Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.13370465755 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.857616202\) \(a_{3}=+1.334540859\) \(a_{4}=+2.450737954\) \(a_{5}=+0.693312890\)
\(a_{6}=-2.479064722\) \(a_{7}=+1.661568909\) \(a_{8}=-2.694914328\) \(a_{9}=+0.780999304\) \(a_{10}=-1.287909258\)
\(a_{11}=+0.084814002\) \(a_{12}=+3.270609934\) \(a_{13}=+0.277350098\) \(a_{14}=-3.086557325\) \(a_{15}=+0.925254380\)
\(a_{16}=+2.555378564\) \(a_{17}=-0.744836723\) \(a_{18}=-1.450796961\) \(a_{19}=+0.653208099\) \(a_{20}=+1.699128214\)
\(a_{21}=+2.217431599\) \(a_{22}=-0.157551865\) \(a_{23}=+0.610449144\) \(a_{24}=-3.596473282\) \(a_{25}=-0.519317236\)
\(a_{26}=-0.515210036\) \(a_{27}=-0.292265376\) \(a_{28}=+4.072069987\) \(a_{29}=-0.176166785\) \(a_{30}=-1.718767527\)
\(a_{31}=+0.808740488\) \(a_{32}=-2.051998295\) \(a_{33}=+0.113187751\) \(a_{34}=+1.383620765\) \(a_{35}=+1.151987142\)
\(a_{36}=+1.914024637\) \(a_{37}=-0.202349037\) \(a_{38}=-1.213409948\) \(a_{39}=+0.370135038\) \(a_{40}=-1.868418841\)
\(a_{41}=+1.044757377\) \(a_{42}=-4.119136864\) \(a_{43}=+1.081028293\) \(a_{44}=+0.207856894\) \(a_{45}=+0.541476885\)
\(a_{46}=-1.133980220\) \(a_{47}=-0.820987677\) \(a_{48}=+3.410257104\) \(a_{49}=+1.760811238\) \(a_{50}=+0.964692112\)
\(a_{51}=-0.994015041\) \(a_{52}=+0.679712412\) \(a_{53}=-1.344531638\) \(a_{54}=+0.542916899\) \(a_{55}=+0.058802641\)
\(a_{56}=-4.477785858\) \(a_{57}=+0.871732898\) \(a_{58}=+0.327250273\) \(a_{59}=+0.502244670\) \(a_{60}=+2.267556026\)
\(a_{61}=-1.416541478\) \(a_{62}=-1.502329434\) \(a_{63}=+1.297684162\) \(a_{64}=+1.256446715\) \(a_{65}=+0.192290398\)
\(a_{66}=-0.210259401\) \(a_{67}=+1.654049216\) \(a_{68}=-1.825399627\) \(a_{69}=+0.814669325\) \(a_{70}=-2.139949980\)
\(a_{71}=+0.227365590\) \(a_{72}=-2.104726215\) \(a_{73}=+0.496182231\) \(a_{74}=+0.375886850\) \(a_{75}=-0.693050071\)
\(a_{76}=+1.600841880\) \(a_{77}=+0.140924309\) \(a_{78}=-0.687568844\) \(a_{79}=+0.949155303\) \(a_{80}=+1.771676898\)
\(a_{81}=-1.171039391\) \(a_{82}=-1.940758231\) \(a_{83}=+0.554140323\) \(a_{84}=+5.434343779\) \(a_{85}=-0.516404901\)
\(a_{86}=-2.008135671\) \(a_{87}=-0.235101772\) \(a_{88}=-0.228566470\) \(a_{89}=-1.526216392\) \(a_{90}=-1.005856235\)
\(a_{91}=+0.460836300\) \(a_{92}=+1.496050886\) \(a_{93}=+1.079297226\) \(a_{94}=+1.525080010\) \(a_{95}=+0.452877595\)
\(a_{96}=-2.738475567\) \(a_{97}=-1.194890059\) \(a_{98}=-3.270911485\) \(a_{99}=+0.066239677\) \(a_{100}=-1.272710461\)

Showing 100 of 546 available coefficients

Rows: Cols: