Properties

Level $29$
Weight $0$
Character 29.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.36226304197 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.444424873\) \(a_{3}=+1.500311848\) \(a_{4}=-0.802486532\) \(a_{5}=-0.565907229\)
\(a_{6}=-0.666775903\) \(a_{7}=+0.751988670\) \(a_{8}=+0.801069849\) \(a_{9}=+1.250935640\) \(a_{10}=+0.251503249\)
\(a_{11}=+1.237174901\) \(a_{12}=-1.203980051\) \(a_{13}=+0.717957362\) \(a_{14}=-0.334202470\) \(a_{15}=-0.849037320\)
\(a_{16}=+0.446471166\) \(a_{17}=+0.871960887\) \(a_{18}=-0.555946913\) \(a_{19}=+0.652040819\) \(a_{20}=+0.454132930\)
\(a_{21}=+1.128217511\) \(a_{22}=-0.549831299\) \(a_{23}=-0.973839151\) \(a_{24}=+1.201854585\) \(a_{25}=-0.679749008\)
\(a_{26}=-0.319078110\) \(a_{27}=+0.376481713\) \(a_{28}=-0.603460780\) \(a_{29}=+0.185695338\) \(a_{30}=+0.377333304\)
\(a_{31}=+1.726458571\) \(a_{32}=-0.999492740\) \(a_{33}=+1.856148161\) \(a_{34}=-0.387521107\) \(a_{35}=-0.425555825\)
\(a_{36}=-1.003859003\) \(a_{37}=-0.344480608\) \(a_{38}=-0.289783158\) \(a_{39}=+1.077159936\) \(a_{40}=-0.453331218\)
\(a_{41}=-1.255405437\) \(a_{42}=-0.501407925\) \(a_{43}=-0.124058850\) \(a_{44}=-0.992816196\) \(a_{45}=-0.707913522\)
\(a_{46}=+0.432798341\) \(a_{47}=+1.880405568\) \(a_{48}=+0.669845980\) \(a_{49}=-0.434513040\) \(a_{50}=+0.302097367\)
\(a_{51}=+1.308213249\) \(a_{52}=-0.576151112\) \(a_{53}=-0.087101243\) \(a_{54}=-0.167317839\) \(a_{55}=-0.700126220\)
\(a_{56}=+0.602395450\) \(a_{57}=+0.978264566\) \(a_{58}=-0.082527627\) \(a_{59}=+0.831379981\) \(a_{60}=+0.681341016\)
\(a_{61}=-0.916346177\) \(a_{62}=-0.767281131\) \(a_{63}=+0.940689429\) \(a_{64}=-0.002271736\) \(a_{65}=-0.406297260\)
\(a_{66}=-0.824918404\) \(a_{67}=-0.340414660\) \(a_{68}=-0.699736874\) \(a_{69}=-1.461062422\) \(a_{70}=+0.189127598\)
\(a_{71}=+1.812530507\) \(a_{72}=+1.002086815\) \(a_{73}=+0.338298957\) \(a_{74}=+0.153095749\) \(a_{75}=-1.019835506\)
\(a_{76}=-0.523253945\) \(a_{77}=+0.930341503\) \(a_{78}=-0.478716685\) \(a_{79}=-1.289524382\) \(a_{80}=-0.252661274\)
\(a_{81}=-0.686095622\) \(a_{82}=+0.557933406\) \(a_{83}=+0.419568998\) \(a_{84}=-0.905379357\) \(a_{85}=-0.493448971\)
\(a_{86}=+0.055134825\) \(a_{87}=+0.278600940\) \(a_{88}=+0.991063508\) \(a_{89}=-1.774121001\) \(a_{90}=+0.314614392\)
\(a_{91}=+0.539895790\) \(a_{92}=+0.781492829\) \(a_{93}=+2.590226230\) \(a_{94}=-0.835699002\) \(a_{95}=-0.368994609\)
\(a_{96}=-1.499550846\) \(a_{97}=-0.281325567\) \(a_{98}=+0.193108437\) \(a_{99}=+1.547626159\) \(a_{100}=+0.545489424\)

Showing 100 of 1500 available coefficients

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