Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 9.20407719967 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.584029540\) \(a_{3}=+1.442478104\) \(a_{4}=-0.658909496\) \(a_{5}=-1.647681116\)
\(a_{6}=+0.842449824\) \(a_{7}=-0.377964473\) \(a_{8}=-0.968852150\) \(a_{9}=+1.080743080\) \(a_{10}=-0.962294445\)
\(a_{11}=-0.748266073\) \(a_{12}=-0.950462521\) \(a_{13}=+0.297355649\) \(a_{14}=-0.220742417\) \(a_{15}=-2.376743932\)
\(a_{16}=+0.093071220\) \(a_{17}=+0.633409086\) \(a_{18}=+0.631185884\) \(a_{19}=-1.411638960\) \(a_{20}=+1.085672734\)
\(a_{21}=-0.545205476\) \(a_{22}=-0.437009491\) \(a_{23}=-0.508089085\) \(a_{24}=-1.397548013\) \(a_{25}=+1.714853059\)
\(a_{26}=+0.173664483\) \(a_{27}=+0.116470125\) \(a_{28}=+0.249044380\) \(a_{29}=+1.149612040\) \(a_{30}=-1.388088666\)
\(a_{31}=-0.885184527\) \(a_{32}=+1.023208492\) \(a_{33}=-1.079357426\) \(a_{34}=+0.369929617\) \(a_{35}=+0.622764925\)
\(a_{36}=-0.712111878\) \(a_{37}=-0.216094080\) \(a_{38}=-0.824438853\) \(a_{39}=+0.428929012\) \(a_{40}=+1.596359392\)
\(a_{41}=+0.947228644\) \(a_{42}=-0.318416104\) \(a_{43}=-0.107553321\) \(a_{44}=+0.493039621\) \(a_{45}=-1.780719965\)
\(a_{46}=-0.296739034\) \(a_{47}=-0.949313826\) \(a_{48}=+0.134253197\) \(a_{49}=+0.142857143\) \(a_{50}=+1.001524844\)
\(a_{51}=+0.913678737\) \(a_{52}=-0.195930461\) \(a_{53}=-1.277039804\) \(a_{54}=+0.068021994\) \(a_{55}=+1.232903878\)
\(a_{56}=+0.366191692\) \(a_{57}=-2.036258290\) \(a_{58}=+0.671407391\) \(a_{59}=+0.183387508\) \(a_{60}=+1.566059146\)
\(a_{61}=-0.090231395\) \(a_{62}=-0.516973912\) \(a_{63}=-0.408482489\) \(a_{64}=+0.504512765\) \(a_{65}=-0.489947287\)
\(a_{66}=-0.630376622\) \(a_{67}=-0.011312142\) \(a_{68}=-0.417359262\) \(a_{69}=-0.732907379\) \(a_{70}=+0.363713113\)
\(a_{71}=-0.148221527\) \(a_{72}=-1.047080257\) \(a_{73}=+1.101692606\) \(a_{74}=-0.126205326\) \(a_{75}=+2.473637990\)
\(a_{76}=+0.930142316\) \(a_{77}=+0.282817992\) \(a_{78}=+0.250507214\) \(a_{79}=-1.616704321\) \(a_{80}=-0.153351692\)
\(a_{81}=-0.912737475\) \(a_{82}=+0.553209509\) \(a_{83}=-1.121724843\) \(a_{84}=+0.359241066\) \(a_{85}=-1.043656189\)
\(a_{86}=-0.062814317\) \(a_{87}=+1.658290195\) \(a_{88}=+0.724959194\) \(a_{89}=-0.968229640\) \(a_{90}=-1.039993062\)
\(a_{91}=-0.112389871\) \(a_{92}=+0.334784723\) \(a_{93}=-1.276859298\) \(a_{94}=-0.554427317\) \(a_{95}=+2.325930857\)
\(a_{96}=+1.475955846\) \(a_{97}=+0.165082998\) \(a_{98}=+0.083432791\) \(a_{99}=-0.808683381\) \(a_{100}=-1.129932965\)

Showing 100 of 1228 available coefficients

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