Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 13.5062656949 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.165203532\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.116816538\) \(a_{7}=-0.195467518\) \(a_{8}=+0.353553391\) \(a_{9}=-0.972707793\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.689083461\) \(a_{12}=+0.082601766\) \(a_{13}=+1.354802699\) \(a_{14}=-0.138216407\) \(a_{15}=+0.073881266\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.782147248\) \(a_{18}=-0.687808276\) \(a_{19}=+0.056365524\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.032291924\) \(a_{22}=-1.194362369\) \(a_{23}=-0.334297853\) \(a_{24}=+0.058408269\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.957990176\) \(a_{27}=-0.325898296\) \(a_{28}=-0.097733759\) \(a_{29}=+1.579992810\) \(a_{30}=+0.052241944\)
\(a_{31}=-1.230986142\) \(a_{32}=+0.176776695\) \(a_{33}=-0.279042554\) \(a_{34}=-1.260168404\) \(a_{35}=-0.087415731\)
\(a_{36}=-0.486353896\) \(a_{37}=-1.332231535\) \(a_{38}=+0.039856444\) \(a_{39}=+0.223818192\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.073277306\) \(a_{42}=-0.022833839\) \(a_{43}=-1.224796838\) \(a_{44}=-0.844541730\) \(a_{45}=-0.435008149\)
\(a_{46}=-0.236384279\) \(a_{47}=-0.583373001\) \(a_{48}=+0.041300883\) \(a_{49}=-0.961792449\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.294417021\) \(a_{52}=+0.677401350\) \(a_{53}=-0.111515130\) \(a_{54}=-0.230444895\) \(a_{55}=-0.755381087\)
\(a_{56}=-0.069108204\) \(a_{57}=+0.009311784\) \(a_{58}=+1.117223630\) \(a_{59}=-0.063044431\) \(a_{60}=+0.036940633\)
\(a_{61}=-0.500910273\) \(a_{62}=-0.870438649\) \(a_{63}=+0.190132778\) \(a_{64}=+0.125000000\) \(a_{65}=+0.605886186\)
\(a_{66}=-0.197312882\) \(a_{67}=-0.587898458\) \(a_{68}=-0.891073624\) \(a_{69}=-0.055227186\) \(a_{70}=-0.061812257\)
\(a_{71}=+0.681303737\) \(a_{72}=-0.343904138\) \(a_{73}=+1.107096061\) \(a_{74}=-0.942029952\) \(a_{75}=+0.033040706\)
\(a_{76}=+0.028182762\) \(a_{77}=+0.330160951\) \(a_{78}=+0.158263361\) \(a_{79}=+0.414830627\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.918868243\) \(a_{82}=-0.051814880\) \(a_{83}=-0.198748579\) \(a_{84}=-0.016145962\) \(a_{85}=-0.797000479\)
\(a_{86}=-0.866062150\) \(a_{87}=+0.261020395\) \(a_{88}=-0.597181184\) \(a_{89}=+0.398292127\) \(a_{90}=-0.307597212\)
\(a_{91}=-0.264819922\) \(a_{92}=-0.167148926\) \(a_{93}=-0.203363264\) \(a_{94}=-0.412507005\) \(a_{95}=+0.025207429\)
\(a_{96}=+0.029204135\) \(a_{97}=+1.537430897\) \(a_{98}=-0.680089963\) \(a_{99}=+1.642984660\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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