58837i 0.0454101 0.0454101i
\(58\) 28.5718 + 180.395i 0.492618 + 3.11026i
\(59\) −10.7101 3.47991i −0.181526 0.0589815i 0.216843 0.976206i \(-0.430424\pi\)
−0.398370 + 0.917225i \(0.630424\pi\)
\(60\) 56.6250 17.0269i 0.943751 0.283781i
\(61\) −9.84864 30.3110i −0.161453 0.496902i 0.837304 0.546737i \(-0.184130\pi\)
−0.998757 + 0.0498356i \(0.984130\pi\)
\(62\) 50.1440 + 98.4132i 0.808775 + 1.58731i
\(63\) 16.4210 8.36689i 0.260650 0.132808i
\(64\) 95.0038 30.8686i 1.48443 0.482322i
\(65\) 11.0920 + 36.8880i 0.170647 + 0.567507i
\(66\) −25.7253 + 79.1744i −0.389777 + 1.19961i
\(67\) −0.351533 + 0.0556774i −0.00524677 + 0.000831006i −0.159057 0.987269i \(-0.550845\pi\)
0.153811 + 0.988100i \(0.450845\pi\)
\(68\) −125.310 125.310i −1.84279 1.84279i
\(69\) 4.83131 6.64972i 0.0700189 0.0963728i
\(70\) 13.6049 + 100.153i 0.194356 + 1.43076i
\(71\) 88.5525 64.3371i 1.24722 0.906157i 0.249161 0.968462i \(-0.419845\pi\)
0.998057 + 0.0623051i \(0.0198452\pi\)
\(72\) −4.36672 + 27.5704i −0.0606488 + 0.382922i
\(73\) −20.1163 + 39.4805i −0.275566 + 0.540828i −0.986764 0.162163i \(-0.948153\pi\)
0.711198 + 0.702992i \(0.248153\pi\)
\(74\) 135.802i 1.83516i
\(75\) 37.6769 + 21.3413i 0.502359 + 0.284550i
\(76\) −14.4296 −0.189864
\(77\) −79.9515 40.7373i −1.03833 0.529056i
\(78\) −43.3670 6.86866i −0.555988 0.0880598i
\(79\) 33.1447 + 45.6197i 0.419553 + 0.577465i 0.965516 0.260344i \(-0.0838361\pi\)
−0.545963 + 0.837809i \(0.683836\pi\)
\(80\) −14.5621 7.82918i −0.182027 0.0978648i
\(81\) 7.28115 + 5.29007i 0.0898908 + 0.0653095i
\(82\) −9.08644 + 9.08644i −0.110810 + 0.110810i
\(83\) −2.71085 17.1156i −0.0326608 0.206212i 0.965961 0.258686i \(-0.0832895\pi\)
−0.998622 + 0.0524736i \(0.983289\pi\)
\(84\) −69.0935 22.4499i −0.822542 0.267260i
\(85\) 2.86327 129.745i 0.0336855 1.52641i
\(86\) −47.3074 145.597i −0.550087 1.69299i
\(87\) −43.6460 85.6602i −0.501679 0.984600i
\(88\) 121.097 61.7018i 1.37610 0.701156i
\(89\) −85.2857 + 27.7110i −0.958267 + 0.311360i −0.746070 0.665867i \(-0.768062\pi\)
−0.212196 + 0.977227i \(0.568062\pi\)
\(90\) −40.5620 + 28.1239i −0.450689 + 0.312488i
\(91\) 14.6248 45.0105i 0.160712 0.494621i
\(92\) −32.0022 + 5.06865i −0.347850 + 0.0550940i
\(93\) −41.1102 41.1102i −0.442046 0.442046i
\(94\) −159.217 + 219.143i −1.69380 + 2.33131i
\(95\) −7.30531 7.63503i −0.0768981 0.0803687i
\(96\) −36.9063 + 26.8140i −0.384440 + 0.279312i
\(97\) 1.37908 8.70714i 0.0142173 0.0897643i −0.979559 0.201155i \(-0.935531\pi\)
0.993777 + 0.111391i \(0.0355305\pi\)
\(98\) −16.8223 + 33.0156i −0.171656 + 0.336894i
\(99\) 43.8198i 0.442625i
\(100\) −45.5339 164.507i −0.455339 1.64507i
\(101\) 4.54639 0.0450138 0.0225069 0.999747i \(-0.492835\pi\)
0.0225069 + 0.999747i \(0.492835\pi\)
\(102\) 131.806 + 67.1585i 1.29222 + 0.658417i
\(103\) 98.1209 + 15.5408i 0.952630 + 0.150882i 0.613357 0.789806i \(-0.289819\pi\)
0.339273 + 0.940688i \(0.389819\pi\)
\(104\) 42.1338 + 57.9922i 0.405133 + 0.557618i
\(105\) −23.1014 47.9246i −0.220013 0.456424i
\(106\) −218.826 158.987i −2.06440 1.49987i
\(107\) 58.0204 58.0204i 0.542247 0.542247i −0.381940 0.924187i \(-0.624744\pi\)
0.924187 + 0.381940i \(0.124744\pi\)
\(108\) −5.54994 35.0410i −0.0513884 0.324453i
\(109\) 77.8317 + 25.2890i 0.714052 + 0.232010i 0.643442 0.765494i \(-0.277506\pi\)
0.0706096 + 0.997504i \(0.477506\pi\)
\(110\) 226.863 + 79.2872i 2.06239 + 0.720793i
\(111\) 22.0893 + 67.9837i 0.199002 + 0.612466i
\(112\) 9.22219 + 18.0996i 0.0823410 + 0.161603i
\(113\) 168.661 85.9369i 1.49257 0.760504i 0.498262 0.867027i \(-0.333972\pi\)
0.994310 + 0.106523i \(0.0339718\pi\)
\(114\) 11.4556 3.72214i 0.100487 0.0326503i
\(115\) −18.8837 14.3669i −0.164206 0.124930i
\(116\) −117.110 + 360.428i −1.00957 + 3.10713i
\(117\) 22.8272 3.61547i 0.195104 0.0309015i
\(118\) −26.2022 26.2022i −0.222053 0.222053i
\(119\) −93.7218 + 128.997i −0.787578 + 1.08401i
\(120\) 79.2913 + 14.3585i 0.660761 + 0.119654i
\(121\) −74.7153 + 54.2839i −0.617482 + 0.448627i
\(122\) 16.4057 103.581i 0.134473 0.849028i
\(123\) 3.07077 6.02673i 0.0249656 0.0489978i
\(124\) 229.181i 1.84823i
\(125\) 63.9916 107.378i 0.511933 0.859025i
\(126\) 60.6437 0.481299
\(127\) −99.6529 50.7757i −0.784668 0.399808i 0.0152756 0.999883i \(-0.495137\pi\)
−0.799944 + 0.600075i \(0.795137\pi\)
\(128\) 220.601 + 34.9397i 1.72344 + 0.272967i
\(129\) 47.3651 + 65.1924i 0.367171 + 0.505368i
\(130\) −22.5854 + 124.722i −0.173734 + 0.959399i
\(131\) −84.3598 61.2910i −0.643968 0.467870i 0.217243 0.976118i \(-0.430294\pi\)
−0.861211 + 0.508247i \(0.830294\pi\)
\(132\) −122.143 + 122.143i −0.925328 + 0.925328i
\(133\) 2.03100 + 12.8232i 0.0152707 + 0.0964152i
\(134\) −1.11384 0.361907i −0.00831221 0.00270080i
\(135\) 15.7311 20.6768i 0.116527 0.153162i
\(136\) −74.6293 229.685i −0.548745 1.68886i
\(137\) 69.3960 + 136.197i 0.506540 + 0.994141i 0.992738 + 0.120293i \(0.0383833\pi\)
−0.486198 + 0.873849i \(0.661617\pi\)
\(138\) 24.0988 12.2789i 0.174629 0.0889778i
\(139\) 149.736 48.6523i 1.07724 0.350016i 0.283937 0.958843i \(-0.408359\pi\)
0.793303 + 0.608827i \(0.208359\pi\)
\(140\) −69.1920 + 197.977i −0.494228 + 1.41412i
\(141\) 44.0601 135.603i 0.312483 0.961724i
\(142\) 355.739 56.3435i 2.50520 0.396785i
\(143\) −79.5693 79.5693i −0.556429 0.556429i
\(144\) −5.83084 + 8.02546i −0.0404920 + 0.0557324i
\(145\) −249.999 + 120.509i −1.72413 + 0.831095i
\(146\) −117.958 + 85.7015i −0.807931 + 0.586996i
\(147\) 3.05115 19.2642i 0.0207561 0.131049i
\(148\) 127.926 251.069i 0.864365 1.69641i
\(149\) 80.4685i 0.540057i 0.962852 + 0.270028i \(0.0870331\pi\)
−0.962852 + 0.270028i \(0.912967\pi\)
\(150\) 78.5837 + 118.855i 0.523891 + 0.792368i
\(151\) 187.435 1.24129 0.620647 0.784090i \(-0.286870\pi\)
0.620647 + 0.784090i \(0.286870\pi\)
\(152\) −17.5212 8.92749i −0.115271 0.0587335i
\(153\) −76.9072 12.1809i −0.502661 0.0796137i
\(154\) −173.553 238.875i −1.12697 1.55114i
\(155\) −121.265 + 116.028i −0.782352 + 0.748567i
\(156\) −73.7061 53.5506i −0.472475 0.343273i
\(157\) −90.0864 + 90.0864i −0.573798 + 0.573798i −0.933188 0.359389i \(-0.882985\pi\)
0.359389 + 0.933188i \(0.382985\pi\)
\(158\) 29.0266 + 183.267i 0.183712 + 1.15991i
\(159\) 135.407 + 43.9964i 0.851616 + 0.276707i
\(160\) 75.0358 + 108.221i 0.468974 + 0.676382i
\(161\) 9.00873 + 27.7260i 0.0559549 + 0.172211i
\(162\) 13.4449 + 26.3871i 0.0829932 + 0.162883i
\(163\) −30.5160 + 15.5487i −0.187215 + 0.0953908i −0.545086 0.838380i \(-0.683503\pi\)
0.357871 + 0.933771i \(0.383503\pi\)
\(164\) −25.3584 + 8.23943i −0.154624 + 0.0502404i
\(165\) −126.466 2.79092i −0.766462 0.0169147i
\(166\) 17.6207 54.2310i 0.106149 0.326693i
\(167\) −58.2426 + 9.22473i −0.348758 + 0.0552379i −0.328356 0.944554i \(-0.606495\pi\)
−0.0204021 + 0.999792i \(0.506495\pi\)
\(168\) −70.0072 70.0072i −0.416710 0.416710i
\(169\) −64.4505 + 88.7086i −0.381364 + 0.524903i
\(170\) 202.218 376.121i 1.18951 2.21248i
