Properties

Level $93$
Weight $0$
Character 93.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 93 = 3 \cdot 31 \)
Weight: \( 0 \)
Character: 93.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.18935380459 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.168241426\) \(a_{3}=-0.577350269\) \(a_{4}=-0.971694823\) \(a_{5}=-0.669827826\)
\(a_{6}=+0.097134232\) \(a_{7}=-1.404319358\) \(a_{8}=+0.331720748\) \(a_{9}=+0.333333333\) \(a_{10}=+0.112692788\)
\(a_{11}=+0.406096029\) \(a_{12}=+0.561008267\) \(a_{13}=-1.019949685\) \(a_{14}=+0.236264691\) \(a_{15}=+0.386725275\)
\(a_{16}=+0.915885651\) \(a_{17}=-0.398640447\) \(a_{18}=-0.056080475\) \(a_{19}=-1.254829590\) \(a_{20}=+0.650868230\)
\(a_{21}=+0.810784159\) \(a_{22}=-0.068322175\) \(a_{23}=+0.865450585\) \(a_{24}=-0.191519063\) \(a_{25}=-0.551330684\)
\(a_{26}=+0.171597789\) \(a_{27}=-0.192450090\) \(a_{28}=+1.364569850\) \(a_{29}=-0.519310785\) \(a_{30}=-0.065063212\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.485810655\) \(a_{33}=-0.234459652\) \(a_{34}=+0.067067837\) \(a_{35}=+0.940652182\)
\(a_{36}=-0.323898274\) \(a_{37}=+1.786852518\) \(a_{38}=+0.211114319\) \(a_{39}=+0.588868225\) \(a_{40}=-0.222195787\)
\(a_{41}=+1.090933302\) \(a_{42}=-0.136407483\) \(a_{43}=+1.063546766\) \(a_{44}=-0.394601409\) \(a_{45}=-0.223275942\)
\(a_{46}=-0.145604640\) \(a_{47}=-1.396365799\) \(a_{48}=-0.528786827\) \(a_{49}=+0.972112860\) \(a_{50}=+0.092756660\)
\(a_{51}=+0.230155169\) \(a_{52}=+0.991079828\) \(a_{53}=-0.308710474\) \(a_{54}=+0.032378077\) \(a_{55}=-0.272014420\)
\(a_{56}=-0.465841868\) \(a_{57}=+0.724476201\) \(a_{58}=+0.087369587\) \(a_{59}=-1.517305758\) \(a_{60}=-0.375778948\)
\(a_{61}=-0.851812671\) \(a_{62}=+0.030217052\) \(a_{63}=-0.468106453\) \(a_{64}=-0.834152174\) \(a_{65}=+0.683190680\)
\(a_{66}=+0.039445826\) \(a_{67}=+1.616543835\) \(a_{68}=+0.387356859\) \(a_{69}=-0.499668128\) \(a_{70}=-0.158256664\)
\(a_{71}=+0.358715286\) \(a_{72}=+0.110573583\) \(a_{73}=-1.181312350\) \(a_{74}=-0.300622615\) \(a_{75}=+0.318310919\)
\(a_{76}=+1.219311416\) \(a_{77}=-0.570288515\) \(a_{78}=-0.099072030\) \(a_{79}=+0.116552401\) \(a_{80}=-0.613485694\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.183540174\) \(a_{83}=-1.561641730\) \(a_{84}=-0.787834770\) \(a_{85}=+0.267020464\)
\(a_{86}=-0.178932624\) \(a_{87}=+0.299824222\) \(a_{88}=+0.134710478\) \(a_{89}=-0.125396179\) \(a_{90}=+0.037564263\)
\(a_{91}=+1.432335087\) \(a_{92}=-0.840953853\) \(a_{93}=+0.103695169\) \(a_{94}=+0.234926573\) \(a_{95}=+0.840519776\)
\(a_{96}=+0.280482913\) \(a_{97}=+0.030635757\) \(a_{98}=-0.163549654\) \(a_{99}=+0.135365343\) \(a_{100}=+0.535725171\)

Showing 100 of 772 available coefficients

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