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: \( 10.2719888709 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.007126241\) \(a_{3}=-0.964629464\) \(a_{4}=+0.014303266\) \(a_{5}=+1.421372556\)
\(a_{6}=-0.971503646\) \(a_{7}=+0.377964473\) \(a_{8}=-0.992721047\) \(a_{9}=-0.069489997\) \(a_{10}=+1.431501600\)
\(a_{11}=-1.257642943\) \(a_{12}=-0.013797352\) \(a_{13}=-1.138745337\) \(a_{14}=+0.380657939\) \(a_{15}=-1.371097847\)
\(a_{16}=-1.014098683\) \(a_{17}=+0.713272188\) \(a_{18}=-0.069985200\) \(a_{19}=-1.434847849\) \(a_{20}=+0.020330270\)
\(a_{21}=-0.364595667\) \(a_{22}=-1.266605210\) \(a_{23}=-0.185383736\) \(a_{24}=+0.957607971\) \(a_{25}=+1.020299942\)
\(a_{26}=-1.146860311\) \(a_{27}=+1.031661563\) \(a_{28}=+0.005406126\) \(a_{29}=-0.695950415\) \(a_{30}=-1.380868621\)
\(a_{31}=-0.734236421\) \(a_{32}=-0.028604348\) \(a_{33}=+1.213159438\) \(a_{34}=+0.718355138\) \(a_{35}=+0.537228329\)
\(a_{36}=-0.000993934\) \(a_{37}=+0.357900619\) \(a_{38}=-1.445072921\) \(a_{39}=+1.098467304\) \(a_{40}=-1.411026451\)
\(a_{41}=+0.094229995\) \(a_{42}=-0.367193864\) \(a_{43}=+1.043494778\) \(a_{44}=-0.017988402\) \(a_{45}=-0.098771175\)
\(a_{46}=-0.186704825\) \(a_{47}=-1.391372186\) \(a_{48}=+0.978229469\) \(a_{49}=+0.142857143\) \(a_{50}=+1.027570846\)
\(a_{51}=-0.688043369\) \(a_{52}=-0.016287778\) \(a_{53}=+0.652782003\) \(a_{54}=+1.039013432\) \(a_{55}=-1.787579164\)
\(a_{56}=-0.375213287\) \(a_{57}=+1.384096512\) \(a_{58}=-0.700909926\) \(a_{59}=+0.171243943\) \(a_{60}=-0.019611177\)
\(a_{61}=-0.889669581\) \(a_{62}=-0.739468767\) \(a_{63}=-0.026264750\) \(a_{64}=+0.985290493\) \(a_{65}=-1.618581370\)
\(a_{66}=+1.221804705\) \(a_{67}=+1.194903830\) \(a_{68}=+0.010202122\) \(a_{69}=+0.178826614\) \(a_{70}=+0.541056748\)
\(a_{71}=-1.294715889\) \(a_{72}=+0.068984183\) \(a_{73}=+1.233245590\) \(a_{74}=+0.360451105\) \(a_{75}=-0.984211386\)
\(a_{76}=-0.020523011\) \(a_{77}=-0.475344352\) \(a_{78}=+1.106295247\) \(a_{79}=-0.621264147\) \(a_{80}=-1.441412036\)
\(a_{81}=-0.925681143\) \(a_{82}=+0.094901500\) \(a_{83}=-0.925085811\) \(a_{84}=-0.005214909\) \(a_{85}=+1.013825513\)
\(a_{86}=+1.050930973\) \(a_{87}=+0.671334276\) \(a_{88}=+1.248488619\) \(a_{89}=+0.609731781\) \(a_{90}=-0.099475042\)
\(a_{91}=-0.430405281\) \(a_{92}=-0.002651593\) \(a_{93}=+0.708266085\) \(a_{94}=-1.401287440\) \(a_{95}=-2.039453354\)
\(a_{96}=+0.027592597\) \(a_{97}=+1.387110097\) \(a_{98}=+0.143875177\) \(a_{99}=+0.087393605\) \(a_{100}=+0.014593622\)

Showing 100 of 1228 available coefficients

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