Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.3681029381 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.518147224\) \(a_{3}=-0.223000496\) \(a_{4}=+1.304770994\) \(a_{5}=+0.335015039\)
\(a_{6}=+0.338547584\) \(a_{7}=-0.855215065\) \(a_{8}=-0.462687238\) \(a_{9}=-0.950270779\) \(a_{10}=-0.508602151\)
\(a_{11}=-0.143643776\) \(a_{12}=-0.290964579\) \(a_{13}=-0.274536615\) \(a_{14}=+1.298342377\) \(a_{15}=-0.074708520\)
\(a_{16}=-0.602343648\) \(a_{17}=+1.132917657\) \(a_{18}=+1.442650945\) \(a_{19}=-1.298131346\) \(a_{20}=+0.437117905\)
\(a_{21}=+0.190713384\) \(a_{22}=+0.218072399\) \(a_{23}=+0.018717958\) \(a_{24}=+0.103179484\) \(a_{25}=-0.887764924\)
\(a_{26}=+0.416787000\) \(a_{27}=+0.434911351\) \(a_{28}=-1.115859810\) \(a_{29}=-1.649998810\) \(a_{30}=+0.113418532\)
\(a_{31}=+0.179605302\) \(a_{32}=+1.377133575\) \(a_{33}=+0.032032633\) \(a_{34}=-1.719935795\) \(a_{35}=-0.286509908\)
\(a_{36}=-1.239885748\) \(a_{37}=+1.648871013\) \(a_{38}=+1.970754500\) \(a_{39}=+0.061221801\) \(a_{40}=-0.155007183\)
\(a_{41}=+1.153467275\) \(a_{42}=-0.289530994\) \(a_{43}=-0.990282215\) \(a_{44}=-0.187422232\) \(a_{45}=-0.318355002\)
\(a_{46}=-0.028416615\) \(a_{47}=-1.191965419\) \(a_{48}=+0.134322932\) \(a_{49}=-0.268607192\) \(a_{50}=+1.347757854\)
\(a_{51}=-0.252641199\) \(a_{52}=-0.358207412\) \(a_{53}=+0.596251447\) \(a_{54}=-0.660259460\) \(a_{55}=-0.048122825\)
\(a_{56}=+0.395697096\) \(a_{57}=+0.289483934\) \(a_{58}=+2.504941113\) \(a_{59}=-0.213305875\) \(a_{60}=-0.097477510\)
\(a_{61}=+0.409231691\) \(a_{62}=-0.272667291\) \(a_{63}=+0.812685886\) \(a_{64}=-1.488347866\) \(a_{65}=-0.091973895\)
\(a_{66}=-0.048630253\) \(a_{67}=-1.443216297\) \(a_{68}=+1.478198097\) \(a_{69}=-0.004174114\) \(a_{70}=+0.434964222\)
\(a_{71}=-1.825745409\) \(a_{72}=+0.439678162\) \(a_{73}=+0.498778869\) \(a_{74}=-2.503228951\) \(a_{75}=+0.197972018\)
\(a_{76}=-1.693764127\) \(a_{77}=+0.122846321\) \(a_{78}=-0.092943708\) \(a_{79}=+1.043429970\) \(a_{80}=-0.201794181\)
\(a_{81}=+0.853285332\) \(a_{82}=-1.751133142\) \(a_{83}=-0.509939975\) \(a_{84}=+0.248837291\) \(a_{85}=+0.379544453\)
\(a_{86}=+1.503394196\) \(a_{87}=+0.367950553\) \(a_{88}=+0.066462142\) \(a_{89}=+0.217108046\) \(a_{90}=+0.483309763\)
\(a_{91}=+0.234787849\) \(a_{92}=+0.024422648\) \(a_{93}=-0.040052071\) \(a_{94}=+1.809578992\) \(a_{95}=-0.434893524\)
\(a_{96}=-0.307101470\) \(a_{97}=-0.108414283\) \(a_{98}=+0.407785264\) \(a_{99}=+0.136500483\) \(a_{100}=-1.158329922\)

Showing 100 of 546 available coefficients

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