Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.2806857382 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.839260432\) \(a_{3}=+0.515751275\) \(a_{4}=-0.295641928\) \(a_{5}=-1.536879125\)
\(a_{6}=-0.432849638\) \(a_{7}=-0.223863399\) \(a_{8}=+1.087381004\) \(a_{9}=-0.734000622\) \(a_{10}=+1.289841838\)
\(a_{11}=+1.736968302\) \(a_{12}=-0.152477701\) \(a_{13}=-1.419860223\) \(a_{14}=+0.187879693\) \(a_{15}=-0.792647368\)
\(a_{16}=-0.616953922\) \(a_{17}=-0.293572279\) \(a_{18}=+0.616017679\) \(a_{19}=-0.818928664\) \(a_{20}=+0.454365908\)
\(a_{21}=-0.115457833\) \(a_{22}=-1.457768766\) \(a_{23}=-0.015895410\) \(a_{24}=+0.560818139\) \(a_{25}=+1.361997446\)
\(a_{26}=+1.191632503\) \(a_{27}=-0.894313032\) \(a_{28}=+0.066183407\) \(a_{29}=-0.643074676\) \(a_{30}=+0.665237573\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.569595989\) \(a_{33}=+0.895843616\) \(a_{34}=+0.246383597\) \(a_{35}=+0.344050985\)
\(a_{36}=+0.217001359\) \(a_{37}=-0.145592136\) \(a_{38}=+0.687294424\) \(a_{39}=-0.732294720\) \(a_{40}=-1.671173166\)
\(a_{41}=-0.515941928\) \(a_{42}=+0.096899191\) \(a_{43}=+1.431303080\) \(a_{44}=-0.513520658\) \(a_{45}=+1.128070235\)
\(a_{46}=+0.013340389\) \(a_{47}=+1.004435734\) \(a_{48}=-0.318194772\) \(a_{49}=-0.949885179\) \(a_{50}=-1.143070565\)
\(a_{51}=-0.151410277\) \(a_{52}=+0.419770214\) \(a_{53}=-0.154504335\) \(a_{54}=+0.750561541\) \(a_{55}=-2.669510325\)
\(a_{56}=-0.243424807\) \(a_{57}=-0.422363503\) \(a_{58}=+0.539707130\) \(a_{59}=+0.833876425\) \(a_{60}=+0.234339796\)
\(a_{61}=-0.813710564\) \(a_{62}=+0.150735623\) \(a_{63}=+0.164315874\) \(a_{64}=+1.094993297\) \(a_{65}=+2.182153538\)
\(a_{66}=-0.751846100\) \(a_{67}=-0.596244894\) \(a_{68}=+0.086792275\) \(a_{69}=-0.008198078\) \(a_{70}=-0.288748378\)
\(a_{71}=+0.162981403\) \(a_{72}=-0.798138333\) \(a_{73}=+1.001799639\) \(a_{74}=+0.122189719\) \(a_{75}=+0.702451920\)
\(a_{76}=+0.242109649\) \(a_{77}=-0.388843628\) \(a_{78}=+0.614585983\) \(a_{79}=-0.859602828\) \(a_{80}=+0.948183604\)
\(a_{81}=+0.272757536\) \(a_{82}=+0.433009645\) \(a_{83}=-0.671821505\) \(a_{84}=+0.034134176\) \(a_{85}=+0.451185107\)
\(a_{86}=-1.201236041\) \(a_{87}=-0.331666584\) \(a_{88}=+1.888746335\) \(a_{89}=-1.620606611\) \(a_{90}=-0.946744712\)
\(a_{91}=+0.317854736\) \(a_{92}=+0.004699350\) \(a_{93}=-0.092631664\) \(a_{94}=-0.842983167\) \(a_{95}=+1.258594369\)
\(a_{96}=-0.293769857\) \(a_{97}=-0.975787230\) \(a_{98}=+0.797201045\) \(a_{99}=-1.274935814\) \(a_{100}=-0.402663551\)

Showing 100 of 546 available coefficients

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