Properties

Level 313
Weight 0
Character 313.1
Symmetry even
Fricke sign +1

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Maass form invariants

Level: \( 313 \)
Weight: \( 0 \)
Character: 313.1
Symmetry: even
Fricke sign: \(+1\)
Spectral parameter: \( 0.68327804198 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.659478532\) \(a_{3}=+1.584239744\) \(a_{4}=-0.565088097\) \(a_{5}=-1.873294934\)
\(a_{6}=+1.044772143\) \(a_{7}=-0.917795345\) \(a_{8}=-1.032142032\) \(a_{9}=+1.509815532\) \(a_{10}=-1.235397793\)
\(a_{11}=+0.981566592\) \(a_{12}=-0.895234921\) \(a_{13}=+0.508047473\) \(a_{14}=-0.605266329\) \(a_{15}=-2.967748373\)
\(a_{16}=-0.115587420\) \(a_{17}=+1.586496134\) \(a_{18}=+0.995690876\) \(a_{19}=-0.844409891\) \(a_{20}=+1.058576638\)
\(a_{21}=-1.454007683\) \(a_{22}=+0.647322187\) \(a_{23}=-0.483283215\) \(a_{24}=-1.635160352\) \(a_{25}=+2.509234108\)
\(a_{26}=+0.335046398\) \(a_{27}=+0.807669901\) \(a_{28}=+0.518635124\) \(a_{29}=-0.269987534\) \(a_{30}=-1.957166332\)
\(a_{31}=+0.271213497\) \(a_{32}=+0.955914633\) \(a_{33}=+1.555036797\) \(a_{34}=+1.046260102\) \(a_{35}=+1.719301225\)
\(a_{36}=-0.853178747\) \(a_{37}=-0.176205851\) \(a_{38}=-0.556870258\) \(a_{39}=+0.804868759\) \(a_{40}=+1.933506395\)
\(a_{41}=-0.551005246\) \(a_{42}=-0.958886785\) \(a_{43}=+0.231286081\) \(a_{44}=-0.554671518\) \(a_{45}=-2.828329712\)
\(a_{46}=-0.318714914\) \(a_{47}=-0.280424046\) \(a_{48}=-0.183118231\) \(a_{49}=-0.157651948\) \(a_{50}=+1.654786029\)
\(a_{51}=+2.513390217\) \(a_{52}=-0.287091510\) \(a_{53}=-1.937658108\) \(a_{54}=+0.532640931\) \(a_{55}=-1.838763921\)
\(a_{56}=+0.947295025\) \(a_{57}=-1.337747546\) \(a_{58}=-0.178051071\) \(a_{59}=-1.524842096\) \(a_{60}=+1.677039198\)
\(a_{61}=+1.565052713\) \(a_{62}=+0.178859530\) \(a_{63}=-1.385701394\) \(a_{64}=+0.745992617\) \(a_{65}=-0.951722520\)
\(a_{66}=+1.025513422\) \(a_{67}=+0.392895879\) \(a_{68}=-0.896510085\) \(a_{69}=-0.765636537\) \(a_{70}=+1.133842236\)
\(a_{71}=+0.728802924\) \(a_{72}=-1.558343932\) \(a_{73}=-0.643447435\) \(a_{74}=-0.116203964\) \(a_{75}=+3.975228280\)
\(a_{76}=+0.477165914\) \(a_{77}=-0.900877188\) \(a_{78}=+0.530793655\) \(a_{79}=-0.345735846\) \(a_{80}=+0.216529256\)
\(a_{81}=-0.230272686\) \(a_{82}=-0.363376153\) \(a_{83}=+0.470312519\) \(a_{84}=+0.821642413\) \(a_{85}=-2.971975198\)
\(a_{86}=+0.152528189\) \(a_{87}=-0.427725086\) \(a_{88}=-1.013116158\) \(a_{89}=+0.339436783\) \(a_{90}=-1.865222840\)
\(a_{91}=-0.466283401\) \(a_{92}=+0.273097600\) \(a_{93}=+0.429667289\) \(a_{94}=-0.184933585\) \(a_{95}=+1.581828748\)
\(a_{96}=+1.514397879\) \(a_{97}=+1.359132307\) \(a_{98}=-0.103968073\) \(a_{99}=+1.481984543\) \(a_{100}=-1.417938265\)

Showing 100 of 976 available coefficients

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