Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 22.1257147034 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.507467572\) \(a_{3}=+0.577350269\) \(a_{4}=-0.742476663\) \(a_{5}=+0.601615986\)
\(a_{6}=-0.292986539\) \(a_{7}=-0.580233135\) \(a_{8}=+0.884250402\) \(a_{9}=+0.333333333\) \(a_{10}=-0.305300604\)
\(a_{11}=+0.266112023\) \(a_{12}=-0.428669101\) \(a_{13}=-1.257511655\) \(a_{14}=+0.294449500\) \(a_{15}=+0.347343151\)
\(a_{16}=+0.293748258\) \(a_{17}=+1.153611990\) \(a_{18}=-0.169155857\) \(a_{19}=-0.081392565\) \(a_{20}=-0.446685830\)
\(a_{21}=-0.334997756\) \(a_{22}=-0.135043222\) \(a_{23}=+1.656704521\) \(a_{24}=+0.510522208\) \(a_{25}=-0.638058206\)
\(a_{26}=+0.638146387\) \(a_{27}=+0.192450090\) \(a_{28}=+0.430809562\) \(a_{29}=-0.472426572\) \(a_{30}=-0.176265386\)
\(a_{31}=-1.720120667\) \(a_{32}=-1.033318117\) \(a_{33}=+0.153639848\) \(a_{34}=-0.585420676\) \(a_{35}=-0.349077529\)
\(a_{36}=-0.247492221\) \(a_{37}=-1.666391767\) \(a_{38}=+0.041304088\) \(a_{39}=-0.726024693\) \(a_{40}=+0.531979177\)
\(a_{41}=-1.063088318\) \(a_{42}=+0.170000498\) \(a_{43}=+0.395293843\) \(a_{44}=-0.197581967\) \(a_{45}=+0.200538662\)
\(a_{46}=-0.840723821\) \(a_{47}=-0.239938022\) \(a_{48}=+0.169595636\) \(a_{49}=-0.663329510\) \(a_{50}=+0.323793849\)
\(a_{51}=+0.666038193\) \(a_{52}=+0.933673058\) \(a_{53}=-1.053847158\) \(a_{54}=-0.097662180\) \(a_{55}=+0.160097247\)
\(a_{56}=-0.513071382\) \(a_{57}=-0.046992020\) \(a_{58}=+0.239741166\) \(a_{59}=-0.596855131\) \(a_{60}=-0.257894184\)
\(a_{61}=+1.002170884\) \(a_{62}=+0.872905459\) \(a_{63}=-0.193411045\) \(a_{64}=+0.230627178\) \(a_{65}=-0.756539114\)
\(a_{66}=-0.077967241\) \(a_{67}=-0.864317352\) \(a_{68}=-0.856529981\) \(a_{69}=+0.956498801\) \(a_{70}=+0.177145526\)
\(a_{71}=+1.090963068\) \(a_{72}=+0.294750134\) \(a_{73}=-1.190899026\) \(a_{74}=+0.845639784\) \(a_{75}=-0.368383077\)
\(a_{76}=+0.060432080\) \(a_{77}=-0.154407013\) \(a_{78}=+0.368433988\) \(a_{79}=-1.329893394\) \(a_{80}=+0.176723648\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.539482848\) \(a_{83}=-0.459432620\) \(a_{84}=+0.248728016\) \(a_{85}=+0.694031414\)
\(a_{86}=-0.200598807\) \(a_{87}=-0.272755609\) \(a_{88}=+0.235309663\) \(a_{89}=+0.366949953\) \(a_{90}=-0.101766868\)
\(a_{91}=+0.729649930\) \(a_{92}=-1.230064444\) \(a_{93}=-0.993112130\) \(a_{94}=+0.121760766\) \(a_{95}=-0.048967068\)
\(a_{96}=-0.596586493\) \(a_{97}=+1.394529419\) \(a_{98}=+0.336618216\) \(a_{99}=+0.088704008\) \(a_{100}=+0.473743327\)

Showing 100 of 1228 available coefficients

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