\(171\) −5.12932 + 3.72667i −0.0299960 + 0.0217934i
\(172\) 49.6919 313.742i 0.288907 1.82408i
\(173\) 35.3231 69.3255i 0.204180 0.400726i −0.766096 0.642726i \(-0.777803\pi\)
0.970276 + 0.242000i \(0.0778035\pi\)
\(174\) 316.349i 1.81810i
\(175\) −139.784 + 63.6194i −0.798765 + 0.363539i
\(176\) 48.2993 0.274428
\(177\) 17.3791 + 8.85509i 0.0981869 + 0.0500287i
\(178\) −291.446 46.1605i −1.63734 0.259329i
\(179\) −89.6932 123.452i −0.501080 0.689677i 0.481304 0.876554i \(-0.340163\pi\)
−0.982383 + 0.186877i \(0.940163\pi\)
\(180\) −101.483 + 13.7856i −0.563797 + 0.0765868i
\(181\) −26.4190 19.1945i −0.145961 0.106047i 0.512408 0.858742i \(-0.328753\pi\)
−0.658369 + 0.752695i \(0.728753\pi\)
\(182\) 110.119 110.119i 0.605047 0.605047i
\(183\) 8.63549 + 54.5223i 0.0471885 + 0.297936i
\(184\) −41.9945 13.6449i −0.228231 0.0741568i
\(185\) 197.611 59.4207i 1.06817 0.321193i
\(186\) −59.1174 181.945i −0.317836 0.978198i
\(187\) 172.116 + 337.797i 0.920408 + 1.80640i
\(188\) −500.792 + 255.166i −2.66379 + 1.35727i
\(189\) −30.3588 + 9.86417i −0.160628 + 0.0521914i
\(190\) −10.0127 33.2984i −0.0526982 0.175255i
\(191\) 15.5033 47.7143i 0.0811692 0.249813i −0.902234 0.431247i \(-0.858074\pi\)
0.983403 + 0.181434i \(0.0580738\pi\)
\(192\) −170.889 + 27.0662i −0.890049 + 0.140970i
\(193\) 49.2763 + 49.2763i 0.255318 + 0.255318i 0.823147 0.567829i \(-0.192216\pi\)
−0.567829 + 0.823147i \(0.692216\pi\)
\(194\) 17.0507 23.4683i 0.0878902 0.120971i
\(195\) −8.98054 66.1106i −0.0460541 0.339029i
\(196\) −62.2017 + 45.1922i −0.317356 + 0.230572i
\(197\) −54.5847 + 344.634i −0.277080 + 1.74941i 0.320174 + 0.947359i \(0.396259\pi\)
−0.597253 + 0.802053i \(0.703741\pi\)
\(198\) 65.4615 128.475i 0.330613 0.648865i
\(199\) 39.9002i 0.200504i −0.994962 0.100252i \(-0.968035\pi\)
0.994962 0.100252i \(-0.0319648\pi\)
\(200\) 46.4895 227.924i 0.232448 1.13962i
\(201\) 0.616463 0.00306698
\(202\) 13.3296 + 6.79175i 0.0659879 + 0.0336225i
\(203\) 336.786 + 53.3416i 1.65904 + 0.262766i
\(204\) 180.418 + 248.324i 0.884401 + 1.21727i
\(205\) −17.1979 9.24625i −0.0838920 0.0451037i
\(206\) 264.464 + 192.145i 1.28381 + 0.932741i
\(207\) −10.0668 + 10.0668i −0.0486319 + 0.0486319i
\(208\) 3.98506 + 25.1607i 0.0191589 + 0.120965i
\(209\) 29.3587 + 9.53923i 0.140472 + 0.0456422i
\(210\) 3.86244 175.021i 0.0183926 0.833431i
\(211\) 59.1092 + 181.919i 0.280138 + 0.862177i 0.987814 + 0.155640i \(0.0497439\pi\)
−0.707676 + 0.706538i \(0.750256\pi\)
\(212\) −254.797 500.068i −1.20187 2.35881i
\(213\) −168.921 + 86.0697i −0.793058 + 0.404083i
\(214\) 256.785 83.4346i 1.19993 0.389882i
\(215\) 191.165 132.546i 0.889141 0.616492i
\(216\) 14.9405 45.9822i 0.0691690 0.212880i
\(217\) 203.667 32.2577i 0.938557 0.148653i
\(218\) 190.416 + 190.416i 0.873467 + 0.873467i
\(219\) 45.1108 62.0897i 0.205985 0.283515i
\(220\) 344.732 + 360.291i 1.56696 + 1.63769i
\(221\) −161.769 + 117.532i −0.731985 + 0.531818i
\(222\) −36.7959 + 232.320i −0.165747 + 1.04649i
\(223\) 82.3253 161.572i 0.369172 0.724540i −0.629449 0.777042i \(-0.716719\pi\)
0.998621 + 0.0525014i \(0.0167194\pi\)
\(224\) 161.800i 0.722320i
\(225\) −58.6724 46.7177i −0.260766 0.207634i
\(226\) 622.875 2.75608
\(227\) −266.514 135.796i −1.17407 0.598220i −0.245509 0.969394i \(-0.578955\pi\)
−0.928563 + 0.371174i \(0.878955\pi\)
\(228\) 24.6852 + 3.90975i 0.108268 + 0.0171480i
\(229\) −128.483 176.841i −0.561060 0.772232i 0.430401 0.902638i \(-0.358372\pi\)
−0.991461 + 0.130405i \(0.958372\pi\)
\(230\) −33.9027 70.3323i −0.147403 0.305792i
\(231\) 125.737 + 91.3535i 0.544317 + 0.395470i
\(232\) −365.194 + 365.194i −1.57411 + 1.57411i
\(233\) −28.5917 180.521i −0.122711 0.774767i −0.969905 0.243484i \(-0.921710\pi\)
0.847194 0.531284i \(-0.178290\pi\)
\(234\) 72.3280 + 23.5008i 0.309094 + 0.100431i
\(235\) −388.551 135.796i −1.65341 0.577856i
\(236\) −23.7598 73.1250i −0.100677 0.309852i
\(237\) −44.3407 87.0235i −0.187092 0.367188i
\(238\) −467.488 + 238.197i −1.96424 + 1.00083i
\(239\) −434.275 + 141.105i −1.81705 + 0.590396i −0.817149 + 0.576427i \(0.804447\pi\)
−0.999902 + 0.0139688i \(0.995553\pi\)
\(240\) 22.7905 + 17.3392i 0.0949605 + 0.0722468i
\(241\) −123.592 + 380.378i −0.512831 + 1.57833i 0.274363 + 0.961626i \(0.411533\pi\)
−0.787194 + 0.616706i \(0.788467\pi\)
\(242\) −300.151 + 47.5393i −1.24029 + 0.196443i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 127.905 176.046i 0.524200 0.721499i
\(245\) −55.4031 10.0327i −0.226135 0.0409499i
\(246\) 18.0064 13.0824i 0.0731967 0.0531805i
\(247\) −2.54698 + 16.0810i −0.0103116 + 0.0651051i
\(248\) −141.792 + 278.283i −0.571743 + 1.12211i
\(249\) 30.0147i 0.120541i
\(250\) 348.027 219.226i 1.39211 0.876905i
\(251\) 153.360 0.610995 0.305497 0.952193i \(-0.401177\pi\)
0.305497 + 0.952193i \(0.401177\pi\)
\(252\) 112.117 + 57.1266i 0.444910 + 0.226693i
\(253\) 68.4628 + 10.8434i 0.270604 + 0.0428595i
\(254\) −216.319 297.738i −0.851652 1.17220i
\(255\) −40.0529 + 221.182i −0.157070 + 0.867380i
\(256\) 271.323 + 197.128i 1.05986 + 0.770030i
\(257\) 208.413 208.413i 0.810947 0.810947i −0.173829 0.984776i \(-0.555614\pi\)
0.984776 + 0.173829i \(0.0556139\pi\)
\(258\) 41.4801 + 261.895i 0.160776 + 1.01510i
\(259\) −241.124 78.3459i −0.930981 0.302494i
\(260\) −159.244 + 209.309i −0.612478 + 0.805034i
\(261\) 51.4566 + 158.367i 0.197152 + 0.606770i
\(262\) −155.773 305.722i −0.594554 1.16688i
\(263\) −9.36797 + 4.77322i −0.0356197 + 0.0181491i −0.471710 0.881754i \(-0.656363\pi\)
0.436090 + 0.899903i \(0.356363\pi\)
\(264\) −223.881 + 72.7434i −0.848035 + 0.275543i
\(265\) 135.600 387.989i 0.511698 1.46411i
\(266\) −13.2016 + 40.6305i −0.0496302 + 0.152746i
\(267\) 153.409 24.2976i 0.574565 0.0910022i
\(268\) −1.71833 1.71833i −0.00641167 0.00641167i
\(269\) 270.816 372.747i 1.00675 1.38568i 0.0856627 0.996324i \(-0.472699\pi\)
0.921089 0.389351i \(-0.127301\pi\)
\(270\) 77.0107 37.1220i 0.285225 0.137489i
\(271\) 120.422 87.4918i 0.444362 0.322848i −0.343004 0.939334i \(-0.611444\pi\)
0.787366 + 0.616486i \(0.211444\pi\)
\(272\) 13.4261 84.7689i 0.0493606 0.311651i
\(273\) −37.2147 + 73.0380i −0.136318 + 0.267538i
\(274\) 502.986i 1.83572i
\(275\) −16.1095 + 364.810i −0.0585798 + 1.32658i
\(276\) 56.1203 0.203335
\(277\) −229.696 117.036i −0.829229 0.422513i −0.0127710 0.999918i \(-0.504065\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(278\) 511.692 + 81.0441i 1.84062 + 0.291526i
\(279\) 59.1895 + 81.4673i 0.212149 + 0.291998i
\(280\) −206.503 + 197.586i −0.737511 + 0.705663i
\(281\) −64.5890 46.9267i −0.229854 0.166999i 0.466897 0.884312i \(-0.345372\pi\)
−0.696751 + 0.717313i \(0.745372\pi\)
\(282\) 331.754 331.754i 1.17643 1.17643i
\(283\) 5.52224 + 34.8661i 0.0195132 + 0.123202i 0.995522 0.0945291i \(-0.0301345\pi\)
−0.976009 + 0.217731i \(0.930135\pi\)
\(284\) 710.761 + 230.940i 2.50268 + 0.813170i
\(285\) 10.4287 + 15.0408i 0.0365918 + 0.0527749i
\(286\) −114.422 352.156i −0.400078 1.23131i
\(287\) 10.8914 + 21.3756i 0.0379491 + 0.0744793i
\(288\) 70.4018 35.8715i 0.244451 0.124554i
\(289\) 365.849 118.871i 1.26591 0.411320i
\(290\) −912.998 20.1485i −3.14827 0.0694775i
\(291\) −4.71844 + 14.5219i −0.0162146 + 0.0499033i
\(292\) −298.810 + 47.3269i −1.02332 + 0.162078i
\(293\) −16.7371 16.7371i −0.0571231 0.0571231i 0.677968 0.735091i \(-0.262861\pi\)
−0.735091 + 0.677968i \(0.762861\pi\)
\(294\) 37.7240 51.9226i 0.128313 0.176608i
\(295\) 26.6631 49.5929i 0.0903834 0.168112i
\(296\) 310.668 225.714i 1.04955 0.762546i
\(297\) −11.8731 + 74.9638i −0.0399768 + 0.252403i
\(298\) −120.210 + 235.925i −0.403389 + 0.791696i
\(299\) 36.5592i 0.122271i
\(300\) 33.3224 + 293.764i 0.111075 + 0.979214i
\(301\) −285.809 −0.949530
\(302\) 549.541 + 280.005i 1.81967 + 0.927170i
\(303\) −7.77763 1.23186i −0.0256688 0.00406553i
\(304\) −4.10763 5.65367i −0.0135119 0.0185976i
\(305\) 157.904 21.4499i 0.517718 0.0703275i
\(306\) −207.287 150.603i −0.677409 0.492167i
\(307\) 14.0410 14.0410i 0.0457363 0.0457363i −0.683869 0.729605i \(-0.739704\pi\)
0.729605 + 0.683869i \(0.239704\pi\)
\(308\) −95.8413 605.118i −0.311173 1.96467i
\(309\) −163.647 53.1722i −0.529603 0.172078i
\(310\) −528.867 + 159.028i −1.70602 + 0.512992i
\(311\) −59.5063 183.142i −0.191339 0.588880i −1.00000 0.000605266i \(-0.999807\pi\)
0.808661 0.588275i \(-0.200193\pi\)
\(312\) −56.3663 110.625i −0.180661 0.354568i
\(313\) 141.673 72.1860i 0.452629 0.230626i −0.212787 0.977099i \(-0.568254\pi\)
0.665416 + 0.746473i \(0.268254\pi\)
\(314\) −398.702 + 129.546i −1.26975 + 0.412567i
\(315\) 26.5349 + 88.2452i 0.0842378 + 0.280143i
\(316\) −118.974 + 366.164i −0.376500 + 1.15875i
\(317\) 378.338 59.9228i 1.19349 0.189031i 0.472093 0.881549i \(-0.343499\pi\)
0.721401 + 0.692518i \(0.243499\pi\)
\(318\) 331.274 + 331.274i 1.04174 + 1.04174i
\(319\) 476.547 655.911i 1.49388 2.05615i
\(320\) 67.2304 + 494.919i 0.210095 + 1.54662i
\(321\) −114.978 + 83.5363i −0.358187 + 0.260238i
\(322\) −15.0066 + 94.7479i −0.0466043 + 0.294248i
\(323\) 24.9031 48.8751i 0.0770994 0.151316i
\(324\) 61.4493i 0.189658i
\(325\) −191.370 + 21.7076i −0.588832 + 0.0667928i
\(326\) −112.698 −0.345699
\(327\) −126.297 64.3513i −0.386228 0.196793i
\(328\) −35.8890 5.68426i −0.109418 0.0173301i
\(329\) 297.247 + 409.125i 0.903486 + 1.24354i
\(330\) −366.617 197.108i −1.11096 0.597296i
\(331\) −450.680 327.439i −1.36157 0.989240i −0.998343 0.0575405i \(-0.981674\pi\)
−0.363229 0.931700i \(-0.618326\pi\)
\(332\) 83.6628 83.6628i 0.251996 0.251996i
\(333\) −19.3683 122.287i −0.0581631 0.367227i
\(334\) −184.542 59.9614i −0.552521 0.179525i
\(335\) 0.0392630 1.77914i 0.000117203 0.00531088i
\(336\) −10.8725 33.4622i −0.0323587 0.0995899i
\(337\) 86.1758 + 169.130i 0.255715 + 0.501868i 0.982799 0.184680i \(-0.0591250\pi\)
−0.727084 + 0.686548i \(0.759125\pi\)
\(338\) −321.482 + 163.803i −0.951131 + 0.484625i
\(339\) −311.817 + 101.316i −0.919814 + 0.298866i
\(340\) 728.165 504.878i 2.14166 1.48494i
\(341\) 151.508 466.295i 0.444306 1.36743i
\(342\) −20.6058 + 3.26365i −0.0602510 + 0.00954282i
\(343\) 261.768 + 261.768i 0.763172 + 0.763172i
\(344\) 254.448 350.217i 0.739674 1.01807i
\(345\) 28.4121 + 29.6944i 0.0823540 + 0.0860708i
\(346\) 207.128 150.487i 0.598635 0.434934i
\(347\) 23.6780 149.497i 0.0682362 0.430827i −0.929793 0.368082i \(-0.880015\pi\)
0.998030 0.0627447i \(-0.0199854\pi\)
\(348\) 298.002 584.862i 0.856327 1.68064i
\(349\) 124.533i 0.356829i 0.983955 + 0.178415i \(0.0570968\pi\)
−0.983955 + 0.178415i \(0.942903\pi\)
\(350\) −504.872 22.2944i −1.44249 0.0636982i
\(351\) −40.0307 −0.114048
\(352\) −342.777 174.654i −0.973800 0.496176i
\(353\) −367.421 58.1938i −1.04085 0.164855i −0.387470 0.921882i \(-0.626651\pi\)
−0.653383 + 0.757027i \(0.726651\pi\)
\(354\) 37.7253 + 51.9244i 0.106569 + 0.146679i
\(355\) 237.643 + 492.997i 0.669416 + 1.38872i
\(356\) −495.338 359.884i −1.39140 1.01091i
\(357\) 195.284 195.284i 0.547015 0.547015i
\(358\) −78.5492 495.940i −0.219411 1.38531i
\(359\) −232.340 75.4918i −0.647186 0.210283i −0.0330130 0.999455i \(-0.510510\pi\)
−0.614173 + 0.789171i \(0.710510\pi\)
\(360\) −131.755 46.0477i −0.365987 0.127910i
\(361\) 110.175 + 339.084i 0.305194 + 0.939290i
\(362\) −48.7835 95.7430i −0.134761 0.264483i
\(363\) 142.526 72.6206i 0.392633 0.200057i
\(364\) 307.318 99.8537i 0.844280 0.274323i
\(365\) −176.321 134.147i −0.483071 0.367525i
\(366\) −56.1313 + 172.754i −0.153364 + 0.472006i
\(367\) −170.553 + 27.0130i −0.464723 + 0.0736049i −0.384405 0.923164i \(-0.625593\pi\)
−0.0803176 + 0.996769i \(0.525593\pi\)
\(368\) −11.0959 11.0959i −0.0301518 0.0301518i
\(369\) −6.88621 + 9.47806i −0.0186618 + 0.0256858i
\(370\) 668.143 + 120.991i 1.80579 + 0.327004i
\(371\) −408.534 + 296.817i −1.10117 + 0.800046i
\(372\) 62.0972 392.066i 0.166928 1.05394i
\(373\) −17.9357 + 35.2007i −0.0480849 + 0.0943718i −0.913799 0.406168i \(-0.866865\pi\)
0.865714 + 0.500539i \(0.166865\pi\)
\(374\) 1247.51i 3.33558i
\(375\) −138.567 + 166.356i −0.369511 + 0.443616i
\(376\) −765.956 −2.03712
\(377\) 381.004 + 194.131i 1.01062 + 0.514937i
\(378\) −103.745 16.4316i −0.274457 0.0434697i
\(379\) −52.2973 71.9811i −0.137988 0.189924i 0.734431 0.678684i \(-0.237449\pi\)
−0.872418 + 0.488760i \(0.837449\pi\)
\(380\) 12.8559 70.9936i 0.0338314 0.186825i
\(381\) 156.721 + 113.864i 0.411341 + 0.298857i
\(382\) 116.734 116.734i 0.305585 0.305585i
\(383\) −50.0372 315.922i −0.130645 0.824863i −0.962779 0.270288i \(-0.912881\pi\)
0.832134 0.554575i \(-0.187119\pi\)
\(384\) −367.920 119.545i −0.958126 0.311314i
\(385\) 271.659 357.066i 0.705608 0.927443i
\(386\) 70.8604 + 218.086i 0.183576 + 0.564989i
\(387\) −63.3646 124.360i −0.163733 0.321344i
\(388\) 53.6304 27.3260i 0.138223 0.0704279i
\(389\) −77.7419 + 25.2599i −0.199851 + 0.0649354i −0.407232 0.913325i \(-0.633506\pi\)
0.207381 + 0.978260i \(0.433506\pi\)
\(390\) 72.4311 207.245i 0.185721 0.531399i
\(391\) 38.0621 117.143i 0.0973456 0.299599i
\(392\) −103.488 + 16.3909i −0.264001 + 0.0418136i
\(393\) 127.710 + 127.710i 0.324961 + 0.324961i
\(394\) −674.878 + 928.889i −1.71289 + 2.35759i
\(395\) −253.978 + 122.427i −0.642983 + 0.309941i
\(396\) 242.049 175.859i 0.611234 0.444088i
\(397\) 8.70402 54.9550i 0.0219245 0.138426i −0.974298 0.225263i \(-0.927676\pi\)
0.996223 + 0.0868371i \(0.0276760\pi\)
\(398\) 59.6060 116.983i 0.149764 0.293928i
\(399\) 22.4873i 0.0563592i
\(400\) 51.4934 64.6702i 0.128734 0.161675i
\(401\) 706.598 1.76209 0.881045 0.473032i \(-0.156840\pi\)
0.881045 + 0.473032i \(0.156840\pi\)
\(402\) 1.80741 + 0.920921i 0.00449604 + 0.00229085i
\(403\) 255.409 + 40.4527i 0.633768 + 0.100379i
\(404\) 18.2457 + 25.1130i 0.0451626 + 0.0621609i
\(405\) −32.5141 + 31.1100i −0.0802817 + 0.0768149i
\(406\) 907.735 + 659.508i 2.23580 + 1.62440i
\(407\) −426.258 + 426.258i −1.04732 + 1.04732i
\(408\) 65.4365 + 413.150i 0.160383 + 1.01262i
\(409\) 225.857 + 73.3853i 0.552217 + 0.179426i 0.571816 0.820382i \(-0.306239\pi\)
−0.0195993 + 0.999808i \(0.506239\pi\)
\(410\) −36.6096 52.8006i −0.0892918 0.128782i
\(411\) −81.8146 251.799i −0.199062 0.612651i
\(412\) 307.938 + 604.362i 0.747421 + 1.46690i
\(413\) −61.6400 + 31.4071i −0.149249 + 0.0760463i
\(414\) −44.5534 + 14.4763i −0.107617 + 0.0349669i
\(415\) 86.6238 + 1.91166i 0.208732 + 0.00460640i
\(416\) 62.7011 192.974i 0.150724 0.463880i
\(417\) −269.340 + 42.6593i −0.645900 + 0.102301i
\(418\) 71.8264 + 71.8264i 0.171833 + 0.171833i
\(419\) 140.550 193.451i 0.335443 0.461697i −0.607661 0.794197i \(-0.707892\pi\)
0.943103 + 0.332500i \(0.107892\pi\)
\(420\) 172.011 319.938i 0.409550 0.761756i
\(421\) −392.951 + 285.496i −0.933375 + 0.678137i −0.946817 0.321773i \(-0.895721\pi\)
0.0134415 + 0.999910i \(0.495721\pi\)
\(422\) −98.4630 + 621.671i −0.233325 + 1.47315i
\(423\) −112.117 + 220.041i −0.265051 + 0.520193i
\(424\) 764.848i 1.80389i
\(425\) 635.791 + 129.682i 1.49598 + 0.305134i
\(426\) −623.838 −1.46441
\(427\) −174.450 88.8867i −0.408548 0.208166i
\(428\) 553.338 + 87.6401i 1.29285 + 0.204767i
\(429\) 114.562 + 157.681i 0.267044 + 0.367554i
\(430\) 758.484 103.033i 1.76392 0.239613i
\(431\) −224.130 162.840i −0.520023 0.377819i 0.296589 0.955005i \(-0.404151\pi\)
−0.816613 + 0.577186i \(0.804151\pi\)
\(432\) 12.1495 12.1495i 0.0281238 0.0281238i
\(433\) 78.8616 + 497.912i 0.182128 + 1.14991i 0.894154 + 0.447760i \(0.147778\pi\)
−0.712026 + 0.702154i \(0.752222\pi\)
\(434\) 645.320 + 209.677i 1.48691 + 0.483127i
\(435\) 460.332 138.420i 1.05824 0.318206i
\(436\) 172.666 + 531.411i 0.396023 + 1.21883i
\(437\) −4.55316 8.93609i −0.0104191 0.0204487i
\(438\) 225.015 114.651i 0.513732 0.261760i
\(439\) −644.964 + 209.562i −1.46917 + 0.477361i −0.930856 0.365385i \(-0.880937\pi\)
−0.538310 + 0.842747i \(0.680937\pi\)
\(440\) 195.682 + 650.765i 0.444732 + 1.47901i
\(441\) −10.4394 + 32.1291i −0.0236720 + 0.0728550i
\(442\) −649.867 + 102.929i −1.47029 + 0.232871i
\(443\) 229.580 + 229.580i 0.518238 + 0.518238i 0.917038 0.398800i \(-0.130573\pi\)
−0.398800 + 0.917038i \(0.630573\pi\)
\(444\) −286.874 + 394.849i −0.646113 + 0.889299i
\(445\) −60.3533 444.293i −0.135625 0.998412i
\(446\) 482.739 350.730i 1.08237 0.786391i
\(447\) 21.8031 137.660i 0.0487766 0.307963i
\(448\) 278.598 546.779i 0.621870 1.22049i
\(449\) 72.7747i 0.162082i −0.996711 0.0810409i \(-0.974176\pi\)
0.996711 0.0810409i \(-0.0258244\pi\)
\(450\) −102.231 224.621i −0.227180 0.499158i
\(451\) 57.0414 0.126478
\(452\) 1151.56 + 586.751i 2.54771 + 1.29812i
\(453\) −320.650 50.7860i −0.707838 0.112110i
\(454\) −578.531 796.280i −1.27430 1.75392i
\(455\) 208.421 + 112.055i 0.458068 + 0.246275i
\(456\) 27.5550 + 20.0199i 0.0604277 + 0.0439033i
\(457\) 209.874 209.874i 0.459243 0.459243i −0.439164 0.898407i \(-0.644725\pi\)
0.898407 + 0.439164i \(0.144725\pi\)
\(458\) −112.519 710.418i −0.245675 1.55113i
\(459\) 128.267 + 41.6764i 0.279448 + 0.0907982i
\(460\) 3.57435 161.966i 0.00777032 0.352100i
\(461\) 41.7392 + 128.460i 0.0905406 + 0.278655i 0.986066 0.166355i \(-0.0531999\pi\)
−0.895525 + 0.445011i \(0.853200\pi\)
\(462\) 232.178 + 455.675i 0.502550 + 0.986310i
\(463\) −657.694 + 335.112i −1.42051 + 0.723784i −0.984373 0.176099i \(-0.943652\pi\)
−0.436133 + 0.899882i \(0.643652\pi\)
\(464\) −174.556 + 56.7167i −0.376198 + 0.122234i
\(465\) 238.888 165.635i 0.513739 0.356204i
\(466\) 185.848 571.981i 0.398815 1.22743i
\(467\) −193.470 + 30.6426i −0.414282 + 0.0656158i −0.360096 0.932915i \(-0.617256\pi\)
−0.0541855 + 0.998531i \(0.517256\pi\)
\(468\) 111.581 + 111.581i 0.238422 + 0.238422i
\(469\) −1.28517 + 1.76889i −0.00274024 + 0.00377162i
\(470\) −936.328 978.588i −1.99219 2.08210i
\(471\) 178.522 129.704i 0.379028 0.275380i
\(472\) 16.3915 103.492i 0.0347278 0.219263i
\(473\) −308.514 + 605.494i −0.652250 + 1.28011i
\(474\) 321.384i 0.678025i
\(475\) 44.0728 29.1397i 0.0927848 0.0613467i
\(476\) −1088.67 −2.28712
\(477\) −219.723 111.955i −0.460636 0.234706i
\(478\) −1484.04 235.049i −3.10469 0.491735i
\(479\) −84.2910 116.017i −0.175973 0.242206i 0.711915 0.702265i \(-0.247828\pi\)
−0.887888 + 0.460060i \(0.847828\pi\)
\(480\) −99.0430 205.468i −0.206340 0.428058i
\(481\) −257.221 186.882i −0.534763 0.388528i
\(482\) −930.598 + 930.598i −1.93070 + 1.93070i
\(483\) −7.89904 49.8726i −0.0163541 0.103256i
\(484\) −599.698 194.854i −1.23905 0.402590i
\(485\) 41.6103 + 14.5426i 0.0857944 + 0.0299847i
\(486\) −15.8509 48.7840i −0.0326150 0.100379i
\(487\) 152.898 + 300.080i 0.313959 + 0.616180i 0.993026 0.117897i \(-0.0376152\pi\)
−0.679067 + 0.734077i \(0.737615\pi\)
\(488\) 264.226 134.630i 0.541447 0.275881i
\(489\) 56.4176 18.3312i 0.115373 0.0374871i
\(490\) −147.449 112.180i −0.300916 0.228939i
\(491\) 196.552 604.925i 0.400310 1.23203i −0.524439 0.851448i \(-0.675725\pi\)
0.924748 0.380579i \(-0.124275\pi\)
\(492\) 45.6137 7.22450i 0.0927108 0.0146839i
\(493\) −1018.70 1018.70i −2.06634 2.06634i
\(494\) −31.4905 + 43.3429i −0.0637459 + 0.0877387i
\(495\) 215.593 + 39.0408i 0.435541 + 0.0788704i
\(496\) −89.7953 + 65.2401i −0.181039 + 0.131532i
\(497\) 105.189 664.139i 0.211649 1.33630i
\(498\) −44.8382 + 88.0000i −0.0900366 + 0.176707i
\(499\) 220.616i 0.442116i −0.975261 0.221058i \(-0.929049\pi\)
0.975261 0.221058i \(-0.0709511\pi\)
\(500\) 849.940 77.4601i 1.69988 0.154920i
\(501\) 102.137 0.203866
\(502\) 449.635 + 229.100i 0.895687 + 0.456375i
\(503\) −377.227 59.7469i −0.749954 0.118781i −0.230255 0.973130i \(-0.573956\pi\)
−0.519699 + 0.854349i \(0.673956\pi\)
\(504\) 100.795 + 138.732i 0.199989 + 0.275262i
\(505\) −4.05056 + 22.3682i −0.00802091 + 0.0442934i
\(506\) 184.527 + 134.067i 0.364678 + 0.264954i
\(507\) 134.293 134.293i 0.264878 0.264878i
\(508\) −119.458 754.229i −0.235154 1.48470i
\(509\) −54.3299 17.6528i −0.106738 0.0346814i 0.255161 0.966899i \(-0.417872\pi\)
−0.361899 + 0.932217i \(0.617872\pi\)
\(510\) −447.850 + 588.649i −0.878137 + 1.15421i
\(511\) 84.1163 + 258.883i 0.164611 + 0.506621i
\(512\) 95.4111 + 187.255i 0.186350 + 0.365732i
\(513\) 9.78462 4.98551i 0.0190733 0.00971835i
\(514\) 922.391 299.703i 1.79454 0.583080i
\(515\) −163.880 + 468.907i −0.318214 + 0.910499i
\(516\) −170.019 + 523.263i −0.329493 + 1.01408i
\(517\) 1187.60 188.098i 2.29711 0.363826i
\(518\) −589.912 589.912i −1.13883 1.13883i
\(519\) −79.2121 + 109.026i −0.152624 + 0.210070i
\(520\) −322.860 + 155.630i −0.620884 + 0.299289i
\(521\) 37.2208 27.0425i 0.0714410 0.0519050i −0.551492 0.834181i \(-0.685941\pi\)
0.622933 + 0.782276i \(0.285941\pi\)
\(522\) −85.7155 + 541.186i −0.164206 + 1.03675i
\(523\) 138.623 272.063i 0.265053 0.520197i −0.719671 0.694315i \(-0.755707\pi\)
0.984725 + 0.174118i \(0.0557075\pi\)
\(524\) 711.954i 1.35869i
\(525\) 256.370 70.9606i 0.488324 0.135163i
\(526\) −34.5965 −0.0657729
\(527\) −776.267 395.528i −1.47299 0.750527i
\(528\) −82.6269 13.0868i −0.156490 0.0247856i
\(529\) 297.701 + 409.751i 0.562763 + 0.774576i
\(530\) 977.173 934.974i 1.84372 1.76410i
\(531\) −27.3316 19.8575i −0.0514719 0.0373965i
\(532\) −62.6811 + 62.6811i −0.117822 + 0.117822i
\(533\) 4.70635 + 29.7147i 0.00882992 + 0.0557499i
\(534\) 486.077 + 157.936i 0.910257 + 0.295760i
\(535\) 233.767 + 337.152i 0.436947 + 0.630191i
\(536\) −1.02336 3.14959i −0.00190926 0.00587610i
\(537\) 119.991 + 235.495i 0.223447 + 0.438539i
\(538\) 1350.84 688.289i 2.51086 1.27935i
\(539\) 156.432 50.8279i 0.290227 0.0943004i
\(540\) 177.346 + 3.91375i 0.328418 + 0.00724769i
\(541\) −72.3805 + 222.764i −0.133790 + 0.411764i −0.995400 0.0958075i \(-0.969457\pi\)
0.861610 + 0.507571i \(0.169457\pi\)
\(542\) 483.768 76.6213i 0.892560 0.141368i
\(543\) 39.9948 + 39.9948i 0.0736553 + 0.0736553i
\(544\) −401.815 + 553.051i −0.738630 + 1.01664i
\(545\) −193.765 + 360.399i −0.355532 + 0.661283i
\(546\) −218.220 + 158.546i −0.399669 + 0.290377i
\(547\) −126.813 + 800.663i −0.231833 + 1.46374i 0.547332 + 0.836916i \(0.315644\pi\)
−0.779164 + 0.626819i \(0.784356\pi\)
\(548\) −473.815 + 929.914i −0.864626 + 1.69692i
\(549\) 95.6126i 0.174158i
\(550\) −592.212 + 1045.52i −1.07675 + 1.90095i
\(551\) −117.306 −0.212896
\(552\) 68.1440 + 34.7211i 0.123449 + 0.0629006i
\(553\) 342.146 + 54.1906i 0.618708 + 0.0979938i
\(554\) −498.609 686.276i −0.900016 1.23877i
\(555\) −354.159 + 48.1094i −0.638124 + 0.0866835i
\(556\) 869.667 + 631.850i 1.56415 + 1.13642i
\(557\) 581.702 581.702i 1.04435 1.04435i 0.0453787 0.998970i \(-0.485551\pi\)
0.998970 0.0453787i \(-0.0144494\pi\)
\(558\) 51.8354 + 327.276i 0.0928949 + 0.586516i
\(559\) −340.876 110.757i −0.609796 0.198135i
\(560\) −97.2660 + 29.2474i −0.173689 + 0.0522275i
\(561\) −202.917 624.514i −0.361706 1.11322i
\(562\) −119.266 234.072i −0.212217 0.416499i
\(563\) −376.119 + 191.642i −0.668062 + 0.340395i −0.754911 0.655827i \(-0.772320\pi\)
0.0868492 + 0.996221i \(0.472320\pi\)
\(564\) 925.857 300.829i 1.64159 0.533385i
\(565\) 272.542 + 906.372i 0.482375 + 1.60420i
\(566\) −35.8950 + 110.473i −0.0634187 + 0.195183i
\(567\) 54.6083 8.64910i 0.0963109 0.0152542i
\(568\) 720.161 + 720.161i 1.26789 + 1.26789i
\(569\) −470.636 + 647.774i −0.827128 + 1.13844i 0.161323 + 0.986902i \(0.448424\pi\)
−0.988451 + 0.151542i \(0.951576\pi\)
\(570\) 8.10664 + 59.6773i 0.0142222 + 0.104697i
\(571\) 545.948 396.655i 0.956127 0.694667i 0.00387883 0.999992i \(-0.498765\pi\)
0.952248 + 0.305326i \(0.0987653\pi\)
\(572\) 120.190 758.848i 0.210122 1.32666i
\(573\) −39.4503 + 77.4255i −0.0688486 + 0.135123i
\(574\) 78.9414i 0.137529i
\(575\) 87.5092 80.1075i 0.152190 0.139317i
\(576\) 299.679 0.520276
\(577\) −809.001 412.206i −1.40208 0.714396i −0.420831 0.907139i \(-0.638262\pi\)
−0.981249 + 0.192743i \(0.938262\pi\)
\(578\) 1250.21 + 198.014i 2.16299 + 0.342585i
\(579\) −70.9468 97.6498i −0.122533 0.168653i
\(580\) −1668.96 897.298i −2.87752 1.54707i
\(581\) −86.1245 62.5731i −0.148235 0.107699i
\(582\) −35.5279 + 35.5279i −0.0610445 + 0.0610445i
\(583\) 187.826 + 1185.89i 0.322172 + 2.03411i
\(584\) −392.111 127.405i −0.671423 0.218159i
\(585\) −2.54958 + 115.530i −0.00435826 + 0.197488i
\(586\) −24.0682 74.0745i −0.0410721 0.126407i
\(587\) 54.6357 + 107.229i 0.0930761 + 0.182672i 0.932851 0.360263i \(-0.117313\pi\)
−0.839775 + 0.542935i \(0.817313\pi\)
\(588\) 118.655 60.4578i 0.201794 0.102819i
\(589\) −67.4671 + 21.9214i −0.114545 + 0.0372180i
\(590\) 152.259 105.570i 0.258066 0.178932i
\(591\) 186.759 574.785i 0.316005 0.972563i
\(592\) 134.787 21.3482i 0.227681 0.0360612i
\(593\) 255.390 + 255.390i 0.430674 + 0.430674i 0.888858 0.458183i \(-0.151500\pi\)
−0.458183 + 0.888858i \(0.651500\pi\)
\(594\) −146.797 + 202.049i −0.247134 + 0.340150i
\(595\) −551.162 576.038i −0.926323 0.968131i
\(596\) −444.486 + 322.938i −0.745781 + 0.541842i
\(597\) −10.8111 + 68.2584i −0.0181090 + 0.114336i
\(598\) −54.6149 + 107.188i −0.0913293 + 0.179244i
\(599\) 546.766i 0.912799i −0.889775 0.456399i \(-0.849139\pi\)
0.889775 0.456399i \(-0.150861\pi\)
\(600\) −141.287 + 377.319i −0.235479 + 0.628865i
\(601\) −768.536 −1.27876 −0.639381 0.768890i \(-0.720809\pi\)
−0.639381 + 0.768890i \(0.720809\pi\)
\(602\) −837.962 426.963i −1.39196 0.709241i
\(603\) −1.05460 0.167032i −0.00174892 0.000277002i
\(604\) 752.219 + 1035.34i 1.24540 + 1.71414i
\(605\) −200.509 415.962i −0.331420 0.687540i
\(606\) −20.9630 15.2305i −0.0345924 0.0251328i
\(607\) −163.485 + 163.485i −0.269333 + 0.269333i −0.828832 0.559498i \(-0.810994\pi\)
0.559498 + 0.828832i \(0.310994\pi\)
\(608\) 8.70754 + 54.9772i 0.0143216 + 0.0904231i
\(609\) −561.695 182.506i −0.922323 0.299681i
\(610\) 495.002 + 173.000i 0.811479 + 0.283607i
\(611\) 195.973 + 603.142i 0.320741 + 0.987140i
\(612\) −241.361 473.699i −0.394381 0.774017i
\(613\) 530.506 270.306i 0.865426 0.440957i 0.0358546 0.999357i \(-0.488585\pi\)
0.829572 + 0.558400i \(0.188585\pi\)
\(614\) 62.1425 20.1913i 0.101209 0.0328849i
\(615\) 26.9155 + 20.4776i 0.0437651 + 0.0332969i
\(616\) 258.006 794.060i 0.418840 1.28906i
\(617\) 319.636 50.6254i 0.518049 0.0820509i 0.108065 0.994144i \(-0.465534\pi\)
0.409984 + 0.912093i \(0.365534\pi\)
\(618\) −400.364 400.364i −0.647839 0.647839i
\(619\) 6.19820 8.53110i 0.0100133 0.0137821i −0.803981 0.594655i \(-0.797289\pi\)
0.813994 + 0.580873i \(0.197289\pi\)
\(620\) −1127.57 204.186i −1.81866 0.329333i
\(621\) 19.9492 14.4939i 0.0321243 0.0233396i
\(622\) 99.1246 625.848i 0.159364 1.00619i
\(623\) −250.100 + 490.848i −0.401444 + 0.787878i
\(624\) 44.1228i 0.0707096i
\(625\) 471.286 + 410.505i 0.754058 + 0.656808i
\(626\) 523.208 0.835795
\(627\) −47.6401 24.2738i −0.0759810 0.0387142i
\(628\) −859.149 136.076i −1.36807 0.216681i
\(629\) 629.625 + 866.605i 1.00099 + 1.37775i
\(630\) −54.0298 + 298.366i −0.0857616 + 0.473597i
\(631\) −25.4826 18.5142i −0.0403844 0.0293410i 0.567410 0.823435i \(-0.307946\pi\)
−0.607794 + 0.794094i \(0.707946\pi\)
\(632\) −371.006 + 371.006i −0.587035 + 0.587035i
\(633\) −51.8282 327.230i −0.0818770 0.516951i
\(634\) 1198.77 + 389.502i 1.89080 + 0.614357i
\(635\) 338.600 445.052i 0.533228 0.700870i
\(636\) 300.394 + 924.518i 0.472318 + 1.45364i
\(637\) 39.3848 + 77.2970i 0.0618285 + 0.121345i
\(638\) 2377.04 1211.16i 3.72576 1.89837i
\(639\) 312.299 101.472i 0.488731 0.158798i
\(640\) −368.445 + 1054.22i −0.575695 + 1.64722i
\(641\) −347.695 + 1070.09i −0.542425 + 1.66941i 0.184609 + 0.982812i \(0.440898\pi\)
−0.727034 + 0.686601i \(0.759102\pi\)
\(642\) −461.896 + 73.1572i −0.719465 + 0.113952i
\(643\) 737.920 + 737.920i 1.14762 + 1.14762i 0.987019 + 0.160602i \(0.0513436\pi\)
0.160602 + 0.987019i \(0.448656\pi\)
\(644\) −116.997 + 161.032i −0.181672 + 0.250050i
\(645\) −362.945 + 174.953i −0.562706 + 0.271245i
\(646\) 146.027 106.095i 0.226048 0.164233i
\(647\) 167.580 1058.06i 0.259011 1.63533i −0.424525 0.905416i \(-0.639559\pi\)
0.683536 0.729916i \(-0.260441\pi\)
\(648\) −38.0181 + 74.6147i −0.0586699 + 0.115146i
\(649\) 164.488i 0.253449i
\(650\) −593.507 222.239i −0.913088 0.341907i
\(651\) −357.159 −0.548631
\(652\) −208.354 106.162i −0.319562 0.162825i
\(653\) −375.029 59.3987i −0.574317 0.0909628i −0.137481 0.990504i \(-0.543901\pi\)
−0.436835 + 0.899542i \(0.643901\pi\)
\(654\) −274.156 377.343i −0.419198 0.576977i
\(655\) 376.710 360.442i 0.575130 0.550293i
\(656\) −10.4469 7.59015i −0.0159252 0.0115704i
\(657\) −93.9956 + 93.9956i −0.143068 + 0.143068i
\(658\) 260.315 + 1643.56i 0.395615 + 2.49782i
\(659\) 329.556 + 107.079i 0.500085 + 0.162487i 0.548188 0.836355i \(-0.315318\pi\)
−0.0481033 + 0.998842i \(0.515318\pi\)
\(660\) −492.121 709.765i −0.745637 1.07540i
\(661\) −246.800 759.573i −0.373374 1.14913i −0.944569 0.328312i \(-0.893520\pi\)
0.571195 0.820814i \(-0.306480\pi\)
\(662\) −832.197 1633.28i −1.25709 2.46719i
\(663\) 308.587 157.233i 0.465441 0.237154i
\(664\) 153.349 49.8260i 0.230947 0.0750392i
\(665\) −64.8995 1.43224i −0.0975933 0.00215374i
\(666\) 125.895 387.466i 0.189032 0.581781i
\(667\) −260.161 + 41.2055i −0.390047 + 0.0617773i
\(668\) −284.695 284.695i −0.426191 0.426191i
\(669\) −184.615 + 254.100i −0.275956 + 0.379821i
\(670\) 2.77294 5.15761i 0.00413871 0.00769793i
\(671\) −376.618 + 273.629i −0.561279 + 0.407793i
\(672\) −43.8400 + 276.795i −0.0652382 + 0.411898i
\(673\) 32.9059 64.5815i 0.0488944 0.0959606i −0.865267 0.501312i \(-0.832851\pi\)
0.914161 + 0.405352i \(0.132851\pi\)
\(674\) 624.607i 0.926716i
\(675\) 87.7142 + 95.8187i 0.129947 + 0.141954i
\(676\) −748.656 −1.10748
\(677\) −529.170 269.626i −0.781640 0.398265i 0.0171675 0.999853i \(-0.494535\pi\)
−0.798807 + 0.601587i \(0.794535\pi\)
\(678\) −1065.57 168.770i −1.57164 0.248923i
\(679\) −31.8325 43.8136i −0.0468814 0.0645267i
\(680\) 1196.54 162.539i 1.75961 0.239028i
\(681\) 419.139 + 304.522i 0.615476 + 0.447169i
\(682\) 1140.79 1140.79i 1.67272 1.67272i
\(683\) 114.459 + 722.664i 0.167582 + 1.05807i 0.917847 + 0.396935i \(0.129926\pi\)
−0.750264 + 0.661138i \(0.770074\pi\)
\(684\) −41.1702 13.3770i −0.0601904 0.0195570i
\(685\) −731.916 + 220.084i −1.06849 + 0.321290i
\(686\) 376.428 + 1158.53i 0.548729 + 1.68881i
\(687\) 171.883 + 337.340i 0.250194 + 0.491033i
\(688\) 137.073 69.8421i 0.199234 0.101515i
\(689\) −602.270 + 195.689i −0.874122 + 0.284019i
\(690\) 38.9416 + 129.505i 0.0564371 + 0.187689i
\(691\) 161.872 498.191i 0.234257 0.720970i −0.762962 0.646444i \(-0.776255\pi\)
0.997219 0.0745265i \(-0.0237445\pi\)
\(692\) 524.694 83.1034i 0.758229 0.120092i
\(693\) −190.350 190.350i −0.274675 0.274675i
\(694\) 292.751 402.938i 0.421832 0.580602i
\(695\) 105.962 + 780.046i 0.152464 + 1.12237i
\(696\) 723.697 525.797i 1.03979 0.755455i
\(697\) 15.8562 100.112i 0.0227492 0.143633i
\(698\) −186.038 + 365.119i −0.266530 + 0.523094i
\(699\) 316.569i 0.452888i
\(700\) −912.400 516.809i −1.30343 0.738299i
\(701\) −699.523 −0.997893 −0.498947 0.866633i \(-0.666280\pi\)
−0.498947 + 0.866633i \(0.666280\pi\)
\(702\) −117.366 59.8009i −0.167188 0.0851865i
\(703\) 86.1468 + 13.6443i 0.122542 + 0.0194087i
\(704\) −857.636 1180.43i −1.21823 1.67675i
\(705\) 627.910 + 337.589i 0.890652 + 0.478850i
\(706\) −990.308 719.501i −1.40270 1.01912i
\(707\) 19.7491 19.7491i 0.0279337 0.0279337i
\(708\) 20.8330 + 131.535i 0.0294252 + 0.185783i
\(709\) 145.144 + 47.1600i 0.204716 + 0.0665162i 0.409580 0.912274i \(-0.365675\pi\)
−0.204864 + 0.978790i \(0.565675\pi\)
\(710\) −39.7327 + 1800.43i −0.0559616 + 2.53581i
\(711\) 52.2756 + 160.888i 0.0735240 + 0.226284i
\(712\) −378.807 743.451i −0.532032 1.04417i
\(713\) −141.929 + 72.3163i −0.199059 + 0.101425i
\(714\) 864.285 280.823i 1.21048 0.393310i
\(715\) 462.371 320.588i 0.646673 0.448375i
\(716\) 321.957 990.882i 0.449661 1.38391i
\(717\) 781.159 123.723i 1.08948 0.172557i
\(718\) −568.421 568.421i −0.791673 0.791673i
\(719\) 431.478 593.879i 0.600109 0.825979i −0.395610 0.918419i \(-0.629467\pi\)
0.995718 + 0.0924401i \(0.0294667\pi\)
\(720\) −34.2902 35.8378i −0.0476253 0.0497748i
\(721\) 493.737 358.721i 0.684794 0.497532i
\(722\) −183.527 + 1158.75i −0.254193 + 1.60491i
\(723\) 314.497 617.235i 0.434989 0.853714i
\(724\) 222.963i 0.307960i
\(725\) −370.167 1337.36i −0.510575 1.84463i
\(726\) 526.358 0.725010
\(727\) 1179.77 + 601.120i 1.62279 + 0.826851i 0.998975 + 0.0452756i \(0.0144166\pi\)
0.623811 + 0.781575i \(0.285583\pi\)
\(728\) 434.939 + 68.8876i 0.597444 + 0.0946258i
\(729\) 15.8702 + 21.8435i 0.0217698 + 0.0299636i
\(730\) −316.556 656.706i −0.433639 0.899597i
\(731\) 976.927 + 709.779i 1.33643 + 0.970970i
\(732\) −266.510 + 266.510i −0.364085 + 0.364085i
\(733\) −133.600 843.514i −0.182264 1.15077i −0.893915 0.448237i \(-0.852052\pi\)
0.711651 0.702533i \(-0.247948\pi\)
\(734\) −540.399 175.586i −0.736238 0.239218i
\(735\) 92.0611 + 32.1748i 0.125253 + 0.0437753i
\(736\) 38.6233 + 118.870i 0.0524773 + 0.161509i
\(737\) 2.36017 + 4.63209i 0.00320240 + 0.00628506i
\(738\) −34.3487 + 17.5016i −0.0465430 + 0.0237148i
\(739\) 32.3337 10.5059i 0.0437534 0.0142163i −0.287059 0.957913i \(-0.592677\pi\)
0.330812 + 0.943697i \(0.392677\pi\)
\(740\) 1121.28 + 853.081i 1.51524 + 1.15281i
\(741\) 8.71436 26.8200i 0.0117603 0.0361944i
\(742\) −1641.19 + 259.938i −2.21184 + 0.350321i
\(743\) −327.809 327.809i −0.441197 0.441197i 0.451217 0.892414i \(-0.350990\pi\)
−0.892414 + 0.451217i \(0.850990\pi\)
\(744\) 317.969 437.647i 0.427378 0.588235i
\(745\) −395.904 71.6925i −0.531414 0.0962316i
\(746\) −105.171 + 76.4112i −0.140980 + 0.102428i
\(747\) 8.13255 51.3469i 0.0108869 0.0687375i
\(748\) −1175.16 + 2306.38i −1.57107 + 3.08339i
\(749\) 504.071i 0.672993i
\(750\) −654.778 + 280.737i −0.873038 + 0.374317i
\(751\) 436.259 0.580905 0.290452 0.956889i \(-0.406194\pi\)
0.290452 + 0.956889i \(0.406194\pi\)
\(752\) −242.535 123.578i −0.322520 0.164332i
\(753\) −262.356 41.5532i −0.348415 0.0551835i
\(754\) 827.057 + 1138.35i 1.09689 + 1.50974i
\(755\) −166.993 + 922.178i −0.221183 + 1.22143i
\(756\) −176.323 128.106i −0.233232 0.169453i
\(757\) −667.784 + 667.784i −0.882145 + 0.882145i −0.993752 0.111607i \(-0.964400\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(758\) −45.7996 289.167i −0.0604216 0.381487i
\(759\) −114.183 37.1003i −0.150439 0.0488805i
\(760\) 59.5334 78.2500i 0.0783334 0.102961i
\(761\) 265.924 + 818.431i 0.349440 + 1.07547i 0.959163 + 0.282853i \(0.0912807\pi\)
−0.609723 + 0.792615i \(0.708719\pi\)
\(762\) 289.391 + 567.961i 0.379778 + 0.745356i
\(763\) 447.947 228.241i 0.587087 0.299136i
\(764\) 325.779 105.852i 0.426412 0.138550i
\(765\) 128.449 367.529i 0.167908 0.480431i
\(766\) 325.245 1001.00i 0.424602 1.30679i
\(767\) −85.6873 + 13.5715i −0.111717 + 0.0176943i
\(768\) −410.747 410.747i −0.534827 0.534827i
\(769\) 534.634 735.861i 0.695233 0.956907i −0.304757 0.952430i \(-0.598575\pi\)
0.999990 0.00447640i \(-0.00142489\pi\)
\(770\) 1329.89 641.055i 1.72713 0.832539i
\(771\) −413.009 + 300.068i −0.535679 + 0.389194i
\(772\) −74.4320 + 469.945i −0.0964146 + 0.608738i
\(773\) −330.014 + 647.689i −0.426926 + 0.837889i 0.572907 + 0.819620i \(0.305816\pi\)
−0.999833 + 0.0182691i \(0.994184\pi\)
\(774\) 459.270i 0.593372i
\(775\) −462.816 699.993i −0.597181 0.903217i
\(776\) 82.0270 0.105705
\(777\) 391.269 + 199.362i 0.503564 + 0.256579i
\(778\) −265.666 42.0774i −0.341474 0.0540841i
\(779\) −4.85110 6.67697i −0.00622734 0.00857120i
\(780\) 329.136 314.923i 0.421969 0.403747i
\(781\) −1293.45 939.748i −1.65615 1.20326i
\(782\) 286.592 286.592i 0.366486 0.366486i
\(783\) −45.1182 284.865i −0.0576222 0.363812i
\(784\) −35.4134 11.5065i −0.0451702 0.0146767i
\(785\) −362.962 523.485i −0.462372 0.666860i
\(786\) 183.649 + 565.214i 0.233650 + 0.719102i
\(787\) −665.324 1305.77i −0.845393 1.65918i −0.747774 0.663953i \(-0.768877\pi\)
−0.0976189 0.995224i \(-0.531123\pi\)
\(788\) −2122.72 + 1081.58i −2.69381 + 1.37257i
\(789\) 17.3194 5.62740i 0.0219510 0.00713232i
\(790\) −927.529 20.4692i −1.17409 0.0259103i
\(791\) 359.345 1105.95i 0.454292 1.39817i
\(792\) 402.710 63.7829i 0.508472 0.0805340i
\(793\) −173.616 173.616i −0.218936 0.218936i
\(794\) 107.615 148.120i 0.135536 0.186549i
\(795\) −337.101 + 627.002i −0.424026 + 0.788681i
\(796\) 220.398 160.128i 0.276882 0.201166i
\(797\) −118.617 + 748.917i −0.148829 + 0.939669i 0.794368 + 0.607436i \(0.207802\pi\)
−0.943197 + 0.332233i \(0.892198\pi\)
\(798\) 33.5933 65.9306i 0.0420969 0.0826198i
\(799\) 2136.62i 2.67412i
\(800\) −599.298 + 272.757i −0.749123 + 0.340946i
\(801\) −269.024 −0.335860
\(802\) 2071.68 + 1055.57i 2.58314 + 1.31617i
\(803\) 639.250 + 101.247i 0.796078 + 0.126086i
\(804\) 2.47400 + 3.40517i 0.00307712 + 0.00423529i
\(805\) −144.438 + 19.6206i −0.179426 + 0.0243734i
\(806\) 688.401 + 500.152i 0.854095 + 0.620536i
\(807\) −564.289 + 564.289i −0.699243 + 0.699243i
\(808\) 6.61760 + 41.7819i 0.00819010 + 0.0517102i
\(809\) −684.508 222.410i −0.846116 0.274920i −0.146298 0.989241i \(-0.546736\pi\)
−0.699818 + 0.714321i \(0.746736\pi\)
\(810\) −141.803 + 42.6393i −0.175065 + 0.0526412i
\(811\) −27.5305 84.7302i −0.0339464 0.104476i 0.932648 0.360789i \(-0.117492\pi\)
−0.966594 + 0.256312i \(0.917492\pi\)
\(812\) 1056.95 + 2074.38i 1.30166 + 2.55466i
\(813\) −229.715 + 117.046i −0.282553 + 0.143968i
\(814\) −1886.52 + 612.968i −2.31760 + 0.753032i
\(815\) −49.3114 163.991i −0.0605048 0.201216i
\(816\) −45.9367 + 141.379i −0.0562950 + 0.173258i
\(817\) 97.1136 15.3813i 0.118866 0.0188265i
\(818\) 552.560 + 552.560i 0.675502 + 0.675502i
\(819\) 83.4540 114.865i 0.101897 0.140250i
\(820\) −17.9451 132.104i −0.0218843 0.161102i
\(821\) 543.123 394.602i 0.661538 0.480635i −0.205644 0.978627i \(-0.565929\pi\)
0.867182 + 0.497991i \(0.165929\pi\)
\(822\) 136.285 860.471i 0.165797 1.04680i
\(823\) 558.523 1096.16i 0.678643 1.33191i −0.252620 0.967566i \(-0.581292\pi\)
0.931263 0.364347i \(-0.118708\pi\)
\(824\) 924.364i 1.12180i
\(825\) 126.405 619.725i 0.153218 0.751182i
\(826\) −227.641 −0.275594
\(827\) 150.479 + 76.6727i 0.181957 + 0.0927119i 0.542596 0.839994i \(-0.317441\pi\)
−0.360639 + 0.932705i \(0.617441\pi\)
\(828\) −96.0065 15.2059i −0.115950 0.0183647i
\(829\) 637.618 + 877.605i 0.769141 + 1.05863i 0.996398 + 0.0847965i \(0.0270240\pi\)
−0.227258 + 0.973835i \(0.572976\pi\)
\(830\) 251.116 + 135.010i 0.302550 + 0.162663i
\(831\) 361.236 + 262.454i 0.434701 + 0.315829i
\(832\) 544.165 544.165i 0.654045 0.654045i
\(833\) −45.7223 288.679i −0.0548888 0.346554i
\(834\) −853.406 277.289i −1.02327 0.332480i
\(835\) 6.50516 294.771i 0.00779061 0.353020i
\(836\) 65.1310 + 200.453i 0.0779079 + 0.239776i
\(837\) −79.1832 155.406i −0.0946036 0.185670i
\(838\) 701.072 357.214i 0.836601 0.426270i
\(839\) 1156.94 375.911i 1.37895 0.448047i 0.476623 0.879108i \(-0.341861\pi\)
0.902323 + 0.431061i \(0.141861\pi\)
\(840\) 406.807 282.062i 0.484294 0.335788i
\(841\) −692.161 + 2130.25i −0.823021 + 2.53300i
\(842\) −1578.59 + 250.024i −1.87481 + 0.296940i
\(843\) 97.7792 + 97.7792i 0.115990 + 0.115990i
\(844\) −767.654 + 1056.59i −0.909543 + 1.25188i
\(845\) −379.023 396.129i −0.448548 0.468792i
\(846\) −657.430 + 477.651i −0.777104 + 0.564599i
\(847\) −88.7525 + 560.361i −0.104785 + 0.661584i
\(848\) 123.399 242.184i 0.145518 0.285595i
\(849\) 61.1426i 0.0720172i
\(850\) 1670.35 + 1330.01i 1.96511 + 1.56472i
\(851\) 195.850 0.230141
\(852\) −1153.34 587.658i −1.35369 0.689740i
\(853\) −182.560 28.9147i −0.214021 0.0338977i 0.0485029 0.998823i \(-0.484555\pi\)
−0.262524 + 0.964925i \(0.584555\pi\)
\(854\) −378.684 521.214i −0.443424 0.610320i
\(855\) −13.7652 28.5564i −0.0160997 0.0333993i
\(856\) 617.668 + 448.762i 0.721574 + 0.524254i
\(857\) 203.015 203.015i 0.236890 0.236890i −0.578671 0.815561i \(-0.696428\pi\)
0.815561 + 0.578671i \(0.196428\pi\)
\(858\) 100.328 + 633.446i 0.116932 + 0.738282i
\(859\) −1263.62 410.575i −1.47103 0.477968i −0.539614 0.841913i \(-0.681430\pi\)
−0.931421 + 0.363944i \(0.881430\pi\)
\(860\) 1499.33 + 524.009i 1.74341 + 0.609313i
\(861\) −12.8404 39.5188i −0.0149134 0.0458987i
\(862\) −413.864 812.253i −0.480120 0.942289i
\(863\) 1200.75 611.814i 1.39137 0.708938i 0.412032 0.911169i \(-0.364819\pi\)
0.979338 + 0.202231i \(0.0648192\pi\)
\(864\) −130.158 + 42.2908i −0.150646 + 0.0489477i
\(865\) 309.610 + 235.554i 0.357930 + 0.272317i
\(866\) −512.606 + 1577.64i −0.591924 + 1.82175i
\(867\) −658.076 + 104.229i −0.759026 + 0.120218i
\(868\) 995.543 + 995.543i 1.14694 + 1.14694i
\(869\) 484.132 666.350i 0.557113 0.766801i
\(870\) 1556.43 + 281.848i 1.78900 + 0.323963i
\(871\) −2.21828 + 1.61167i −0.00254681 + 0.00185037i
\(872\) −119.120 + 752.092i −0.136605 + 0.862491i
\(873\) 12.0067 23.5645i 0.0137534 0.0269925i
\(874\) 33.0016i 0.0377592i
\(875\) −188.467 744.416i −0.215391 0.850761i
\(876\) 524.006 0.598181
\(877\) 892.419 + 454.710i 1.01758 + 0.518484i 0.881485 0.472212i \(-0.156544\pi\)
0.136096 + 0.990696i \(0.456544\pi\)
\(878\) −2204.03 349.084i −2.51028 0.397590i
\(879\) 24.0976 + 33.1675i 0.0274148 + 0.0377332i
\(880\) −43.0318 + 237.632i −0.0488997 + 0.270036i
\(881\) 610.778 + 443.756i 0.693278 + 0.503696i 0.877736 0.479145i \(-0.159053\pi\)
−0.184458 + 0.982840i \(0.559053\pi\)
\(882\) −78.6040 + 78.6040i −0.0891202 + 0.0891202i
\(883\) −143.134 903.715i −0.162100 1.02346i −0.925835 0.377929i \(-0.876636\pi\)
0.763735 0.645530i \(-0.223364\pi\)
\(884\) −1298.43 421.884i −1.46881 0.477245i
\(885\) −59.0506 + 77.6155i −0.0667238 + 0.0877011i
\(886\) 330.140 + 1016.07i 0.372619 + 1.14680i
\(887\) 668.313 + 1311.64i 0.753453 + 1.47874i 0.873947 + 0.486021i \(0.161552\pi\)
−0.120494 + 0.992714i \(0.538448\pi\)
\(888\) −592.626 + 301.958i −0.667372 + 0.340043i
\(889\) −653.449 + 212.318i −0.735038 + 0.238828i
\(890\) 486.770 1392.78i 0.546932 1.56492i
\(891\) 40.6232 125.025i 0.0455929 0.140320i
\(892\) 1222.87 193.684i 1.37093 0.217134i
\(893\) −123.018 123.018i −0.137758 0.137758i
\(894\) 269.571 371.033i 0.301534 0.415025i
\(895\) 687.294 331.301i 0.767926 0.370169i
\(896\) 1110.05 806.495i 1.23889 0.900106i
\(897\) 9.90580 62.5427i 0.0110433 0.0697243i
\(898\) 108.716 213.368i 0.121065 0.237604i
\(899\) 1863.12i 2.07244i
\(900\) 22.5905 511.579i 0.0251006 0.568421i
\(901\) 2133.53 2.36796
\(902\) 167.240 + 85.2128i 0.185410 + 0.0944710i
\(903\) 488.940 + 77.4405i 0.541462 + 0.0857592i
\(904\) 1035.27 + 1424.92i 1.14521 + 1.57624i
\(905\) 117.974 112.880i 0.130358 0.124729i
\(906\) −864.247 627.912i −0.953914 0.693059i
\(907\) −511.441 + 511.441i −0.563882 + 0.563882i −0.930408 0.366526i \(-0.880547\pi\)
0.366526 + 0.930408i \(0.380547\pi\)
\(908\) −319.482 2017.13i −0.351853 2.22151i
\(909\) 12.9716 + 4.21474i 0.0142702 + 0.00463667i
\(910\) 443.672 + 639.890i 0.487552 + 0.703176i
\(911\) −196.843 605.821i −0.216074 0.665007i −0.999076 0.0429874i \(-0.986312\pi\)
0.783002 0.622019i \(-0.213688\pi\)
\(912\) 5.49515 + 10.7848i 0.00602539 + 0.0118255i
\(913\) −225.530 + 114.913i −0.247020 + 0.125863i
\(914\) 928.856 301.803i 1.01625 0.330201i
\(915\) −275.943 6.08964i −0.301577 0.00665534i
\(916\) 461.193 1419.41i 0.503486 1.54957i
\(917\) −632.694 + 100.209i −0.689961 + 0.109279i
\(918\) 313.805 + 313.805i 0.341836 + 0.341836i
\(919\) −576.765 + 793.848i −0.627600 + 0.863818i −0.997879 0.0651032i \(-0.979262\pi\)
0.370278 + 0.928921i \(0.379262\pi\)
\(920\) 104.547 194.456i 0.113638 0.211365i
\(921\) −27.8248 + 20.2159i −0.0302115 + 0.0219500i
\(922\) −69.5284 + 438.985i −0.0754105 + 0.476123i
\(923\) 382.826 751.338i 0.414762 0.814017i
\(924\) 1061.16i 1.14844i
\(925\) 116.289 + 1025.18i 0.125718 + 1.10831i
\(926\) −2428.91 −2.62301
\(927\) 265.548 + 135.304i 0.286460 + 0.145959i
\(928\) 1443.91 + 228.692i 1.55593 + 0.246436i
\(929\) −503.341 692.790i −0.541810 0.745737i 0.447063 0.894503i \(-0.352470\pi\)
−0.988873 + 0.148765i \(0.952470\pi\)
\(930\) 947.835 128.755i 1.01918 0.138446i
\(931\) −19.2535 13.9885i −0.0206804 0.0150252i
\(932\) 882.402 882.402i 0.946784 0.946784i
\(933\) 52.1764 + 329.429i 0.0559232 + 0.353085i
\(934\) −613.010 199.179i −0.656327 0.213254i
\(935\) −1815.30 + 545.852i −1.94150 + 0.583799i
\(936\) 66.4532 + 204.522i 0.0709970 + 0.218506i
\(937\) −80.6308 158.247i −0.0860521 0.168887i 0.843970 0.536390i \(-0.180213\pi\)
−0.930022 + 0.367504i \(0.880213\pi\)
\(938\) −6.41050 + 3.26631i −0.00683422 + 0.00348221i
\(939\) −261.923 + 85.1038i −0.278938 + 0.0906324i
\(940\) −809.239 2691.23i −0.860892 2.86301i
\(941\) −254.617 + 783.630i −0.270581 + 0.832763i 0.719774 + 0.694209i \(0.244245\pi\)
−0.990355 + 0.138554i \(0.955755\pi\)
\(942\) 717.171 113.589i 0.761328 0.120583i
\(943\) −13.1042 13.1042i −0.0138963 0.0138963i
\(944\) 21.8875 30.1255i 0.0231859 0.0319126i
\(945\) −21.4837 158.153i −0.0227341 0.167358i
\(946\) −1809.07 + 1314.36i −1.91233 + 1.38939i
\(947\) 34.8644 220.125i 0.0368156 0.232444i −0.962419 0.271570i \(-0.912457\pi\)
0.999234 + 0.0391254i \(0.0124572\pi\)
\(948\) 302.745 594.170i 0.319351 0.626762i
\(949\) 341.360i 0.359705i
\(950\) 172.748 19.5953i 0.181840 0.0206266i
\(951\) −663.469 −0.697654
\(952\) −1321.92 673.550i −1.38857 0.707510i
\(953\) −794.568 125.847i −0.833754 0.132054i −0.275060 0.961427i \(-0.588698\pi\)
−0.558694 + 0.829374i \(0.688698\pi\)
\(954\) −476.960 656.479i −0.499958 0.688133i
\(955\) 220.941 + 118.787i 0.231352 + 0.124384i
\(956\) −2522.26 1832.53i −2.63835 1.91688i
\(957\) −992.962 + 992.962i −1.03758 + 1.03758i
\(958\) −73.8181 466.069i −0.0770544 0.486502i
\(959\) 893.080 + 290.179i 0.931261 + 0.302585i
\(960\) 19.0868 864.887i 0.0198820 0.900924i
\(961\) 51.2046 + 157.592i 0.0532826 + 0.163987i
\(962\) −474.968 932.176i −0.493729 0.968998i
\(963\) 219.330 111.754i 0.227757 0.116048i
\(964\) −2597.11 + 843.851i −2.69409 + 0.875364i
\(965\) −286.341 + 198.536i −0.296726 + 0.205737i
\(966\) 51.3443 158.022i 0.0531515 0.163583i
\(967\) 193.991 30.7251i 0.200611 0.0317736i −0.0553203 0.998469i \(-0.517618\pi\)
0.255931 + 0.966695i \(0.417618\pi\)
\(968\) −607.629 607.629i −0.627716 0.627716i
\(969\) −55.8452 + 76.8644i −0.0576318 + 0.0793234i
\(970\) 100.272 + 104.798i 0.103374 + 0.108039i
\(971\) −465.952 + 338.534i −0.479868 + 0.348645i −0.801275 0.598297i \(-0.795844\pi\)
0.321406 + 0.946941i \(0.395844\pi\)
\(972\) 16.6498 105.123i 0.0171295 0.108151i
\(973\) 439.100 861.783i 0.451285 0.885697i
\(974\) 1108.21i 1.13780i
\(975\) 333.264 + 14.7164i 0.341809 + 0.0150938i
\(976\) 105.387 0.107978
\(977\) −478.563 243.840i −0.489829 0.249581i 0.191588 0.981475i \(-0.438636\pi\)
−0.681418 + 0.731895i \(0.738636\pi\)
\(978\) 192.795 + 30.5357i 0.197132 + 0.0312226i
\(979\) 769.907 + 1059.69i 0.786422 + 1.08242i
\(980\) −166.927 346.295i −0.170334 0.353362i
\(981\) 198.623 + 144.308i 0.202470 + 0.147103i
\(982\) 1479.96 1479.96i 1.50708 1.50708i
\(983\) −81.0532 511.749i −0.0824549 0.520600i −0.993998 0.109396i \(-0.965108\pi\)
0.911543 0.411204i \(-0.134892\pi\)
\(984\) 59.8561 + 19.4484i 0.0608294 + 0.0197647i
\(985\) −1646.96 575.604i −1.67204 0.584369i
\(986\) −1464.92 4508.55i −1.48572 4.57257i
\(987\) −397.655 780.441i −0.402892 0.790720i
\(988\) −99.0484 + 50.4677i −0.100251 + 0.0510807i
\(989\) 209.976 68.2255i 0.212312 0.0689843i
\(990\) 573.774 + 436.533i 0.579570 + 0.440942i
\(991\) −372.803 + 1147.37i −0.376189 + 1.15779i 0.566485 + 0.824072i \(0.308303\pi\)
−0.942673 + 0.333717i \(0.891697\pi\)
\(992\) 873.185 138.299i 0.880226 0.139414i
\(993\) 682.271 + 682.271i 0.687080 + 0.687080i
\(994\) 1300.55 1790.05i 1.30840 1.80085i
\(995\) 196.308 + 35.5487i 0.197295 + 0.0357273i
\(996\) −165.793 + 120.455i −0.166459 + 0.120939i
\(997\) 24.0632 151.929i 0.0241356 0.152386i −0.972677 0.232161i \(-0.925420\pi\)
0.996813 + 0.0797753i \(0.0254203\pi\)
\(998\) 329.573 646.824i 0.330234 0.648120i
\(999\) 214.447i 0.214662i
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 75.3.k.a.58.10 yes 80
3.2 odd 2 225.3.r.b.208.1 80
5.2 odd 4 375.3.k.c.232.1 80
5.3 odd 4 375.3.k.b.232.10 80
5.4 even 2 375.3.k.a.268.1 80
25.3 odd 20 375.3.k.a.7.1 80
25.4 even 10 375.3.k.b.118.10 80
25.21 even 5 375.3.k.c.118.1 80
25.22 odd 20 inner 75.3.k.a.22.10 80
75.47 even 20 225.3.r.b.172.1 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.k.a.22.10 80 25.22 odd 20 inner
75.3.k.a.58.10 yes 80 1.1 even 1 trivial
225.3.r.b.172.1 80 75.47 even 20
225.3.r.b.208.1 80 3.2 odd 2
375.3.k.a.7.1 80 25.3 odd 20
375.3.k.a.268.1 80 5.4 even 2
375.3.k.b.118.10 80 25.4 even 10
375.3.k.b.232.10 80 5.3 odd 4
375.3.k.c.118.1 80 25.21 even 5
375.3.k.c.232.1 80 5.2 odd 4