Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 10.6557340712 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.301665265\) \(a_{3}=-0.125085918\) \(a_{4}=-0.908998068\) \(a_{5}=-0.493189806\)
\(a_{6}=+0.037734077\) \(a_{7}=-0.377964473\) \(a_{8}=+0.575878408\) \(a_{9}=-0.984353513\) \(a_{10}=+0.148778234\)
\(a_{11}=-1.842571900\) \(a_{12}=+0.113702858\) \(a_{13}=+1.498810514\) \(a_{14}=+0.114018753\) \(a_{15}=+0.061691100\)
\(a_{16}=+0.735275555\) \(a_{17}=+0.218602954\) \(a_{18}=+0.296945264\) \(a_{19}=+0.996896297\) \(a_{20}=+0.448308581\)
\(a_{21}=+0.047278033\) \(a_{22}=+0.555839941\) \(a_{23}=+0.994873640\) \(a_{24}=-0.072034280\) \(a_{25}=-0.756763815\)
\(a_{26}=-0.452139071\) \(a_{27}=+0.248214681\) \(a_{28}=+0.343568976\) \(a_{29}=+0.303997816\) \(a_{30}=-0.018610062\)
\(a_{31}=+0.991509120\) \(a_{32}=-0.797685504\) \(a_{33}=+0.230479798\) \(a_{34}=-0.065944918\) \(a_{35}=+0.186408225\)
\(a_{36}=+0.894775441\) \(a_{37}=-1.448115631\) \(a_{38}=-0.300728986\) \(a_{39}=-0.187480090\) \(a_{40}=-0.284017361\)
\(a_{41}=+0.508182532\) \(a_{42}=-0.014262140\) \(a_{43}=-0.284620391\) \(a_{44}=+1.674894297\) \(a_{45}=+0.485473118\)
\(a_{46}=-0.300118820\) \(a_{47}=-0.757668159\) \(a_{48}=-0.091972618\) \(a_{49}=+0.142857143\) \(a_{50}=+0.228289357\)
\(a_{51}=-0.027344151\) \(a_{52}=-1.362415862\) \(a_{53}=-0.261606782\) \(a_{54}=-0.074877748\) \(a_{55}=+0.908737678\)
\(a_{56}=-0.217661579\) \(a_{57}=-0.124697689\) \(a_{58}=-0.091705582\) \(a_{59}=+0.553871660\) \(a_{60}=-0.056077091\)
\(a_{61}=+1.540480466\) \(a_{62}=-0.299103862\) \(a_{63}=+0.372050657\) \(a_{64}=-0.494641546\) \(a_{65}=-0.739198067\)
\(a_{66}=-0.069527749\) \(a_{67}=-0.001753729\) \(a_{68}=-0.198709663\) \(a_{69}=-0.124444683\) \(a_{70}=-0.056232887\)
\(a_{71}=-0.649132376\) \(a_{72}=-0.566867934\) \(a_{73}=+1.002503265\) \(a_{74}=+0.436846186\) \(a_{75}=+0.094660497\)
\(a_{76}=-0.906176808\) \(a_{77}=+0.696426717\) \(a_{78}=+0.056556231\) \(a_{79}=-0.007053875\) \(a_{80}=-0.362630408\)
\(a_{81}=+0.953305352\) \(a_{82}=-0.153301018\) \(a_{83}=+0.768363987\) \(a_{84}=-0.042975641\) \(a_{85}=-0.107812749\)
\(a_{86}=+0.085860086\) \(a_{87}=-0.038025846\) \(a_{88}=-1.061097373\) \(a_{89}=+0.570534594\) \(a_{90}=-0.146450377\)
\(a_{91}=-0.566497126\) \(a_{92}=-0.904338216\) \(a_{93}=-0.124023829\) \(a_{94}=+0.228562166\) \(a_{95}=-0.491659092\)
\(a_{96}=+0.099779224\) \(a_{97}=+0.389811784\) \(a_{98}=-0.043095038\) \(a_{99}=+1.813742123\) \(a_{100}=+0.687896846\)

Showing 100 of 1228 available coefficients

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