Properties

Level $34$
Weight $0$
Character 34.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 34 = 2 \cdot 17 \)
Weight: \( 0 \)
Character: 34.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.44151236888 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.157773087\) \(a_{4}=+0.500000000\) \(a_{5}=-1.670622921\)
\(a_{6}=+0.818669201\) \(a_{7}=+1.848881608\) \(a_{8}=-0.353553391\) \(a_{9}=+0.340438521\) \(a_{10}=+1.181308796\)
\(a_{11}=-0.408037523\) \(a_{12}=-0.578886544\) \(a_{13}=-0.382570112\) \(a_{14}=-1.307356722\) \(a_{15}=+1.934202256\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.242535625\) \(a_{18}=-0.240726387\) \(a_{19}=+0.951712005\) \(a_{20}=-0.835311460\)
\(a_{21}=-2.140585367\) \(a_{22}=+0.288526099\) \(a_{23}=+0.167240689\) \(a_{24}=+0.409334600\) \(a_{25}=+1.790980943\)
\(a_{26}=+0.270517921\) \(a_{27}=+0.763622529\) \(a_{28}=+0.924440804\) \(a_{29}=+0.802105775\) \(a_{30}=-1.367687532\)
\(a_{31}=-0.387855993\) \(a_{32}=-0.176776695\) \(a_{33}=+0.472414862\) \(a_{34}=-0.171498585\) \(a_{35}=-3.088783992\)
\(a_{36}=+0.170219261\) \(a_{37}=+0.360863875\) \(a_{38}=-0.672962012\) \(a_{39}=+0.442929380\) \(a_{40}=+0.590654398\)
\(a_{41}=+0.432949923\) \(a_{42}=+1.513622428\) \(a_{43}=-1.761667857\) \(a_{44}=-0.204018761\) \(a_{45}=-0.568744397\)
\(a_{46}=-0.118257025\) \(a_{47}=+1.346969501\) \(a_{48}=-0.289443272\) \(a_{49}=+2.418363199\) \(a_{50}=-1.266414770\)
\(a_{51}=-0.280801219\) \(a_{52}=-0.191285056\) \(a_{53}=-0.700022557\) \(a_{54}=-0.539962669\) \(a_{55}=+0.681676838\)
\(a_{56}=-0.653678361\) \(a_{57}=-1.101866546\) \(a_{58}=-0.567174433\) \(a_{59}=+0.476702928\) \(a_{60}=+0.967101128\)
\(a_{61}=+1.324412270\) \(a_{62}=+0.274255603\) \(a_{63}=+0.629430521\) \(a_{64}=+0.125000000\) \(a_{65}=+0.639130399\)
\(a_{66}=-0.334047753\) \(a_{67}=-0.818638077\) \(a_{68}=+0.121267813\) \(a_{69}=-0.193626768\) \(a_{70}=+2.184100106\)
\(a_{71}=+0.126400833\) \(a_{72}=-0.120363193\) \(a_{73}=-0.135277603\) \(a_{74}=-0.255169293\) \(a_{75}=-2.073549536\)
\(a_{76}=+0.475856002\) \(a_{77}=-0.754413071\) \(a_{78}=-0.313198368\) \(a_{79}=+1.851856084\) \(a_{80}=-0.417655730\)
\(a_{81}=-1.224540135\) \(a_{82}=-0.306141826\) \(a_{83}=+0.141463530\) \(a_{84}=-1.070292683\) \(a_{85}=-0.405185574\)
\(a_{86}=+1.245687288\) \(a_{87}=-0.928656480\) \(a_{88}=+0.144263050\) \(a_{89}=+0.207057655\) \(a_{90}=+0.402163020\)
\(a_{91}=-0.707326845\) \(a_{92}=+0.083620344\) \(a_{93}=+0.449049230\) \(a_{94}=-0.952451268\) \(a_{95}=-1.589951889\)
\(a_{96}=+0.204667300\) \(a_{97}=+0.457408188\) \(a_{98}=-1.710041018\) \(a_{99}=-0.138911691\) \(a_{100}=+0.895490472\)

Showing 100 of 330 available coefficients

Rows: Cols: