Properties

Level $347$
Weight $0$
Character 347.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 347 \)
Weight: \( 0 \)
Character: 347.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.9792376016 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.343774075\) \(a_{3}=+1.184941098\) \(a_{4}=-0.881819383\) \(a_{5}=+1.478005186\)
\(a_{6}=-0.407352031\) \(a_{7}=-0.290319374\) \(a_{8}=+0.646920747\) \(a_{9}=+0.404085391\) \(a_{10}=-0.508099881\)
\(a_{11}=-0.387231531\) \(a_{12}=-1.044904059\) \(a_{13}=-0.365857173\) \(a_{14}=+0.099804267\) \(a_{15}=+1.751349114\)
\(a_{16}=+0.659424814\) \(a_{17}=+0.261710430\) \(a_{18}=-0.138914076\) \(a_{19}=+0.912045046\) \(a_{20}=-1.303333621\)
\(a_{21}=-0.344011342\) \(a_{22}=+0.133120162\) \(a_{23}=-1.367579886\) \(a_{24}=+0.766562972\) \(a_{25}=+1.184499307\)
\(a_{26}=+0.125772208\) \(a_{27}=-0.706123712\) \(a_{28}=+0.256009247\) \(a_{29}=-0.644388071\) \(a_{30}=-0.602068416\)
\(a_{31}=+1.065516943\) \(a_{32}=-0.873613899\) \(a_{33}=-0.458846552\) \(a_{34}=-0.089969255\) \(a_{35}=-0.429093531\)
\(a_{36}=-0.356330366\) \(a_{37}=-0.682589341\) \(a_{38}=-0.313537447\) \(a_{39}=-0.433519201\) \(a_{40}=+0.956152178\)
\(a_{41}=+0.093051907\) \(a_{42}=+0.118262191\) \(a_{43}=+0.710736033\) \(a_{44}=+0.341468281\) \(a_{45}=+0.597240334\)
\(a_{46}=+0.470138521\) \(a_{47}=-0.385172265\) \(a_{48}=+0.781379572\) \(a_{49}=-0.915714691\) \(a_{50}=-0.407200157\)
\(a_{51}=+0.310111421\) \(a_{52}=+0.322619980\) \(a_{53}=+1.559516244\) \(a_{54}=+0.242747038\) \(a_{55}=-0.572330214\)
\(a_{56}=-0.187813606\) \(a_{57}=+1.080719638\) \(a_{58}=+0.221523933\) \(a_{59}=+0.291771814\) \(a_{60}=-1.544373593\)
\(a_{61}=-1.428793377\) \(a_{62}=-0.366297106\) \(a_{63}=-0.117313823\) \(a_{64}=-0.359099009\) \(a_{65}=-0.540738814\)
\(a_{66}=+0.157739541\) \(a_{67}=-0.561238167\) \(a_{68}=-0.230781342\) \(a_{69}=-1.620501596\) \(a_{70}=+0.147511221\)
\(a_{71}=+1.564598701\) \(a_{72}=+0.261411239\) \(a_{73}=+0.827183834\) \(a_{74}=+0.234656513\) \(a_{75}=+1.403561941\)
\(a_{76}=-0.804259001\) \(a_{77}=+0.112420797\) \(a_{78}=+0.149032659\) \(a_{79}=+1.722757742\) \(a_{80}=+0.974633277\)
\(a_{81}=-1.240800401\) \(a_{82}=-0.031988865\) \(a_{83}=+0.781931322\) \(a_{84}=+0.303355860\) \(a_{85}=+0.386809369\)
\(a_{86}=-0.244332623\) \(a_{87}=-0.763561912\) \(a_{88}=-0.250508084\) \(a_{89}=+1.225901101\) \(a_{90}=-0.205315732\)
\(a_{91}=+0.106215433\) \(a_{92}=+1.205958457\) \(a_{93}=+1.262574810\) \(a_{94}=+0.132412235\) \(a_{95}=+1.348007308\)
\(a_{96}=-1.035181003\) \(a_{97}=+1.087620852\) \(a_{98}=+0.314798969\) \(a_{99}=-0.156474626\) \(a_{100}=-1.044514429\)

Showing 100 of 1060 available coefficients

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